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Computational transcranial magnetic stimulation (TMS)
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Computational transcranial magnetic stimulation (TMS)
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Content
COMPUTATIONAL TRANSCRANIAL MAGNETIC STIMULATION (TMS)
by
Feng Qi
A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(NEUROSCIENCE)
May 2010
Copyright 2010 Feng Qi
ii
Acknowledgements
Studying towards this Doctor of Philosophy was a long journey. Looking back,
the previous six years in USC was perhaps the toughest and most valuable time in my life.
I always feel lucky to have Dr. Nicolas Schweighofer as my advisor in these days. Being
a passionate scientist, he has been extremely supportive and motivating in my student life
and human life, and there are many things that I can learn from him: science, optimism,
patience, dedication, care for family, etc. Upon finishing my study with him, I wish Dr.
Schweighofer will keep being successful in his career and can always enjoy life with his
family.
I also owe a lot to Dr. Allan Wu, who is my mentor in Transcranial Magnetic
Stimulation (TMS). TMS is the core technique that I have been using for the past six
years, and it also plays a fundamental role in my thesis. Without Dr. Wu’s guidance, I
could not have finished the interdisciplinary studies in this thesis.
My thanks must also be given to Dr. Zhonglin Lu, Dr. Stefan Schaal, Dr. Fei Sha,
Dr. James Gordon, Dr. Beth Fisher, and Dr. Lucinda Baker, who have given me
important suggestions and helps in my study. Their expertise and kindness have greatly
impressed me.
I am also in debt to my friends in the CNRL lab: Dr. Younggeun Choi, Dr. Choel
Han, Jeong-yoon Lee, Yukikazu Hidaka, Jihye Lee, Duckho Kim, Sungshin Kim,
Yupeng Xiao, and Hyeshin Park, as well as my friends from the Neuroscience program
and the Biokinesiology division of USC: Huiting Goh, Tong Sheng, Dr. Shailesh Kantak,
Dr. Janice Lin, and Erica Pitch. Their support is indispensible for my study.
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Last but not least, I want to thank my parents, Xiaolin Ji and Xiaoheng Liu, and
my most important friend Ariel Chen. They have provided me with enormous encourage
and advises of wisdom.
I must share this joy with all of you.
iv
Table of Contents
Acknowledgements
List of Figures
Abstract
Chapter 1. Introduction
1.1. An overview of Transcranial Magnetic Stimulation (TMS)
1.2. Basic principles of TMS
1.3. Neurophysiology for TMS
1.4. TMS techniques
1.5. Motivating computational TMS
Chapter 2. Fast estimation of TMS motor threshold
2.1. Introduction
2.2. Materials and methods
2.3. Results
2.4. Discussion
2.5 Supplementary material
Chapter 3. Fast TMS mapping
3.1. Introduction
3.2. Materials and methods
3.3. Results
Table 3.1 Number of TMS trials required by each subject’s TMS
maps to achieve the accuracy of the traditional map generated by
250 trials.
3.4. Discussion
Chapter 4. Analysis of the effect of TMS coil placement
4.1. Introduction
4.2. Material and methods
4.3. Results
4.4. Discussion
Chapter 5. Conclusion and future work
5.1. Technical advantages of computational TMS
5.2 Neuroscience explored by computational TMS tools
5.3. Future work
Bibliography
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List of Figures
Figure 2.1: Probability distributions of MTs estimated after different number of
trials in the Bayesian PEST procedure. The true MT in this
simulated subject was 40 %MSO. In each panel, the x axis
represents MT in %MSO, and the y axis represents probability. A:
The prior is a Gaussian distribution with mean 50 %MSO and
standard deviation 4.5 %MSO. B: Posterior MT distribution after 3
trials. C: Posterior MT distribution after 14 trials. D: Posterior MT
distribution after 20 trials.
Figure 2.2: Comparison of stopping trial and relative error of “best-PEST”
(ML) and BayesianPEST. Mean relative errors of 10 data
generators as a function of stopping trials, for the “best-PEST”
(square) and for different maximal
95
PI width (21, 11, 9, 7, 6 and 5
from left to right) for the Bayesian PEST (triangles). The maximal
95
PI width tested is labeled as a number next to each triangle data
point. Horizontal bars represent ±1 standard deviation for stopping
trials; vertical bars represent ±1 standard deviation for the relative
error.
Figure 2.3: The stopping relative error and trial number of Bayesian PEST
when maximal
95
PI width were equal to 5 (A, B), 7 (C, D), and 9
(E, F) %MSO. In each subplot, the MT
0
changes from true MT-10
%MSO to true MT+10 %MSO. Bars represent average ±1 standard
deviation across results of 10 data generators. When the maximal
95
PI width was 7 %MSO and MT
0
is in the range of true MT±5
%MSO, Bayesian PEST stopping relative error was less than the
“best-PEST” stopping relative error 0.027, therefore the maximal
95
PI width of 7 %MSO was selected.
Figure 2.4: A. Average number of pulses used and B. Average MT estimated by
different methods. C. Single subject MTs measured by different
methods (labeled on the x-axis). One had 6 %MSO difference
between MT measured by the IFCN method and the Bayesian PEST
with common prior (filled circle). All data are based on the results
of ten subjects. All error bars represent ±one standard deviation.
‘ML’ –“best-PEST” with the stopping-once criterion; ‘Common’ –
Bayesian PEST with common prior; ‘Subject’ – Bayesian PEST
with subject-specific prior. The marks “*” indicate statistically
significant differences. The mark “+” indicates the MT measured by
Bayesian PEST was 6 %MSO lower than the MT measured by
IFCN method.
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Figure 2.1S: Average relative error is plotted as a function of increasing TMS
trial number for 50 simulation runs. Shown are IFCN, “best-PEST”
(ML) and Bayesian PEST (Bayesian) methods. Only data from trial
3 to trial 25 are shown because both ML and Bayesian PEST
converged by trial 25 and the error for ML in the first 2 trials was
very large.
Figure 3.1: 250 data points sampled from one subject and the corresponding
maps formed by different methods. The color bars indicate MEP
amplitude in µV. (A) the raw data recorded from EMG and
neuronavigation system. (B) Traditional map. (C) BL map. (D) GP
map.
Figure 3.2: Two example MEPs recorded by stimulating two different scalp
sites A and B of one subject. The indices 1 and 2 show the first and
second vawe, respectively. The muscle recorded is right FDI. TMS
intensity is at 110% resting motor threshold. Refer to method
section for details.
Figure 3.3: Histogram the peak times for the two MEP wave for one subject.
The peak time of the first peak is around 19 msec after the TMS
pulse, and the second around 28 msec for this subject, and 16 msec
and 24 msec on average for our nine subjects.
Figure 3.4: A. Distance between CoG for different maps and best-effort CoG as
a dependent variable of TMS trial number. Each point is the
average of nine subjects. Bars represent ±1 standard deviation. Y
axis is in centimeter. B. Comparing each data point in A to the
traditional map with 250 trials. The p-values of paired t-tests for the
null hypotheses that the error of CoG estimation of a map is the
same as that of the traditional map with 250 trials are shown. In
each curve, the initial increase in p-values reflects the decreasing
estimation error with the increasing trial number for each mapping
method. The peaks of the curves reflect the estimation errors that
were closest to that of the traditional method with 250 trials. The
following decrease in curves of the p-values reflects the decreasing
estimation errors dropping lower than that of the traditional method
with 250 trials. The dash horizontal line is the significant criterion
of alpha = 0.1
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Figure 4.1: The coil rotation orientations sampled from one subject. A.
Defining the three axes of coil rotation, Vx, Vy, and Vz, on a figure-
of-8 coil. Vx points rightward, and falls in the straight line that
overlaps with the radiuses of both circles of the coil. Vy points
forward, and falls in the common tangent line of the two circles. Vz
points upward perpendicular to the coil plane, and pass the center of
the coil. B. Yaw is defined as the rotation with respect to Vz. C.
Pitch is defined as the rotation with respect to Vx. D. Roll is
defined as the rotation with respect to Vy. In each of B, C, and D,
we tried to explore one of the three rotation dimensions, but varying
one angle while keeping the other two completely steady was not
possible.
Figure 4.2: The distribution of coil center position in 3D space, example from
one subject. A. The coil center positions recorded by Brainsight. B.
The same date shown in A, with head landmarks. Vortex represents
the top of the head. The dashed rectangle in A and B represent the
same location. In B, nasion is the nose bridge, and inion is the most
prominent projecting point of the occipital bone at the base of the
skull.
Figure 4.3: Regression result for 1 subject. The continuous line in each subplot
represents the MEP estimation changing with the variable, while
other variables are fixed at the optimal value. Dots represent the
real samples in a small tolerance interval, ±2 mm in X, Y, Z and ±3
degrees in each angle, surrounding the optimal values except for the
varying variable indicated by the subplot. Grey area is the estimated
±1 standard deviation range.
Figure 4.4: The model estimated MEP to maximum MEP ratio as a dependent
variable of the deviation of coil placement from the optimal
placement, which elicits the maximum average MEP amplitude. A.
Varying coil orientation by yaw, pitch and roll. B. Varying coil
center position x, y, and z. Each curve uses one of the coil
placement dimensions as variable and set the other five dimensions
at their optimal values. All curves are the average results of six
subjects. The bars indicate ±1 standard error across six subjects.
Figure 4.5: The mean hyperparameters ld of six subjects. A. ld for the three
angles. Paired t-tests showed significant different difference
between yaw and roll, and between yaw and pitch. B. ld for the
three dimensions of the coil center position.
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Figure 4.6: The optimal coil center projected along the optimal orientation
vector –Vz, into the brain. Each row contains three slices of one
subject, the projection depth of which increases from left to right. In
each subject, the projected path crossed the anterior bank of the
central sulcus. The crosshair in each figure represents the projection
of the optimal coil center. The arrows point to the direction of the
optimal yaw angle.
81
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Abstract
Transcranial Magnetic Stimulation (TMS) is a noninvasive brain stimulation
technique that is increasingly used in clinical neuroscience research. Since the invention
of TMS in 1985, new applications and stimulation patterns for this technique have been
developed and advanced very fast. However, compared with other research techniques
used in neuroscience, the use of computational tools for TMS is limited. The studies
introduced in this thesis applied computational methods adapted from the field of
machine learning to TMS experimental procedures and data analysis, and inspired the
idea of computational TMS. These studies showed that computational TMS improved the
accuracy and efficiency of TMS, and could be used to investigate neuroscience problems.
In Chapter 1, the background, basic principles, and variations of TMS techniques are
introduced, and the idea of computational TMS is motivated. Then three example
computational TMS studies are demonstrated: Chapter 2 introduces a new protocol
facilitating the TMS motor threshold (MT) estimation. This protocol uses Bayesian
framework to incorporate prior knowledge of MT and is two to five times faster than the
fastest existing method. Chapter 3 introduces a fast protocol for TMS mapping. This
protocol uses high-resolution coordinate data obtained from a neuronavigation system
and non-parametric regression techniques to generate TMS maps. Chapter 4 is a
quantitative analysis of the relationship between Motor Evoked Potential (MEP) and
TMS coil placement, which highlights the importance of TMS spatial information. This
analysis also supports the neurophysiology hypothesis that TMS excites the column
x
structures on the anterior bank of central sulcus. Chapter 5 includes conclusion and future
work of computational TMS.
1
Chapter 1 Introduction
1.1 An overview of Transcranial Magnetic Stimulation (TMS)
Transcranial Magnetic Stimulation (TMS) is a technique that allows non-invasive
stimulation on human brain. In 1980, Merton and Morton developed a high-voltage
electrical stimulator that could activate the cerebral cortex of intact human brain (Merton
and Morton, 1980). This technique is known as Transcranial Electrical Stimulation (Nudo
et al.). A problem associated with TES is that it is painful. In 1985, Anthony Barker
showed that magnetic stimulation could also activate intact human brain (Barker et al.,
1985), and presented this technique for the first time at the London Congress of the
International Federation of Clinical Neurophysiology (IFCN). This technique is known as
Transcranial Magnetic Stimulatin (TMS). Compared with TES, TMS is relatively
painless. After 25 years, today TMS is extensively used as a research tool in clinical
physiology, and its potential as a diagnostic and therapeutic tool is also recognized and
studied by researchers (Hallett, 2007; Ziemann, 2004) (Rossini and Rossi, 2007).
Since its invention in 1985, the most important issue associated with TMS has
been safety. In June 1996, the consensus conference of National Institutes of Health (NIH)
summarized safety precautions and practice recommendations for TMS (Wassermann,
1998). International Federation for Clinical Neurophysiology (IFCN) adapted these
recommendations with minor modifications (Hallett et al., 1999). After 1996, new
techniques of TMS fast developed and challenged traditional experimental safety
guidelines. In addition, the large body of TMS studies accumulated also provided new
data for updating traditional safety guidelines. In March 2008, another TMS consensus
2
conference was held in Italy. This conference updated safety guidelines covered in the
previous consensus conference based on meta-analysis of newly accumulated data, and
proposed guidelines for new TMS techniques developed after 1996 (Rossi et al., 2009).
1.2 Basic principles of TMS
TMS operates on Faraday’s principle of electromagnetic induction. A large
current is passed through an insulated wire coil held flat on the surface of a subject’s
scalp over a fraction of a millisecond. This current pulse induces a rapidly changing
magnetic field perpendicular to the coil that passes noninvasively though scalp and skull.
As the magnetic field flux encounters electrically excitable tissue (i.e. surface brain), a
weak electrical current is induced within that tissue. The magnitude of the magnetic field
can be as large as 2 Tesla near the coil surface and last for 100 μs (Hallett, 2007). The
detailed distribution of the electromagnetic field depends on the shape of the coil (Cohen
et al., 1990; Salinas et al., 2007; Thielscher and Kammer, 2004), the waveform and
intensity of the electrical pulse (Antal et al., 2002; Brasil-Neto et al., 1992a), and the
material and structure of the head tissue (Fox et al., 2004; Wagner et al., 2006; Esser et
al., 2005). If we assume the head tissue (including the air layer between the TMS coil and
the head) to be homogeneous, the electrical field induced inside the brain will be parallel
to the coil plane (Hallett, 2000). Because the coil is usually held tangentially over the
scalp, the induced electrical field is almost parallel to the cortical layers of the crowns of
gyri and perpendicular to the banks of sulci (Fox et al., 2004). The strength of the
electrical field decreases as the depth into the brain tissue increases. For estimation,
assuming using the most commonly used figure-of-8 coil, a 7 by 6 cm area can be
3
activated 5 mm below the coil, and a 4 by 3 cm area can be activated at 20 mm below the
coil (Walsh, 2005).
Spatial and temporal resolutions of TMS depend on various factors and have been
improved in the past 20 years. The traditionally accepted functional spatial resolution for
TMS is 0.5-1.0 cm (Thickbroom and Mastaglia, 2002), which is the smallest spacing
distance allowed by the size of the coil center (Brasil-Neto et al., 1992b). The
introduction of frameless neuronavigation systems and computer-guided coil placement
improved this resolution to 1-2 mm (Gugino et al., 2001; Schonfeldt-Lecuona et al.,
2005). The temporal resolution of TMS can be measured by the time required by the
treatment. When the frequency of the stimuli is fixed, the temporal resolution can also be
measured by the number of stimuli required. The resolution therefore depends on the
specific TMS technique used. I will discuss this issue in later section of this chapter. In
addition, Chapter 2 and Chapter 3 will focus on improving the temporal resolutions of
two TMS techniques: motor threshold estimation and center of gravity estimation for
TMS maps.
TMS is conveniently used for motor studies. When a TMS pulse is discharged
over the primary motor cortex (M1), if the amplitude is larger than a threshold, there is a
chance that a contralateral muscle twitch can be observed and a motor evoked potential
(MEP) can be recorded. Location of stimulation over M1 is reliably assured by
neurophysiologic confirmation that the coil is centered over the brain region (called the
“hot-spot”) that produces maximal amplitude MEP in the desired target muscle (Neggers
et al., 2004).
4
1.3 Neurophysiology for TMS
1.3.1 Neurophysiology for magnetic stimulation on single neuron
To understand the mechanism of magnetic stimulation over cerebral cortex, which
consists of hundreds of millions of neurons, we can start with the simplified scenario of
one neuron.
Basic physics and biological principles apply to magnetic stimulation of neurons.
Roth and Basser decompose the mechanism of magnetic stimulation into three elements
(Roth and Basser, 1990). The current source and stimulating coil were modeled as a
series RLC circuit. The induced electric field distribution was calculated from the shape
of the coil and the time course of the current using Maxwell’s equations. The nerve fiber
was modeled with cable theory, containing active Hodgkin-Huxley elements. Their
simulation suggested several principles of magnetic stimulation. First, within a plane in
the 3D space, the strongest electric field for stimulating the nerve fiber depends on the
plane’s distance to the coil plane. Second, nerve fibers parallel to the diameter of the coil
are the easiest to activate. Finally, only current above a threshold is enough to induce an
action potential in the nerve fiber. If the stimulus is sub-threshold, the MP acts like a
passive delayed field, which follows the time course of the electric field induced by the
coil. If the stimulus is slightly above the threshold, two action potentials will rise at the
same position but propagate to opposite directions (antidromic and orthodromic). When
the intensity is much higher than the threshold, a whole region of the nerve is activated
and the resulted dynamics becomes complicated.
5
Gradient of the electric field or longitudinal conductivity is necessary for
activating neuronal elements in magnetic stimulation. The Cable theory suggests that the
density of the membrane outflow current is proportional to the negative secondary
derivative of the membrane potential along the longitudinal direction of the neuronal
membrane, which is exactly the gradient of the electric field in this direction. In addition,
compartment models such as (Kamitani et al., 2001) indicate that local outflow current
equals the difference between the longitudinal currents of the two adjacent compartments.
Since a homogeneous electric field generates longitudinal current proportionally with the
longitudinal conductivity of the neuron fiber, a gradient of this conductivity can cause
outflow current. Therefore, excitation of a neuron can occur in several ways (Amassian et
al., 1998): (1) the TMS coil can generates inhomogeneous electric field over the neuron;
(2) bending of a neuron fiber in a homogeneous electric field can cause electric field
gradient along the fiber; (3) the inhomogeneous physical property of the neuronal fiber
can cause conductivity gradient.
The alignment of nerve fiber with respect to the orientation of the electric field
determines the efficiency of excitation. Although an electric field perpendicular to the
nerve fiber seems to be more effective in changing the concentration of ions across the
neuronal membrane, experimental results have shown that it requires more current to
excite neurons with transversely placed electric field than with longitudinally placed
electric field (Rudin and Eisenman, 1954; Rushton, 1927). This phenomenon can also be
explained by compartment neuron models in which the local trans-membrane current
depends on the difference between the longitudinal currents of the two adjacent
compartments (Tranchina and Nicholson, 1986). The study of Rushton suggested that the
6
threshold of neuron excitation is inversely proportional to the cosine of the angle between
the nerve fiber and the electric field (Rushton, 1927).
So far, the introduction has focused on magnetic stimulation on neuronal fiber,
but the conclusion can be generalized to the principle axis of a complete neuron. Along
the principle axis, the most efficiently activated neuronal element is soma (Chan and
Nicholson, 1986; Gorman, 1966). The modeling study of (Tranchina and Nicholson,
1986) suggested that the axon’s membrane potential decays exponentially with its
distance from soma, so soma has the lowest threshold for magnetic stimulation.
In summary, magnetic stimulation of single neuron can be understood by basic
physics and biology principles. Electric field gradient or conductivity gradient alone the
longitudinal direction of a neuron is necessary for magnetic stimulation. In a
homogeneous electric field, the most efficient activation of a neuron happens when its
principle axis is parallel with the electric field. When the soma of a neuron is in the
electric field, it is easier to activate.
1.3.2 Neurophysiology for TMS on cortex
There are different views on which part of the cortex TMS activates. Since the
strength of the electric field generated by the coil deceases with the distance between the
location and the coil (see previous section), the cortical region that is immediately under
the coil, which corresponds to the crown regions of gyri, was proposed to be the most
easily activated (Day et al., 1989; Wassermann et al., 1996; Brasil-Neto et al., 1992b). If
this is true, given the neuronal fibers which are parallel to the electric field are most
easily activated (see previous section), the horizontal fibers in the cortex which are
7
parallel to the coil plane should be the point of activation by TMS (Day et al., 1989).
However, these hypotheses fail to explain the why coil orientation with respect to the
midline of the head also affects the activation threshold (Balslev et al., 2007; Brasil-Neto
et al., 1992a; Fox et al., 2004). The orientations of horizontal fibers within the cortex are
uniformly distributed, so a coil placed with different angles should have the same effect
on cortical activation (Fox et al., 2004). In solving this conflict, Fox et al. showed that the
cortical region activated by TMS and by voluntary finger movement, as detected by
positron emission tomography (PET), overlap on the anterior bank of the central sulcus
(Fox et al., 2004). This observation was consistent with previous studies such as
(Wassermann et al., 1996). Fox et al. thus hypnotized that the cortical columns (Hubel
and Wiesel, 1979) that are buried in the sulci are the cortical structures activated by TMS.
These columns are perpendicular to the cortical layers. Because the cortical layers in the
sulci are perpendicular to the coil plane, the columns are parallel with the coil plane, and
hence easily activated. This hypothesis explains the optimal orientation of the TMS coil,
because all the columns are aligned perpendicular to the plane of the sulcus, and this
direction is exactly the optimal orientation for the electric field of TMS (Fox et al., 2004).
Fox et al. further hypnotized that the TMS activation of the cortical columns should
follow the cosine rule observed in (Rushton, 1927), which indicates the cosine of the
angle between the TMS generated electric field and the column should be proportional to
the activation effect. However, there is no direct evidence for this cosine rule hypothesis
by far.
TMS can induce directly or indirectly induce responses in cortex, as shown by
electrophysiology recordings of spinal cord descending volleys. When the action
8
potential is induced at the pyramidal tract axons by the electric field generated by the
TMS coil, the induced neural activity is considered direct. The corresponding spinal cord
descending volley is named D-wave (Patton and Amassian, 1954). When the action
potential is induced on a pyramidal tract cell via synaptic activation, the induced neural
activity is considered indirect, and corresponding spinal cord descending volley is named
I-wave (Patton and Amassian, 1954). Removal of cortical grey matters eliminates I-
waves since there are no synapses can mediate the activity (Patton and Amassian, 1954).
Though D-wave and I-wave were first identified using direct cortical stimulation (Patton
and Amassian, 1954), it has been confirmed that TES and TMS also active the cortex
with this mechanism (Day et al., 1989; Amassian et al., 1990; Edgley et al., 1997). D-
waves have short, invariant latency since it is resulted from direct activation of
corticospinal neuron axons. I-waves have a preferred set of latencies. The earliest I-wave,
I1, is 1-2 ms after the D-wave, and the following I-waves, I2, I3, etc., are each 1-2 ms
later (Lemon, 2002). Different I-waves can origin from different synaptic activations of a
single neuron (Lemon, 2002).
Analysis of D-waves and I-waves revealed several principles of TMS
neurophysiology. (1) D-waves can only be induced at TMS intensities that are higher
than the threshold. The threshold is defined as the intensity that induces muscle evoked
potential (MEP) with 50% chance (see next section). At threshold, TMS evokes only I-
waves (Edgley et al., 1997; Di Lazzaro et al., 1998). This suggests that TMS intensity
affects the origin of neuronal activation. (2) TMS induced D-wave threshold and
amplitude is influenced by the level of cortical excitability (Burke et al., 1993; Baker et
al., 1995). (3) The TMS coil oriented in different direction with respect to the central
9
sulcus preferentially evokes different I-waves. Specifically, if forward flowing current is
induced, I1 wave is preferentially evoked. If backward flowing current is induced, I3
wave is preferentially evoked. This suggests that different and independent cortical
mechanisms are responsible for different I-waves (Sakai et al., 1997). (4) Due to I-waves’
dependency on cortical synaptic transmission, the number of I-waves and their
amplitudes are positively correlated with cortical excitability (Di Lazzaro et al., 2003).
1.4 TMS techniques
Cortical excitability is defined as the responsiveness of the cortex to external
stimulation. When a TMS pulse is delivered over the primary motor cortex (M1), a
quantifiable motor response (motor evoked potential, MEP) is observed in surface
electromyographic recordings from the muscles controlled by that segment of the motor
cortex. This process allows one to test the cortical excitability of the corticospinal motor
tract. Based on the interval of pulses, TMS techniques can be categorized into single-
pulse TMS, paired-pulse TMS, and repetitive TMS (rTMS). Single-pulse TMS refers to
the TMS techniques with inter-stimulus interval that is longer than five seconds. A
number of different neurophysiologic measures of cortical excitability can be derived
from single-pulse TMS, these include motor threshold, motor evoked potential (MEP),
representational motor mappings, input-output curves (MEP amplitude versus TMS
intensity), and silent period duration. In this section, we will selectively discuss the
strengths and limitations of the single-pulse TMS techniques related to this thesis. Paired-
pulse and repetitive TMS are not of the focus of this thesis, so I will only briefly
10
introduce them in section 1.4.4, and related concepts will only appear in Chapter 5,
Conclusion and future work.
1.4.1 Motor Evoked Potential (MEP):
With fixed suprathreshold TMS intensity over the “hot spot” (M1), the amplitude
and latency of MEPs can be recorded. MEP amplitude is the summed result of direct and
indirect (trans-synaptic) excitation of a pool of corticospinal neuronal elements beneath
the TMS (section 1.2) and provides an immediate measure of cortical excitability at any
given moment or condition (i.e. context or task dependence).
MEP is the base level measurement for motor cortex excitability in the sense that
nearly all other TMS techniques rely on it. Therefore, the accuracy of MEP measured is
crucial for the entire field of TMS. The development and fast spread of TMS supporting
neuronavigation systems reflect the common concern that the coil placement error being
a major source of inaccuracy as well as provide the possibility to have closer examination
of this error. Current studies have focused on whether the neuronavigation systems can
improve placement accuracy and affect the MEP measured (Gugino et al., 2001; Sparing
et al., 2008), but with little systematic description of the coil placement and MEP
relationship. The fact that coil orientation has three degree of freedom is also simplified
or neglected in current literatures.
1.4.2 Motor threshold (MT):
The international committee of clinical neurophysiology (IFCN) defines MT as
the minimum TMS output intensity that can induce MEPs, which are larger than the MEP
amplitude criterion (usually 50 μV), with a probability of 50% (Rossini et al., 1994). MT
11
represents a measure of cortex excitability within neural elements beneath the TMS coil
(Hallett, 2000). It shows wide individual variation, which reflects factors such as intrinsic
variation of excitability, state of neuronal membrane excitability, and individual thickness
of scalp or skull. Therefore, MT is used to adjust for inter-individual variation by
expressing TMS intensities as a percentage of an individual’s MT. This adjustment is
usually done at the beginning of each TMS session.
There are several different protocols for MT estimation (see Chapter 2). Good MT
estimation method should be accurate and fast. In Chapter 2, we propose an MT
estimation protocol that is approximately 1.7 to 4 times faster than the currently fastest
protocol and has competitive accuracy compared with all existing protocols.
1.4.3 Representational motor mapping:
While maintaining fixed suprathreshold intensity, the spatial location of TMS can
be varied systematically over a series of scalp sites surrounding the “hot spot” while
recording over target muscles. A TMS map is generated by projecting the TMS
measurement to its stimulation sites. Any TMS measurements that depend on the
stimulation site, such as MEP amplitude, can be used for generating maps (Thickbroom
and Mastaglia, 2002).
The information conveyed by TMS map is rich, including the position of the
motor cortex region representing a muscle (Classen et al., 1998), the relative distribution
of muscle groups (Wassermann et al., 1992) and cortical excitability (Thickbroom and
Mastaglia, 2002). The center of gravity (CoG) of TMS map is surprisingly consistent and
12
reliable given the large variability of individual MEP (Thickbroom et al., 1999), but this
is at a cost of large number of MEP measurement (Classen et al., 1998).
Traditionally, values at a stimulating site of a map are calculated by averaging all
the measured results on this site, which makes traditional maps discrete. Efforts are made
to mathematically model TMS map. Spline interpolation is one method to generate maps
with contours (Borghetti et al., 2008). Matthaus et al. viewed a map as a description of
correlation between the stimuli on a site and the induction of MEP (Matthaus et al., 2008).
Modeling has the potential to describe the map more concisely and systematically,
therefore the question comes naturally that whether proper models can save TMS pulses
needed to build accurate maps. In Chapter 3, we will introduce TMS mapping techniques
that are 3 to 5 times faster than the traditional mapping method.
1.4.4 Paired and repetitive TMS techniques
Paired-pulse TMS techniques are consisted of pairs of TMS stimuli, which are
separated by time intervals ranging in the scale of milliseconds(Hallett, 2007). The first
stimulus is called conditional stimulus (CS), and the second is called testing stimulus
(TS). By tuning the intensity (suprathreshold or subthreshold) and interval of the stimuli,
paired-pulse TMS can have different effects on cortex, for example: Short Intracortical
Inhibition (SICI), Facilitation (ICF) (Ziemann et al., 1996), and Long Intracortical
Inhibition(Sanger et al., 2001). The paired stimuli can also be consisted of one peripheral
stimulus and one TMS stimulus. For example, Short Afferent Inhibition (SAI) is induced
in cortex by median nerve electrical stimulation (Di Lazzaro et al., 2005), and Paired
Associative Stimulation (PAS) can induce cortical plasticity similar to that observed in
13
vitro electrophysiology experiments (Stefan et al., 2002; Stefan et al., 2000; Wolters et al.,
2005).
Repetitive TMS (rTMS) consists of trains of high frequency TMS stimuli. Its
effect can be either excitatory or inhibitory based on the frequency (Rossi et al., 2009;
Wassermann, 1998). Newly developed patterned stimulation techniques such as theta
burst is fast in inducing cortical plasticity (Huang et al., 2005).
1.5 Motivating computational TMS
As reviewed in the above sections, there are two reasons for computation TMS:
first, current data acquisition techniques are very primitive. For example, MT and maps
are desirable but measured slowly. Second, some aspects of TMS principles and
neurophysiology are unclear. For example, TMS the effect of TMS coil placement,
especially the orientation, on measurement is unclear, and there is no direct evidence for
the cosine rule hypothesis proposed by Fox et al.
Our general hypothesis is that by purposely selecting and applying computational
models to solve TMS problems, the efficiency of it can be improved, e.g. MT and
mapping, the description of TMS can be more quantitative, e.g. coil placement, and
quantitative hypothesis can be tested, e.g. the cosine rule for TMS activation of cortical
columns. For each following chapter, we will provide detailed reviews and motivations
for each project, but the application of computational models in TMS is by no way
limited to single pulse TMS, motor cortex, or measurement techniques.
14
Chapter 2 Fast Estimation of TMS Motor Threshold
2.1 Introduction
In motor cortex studies, if TMS is applied at an intensity above a threshold, the
target muscle contralateral to the stimulated cortical neurons will respond with a
distinguishable electrical waveform, the motor evoked potential (MEP). The International
Committee of Clinical Neurophysiology (IFCN) defined the motor threshold (MT) as the
minimum TMS machine output intensity that can induce reliable MEPs (usually >100
μV), with a probability of 50% (Rossini et al., 1994).
Most TMS studies require determining the MT accurately (i.e., with small bias,
the difference between the measured MT and the true MT value) and precisely (i.e., with
little variance), because the choice of stimulator intensity for each participant is adjusted
according to their MTs. The earlier MT determination protocols were based on
systematic search. According to the protocol for MT determination proposed by the IFCN
(Rossini et al., 1994), the experimenter should start from a subthreshold intensity, then
increase the intensity in steps of 5% machine output until 50% of 10 to 20 consecutive
pulses can induce MEPs. In a revised IFCN protocol (Rothwell et al., 1999), the
experimenter should start from a suprathreshold intensity, then decrease it in steps of 2%
or 5% until 50% MEP-induction can no longer be achieved in 10 to 20 consecutive pulses.
Mills and Nithi (1997) proposed a protocol averaging an upper and lower threshold to
determine MT. This protocol requires about 50 TMS pulses for accurate MT
determination (Mills and Nithi, 1997; Mishory et al., 2004).
15
Shortening MT determination with adaptive protocol has the potential to both
save experimental time and reduce the likelihood of inducing physiological changes by
multiple pulses of TMS. A breakthrough in MT determination was the introduction of the
“best-PEST” method, an adaptive method based on Parameter Estimation by Sequential
Testing (PEST) and Maximum Likelihood (ML) regression (Awiszus, 2003). Unlike
other systematic methods, this “best-PEST” is model-based, in that it uses an S-shaped
metric function to model the relationship between the probability of eliciting an MEP and
the TMS intensity. At each trial, the intensity that is predicted to yield a 50% probability
of generating an MEP according to the model is selected as the intensity for the next
TMS pulse. This method is effective because stimulation at 50% intensity yields the
highest information gain (MacKay, 1992; Pentland, 1980). Compared to the Mills and
Nithi (1997) protocol, the “best-PEST” has been shown to find the MT with 24 TMS
pulses on average in simulation (Awiszus, 2003), and with 16 TMS pulses on average in
experiment that used MEP to detect MT (Mishory et al., 2004).
Although prior knowledge of MT is often available before experiments and has
the potential to speed up MT determination, it has only been used scantly in previous
studies. Awiszus used two artificial data points (MEP induction at 100% machine output
and no MEP induction at 0% machine output) to initialize the “best-PEST”, which
reflects belief about MEP induction under extreme machine output conditions (Awiszus,
2003). Borckardt et al. found that if an experimenter has “a reasonably accurate guess” of
MT and starts the PEST procedure with this guess, a non-parametric version of PEST
required fewer trials, although the “best-PEST” suffered a loss of accuracy (Borckardt et
al., 2006).
16
Knowing when to stop MT determination can furthermore potentially speed up
the procedure; care must be taken however to ensure that accuracy is not jeopardized by
(too) early stopping. Mishory et al. (2004) used a repeat-once stopping criterion that
requires two consecutive estimations with the same MT prediction. Borckard et al. (2006)
required that the difference between two consecutive estimations is lower than a
threshold. In their freely distributed software, Borckardt et al. used a progress bar to give
“a rough visual estimate of how close the user is to reaching the rMT estimate”; no
explanation of its mathematical detail was provided however.
Here, we propose to use Bayesian regression for PEST to add two modifications
to the “best-PEST” method, and determine the MT quickly, accurately, and precisely.
The first modification is to integrate prior MT data, which in theory, can speed up MT
determination. The second modification is to determine a systematic and theoretically
sound stopping criterion.
The use of Bayesian regression in PEST is an established method in the field of
psychophysics (Treutwein, 1995), but has not yet been applied to TMS in general, and
MT determination in particular. The Bayesian framework has two potential advantages:
The first advantage is that it is ideal for the systematic incorporation of prior knowledge
(Bishop, 2006). After each trial, the likelihood that the MEP is generated by the model is
combined with the prior probability of the MT to generate a posterior probability
distribution of MT. This “posterior” can then be used either to determine the threshold or
to determine the next sample (Alcala-Quintana and Garcia-Perez, 2005; Watson and Pelli,
1983). Here, we leveraged two kinds of prior information separately. (1) A distribution of
17
MTs is often available for the subject pool of the laboratory or the institution. We call
this the common prior. (2) In multi-session experiments, if a subject has MT determined
in a previous session, its value can be used to estimate the MT of the current session,
because MT measured from a same subject is relatively stable over time (Stewart et al.,
2001). We call this the subject-specific prior. The second advantage of Bayesian
regression is that it naturally lends itself to derive a stopping criterion based on the
posterior probability to ensure a pre-determined level of precision (Treutwein, 1995,
1997).
We show here that combining the incorporation of prior knowledge with a
posterior probability-based stopping criterion in the Bayesian PEST allows the MT
determination with fewer pulses than the “best-PEST” for equal accuracy and with an
explicitly stated degree of precision. Our results show that MT can be determined with as
few as three pulses when a subject-specific prior is available.
2.2 Materials and methods
2.2.1 Experimental comparison of MT estimation methods
Ten right-handed subjects (5 male and 5 female, age average 27.7, and age
standard deviation 3.0) gave their informed consent for study procedures approved by the
local IRB. We measured the resting MT of the right FDI in each subject with four
methods: (1) IFCN protocol; (2) “best-PEST”; (3) Bayesian PEST with common prior;
and (4) Bayesian PEST with subject-specific prior. Since the true MT of the subjects is
not known as it is always empirically determined, we chose to compare each method’s
18
estimated MT with the MT assessed by the IFCN protocol as a standard for MT
estimation. All subjects had their FDI resting MT previously measured with the IFCN
protocol, at least one week before the experiment. All four methods were tested on each
subject in a pseudo-random order, and two consecutive methods were separated by a 10-
mintue interval in one session.
2.2.2 Single pulse TMS
Focal single pulse TMS was delivered with a figure-of-8 coil connected to a
commercially available magnetic stimulator (Magstim 200). The coil was placed on the
scalp at the optimal position for stimulation of the right first dorsal interosseus (FDI), and
at 45 degree with respect to the posterior-anterior direction towards right. Surface EMG
electrodes were attached to the skin over the FDI muscle using electrode gel and tape.
Signal was sampled at 2 kHz with differential amplifiers (Grass Instruments IP511) with
a bandwidth of 1 Hz-1 kHz. Electrophysiological signals from the muscle were amplified
and recorded for analysis. Participants, who sat in a chair adjusted to a comfortable height,
put their right hands on a soft pillow, and were instructed to relax during the stimulation
session. A Lycra swim cap was worn over the head in order to mark locations on the head
so that the TMS coil could be reliably placed over same scalp regions during the course
of the test session. The hotspot for FDI was determined by a standard protocol (Schluter
et al., 1998) at the beginning of each experimental session before MT estimation. A
computer software displayed the EMG baseline activity, for which good resting condition
was considered qualified if the amplitude remains within ±20 μV. We used the criterion
that any MEP peak-to-peak amplitude should be larger than 50 µV.
19
2.2.3 Description of MT estimation protocols
The IFCN protocol was performed as in (Rothwell et al., 1999). We started from a
suprathreshold intensity determined during hotspot hunting, and decreased it by steps of 2
% maximal stimulator output (MSO), until 5 out of 10 consecutive TMS pulses can
induce MEPs. If fewer than 10 pulses were delivered but more than 5 induced MEPs, the
next lower intensity was tested.
The “best-PEST” protocol is as in (Mishory et al., 2004). At first, two artificial
data points, MEP induction at 100 %MSO and no MEP induction at 0 %MSO, were used
to initialize the “best-PEST”. Accordingly, the first TMS trial intensity was set at 50
%MSO. After each trial, all available data were used for ML regression to find the probit
function of the MEP probability-TMS intensity relationship (the probit function is S-
shaped function obtained by the cumulative distribution function associated with the
normal distribution). The threshold parameter of this function equals the estimated MT.
The next TMS pulse intensity was set to this estimated MT and the procedure continued
until the repeat-once criterion was met. The experimenter manually entered the TMS
intensity and the resulting MEP observation (0 or 1) for each trial, as prompted by in-
house developed software. After the stopping criterion had been reached, a red square on
the graphical user interface turned green, and the experimenter stopped the procedure.
Bayesian PEST was tested with both common and subject-specific priors. This
method starts from a prior distribution of MT, modeled by a Gaussian distribution with
mean MT
0
and standard deviation σ
0
. Bayesian probit regression was performed on all
available data before the delivery of each TMS pulse. The intensity of the next TMS
pulse was then set to be the MT predicted by the regression. After this next pulse, both
the independent variable (the intensity) and the binary dependent variable (whether MEP
is observed or not) were added to the entire dataset, and a new regression was carried out
on the increased dataset to give the next MT intensity. The procedure was iterated until
the stopping criterion is met. The stopping criterion used in the Bayesian PEST follows
(Treutwein, 1997) and is defined as below: The (1- α)% probability interval (
(1- α)
PI) is the
region ( θ
l
, θ
u
) corresponding to
2
1 ) ( ) (
α
θ
θ
− = =
∫ ∫
∞
∞ −
l
u
dMT MT Posterior dMT MT Posterior , (2.1)
where “Posterior(MT)" is the posterior distribution of MT. We require the value θ
u
- θ
l
to
be smaller than a threshold for Bayesian PEST to stop and refer this stopping criterion as
(1- α)
PI criterion. Narrower thresholds correspond to smaller variance of the MT estimation.
We refer to this threshold as the maximal
(1- α)
PI width. Except for the mean of subject-
specific prior, the prior parameters were determined by computer simulations carried out
before experiments (see below).
2.2.4 Using computer simulations to determine the MT prior distribution
maximal
95
PI width
The purpose of computer simulation is to determine the MT prior distribution and
maximal
95
PI width for the stopping criterion for actual experiments. We generated
synthetic TMS data with Monte Carlo simulations, by building 10 data generators with
probit regression based on 10 datasets previously collected in TMS MT estimation
20
21
(Awiszus, 2003; Borckardt et al., 2006). Each data generator was associated with one
probit function determined by the data from one subject. Given a TMS intensity, the data
generator stochastically generated 1 or 0 (MEP or no MEP) with probability calculated
according to the probit function. The true MT of a data generator was equal to the value
of the threshold parameter of the probit function.
A Gaussian distribution was used to model the common prior. The common prior
had a mean MT
0
equals to 40 %MSO and a standard deviation σ
0
equals to 8 %MSO.
These two parameters were determined with the mean and standard deviation of the true
MTs of the data generators. To determine the maximal
95
PI width for Bayesian PEST
with the common prior, we tested maximal
95
PI widths of 21, 11, 9, 7, 6, and 5 %MSO.
We selected the largest maximal
95
PI width that enabled the Bayesian PEST to yield an
average estimation error not significantly different from that of the simulated “best-
PEST” with the repeat-once criterion (Mishory et al., 2004).
A Gaussian distribution was also used to model the subject-specific prior. The
standard deviation σ
0
of the subject-specific prior was taken as 3 %MSO (see
supplementary material for rationale). Since the mean MT
0
for individual subjects was
not available, we tested the range of true MT±10 %MSO for prior mean MT
0
for each
data generator. To determine the maximal
95
PI width for Bayesian PEST with the subject-
specific prior, we tested maximal
95
PI widths of 5, 7, and 9 %MSO. We selected the
maximal
95
PI width that enables Bayesian PEST to yield an average stopping error not
significantly different from what given by the “best-PEST” with the repeat-once criterion
(Mishory et al., 2004) when MT
0
was in the range of MT±5 %MSO. This range of true
MT±5 %MSO for MT
0
was chosen based on our observations in the lab that the
difference of between-session MT in healthy subjects is less than 5 %MSO. This
observation is consistent with the data shown in figure 2 of (Stewart et al., 2001), in
which six out of seven healthy subjects had between-session MT differences less than 5
%MSO.
To evaluate the stopping error, we compared the estimated MT against the true
MT of the corresponding data generator, and used the relative error as stopping error:
MT True
MT Estimated Model MT True
Error Relative
_
_ _ _
_
−
= (2.2)
We repeated 50 simulation runs to evaluate the relative error for each condition.
Further details and rationale of the computer simulation can be found in the
supplementary material.
2.2.5 Data analysis
22
We compared the MTs determined with each method with those measured by the
IFCN protocol by paired t-test and Pearson’s correlation, taking the IFCN protocol has
the published standard recommendation for MT estimation. We also examined the
individual differences among the MTs measured by all methods. We considered a
difference of 5 %MSO from the IFCN estimation a large deviation because the IFCN
protocol recommended TMS intensity steps of 2-5 %MSO (Rothwell et al., 1999). To
evaluate the speed of each method, we compared the numbers of trials with paired t-tests.
The significance level for all statistical tests was p<0.05.
23
2.3 Results
2.3.1 Demonstration of MT distribution change in Bayesian PEST
A simulation demonstration for change in MT distribution in Bayesian PEST is
shown in figure 2.1. The true MT is 40 %MSO. The prior is a broad Gaussian distribution
with mean at 50 %MSO and standard deviation at 4.5 %MSO (figure 2.1A). As the
number of pulses available increases, two changes happen to the estimated distribution of
MT (figure 2.1B-D): (1) the mean shifts towards 40 %MSO (the accuracy increases), and
(2) the standard deviation of the estimator decreases (the precision increases). The second
change will eventually allow the posterior distribution to satisfy the
(1- α)
PI criterion.
Figure 2.1. Probability distributions of MTs estimated after different number of trials in
the Bayesian PEST procedure. The true MT in this simulated subject was 40 %MSO. In
each panel, the x axis represents MT in %MSO, and the y axis represents probability.
A: The prior is a Gaussian distribution with mean 50 %MSO and standard deviation 4.5
%MSO. B: Posterior MT distribution after 3 trials. C: Posterior MT distribution after
14 trials. D: Posterior MT distribution after 20 trials.
24
25
2.3.2 Using computer simulations to determine maximal
95
PI width
To determine the maximal
95
PI width for the Bayesian PEST with common prior,
we compared the “best-PEST” and the Bayesian PEST in simulation. The maximal
95
PI
widths considered were 21, 11, 9, 7, 6, and 5 % MSO (figure 2.2 triangles). The “best-
PEST” stopped, on average, at 10.7±0.6 (mean ± standard deviation) trials with a relative
error of 0.027 (figure 2.2 squares). As the maximal
95
PI width decreased, the stopping
error of Bayesian PEST decreased, but the number of TMS trials required increased.
Bayesian PEST was as accurate as the “best-PEST” (paired t-test, p = 0.605, relative
error 0.027) for maximal
95
PI width equal to 7 %MSO. For this condition, the Bayesian
PEST stopped after 6.3±2.1 (mean ± standard deviation) trials, which is significantly
lower than that of “best-PEST” (paired t-test, p = 0.00006). The maximal
95
PI width was
thus determined as 7 %MSO for the Bayesian PEST with common prior.
21
11
9
7
6
5
Figure 2.2 – Comparison of stopping trial and relative error of “best-PEST” (ML) and
BayesianPEST. Mean relative errors of 10 data generators as a function of stopping
trials, for the “best-PEST” (square) and for different maximal
95
PI width (21, 11, 9, 7, 6
and 5 from left to right) for the Bayesian PEST (triangles). The maximal
95
PI width
tested is labeled as a number next to each triangle data point. Horizontal bars represent
±1 standard deviation for stopping trials; vertical bars represent ±1 standard deviation
for the relative error.
To determine maximal
95
PI width for the Bayesian PEST with subject-specific
prior, we considered maximal
95
PI widths of 5, 7, and 9 %MSO with MT
0
within the
range MT±10 %MSO. The top row of figure 2.3 presents the stopping error (figure 2.3A)
and number of trials (figure 2.3B) when the maximal
95
PI width was 5 %MSO. In the
range of true MT±5 %MSO, the average stopping relative error was below 0.021 (figure
2.3A), and the average number of trials was below 15 (figure 2.3B). The middle row of
figure 2.3 presents the stopping error (figure 2.3C) and the number of trials (figure 2.3D)
when the maximal
95
PI width was 7 %MSO. In the range of true MT±5 %MSO, the
average stopping relative error was below 0.027 (figure 2.3C), which was equal to the
stopping error of the “best-PEST” (figure 2.2 square); the average number of trials was
fewer than 6 (figure 2.3D). The lower row of figure 2.3 represents the stopping error
26
27
(figure 2.3E) and the number of trials (figure 2.3F) when the maximal
95
PI width was 9%.
The average stopping relative error was not lower than 0.027 for full range of true MT±5
%MSO (figure 2.3E). In light of these simulations results, the maximal
95
PI width was
determined as 7 %MSO for the Bayesian PEST with subject-specific prior.
A B
C D
E F
Figure 2.3 – The stopping relative error and trial number of Bayesian PEST when
maximal
95
PI width were equal to 5 (A, B), 7 (C, D), and 9 (E, F) %MSO. In each
subplot, the MT
0
changes from true MT-10 %MSO to true MT+10 %MSO. Bars
represent average ±1 standard deviation across results of 10 data generators. When the
maximal
95
PI width was 7 %MSO and MT
0
is in the range of true MT±5 %MSO,
Bayesian PEST stopping relative error was less than the “best-PEST” stopping relative
error 0.027, therefore the maximal
95
PI width of 7 %MSO was selected.
28
29
2.3.3 Experimental comparison of MT estimation methods
Our experiment results showed the Bayesian PEST with subject-specific prior
required the fewest number of TMS pulses (figure 2.4A). Specifically, the mean number
and standard deviation of pulses are 29.9 ±11.6 for the IFCN method, 12.2 ±5.5 for the
“best-PEST” method, 6.6 ± 2.6 for the Bayesian PEST with common prior, and 2.7 ± 0.5
for the Bayesian PEST with subject-specific prior. The subject-specific prior required
fewer pulses than the common prior (paired t-test p = 0.0005), which itself required fewer
trials than the no prior “best-PEST” (paired t-test, p = 0.0155). Finally, the “best-PEST”
required fewer pulses than the IFCN method (paired t-test; p = 0.0046), as previously
reported (Mishory et al., 2004) (Figure 2.4A).
There was no difference in average in the estimated MTs between the IFCN, the
“best-PEST”, the Bayesian PEST with common prior, and the Bayesian PEST with
subject-specific prior (Figure 2.3B). Specifically, for paired t-test on the null hypothesis
that the estimated MTs of two methods are the same, the p-value for the “best-PEST” and
the IFCN method was 0.31, the p-value for the Bayesian PEST with common prior and
the IFCN method was 0.84, the p-value for the Bayesian PEST with subject-specific prior
and the IFCN method was 1.0000. The average and standard deviation of the difference
were 0.7 ± 2.1 %MSO between the “best-PEST” and the IFCN method, 0.2 ± 3.1 %MSO
between the Bayesian PEST with common prior and the IFCN method, and 0.0 ±1.6 %
MSO between the Bayesian PEST with subject-specific prior and the IFCN method. The
MT estimated by the IFCN method and by the “best-PEST” were significantly correlated
with coefficient 0.95 (p <0.001), the MT estimated by the IFCN method and by the
30
Bayesian PEST with common prior were significantly correlated with coefficient 0.8791
(p <0.001), and the MT estimated by the IFCN method and by the Bayesian PEST with
subject-specific prior were significantly correlated with coefficient 0.9856 (p < 0.001).
MTs estimated by each method for individual subjects are shown in figure 2.4C.
The estimation difference between IFCN method and “best-PEST” for all subjects was
below 4 %MSO. The estimation difference between Bayesian PEST with common prior
and IFCN method for one subject was 6 %MSO (“+” marker in figure 2.4C), and for the
other of nine subjects was below 5 %MSO. The estimation difference between Bayesian
PEST with subject-specific prior and the IFCN method was below 3 %MSO for all
subjects. We considered a difference of 5 %MSO from the IFCN estimation a large
deviation because the IFCN recommended using 2-5 %MSO as step size for MT
estimation. Thus, except for one subject in the Bayesian PEST with common prior, all
deviations are acceptable.
Figure 2.4. A Average number of pulses used and B. Average MT estimated by
different methods. C. Single subject MTs measured by different methods (labeled on
the x-axis). One had 6 %MSO difference between MT measured by the IFCN method
and the Bayesian PEST with common prior (filled circle). All data are based on the
results of ten subjects. All error bars represent ±one standard deviation. ‘ML’ –“best-
PEST” with the stopping-once criterion; ‘Common’ – Bayesian PEST with common
prior; ‘Subject’ – Bayesian PEST with subject-specific prior. The marks “*” indicate
statistically significant differences. The mark “+” indicates the MT measured by
Bayesian PEST was 6 %MSO lower than the MT measured by IFCN method.
2.4 Discussion
Our results showed that the Bayesian PEST with posterior
95
PI stopping criterion
is a fast, precise, and accurate MT determination method. Our experiment showed that,
on average, the common prior requires seven TMS trials and the subject-specific prior
31
32
requires as few as three TMS trials (figure 2.4A). The MT determined by the Bayesian
PEST methods were not different from that estimated by the IFCN method (figure 2.4B),
except for one subject for which a 6 %MSO difference was found between the MT
estimated by IFCN method and the MT estimated by Bayesian PEST with common prior
(figure 2.4C).
As we showed, introduction of prior knowledge in the Bayesian framework can
speed up MT determination. But what happens if the prior is wrong? When the prior is
not a uniform distribution, or exactly the same as the true distribution, a bias (which
decreases with the number of trials, as shown in figure 2.1) is introduced into MT
estimation. When the mean MT
0
of the prior is different from the true MT, both the
number of trials and error increase. However, different stopping criteria can control
different level of prior bias (figure 2.3). The maximal 95PI width controls the stopping
variability of the estimation and therefore controls the precision of the MT estimator. As
precision improves together with accuracy (figure 2.1), the
95
PI stopping criterion
controls the stopping accuracy (figure 2.2 and 2.3). We assumed MT
0
and true MT
difference should be within 5 %MSO. According to the figure, this amount of prior bias
can be well controlled by 7 %MSO maximal
95
PI width to maintain a relative error lower
than the relative error of the “best-PEST” (0.027). If an experimenter assume the real
world MT
0
and true MT difference can be as large as 10 %MSO, then he/she should
choose the stopping criterion as for figure 2.3 A and B. In such a case, the number of
trials will be increased to improve accuracy.
33
Our method is especially advantageous when a subject-specific prior is available.
In practice, such a prior is available in clinical applications that requite multiple visits,
such as the use of TMS for treatment of depression (Simpson et al., 2009). It may seem
surprising that MT can be obtained in as few as three trials when a subject specific prior
is available. However, this can be understood as the prior information accounts for the
information provided by multiple trials. Indeed a posterior after N trials can be viewed as
the prior before the N+1
st
trial, and having a prior at the beginning is equivalent to
starting with multiple trials.
Previous Bayesian PEST studies suggested that this method requires at least 20
samples to be collected because of the concern that too little samples may not be
sufficient for threshold estimation (Alcala-Quintana and Garcia-Perez, 2005; Treutwein,
1995). Two major differences exist however between our study and these studies: (1) We
focused on the field of TMS and use sound domain-specific prior, while other studies
usually examined the algorithm in general and used uniform prior (Alcala-Quintana and
Garcia-Perez, 2005). (2) TMS has a relatively low accuracy requirement compared with
that of other studies. For example, calculation based on the results of (Alcala-Quintana
and Garcia-Perez, 2005) indicated that after 10 trials the error of MT estimation can be as
small as 0.2 %MSO, which is lower than the possible 1 %MSO tunable in TMS
experiments.
Finally, our study, like the study of (Awiszus, 2003), assumed that the hotspot,
defined as the optimal position that has the lowest MT on the scalp for placing the TMS
coil, had already been found before MT estimation. In actual TMS experiments, however,
locating the hotspot is not a trivial task. Further, hotspot location and MT determination
are often carried out simultaneously. Therefore, the practical TMS trial reduction by our
method may be limited in actual settings. TMS studies would thus greatly benefit from
adaptive methods that extend our proposed Bayesian adaptive MT determination method
with the addition of priors in 2D space to concurrently optimize the sampling location
and the sampling intensity.
2.5 Supplementary material
2.5.1 Bayesian PEST for MT determination
Ideally, Bayesian methods should analytically solve the function form of posterior
distribution, and compute the expectation value for the posterior. However, the posterior
is usually difficult to solve unless the likelihood function and the prior function have
“friendly” mathematical features. A computationally easy solution for Bayesian problems
is the Maximum A Posteriori (MAP) solution, which simply finds the value that
maximizes the posterior distribution.
34
) | ( D MT
To find the MAP solution for the Bayesian PEST of MT, we need to determine
the MT that has the highest probability given observation D, p . Here
observation D consists of a series of MSO-MEP pairs, where MSO represents maximal
machine output in percentage and MEP represents muscle evoked potential in binary
Yes/No variable. If the EMG peak-to-peak value is larger than 50 μV, the MEP is coded
as 1 (for ‘Yes’); otherwise MEP is coded as 0 (for ‘No’). Let MT
*
be the solution of the
35
) | ( max D MT p
( p
| (D p
) (MT p
regression problem, and arg be a function that returns the argument value
MT that maximizes . The regression for MT is formulated as:
MT
) | D MT
) | D
| ( D MT p
(MT
) MT
) (D p
max arg
*
p MT
MT
= (2.1S)
The conditional distribution is known as the posterior. The conditional
distribution is known as the likelihood (see below). The Bayesian theorem
combines the likelihood with the prior distribution of MT, , and the prior
distribution of D, :
)
(
) | (
D p
D MT p =
)
) (MT p
(
) |
D p
MT
(2.2S)
The regression problem stated in equation (2.1S) is thus transformed into:
) (
) ( ) | (
max arg )
D p
D
MT
=
| ( ( max arg ) D p D
MT
=
| MT
| MT
( max arg
*
D p
MT p MT
p MT
MT
= (2.3S)
Because does not depend on MT, the regression can thus be formulated as: ) (D p
)) ( ) ( max arg
*
MT p MT p MT
MT
= (2.4S)
Maximum Likelihood (ML) regression, which is used in the “best-PEST” method
developed by (Awiszus, 2003; Mishory et al., 2004) is the special case of Bayesian
regression with a uniform prior distribution. In ML regression, Equation (2.4S) is
therefore further reduced to:
) | ( max arg ) | ( max arg
*
MT D p D MT p MT
MT MT
= = (2.5S)
36
) | ( MT t p
To solve the Bayesian regression problem in equation (2.4S), we need to compute
the likelihood. For this purpose, we assume the MEPs are elicited and recorded
independently trial-by-trial. In the i
th
trial, the TMS intensity is m
i
% MSO, and the
induction of a valid MEP (amplitude larger than 50 μV) t
i
follows the binary distribution
. We use t
i
=1 for valid MEP and t
i
=0 for invalid MEP. D is the collection of
all {t
i
, m
i
}
i=1,2…n
. The log likelihood for n observations is:
i
] )) | ( 1 )( | ( [ log ) | ( log
1
1
i i
t
i i
t
n
i
MT m p MT m p MT D p
−
=
− ∏ = (2.6S)
Using the property of log, we have:
∑
=
− − + =
n
i
i i i i
MT m p t MT m p t MT D p
1
))] | ( 1 log( ) 1 ( ) | ( log [ ) | ( log (2.7S)
In this study, the prior is modeled as a Gaussian distribution because its
bell-shaped function satisfies the machine-prior of less chance for MT to be extreme
values like 0% or 100% MSO. Using MT
0
as the mean and σ
0
as the standard deviation
for the prior, we have:
) (MT p
()
2
0
2
0
2
0
2
1
) (
σ
π σ
MT MT
e MT p
−
−
= (2.8S)
Because the log function is monotonically increasing, equation (2.4S) can be written as:
))) ( log( )) | ( (log( max arg )) ( ) | ( ( max arg
*
MT p MT D p MT p MT D p MT
MT MT
+ = = (2.9S)
Substituting with equation (2.7S), and with equation (2.8S): ) | ( log MT D p ) (MT p
∑
=
−
− − − + =
n
i
i i i i
MT
MT MT
MT m p t MT m p t MT
1
2
0
2
0 *
)
2
) (
))] | ( 1 log( ) 1 ( ) | ( log [ ( max arg
σ
(2.10S)
To model the probability of MEP induction at a TMS intensity m
i
, we
use the Cumulative Gaussian function (also called the probit function) as in the “best-
PEST” (Awiszus, 2003; Mishory et al., 2004). The probit function is calculated by
integrating a Gaussian probability function, so when its inputs increase from negative
infinity to maximum infinity, its output increases from 0 to 1 monotonically, forming an
S-shape in input-output space. The equation of the probit function is:
) | ( MT m p
i
∫
∞ −
−
−
=
m MT x
dx e MT m p
2
2
2
) (
2
1
) , | (
σ
π σ
σ , (2.11S)
Where m is the TMS intensity, and
) , | ( σ MT m p
is the probability of observing an MEP
at m. Psychophysics studies generally assume the candidate S-shaped metric functions
differ only in position/threshold, and not in shape (Treutwein, 1995; Watson and Pelli,
1983). However, Awiszus (2003) showed that in TMS the S-shaped metric function
“threshold spread” is linearly dependent on its position/threshold. Specifically, MT and
the threshold standard deviation σ follow the linear relationship MT 07 . 0 = σ (Awiszus,
2003; Mishory et al., 2004). The function is thus reduced to:
37
∫
∞ −
−
−
=
m
MT
MT x
dx e
MT
MT m p
2
2
) 07 . 0 ( 2
) (
2 07 . 0
1
) | (
π
(2.12S)
We can now replace in the Bayesian problem equation (2.10S) by its
expression given in equation (2.12S).
) | ( MT m p
Our Bayesian PEST starts from the Gaussian prior in equation (2.8S). Bayesian
probit regression is performed on all available data before the delivery of each TMS pulse.
The pulse intensity is then set to be the
*
MT of the regression result. After the new TMS
pulse is delivered, the intensity of the pulse and whether MEP is observed are added to
the entire dataset, and then a new regression is carried out on the increased dataset to give
the next
*
MT prediction. The log posterior distribution of the Bayesian
regression is defined by equation (2.10S). The probability in equation (2.10S)
is calculated by equation (2.12S). We used Brent’s Method to perform the maximization
of the posterior with respect to parameter MT in equation (2.10S). This procedure is
iterated until a stopping criterion is met. The stopping criterion used in our Bayesian
PEST is the width of the 95% probability interval (
95
PI) (Alcala-Quintana and Garcia-
Perez, 2005; Treutwein, 1995). This criterion is introduced in the main article.
) | ( log D MT p
) | ( MT m p
i
All computations and the S-shaped probit function used in “best-PEST” of
(Awiszus, 2003; Mishory et al., 2004) are identical as above, except that the log
likelihood is defined by equation (2.6S), and that it used the “repeat-once”
stopping criterion introduced in the main article.
) | ( log MT D p
38
When comparing the objective functions maximized in Maximum Likelihood methods
defined in equation (2.6S) and in the Bayesian methods defined in equation (2.10S), the
difference is that the latter has an additional term
2
0
0
2
) (
σ
MT MT
−
2
−
) | ( D MT p
, which is from the log
of the prior distribution. This term can be understood as a penalizing term that reduces
the probability when MT is away from the prior knowledge of MT
0
. If the
prior is correct (MT
0
is close to the subject’s real MT) and confident ( σ
0
is small), its
accelerating effect becomes more prominent because it penalizes heavily on MT
estimations that are away from the real MT. A low confident prior causes the term
2
0
2
0
2
) (
σ
MT MT −
−
diminish by setting the σ
0
to a large value, and the accelerating effect is
thus reduced. A very large σ
0
reduces the Bayesian approach to an ML approach.
Equation (2.10S) is solved by comparing the posterior among candidate
MTs. To calculate the posterior, we approximate it by considering all discrete integer MT
values from 1 to 100, and use the property of probability:
) | ( D MT p
∑
=
≈
100
1
) ( ) | ( ) (
MT
MT p MT D p D p (2.13S)
Substitute in equation (2.2S) by equation (2.13S):
) (D p
∑
=
≈
100
1
) ( ) | (
) ( ) | (
) | (
mt
mt p mt D p
MT p MT D p
D MT p (2.14S)
39
In equation (2.14S), is given by equation (2.8S) and is given by the
exponential of equation (2.7S).
) | ( MT D p
) (MT p
40
We used equation (2.1S) for Bayesian regression. Methods that are more
sophisticated include using the expectation or median of the posterior MT for MT
inference.
2.5.2 Computer Simulations
Before testing the Bayesian PEST in actual experiments, we used computer
simulations to 1) show that the algorithm prediction converges to the true MT, 2)
determine the common prior and subject-specific prior, and 3) determine the maximal
95
PI width of the posterior distribution. The advantage of simulations is two-fold. First,
we know the true MT (see below), so we can evaluate the prediction error of the
algorithms. Second, we can fine-tune the algorithm by performing as many
“experiments” as needed without ethical or practical concerns.
2.5.2.1 Data generators
Generating MEPs for MT determination in simulation requires building MEP
generators with probabilistic models. TMS pulses are then generated from the models
with Monte-Carlo sampling. We use equation (2.11S) as the MEP model and use MT
measurement data collected from previous experiments in 8 healthy subjects to determine
the parameters MT and σ in (2.11S). Subjects gave their informed consents and all study
procedures were approved by local IRB. For 5 of the subjects, the resting MT for a hand
muscle, the right first dorsal interosseous (FDI), was obtained. For the other 3 subjects,
the active MT for a leg muscle, the Gluteus Maximus was obtained. For two of these
subjects, GM MT was determined twice, with an interval of at least 1 week between
41
experiments. A Magstim 200 stimulator (The Magstim Company, Dyfed, UK) was used
for TMS. For upper extremity MT determination, a figure-of-8 coil was used. For lower
extremity MT determination, a cone shaped coil was used. In all cases, MTs were
measured following the IFCN definition. Each data set consisted of 25 to 50 pulses. For
each dataset, we use a general linear model (Dobson, 1990) probit regression to
determine the parameters MT and σ in equation (2.11S).
To compare the accuracy of the simulated models, we use the relative error
defined by equation 2.2.
2.5.2.2 Prior distribution function parameters
The common prior reflects our knowledge of our subject population’s MT
distribution before MT determination. We examined the MTs of the 10 datasets to
determine the Gaussian prior parameters MT
0
and σ
0
. We set MT
0
= 40% MSO, as the
average of all data generators’ true MTs. We set σ
0
= 8 as this is the standard deviation of
all data generator’s true MTs. The subject-specific prior reflects our knowledge of one
subject’s MT before MT determination. It is also modeled by a Gaussian distribution, the
MT
0
of which is the MT determined in a previous experimental session and the σ
0
of
which is 3 %MSO. The heuristic for choosing the value for σ
0
is that the posterior of a
previous Bayesian PEST measurement is the prior of the current “best-PEST”, and since
the previous measurement is “outdated”, σ
0
should be a little larger than the previous
posterior standard deviation. If we assume that the previous test also stopped when the
95% probability interval for MT was narrower than the width defined by the
95
PI
stopping criterion, 3.92 σ
0
(95% probability interval width for the Gaussian prior) should
42
be a little larger than 7 %MSO (maximal
95
PI width determined by simulation, see the
main article). Therefore, σ
0
should be larger than 1.78 ≈ 2 %MSO. We chose 3% MSO
for σ
0
.
2.5.2.3 Convergence test
Convergence of Bayesian PEST to the true MT when the number of TMS trials
increases was tested in simulation. As a gold standard for convergence, we also simulated
the relative error of the IFCN method, as in (Awiszus, 2003). To simulate the IFCN
method, each model generator generated TMS trials at all 100 possible TMS intensities
(from 1% to 100%), and we chose the smallest TMS intensity that elicits 5 MEPs out of
10 trials as the estimated MT. We repeated 50 simulation runs for each data generator in
each condition.
Simulations showed that after 22 trials, the “best-PEST” has the same error as that
of the IFCN protocol (p > 0.05, paired t-test on relative error) – see Figure 2.1S. This
result is consistent with the result of (Awiszus 2003). The Bayesian PEST after 19 TMS
trials has the same error as that of the IFCN protocol (p > 0.05, paired t-test on relative
error). The Bayesian “best-PEST” also converged faster, for example, after three trials,
the Bayesian “best-PEST” average error was 0.055, while “best-PEST” average error was
0.227; the difference is significant (p < 0.05, paired t-test on relative error).
Figure 2.1S. Average relative error is plotted as a function of increasing TMS trial
number for 50 simulation runs. Shown are IFCN, “best-PEST” (ML) and Bayesian
PEST (Bayesian) methods. Only data from trial 3 to trial 25 are shown because both ML
and Bayesian PEST converged by trial 25 and the error for ML in the first 2 trials was
very large.
43
44
Chapter 3 Fast TMS mapping with spatial and temporal information
3.1 Introduction
When a supra-threshold TMS pulse is applied on the scalp overlying the motor
cortex, a contralateral muscle twitch in a target muscle can be recorded with surface
electromyography (EMG) as a motor evoked potential (MEP). By moving the coil
systematically across the scalp over a sub-region of cortex, and by stimulating at fixed
supra-threshold intensity, one can generate spatial maps that relate coil position to MEPs.
In “traditional” mapping, a grid is drawn on the scalp (usually about 5 x 5 cm) and each
location of the map is stimulated repeatedly (10 or 20 times); the MEP is then averaged at
each map location to reduce variability. The position of the map Center of Gravity (CoG),
which is computed as the MEP-weighted average of stimuli positions, correlated with the
cortical position of this muscle (Classen et al., 1998) with a resolution of one millimeter.
Because of this high resolution, TMS mapping is increasinly used in 1) scientific
experiments, 2) clinical studies of brain organization in patients, and 3) presurgical
planning and post-operative mapping, as we now review.
TMS mapping can document motor learning in healthy individuals as motor
learning induces shifts in changes in map excitability as well as COG (Kleim et al., 2006;
Pascual-Leone et al., 1995). Note, however, that because changes in the extent of TMS
motor maps may be due to actual enlargement of the cortical representation, or changes
in subcortical and/or cortical excitability (Koski and Dobkin, 2005) a systematic mapping
45
protocol for motor learning studies recommends normalization of the overall map activity
by baseline excitability (Kleim et al., 2007).
TMS maps can be used as biomarkers to predict recovery from stroke as motor
therapy leads to map enlargement and shifts in COG (Cicinelli et al., 1997) (Liepert et al.,
1998) (Liepert et al., 2000) (Delvaux et al., 2003), even after normalization by baseline
excitability (Sawaki et al., 2008). Only COG shifts in the affected hemisphere, but no
other TMS measures (excitability, etc…), predict motor recovery (Platz et al., 2005), and
COG move in the direction of lowest intracortical inhibition prior to therapy (Liepert et
al., 2006). TMS mapping is also used in a number of different neurological disorders:
COG shifts and/map distortions have been found in Alzheimer's disease patients (Ferreri
et al., 2003), in epileptic patients (Labyt et al., 2007) and in congenital hemiplegia
patients (Vandermeeren et al., 2009). Finally, in a study of focal hand dystonia (Schabrun
et al., 2008), three hand muscles were mapped before and after non-associative electrical
stimulation. Map size was reduced in all muscles, and COGs for the different muscles
moved further apart.
Finally, TMS mapping has received much attention recently in neurosurgery
because, compared to direct electrical cortical stimulation mapping, it is much less
invasive, and allow more areas of the brain to be mapped in more subjects (Krings et al.,
1997; Krings et al., 2001; Tharin and Golby, 2007). In particular navigated TMS is a
reliable method for non-invasive analysis of cortical function before tumor surgery
(Fujiki et al., 2007; Pichta et al., 2009). Finally, TMS mapping is also starting to be used
for surgery in epilepsy (Vitikainen et al., 2009).
46
All these applications of TMS mapping, particularly the clinical applications,
would largely benefit from fast and accurate mapping techniques. Traditional mapping
requires a large number of pulses (upwards of 500 pulses for good accuracy (Classen et
al., 1998)) and up to one hour per muscle, though the number of pulses can be somewhat
reduced by various techniques, including spiral out from hotspot (Koski et al., 2004;
Wassermann et al., 1992) or a combination of systematic sampling back and forth across
the hotspot (Liepert et al., 1998). This long mapping procedure is a scientific concern
because it limits the temporal resolution of mapping studies when changes across time
are critical, such as in motor learning (Pascual-Leone et al., 1994), or the gradual increase
of phosphene thresholds when the subject is blindfolded (Boroojerdi et al., 2000). Further,
although single pulse TMS is relatively painless and safe, some subjects find repeated
stimulations over a long experimental session uncomfortable. Finally, in the clinic, beside
the obvious practical and financial advantages to faster mapping techniques, it has been
recommended that the number of single pulse TMS stimulations be reduced to the
minimum in neurological patients because of the low but non-zero risk of seizures.
To accelerate TMS map formation and CoG estimation, we suggest using 1)
neuronavigation system, 2) spatial correlation between neighbouring locations, and 3)
temporal correlations observed in the multiple responses to each pulse. Frameless
neuronavigation systems have been developed for TMS experimenters since the early
1990’s and have proved to be an accurate coil placement aiding method with accuracy
within several millimeters (Gugino et al., 2001; Schonfeldt-Lecuona et al., 2005; Sparing
et al., 2008). If the experimenter is more interested in CoG than map contour, the raw
47
spatial data obtained from neuronavigation can be used directly according to the
definition of the CoG.
Because activity at neighboring points provides additional information for each
point, we expect that using the correlation between spatial activities can be used to
generate maps more accurately and more efficiently than traditional mapping methods.
Spatial correlation in TMS mapping can occur for two reasons. First, the coil excites
about four cm
2
of motor cortex (figure-of-eight coil) (Thielscher and Kammer, 2004), so
the excited area by stimulating different scalp sites may overlap. Second, individual
muscles have multiple spatial representations in the motor cortex (Kandel, 2000).
Nonparametric technique Gaussian Process (GP) regression is notably well indicated to
generate map contours from scattered samples, as its geostatistics counterpart, known as
“kriging”, is frequently used in interpolation of map surfaces (Stein, 1999). One
advantage of GP regression is that its performance is one of the best in nonlinear
regression problems (Rasmussen and Williams, 2006). A second advantage of GP
regression is that it estimates hyperparameters of a covariance function, which models the
covariance between data points of different positions. This is suitable for TMS maps
because the muscle maps obtained with traditional techniques are not concentrated to a
single grid point, instead each map contour covers a small area of the grid and often form
relatively smooth oblong shapes, suggesting a spatial correlation between neighboring
points. Current “traditional” mapping techniques, by averaging MEPs at each grid point,
ignore this spatial correlation.
48
To further accelerate TMS mapping, we tested the potential advantage of
incorporating additional amplitude information from the smaller secondary MEP
waveform peaks, which follow the primary larger MEP waveform (see method), to build
the TMS GP maps. MEP’s are characteristically quantified by the peak-to-peak amplitude
or area-under-the curve in the primary MEP waveform. However, MEPs often show
subsequent waveform phases that may also contain relevant information to excitability
measurement. The primary waveform is likely due to the convergence of the fastest fibers
from the cortical stimulation to the muscle, but temporal dispersion and phase
cancellation result in delayed phases for which the first may be quantified by the
amplitude of the second waveform recorded on each MEP. Our MEP analysis showed
that the amplitudes of these two waves were highly correlated, with an average
correlation coefficient of 0.80 (see method), so we hypothesized that the two waves share
the same cortical mechanism and thus the secondary waves can provide information and
reduce noise for the TMS maps of the large waves. The large but non-perfect correlation
for these two waves’ amplitudes is ideal. To use the two types of waves, we propose
using the concept of multitask learning (Caruana, 1997). Multitask learning refers to the
situation that one model learns several related tasks in parallel. Only one of these tasks is
of the primary interests, but learning the other tasks can improve the performance of the
primary task because their domain-specific information is relevant to the primary task
(Caruana, 1997). Multitask learning with GP can be implemented by combing the
marginal likelihood of all the tasks and maximizing it with respect to the shared
covariance function (Rasmussen and Williams, 2006).
49
The goal of this study is to reduce stimuli required by TMS mapping without
losing accuracy in CoG estimation. We propose using GP regression on high-resolution
stereotactic coil position data to leverage the spatial information provided by the neural
navigation system and using multitask GP (mGP) to further incorporate the information
from the secondary MEP wave to reduce stimulus requirement and accelerate TMS
mapping. We use CoG as an evaluation measurement, and compare the performance of (1)
grid based traditional map, (2) bilinear interpolation (BL) map which represents simple
interpolation methods, (3) model free (MF) ‘map’ which is a collection of samples with
stereotactic coordinates and does not have map contour, (4) GP map, and (5) mGP map.
Our hypothesis is that to achieve the same accuracy, mGP maps require the least stimuli,
followed by GP and MF maps, and the traditional and BL maps require the most stimuli.
3.2 Materials and methods
3.2.1 TMS data collection
Nine subjects participated in this study. All subjects fulfilled the inclusion criteria
and had no TMS exclusions. Informed consent was given to the subjects. The
Institutional Review Board at USC approved the experimental protocol.
We determined the left scalp “hot spot” for the first dorsal interosseous (FDI), that
is, the scalp position where the TMS coil can optimally elicit MEPs in the FDI muscle.
Surface EMG electrodes were attached to the skin over the FDI muscle using electrode
gel and tape. Signal was filtered between 1-500Hz. Signal was sampled at 1 kHz with
differential amplifiers (Grass Instruments IP511). Electrophysiological signals from the
50
muscle were amplified and recorded for analysis. Participants, who sat in a chair adjusted
to a comfortable height, put their right hands on a soft pillow, and were instructed to relax
during the stimulation session. The resting motor threshold (MT) was then determined as
the minimum TMS intensity required to elicit MEP’s of at least 50 μV in 50% of test
trials. Each subject wore a swimming cap. After marking the hot spot for the FDI on the
swim cap, a square grid of 5x5 points, each spaced by 1 cm, was drawn on the cap with
the hot spot in the center. The coordinates of these 25 points and important landmarks of
each subject’s head were recorded by the neuronavigation system Brainsight
TM
(Rogue
Research, Montreal, Canada). Focal single pulse TMS was delivered with a figure-of-
eight coil connected to a commercially available magnetic stimulator (Magstim 200)
(Magstim, UK). The coil was placed on the scalp at the desired positions within the 5x5
cm area during stimulation and in 45 degree with respect to the posterior-anterior
direction towards right. TMS intensity was set suprathreshold at 110% of MT. The
equipment was configured such that each TMS pulse triggered both EMG recording by a
PC data acquisition board and the 3D coil position recording by the neuronavigation
system. If a trial contained artifacts that contaminated the MEP, or has background wave
amplitudes larger than 20 μV, it was discarded and re-sampled. The peak-to-peak
amplitudes of MEP primary and secondary waves following the pulses were analyzed
offline.
The experiment was divided in two stimulation blocks. In the first block, 250
pulses were delivered systematically along the grid: one pulse was applied at each of the
25 grid points sequentially. After the 25 grid points were stimulated, the sequence of
stimulation was repeated again until 10 cycles were performed. In the second block, 100
51
stimuli were randomly delivered to the 5x5 cm area. To ensure a non-biased sampling
over the grid, the stimulation coordinates were generated with uniform distribution over
the area and were displayed in a computer screen to the experimenter who then
stimulated at this location. We projected the stereotactic 3D coordinates to the 5x5 cm
area on scalp surface in order to form 2D TMS maps. We refer the transformed surface
2D coordinate as neuronavigation system coordinate or stereotactic coordinate. It is
continuous and has one-millimeter resolution.
3.2.2 TMS map generation and evaluation
To make use of the limited data pool collected from each subject, we repeated the
procedure of map generation from 1 to 10 data cycles 10 times by simulation. When we
evaluated a map generated by n data cycles, where n is an integer from 1 to 10, we
randomly chose n data cycles from the total of 10 data cycles of the first block (a total of
250 data points available), and averaged the performance (CoG to best-effort CoG
distance, see below) of the 10 runs. The performance of CoG estimation was evaluated
for each subject, and the average performance of nine subjects was calculated. The
performance of each of the below TMS mapping techniques was evaluated with 1 to 10
data cycles.
“Traditional” maps were obtained by averaging the MEP responses at each of the
25 grid coordinate. For example, after 10 cycles, the responses of the 10 pulses were
averaged for each grid point.
52
Bilinear interpolation (BL) maps were obtained by first averaging the MEP
responses at each of the 25 grid coordinates, and then use bilinear interpolation for
inference of the map surface.
Model-Free (MF) “maps” do not depend on any model assumptions or parameters.
One “map” is just a collection of all currently available data. No inference on MEP
amplitudes is possible, but CoG can be calculated by using all data points. The MF maps
are used to test the contribution of the stereotactic coordinate to mapping in model-free
condition, so we used stereotactic coordinate in CoG calculation.
Gaussian Process (GP) maps: Gaussian Process models were created to map
neuronavigation system coordinates to the MEP amplitudes. We used the Matlab-based
software gplm, provided by C.E. Rasmussen and C. Williams as a complement of their
book (Rasmussen and Williams, 2006) for GP regression. We used the square error
covariance function. See Gaussian process regression section.
Multitask Gaussian Process (mGP) maps were created to map neuronavigation
system coordinates to the MEP amplitudes. We implemented the algorithm by modifying
the Matlab-based software gplm (Rasmussen and Williams, 2006). We used the square
error covariance function. See Multitask learning with Gaussian process section and
Primary wave and secondary wave analysis section.
To assess the quality of the TMS maps, we calculated the CoG position of each
map. For the traditional maps, BL maps, GP maps and mGP maps, 10x10 MEP
amplitudes uniformly sampled from the map surfaces were used for CoG computing. For
model-free maps, all available data points were used for CoG computing. Given MEP
{MEPi} and their corresponding coordinates {Xi}, where i represent the index of the i
th
data point and X is a 2D vector of coil position, the CoG is calculated as below:
∑
∑
=
i
i
MEPi
Xi MEPi
CoG
*
(3.1)
To evaluate the accuracy of the map CoG’s, for each subject, we used the high-
resolution stereotactic coordinates recorded at all of the 350 data points from both data
blocks. These 350 TMS trials were uniformly sampled across the 5x5 cm area since the
first 250 trials consisted of 10 trials on each grid spot, and the last 100 trials were
sampled at the guidance of a uniform coordinate generator. Chi-square tests on the
hypothesis that each subject’s total 350 data points were uniformly distributed showed
the null hypothesis cannot be rejected (p>0.05) for any subject, and the average p-value
for the nine subjects was 0.746. The CoG computed from the 350 data points represented
our best effort in CoG estimation (best-effort CoG). The distance between the map CoGs
and the best-effort CoGs were used to evaluate the map CoG’s accuracy.
3.2.3 Primary and secondary MEP wave analysis
Quantifying the amplitudes of primary and secondary waves is necessary for
generating the mGP model, which incorporate the information from both waves to speed
up mapping. In figure 3.2 we show two example MEP’s recorded from a subject’s right
first dorsal interosseous (FDI). The primary wave is larger, and its peak-to-peak
53
54
amplitude is generally analyzed as the amplitude of MEP in TMS experiments. The
secondary wave is smaller (see result). Since the same cortical stimulus induces both
primary and secondary components of the MEP, we hypothesize that they will share the
same covariance function. For example, in figure 3.2, assume A1 and A2 are the
amplitudes of the primary and secondary waves induced by stimulating site A, and B1
and B2 are the amplitudes of the primary and secondary waves induced by stimulating
site B, then the covariance of A1 and B1 is the same as that of A2 and B2, provided that
the primary and secondary amplitudes are normalized to have unitary mean. If a
secondary wave does not exist, its amplitude is zero.
For each MEP, all waves that have amplitudes larger than 50 μV are analyzed.
The primary and secondary waves are identified based on their peak latencies. When
there are two waves in MEP, the latency of the second wave is difficult to determine
because it overlaps with the primary wave (figure 3.2). Instead, we analyzed the peak
latencies of all the waves found in each MEP in the first data blocks of all nine subjects.
For each subject, we plotted the number of MEP peaks against peak latencies (figure 3.3).
For the nine subjects, all such figures showed two clusters of peaks, corresponding to the
primary wave and the secondary wave (figure 3.3). For each subject, based the MEP peak
plot, we determined a threshold time which optimally distinguished the primary and the
secondary peaks. For example, in figure 3.2, the threshold is at 22 ms, where the
histogram of peak latencies shows a local minimum. If a wave is missing or its amplitude
is less than 50 uV, its amplitude is treated as 0.
55
For each primary and secondary waveform we analyzed the amplitude between
the peak and the subsequent trough. The primary and secondary are used for multitask
GP (see the section: Multitask learning with Gaussian process) to determine the
covariance function for GP, and the largest MEP amplitude was used for GP map
generation (see the section: Gaussian process for regression). In our dataset, the primary
amplitude is generally equal to the largest amplitude (see results).
3.2.4 Gaussian process for regression
Non-linear regression models based on Gaussian Processes (GP) have recently
been used in a variety of problems, including those requiring spatial statistics, in which,
as in TMS, the responses depends on the spatial location of the inputs (Williams, 1998).
GP models are attractive in nonlinear-regression modeling because of their flexible non-
parametric nature, computational simplicity, fast convergence, and excellent
generalization performance, which outperforms that of neural networks (Rasmussen and
Williams, 2006). Further, GP models require “hand tuning” of few free parameters. The
main drawback of Gaussian Process models is their poor scaling to large data sets
(Rasmussen and Williams, 2006). This is not an issue here, however, because single
pulse TMS studies do not generate data sets with more than a few hundred data points.
In regression problems, a “training” dataset that contains the inputs X and their
associated outcomes y is used to build the model that will then be used for later
predictions of the responses to novel inputs. In TMS experiments, such as MEP mapping,
we consider X to be coil position data, and y the amplitude of the associated MEP
56
2
~(0, ( , ) )
amplitudes. In a Gaussian process, the observations have a joint Gaussian
distribution y NKXX I σ + , where y is the outcome (here the centralized MEP
amplitude so the mean is zero), K(X, X) the covariance matrix of the joint Gaussian
distribution,
2
σ the variance of an additive Gaussian noise associated with y, and I the
identity matrix. To predict the outcome f* for a new input X* in the training set, one can
write the new joint distribution formed by both the known data and the unknown query:
2
*
* **
(, ) ( , )
~(0, )
(, ) ( , )
y KX X I KX X
N
f KX X KX X
σ⎡⎤ + ⎡⎤
⎢ ⎢⎥
⎣⎦⎣⎦*
⎥
(3.2)
where K(X, X
*
) and K(X
*,
X) are the covariance of the queried input and the input values
in the training dataset, and K(X
*
, X
*
) is the variance of the queried input. The prediction
for mean and covariance of f* at X* are derived from the conditional distribution of this
Gaussian process. See (Rasmussen and Williams, 2006) for details. The mean
*
f
and
variance
2
*
σ of the conditional distribution are given by
21
* *
()
T
f kK I y σ
−
=+ (3.3)
2
*** *
()
T
n
kk K I k σ
−
=− +
21
*
σ , (3.4)
where , , (, ) KKXX =
**
(, ) kKXX =
** * *
(, kKXX) = ,
*
f is the expectation of , and f *
2
*
σ the variance of . In TMS mapping, for example, y and X are the (centered) MEP
amplitude and coil positions in the training dataset, and X* are positions at which we
want to estimate the MEP amplitudes.
f *
In our experiments, we use the commonly used 2-dimensional squared exponential
(SE) covariance function:
) ) (
1
) (
1
exp( )) ( ), ( cov(
2 ) 2 ( ) 2 (
2
2
2 ) 1 ( ) 1 (
2
1
, j i j i j i x x
x x
l
x x
l
A x f x f K
j i
− − − − = = (3.5)
where represents the value of the k
th
data point on the d
th
dimension, the hyper-
parameter A controls the scale of the covariance, and l
1
and l
2
control how fast the
covariance decrease with distance in each direction of the 2-D space, respectively. As we
assume a Gaussian noise model (equation 3.1), an additive noise σ
2
is added to the
covariance when x
i
=x
j
.
) (d
k
x
In GP regression, these parameters are optimized by maximizing the marginal
likelihood of the dataset, which is in the form of the Gaussian process model:
)) , ( , 0 | ( ) , , , | (
2 1
X X K y A l l y L Ν = σ (3.6)
We used gradient ascent method to find the hyperparameters corresponding to the
maximum log marginal likelihood. See (Rasmussen and Williams, 2006) for details.
3.2.5 Multitask learning with Gaussian process
Our multi-task TMS map leverages the MEP primary and secondary waves. We
assume that the two types of waves each follows an independent GP model, and that they
share the same covariance function. The summation of the log marginal likelihood of
57
58
both datasets can be maximized with respect to the hyperparameters (Rasmussen and
Williams, 2006).
3.2.6 Data analysis and statistical methods
We used paired t-test to compare the distances from map CoG to best-effort CoG
of two maps. We used α=0.10 for threshold of significance. If two types of maps, for
example, traditional maps built with 250 data points and mGP maps built with 50 data
points, have paired t-test p-value larger than 0.1, we consider them as having equivalent
performance. Specifically, we compared all types of maps to the traditional maps built
with 250 data points and tried to find the smallest number of data points required by each
type of maps to catch up this performance. This comparison was carried out both across
all nine subjects and on individual subject. Compared with commonly used standard
α=0.05, the significance requirement of α=0.10, which makes the null hypothesis easier
to be rejected, sets up a higher criterion for performance equivalence. We provide all p-
values.
3.3 Results
3.3.1 Map generation
We first tested the feasibility of using GP regression on the high-resolution
stereotactic coordinate data to generate TMS maps. An example of the 250 raw data
points, the traditional map, the BL map, and the GP map for one subject is shown in
figure 3.1. In the mapping process, the experimenter moves the coil from one spot to
another. As a result, even with the guidance of the grid drawn over the subject’s scalp,
the sampling positions, as recorded by the neuronavigation system, are scattered (figure
3.1 A). After the regression for the hyperparameters, the mGP map generation procedure
is the same as that of GP (equation 3.3), so the appearance of mGP maps is similar to
their GP counterpart.
Figure 3.1. 250 data points sampled from one subject and the corresponding maps
formed by different methods. The color bars indicate MEP amplitude in µV. (A) the raw
data recorded from EMG and neuronavigation system. (B) Traditional map. (C) BL
map. (D) GP map.
59
60
3.3.2 Primary and secondary wave analysis
Our analysis showed that in all subjects, the primary wave amplitude is
statistically larger than the secondary wave amplitude (paired t-test, p<0.05). In all the
673 MEPs analyzed, 95.0% have larger primary waves, 52.9% have two peaks, and
47.1% have one peak. Among all the MEPs, 43.7% only have primary waves, and 3.4%
have only secondary waves. In the total of 673 MEP’s analyzed, 52.9% have two peaks,
and 47.1% have one peak. The average correlation of the two wave amplitudes across
nine subjects is 0.80±0.21 (mean±std). The mean latency difference between the primary
and secondary waves is 7.5±0.8 ms (mean±std), and the mode time difference is 7±1.0
ms (mean±std), across the nine subjects.
Figure 3.2. Two example MEPs recorded by stimulating two different scalp sites A
and B of one subject. The indices 1 and 2 show the first and second vawe,
respectively. The muscle recorded is right FDI. TMS intensity is at 110% resting
motor threshold. Refer to method section for details.
61
Figure 3.3. Histogram the peak times for the two MEP wave for one subject. The
peak time of the first peak is around 19 msec after the TMS pulse, and the second
around 28 msec for this subject, and 16 msec and 24 msec on average for our
nine subjects.
3.3.3 CoG evaluation
We then evaluated the CoG estimation accuracy of traditional maps, BL maps,
MF maps, GP maps, and mGP maps. The nine subjects’ average result of the distances
between map CoG and best-effort CoG is shown as a dependent variable of the number
of TMS trials, in figure 3.4A. All methods showed improved CoG estimation as the
number of trials increased, and this was indicated by the shortened distances to best-effort
CoG. Using the 250-data-point traditional maps’ CoG estimation as a standard, we used
paired t-tests to examine the trial number required by each method to achieve this
accuracy, and the p-values of the comparisons are shown as a dependent variable of the
number of TMS trials, in figure 3.4B. BL maps required 175 trials (p = 0.217), MF maps
required 50 trials to achieve this accuracy with borderline p-value (p = 0.112) and 75
62
63
trials to achieve this accuracy (p=0.440), GP maps required 50 trials to achieve borderline
p-value (p = 0.107) and 75 trials to achieve this accuracy (p=0.482), and mGP maps
required 50 trials (p = 0.710). Therefore, methods aided by the neuronavigation system,
MF, GP and mGP maps, required 50 to 75 trials to achieve the accuracy of CoG
estimation of the traditional method with 250 trials.
After 50 trials, mGP maps were more accurate than MF maps (paired t-test,
p=0.004) and GP maps (paired t-test, p = 0.009), while GP maps and MF maps were not
significantly different (p = 0.477). After 75 trials, mGP maps were more accurate than
MF maps (paired t-test, p=0.052) and GP maps (paired t-test, p = 0.039), while GP and
MF maps are not significantly different (p = 0.436). Therefore, among the
neuronavigation system aided methods, mGP is the most accurate, while GP and MF
have similar accuracy.
Table 3.1 shows the number of TMS trial for each method and each subject. We
compared the number of trials needed to achieve the accuracy of traditional map with 250
trials. The mGP method required fewer trials than other methods for all subjects to reach.
The GP method required fewer trials trials than the traditional and BL methods. For five
subjects, the MF method required less or equal number of trials compared with the
traditional and BL methods. For two subjects, the MF method failed to achieve the
accuracy of traditional map with 250 trials.
Figure 3.4. A. Distance between CoG for different maps and best-effort CoG as a
dependent variable of TMS trial number. Each point is the average of nine subjects.
Bars represent ±1 standard deviation. Y axis is in centimeter. B. Comparing each data
point in A to the traditional map with 250 trials. The p-values of paired t-tests for the
null hypotheses that the error of CoG estimation of a map is the same as that of
the traditional map with 250 trials are shown. In each curve, the initial increase in p-
values reflects the decreasing estimation error with the increasing trial number for each
mapping method. The peaks of the curves reflect the estimation errors that were closest
to that of the traditional method with 250 trials. The following decrease in curves of
the p-values reflects the decreasing estim
ng lower than that of the
traditional method with 250 trials. The dash horizontal line is the significant criterion
of al
ation errors droppi
pha = 0.1
64
Table 3.1 Number of TMS trails required by each subject’s TMS maps to achieve the
accuracy of the traditional map generated by 250 trials. ‘NA’ indicates the method
failed to achieve this accuracy.
Subject 1 2 3 4 5 6 7 8 9
Traditional 25 50 50 75 125 125 100 125 150
BL 25 50 50 75 125 125 75 125 75
MF 25 75 NA 50 100 75 150 NA 75
GP 25 75 75 25 100 75 50 50 75
mGP 25 50 50 25 100 75 50 25 50
3.4 Discussion
In this study, we aimed at reducing the number of TMS pulses required for
muscle mapping without loss of accuracy compared to the “traditional” mapping methods.
Our results show that, for our subject population (9 healthy subjects), for the muscle
studied (FDI), and for the TMS parameters used (110% of motor threshold), 250 pulses
were required to attain convergence of the GOG with the traditional mapping method. In
contrast, the GP mapping method, by leveraging spatial information, required fewer than
75 pulses on average. Furthermore, the mGP mapping method, by leveraging both spatial
and temporal information, required fewer than 50 pulses on average (figure 3.4). The MF
mapping method, which, unlike GP and mGP methods, has the advantage of not requiring
any computational model but simply averaging of MEPs weighted by spatial coordinates,
showed the same average performance as the GP mapping method on average. The MF
method even achieved lower error than the mGP method, in three subjects, when the trial
number was larger than 175. However, the MF method failed to achieve the accuracy of
CoG estimation of the traditional map generated with 250 trials in two out of nine
subjects (subjects 3 and 8; table 3.1). Therefore, although the MF method achieved
65
66
similar error as the GP method, it does so less reliably. It thus appears that the smoothing
effect of GP regression improves the reliability of the determination of the CoG
compared to the MF approach.
Compared to the traditional mapping method, and the associated bilinear
interpolation method, the MF, GP, and mGP methods require the collection of high-
resolution coil position data with a neuronavigation system. Such systems are now
available in many labs and clinics. Furthermore, the current mGP method only works
when a secondary wave exists and when the correlation between the primary and the
secondary waves is relatively large but less than 1. Although we only examined FDI
MEP at 110% resting MT, MEP’s of other muscles under a different experimental setting
may also show several waves (e.g. figure 1, (Rothwell et al., 1987). Note however that
the physiological origins of the multiple waves of the MEPs are unclear and it is not
known whether the secondary wave will still exist when the intensity is lower than 110%
MT, or in patients with neurological disorders. In any case, the reliability of our methods
should be tested in various conditions. Fortunately, data used to establish GP and mGP
maps could easily be used to construct traditional maps. Therefore, the comparison does
not require extra data collection.
Although we showed that our GP and especially mGP mapping methods
considerable speed up TMS mapping, further improvements are still possible with three
non-mutually exclusive improvements. First, Bayesian techniques can be used to include
prior map information (Bishop, 2006). We previously showed (Qi et al., 2010) that when
prior a MT was available, MT estimation can be speed up by three to six times by a
67
Bayesian version of Parameter Estimation by Sequential Testing (PEST) (Awiszus, 2003).
Similarly, maps obtained previously from the same subject or a group of subjects may be
informative for generating a new map. Second, active sampling technique could be used
to determine “on-line” the optimal site to stimulate. Unlike traditional methods and our
proposed methods, active sampling techniques choose the optimal stimulating site at each
trial based the predicted maximal information gain (MacKay, 1992; Seo et al., 2000).
Finally, other MEP measurements, such as silent period and onset latency, might also be
useful secondary tasks for multitask learning in mGP methods.
68
Chapter 4 Evaluating TMS coil placement effects on motor evoked potential
4.1 Introduction
TMS has a wide range of scientific and clinical applications including non-
invasively evaluating corticomotor excitability (CE) of given target muscles in humans.
Although TMS measurements such as motor evoked potential (MEP) over a single “hot
spot” on the motor cortex are easy to obtain, they are sensitive to TMS coil placement
(Brasil-Neto et al., 1992a; Brasil-Neto et al., 1992b). There are two levels of positioning
errors in TMS-MEP assessment: (1) the error of “hot spot”, or optimal placement,
determination at the very beginning of an experiment, and (2) the experimental error
caused by failing to stick to the determined “hot spot” during the experiment process.
Two factors contribute to the unintended but common failure in positioning the TMS coil
over a given scalp location. First, in many TMS experiments, the experimenter manually
holds the coil on the subject’s head over a predefined marker (“hot spot”) drawn on the
subject’s scalp. Second, subjects will make small unintentional head movements. This
can be a particular issue for some patient populations (such as Parkinson’s disease or
stroke) where holding the head still is even more difficult than for normal control subjects.
Our study focuses on the effects of coil placement, including both center position
and rotation angle, on MEP amplitude. The effects of large-scale (centimeter) coil center
position on MEP has been extensively studied and used in TMS mapping studies
(Classen et al., 1998; Wassermann et al., 1992). However, the effect of small-scale
(millimeter) coil center position on MEP is more relevant to experimental error and has
69
not been quantitatively evaluated. Studies involving neuronavigation systems showed that
such error caused significant MEP induction rate decrease as well as MEP
amplitude/under-curve-area decrease (Gugino et al., 2001; Sparing et al., 2008). However,
these studies did not systematically model the position effect in 3D space. The effects of
coil orientation on TMS are also important: For a specific muscle, the optimal coil
orientation varies from subject to subject (Balslev et al., 2007). Different coil orientation
can preferably induce different MEP component (Sakai et al., 1997). However, to our
knowledge, most studies focus only on the coil rotation with respect to the axis
perpendicular to the coil plane. For analysis of coil placement error, we need to evaluate
the effect of coil rotation with respect to each of the three axes of the coil.
To investigate the effects of coil placement, we propose a mathematical
evaluation on the TMS coil placement and MEP relationship. Previous studies have
showed the effects were highly non-linear. TMS mapping studies generally showed one
optimal stimulating position that elicits the highest MEP amplitude on average, and the
average MEP amplitudes elicited by stimulating surrounding positions decrease as the
coil moved further from the optimal position (Classen et al., 1998; Wassermann et al.,
1992). TMS angle studies also showed the existence of optimal stimulating angle(s)
(Brasil-Neto et al., 1992a; Mills et al., 1992). Non-linear regression models based on
Gaussian Processes (GP) have recently been used in a variety of problems, including
those requiring spatial statistics, in which, as in TMS, the responses depends on the
spatial location of the inputs (Williams, 1998). GP models are attractive in non-linear
regression modeling because of their flexible non-parametric nature, computational
simplicity, fast convergence, and good generalization performance (Rasmussen and
70
Williams, 2006). Further, GP models require “hand tuning” of few free parameters. The
main drawback of Gaussian Process models is their computational complexity, especially
when scaling to large datasets (Rasmussen and Williams, 2006). This is not an issue here,
however, because single pulse TMS studies do not generate data sets with more than a
few hundred data points. We used GP regression models that took 3D position and 3D
angle rotation into consideration and quantitatively analyzed the effects of each
dimension on MEP measurement. With these quantitative models of coil placement
effects, we tested the possibility of correcting the MEP amplitudes measured with coil
placement error with the models.
According to the column-based model for TMS excitation proposed by (Fox et al.,
2004), the cortical column structure in the anterior bank of the central sulcus are excited
during TMS activation of muscle. This region is reported in to be activated by both
voluntary finger movement (Fox et al., 2004) and TMS activation (Classen et al., 1998;
Fox et al., 2004; Wassermann et al., 1992). Fox et al. proposed that because the
alignment of the cortical columns in this region are parallel with the optimal electric field
orientation reported (Brasil-Neto et al., 1992a), the columns should be the site of
activation, and that the activation should followed the cosine rule of electric stimulation
of neuron fiber (Fox et al., 2006; Rushton, 1927). If this column-based TMS model is
correct, we should expect the coil orientation predicted by our model to be perpendicular
to the anterior bank of central sulcus, and the MEP amplitude decrease as the coil yaw
(rotation with respect to the axis perpendicular to the coil plane) away from the optimal
orientation. For coil rotations with respect to the other two degrees of freedom, the
neuron will shift its position in the inhomogeneous electric field generated by the coil
71
(Cohen et al., 1990; Thielscher and Kammer, 2004), so the cosine rule will no longer be
dominant.
4.2 Material and methods
4.2.1 TMS data collection
Six right-handed subjects, four female and two male, participated in this study.
The average age of subjects is 30.8±5.4 (mean ± std). All subjects fulfilled inclusion
criteria and had no TMS exclusions. Informed consent was obtained and the protocol was
approved by the Institutional Review Board at USC. All subjects were right-handed. We
determined the left scalp “hot spot” for the first dorsal interosseous (FDI), which is the
scalp position optimal for placing the TMS coil to elicit MEPs in the FDI muscle. Surface
EMG electrodes were used to record the signal of the FDI muscle. The signal was filtered
between 1-500Hz, sampled at 1 kHz with differential amplifiers (Grass Instruments
IP511) for analysis. Participants sat in a chair adjusted to a comfortable height, put their
right hands on a soft pillow, and were instructed to relax during the stimulation session. If
a trial contained artifacts that contaminated the MEP, or has background wave amplitudes
larger than 20 μV, it was discarded and re-sampled. We used the criterion that an MEP
must have the largest peak-to-peak amplitude larger than 50 μV. If this criterion was not
met, the MEP amplitude is considered zero. The resting motor threshold (MT), defined as
the minimum TMS intensity required to elicit MEP’s of at least 50 μV in 50% of test
trials, was then determined. Single pulse TMS was delivered with a figure-of-eight coil
72
connected to a commercially available magnetic stimulator (Magstim 200) (Magstim,
UK), and stimulating intensity was set at 110% of MT.
4.2.2 Experimental design
Frameless stereotaxic neuronavigation system Brainsight (Rogue Research,
Montreal, Canada) were used to precisely capture coil placement (resolution 1mm). Each
subject experienced 250 trials of single pulse TMS.
Different angles and positions of the coil were sampled. The coil orientation was
systematically varied for each of the three angles, yaw, pitch, and role, within the subject-
specific range in which MEPs can be induced (figure 4.1). In figure 4.1 A, the three axes,
Vx, Vy, and Vz, with respect to which the coil was rotated were defined. Vx points
rightward, and falls in the straight line that overlaps with the radiuses of both circles of
the coil. Vy points forward, and falls in the common tangent line of the two circles. Vz
points upward perpendicular to the coil plane, and pass the center of the coil. Yaw is
defined as the rotation with respect to Vz (figure 4.1B). Pitch is defined as the rotation
with respect to Vx (figure 4.1C). Roll is defined as the rotation with respect to Vy (figure
4.1D). We tried to explore one of the three rotation dimensions at a time, but due to
experimenter’s error varying one angle while keeping the other two completely steady
was not possible. In figure 4.1 B, C, and D, show how the largest variation of the coil
orientation was in one of the three rotation dimensions while small variation exist in the
other two dimensions, for each group of samples.
Figure 4.1. The coil rotation orientations sampled from one subject. A. Defining the
three axes of coil rotation, Vx, Vy, and Vz, on a figure-of-8 coil. Vx points rightward,
and falls in the straight line that overlaps with the radiuses of both circles of the coil.
Vy points forward, and falls in the common tangent line of the two circles. Vz points
upward perpendicular to the coil plane, and pass the center of the coil. B. Yaw is
defined as the rotation with respect to Vz. C. Pitch is defined as the rotation with
respect to Vx. D. Roll is defined as the rotation with respect to Vy. In each of B, C,
and D, we tried to explore one of the three rotation dimensions, but varying one angle
while keeping the other two completely steady was not possible.
V
C
Vx
D
Pitch Raw
Vz
Vy
Vx
Vz
Vy
Yaw
B
Vz
Vy
Vx
A
V
V
Due to the constraint of head surface, the movement of coil center was inevitable
during the process (figure 4.2), and the position was also recorded in x, y, z 3D
coordinates. The equipments were synchronized so that each TMS pulse triggered both
the EMG recording by a data acquisition board connected to a PC and the 6D coil
73
placement recording by the neuronavigation system. The peak-to-peak amplitudes of
MEP and GP regression were analyzed offline (see below).
B A
Figure 4.2. The distribution of coil center position in 3D space, example from one
subject. A. The coil center positions recorded by Brainsight. B. The same date shown in
A, with head landmarks. Vortex represents the top of the head. The dashed rectangle in
A and B represent the same location. In B, nasion is the nose bridge, and inion is the
most prominent projecting point of the occipital bone at the base of the skull.
4.2.3 Gaussian process for regression
We use Gaussian process (GP) (Rasmussen and Williams, 2006) to model the
relationship between MEP amplitude and coil placement. The latter can be decomposed
into six dimensions: coil center position x, y, and z in 3D space and coil angle rotations
yaw, pitch, and roll. We use X to represent this six-dimentional variable.
GP models the MEP amplitudes from N data points as an N-dimensional joint
Gaussian distribution. Each MEP amplitude is thus treated as a sample drawn from one
74
dimension of this Gaussian distribution. The mean of this Gaussian distribution is set to
zero and all the amplitudes of all MEPs are normalized to have zero mean. The
covariance matrix of this Gaussian distribution is controlled by a covariance function
(equation 4.4, see below). Given the coil placement X of two MEPs, the covariance
function can be used to calculate the covariance of the two MEP amplitudes. To estimate
the MEP amplitude at a new coil placement, we first write down the joint distribution of
the new data point and all the observations (equation 4.1), and then take the distribution
conditioned on all the observed dimensions to compute the Gaussian distribution for this
unknown amplitude. This Gaussian distribution has mean and variance in the form of
equation 4.2 and 4.3. A calculation of such conditional Gaussian distribution is shown in
Chapter 2.3.1 of(Bishop, 2006).
2
*
* **
(, ) ( , )
~(0, )
(, ) ( , )
y KX X I KX X
N
f KX X KX X
σ⎡⎤ + ⎡⎤
⎢⎥ ⎢⎥
⎣⎦⎣ *⎦
(4.1)
21
* *
()
T
f kK I y σ
−
=+
(4.2)
22
*** *
()
T
n
kk K I k σ
−
=− +
1
*
σ
(4.3)
) ) (
1
exp( )) ( ), ( cov( ) , (
2 ) ( ) (
2
∑
− − = =
d
d
j
d
i
d
j i j i
x x
l
A x f x f x x K
(4.4)
In the above equations x
i
is the ith data point of the dataset, and x
i
(d)
is the element
on the d
th
dimension. I is an identity matrix, K ) , ( X X K = , ,
,
) , ( X X K k =
) , ( X X K k =
* *
* * * * *
f f is the expectation of , and is the variance of . The
*
2
*
σ
*
f
75
76
covariance function (equation 3.4) shows the most frequently used covariance function.
This function assumes the covariance decreases exponentially as the square distance
between two data points increases. The l
d
in equation 3.4 determines the rate of decrease
for the d
th
dimension. The parameters A and l
d
are called hyperparameters. In GP
regression problems, the hyperparameters are optimized with respect to the likelihood.
See (Seeger, 2004) for a brief introduction of GP, and (MacKay, 1997) and (Rasmussen
and Williams, 2006) for more details.
4.2.4 Quantitative analysis of the effects of coil placement on MEP
amplitude based on GP model
After building a GP model for each subject, we were able to predict the optimal
coil placement for each subject. To evaluate the effect of each dimension of placement on
MEP amplitude, we fix five dimensions at their optimal values and vary the rest one. The
predicted MEP amplitudes were plotted against the varying dimensional variable to
visualize its effect. The hyperparameter l
d
is a measurement of the relevance of a
dimension to MEP amplitude, with larger l
d
indicating lower relevance(Rasmussen and
Williams, 2006). We compared the averaged MEP plot and l
d
across all six subjects.
4.2.5 Projecting predicted optimal coil placement onto MRI
For three subjects, Brainsight were co-registered with their anatomical MRI. We
were able to locate the optimal coil center and orient the optimal coil angle with respect
to their brain anatomical images. For each of the subject, starting from the optimal coil
center, by following the inverse direction of Vz, we could find the model predicted
77
regions of that was perpendicularly beneath the coil center. These regions are the model
predicted activation areas for the subjects. As Vy points to direction of the electric field
immediately beneath the coil, we projected Vy of optimal placement onto the MRI for
each subject, and examined the relationship between the GP predicted direction of
optimal electric field and central sulcus.
4.3 Results
R-square value of regression and visual inspection showed that the GP model
partially explained the variability of MEP amplitude. The mean R-square value of the
GP models for the six subjects is 43±16% (mean±std), which measures the proportion of
MEP variance that can be explained by coil placement information. For each coil
placement dimension, in each subject, we found an optimal positioning value, determined
by the value that corresponds to the largest MEP predicted by GP model. Figure 4.3
shows the regression results of one subject. In each plot in figure 4.3, one dimension of
the coil placement is varied, and the other five dimensions are conditioned and fixed at
their optimal positioning values.
Figure 4.3. Regression result for 1 subject. The continuous line in each subplot
represents the MEP estimation changing with the variable, while other variables are
fixed at the optimal value. Dots represent the real samples in a small tolerance interval,
±2 mm in X, Y, Z and ±3 degrees in each angle, surrounding the optimal values except
for the varying variable indicated by the subplot. Grey area is the estimated ±1 standard
deviation range.
To quantify the variation of MEP amplitude as a variable of coil placement, we
averaged the regression results of all six subjects (figure 4.4). Varying only one coil
placement dimension and keeping other dimensions at optimal values, we obtained below
estimation. For coil pitch or roll deviating from the optimal angle by 5-10 degree, the
MEP measurement can be negatively biased by 20-40% (figure 4.4 A). MEP is less
sensitive to yaw. By 5-10 degree of yaw from optimal angle, the negative error is 10-20%
(figure 4.4 A). For coil center placement deviating from the optimal position by 2-3 mm,
the MEP measurement can be negatively biased by 20-30% (figure 4.4 B).
78
Figure 4.4. The model estimated MEP to maximum MEP ratio as a dependent variable
of the deviation of coil placement from the optimal placement, which elicits the
maximum average MEP amplitude. A. Varying coil orientation by yaw, pitch and roll.
B. Varying coil center position x, y, and z. Each curve uses one of the coil placement
dimensions as variable and set the other five dimensions at their optimal values. All
curves are the average results of six subjects. The bars indicate ±1 standard error across
six subjects.
We analyzed the hyperparameter l
d
that determines the covariance for each
dimension of coil placement. The value of l
d
measures the “relevance” of each dimension
(Rasmussen and Williams, 2006). Small l
d
indicates large covariance dependency on the
d
th
dimension. The mean and standard deviation for these hyperparameters across all
subjects is shown in figure 4.5. Yaw is significantly less relevant than pitch and roll
(paired t-test, p=0.016, 0.018 respectively).
79
Figure 4.5. The mean hyperparameters l
d
of six subjects. A. l
d
for the three angles.
Paired t-tests showed significant different difference between yaw and roll, and between
yaw and pitch. B. l
d
for the three dimensions of the coil center position.
The GP model predicted optimal coil placement indicates the anterior bank of the
central sulcus is activated when the coil is optimally placed. In each of the three subjects
whose MRI were available, the trajectory of the inverse direction of Vz crosses the
anterior bank of the central sulcus located by MRI, and remained in the precentral gyrus
for a distance (figure 4.6). Also in each subject, the Vy axis of the optimal placement
forms an angle with the layer direction of precentral gyrus. Due to irregular shape of
precentral gyrus, the exact angle is difficult to quantify. However, each angle allows the
TMS electric field direction to project effectively to the cortical column direction (figure
4.6).
80
G H I
A
F
B
C
E
D
Figure 4.6. The optimal coil center projected along the optimal orientation vector –Vz,
into the brain. Each row contains three slices of one subject, the projection depth of
which increases from left to right. In each subject, the projected path crossed the
anterior bank of the central sulcus. The crosshair in each figure represents the
projection of the optimal coil center. The arrows point to the direction of the optimal
yaw angle.
81
82
4.4 Discussion
One goal of this study is to quantify the effects of TMS coil placement on MEP
amplitude. This is the first attempt to use nonlinear regression for the relationship
between MEP and the 6D coil placement. We used a commercially available
neuronavigation system Brainsight to record the coil placement data in 6D space, and
synchronized surface EMG to document MEP amplitude. With coil placement as
independent variable and MEP amplitude as dependent variable, GP regression technique
was used to model these non-linear effects. On average of the regressions of six subjects,
the GP models explained 43% of the MEP variance. Visual examination showed GP
models captured the trend of local MEP amplitudes (figure 4.3). Decomposing the 6D
models into each of the dimensions (figure 4.4) and analyzing the hyperparaemeters l
d
(figure 4.5) revealed that moving the coil center towards any direction x, y, or z had
similar effects on MEP amplitude (figure 4.4B, figure 4.5B), while rotating the coil by
yaw had less effect than by pitch or roll (figure 4.4A, figure 4.5A). These comparisons
should be interpreted as effective in the small region sampled near the “hot spot”.
To minimize movements of the coil relative to the head, several methods have
been developed. First, “frameless stereotaxic” techniques (Paus et al., 1997; Comeau et
al., 1999) can record and display the relative position and orientation of the coil vs. the
head on a computer screen in front of the experimenter. While frameless stereotaxy
improves reliability in coil position (Sparing et al., 2007), it has yet to be shown that
frameless stereotaxic techniques improve reliability in coil orientation. Second, coil
holders and devices that constrain the subject’s head (such as a chin rest) can reduce, but
83
not eliminate unintended relative motion of TMS coil vs. head. Literatures showed with
such neuronavigation systems the coil center placement error can be reduced to 2~5mm
(Sparing et al., 2008), and coil angle placement error can be reduced to 2 degree. Current
data shows such small coil placement deviation can still induce large MEP reduction
(figure 3.6) and cause significant measurement error (figure 3.7). Robotized TMS that
automatically place the coil are currently being developed, and the reported error in
placement is 2 mm in coil center position and less than 1.3 degree (Lancaster et al.,
2004). Therefore, our results suggest robotized TMS is very helpful in getting accurate
TMS stimulation results. These robots are expensive, however, and raise potential safety
issues.
Another goal of this study is to test the cosine rule for TMS excitation suggested
by the column-based activation hypothesis (Fox et al., 2004). The GP models suggested
that the electric field generated at optimal coil placement pass through, nearly
perpendicularly, the anterior bank of central sulcus (figure 4.6). Rotating the coil away
from its optimal orientation by yaw caused the MEP amplitude decrease gradually (figure
4.4A). Previous studies have consistently suggested that TMS that tuned to active
muscles excites the anterior bank of the central sulcus, which is the primary motor cortex
(M1) (Classen et al., 1998; Fox et al., 2004; Wassermann et al., 1996). Other studies also
consistently demonstrated that the optimal current orientation for TMS activation is
approximately perpendicular to the central sulcus (Brasil-Neto et al., 1992a). To our
knowledge, the current study is the first to consider all six dimensions of coil movement,
as a continuous variable, and identifying both the position and orientation of the optimal
activation electric current. Our results are consistent with previous findings and in
84
support of the cosine rule proposed by (Fox et al., 2004). Considering the figure-of-8 coil,
which has focal electric field distribution beneath the coil center, the rotation by pit and
roll will shift the motor cortex out off the high strength region of the electric field, which
explains the faster decline of MEP amplitudes caused by these rotations.
One limitation of the current study is the model dimension of six is relatively high
considering the data points used to build each model is 250. Because if for a 1D model
we require ten data points, we will require 10
6
data points for a 6D model. TMS
experiments that deliver a few hundred of pulses to one subject are already intense for
subjects due to ethical concern. We focused on sampling in the three orientation
dimensions and left the center of coil non-evenly sampled, which may miss information
for the model.
To further test the current model, it can be compared with the computational
models which take head geometry and issue property into account, such as (Wagner et al.,
2004). Being two approaches to model the same mechanism, their input-output
relationship should be similar. Parametric regression which include cosine of the rotation
angle can also test the cosine rule hypothesis, but it needs to consider the TMS input-
output curve (Hallett, 2007). To help experimenters to improve MEP measurement
accuracy for individual subject, a model that can be built with data of fewer trials is
necessary, because it is not realistic for the experimenters to sample hundreds of data
points for building a model introduced in this study.
85
Chapter 5 Conclusion and future work
In this chapter, I shall first discuss safety, accuracy, and efficiency advantages of
computational TMS. Then I shall summarize the neurophysiology included in the studies
introduced in previous chapters. Finally, future works inspired by current studies will be
proposed.
5.1 Technical advantages of computational TMS
5.1.1 Safety and computational TMS
As reviewed in the chapter 1.1, safety is of the highest priority for TMS practice.
The method developed in the current proposal follows the safety guidelines
recommended by the TMS consensus conferences, and will contribute to the safety of
TMS.
In Chapter 2, we introduced a Bayesian method for MT estimation. Estimating
MT is crucial for safety practice, because other TMS parameters are tuned by MT. For
example, the maximum safe duration of single trains of rTMS depends on the intensity-
to-MT ratio (Rossi et al., 2009). Several aspects of this study ensured and strengthened
the safety of the MT estimation process. First, the proposed method was compared with
two established methods in both simulation and experiment, and its error was shown to
be comparable to those of established methods. Second, an analysis of the bias magnitude
was provided (figure 2.3), and the suggestion that potential users should tune the stopping
criterion according to their measurement requirement was made. Third, the method
reduced the stimuli requirement by 50% to 78%, reducing subjects’ exposure to magnetic
86
stimulation. Fourth, when the prior is set to favor low or median intensity, it has the
protective effect against sampling by high intensity.
The fast mapping method developed in Chapter 3 and the models for optimal coil
placement developed in Chapter 4 are inline with the safety guidelines proposed by the
TMS consensus conference. Fast mapping by GP reduced the TMS stimuli requirement
from 250 to at most 75, which decreased the subjects’ exposure to magnetic stimulation
dramatically. Optimal coil placement is also important for safety. By definition, the
optimal placement corresponds to the coil placement that requires the lowest current
density to activate cortex, so knowledge about the relationship between cortex activation
and coil placement will help reducing the stimulus intensity and increasing experimental
safety.
To generalize the discussion, all computational TMS methods should follow the
safety guidelines recommended by clinical research authorities such as IFCN and NIH.
One of the purposes of computational TMS should be to reduce experimental risk, for
example, by reducing TMS stimuli, intensity, etc. The potential of computational TMS in
increasing the measurement accuracy (see the following section) can reduce the subject
number required for each study (Sack et al., 2009), which is also in line with
experimental ethics.
5.1.2 Measurement accuracy and computational TMS
The second important issue for TMS is measurement accuracy. Computational
TMS can contribute to the accuracy of TMS experiments in different ways.
87
First, computational models can incorporate data of high resolution and additional
dimensions to increase the accuracy of measurement. The fast mapping method
introduced in Chapter 3 incorporated both Brainsight coordinate data and multi-waves of
MEP data. Although the chapter was organized to show the method was faster than
traditional methods, it is easy to see that given the same amount of TMS stimuli, the
proposed GP and mGP methods achieved higher accuracy than traditional methods
(figure 3.4). Our simulation results suggested that repeatedly sampling on the grids will
become less informative as the TMS trials increased, and active sampling based on
information criteria (Seo et al., 2000) can guide the coil placement to positions off the
grids and help improve TMS map accuracy (Qi, 2007).
Second, computational models can evaluate the accuracy of TMS measurements.
Traditional TMS techniques provide accuracy assessments for their measurements by
computing standard deviation of repeated measures. Direct assessments of certain
techniques are also available, for example, MEP measured with and without
neuronavigation system (Gugino et al., 2001), with different distance from the optimal
stimulation site (Brasil-Neto et al., 1992b), and map CoG measured with different
number of grid spots and stimuli numbers (Classen et al., 1998). The computational
models proposed in this thesis enabled several evaluations that were difficult to do with
traditional methods. In Chapter 2, the stopping criterion of MT was based on the
probability interval of MT estimation. This probability interval reflects the accuracy of
the estimation, and can be monitored by experimenters for quality control purposes.
Although not In Chapter 3, the TMS maps based on GP models can also estimate the
standard deviation for the MEP amplitude at each stimulation position (equation 3.4).
88
Chapter 4 serves as a direct example of accuracy evaluation, as the study quantitatively
measured the error of MEP amplitude induced by coil placement error in each of the six
placement dimensions (figure 4.4).
Third, recent TMS researches point to the ultimate goal (Rossi et al., 2009) of
individualized modeling, current density computation, and TMS parameter setting. TMS
“Hot spot” has long been known to be individual, and optimal coil angle has been shown
to be individual too(Nadeem et al., 2003). Neuronavigation system (Comeau et al., 1999)
and robotized TMS system (Lancaster et al., 2004) have provided possibility of accurate
placement of TMS coil in the 6D space, based on individual anatomical images. Further,
the study introduced in Chapter 4 obtained the optimal coil placement for individual
subject in 6D space. Therefore, so far, we can sample each subject to collect TMS data,
compute his/her optimal coil placement by computational modeling, and then place the
coil optimally for subsequent experiments. However, sampling and building the model
would be very expensive in terms of TMS stimuli delivered. Computational models have
suggested the importance of individual factors such as head size, geometry, (Wagner et
al., 2006), tissue (Nadeem et al., 2003; Wagner et al., 2008) and disease progress
(Wagner et al., 2008) for electric field and current density induction. These factors are the
origin of TMS individuality, therefore we should expect that understanding the
relationship between these factors and TMS measurement will lead to a method of
generating individualized TMS model, which do now require intensive TMS sampling.
89
5.1.2 Experiment efficiency and computational TMS
The studies introduced in Chapter 2 and 3 have demonstrated that modeling can
boost TMS experiment efficiency while maintain safety and accuracy. The framework of
Bayesian framework and multitask learning are particularly suitable of for incorporating
prior knowledge and related measurement, so they have the potential to be applied in
TMS techniques and boost experiment efficiency.
Prior knowledge and correlated measurements are common in TMS studies. Since
this field is relatively young and the availability of human subjects is limited, meta-
analysis is useful for evaluating risk and determining parameters (Janicak et al., 2008;
Machii et al., 2006). The results of such studies can serve as prior knowledge for
computational models. Some times prior knowledge is indispensible, for example,
individual MT may be impossible to determine due to concomitant drugs, underlying
pathology or other anatomo-physiological reason. Current solution to this problem is to
use the lower 95% confidence interval of the average value of the MT in the remaining
subject population as the intensity of stimulation (Rossi et al., 2009). A more
sophisticated method may be developed based on the same prior knowledge. TMS
measurements are sometimes correlated. For example, In Chapter 3, we showed the
correlation between the two waves of MEP. Another example is that the motor and
phosphene (visual cortex) thresholds are correlated, so it is possible to use MT, which is
easier to obtain, to calibrate TMS intensities for other brain regions (Deblieck et al.,
2008).
All of the above prior knowledge and correlations can be leveraged by
computational models for enhancing TMS efficiency.
90
5.2 Neuroscience explored by computational TMS tools
Computational TMS tools not only benefit the safety, accuracy and efficiency of
TMS practice, but also improve our understanding of neurophysiology.
As mentioned in section 1.3 and section 5.1.2, computational modeling on coil,
head tissue, and head geometry has revealed the mechanisms of the generation of local
electric field and current. Without detailed modeling, the study introduced in Chapter 4
provided support to the column-based TMS excitation model proposed by(Fox et al.,
2004), by showing that the MEP amplitude approximately follows the cosine rule of
magnetic stimulation(Rushton, 1927), and that the optimal coil orientation is almost
perpendicular to the anterior bank of the central sulcus. Other model parameters used in
Chapter 3 and Chapter 4 can also used for understanding neurophysiology. For example,
the hyperparameters of the covariance of GP maps determine the spatial correlation.
These hyperparameters should therefore document motor cortex spatial correlation
changes during interventions such as motor practice (Pascual-Leone et al., 1994; Pascual-
Leone et al., 1995) and drug treatment(Ziemann, 2004; Ziemann et al., 1997).
To generalize the discussion of this section, computational models of TMS
mechanisms, theory-driven models, and interpretation of model parameters are all
potential ways of using computational TMS to explore answers to neuroscience questions.
5.3 Future work
The future of computational TMS has two branches. As discussed in section 5.1,
computational tools can be used to improve technical qualities of TMS such as safety,
accuracy, and efficiency. The ultimate goal of this branch will be fast, individualized
91
TMS techniques, which adjust coil placement, stimulus intensity, frequency, etc. based
on individual anatomical and physiological information. Another branch, as discussed in
section 5.2, is using computational tools to understand neuroscience and test hypothesis.
In this section, we propose several extensions and complementary works for the studies
introduced in previous chapters.
5.3.1 Exploring more resources of prior knowledge
In Chapter 2, we leveraged common prior and subject-specific prior to facilitate
MT hunting procedure. Such prior may not be available in some situations. Except for
making the effort to determine the MT using traditional method, we can also look for
other priors. For example, the threshold for motor area and visual area maybe correlated
when determined with the same procedure(Deblieck et al., 2008), we may use one as
prior knowledge for another. We can also expect that anatomical factors such as scalp-to-
brain distance should influence MT and therefore can be used as a prior. These new
priors will either require or lead to new knowledge of TMS physiology.
5.3.2 Understanding the neurophysiologic mechanisms of the multiple
waves in MEP, and identifying other measurements that could be used in
multitask learning
In Chapter 3, the multiple waves in MEP were used to build multitask GP maps.
We hypothesized that different waves shared the same cortical mechanisms, so their
covariance functions should be the same. Our results that multitask learning facilitated
TMS map generation supported this hypothesis, which implies the origin of different
92
MEP waves should be sub-cortical. Magnetic stimulation at the spinal cord level or
peripheral nerve level should able to further test this hypothesis. Other measurements of
MEP, such as silent period or the area under EMG curve are also candidates for multitask
learning.
5.3.3 Fast “hot spot” detection
“Hot spot” for TMS is defined as the scalp site that requires the lowest TMS
intensity to activate. It is similar to MT in several aspects that make optimization of “hot
spot” hunting highly beneficial to the field of TMS: First, most TMS sessions require
locating the “hot spot” at the beginning. Second, “hot spot” hunting usually takes many
(usually more than 80) TMS pulses. Third, as an individual measurement, prior
knowledge of approximate “hot spot” position for a specific muscle of either an
individual or a population can be documented. To locate a “hot spot”, the experimenter
must stimulate each site on the grid covering the scalp for several times to estimate the
average MEP amplitudes. If stimulating several sites all induce large MEP amplitudes,
the experimenter should gradually decrease the output intensity until there is only one
spot responding with clearly larger average MEP amplitude than those of others.
Therefore, experimenters usually mix the procedure of MT estimation and “hot spot”
hunting.
In order to facilitate this procedure, both modeling of the scalp and incorporation
of prior knowledge should be considered. To my knowledge, currently there are no
computational models such as those introduced in Chapter 2 for TMS “hot spot” hunting.
A TMS map such as the GP model introduced in Chapter 3 can be used as the “hot spot”
93
model, and its peak position by definition should be the “hot spot”. Individual prior and
common prior similar to those in Chapter 2 can be documented and incorporated into the
model. The active sampling methods discussed in Chapter 3 can be considered to guide
this procedure. Further, a hybrid method that finds “hot spot” and threshold together can
also be considered.
94
Bibliography
Alcala-Quintana, R., Garcia-Perez, M.A., 2005. Stopping rules in Bayesian adaptive
threshold estimation. Spat Vis 18, 347-374.
Amassian, V.E., Cracco, R.Q., Maccabee, P.J., Cracco, J.B., Rudell, A.P., Eberle, L.,
1998. Transcranial magnetic stimulation in study of the visual pathway. J Clin
Neurophysiol 15, 288-304.
Antal, A., Kincses, T.Z., Nitsche, M.A., Bartfai, O., Demmer, I., Sommer, M., Paulus, W.,
2002. Pulse configuration-dependent effects of repetitive transcranial magnetic
stimulation on visual perception. Neuroreport 13, 2229-2233.
Awiszus, F., 2003. TMS and threshold hunting. Suppl Clin Neurophysiol 56, 13-23.
Balslev, D., Braet, W., McAllister, C., Miall, R.C., 2007. Inter-individual variability in
optimal current direction for transcranial magnetic stimulation of the motor cortex. J
Neurosci Methods 162, 309-313.
Barker, A.T., Jalinous, R., Freeston, I.L., 1985. Non-invasive magnetic stimulation of
human motor cortex. Lancet 1, 1106-1107.
Bishop, C.M., 2006. Pattern recognition and machine learning. Springer, New York.
Borckardt, J.J., Nahas, Z., Koola, J., George, M.S., 2006. Estimating resting motor
thresholds in transcranial magnetic stimulation research and practice: a computer
simulation evaluation of best methods. J ECT 22, 169-175.
Boroojerdi, B., Bushara, K.O., Corwell, B., Immisch, I., Battaglia, F., Muellbacher, W.,
Cohen, L.G., 2000. Enhanced excitability of the human visual cortex induced by short-
term light deprivation. Cereb Cortex 10, 529-534.
Brasil-Neto, J.P., Cohen, L.G., Panizza, M., Nilsson, J., Roth, B.J., Hallett, M., 1992a.
Optimal focal transcranial magnetic activation of the human motor cortex: effects of coil
orientation, shape of the induced current pulse, and stimulus intensity. J Clin
Neurophysiol 9, 132-136.
Brasil-Neto, J.P., McShane, L.M., Fuhr, P., Hallett, M., Cohen, L.G., 1992b. Topographic
mapping of the human motor cortex with magnetic stimulation: factors affecting accuracy
and reproducibility. Electroencephalogr Clin Neurophysiol 85, 9-16.
Caruana, R., 1997. Multitask learning. Machine Learning.
Chan, C.Y., Nicholson, C., 1986. Modulation by applied electric fields of Purkinje and
stellate cell activity in the isolated turtle cerebellum. J Physiol 371, 89-114.
95
Cicinelli, P., Traversa, R., Rossini, P.M., 1997. Post-stroke reorganization of brain motor
output to the hand: a 2-4 month follow-up with focal magnetic transcranial stimulation.
Electroencephalogr Clin Neurophysiol 105, 438-450.
Classen, J., Knorr, U., Werhahn, K.J., Schlaug, G., Kunesch, E., Cohen, L.G., Seitz, R.J.,
Benecke, R., 1998. Multimodal output mapping of human central motor representation on
different spatial scales. J Physiol 512 ( Pt 1), 163-179.
Cohen, L.G., Roth, B.J., Nilsson, J., Dang, N., Panizza, M., Bandinelli, S., Friauf, W.,
Hallett, M., 1990. Effects of coil design on delivery of focal magnetic stimulation.
Technical considerations. Electroencephalogr Clin Neurophysiol 75, 350-357.
Comeau, R.M., Peters, T.M., Paus, T., 1999. Optically Based Frameless Stereotaxy for
Image Guided Transcranial Magnetic Stimulation (TMS) Human Brain Mapping annual
meeting, Duesseldorf.
Day, B.L., Dressler, D., Maertens de Noordhout, A., Marsden, C.D., Nakashima, K.,
Rothwell, J.C., Thompson, P.D., 1989. Electric and magnetic stimulation of human motor
cortex: surface EMG and single motor unit responses. J Physiol 412, 449-473.
Deblieck, C., Thompson, B., Iacoboni, M., Wu, A.D., 2008. Correlation between motor
and phosphene thresholds: a transcranial magnetic stimulation study. Hum Brain Mapp
29, 662-670.
Delvaux, V., Alagona, G., Gerard, P., De Pasqua, V., Pennisi, G., de Noordhout, A.M.,
2003. Post-stroke reorganization of hand motor area: a 1-year prospective follow-up with
focal transcranial magnetic stimulation. Clin Neurophysiol 114, 1217-1225.
Di Lazzaro, V., Oliviero, A., Pilato, F., Saturno, E., Dileone, M., Marra, C., Ghirlanda, S.,
Ranieri, F., Gainotti, G., Tonali, P., 2005. Neurophysiological predictors of long term
response to AChE inhibitors in AD patients. J Neurol Neurosurg Psychiatry 76, 1064-
1069.
Dobson, A.J., 1990. An Introduction to Generalized Linear Models. Chapman & Hall,
New York.
Esser, S.K., Hill, S.L., Tononi, G., 2005. Modeling the effects of transcranial magnetic
stimulation on cortical circuits. J Neurophysiol 94, 622-639.
Ferreri, F., Pauri, F., Pasqualetti, P., Fini, R., Dal Forno, G., Rossini, P.M., 2003. Motor
cortex excitability in Alzheimer's disease: a transcranial magnetic stimulation study. Ann
Neurol 53, 102-108.
Fox, P.T., Narayana, S., Tandon, N., Fox, S.P., Sandoval, H., Kochunov, P., Capaday, C.,
Lancaster, J.L., 2006. Intensity modulation of TMS-induced cortical excitation: primary
motor cortex. Hum Brain Mapp 27, 478-487.
96
Fox, P.T., Narayana, S., Tandon, N., Sandoval, H., Fox, S.P., Kochunov, P., Lancaster,
J.L., 2004. Column-based model of electric field excitation of cerebral cortex. Hum Brain
Mapp 22, 1-14.
Fujiki, M., Hikawa, T., Abe, T., Anan, M., Sugita, K., Kobayashi, H., 2007. Navigated
Brain Stimulation for Preoperative Anatomic and Functional Identification of Impaired
Motor Cortex in a Patient With Meningioma. Neurosurgery Quarterly 17, 33-39.
Gorman, A.L., 1966. Differential patterns of activation of the pyramidal system elicited
by surface anodal and cathodal cortical stimulation. J Neurophysiol 29, 547-564.
Gugino, L.D., Romero, J.R., Aglio, L., Titone, D., Ramirez, M., Pascual-Leone, A.,
Grimson, E., Weisenfeld, N., Kikinis, R., Shenton, M.E., 2001. Transcranial magnetic
stimulation coregistered with MRI: a comparison of a guided versus blind stimulation
technique and its effect on evoked compound muscle action potentials. Clin Neurophysiol
112, 1781-1792.
Hallett, M., 2000. Transcranial magnetic stimulation and the human brain. Nature 406,
147-150.
Hallett, M., 2007. Transcranial magnetic stimulation: a primer. Neuron 55, 187-199.
Hallett, M., Wassermann, E.M., Pascual-Leone, A., Valls-Sole, J., 1999. Repetitive
transcranial magnetic stimulation. The International Federation of Clinical
Neurophysiology. Electroencephalogr Clin Neurophysiol Suppl 52, 105-113.
Huang, Y.Z., Edwards, M.J., Rounis, E., Bhatia, K.P., Rothwell, J.C., 2005. Theta burst
stimulation of the human motor cortex. Neuron 45, 201-206.
Hubel, D.H., Wiesel, T.N., 1979. Brain mechanisms of vision. Sci Am 241, 150-162.
Janicak, P.G., O'Reardon, J.P., Sampson, S.M., Husain, M.M., Lisanby, S.H., Rado, J.T.,
Heart, K.L., Demitrack, M.A., 2008. Transcranial magnetic stimulation in the treatment
of major depressive disorder: a comprehensive summary of safety experience from acute
exposure, extended exposure, and during reintroduction treatment. J Clin Psychiatry 69,
222-232.
Kamitani, Y., Bhalodia, V.M., Kubota, Y., Shimojo, S., 2001. A model of magnetic
stimulation of neocortical neurons. Neurocomputing 38, 697-703.
Kandel, E., 2000. Voluntary Movement. Principles of Neural Science. McGraw-Hill
Medical, p. 759.
Kleim, J.A., Chan, S., Pringle, E., Schallert, K., Procaccio, V., Jimenez, R., Cramer, S.C.,
2006. BDNF val66met polymorphism is associated with modified experience-dependent
plasticity in human motor cortex. Nat Neurosci 9, 735-737.
97
Kleim, J.A., Kleim, E.D., Cramer, S.C., 2007. Systematic assessment of training-induced
changes in corticospinal output to hand using frameless stereotaxic transcranial magnetic
stimulation. Nat Protoc 2, 1675-1684.
Koski, L., Dobkin, B.H., 2005. Standardizing and validating transcranial magnetic
stimulation measures for use in stroke rehabilitation research. Clin Neurophysiol 116,
740-741.
Koski, L., Mernar, T.J., Dobkin, B.H., 2004. Immediate and long-term changes in
corticomotor output in response to rehabilitation: correlation with functional
improvements in chronic stroke. Neurorehabil Neural Repair 18, 230-249.
Krings, T., Buchbinder, B.R., Butler, W.E., Chiappa, K.H., Jiang, H.J., Cosgrove, G.R.,
Rosen, B.R., 1997. Functional magnetic resonance imaging and transcranial magnetic
stimulation: complementary approaches in the evaluation of cortical motor function.
Neurology 48, 1406-1416.
Krings, T., Foltys, H., Reinges, M.H., Kemeny, S., Rohde, V., Spetzger, U., Gilsbach,
J.M., Thron, A., 2001. Navigated transcranial magnetic stimulation for presurgical
planning--correlation with functional MRI. Minim Invasive Neurosurg 44, 234-239.
Labyt, E., Houdayer, E., Cassim, F., Bourriez, J.L., Derambure, P., Devanne, H., 2007.
Motor representation areas in epileptic patients with focal motor seizures: a TMS study.
Epilepsy Res 75, 197-205.
Lancaster, J.L., Narayana, S., Wenzel, D., Luckemeyer, J., Roby, J., Fox, P., 2004.
Evaluation of an image-guided, robotically positioned transcranial magnetic stimulation
system. Hum Brain Mapp 22, 329-340.
Lemon, R., 2002. Basic physiology of transcranial magnetic stimulation. In: Pascual-
Leone, A., Davey, N., Rothwell, J., Wasserman, E., Puri, B.K. (Eds.), Handbook of
Transcranial Magnetic Stimulation. A Hodder Arnold Publication, pp. 61-77.
Liepert, J., Bauder, H., Wolfgang, H.R., Miltner, W.H., Taub, E., Weiller, C., 2000.
Treatment-induced cortical reorganization after stroke in humans. Stroke 31, 1210-1216.
Liepert, J., Haevernick, K., Weiller, C., Barzel, A., 2006. The surround inhibition
determines therapy-induced cortical reorganization. Neuroimage 32, 1216-1220.
Liepert, J., Miltner, W.H., Bauder, H., Sommer, M., Dettmers, C., Taub, E., Weiller, C.,
1998. Motor cortex plasticity during constraint-induced movement therapy in stroke
patients. Neurosci Lett 250, 5-8.
Machii, K., Cohen, D., Ramos-Estebanez, C., Pascual-Leone, A., 2006. Safety of rTMS
to non-motor cortical areas in healthy participants and patients. Clin Neurophysiol 117,
455-471.
98
MacKay, D., J.C., 1992. Information-based objective functions for active data selection.
Neural Computation 4, 590-604.
MacKay, D.J.C., 1997. Gaussian processes - a replacement for supervised neural
networks? , Tutorial lecture notes for NIPS 1997, p. Tutorial lecture notes for NIPS 1997.
Merton, P.A., Morton, H.B., 1980. Stimulation of the cerebral cortex in the intact human
subject. Nature 285, 227.
Mills, K.R., Boniface, S.J., Schubert, M., 1992. Magnetic brain stimulation with a double
coil: the importance of coil orientation. Electroencephalogr Clin Neurophysiol 85, 17-21.
Mills, K.R., Nithi, K.A., 1997. Corticomotor threshold to magnetic stimulation: normal
values and repeatability. Muscle Nerve 20, 570-576.
Mishory, A., Molnar, C., Koola, J., Li, X., Kozel, F.A., Myrick, H., Stroud, Z., Nahas, Z.,
George, M.S., 2004. The maximum-likelihood strategy for determining transcranial
magnetic stimulation motor threshold, using parameter estimation by sequential testing is
faster than conventional methods with similar precision. J ECT 20, 160-165.
Nadeem, M., Thorlin, T., Gandhi, O.P., Persson, M., 2003. Computation of electric and
magnetic stimulation in human head using the 3-D impedance method. IEEE Trans
Biomed Eng 50, 900-907.
Nudo, R.J., Wise, B.M., SiFuentes, F., Milliken, G.W., 1996. Neural substrates for the
effects of rehabilitative training on motor recovery after ischemic infarct. Science 272,
1791-1794.
Pascual-Leone, A., Grafman, J., Hallett, M., 1994. Modulation of cortical motor output
maps during development of implicit and explicit knowledge. Science 263, 1287-1289.
Pascual-Leone, A., Nguyet, D., Cohen, L.G., Brasil-Neto, J.P., Cammarota, A., Hallett,
M., 1995. Modulation of muscle responses evoked by transcranial magnetic stimulation
during the acquisition of new fine motor skills. J Neurophysiol 74, 1037-1045.
Pentland, A., 1980. Maximum likelihood estimation: the best PEST. Percept Psychophys
28, 377-379.
Pichta, T., Kombosa, T., Vajkoczya, P., Süssa, O., 2009. TMS in Neurosurgery: One year
experience with navigated TMS for preoperative analysis. Clinical Neurophysiology 120,
18.
Platz, T., van Kaick, S., Moller, L., Freund, S., Winter, T., Kim, I.H., 2005. Impairment-
oriented training and adaptive motor cortex reorganisation after stroke: a fTMS study. J
Neurol 252, 1363-1371.
99
Qi, F., Wu, A., Schweighofer, N.,, 2007. Fast TMS mapping. Annual Society For
Neuroscience Conference, San Diego.
Rasmussen, C.E., Williams, C.K.I., 2006. Gaussian processes for machine learning. MIT
Press, Cambridge, Mass.
Rossi, S., Hallett, M., Rossini, P.M., Pascual-Leone, A., 2009. Safety, ethical
considerations, and application guidelines for the use of transcranial magnetic stimulation
in clinical practice and research. Clin Neurophysiol 120, 2008-2039.
Rossini, P.M., Barker, A.T., Berardelli, A., Caramia, M.D., Caruso, G., Cracco, R.Q.,
Dimitrijevic, M.R., Hallett, M., Katayama, Y., Lucking, C.H., et al., 1994. Non-invasive
electrical and magnetic stimulation of the brain, spinal cord and roots: basic principles
and procedures for routine clinical application. Report of an IFCN committee.
Electroencephalogr Clin Neurophysiol 91, 79-92.
Rossini, P.M., Rossi, S., 2007. Transcranial magnetic stimulation: diagnostic, therapeutic,
and research potential. Neurology 68, 484-488.
Rothwell, J.C., Hallett, M., Berardelli, A., Eisen, A., Rossini, P., Paulus, W., 1999.
Magnetic stimulation: motor evoked potentials. The International Federation of Clinical
Neurophysiology. Electroencephalogr Clin Neurophysiol Suppl 52, 97-103.
Rothwell, J.C., Thompson, P.D., Day, B.L., Dick, J.P., Kachi, T., Cowan, J.M., Marsden,
C.D., 1987. Motor cortex stimulation in intact man. 1. General characteristics of EMG
responses in different muscles. Brain 110 ( Pt 5), 1173-1190.
Rudin, D.O., Eisenman, G., 1954. The action potential of spinal axons in vitro. J Gen
Physiol 37, 505-538.
Rushton, W.A., 1927. The effect upon the threshold for nervous excitation of the length
of nerve exposed, and the angle between current and nerve. J Physiol 63, 357-377.
Sack, A.T., Cohen Kadosh, R., Schuhmann, T., Moerel, M., Walsh, V., Goebel, R., 2009.
Optimizing functional accuracy of TMS in cognitive studies: a comparison of methods. J
Cogn Neurosci 21, 207-221.
Sakai, K., Ugawa, Y., Terao, Y., Hanajima, R., Furubayashi, T., Kanazawa, I., 1997.
Preferential activation of different I waves by transcranial magnetic stimulation with a
figure-of-eight-shaped coil. Exp Brain Res 113, 24-32.
Salinas, F.S., Lancaster, J.L., Fox, P.T., 2007. Detailed 3D models of the induced electric
field of transcranial magnetic stimulation coils. Phys Med Biol 52, 2879-2892.
Sanger, T.D., Garg, R.R., Chen, R., 2001. Interactions between two different inhibitory
systems in the human motor cortex. J Physiol 530, 307-317.
100
Sawaki, L., Butler, A.J., Xiaoyan, L., Wassenaar, P.A., Mohammad, Y.M., Blanton, S.,
Sathian, K., Nichols-Larsen, D.S., Wolf, S.L., Good, D.C., Wittenberg, G.F., 2008.
Constraint-induced movement therapy results in increased motor map area in subjects 3
to 9 months after stroke. Neurorehabil Neural Repair 22, 505-513.
Schabrun, S.M., Stinear, C.M., Byblow, W.D., Ridding, M.C., 2008. Normalizing Motor
Cortex Representations in Focal Hand Dystonia. Cereb Cortex.
Schluter, N.D., Rushworth, M.F., Passingham, R.E., Mills, K.R., 1998. Temporary
interference in human lateral premotor cortex suggests dominance for the selection of
movements. A study using transcranial magnetic stimulation. Brain 121 ( Pt 5), 785-799.
Schonfeldt-Lecuona, C., Thielscher, A., Freudenmann, R.W., Kron, M., Spitzer, M.,
Herwig, U., 2005. Accuracy of stereotaxic positioning of transcranial magnetic
stimulation. Brain Topogr 17, 253-259.
Seeger, M., 2004. Gaussian processes for machine learning. International Journal of
Neural Systems 14, 69-106.
Seo, S., Wallat, M., Graepel, T., Obermayer, K., 2000. Gaussian Process Regression:
Active Data Selection and Test Point Rejection. International Joint Conference on Neural
Networks pp. 241-246.
Simpson, K.N., Welch, M.J., Kozel, F.A., Demitrack, M.A., Nahas, Z., 2009. Cost-
effectiveness of transcranial magnetic stimulation in the treatment of major depression: a
health economics analysis. Adv Ther 26, 346-368.
Sparing, R., Buelte, D., Meister, I.G., Paus, T., Fink, G.R., 2007. Transcranial magnetic
stimulation and the challenge of coil placement: A comparison of conventional and
stereotaxic neuronavigational strategies. Hum Brain Mapp.
Sparing, R., Buelte, D., Meister, I.G., Paus, T., Fink, G.R., 2008. Transcranial magnetic
stimulation and the challenge of coil placement: A comparison of conventional and
stereotaxic neuronavigational strategies. Hum Brain Mapp 29, 82-96.
Stefan, K., Kunesch, E., Benecke, R., Cohen, L.G., Classen, J., 2002. Mechanisms of
enhancement of human motor cortex excitability induced by interventional paired
associative stimulation. J Physiol 543, 699-708.
Stefan, K., Kunesch, E., Cohen, L.G., Benecke, R., Classen, J., 2000. Induction of
plasticity in the human motor cortex by paired associative stimulation. Brain 123 Pt 3,
572-584.
Stein, M.L., 1999. Statistical Interpolation of Spatial Data: Some Theory for Kriging.
Springer, New York.
101
Stewart, L.M., Walsh, V., Rothwell, J.C., 2001. Motor and phosphene thresholds: a
transcranial magnetic stimulation correlation study. Neuropsychologia 39, 415-419.
Tharin, S., Golby, A., 2007. Functional brain mapping and its applications to
neurosurgery. Neurosurgery 60, 185-201; discussion 201-182.
Thickbroom, G.M., Mastaglia, F.L., 2002. Mapping studies. In: A., P.-L., Davey, N.J.,
Rothwell, J., Wassermann, E.M., Puri, B.K. (Eds.), Handbook of transcranial magnetic
stimulation. Arnold, a member of the Hodder Headline Group, pp. 127-140.
Thickbroom, G.W., Byrnes, M.L., Mastaglia, F.L., 1999. A model of the effect of MEP
amplitude variation on the accuracy of TMS mapping. Clin Neurophysiol 110, 941-943.
Thielscher, A., Kammer, T., 2004. Electric field properties of two commercial figure-8
coils in TMS: calculation of focality and efficiency. Clin Neurophysiol 115, 1697-1708.
Tranchina, D., Nicholson, C., 1986. A model for the polarization of neurons by
extrinsically applied electric fields. Biophys J 50, 1139-1156.
Treutwein, B., 1995. Adaptive psychophysical procedures. Vision Res 35, 2503-2522.
Treutwein, B., 1997. YAAP: yet another adaptive procedure. Spat Vis 11, 129-134.
Vandermeeren, Y., Davare, M., Duque, J., Olivier, E., 2009. Reorganization of cortical
hand representation in congenital hemiplegia. Eur J Neurosci 29, 845-854.
Vitikainen, A.M., Lioumis, P., Paetau, R., Salli, E., Komssi, S., Metsahonkala, L., Paetau,
A., Kicic, D., Blomstedt, G., Valanne, L., Makela, J.P., Gaily, E., 2009. Combined use of
non-invasive techniques for improved functional localization for a selected group of
epilepsy surgery candidates. Neuroimage 45, 342-348.
Wagner, T., Eden, U., Fregni, F., Valero-Cabre, A., Ramos-Estebanez, C., Pronio-
Stelluto, V., Grodzinsky, A., Zahn, M., Pascual-Leone, A., 2008. Transcranial magnetic
stimulation and brain atrophy: a computer-based human brain model study. Exp Brain
Res 186, 539-550.
Wagner, T., Fregni, F., Eden, U., Ramos-Estebanez, C., Grodzinsky, A., Zahn, M.,
Pascual-Leone, A., 2006. Transcranial magnetic stimulation and stroke: a computer-
based human model study. Neuroimage 30, 857-870.
Wagner, T., Gangitano, M., Romero, R., Theoret, H., Kobayashi, M., Anschel, D., Ives,
J., Cuffin, N., Schomer, D., Pascual-Leone, A., 2004. Intracranial measurement of current
densities induced by transcranial magnetic stimulation in the human brain. Neurosci Lett
354, 91-94.
Walsh, V., Pascual-Leone, A., 2005. Transcranial Magnetic Stimulation: A
Neurochronometrics of Mind. The MIT Press.
102
Wassermann, E.M., 1998. Risk and safety of repetitive transcranial magnetic stimulation:
report and suggested guidelines from the International Workshop on the Safety of
Repetitive Transcranial Magnetic Stimulation, June 5-7, 1996. Electroencephalogr Clin
Neurophysiol 108, 1-16.
Wassermann, E.M., McShane, L.M., Hallett, M., Cohen, L.G., 1992. Noninvasive
mapping of muscle representations in human motor cortex. Electroencephalogr Clin
Neurophysiol 85, 1-8.
Wassermann, E.M., Wang, B., Zeffiro, T.A., Sadato, N., Pascual-Leone, A., Toro, C.,
Hallett, M., 1996. Locating the motor cortex on the MRI with transcranial magnetic
stimulation and PET. Neuroimage 3, 1-9.
Watson, A.B., Pelli, D.G., 1983. QUEST: a Bayesian adaptive psychometric method.
Percept Psychophys 33, 113-120.
Williams, C.K.I., 1998. Prediction with Gaussian processes: From linear regression to
linear prediction and beyond". In: Jordan, M.I. (Ed.), Learning in graphical models. MIT
Press, pp. 599-612.
Wolters, A., Schmidt, A., Schramm, A., Zeller, D., Naumann, M., Kunesch, E., Benecke,
R., Reiners, K., Classen, J., 2005. Timing-dependent plasticity in human primary
somatosensory cortex. J Physiol 565, 1039-1052.
Ziemann, U., 2004. TMS and drugs. Clin Neurophysiol 115, 1717-1729.
Ziemann, U., Rothwell, J.C., Ridding, M.C., 1996. Interaction between intracortical
inhibition and facilitation in human motor cortex. J Physiol 496 ( Pt 3), 873-881.
Ziemann, U., Tergau, F., Bruns, D., Baudewig, J., Paulus, W., 1997. Changes in human
motor cortex excitability induced by dopaminergic and anti-dopaminergic drugs.
Electroencephalogr Clin Neurophysiol 105, 430-437.
Abstract (if available)
Abstract
Transcranial Magnetic Stimulation (TMS) is a noninvasive brain stimulation technique that is increasingly used in clinical neuroscience research. Since the invention of TMS in 1985, new applications and stimulation patterns for this technique have been developed and advanced very fast. However, compared with other research techniques used in neuroscience, the use of computational tools for TMS is limited. The studies introduced in this thesis applied computational methods adapted from the field of machine learning to TMS experimental procedures and data analysis, and inspired the idea of computational TMS. These studies showed that computational TMS improved the accuracy and efficiency of TMS, and could be used to investigate neuroscience problems. In Chapter 1, the background, basic principles, and variations of TMS techniques are introduced, and the idea of computational TMS is motivated. Then three example computational TMS studies are demonstrated: Chapter 2 introduces a new protocol facilitating the TMS motor threshold (MT) estimation. This protocol uses Bayesian framework to incorporate prior knowledge of MT and is two to five times faster than the fastest existing method. Chapter 3 introduces a fast protocol for TMS mapping. This protocol uses high-resolution coordinate data obtained from a neuronavigation system and non-parametric regression techniques to generate TMS maps. Chapter 4 is a quantitative analysis of the relationship between Motor Evoked Potential (MEP) and TMS coil placement, which highlights the importance of TMS spatial information. This analysis also supports the neurophysiology hypothesis that TMS excites the column structures on the anterior bank of central sulcus. Chapter 5 includes conclusion and future work of computational TMS.
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Asset Metadata
Creator
Qi, Feng
(author)
Core Title
Computational transcranial magnetic stimulation (TMS)
School
College of Letters, Arts and Sciences
Degree
Doctor of Philosophy
Degree Program
Neuroscience
Publication Date
05/05/2010
Defense Date
03/30/2010
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brain stimulation,computation,machine learning,motor cortex,Neuroscience,OAI-PMH Harvest,TMS,transcranial magnetic stimulation
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English
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Schweighofer, Nicolas (
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), Lu, Zhong-Lin (
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), Schaal, Stefan (
committee member
), Sha, Fei (
committee member
)
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fengqi0423@hotmail.com,fqi@usc.edu
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Tags
brain stimulation
computation
machine learning
motor cortex
TMS
transcranial magnetic stimulation