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Spectral analysis of linear head motion during walking and jogging
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Spectral analysis of linear head motion during walking and jogging
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INFORMATION TO USERS This manuscript has been reproduced from the microfilm master. UMI films the text directly from the original or copy submitted. Thus, some thesis and dissertation copies are in typewriter face, while others may be from any type of computer printer. The quality of this reproduction is dependent upon the quality of the copy submitted. Broken or indistinct print, colored or poor quality illustrations and photographs, print bleedthrough, substandard margins, and improper alignment can adversely affect reproduction. In the unlikely event that the author did not send UMI a complete manuscript and there are missing pages, these will be noted. Also, if unauthorized copyright material had to be removed, a note will indicate the deletion. Oversize materials (e.g., maps, drawings, charts) are reproduced by sectioning the original, beginning at the upper left-hand comer and continuing from left to right in equal sections with small overlaps. Each original is also photographed in one exposure and is included in reduced form at the back of the book. Photographs included in the original manuscript have been reproduced xerographically in this copy. Higher quality 6” x 9” black and white photographic prints are available for any photographs or illustrations appearing in this copy for an additional charge. Contact UMI directly to order. UMI A Bell & Howell Information Company 300 North Zed) Road, Ann Arbor MI 48106-1346 USA 313/761-4700 800/521-0600 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. SPECTRAL ANALYSIS OF LINEAR HEAD MOTION DURING WALKING AND JOGGING by Jody Patrice Ambalong A Thesis Presented to the FACULTY OF THE GRADUATE SCHOOL UNIVERSITY OF SO UTHERN CALIFORNIA In Partial Fulfillment o f the Requirements for the Degree M ASTER OF SCIENCE (Biomedical Engineering) M ay 1997 © 1997 Jody Patrice Ambalong Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. UMI Number: 1384882 UMI Microform 1384882 Copyright 1997, by UMI Company. All rights reserved. This microform edition is protected against unauthorized copying under Title 17, United States Code. UMI 300 North Zeeb Road Ann Arbor, MI 48103 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. This thesis, written by Jody P atrice Ambalong under the guidance o f his/her Faculty Committee and approved by all its members, has been presented to and accepted by the School of Engineering in partial fulfillm ent o f the re quirements for the degree o f Master of Science Biomedical Engineering May, 1997 Date Faculty Committee Chai rman ylM /T c'k.-A -fiX C JC jfC Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Table o f Contents Introduction.................................................................................................................. 1 Coordinates and Notation .......................................................................................... 4 Subjects ........................................................................................................................4 Apparatus......................................................................................................................6 Research Protocol ....................................................................................................... 6 R esults.......................................................................................................................... 8 Equation of Linear Acceleration Along the X, Y, and Z A x e s ..............................13 Analysis of D ata..........................................................................................................14 Conclusion.................................................................................................................. 16 Works C ited ................................................................................................................33 A ppendix....................................................................................................................35 Table Spectral analysis of linear acceleration of head m otion........................................29 ii Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. List o f Figures Axes Coordinate System ............................................................................................ 5 Segment of Raw Data, Experiment 1 .......................................................................9 Segment of Raw Data, Experiment 2 ..................................................................... 10 Segment of Raw Data, Experiment 3 ..................................................................... 12 Example of Head Position.........................................................................................15 Power Spectrum of Linear Acceleration from X-Head Motion, Experiment 1 .. 18 Power Spectrum of Linear Acceleration from Y-Head Motion, Experiment 1 .. 19 Power Spectrum of Linear Acceleration from Z-Head Motion, Experiment I .. 20 Power Spectrum of Linear Acceleration from X-Head Motion, Experiment 2 .. 21 Power Spectrum of Linear Acceleration from Y-Head Motion, Experiment 2 . .22 Power Spectrum of Linear Acceleration from Z-Head Motion, Experiment 2 .. 23 Power Spectrum of Linear Acceleration from X-Head Motion, Experiment 3 .. 24 Power Spectrum of Linear Acceleration from Y-Head Motion, Experiment 3 .. 25 Power Spectrum of Linear Acceleration from Z-Head Motion, Experiment 3 .. 26 Power Spectrum of Angular Velocity, Experiment 1 ............................................30 Power Spectrum of Angular Velocity, Experiment 2 ............................................31 Power Spectrum of Angular Velocity, Experiment 3 ............................................32 iii Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Introduction The vestibulo-ocular reflex (VOR) is a physiological reflex that enables a person to maintain clear vision during voluntary and involuntary head movements(Grossman, Performance 264). Daily life requires people to be constantly moving. One of the most common actions performed by human beings is locomotion. Head movements during walking and running are subject to many influences. Not only is head motion under voluntary control by the moving person, but it is also subject to high frequency vibrations caused by the impact of the foot hitting the ground and the stepping frequency o f the walker or runner (Grossman, Frequency 474-75). During the higher frequencies of head movement, the VOR is the predominant system responsible for making the environment appear stable (O’Leary, Vestibular Autorotation 229). The frequency that marks the division between high and low frequencies for the VOR is 2 Hz. It has been found experimentally that below 2 Hz other ocular motor systems are responsible for stable vision. These motor systems are capable of altering or overpowering the effect of the VOR. For frequencies of rotational head movement above 2 Hz, the VOR becomes functional as the system controlling stable vision(0’Leary, Vestibular Autorotation 230). Since the VOR is defined as a reflex that produces eye movements that are ideally equal in magnitude and 180° out of phase with angular head movements, eye movements related to the VOR will have a frequency of 2Hz or more. 1 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The VOR is a title applied to the neural pathways in the brain that connect the semicircular canals to the extraocular muscles. The canals detect angular acceleration and the vestibulo-ocular connections relay a stimulus to specific extraocular muscles so that the eyes will move in a compensatory manner to that of the head movements(Fuchs 582-595). However, VOR gain, defined as the eye movement magnitude divided by the head movement magnitude (O’Leary, Vestibular Autorotation 230), is essentially never equal to the ideal value of 1.0 which would permit perfect stabilization of distance images on the retina(Demer, Visual 296). VOR gain is dependent on the frequency of head motion (O’Leary, Physiology 224) and limited by the ability of the eye to react. During locomotion and running, the major frequencies of horizontal and vertical head rotations can range from 0.6Hz up to 8.2Hz (Grossman, Frequency 471). This frequency range is within acceptable limits for the VOR to function (Leigh 1289). Head rotational frequencies beyond 10Hz are considered unimportant for VOR operation since the upper limit of VOR effectiveness is bounded by the mechanical resonance of the ocular globe (O’Leary, Vestibular Autorotation 231). The VOR gain is subject to restrictions imposed by the physical abilities of the ocular anatomy to respond to various head motions. VOR gain can approach unity only until approximately 5Hz, above this frequency gain begins to fall (O’Leary, Vestibular Autorotation 230). Consequently, it is the frequency of the head rotations that threaten clear vision (Leigh 1289). 2 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Much of the VOR research has focused on the angular components of head movement since it is rotational perturbations of the head that stimulate the reflex(Grossman, Frequency 470). During walking and running, the center of gravity of the human body moves up and down in time with each step. Translation of the center of gravity along the z-axis in turn causes the head to undergo a complete vertical (pitch) rotation with each step, and for every two vertical rotations, one horizontal (yaw) rotation occurs. In addition to the pitch movement having frequencies almost twice as large as the yaw movement, pitch also has more harmonics of the primary frequencies than yaw(Grossman, Frequency 474). These rotational head movements have been measured to be as high as 170 degrees per second. The mean values of the frequency and velocity of angular head movement are dependent on the axis o f rotation and the type of movement being performed by the subject(Demer, Visual 302). While it is apparent from the amount of information available on the angular motions of the head that the angular component of the VOR has been thoroughly researched, the linear component of the angular rotational motion has not been explored in depth. A major difficulty in calculating the linear component of head motion is presented in Einstein’s general theory of relativity. This theory states that if it is impossible to experimentally differentiate between a uniform gravitational field at a given position and a reference frame undergoing uniform acceleration, then there is no difference between the two situations (Young 1219). Therefore, the major task of the research was to extract the component of acceleration due solely 3 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. to head movement from the acceleration data measured by the linear accelerometers. The acceleration that these accelerometers measured is a combination of both head movement and a component due to the force of gravity. Coordinates and Notation Linear axes are defined as follows. The x-y-z axes are defined as having the origin in the center of the head with the positive x-direction being directly in front of the subject, the positive y-direction pointing to the subject’s right, out of the ear canal, and the positive z-direction pointing up out of the top of the subject’s head. Angular rotational axes are defined as follows. Pitch, rotation of the head forward and back, is executed about an axis approximately 2cm below and 1cm in front of the bony and membranous labyrinths in the inner ear and is parallel with the y-axis. Yaw, rotation of the head from side to side, is executed about the z-axis (Vesterhauge 8). Roll, rotation of the head left and right, is executed about an axis parallel with the x-axis and perpendicular to the z-axis. However, this axis does not pass through the origin of the linear axes since the intersection of the roll axis with the z-axis varies along the z-axis according to the individual walking motions of different people. Subjects Two female adult subjects aged 23-24 with no known vestibular disorders were used in the experiments. 4 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Axes Coordinate Systems Linear axes: + + z side + z front Axes o f angular rotation: s=sensor location, paFpitch axis, ya=yaw axis, ra=roll axis. S S ra ♦ pa ya ♦ ra The top graph shows the linear axes in relationship to the human head. The bottom graph shows the axes about which rotational movements take place. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Apparatus Three linear accelerometers and one angular accelerometer were affixed to a bite block which the subject held between the teeth while performing the experiments. The distance from the individual accelerometers to the axes of the head were measured to be 19.05cm for roll, 20.955cm for pitch and 15cm for yaw. An IBM-compatible portable computer was connected to the accelerometers to collect data at a sampling rate of 100 samples per second. For the experiments requiring the subject to walk freely, the computer was mounted to a cart so that the subject could be followed. Strips of Velcro were used to attach the accelerometer cables at the waist of the subject and to the cart to prevent the cables from dragging on the ground. Research Protocol Calibration of equipment occurred during the first 7 seconds after the data collection computer program was started. For the 1 st second of the test the subject was instructed to fixate her gaze on a point in the distance while standing motionless. Then, while still fixating her gaze, the subject is instructed to first turn her head from left to right at a frequency of 1 Hz for 3 seconds and then to nod her head up and down at the same frequency for another 3 seconds. All relevant data collection occurred during the last 29 seconds of the test. The total duration of each test was 36 seconds. Experiment 1: The subject is instructed to walk in place with as normal a 6 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. a stride as possible while staring at a target. Experiment 2: The subject is instructed to jog in place while staring at the same target as in the first experiment. Experiment 3: This experiment was performed outdoors on a wide sidewalk. The subject is instructed to walk freely while another person followed the subject while pushing the data collection computer on a cart. Several trials were made of each type of movement to ensure that a data set could be gathered that was not unduly influenced by a sudden unusual stimuli such as uneven pavement or an unexpected tree branch. The exact distance from the subject to the point on which the gaze was fixated was arbitrary so long as it simulated a point at infinity. Focusing the eyes at a near point could have caused the gain and phase of the VOR to be artificially influenced(0’Leary, Vestibular Physiology 404) with gains increasing as target distance decreased(0’Leary, Vestibular Autorotation 233). Also, fixating the eyes was necessary so as to not activate the pursuit system of the visual system which would cause not only the eyes to drift in the direction of a moving target, but also the head as wel 1(0’Leary, Physiology 240). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Results Linear accelerometer data was presented so that the positive half of the base line corresponded to the positive direction of the linear axes as defined earlier. The angular accelerometers followed this convention so that rotation towards the positive direction of the linear axes was considered positive. Experiment 1 : The first graph of raw data shows a segment of the stationary walking data obtained from both the angular and linear accelerometers. The angular velocity had a range of +35 to -35 degrees per second in roll, +170 to - 170 degrees per second in pitch, and +35 to -35 degrees in yaw. The linear accelerometers had a range of +0.25 to -0.25 cm/sec2 along the x-axis, +0.416 to - 0.416 cm/sec2 along the y-axis, and +0.6 to -0.4 cm/sec2 along the z-axis. Experiment 2: The second graph of raw data shows a segment of the stationary jogging data for all accelerometers. The angular velocity had a range of +25 to - 25 degrees/sec in roll, +166 to -166 degrees/sec in pitch, and +50 to -25 degrees/sec in yaw. Linear acceleration had a range of +0.33 to -0.33cm/sec2 along the x-axis, +0.33 to -0.25 cm/sec2 along the y-axis, and +1.33 to -1.33 cm/sec2 along the z-axis. Measurement of stationary jogging was saturated in the z direction where the magnitude of movement was beyond than the detection abilities of the sensor. 8 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Segment o f Raw Data, Experiment 1 Angular Velocity Linear Acceleration - 0.5 50 0 50 0 100 200 0 100 200 200 - 0.5 100 200 pitch 0 -50 0 100 200 0 100 200 yaw z The above graphs show a segment of the raw head data from the stationary walking experiment. The x-axis is time in units of tens of msec. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Segment o f Raw Data, Experiment 2 Angular Velocity Linear Acceleration -50 0 0 100 yaw 100 200 - 0.5 pitch 50 0 50 200 100 200 0 200 0 0) (/) 0 •w ' ■ ' s (A 0) < to u 200 200 100 100 2 0 2 100 z 200 The above graphs show a segment of the raw head data from the stationary jogging experiment. The x-axis is time in units of tens of msec. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Experiment 3: The third graph of raw data shows a segment of the outdoor walking data. The angular velocity had a range o f +16 to -22 degrees/sec in roll, +90 to -90 degrees/sec in pitch, and +45 to -60 degrees/sec in yaw. Linear acceleration had a range of +0.25 to -0.45 cm/sec2 along the x-axis, +0.45 to -0.18 cm/sec2 along the y-axis and +1.0 to -0.95 cm/sec2 along the z-axis. No saturation occurred in any accelerometer. 1 1 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Segment o f Raw Data, Experiment 3 Angular Velocity Linear Acceleration 50 0 50 0 100 roll 100 yaw 0.5 0 pitch 100 0 -100 200 5*-100 The above graphs show a segment of the raw head data from the freely walking experiment. The x-axis is time in units of tens of msec. 12 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Equations of Linear Acceleration Along the X, Y, and Z Axes The equations used in calculating the linear acceleration of the head along the three axes were developed as part of the research of Dr.Dennis P. O’Leary. " , =^ - ( ^ XV J - ( ^ X^ ) - ( “ x X( " x X^ , C J ) - ( 0 x X( “ x X^ ) ) +g s i n ( (l)) d =AV -(Q xF ) -((0 / ( 0 xr )) +gsin(0) dz =Az - ( Q /f p i(c J ~(w.xrro//) -(© /( u / V * ) ) -(« .* (o ,* rro//)) +g(l -cos(<J>)-cos(0)) where a^yj. = linear acceleration along each axis A*- y - 2 = total linear acceleration along each axis Q ^ = angular acceleration about each axis & )„,/ angular velocity about each axis rr o iL p itc h . y » w = distance from the origin of the angular velocity sensor axis to each axis of rotation in the head-centered coordinate system <|>=angle formed by rotation around the y-axis 0=angle formed by rotation around the x-axis g=acceleration due to gravity, 980.655 cm/sec2 13 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Analysis o f Data Raw data was first detrended and any offsets were removed. First, the angular velocity data was integrated according to Simpson’s rule to obtain the angular position of the head at each sampling point. Simpson’s rule approximates the integration of the function f(x) using the following equation, • r t J where integration of the function f(x) ffom sampling points x, to x3 is accomplished by selectively weighing the sum of the function at three consecutive sampling points and multiplying the result by the sampling interval h=0.01 and dividing by 3(Biran 459). Next, angular velocity was then differentiated to obtain the angular acceleration of the head before programming the equations of linear acceleration of the head. Spectral analysis of the angular velocity and linear head acceleration were done using an averaged periodogram method known as Welch’s method, L , = i where Pa v c is the averaged periodogram, P; is the individual periodogram, L is the number of segments the data is divided into, and to is the frequency. This method involved segmenting the data set into overlapping sections of 500 samples with a 50% overlap of segments. Each segment is windowed using a 14 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Hanning window to reduce sidelobe frequency leakage and taking the Fast Fourier Transform o f each segment before averaging all the segments together (Akay, 92). Example o f Head Position < / > 0) l. O) 0) *0 Angular head position 100 200 Roll 300 100 200 300 100 200 Yaw 300 400 2 0 400 -2 400 Head position at any given time during the experiments was within a range of approximately +/- 0.4 degrees in roll, + •/- 2.0 degrees in pitch, and +/-1.25 degrees in yaw. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Conclusion Spectral analysis was performed on the component of linear acceleration due to head motion along each axis and it was found that all of the frequencies were well within the range o f VOR activation(0’Leary, Vestibular Physiology 408). Acceleration of the head along the linear axes had frequencies in the range of approximately 1 to 8 Hz, with the y-axis having the smallest range in frequency and the z-axis having the largest range in frequency. A normal VOR should be able to maintain stable vision within these ranges(0’Leary, Vestibular Physiology 406). Therefore, the linear acceleration due solely to movements of the head may be another way in which the VOR can be studied. Head acceleration along the x and y axes was minimally effected by the type of motion performed by the subject. Movement along the z-axis, however, was extremely dependent on the manner in which the subject moved. For all three types of motion that the subject was instructed to perform, the frequency range of head acceleration along the x and y axes remained constant. Motion along the x-axis stayed within the range of 2.5Hz to 5.5Hz and motion along the y-axis was within the range of 1 Hz to 4Hz The frequency of movement along the z-axis was dependent on the ability of the subject to perform an unrestricted stride. When instructed to walk or jog in place, the subject had to execute a constrained step so as to maintain the same location while moving her legs. Thus, the frequency of head motion along the z-axis would occur more frequently as the subject moved with a faster stepping rate. When the test was performed 16 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. outdoors, the subject was able to move forward freely and the frequency of motion in the z-axis decreased as the stepping frequency decreased. The subject’s body was able to translate forward with the normal walking movement and the head became less affected by an artificially shortened gait. Therefore, the frequency range of 2Hz to 4 Hz for head motion corresponds directly to the stepping frequency range of most humans which is from 1 Hz to 2 Hz(Grossman, Frequency 474). The magnitude of linear acceleration at the predominant frequencies of the z-axis power spectrum, increased from a range of 59-60cm/sec2 when walking in place to a range of 69cm/sec2 when the subject was tested outdoors. This occurrence suggests that the head of the subject was able to increase linear velocity at a faster rate while walking outdoors than during stationary walking or jogging. More translation of the head occurred along the z-axis when the subject was allowed to walk freely even though the frequency at which this movement occurred was lower. Stationary movements resulted in a smaller translation of the head along the z-axis while moving with an smaller magnitude of acceleration. Jogging in place resulted in movements along the z-axis that can be considered a transition point between stationary and free walking. While the subject still had to contend with a shortened stride to stay in one place, the head was more influenced by the stepping rate. During jogging, the vestibulocollic reflex (VCR), a reflex that relays vestibular information to neck muscles, or the cervicocollic reflex, a neck-stretch reflex that aids the VCR in stabilizing the 17 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Power Spectrum o f Linear Acceleration from X-Head Motion, Experiment 1 power spectrum of stationary walking acceleration in x-direction 60 $40 1 20 2 v V 3 c 1 0) n E 0 0 5 10 15 frequency in Hz Acceleration of the head along the x-axis. Upper graph displays the levels of acceleration where the peaks of the power spectrum occurred. Lower graph displays the peaks of the power spectrum. 18 10 frequency in H z Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Power Spectrum of Linear Acceleration from Y-Head Motion, Experiment I power spectrum of stationary walking acceleration in y-direction 60 < * 4 0 0 ) (ft £20 o 0 0 5 10 15 frequency in Hz x 10 6 C E 2 0 I ---------------\ ^ - - 1 ---------------- I 0 5 10 15 frequency in Hz Acceleration of the head along the y-axis. Upper graph displays the levels of acceleration where the peaks of the power spectrum occurred. Lower graph displays the peaks of the power spectrum. 19 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Power Spectrum o f Linear Acceleration from Z-Head Motion, Experiment 1 power spectrum of stationary walking acceleration in z-direction 01 < 0 0 V) 40 0 0 5 10 15 frequency in Hz TJ 3 C l 01 m E A 0 5 10 frequency in Hz 15 Acceleration of the head along the z-axis. Upper graph displays the levels of acceleration where the peaks of the power spectrum occurred. Lower graph displays the peaks of the power spectrum. 20 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Power Spectrum o f Linear Acceleration from X-Head Motion, Experiment 2 power spectrum of stationary jogging acceleration in x-direction 60 N $40 E O 20 10 « ■ o 3 % 5 01 n E 0 0 5 10 15 frequency in Hz Acceleration of the head along the x-axis. Upper graph displays the levels of acceleration where the peaks of the power spectrum occurred. Lower graph displays the peaks of the power spectrum. 21 xIO frequency in Hz Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Power Spectrum of Linear Acceleration from Y-Head Motion, Experiment 2 power spectrum of stationary jogging acceleration in ^direction (N < 0 < D W v E O 0 0 0 5 10 15 frequency in Hz * « V 4 - 1 I I c 0) I 1 5 10 frequency in Hz 15 Acceleration of the head along the y-axis. Upper graph displays the levels of acceleration where the peaks of the power spectrum occurred. Lower graph displays the peaks of the power spectrum. 22 jjlljll " < .< m m m - - - - - -i . i — . . . . ■ —----------------------------------------------- Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Power Spectrum of Linear Acceleration from Z-Head Motion, Experiment 2 power spectrum of stationary jogging acceleration in z-direction 65 n 6 0 0 S i 55 “ 50 45 0 5 10 15 v in 8 frequency in Hz 10 3 c 5 a « E 0 0 5 10 15 frequency in Hz Acceleration of the head along the y-axis. Upper graph displays the levels of acceleration where the peaks of the power spectrum occurred. Lower graph displays the peaks of the power spectrum. 23 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Power Spectrum o f Linear Acceleration from X-Head Motion, Experiment 3 power spectrum of outdoor walking acceleration in x-direction E 40 0 ■o 3 C 01 0 5 10 15 frequency in Hz 10 5 10 frequency in Hz 15 Acceleration of the head along the x-axis. Upper graph displays the levels of acceleration where the peaks of the power spectrum occurred. Lower graph displays the peaks of the power spectrum. 24 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Power Spectrum of Linear Acceleration from Y-Head Motion, Experiment 3 power spectrum of outdoor walking acceleration in y-direction N < 0 4 ) W E O 0 0 5 10 15 frequency in Hz xIO C V 0 5 10 frequency in Hz 15 Acceleration of the head along the y-axis. Upper graph displays the levels of acceleration where the peaks of the power spectrum occurred. Lower graph displays the peaks of the power spectrum. 25 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Power Spectrum o f Linear Acceleration from Z-Head Motion, Experiment 3 power spectrum of outdoor walking acceleration in z-direction 0 0 40 5 10 15 frequency in Hz C 0 1 4 E 1 5 10 frequency in Hz 15 Acceleration of the head along the y-axis. Upper graph displays the levels of acceleration where the peaks of the power spectrum occurred. Lower graph displays the peaks of the power spectrum. 26 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. head (Fuchs 598-599), may be stimulated and cause the head to be held steady. This type of control would aid in stabilizing the image of the target on the retina by limiting head movement and preventing the degradation of visual acuity. Linear acceleration along the y-axis is an interesting result, in that it is very similar for all three types of motion. The head simply does not translate along the y-axis very much. For all experiments, frequencies with the most power were all under 5 Hz with the most common frequency range being from 1 to 1.5 Hz. The corresponding level of acceleration was almost half of the acceleration rates achieved in the x and z axes. Acceleration frequencies from jogging in place were similar to that from the walking methods but the lack of a second frequency peak lends credibility to the hypothesis that perhaps the vestibulocollic reflex and cervicocollic reflex are using neck muscles to hold the head steady while jogging. Motion in the x-direction showed the most distinct peaks in the power spectrum of the linear acceleration. The major peaks of the power spectrum were all within the range of approximately 2.5 to 5.5 Hz and no harmonics were consistently visible in any of the experimental trials. This particular axis also showed very little variation with the different types of body motion. The head of the subject continued to translate along the x-axis at about the same frequency and magnitude of acceleration no matter how fast the body moved or whether the body was able to translate freely. 27 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The experiments performed were illustrative of the general relationship between angular velocity and linear velocity. Velocity, the linear speed of a point on a rotating body is directly proportional to the body’s angular velocity v=rw where v is the linear velocity, co is the angular velocity, and r is a constant (Young 274). Further, since integration of a periodic signal does not change the frequency of the signal, linear acceleration of a periodic translation along an axis will have the same frequency as its linear velocity. The predominant frequencies of linear acceleration in the y and z axes found experimentally were very similar to the frequency of angular velocity in yaw and pitch. Acceleration along the x- axis had no correlation with roll since the angular rotation occurs perpendicularly to the x-axis. For this subject, the predominant frequencies for the velocity of pitch rotation were 1.3 and 2.8 Hz with higher harmonics for stationary walking, 6.3Hz with no harmonics for stationary jogging, and 2Hz with higher harmonics for outdoor walking. The main frequencies for yaw were 1.3 and 4.2 Hz for stationary walking, 4.9 Hz. for stationary jogging and I and 3 Hz for outdoor walking. According to the equations used in calculating the linear acceleration component of head motion, the acceleration along the x axis is dependent on the angle formed by rotation around the y axis and the acceleration along y is dependent on the angle formed by rotation about x. Z-axis acceleration is 28 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. dependent on both angles. As seen by the similarities that the frequencies of linear accelerations had to the frequencies of angular velocities, it is apparent that the linear acceleration of the head is an integral part of VOR stimulation. Table o f spectral analysis of linear acceleration o f head motion axis of predominant frequency range acceleration level linear frequencies of obvious of predominant motion harmonics* frequencies Walking in place X 2.7,4 and 5.5 Hz none 50-60 cm/sec2 y 1.2 and 4 Hz none 30-40 cm/sec2 z 8 Hz none 59-60 cm/sec2 Jogging in place X 3 and 4.9 Hz none 52-54 cm/sec2 y 1.5 Hz up to 4.5 Hz 38 cm/sec2 z 6.5 Hz up to 13 Hz 63 cm/sec2 Walking freely X 3 and 5 Hz none 55-65 cm/sec2 y 1 and 3 Hz up to 5 Hz 37-38 cm/sec2 z 2 and 4 Hz up to 10 Hz 69 cm/sec2 * “none” indicates that while minor power spectrum peaks may have occurred in some of the tests, no peak appeared often enough to be classified as a harmonic. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Power Spectrum o f Angular Velocity, Experiment 1 power spectrum of stationary walking velocity 10 0 15 10 yaw Power spectrum of the angular head velocities while the subject walks in place. Y-axis displays the level of velocity. X-axis is frequency in hertz. 30 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Power Spectrum o f Angular Velocity, Experiment 2 power spectrum of stationary jogging velocity roll O 0) 810 L. Ui T3 0 pitch yaw 40 20 Power spectrum of the angular head velocities while the subject jogs in place. Y- axis displays the level of velocity. X-axis is frequency in hertz. 31 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Power Spectrum o f Angular Velocity, Experiment 3 power spectrum of outdoor walking velocity O 0) i/i u Hi 0 T3 0 0 10 5 10 y aw 15 pitch 15 Power spectrum of the angular head velocities while the subject was walking freely. Y-axis displays the level of velocity. X-axis is frequency in hertz. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Works Cited Akay, Metin. Biomedical Signal Processing. San Diego: Academic, 1994. Biran, Adrian and Moshe Breiner. Matlab for Engineers. Wokingham: Addison- Wesley, 1995. Demer, Joseph L. “Mechanisms of Human Vertical Visual-Vestibular Interaction.” Journal of Neurophvsiologv 68 (1992): 2128-2146. Fuchs, Albert F. “The Vestibular System.” Textbook of Physiology. 21st ed. 2 vol. Eds. Harry D. Patton, et al.. Philadelphia: Saunders, 1989. Demer, Joseph L. and Erik S. Viirre. “Visual-Vestibular Interaction During Standing, Walking, and Running.” Journal of Vestibular Research 6 (1996): 259-313. Grossman, G. E., R. J. Leigh, L. A. Abel, D. J. Lanska, and S. E. Thurston. “Frequency and velocity of rotational head perturbations during locomotion.” Experimental Brain Research 70 (1988): 470-476. Grossman, Gerald E., R. John Leigh, Eugene N. Bruce, William P. Huebner, and Douglas J. Lanska. “Performance of the Human Vestibuloocular Reflex During Locomotion.” Journal of Neurophysiology 62 (1989): 264-272. Leigh, R. John, and Thomas Brandt. “A reevaluation of the vestibulo-ocular reflex: New ideas of its purpose, properties, neural substrate, and disorders.” Neurology 43 (1993): 1288-1295. O’Leary Dennis P. “Vestibular Physiology.” Otolaryngology Head and Neck Surgery. Eds. William L. Meyerhoff and Dale H. Rice. Philadelphia: Saunders, 1992. —. “Physiology of the Vestibular System.” Otologic Medicine and Surgery. 2 vol. Eds. Peter W. Alberti and Robert J. Ruben. New York: Churchill Livingstone, 1988. O’Leary, Dennis P., and Linda L. Davis. “Vestibular Autorotation with Active Head Movements.” Neurotologv. Eds. R.K. Jackler and D.E. Brackman. St Louis: Mosby-Year, 1994. 229-240. 33 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Vesterhauge, Soren. Eye Movements Compensatory to Active Head Movements Gravity Dependence. Diss. Dept, of Otolaryngology, Head & Neck Surgery, Rigshospitalet, Copenhagen: IJEGEFORENINGENS FORLAG, 1992. Young, Hugh D. and Roger A. Freedman., eds. University Physics. 9th ed. Reading: Addison-Wesley, 1996. 34 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Appendix The program implementing the equation for Simpson’s rule integration is as follows: % filename simp.m, updated 4/4/97 - 8:10pm h=0.01; % sampling interval c=l; for r=700:3604 ss(c,:)=swtl(r,:); % original data in matrix “swtl" fl(l,:)=swtl(r,:); £2(l,:)=swtl(rH,:); f3(l,:)=swtl(r+2,:); intg(c,:Hh/3)*[fl+(4*f2)+D]; c=c+1; end %size of ss and intg are 2905 x I %remove offset from data forrr=l:6 ms( 1 ,rr)=mean(ss(:,rr)); mi( 1 ,rr)=mean(intg(:,rr)); ss( :,rr)=ss( :,rr)-ms( 1 ,rr); intg( :,rr)=intg(:,rr)-mi( 1 ,rr); end save iswtl.mat intg; save sswtl.mat ss; disp(‘original data in matrix ss’); disp(‘integration data in matrix intg’); disp(‘col 1-roll, col 2-pitch, col 3-yaw’); disp(‘col 4-x, col 5-y, col 6-z’); disp(‘size of ss and in tg : 2905 x 6'); disp(‘integration data saved in iswtl.mat’);. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Differentiation of the angular velocity data was done by taking the difference of two adjacent velocity points and dividing by the sampling interval of 0.01 seconds. The program is as follows: % file name differ.m, updated 4/7/97 - 9:18pm % program differentiates the accelerometer data load sswtl.mat;% loads original data in matrix ss for r=l:6 dy(:,r)=diff(ss(:,r));% takes the difference of y2 -yi, yj-y2 , and so on end dydx=dy/0.01; dydx=[0,0,0,0,0,0 ; dydx]; save dswtl.mat dydx; disp(‘differentiation data saved in dswtl.mat in matrix dydx’); 36 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The program that combines the equations for linear acceleration with the experimental and derived data is as follows: % filename head.m, updated 4/9/97 - 10:21pm clear load sswtl.mat; load dswtl.mat; load iswtl.mat; % original data in matrix ‘ss’ % derivative data in matrix ‘dydx’ % integration data in matrix ‘intg’ acx(:,l)=ss(:,4);% linear acceleration in x-direction acy(:,l)=ss(:,5);% linear acceleration in y-direction acz(:,l)=ss(:,6);% linear acceleration in z-direction dwx(:,l)=dydx(:,l);% angular acceleration about x-axis dwy(:, 1 )=dydx(:,2);% angular acceleration about y-axis dwz(:,l)=dydx(:,3);% angular acceleration about z-axis phi(:,l)=intg(:,2);% angle from rotation round y-axis theta(:,l)=intg(:,l);% angle from rotation around x-axis % constants g=980.655;% gravity in cm/secA 2 rr=19.05;% roll axis distance to sensor in cm rp=20.95;% pitch axis distance to sensor in cm ry=l5cm;% yaw axis distance to sensor in cm % eqn for linear acceleration along x-axis ax(:, 1 )=acx-((dwx*rp)*sin(44.29)H(dwx*ry)*sin(0)) -(wx.*((wx*rp)*sin(44.29)))-(wx.*((wx*ry)*sin(0)))+(g*sin(phi)); % eqn for linear acceleration along y-axis ay(:, 1 )=acy-((dwy*ry)*sin(0))-(wy.*((wy*ry)*sin(0)))+(g*sin(theta)); % eqn for linear acceleration along z-axis az(:, 1 )=acz-((dwz*rp)*sin(44.29))-((wz*rr)*sin(38.06)) -(wz.*((wz*rp)*sin(44.29)))-(wz.*((wz*rr)*sin(38.06))) +(g*( 1 -cos(phi)-cos(theta))); Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The program to do a spectral analysis of linear acceleration is as follows: % filename axcompw.m, updated 4/10/97 -12:11pm fs=100; % sampling frequency w=hanning(500); % Hanning window with length of 500 samples [Pzz,fx]=psd(ax,2048,fs,w,250,’mean’); subp!ot(2,1,1 ),plot(fx( 1:300,1), 10*logl0(Pzz( 1:300,1 )*norm(w)A 2/sum(w)A 2)); ylabel( ‘ cm/secA 2'); xlabel(‘frequency in Hz’); title(‘power spectrum of stationary walking acceleration in x-direction’); subplot(2,1,2),plot(fx( 1:300,1 ),Pzz( 1:300,1)); ylabel(‘magnitude’); xlable(‘frequency in Hz’); 38 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
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Spectral analysis of linear head motion during walking and jogging
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