Fractal analysis on dental radiographs to detect trabecular patterns in patients affected by periodontitis

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Content FRACTAL ANALYSIS ON DENTAL RADIOGRAPHS TO DETECT TRABECULAR PATTERNS IN PATIENTS AFFECTED BY PERIODONTITIS by Sophia Sy-Hann Xiang A Thesis Presented to the FACULTY OF THE GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree MASTER OF SCIENCE (CRANIOFACIAL BIOLOGY) May 2007 Copyright 2007 Sophia Sy-Hann Xiang ii DEDICATION This thesis is dedicated to my husband, parents, sister, and friends who have helped make it possible. iii ACKNOWLEDGEMENTS Dr. Hessam Nowzari: To my principal investigator, research advisor, my mentor, and friend, I would like to thank you for all your help and support to this research project. Your enthusiasm and insights have encouraged and guided me through not only the difficult part of the research but also my personal growth. Dr. Glenn Sameshima: To my committee member, program chair, mentor, and friend, I would like to thank you for all your help and support on this research. Your leadership has guided me though the residency. I would not have made it though the program without your support, understanding, and most definitely your humor. Dr. Sandra Rich: To my other committee member, I would also like to thank you for all your help and guidance on this project iv TABLE OF CONTENTS Dedication ii Acknowledgements iii List of Tables vi List of Figures viii Abstract x Chapter 1: Introduction 1 Periodontal Diseases 1 Bone Physiology 5 Imaging 15 Fractal Analysis 27 Chapter 2: Methodology 43 Sample Selection 43 Group Classification 43 Image Preparations 44 Fractal Analysis 50 Statistical Analysis 53 Age Correlation 53 Sensitivity and Specificity of the fractal analysis 53 Chapter 3: Results 55 Data Set Description 59 Fractal Dimensions in the lower anterior region 60 Fractal Dimensions in the lower posterior region 62 Fractal Analysis as a Diagnostic Tool 64 Effects of Age 69 Effects of Gender 71 Chapter 4: Discussion 75 v Chapter 5: Conclusion 86 Bibliography 88 vi LIST OF TABLES Table 1: Comparison of 4 radiographic projections 25 Table 2: Fractal dimensions for subjects with healthy gingiva 56 Table 3: Fractal dimensions for subjects with moderate periodontitis 57 Table 4: Fractal dimensions for subjects with severe periodontitis 58 Table 5: Descriptive statistics for patients’ ages – ant mandible 59 Table 6: Description of patient’s gender – ant mandible 59 Table 7: Descriptive statistics for patients’ ages – posterior mandible 60 Table 8: Description of patient’s gender – posterior mandible 60 Table 9: Descriptive statistics of measured fractal dimensions- 60 anterior mandible Table 10: Statistics for ANOVA test- anterior mandible 62 Table 11: Tukey HSD post-hoc test comparisons- anterior mandible 62 Table 12: Descriptive statistics of measured fractal dimensions-- 62 posterior mandible Table 13: Statistics for ANOVA test- lower posterior region 63 Table 14: Tukey HSD post-hoc test comparisons – lower posterior region 63 Table 15: Descriptive statistics for 2 groups (healthy and periodontitis groups) 64 in the lower anterior region. Table 16: Observed contingency table 65 Table 17: Chi-Square Tests 66 Table 18: Fisher Exact Test 66 Table 19: Quantities derived from a 2-by-2 contingency table 67 vii Table 20: Comparison of fractal dimension in the healthy group – 72 anterior mandible Table 21: Comparison of fractal dimension in the moderate periodontitis group— 72 anterior mandible Table 22: Comparison of fractal dimension in the severe periodontitis group— 72 anterior mandible Table 23: Comparison of fractal dimension in all groups combined – 72 anterior mandible Table 24: Comparison of fractal dimension in the healthy group – 73 posterior mandible Table 25: Comparison of fractal dimension in the moderate periodontitis group – 73 posterior mandible Table 26: Comparison of fractal dimension in the severe periodontitis group – 73 posterior mandible Table 27: Comparison of fractal dimension in all groups combined – 73 posterior mandible viii LIST OF FIGURES Figure 1: Sierpinsky triangle 29 Figure 2: Fractal examples 33 Figure 3: Koch curve 33 Figure 4: A solid square 33 Figure 5: Caliper method for ascertaining the boundary length of an image 34 Figure 6: Minkowski’s sausage 35 Figure 7: Fractal dimension algorithm 37 Figure 8: Extreme examples of the bone 41 Figure 9: An example of the full mouth radiographs scanned 44 Figure 10: An example of a region of interest selected 45 in the mandibular anterior region Figure 11: An example of a region of interest selected 46 in the mandibular posterior region Figure 12: Steps used in image processing 47 Figure 13: ImageJ software option that converts images to binary format 48 Figure 14: A binary image 49 Figure 15: ImageJ menu for box-counting method to estimate fractal dimension 51 Figure 16: An example of the results from the box-counting method in ImageJ 51 Figure 17: Example of grid shifting algorithm 52 Figure 18: Fractal dimensions of the three periodontal groups 61 in the lower anterior area Figure 19: Fractal dimensions of the three periodontal groups 63 in the lower posterior area ix Figure 20: Method to assign subjects into two periodontal groups: 65 healthy or periodontal disease Figure 21: ROC curve: healthy vs. periodontal group 68 Figure 22: ROC curves for the lower anterior region 69 Figure 23: Plot of fractal dimension in the lower anterior region vs. age 70 Figure 24: Plot of fractal dimension in the lower posterior region vs. age 71 Figure 25: Effect of gender on fractal dimension 72 in the mandibular anterior region Figure 26: Effect of gender on fractal dimension 74 in the mandibular posterior region x ABSTRACT Objective: To evaluate fractal analysis as a tool to quantitatively measure the impact of periodontal disease on surrounding bone. Background: The current standard use of dental radiographs is visual inspection, often with no quantitative analysis. Fractal analysis can be used to examine trabecular bone pattern among periodontal patients. Methods: Patients (n=108) from the USC School of Dentistry were classified into three groups: healthy, moderate, and severe periodontitis. The box-counting-method was used to calculate a fractal dimension. Results: Significant differences in average fractal dimensions were measured between healthy and moderate-periodontitis groups (p<0.01) and between healthy and severe-periodontitis groups (p< 0.001) in the anterior mandibular region. Higher fractal dimensions were measured in healthy periodontal patients. Conclusions: Fractal analysis evidenced significant differences between patients affected and not affected by periodontitis in the anterior mandible. The box-counting method quantitatively describes the severity of bone disease and can be used to improve current diagnostic techniques. 1 CHAPTER 1-- Introduction: Background Periodontal Diseases Definitions Periodontal disease affects up to 90% of the world population (Pihlstrom et al. 2005). It refers to a group of disorders that attack the periodontium, such as the gingiva, sulcus, cementum, connective tissue attachments, and the supporting bone. Although etiologies of the disease include genetic, neoplastic, and metabolic origin, the most common cause is the bacteria-induced inflammation of the gingiva and periodontium. Periodontal diseases are divided into two major categories: gingival disease and periodontitis. Gingivitis, inflammation of the gingiva, is the most common form of gingival disease. Chronic marginal gingivitis or simple gingivitis is caused by bacterial plaque attached to the tooth surface. This inflammatory process can remain constant for indefinite periods of time or can go on to become more aggressive and destroy supporting structures (Carranza et al. 2002). The gingiva can also be involved in other diseases not related to inflammatory processes, such as atrophy, hyperplasia, neoplasia, allergic reactions, and others. 2 Periodontitis, the second type of periodontal disease, affects supporting tooth structures. Similar to gingivitis, the most common periodontal disease is also caused by inflammation initiated by bacterial plaque. Chronic periodontitis occurs primarily in adults, but it can be seen in younger people. The destruction of supporting tissue is related to the amount of plaque and local factors. In these cases, subgingival calculus is commonly found in periodontal pockets. The disease usually progresses at a steady rate but may have bursts of destruction. Pathogenesis Both bacteria and a susceptible host are equally important components for periodontal disease. The inflammatory response supplied by the host’s immune system usually develops in the periodontal pocket because of the chronic irritation from the bacterial plaque. This results in the destruction of structural parts of the periodontium and eventually causes periodontitis. There are many risk factors for periodontitis as mentioned earlier; most of these risks can be linked to gingival inflammation in response to plaque accumulation. The host’s protective response plays an important role in the health of periodontium. When the host is hypo- responsive or hyper-responsive, it can lead to enhanced tissue destruction (Pihlstrom et al. 2005). 3 Both the bacteria and the host release proteolytic enzymes that are damaging to the periodontium: they release chemotactic factors that recruit polymorphonuclear leucocytes, which if sustained could release various chemicals that break down tissues. The host produces many microbial antigens which evoke both cell-mediated and humoral antibody-mediated immune responses. However, sustained microbial challenges can evoke cytokine and prostanoid cascades and result in the destruction of both hard and soft tissue (Pihlstrom et al. 2005). Histologically, non-progressive inflammatory foci are composed of mainly T lymphocytes and macrophages, which suggests that the cell-mediated response can control disease. In destructive lesions, the inflammatory foci are predominated by B lymphocytes and plasma cells, which suggests that humoral immunity is not effective. When a periodontal pocket is formed and becomes the habitat for bacteria, the situation is usually irreversible. Gingival epithelium proliferates to line the pocket and complete restoration of tooth support becomes impossible even with the most optimal treatment. Without proper periodontal treatment, active periodontitis will ultimately lead to tooth loss (Pihlstrom et al. 2005). Diagnosis of Periodontal Diseases Chronic gingivitis often presents with bleeding upon brushing while chronic periodontitis is often asymptomatic except during its advanced stage, which can have 4 signs such as tooth mobility, recurrent periodontal abscesses, halitosis, and pain. The diagnosis of chronic periodontal disease is based on both clinical and radiographic assessment of periodontal tissue. When measuring the periodontal pocket depth, the distance between the base of the pocket and the gingival margin is used as one of the indicators of the tissue health: the reading in healthy sites is normally 1-3mm and increases as the supporting connective tissue and bone are lost. In a comprehensive clinical exam, pocket depths are measured at four to six locations around each tooth, and the amount of plaque, dental calculus, gingival bleeding, and exudates are recorded in each area. Radiographic assessment of periodontal disease is often based on visual inspection of the inter-dental bone level and furcation involvement. There are several emerging diagnostic methods for periodontal disease. Some commercial assays use the inflammatory exudates containing biomarkers for periodontal inflammation. These biomarkers include prostaglandin E 2 , cathepsin B, neutrophil elastase, collagenase, glucuronidase, arylsulphatase, aspartate aminotransferase, non-specific neutral proteinase, etc. However, they are not widely used because of their low predictive values and cost. Other diagnostic approaches include image analysis of dental radiographs or three- dimensional scans. Technology, such as NewTom, provides practitioners with 3D views of the alveolar bone and soft tissue and may provide the ability to detect small 5 changes in trabecular patterns and supporting bone structures in the near future (Pihlstrom et al. 2005). Bone Physiology Bone Structure: Osteology of the Maxilla and Mandible Bone is a metabolically active organ and is composed of two phases: organic and mineral. The organic phase consists of one third of the weight and the mineral phase fills in the rest. It is formed from a combination of dense, compact cortical bone and cancellous (trabecular) bone to withstand stress placed on the bone. Cortical bone makes up about 80% of the bone in the body and cancellous bone consists of about 20%. Because the cancellous bone is more active, the skeletal metabolism is about equal between the two types of bones. They are regulated by different hormones, factors, and treatment modalities (Schwartz et al. 2003). Cortical Bone is composed of repeating, circular units called Haversian systems. Within each Haversian system, there is a central canal where nerves and blood vessels can be found. Each Haversian canal is surrounded by concentric layers of the matrix material called lamellae. Cortical bone is surrounded on the outside by the 6 periosteum and on the inside by the endosteum, which exhibits significant osteoclastic and osteoblastic activity on the surface (Schwartz et al. 2003). Trabecular bone is rigid but appears spongy. It consists of a complex porous network of fibers, shaped like small rods and plates, called trabeculae. These trabeculae range from 50 to 400nm and are interconnected in a honeycomb pattern in order to provide optimal mechanical properties despite compressive forces. The center of the bone contains red cells, yellow marrow, bone cells and other tissue (MEDES 2006). The cortical bone is found primarily in the long bones of the limbs, and cancellous bone is found mainly in the vertebral column and pelvis. Both of these types are found in the maxilla and mandible. Yet, the mandible has more cortical bone relative to the maxilla (Schwartz et al. 2003). Even though there are similar amount of functional loads delivered to the maxilla and mandible, the maxilla is able to transfer stress to the entire cranium while the mandible needs to absorb the entire load. Because of this, the mandible is much stronger and the alveolar bone is denser than in the maxilla. When looking at the cross-sectional view of the maxilla, it is found that maxilla has relatively thin cortices that are interconnected by a network of trabeculae. Since the loading in the maxillary region is primarily through compression, its structure is very similar to the 7 body of a vertebra. The Mandible, on the other hand, has thick cortices and more radially-oriented trabeculae. Because the trabeculation is similar to that from the shaft of a long bone, it suggests that the mandible is loaded mainly by bending and torsion (Roberts et al. 2005). Skeletal Adaptation/Compromise Bone is a living tissue and changes constantly in response to various stimuli, such as mechanical, hormonal, genetic, pathological, and environmental influences. There are several ways changes can occur in bones, and these include bone mass, geometric distribution, matrix organization, and collagen orientation of the lamellae. Trabecular and cortical bones mature, adapt, and turn over in two distinct ways: modeling and remodeling. In bone modeling, there are independent sites for bone resorption and formation. It occurs primarily at the periosteum and endosteum, resulting in changes in size and/or shape of the bone. In bone remodeling, old bone is removed and new bone is added to replace the pre-existing bone at the same location. Two main cell types are responsible for remodeling: osteoclasts remove old bone while osteoblasts add new bone. These two cell types may communicate by chemical coupling factors such as transforming growth factor β (TGF β) and fibroblast growth factor (FGF). The mechanism for internal remodeling of dense 8 compact bone involves axially-oriented cutting and filling cones. Because cancellous bone has a higher surface area than cortical bone, the remodeling process is about eight times faster. Therefore, cancellous bone is lost at a faster rate than cortical bone. Constant internal turnover mobilizes and re-deposits calcium by coupled reactions. While modeling is continuous and covers a large surface, remodeling is episodic and usually covers only a small area (Schwartz et al. 2003). Bone formation involves two main steps: (1) the production of a new organic matrix by the osteoblasts and (2) the mineralization of the matrix. These two steps are controlled by local factors and systemic hormones. The local regulators are primarily growth factors that act directly on osteoblastic cells. They act either as autocrine or paracrine factors (Canalis et al. 1989). Systemic factors have direct effects on osteoblasts and can stimulate the production of local growth factors (Schwartz et al. 2003). Bone resorption is controlled by several local factors. Because of the close proximity of trabecular bone to marrow, cytokine regulation plays a more important role for trabecular bone. Moreover, cytokines appear to participate in bone pathology and have been associated with bone destruction seen in chronic inflammatory conditions, such as periodontal disease. The observed increase in cytokines during the diseased period suggests that they might be the cause of increased localized osteolytic bone destruction (Schwartz et al. 2003). 9 The height of the alveolar bone is normally maintained by the homeostatic systems in the body. The systemic and local factors regulate bone formation and resorption. When bone resorption exceeds bone formation, alveolar height is reduced and vice versa. In addition, there is a considerable amount of normal variation in the morphologic features of the alveolar bone that can affect bone remodeling patterns produced by local and systemic factors. These features include: (1) the thickness, width, and crestal angulation of the interdental septa; (2) the thickness of the facial and lingual alveolar plates; (3) the presence of fenestrations and/or dehiscences; (4) the increased thickness of the alveolar bone margins to accommodate functional needs; (5) the alignment of the teeth. Bone is the primary calcium reservoir in the body: the principal source of serum calcium under steady-state conditions is trabecular bone followed by cortical bone. Trabecular bone turns over about 20% to 30% per year while the turnover rate for cortical bone is about 2% to 10% per year (Parfitt 1983). Due to its high turnover rate, trabecular bone is more susceptible to loss under conditions of negative calcium balance. Therefore, patients with skeletal compromise, such as osteoporosis, have higher tendency for structural failure at sites heavily dependent on trabecular bone, such as the hip, wrist, and spine. Bones also undergo changes with age. The aging process starts around age 25 to 30, when the maximal bone strength is attained. A steady decline in bone mass begins 10 around 30 years of age. The decrease in bone mass leads to thinning of cortical bone from the trabeculation of the endosteal cortical envelope and from the expansion of the marrow activity accompanied by some gain in bone diameter (Schwartz et al. 2003). Mosekilde and colleagues have shown that trabecular bone in subjects ranging from 15 to 87 year old demonstrates a decrease of about 45% in fractional volume and a decrease in the mean thickness of the horizontal trabeculae but not the vertical trabeculae. An increase in the distance between horizontal trabeculae with age has been seen in both males and females. Additionally, there is a significant age-related increase in marrow space volume, especially for females (Mosekilde et al. 1988). Skeletal health is related to lifestyle, diet, exercise, and other organs. A failure of any of the homeostatic mechanisms can result in metabolic bone disease. One of the main diseases that compromises skeletal bone integrity is osteoporosis, a generic term used to describe low bone mass. About 20% of individuals who eventually develop osteoporosis have no known history of any risk factors suggested by research studies. Timely medical referral for patients with high risk profiles can provide considerable benefits (Roberts 2005). 11 Periodontal Disease and Bone Destruction In periodontal disease, bone destruction is caused by two main local factors: inflammation and occlusal trauma. When bone loss is induced by gingival inflammation, alveolar height is reduced; when the bone loss is induced by occlusal trauma, bone loss occurs laterally to the root surface. The level of alveolar height is the consequence of pathologic experience in the past while changes in the soft tissue surrounding periodontal pockets reflect the present inflammatory condition (Carranza 2002). Periodontal destruction usually happens in an intermittent and episodic way. The destruction results in loss of collagen and alveolar bone around periodontal pockets. There are several theories describing the onset of the destruction: (1) subgingival ulceration and acute inflammatory reactions cause rapid loss of alveolar bone; (2) the conversion of a predominantly T-lymphocyte lesion to one with B-lymphocyte- plasma cells marks the sudden burst of destruction; (3) the increase of loose, unattached, motile, gram-negative, anaerobic bacteria flora accelerates periodontal destruction (Carranza 2002). Bone destruction is initiated by tissue inflammation. Pharmacologically, there are several chemical factors that can be found in inflamed gingiva. Some researchers have suggested that bone resorption could be induced by prostaglandin, osteoclast- 12 activating factors produced by lymphocytes, and proteolytic enzymes and hyaluronidase generated by bacteria (Carranza 2002). During the active phase of periodontal disease, the main objective of the body is to protect and maintain the equilibrium established in a healthy state. Contrary to the common belief that periodontal bone destruction is caused by bone resorption done by osteoclasts, bone formation could still be found in areas adjacent to active resorption sites and along trabecular surfaces in order to reinforce the remaining bone support (Carranza et al. 1971). This new bone formation slows down bone loss caused by inflammation; thus, bone loss in periodontal disease results from the predominance of bone resorption over formation (Carranza 2002). The second cause of periodontal disease is through occlusal trauma, which can cause compression and tension of the periodontal ligament (PDL), necrosis of the PDL, and resorption of adjacent bone and tooth structure (Lopez-Otero et al. 1973). The occlusal trauma creates a funnel-shaped widening of the crestal region of the PDL while resorbing the adjacent bone. It can also cause a thickening of the cervical margin of the alveolar bone or create some angular defects and buttressing bone. The changes in bone shape represent adaptation of the periodontal tissue to provide extra support for the increased occlusal load (Carranza 2002). 13 There are several types of bone defects: horizontal defects not only reduce alveolar height, they produce other types of changes in the adjacent bone. Vertical or angular defects occur in an oblique direction, and usually leave a hollowed out trough in the bone adjacent to the root. These vertical defects often are accompanied by infrabony pockets and make cleaning extremely difficult. Vertical defects are classified based on the number of walls involved. Interdental vertical defects usually can be seen on radiographs and are found most commonly distal to the molars (Nielsen et al. 1980). In addition, three-wall defects, commonly called intrabony defects, are often found mesially of the upper and lower molars (Larato 1970). Periodontal disease can also produce defects such as osseous craters. These are concavities between two neighboring teeth and are confined within facial and lingual walls. They comprise about one third of all defects and about two thirds of all mandibular defects. They are more common in the posterior regions than anterior regions (Masters et al. 1963). A few ideas have been suggested regarding the frequency of the osseous craters: because inter-dental areas collect plaque and are difficult to clean, the flat or sometimes concave faciolingual walls in the lower molars favor crater formation. The vascular arrangements from the gingiva to the center of the crest can provide a path for inflammation (Carranza 2002). When bone loss occurs in such a way that the furcation area of the molars is exposed, it becomes almost impossible to clean and can lead to extensive lesions in the area. 14 It is found that mandibular first molars are the most commonly affected sites and maxillary premolars are the least, and the number of furcation involvements increases with age (Larato 1970). The furcation involvement can be divided into grades I, II, III, and IV based on the amount of tissue destruction. Grade I starts with insipient bone loss; grade II is cul-de-sac; grade III involves through and through opening of the furcation; grade IV is similar to grade III except there is gingival recession that exposes the furcation area. Radiographic examination may reveal the presence of furcation involvement in periodontal patients, but it could be obscured by neighboring objects or by angulations of the X-ray beam (Carranza 2002). 15 Imaging Historical Overview Images of craniofacial region are important components of the dental patient record. Imaging is one of the most common tools dentists used to measure and record the size and form of craniofacial structures. Despite diverse imaging technologies currently available, the imaging types presently used in dental practice have been adopted in an effort to balance the anticipated benefits with associated costs and risks to the patient. For several reasons, dentists routinely use an array of site specific two-dimensional imaging. Various methods have been used to describe the anatomic information contained in these two-dimensional images. Most analyses use linear and angular measurements that are generated either manually or via computer assistance. These measurements are frequently incorporated into treatment prediction and are used for treatment evaluation (Mah et al. 2005). Common imaging goals include detection of anatomic structures and morphologic measurements. The ideal images should record the complete region of interest, contain maximal detail, minimal distortion, minimal superimposition, and have optimal density and contrast. Finally, the diagnostic value of the imaging study must be in balance with risks and benefits associated with the imaging tool. 16 Craniofacial imaging is often used to interpret complex interrelationships among craniofacial diagnosis, growth, and treatment. It can also be used to monitor the status quo of the present dental condition (Mah et al. 2005). There are several ways to improve the quality of current radiographs to allow for more accurate analysis and measurements. Strict standardization of projection geometry for serial radiographs with enhanced image processing can result in a more sensitive detection and quantification of minor changes in radiographic structures. The incorporation of image processing may reduce both intra-rater and inter-rater variability. The biological significance lies in the possibility of gaining noninvasive information about tissue conditions that can reflect physiological tissue turnover, changes in bone density, and other information (Bragger 2005). Although many radiographic modalities provide diagnostic information, there are still limitations. One of the main limitations is that a three dimensional structure is represented by a two-dimensional image. Sometimes, morphologic or pathologic aspects of the alveolar bone may become undetectable due to the superimposition of images. Only the interproximal bone level can be determined with some degrees of confidence. According to a paper published by Mol, there needs to be a substantial amount of alveolar bone loss, about 30% to 50%, before bone resorption can be seen on traditional radiographs. Misdirection of the central ray of the X-ray beam and exposure and processing errors can further degrade the situation. Therefore, proper 17 use of radiographs requires that high quality images are produced and that limitations imposed are recognized in the interpretation process (Mol 2004). Intraoral exams are the backbone of dental radiography. Intraoral radiographs can be divided into three categories: periapical projections, bitewing projections, and occlusal projections. Periapical radiographs should include the whole tooth and the surrounding bone. It is often indicated in adult patients to assess the overall dental and periodontal status, root morphology and length. Bitewing radiographs show only the crowns of teeth and the adjacent alveolar crests. Occlusal radiographs provide right-angle views to the normal periapical projection and show an area of teeth and bone larger than periapical films (White et al. 2000). Another common imaging technique used by dental profession is the panoramic projection. The panoramic radiograph has better screening value than diagnostic value. It provides information on present, missing or supernumerary teeth, gross periodontal condition, sinus, TMJ, and possible pathological conditions. However, the panoramic radiograph lacks the detail and accuracy and may compromise the image of the crestal alveolar bone, especially in the frontal area of the mouth (Mah et al. 2005). The fan beam is directed upward and an image layer is formed by the coordinated movement of the beam and the receptor. Horizontal and vertical magnifications are determined by different mechanisms and vary as a function of the location of a structure within the image layer (Mol 2000). The overlap of contacts between teeth in the canine and premolar region can give rise to some unmeasurable 18 sites (Akesson et al. 1989). Errors in patient positioning often result in suboptimal projections and difficulties in comparison with follow-up images. The choice of radiographic projection will expose patients to different amounts of radiation dosages. Typical effective doses for one periapical radiograph taken with 70kV at 200mm focal spot to skin distance with a rectangular collimator and E-speed film is 0.001 millisievert (mSv). For a panoramic projection with rare earth intensifying screen, the dosage is 0.007mSv (NRPB 1994). A panoramic projection has less risk than a full mouth periapical survey. The low level of risk is associated with the state of the art equipment used under optimum conditions. When compared with radiation used in the medical field, dental exposures have a very low dosage. There are two ways to effectively reduce patient radiation dosage: use a fast image receptor or use a rectangular collimator. Fast receptors include E- or F-speed film and digital detectors. These receptors appear to produce the same result as D-speed film, which requires double the exposure of the fast receptors. A rectangular collimator can also reduce dosage and improve image contrast by reducing scatter radiation (Mol 2004). 19 Radiographs and the Assessment of Periodontal Condition Periodontal diagnosis is based on a considerable amount of information obtained from clinical exams. Gingivitis is detected by changes in soft tissue characteristics while periodontitis is detected by bleeding on probing, probing pocket depths, loss of attachment, mobility, suppuration (Nyman et al. 1997), presence of calculus, other plaque retention factors, and furcation involvement. However, clinical detection of all features of periodontitis is difficult without the aid of radiographs, which can indicate bone levels and patterns of bone loss. Radiographs contribute not only in the diagnosis of periodontitis but also in the assessment of the prognosis of periodontally involved teeth, the treatment plan, the evaluation of the progression or recurrence of the disease, and treatment outcome. Moreover, periapical pathology may be suspected clinically but can only by visualized on appropriate radiographs (Tugnait et al. 2000). The most common methods of assessment of periodontitis are through radiographic imaging and estimation of attachment loss and probing depths. Clinical attachment loss is measured from CEJ to the base of the periodontal pockets while probing depths are measured from the gingival margin to the base of the pocket. The use of clinical attachment loss and probing depth measurements may fail to locate the base of the pocket accurately since it is difficult to detect CEJ locations with a manual 20 probe and probing depths can be affected by the degree of gingival inflammation and recession (Hammerle et al. 1990). There are several ways to assess bone levels: radiographs, sounding under local anesthesia, and visualizing during surgery (Akesson et al. 1992). The most common and least invasive approach to evaluate bone level is by conventional radiographs. The position of the alveolar bone level in health is established as “no clinical attachment loss”, which is consistent with a distance from the cemental-enamel junction (CEJ) of between 0.4 and 1.9mm on bitewings (Hausmann et al. 1991). Other studies have used a crestal position of more than 2mm (Hansen et al. 1984) or 3mm (Hull et al. 1975) from CEJ as thresholds for evidence of bone loss. Radiographic bone levels could be determined by different techniques such as direct measurement in millimeters from CEJ or a percentage of tooth or root length. Even though measurements can easily be made on radiographs, several cases present some difficulty in measurement due to overlapping structures on the image or inability to locate the CEJ or tooth apex. Studies have reported that the amount of bone destruction in panoramic and periapical radiographs does not accurately reflect the degree of actual bone loss. They seem to underestimate in the initial periodontal phase, they are relatively accurate in moderate periodontal disease and they overestimate in severe periodontitis (Pepelassi et al. 1997). Nevertheless, a 21 relationship can be demonstrated between the clinical and radiographic parameters of disease. There are other measurements that can be used to provide means to quantify the periodontal condition of a radiographic image and to generate a diagnosis besides the linear distance between the CEJ and the alveolar crest: the location of the alveolar crest in relation to root or tooth length, the presence of vertical defects, defect angle, density of the crestal alveolar lamina dura, the furcation involvement, and other measurements. Hugoson and Jordan in 1982 proposed a classification of the severity of periodontal disease based on the location of the alveolar crest relative to root length: <1/3, between 1/3 and 2/3, and > 2/3 of the total root length (Hugoson et al. 1982). Other researchers like Bjorn have suggested measuring proximal bone level as a percentage of the total length of a tooth using a ruler with 10 equidistant divisions (Bjo¨rn 1974). Moreover, the presence of a vertical periodontal defect indicates advanced infrabony destruction and is a diagnostic sign of severe periodontitis. Untreated angular osseous defects show an increased risk for more alveolar bone loss relative to horizontal bone destruction (Papapanou et al. 1991). Tsituoura and colleagues have found that there is a significant association between defect angle and clinical attachment gain. They showed in their study that narrow periodontal defects ≤ 22° heal better than defects ≥ 36. Generally, more favorable healing occurs in defects < 22 45° as opposed to larger angles. Periodontal regenerative treatment seems to be more successful in deep and narrow defects. The wider a periodontal defect is coronally and the fewer bony walls present, the worse the prognosis following therapy (Tsitoura et al. 2004). The presence or absence of radiographically visible crestal alveolar lamina dura can also be used as an indicator of either a stable or worsening periodontal condition. Nonetheless, in predicting periodontal attachment loss, the absence of alveolar lamina dura has a positive predictive value and a high sensitivity but a low specificity (Bragger 2005). Finally, the radiographic assessment of furcation area is highly influenced by the anatomic complexity and radiographic over-projection of anatomic structures. On average, the location of the bifurcation in mandibular molars may deviate about 0.26mm ± 0.5 mm in the apical direction from the true location at the first molars and about 0.65mm ±1.15mm in the coronal direction at the second molars (Gu¨rgan et al. 1994). Researchers have suggested that the agreement between the clinical diagnosis of attachment loss and the radiographic assessment of periodontal disease is not high. It suggests that the conventional radiography is a relatively insensitive method for detection of small changes in the alveolar bone (Goodson et al. 1984); however, its high specificity makes it successful in confirmation of the presence of periodontal defects or the progressive loss of alveolar bone (Kornman 1987). Currently the 23 degree of deviation of the radiographic assessment of periodontal osseous lesions from the actual osseous destruction has not been thoroughly studied. The sensitivity of radiographs to identify features such as furcation involvement or early bone loss depends on the different radiographic projections. Small areas of bone destruction were detected 4.7 times more frequently by periapical radiographs than by panoramic radiographs despite the fact that the detection of these areas is very difficult in comparison to the gold standard of surgical exposure. Thus, periapical films are more accurate than panoramic radiographs in detection of bony defects regardless of the location of the dental surfaces and degrees of osseous destruction (Pepelassi et al. 1997). Although many anatomical vertical defects cannot be detected easily, the prevalence of radiographically detectable angular bony defects is about 18-32% (Nielsen et al. 1980). Rohlin and colleagues have shown that 43% of the total angular defects were found by both panoramic and periapical radiographs, 21% by panoramic only, and 32% by periapical only. For furcation defects, 69% were found by both periapical and panoramic radiographs, 15% by periapical only and 16% by panoramic alone (Rohlin et al. 1989). The addition of more projections such as bitewings can increase the detection rate of both vertical and furcation defects. Calculus deposits can also be detected by radiographs. Depending on the radiographic projections, the amount of calculus seen on the images varies. 24 Panoramic radiographs were the least effective at detecting calculus in the anterior region while anterior bitewings and periapicals seem to have a better detection rate. Although calculus detection improved significantly with the aid of radiographs, Buchanan and colleagues have found that radiographs are highly specific with limited sensitivity (Buchanan et al. 1987). Clinical detection of subgingival calclus still depends on tactile sensing, but this technique has a low inter-rater agreement. In general, periapical radiographs can detect more furcation defects, vertical bone defects, sites of early bone loss and calculus than panoramic views. Sometimes, defects picked up by panoramic projections may not be a subset of those found by periapical views (Tugnait et al. 2000). Thus for periodontal assessment, a panoramic radiograph should be supplemented with periapical films in areas where image quality is poor. A paper published by Tugnait (Tugnait et al. 2000) and colleagues compared features of periodontal significance that can be detected on four radiographic projections: periapical, horizontal bitewing, vertical bitewing, and panoramic film. A table from the paper that summarizes different dental features viewable by these four projections is shown on the following page: 25 Table 1. Comparison of 4 radiographic projections (adopted from Tugnait et al 2000) It is surprising that many simple radiographic parameters (linear measurement of bone level, defect angle, presence of alveolar lamina dura, and others) are not utilized consistently in periodontal diagnosis. Currently, the standard use of radiographs is a mere review of these images, rarely supported by a magnifying glass, a ruler, or other types of more sophisticated analysis to extract data. In contrast, 26 probing depth, gingival recession, and clinical attachment level are noted at 4-6 sites per tooth. The changes in mm readings of probing depth may represent the progression or reversion of disease, but they can also represent changes in gingival inflammation or changes in applied probing force (Bragger et al. 2005). More information can be utilized from existing technology to complement clinical signs to provide a more accurate diagnosis and treatment objectives of periodontal disease. Simple, low-cost changes in current radiographic procedures can have a major impact on the value of radiography. Prescribing the appropriate type and number of radiographs is important for optimizing the impact of radiographs on treatment and patient outcome. Most clinicians are proficient in recognizing radiographic features of anatomy and pathology, but the information embedded in the relative location of image features under different projection conditions is often underutilized (Ludlow et al. 1995). The ability to capture dental radiographic images in a digital format has recently motivated scientists to take a new look at existing diagnostic needs and to study novel approaches to address these needs. One approach is to develop image processing techniques to characterize radiographic features in ways previously not possible. Examples include characterization of the structure and complexity of the radiographic trabecular pattern and computer-aided detection and quantification of osseous changes. Another approach is to take advantage of the ability to digitally 27 combine multiple conventional images in order to synthesize new ones. When two images with identical projection angles are combined, a subtraction or addition image can be made. When more than two images with different projection angles are combined, a set of tomosynthic views can be used to provide some 3D information (Mol 2004). Fractal Analysis Background and History Fractals are unusual geometric structures that can be divided into smaller parts, each of which resembles the original object. True fractal objects have infinite detail with a self-similar structure that occurs at different levels of magnification. Fractals have been applied in science, technology, and computer-generated art. They can be used to analyze many biological structures not amendable to conventional analysis. The conceptual roots of fractals can be traced to measurement of the size of objects for which traditional definitions based on Euclidean geometry and calculus do not work (Wikipedia 2006). The idea of “recursive self-similarity” was first developed by the philosopher Leibniz in the 17 th century. In 1872, Karl Weierstrass found a function that is 28 everywhere continuous but nowhere differentiable; the graph of this function is now considered a fractal. In 1904, Helge von Koch provided a more geometric definition of a similar function which is now called the Koch snowflake. The idea of self- similar curves was taken further by Paul Pierre Levy who described a new fractal curve, the Levy C curve, in his 1938 paper Plane or Space Curves and Surfaces Consisting of Parts Similar to the Whole. Iterated functions in the complex plane had been studied in the late 19 th and early 20 th centuries by Henri Poincare, Felix Klein, Pierre Fatou, and Gaston Julia. Finally, the term “fractal” was coined from the Latin word fractus, meaning “broken” or irregular, by Benoit Mandelbrot in 1975. The defining characteristics of fractals are hard to condense into a mathematically precise definition. Mandelbrot defined a fractal as a “set for which the Hausdorff- Besicovitch dimension strictly exceeds the topological dimension” (Wikipedia 2006). Fractals can be grouped into three broad categories based on how they are defined or generated: (1) iterated function systems, which have a fixed geometric replacement rule; (2) escape-time fractals, defined by a recurrence relation at each point in space; (3) random fractals, generated by stochastic processes. Fractals can also be classified according to their self-similarity property: (1) exact self-similarity, with identical appearance at different scales and often defined by iterated function systems; (2) quasi-self-similarity, a loose form of self-similarity which has fractal appearance approximately at different scales. This type of fractal contains small copies of the entire fractal in degenerate and distorted form and is defined by 29 recurrence relations; (3) statistical self-similarity, the weakest type of self-similarity where the fractal has numerical measures preserved across scales. Most reasonable definitions of fractal imply some form of statistical self-similarity (Wikipedia 2006). A fractal object will show self-similarity over many scales of observation, from full- sized object down to the microscopic level. For example, the Sierpinsky triangle below is composed of four triangles, each of which is composed of four smaller triangles and so on. Figure 1. Sierpinsky triangle Another property of a fractal object is the lack of a well defined scale. For example, a cloud tends to look very similar despite its size or the observer’s distance. It is difficult to convey the size without some external reference (Richardson et al. 2000). In addition, the perimeters of fractals are indeterminate because the measured perimeter changes according to the length of the measuring stick being used. Because true fractals have infinite granularity, no natural objects can be included in this category. However, many natural objects display fractal-like properties across a 30 limited range of scales. These naturally occurring fractals, such as snowflakes, clouds, and blood vessel networks, have upper and lower cut-offs separated by several orders of magnitude. In nature, trees and ferns have fractal-like properties and can be modeled on a computer using a recursive algorithm: a branch from a tree or a frond from a fern is a miniature of the whole object (Wikipedia 2006). Fractal Dimensions Most people are familiar with traditional Euclidean geometry, which describes the three spatial dimensions that we live in and which includes circles, rectangles, and ellipses. These dimensions, known as topological dimensions, are always whole numbers and are used to describe the shape and position of objects. However, there are some geometric objects that cannot be described well with Euclidean geometry. Descriptions of these complex objects are often estimates of how closely they resemble some known Euclidean objects. Benoit Mandelbrot formulated the idea of a fractional or fractal dimension, which exists somewhere between the usual topological dimensions (Richardson et al. 2000). Thus, he was able to describe the complexity of an object by a number known as the fractal dimension. The mathematician Lewis Fry Richardson was one of the first people to come up with the estimation of the fractal dimension for 2-D objects. Richardson noticed that the length of the coastlines was dependent upon the length of the measuring sticks 31 used. If a 1-kilometer-long measuring stick was used, the measured perimeter would be less than if a 1-meter-long measuring stick was used. A 1-kilometer-long measuring stick would miss fine details such as small inlets and bays while a 1- meter-long measuring stick would be able to resolve this issue. Based on this, the perimeter of the coastline would increase proportionately with the decreasing size of the measuring sticks. When the log of the perimeter was plotted against the log of the length of the measuring stick, a straight line could be fitted into these points. This log-log plot, also called the Richardson plot, would yield the fractal dimension in its slope (Mandelbrot 1983). The fractal dimension (D f ) is calculated by the least squares linear regression analysis from the Richardson plot, which has the slope of 1-D f. All fractal analyses use log-log plots to determine fractal dimension. If the linearity or scale invariance extends over a sufficient range of scale, the material of interest can be considered fractal (Avnir et al. 1998). In theory, the perimeter of a true fractal object will increase infinitely as the length of measuring sticks get smaller. However, if the points on the log-log graphs do not provide linearity but could be approximated on a straight line, the fractal dimension can still be considered a valid measurement of complexity and is known as the effective fractal dimension; this applies to many biological systems that are visualized on 2-D images (Vicsek et al. 1990). The perimeter of a natural fractal will not continue to increase to infinity with 32 increased resolution but will gradually reach a constant. This is due to the outline being bounded in its relative fractal behavior. The outline of the boundary will become Euclidean when the length of the measuring stick reaches a critical value. In Kaye’s book, A Random Walk through Fractal Dimensions, it is suggested that the range of the length for the measuring tool should not be less than 0.02 or greater than 0.3 of the maximum projection of the object because passing the two extremes, the outline of the object became Euclidean (Kays 1994, Parkinson 1992). In other word, the lower bound of the measuring stick should be about the magnitude of the smallest feature of interest, and the upper limit should not surpass the largest feature of interest. Fractal objects have non-integer dimensions, such as 1.4 and 2.6, and they are always smaller than the dimension they exist in. For example, a fractal drawing on a piece of paper has a fractal dimension smaller than that of the paper. In the figure below, each of the two objects has a topological dimension of one. Nonetheless, the more complex they are, the more they tend to fill the space. The amount of space filled by one of these objects is represented by the fractal dimension or fractal index (D f ), which can be thought of as a "filling factor." 33 (A) (B) Figure 2. (A) a circle (B) a line. Both the objects have fractal dimension of 1. Both the circle and the line above have a fractal dimension of 1 while the more complex Koch curve shown below has a fractal dimension of 1.26. Figure 3. Koch curve When a structure fills all available space on a plane, such as the square below, its fractal dimension is 2 (Richardson et al. 2000). Figure 4. A solid square 34 Different Methods of Fractal Analysis There are two ways to measure the fractal dimension of a complex object: manual techniques or computerized image analyzers. The manual technique involves using calipers with a varying gap around an outline of the object. To determine the fractal dimension, D f , a ruler of decreasing size n is used to measure the boundary of an image. The perimeter of an object equals the size of the ruler times the number of steps taken to trace the image. The perimeter is a function of the span of the caliper used in the measurement and is not a stable value but increases as caliper span decreases (Fernandez et al. 2001). An example from a paper published by Fernandez and Jelinek is shown below: Figure 5. Caliper method for ascertaining the boundary length of an image. (A)Measuring the length of the coastline of the Australian continent. (B) Graph of resulting log–log plot. 35 Another manual technique for measuring the perimeter of complex shapes involves using circles of varying diameters placed on the boundary. This is known as Minkowski’s sausage logic. This method places circles of varying size around the boundary of the object. The perimeter of the profile is calculated as the diameters of the circle times the number of circles used. The perimeter would increase as the diameter of circles decreases, similar to the caliper method (Parkinson 2002). Figure 6. Minkowski’s sausage logic to estimate the perimeter of complex shapes. This is adopted from Kaye BH, A random walk through fractal dimensions. VCH Weinheim 1994. In the 1970s, the rapid advances in computer technology allowed researchers to automate fractal analysis. Two-dimensional images of complex objects are converted into a digital array, with each pixel in the array having a number representing its light intensity, which ranges from 0 (black) to 255 (white). To simplify computational processes, colored images are often changed into binary image with only black and white information, meaning that each pixel can only have one of the two values, on or off (Parkinson 2002). 36 An adaptation of the Minkowsk sausage technique, called the box-counting method, is one of the most popular methods for calculating fractal dimension of complex objects. The fractal dimension is obtained by dividing the Euclidean space containing the image into a grid of boxes of size r, with the initial box size being the size of the image. The length r is made progressively smaller and the number of boxes, N(r) covering the object is then counted. The log-log graph of N(r) versus r is plotted. The fractal dimension is calculated through the slope of the graph (Fernandez et al. 2001). An example is shown below (Richardson et al. 2000): 37 Box Size n 1 6 1/4 9 1/16 18 1/256 59 Figure 7. (A), (B), (C) grids of different dimensions were overlaid on top of the image of interest. (D) A table of box size vs. number of boxes needed to cover the image on the left; on the right the Richardson plot provides the fractal dimension via the slope value. (A) (B) (C) (D) 38 Applications of Fractal Analysis Fractal analysis is used widely in physical and material science, which include aerosol particle dynamics, crystallography, fine particle science, geology, geography, hydrodynamics, metallurgy, petrology, polymer science, profilometry, thermodynamics, and volcanography. Fractal analysis has an important role in developing our understanding of the complex systems that are studied by material scientists (Parkinson 2002). In medicine, fractal analysis has been used to describe the morphological complexity of many systems, such as pulmonary blood flow, cardiac blood flow, renal vasculature, cell morphology, cell junctions, cytoskeletal morphology, breast parenchyma, liver parenchyma, nodular lung disease, tumor angiogenesis, pigmented skin lesions, fungal hyphae, prosthetic wear particles, and other biological entities. Many studies have used the fractal dimension to describe the complexity of the normal and to distinguish between the normal and diseased state. Fractal analysis is an additional objective tool in describing biological systems and has the advantage of being a non-invasive technique for clinical studies (Parkinson 2002). . Fractal analysis is usually done on digitized images, which are processed into binary format to outline the shape of the object before the analysis. The box-counting method is the most widely used and most suited for analysis of binary images. The 39 examples of biological systems mentioned above are only a small number in this growing field. Studies employing traditional Euclidean geometry could be inaccurate and unreliable; the fractal technique is a new approach to analyzing complex biological systems. Trabecular Bone and Fractasl Many biological structures can be modeled on a computer with simple shapes such as lines, circles, spheres, and simple polygons in order to allow estimation of their intrinsic properties. For example, the earth could be modeled as a sphere, while an artery can be modeled as a hollow cylinder. However, there are many complex biologic structures that cannot be modeled by simple shapes such as these. One of the most common complex structures is the branching pattern of many biological systems. Branching patterns in the human body include arteries, veins, nerves, the bundle of His, parotid gland ducts, the bronchial tree, and trabecular bone (Richardson et al. 2000). There are two types of quantitative analyses that are routinely performed on the histological sections of trabecular bone: (1) dynamic histomorphometry, which studies the metabolic state of the bone and is used to detect metabolic disorder; (2) structural analysis, which applies measurement of the area and perimeter of the bone to a mathematical model to yield structural parameters, such as bone volume/total 40 volume, bone surface/total volume, bone surface/bone volume, trabeculae number, etc (Parkinson 2002). Many researchers have tried to model the bone to study its breaking strength. Although they have modeled breaking strength as a function of bone mineral density, there are other biological variations in breaking strength in subjects with similar bone mineral density. Some clinical observation has shown that bone mineral density measured by dual-energy x-ray absorptiometry (DXA) is not a perfect predictor of fracture risk. Research has shown that a given volume of mineralized bone can be distributed in many ways within a given volume of tissue. The pattern of bone distribution greatly influences the mechanical integrity of the skeleton. Better understanding of the trabecular bone architecture is needed to determine its role in an individual’s fracture risk (Parkinson 2002). This has inspired researchers to seek other models of bone strength, such as how trabeculae are arranged in the bone. Trabecular bone has a branching pattern that exhibits fractal properties, such as self-similarity and lack of well defined scale (Parkinson et al. 1994). The trabeculae and the marrow spaces between them appear to be very similar despite different magnification factors. Also, if the perimeter and area of histological slices of cancellous bone is measured at an increasingly higher magnification, the measured perimeter will increase while the area remains relatively 41 constant. Thus, one way to study the branching pattern of the trabeculae is to examine its fractal index (Richardson et al. 2000). Normal bone can be modeled at two extremes: a hollow cylinder of bone and a solid cylinder: (A) Bone with no trabeculae ("osteoporosis") (B)Bone with solid center ("osteopetrosis") Figure 8. Extreme examples of the bone: (A) hollow bone; (B) solid bone. When calculating the fractal index of the two bone slices above, one would measure a fractal index of 1.0 for the hollow bone and 2.0 for the solid bone. The fractal dimension for normal bone can be found somewhere in the range 1.7 to 1.8 (Richardson et al. 2000). The early studies of fractal analysis were concerned with establishing methodology or determining if trabecular bone is considered fractal in nature. Recently there have been numerous studies that deal with the differences of trabecular bone between normal and diseased groups and between young and old groups (Parkinson 2002). Our study is aimed at examining the relationships between the fractal dimension and 42 features in trabecular bone, in order determine the effect of periodontal disease on the trabecular bone pattern. 43 Chapter 2: Methodology Sample Selection After obtaining Institutional Review Board approval (UP-05-00078), dental charts were reviewed from the University of Southern California School of Dentistry (USCSD) until 36 adult subjects were identified in each of the 3 categories: healthy (n=36), moderate periodontitis (n=36), and severe periodontitis (n=36). The inclusion criteria were established as the following: (1) diagnostic periapical radiographs were taken at the USC School of Dentistry; (2) written periodontal diagnosis was present; (3) the health survey included medical history (e.g. high blood pressure, angina, heart attack, stroke, diabetes, rheumatoird arthritis, cancer, glaucoma, and others), basic demographic information (birth date and sex), selected drugs (blood pressure medication, digitalis, indocin, non-prescription pain medication), personal habits (cigarette smoking, alcohol consumption), and menstrual and reproductive history, such as estrogen replacement therapy. Group Classification The healthy group consisted of patients with less than 3mm pocket probing depth and no other periodontal problem such as attachment loss. The moderate periodontitis group consisted of patients with 3-4mm of attachment loss. The severe 44 periodontitis group consisted of patients with > 5mm of clinical attachment loss and many involved teeth had guarded to poor prognosis. Within each periodontal group, male and female subcategories were formed to study the effect of gender. Image Preparations Periapical radiographs were digitized into BMP format at a resolution of 600 dpi (Epson Expression 1680, Nagano, Japan). A digitized example is shown below: Figure 9. An example of the full mouth radiographs scanned The radiographs were produced by certified radiology technicians in the USC radiology department. Parallel techniques at 70kVP and 7mA were used. Films were processed in an automatic film processor. Two regions of interest were selected for this study: (1) a mandibular anterior area and (2) a mandibular posterior area. The first region of interest (ROI) was selected from one of the four periapical films of the mandibular anterior teeth: the largest rectangular region of interest was 45 selected (1) horizontally between mesial of tooth #22 and mesial of tooth #27; (2) vertically from the apices of the teeth to the border of the image or a major structure, such as mandibular symphsis. Figure 10. An example of a region of interest selected in the mandibular anterior region A second region of interest was selected from posterior periapical radiographs: the largest rectangular ROI was selected (1) horizontally from the mandibular 1 st molars to the terminal molars or the border of the image; (2) vertically from the apices of the molars to the border of the image or a major structure, such as mandibular canal. The posterior ROIs were selected mainly from the right side unless there were problems obtaining bone images or unless there was a possibility that bone integrity might be affected from iatrogenic means such as endodontic work or large carious 46 lesions. In those cases, ROIs were selected from the left side. Only one fractal value was obtained for each patient. Figure 11. An example of a region of interest selected in the mandibular posterior region. Because some patients did not have mandibular molars and some full mouth radiographs did not include bones apical to the mandibular first molars, the sample size for the posterior ROIs was reduced. Furthermore, if some mandibular molars had previous endodontic work, the data was discarded due to the possibility of some effects on the adjacent bone integrity. The ROIs were selected in the apical region because the analysis requires large area of uninterrupted trabecular bone. Also, for moderate and severe periodontitis, the disease region is relatively close to the root apex. Adobe Photoshop was used to crop regions of interest. Parameters inherent to the patients and the capture of images led 47 to different ROI sizes. Tooth size, the location of major structures, the angulations of radiographic projection, and the distance of radiographic films to the teeth affected the size of the ROI. The following image processing, modified from White’s paper (White et al. 2005), was performed on each ROI image to remove low frequency noise: (1) a 10-pixel Gaussian filter was applied to each image to create a blurred version of the original image; (2) the blurred image was subtracted from the original image; (3) the resulting image was normalized by setting the intensity mean to 128, the center of the intensity range for an 8-bit image. This process allowed each image to have a uniform density on a scale much larger than the size of individual trabeculae. Figure 12. Steps used in image processing. (A) Original dental radiograph in anterior mandible. (B) Blurred image using a Gaussian filter with a sigma of 10 pixels. (C) Image of original radiograph made uniform in overall lighting intensity by subtracting blurred image B from original A. The density-corrected image was converted to a binary format of black and white, making it easier to recognize the trabeculae and marrow spaces. ImageJ (Rasband 48 2005 and Abramoff et al. 2004 ), a public software distributed by the National Institute of Health (NIH), was used for the binarization process. The threshold level for the binary decision was determined by analyzing the histogram of the entire image. The following figures show how to convert grayscale image into binary format in ImageJ and what a converted image looks like. Figure 13. ImageJ software option that converts images to binary format. 49 Figure 14. A binary image, derived from the figure 12(c) using ImageJ software. 50 Fractal Analysis After correcting for lighting irregularity and binarizing each image, fractal analysis from ImageJ was applied to quantify density of the trabecular bone pattern. A square mesh or grid of various sizes, S, was placed over the ROI, and the number of boxes N(s) containing trabeculae was counted with each changing box dimension S. The fractal dimension (D) was calculated by creating a Richardson plot of N versus S and solving for the slope of the linear regression, according to the formula: This algorithm was repeated for grids of squares with side-lengths 2,3,4,6,8,12, and 16 pixels, determined by Kays’ recommendation that grid size should fall between 2% and 30% of maximum trabeculae projection. We estimated the relevant trabeculae size to be about 0.1mm to 2mm. Passing either extreme, the outline of the object becomes Euclidean (Kays 1994, Parkinson et al. 2000) In other words, the lower bound of the measuring stick should be near the magnitude of the smallest feature of interest and the upper limit should not surpass the largest feature of interest. 51 Figure 15. ImageJ menu for box-counting method to estimate fractal dimension Figure 16. An example of the results from the box-counting method in ImageJ. 52 Because there was no preferred origin for the grids of boxes, multiple measures for N(s) were computed for different mesh origins. For example given a fixed box size, the entire image was covered with a grid of boxes and the total number of boxes with binarized trabeculae present was counted. The grid was then shifted to all possible offsets, and the number of boxes containing trabeculae was counted each time, yielding an average for that fixed box size. Figure 17. Example of how grids were overlaid on the object of interest and shifted to sample all possible offsets. The first set of boxes could begin at coordinate (0,0), at location A. Then the 2 nd set of boxes could begin at coordinate (1,0), at location B, and so forth in order to obtain an average for that box size. An excel sheet was generated to record the fractal dimension of each subject at each location with his identifier, age, and medical information. 53 Statistical Analysis Statistical tests were performed using SPSS 10.1 and Microsoft Excel. Descriptive statistics (e.g. mean, standard deviation, minimum, maximum, variance, sample size, and standard error of mean) were calculated for different periodontal groups and for males and females in each group. The null hypothesis was that the fractal dimension is the same in subjects with or without periodontal disease. One-way analysis of variance (ANOVA) was used to compare fractal dimensions among the three periodontal groups; Tukey Honestly Significantly Different (HSD) post-hoc tests were used to determine pair-wise significance. Student’s t-tests measured differences between males and females in each periodontal group (p-value, 0.05). Age Correlation Because the three periodontal groups studied had subjects with varying ages, a graph was constructed to compare the effect age on the fractal dimension. The slope and correlation factors were calculated using Microsoft Excel. Sensitivity and Specificity of the Fractal Analysis In order to determine the usefulness of a diagnostic test, clinical research often investigates the statistical relationship between the test results and the presence of disease. Subjects were classified into two groups: the healthy group and the 54 periodontal group, with the latter consisting of both moderate and severe periodontitis patients. A receiver-operating characteristic (ROC) curve was used to provide a global view of the relationship between sensitivity and specificity for our fractal tool. ROC curves for each pair of groups were also plotted 55 Chapter 3: Results The following table shows the fractal data for all subjects, along with age, gender, and medical health history. 56 Patient Identifier Age Gender Medical condition FD Ant FD post 1 34 Male healthy 1.7678 1.7298 2 50 Male HBP, TMJ, chronic neck pain, headache, rheumatoid arthritis, weakness, anxiety, depression, mental ill, insomnia, allergy 1.8111 1.5802 3 25 Female healthy 1.8135 1.7924 4 24 Female TMJ 1.7892 1.7293 5 25 Female healthy 1.7331 1.4915 6 40 Female HBP, diabetes 1.7159 1.4458 7 28 Female allergy 1.7722 1.409 8 38 Female chronic pain 1.8191 1.7124 9 23 Female` anemia 1.7512 1.7695 10 49 Female healthy 1.7759 1.7947 11 24 Female anxiety 1.7915 1.7335 12 78 Female osteoarthritis 1.7585 1.571 13 45 Male Hep B, asthma, frequent hunger 1.8619 1.7327 14 31 Male chronic headache 1.7578 1.7649 15 28 Female healthy 1.5892 1.5225 16 20 Male TMJ, neck pain 1.7441 1.7338 17 33 Female healthy 1.6558 1.7918 18 26 Female healthy 1.857 1.7721 19 18 Female healthy 1.8484 1.6886 20 21 Female healthy 1.6941 1.6984 21 31 Male depression, mental health 1.7345 1.5548 22 19 Male TMJ 1.6978 1.6348 23 20 Female healthy 1.7165 1.6866 24 36 Male TMJ 1.7837 1.7092 25 19 Male healthy 1.832 1.6571 26 41 Male headache 1.6811 1.608 27 49 Male HBP 1.833 1.6451 28 26 Male healthy 1.7805 1.5656 29 58 Female healthy 1.6007 1.4398 30 26 Female healthy 1.6719 1.5584 31 53 Male hay fever, allergy 1.7551 1.598 32 32 Male healthy 1.5187 1.737 33 28 Male healthy 1.5684 1.704 34 23 Male TMJ, insomnia 1.6668 1.2376 35 34 Male healthy 1.6700 1.671 36 29 female healthy 1.7125 1.1262 Table 2. Fractal dimensions for subjects with healthy gingiva (control group) 57 Patient Identifier Age Gender Medical condition FD Ant FD post 101 66 Male HBP, Hep A, hearing problem 1.7500 1.2215 102 58 Male osteoarthritis 1.6440 1.6407 103 63 female rheumatoid arthritis 1.5727 NA 104 53 Female diabetes 1.7169 1.6674 105 41 Female frequent thirst 1.7461 1.6176 106 37 Female healthy 1.5755 1.5199 107 56 Female anemic, spinal cord injury 1.5514 NA 108 48 Male healthy 1.5662 NA 109 47 Female high cholesterol 1.7872 1.6971 110 75 Female healthy 1.6279 NA 111 59 Male rheumatoid arthritis, fatigue, anxiety, depression, mental illness 1.7467 1.4352 112 53 Male healthy 1.7205 1.3986 113 60 Female used phen-pham 1.6839 1.5615 114 59 Female HBP, anxiety 1.6714 1.6867 115 77 Male diabetes 1.8043 NA 116 64 Male HBP, bypass surgery, hay fever 1.3928 1.2033 117 69 Male prostate cancer, radiation therapy, visual and hearing impairment 1.4628 1.3207 118 49 Female heart murmur, anemia 1.4097 1.2873 119 56 Male high BP, cholesterol, weakness, visual impairment, anxiety, mental, insomnia 1.6822 1.6240 120 68 Male HBP 1.7522 1.5304 121 42 Female healthy 1.6766 NA 122 76 Male HBP, hip replacement 1.5650 1.5811 123 70 Female HBP, Increase cholesterol. Thyroid disorder, osteoarthritis, anxiety, asthma 1.7037 NA 124 42 Male healthy 1.7309 1.7141 125 68 Female HBP, heart murmur, increased cholesterol, diabetes, joint replacement, osteoarthritis, night sweat 1.6454 1.6035 126 58 Male heart attack, increased cholesterol 1.5884 NA 127 55 Female healthy 1.7987 1.6133 128 67 Male healthy 1.7663 NA 129 53 Male HBP, diabetes 1.6439 1.7485 130 78 Female HBP, irregular heart beat, knee joint replaced, osteoarthritis, visual impairment, anxiety 1.7131 1.6839 131 46 Male diabetes 1.7877 1.7422 132 72 Female rheumatoid arthritis 1.6135 NA 133 75 Male increased cholesterol, lymphoma, radiation therapy, glaucoma, hearing problem 1.7332 1.7594 134 50 Female HBP, murmur, high cholesterol, thyroid disorder, osteoarthritis, HepC, anxiety 1.6593 1.5556 135 62 Female healthy 1.6907 1.4504 136 58 female HBP, diabetes, cancer, insomnia 1.5638 1.5021 Table 3. Fractal dimensions for subjects with moderate periodontitis 58 Patient Identifier Age Gender condition FD Ant FD post 201 50 Male healthy 1.6729 1.611 202 39 Female dizzy, insomnia, anxiety 1.736 1.8611 203 50 Female use phen-phem 1.5662 1.664 204 37 Male healthy 1.6985 1.7571 205 33 Male Down-syndrome 1.6769 1.7823 206 41 Female rheumatoid arthritis 1.5586 1.4995 207 49 Male healthy 1.6537 1.6044 208 49 Female healthy 1.7253 1.6238 209 65 Male HBP, diabetes 1.7249 NA 210 62 Male HBP 1.6403 1.8361 211 45 Male healthy 1.6991 1.7193 212 48 Female osteoarthritis, high cholesterol, anxiety, insomnia, night sweat 1.4575 1.4983 213 58 Female heart attack, TMJ 1.6834 1.3229 214 48 Male healthy 1.7708 1.6451 215 39 Female headache 1.4584 1.1023 216 61 Male high cholesterol, diabetes, HTN 1.7497 1.604 217 66 Male asthma 1.7389 1.6831 218 56 Female HBP, seizure 1.6948 1.7440 219 60 Male healthy 1.5212 1.4985 220 38 Male healthy 1.5986 1.4403 221 38 Female heart murmur 1.4936 1.5164 222 61 Female weakness, glaucoma, hearing impairment, night sweat 1.5759 1.694 223 52 Female type I diabetes 1.597 1.78513 224 52 Male healthy 1.6108 1.6019 225 42 Female STD, night sweat 1.5647 1.3439 226 78 Male HBP, heart problem, diabetes 1.4987 1.1737 227 63 Male healthy 1.5719 1.6502 228 47 Female HBP, diabetes, codein allergy 1.767 1.3819 229 46 Male knee osteoarthritis, ulcers, pen allergy 1.6637 1.3637 230 65 Male HBP, heart attack, surgery, angina, increased cholesterol, weakness, visual/hearing impairment, ulcers 1.7889 NA 231 44 Male high cholesterol, TMJ, glaucoma 1.7354 1.6754 232 64 Male dizzy 1.4965 1.5048 233 63 Male HBP, increased cholesterol, type II diabetes, 1.7308 1.7984 234 59 Female asthma, ulcers, aspirin allergy 1.582 1.8578 235 62 Male Hepatitis 1.5679 1.8364 236 60 Female rhematoid arthritis, visual impairment 1.6424 1.7439 Table 4. Fractal dimensions for subjects with severe periodontitis 59 Data set description 108 Subjects had periapical radiographs of the anterior mandible available for analysis. The mean age for all three combined groups was 48 years; the mean age for the control (healthy) subgroup was 33 years; the mean age for the moderate periodontitis subgroup was 58 years; the mean age for the severe periodontitis subgroup was 53 years. Patient Group N Mean Age SD Age Control 36 33.2 13.1 Moderate Periodontitis 36 58.2 11.1 Severe Periodontitis 36 52.5 10.6 Combined 108 48.2 15.9 Table 5. Descriptive statistics for patients’ ages – ant mandible The sex distribution of each group is shown in the following table. Patient Group # male # females total Control 18 18 36 Moderate Periodontitis 17 19 36 Severe Periodontitis 21 15 36 Total 56 52 108 Table 6. Description of patient’s gender – ant mandible Because some subjects did not have diagnostic radiographs for the posterior molars, there were only 96 samples available for the analysis of the posterior mandible. The sample for the entire posterior group had a mean age of 47 years: the mean age for the control subgroup was 33 years; the mean age for the moderate periodontitis subgroup was 57 years; the mean age for the severe periodontitis subgroup was 52 years. 60 Patient Group N Mean Age SD Age Control 36 32.9 13.1 Moderate Periodontitis 26 57.8 10.8 Severe Periodontitis 34 51.8 10.5 Combined 96 46.3 15.7 Table 7. Descriptive statistics for patients’ ages – posterior mandible The sex distribution of each group is shown in the following table. Patient Group # male # females total Control 17 19 36 Moderate Periodontitis 13 13 26 Severe Periodontitis 19 15 34 Total 49 47 96 Table 8. Description of patient’s gender – posterior mandible Fractal dimensions in the lower anterior region The average fractal dimension for the control (1.74 ± 0.083), moderate-periodontitis (1.66 ±0.104), and severe-periodontitis (1.64 ± 0.095) groups was measured in the mandibular anterior region (table 9, figure 18). Group N Mean SD Std. Error Min Max Healthy Gingiva 36 1.74 .083 .014 1.52 1.86 Moderate Periodontitis 36 1.66 .104 .017 1.39 1.80 Severe Periodontitis 36 1.64 .095 .016 1.46 1.79 Total 108 1.68 .103 .010 1.39 1.86 Table 9. Descriptive statistics of measured fractal dimensions- anterior mandible 61 Fractal Dimensions of the lower anterior region 1.74 1.66 1.64 1.4 1.45 1.5 1.55 1.6 1.65 1.7 1.75 1.8 1.85 healthy Moderate severe Periodontal groups fractal dimension Figure 18. Fractal dimensions of the three periodontal groups in the lower anterior area According to the Tukey HSD one-way ANOVA post-hoc tests, significant differences in fractal dimensions were measured between the control and moderate- periodontitis groups (p<0.01) and between healthy and severe-periodontitis groups (p< 0.001) (Table 10, 11). Healthy periodontal patients had higher fractal dimensions. The result allowed us to reject the null hypothesis and conclude that fractal dimension was not the same in subjects with or without periodontal disease in the mandibular anterior region. 62 Grouping Sum of Squares Deg. Freedom Mean Square Significance Intergroup 0.199 2 0.100 3.66e-5 Intragroup 0.929 105 0.009 NA Total 1.13 107 NA NA Table 10. Statistics for ANOVA test- anterior mandible GROUP A GROUP B Mean Difference (A-B) Sig. Healthy Moderate 0.077 0.002* Healthy Severe 0.100 0.000* Moderate Severe 0.023 0.552 Table 11. Tukey HSD post-hoc test comparisons. (*The mean difference is significant at the 0.05 level.) Fractal dimensions in the lower posterior region The average fractal dimension for the control (1.63 ± 0.152), moderate-periodontitis (1.55 ±0.161), and severe-periodontitis (1.60 ± 0.192) groups was measured in the mandibular posterior region (table 12, figure 19). According to the Tukey HSD one- way ANOVA post-hoc tests, there is no significant differences in fractal dimensions among the three groups (table 14). For this reason the null hypothesis was not rejected, and we could not conclude whether fractal dimension is the same in subjects with or without periodontal disease in the posterior region. Group N Mean SD Std. Error Min Max Healthy Gingiva 36 1.63 .152 .025 1.13 1.79 Moderate Periodontitis 26 1.55 .161 .031 1.20 1.76 Severe Periodontitis 34 1.60 .192 .033 1.10 1.86 Total 96 1.59 .170 .017 1.10 1.86 Table 12. Descriptive statistics of measured fractal dimensions- posterior mandible 63 Fractal dimensions of the lower posterior region 1.63 1.55 1.60 1.20 1.30 1.40 1.50 1.60 1.70 1.80 1.90 healthy moderate severe periodontal groups fractal dimension Figure 19. Fractal dimensions of the three periodontal groups in the lower posterior area Grouping Sum of Squares Deg. Freedom Mean Square Significance Intergroup .086 2 .043 3.66e-5 Intragroup 2.669 93 .029 NA Total 2.755 95 NA NA Table 13. Statistics for ANOVA test- lower posterior region GROUP A GROUP B Mean Difference (A-B) Sig. Healthy Moderate 0.075 0.202 Healthy Severe 0.027 0.784 Moderate Severe 0.048 0.552 Table 14. Tukey HSD post-hoc test comparisons. (*The mean difference is significant at the 0.05 level.) 64 Fractal analysis as a diagnostic tool Clinical research often investigates the statistical relationship between symptoms, or test results, and the presence of disease in order to determine the usefulness of the diagnostic test. Chi-square analysis can be applied to the fractal data of the lower anterior region in the form of a 2 by 2 table in order to assess the statistical significance of the association between the trabecular bone pattern, the symptom, and the presence or absence of the periodontal disease under study. Because data from the lower anterior region provided statistical significance, we selected data from this area to analyze the sensitivity and specificity of the test. Fractal data was first converted into categorical data by the following method: subjects for the study were divided into two groups — a healthy group and a periodontal group, which included subjects with either moderate or severe periodontitis. The means for the two groups were calculated as shown below: GROUPS Mean N Std. DeviationVariance Healthy Group 1.74 36 .083 .007 Periodontitis Group 1.65 72 .099 .010 Total 1.68 108 .103 .011 Table 15. Descriptive statistics for 2 groups (healthy and periodontitis groups) in the lower anterior region. 65 The midpoint between the healthy and the periodontitis group means was found to be 1.69. Patients were described as healthy if they had a fractal dimension above 1.69 and described as having periodontal disease if they had fractal dimensions below 1.69. Figure 20. Method to assign subjects into two periodontal groups: healthy or periodontal disease Once this was accomplished, the fractal analysis as a diagnostic tool could be evaluated by creating a contingency table. A two way contingency table analysis (Pezzullo 2006) was used and the result is shown below: The sensitivity of this test is 0.611 and the specificity of the test is 0.750. . Periodontal Disease Healthy Group Totals D f < 1.69249 (Risk Factor Present or Dx Test Positive) 44 = a 9 = b 53 = r1 D f > 1.69249 (Risk Factor Absent or Dx Test Negative) 28 = c 27 = d 55 = r2 Totals 72 = c1 36 = c2 108 = t Confidence Level: 95 % Table 16. Observed contingency table (Pezzullo 2006) FD=1.69 Healthy group Periodontitis group Fractal Dimension 66 Type of Test Chi Square d.f. p-value Pearson Uncorrected 12.523 1 0.000 Yates Corrected 11.120 1 0.001 Mantel-Haenszel 12.407 1 0.000 Table 17. Chi-Square Tests (Pezzullo 2006) Type of comparison (Alternate Hypothesis) p-value Two-tailed (to test if the Odds Ratio is significantly different from 1): This is the p-value produced by SAS, SPSS, R, and other software. 0.000 Left-tailed (to test if the Odds Ratio is significantly less than 1): 1.000 Right-tailed (to test if the Odds Ratio is significantly greater than 1): 0.000 Two-tailed p-value calculated as described in Rosner's book: (2 times whichever is smallest: left-tail, right-tail, or 0.5) It tends to agree closely with Yates Chi-Square p-value. 0.001 Probability of getting exactly the observed table: (This is not really a p-value; don't use this as a significance test.) 0.000 Verification of computational accuracy: (This number should be very close to 1.0; the closer, the better.) 1.000000000000 Table 18. Fisher Exact Test (Pezzullo 2006) 67 Quantities Derived from the 2-by-2 Contingency Table Value 95% Conf. Interval Odds Ratio (OR) = (a/b)/(c/d) 4.714 1.956 11.323 Relative Risk (RR) = (a/r1)/(c/r2) 1.631 1.247 2.035 Kappa 0.319 0.146 0.455 Overall Fraction Correct = (a+d)/t 0.657 0.570 0.726 Mis-classification Rate, = 1 - Overall Fraction Correct 0.343 0.274 0.430 Sensitivity = a/c1 0.611 0.546 0.662 Specificity = d/c2 0.750 0.619 0.852 Positive Predictive Value (PPV) = a/r1 0.830 0.741 0.900 Negative Predictive Value (NPV) = d/r2 0.491 0.405 0.558 Difference in Proportions = a/r1 - c/r2 0.321 0.147 0.458 # Needed to Treat = 1 / Difference in Proportions 3.114 2.185 6.805 Absolute Risk Reduction (ARR) = c/r2 - a/r1 -0.321 -0.458 -0.147 Relative Risk Reduction (RRR) = ARR/(c/r2) -0.631 -1.035 -0.247 Positive Likelihood Ratio (+LR) = Sensitivity / (1 - Specificity) 2.444 1.434 4.486 Negative Likelihood Ratio (-LR) = (1 - Sensitivity) / Specificity 0.519 0.396 0.733 Diagnostic Odds Ratio = (Sensitivity/(1-Sensitivity))/((1- Specificity)/Specificity) 4.714 1.956 11.323 Error Odds Ratio = (Sensitivity/(1-Sensitivity))/(Specificity/(1- Specificity)) 0.524 0.738 0.340 Youden's J = Sensitivity + Specificity - 1 0.361 0.165 0.515 Number Needed to Diagnose (NND) = 1 / (Sensitivity - (1 – Specificity) ) = 1 / (Youden's J) 2.769 1.943 6.051 Forbes' NMI Index 0.094 0.019 0.200 Contingency Coefficient 0.322 0.154 0.437 Adjusted Contingency Coefficient 0.456 0.218 0.617 Phi Coefficient (= Cramer's Phi, and = Cohen's w Index, for 2x2 ) -0.360 -0.356 -0.362 Yule's Q = (a*d-b*c)/(a*d+b*c) = (OR - 1) / (OR + 1) 0.650 0.323 0.838 Table 19. Quantities derived from a 2-by-2 contingency table ( (Pezzullo 2006) 68 ROC Curve The ROC curve was constructed to assess the ability of the fractal tool to differentiate between healthy and periodontal patients. In this case, the area under the curve is 0.758 (figure 21) ROC Curve 1 - Specificity 1.00 .75 .50 .25 0.00 Sensitivity 1.00 .75 .50 .25 0.00 Figure 21. ROC curve: healthy vs. periodontal group When the ROC curve was plotted to compare among groups, the areas were 0.726 (healthy vs. mod perio), 0.791 (healthy vs. severe perio), and 0.577 (moderate vs. severe perio) (Figure 22) 69 (A) ROC Curve 1 - Specificity 1.00 .75 .50 .25 0.00 Se nsitivity 1.00 .75 .50 .25 0.00 (B) ROC Curve 1 - Specificity 1.00 .75 .50 .25 0.00 Sensitivity 1.00 .75 .50 .25 0.00 (C) ROC Curve Diagonal segments are produced by ties. 1 - Specificity 1.00 .75 .50 .25 0.00 Se n sitivity 1.00 .75 .50 .25 0.00 Figure 22. ROC curves for the lower anterior region: (A) healthy vs. moderate periodontitis group; (B) healthy vs. severe periodontitis group; (C) moderate vs. severe periodontitis group. The ROC results indicate that fractal analysis could be considered a fair to good diagnostic tool to differentiate between subjects with healthy and either moderate or severe periodontitis. In this study it was a poor tool to detect differences between the two types of periodontal conditions. Effects of age Anterior Mandible Since the three periodontal groups studied in the anterior mandible had subjects with age ranging from 18 to 78, a graph was constructed to compare the effect age on the fractal dimension. There did not seem to be much correlation between age and 70 fractal dimension, as only 6.64% of the variance in fractal dimension was explained by age (R 2 = 0.0664) Age vs. fractal dimension R 2 = 0.0664 y = -0.0016x + 1.7569 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 0 2040 6080 100 age fractal dimension Figure 23. Plot of fractal dimension in the lower anterior region vs. age Posterior Mandible When a similar graph (age vs. fractal dimension) was plotted in the posterior mandibular region, there was less correlation between age and fractal dimension as compared to the anterior mandible region. In this case only 2.03% of the variance in fractal dimension was explained by age (R 2 = 0.0203) 71 Age vs. Fractal Dimension -Post Manidble y = -0.0015x + 1.6692 R 2 = 0.0203 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 0 1020 30 4050 60 708090 Age Fractal Dimension Linear (Series1) Figure 24. Plot of fractal dimension in the lower posterior region vs. age Effects of gender Anterior Mandibular Region Because the data set combined males and females in each group, a study was designed to test the effect of gender on fractal dimension. The effect of gender on fractal dimension in the anterior mandibular area was examined within each group using a student t-test. P-values for each intra-group comparison were 0.79, 0.77, and 0.12 (Table 20,21,22). When data was combined from the three groups, P-value was 0.51. (Table 23) The data did not disprove the null hypothesis – that there is no statistical significant difference between gender and fractal dimension. 72 Male (n=18) Female (n=18) T-Test Mean 1.73 1.73 NA Variance 1.14e-2 5.33e-3 NA SD 1.07e-1 7.30e-2 7.90e-1 Table 20. Comparison of fractal dimension in the healthy group -- anterior mandible Male (n=17) Female (n=19) T-Test Mean 1.67 1.66 NA Variance 1.38e-2 9.13e-3 NA SD 1.17e-1 9.56e-2 7.74e-1 Table 21. Comparison of fractal dimension in the moderate periodontitis group -- anterior mandible Male (n=21) Female (n=15) T-Test Mean 1.66 1.61 NA Variance 7.82e-2 9.70e-3 NA SD 8.84e-2 9.85e-2 1.23e-1 Table 22. Comparison of fractal dimension in the severe periodontitis group-- anterior mandible Male (n=56) Female (n=52) T-Test Mean 1.68 1.67 NA Variance 1.13e-2 1.04e-2 NA SD 1.06e-1 1.02e-1 5.05e-1 Table 23. Comparison of fractal dimension in all groups combined -- anterior mandible Gender and Fractal Dimension in the mandibular anterior region 1.54 1.56 1.58 1.6 1.62 1.64 1.66 1.68 1.7 1.72 1.74 Healthy Male Healthy Female Moderate Perio Male Moderate Perio Female Severe Perio Male Severe Perio Female Categories Fractal Dimension (FD) Healthy Male Healthy Female Moderate Perio Male Moderate Perio Female Severe Perio Male Severe Perio Female 0.79 p=0.77 p=0.12 Figure 25. Effect of gender on fractal dimension in the mandibular anterior region 73 Posterior Mandibular Region The effect of gender on fractal dimension in the mandibular posterior region was also examined within each group using a student t-test. P-values for each intra-group comparison were 0.67, 0.53, and 0.53 (Table 24, 25, 26). When data was combined from the three groups, P-value was 0.74. (Table 27) The data did not disprove the null hypothesis – that there is no statistical significant difference between gender and fractal dimension. Male (n=18) Female (n=18) T-Test Mean 1.64 1.62 NA Variance 1.51e-2 3.15e-2 NA SD 1.23e-1 1.78e-1 6.73 e-1 Table 24. Comparison of fractal dimension in the healthy group – posterior mandible Male (n=17) Female (n=19) T-Test Mean 1.53 1.57 NA Variance 3.96e-2 1.32e-2 NA SD 1.99e-1 1.15e-1 5.33e-1 Table 25. Comparison of fractal dimension in the moderate periodontitis group – posterior mandible Male (n=21) Female (n=15) T-Test Mean 1.62 1.58 NA Variance 2.86e-2 4.86e-2 NA SD 1.69e-1 2.20e-1 5.25e-1 Table 26. Comparison of fractal dimension in the severe periodontitis group – posterior mandible Male (n=56) Female (n=52) T-Test Mean 1.60 1.59 NA Variance 2.76e-2 3.10e-2 NA SD 1.66e-1 1.76e-1 7.42e-1 Table 27. Comparison of fractal dimension in all groups combined – posterior mandible 74 Gender and Fractal Dimension 1.46 1.48 1.5 1.52 1.54 1.56 1.58 1.6 1.62 1.64 1.66 Healthy Male Healthy Female Moderate Perio Male Moderate Perio Female Severe Perio Male Severe Perio Female Categories Fractal Dim ension (FD) Healthy Male Healthy Female Moderate Perio Male Moderate Perio Female Severe Perio Male Severe Perio Female p=0.67 p=0.53 p=0.53 Figure 26. Effect of gender on fractal dimension in the mandibular posterior region 75 Chapter 4: Discussion An individual’s oral condition is a window to his systemic health, and studies have shown that severe oral infections, especially periodontal disease, in otherwise healthy individuals, appear to place these people at significantly increased risks for developing certain health problems such as stroke and myocardial infarction. Some studies have even indicated that the magnitude of negative effects to cardiovascular fitness from periodontal disease is as serious as smoking or high cholesterol (Wilson et al. 2003). It seems that patients with chronic periodontitis have elevated bacterial pathogens, such as P. gingivalis, B forsythus, and T denticola. Some of these pathogens could invade the epithelium or penetrate through periodontal lesions. Others create toxic reservoirs of bacterial lipopolysaccharide (LPS) and cause inflammatory reactions (Wilson et al. 2003). Studying the trabecular bone pattern in individuals with periodontal involvement could help us identify individuals at risk for systemic problems. Early diagnoses of periodontal disease could become a preventive model in medical therapy for systemic diseases. Fractal analysis, a quantitative method used to evaluate complex structures by examining elementary components, has been used to analyze biological images for the past several years. The aim of some of these applications was to assess changes in bone, to measure bone fragility, and to show the increased risks for fracture or osteoporosis. 76 The motivation for our study was based on the fact that periodontal disease could cause destruction of alveolar bone, changes in trabecular bone pattern, and possible loss of bone mineral density, which is to some extent similar to the effects of osteoporosis. Since fractal analysis has been used to describe the morphological complexity of many complex systems, it could be used as a tool to describe the trabecular bone pattern under different periodontal conditions. Because the analysis requires the use of quantitative imaging of the bones, it has the advantage of being non-invasive for many clinical studies. In addition, this study allows us to develop and implement a standardized protocol for fractal analysis of trabecular bone on dental radiographs. The purpose of these endeavors has been to develop morphological descriptors of bone quality that explain the properties of the cancellous bone structure under the effect of periodontal disease and possibly the effect of therapeutic agents on the diseased bone in the future. In the last few decades several efforts have been directed at the detection of trabecular pattern changes on dental radiographs. Tosoni and colleagues (Tosoni et al. 2006) used fractal analysis to study osteoporotic-associated bone density changes on panoramic radiographs. Yet, these investigators have used panoramic radiographs, instead of the higher-resolution periapical films, to detect trabecular pattern changes. The studies had high sensitivity but lower specificity which explained the lack of statistical significance in their results. In 2006, Jolley (Jolley et al. 2006) and colleagues showed that periapical radiographs could provide a reliable method for 77 determining fractal dimension to analyze changes in alveolar bone density in various bone diseases. There have been few studies that quantitatively analyzed trabecular bone pattern on radiographs under different periodontal conditions. Shrout (Shrout et al. 1998) used a caliper method of fractal analysis to compare the trabecular pattern differences among healthy and moderate periodontal patients. It is known that there are many other fractal techniques, such as the pixel-dilation method, mass-radius method, and the box-counting method. Different types of fractal techniques produce different fractal dimensions. We have recognized the difficulty in calculating and comparing fractal values among different researchers, but we were curious to see the trend of previous fractal studies, such as Shrout’s, when compared to another fractal analysis. The authors here decided to use one of the most common techniques, the box- counting method provided by ImageJ, to detect pattern changes induced by periodontitis. Our goal was to develop an additional protocol to quantitatively analyze trabecular bone pattern. In this thesis, two locations were selected to test the null hypothesis that fractal dimension is the same in subjects regardless of the periodontal condition. The fractal analysis was able to detect morphological differences in the trabecular bone pattern located in the anterior mandible between subjects affected and not affected by periodontal disease. However, the data showed no statistical significance in the 78 trabecular bone pattern among the three periodontal groups when analyzing the posterior mandibular region. The differences in the results at the two locations could be attributed to the fact that the lower anterior trabecular region has the least amount of overlap with other anatomical structures in comparison to the mandibular posterior area. In the mandibular anterior region, it is easier to obtain a larger region of interest, which would assist in obtaining a more accurate analysis. Furthermore, according to White et al, the lower anterior location is more suitable for analysis of trabecular pattern. The fractal results at the mandibular anterior region disproved our null hypothesis and indicated that fractal dimensions can detect differences in cancellous bone structure between healthy and periodontal patients. Although there is no statistical difference between subjects affected by moderate periodontitis and subjects affected by severe periodontitis, there is still a positive trend between periodontal condition and fractal index. Periodontal health seemed to be positively correlated to the fractal index: as periodontal health deteriorated, fractal index decreased. When the periodontium becomes less healthy due to periodontal involvement, alveolar bone loss occurs, and this affects trabecular bone pattern. It seems likely in this case that the trabecular arrangement becomes less complex and less space-filling, and therefore fractal dimension decreases with declining periodontal health. The relationship between fractal dimension and periodontal condition is similar to that found in Shrout’s caliper method of fractal analysis 79 When comparing the fractal index from the anterior region with that from the posterior area, a trend is established: the average posterior fractal dimension is consistently smaller than the anterior fractal dimension. Again, the results make intuitive sense: the mandibular posterior region has lower bone density than the lower anterior region. The bone in the posterior may be less compact and space filling, thus it has a lower fractal index. At this time there has been no consensus between various authors in the relationship between fractal dimension and trabecular bone complexity. Some findings support the idea that fractal dimension increases in the diseased, osteoporotic state. Many others support our finding that the diseased state reduces trabecular complexity and decreases fractal dimension. It is possible that both may be correct, depending on the diseases that affect trabecular bone and how they destroy the fine trabeculae in different parts of the body. Our periodontal diagnosis was based on clinical attachment and alveolar bone loss. It was difficult to obtain objective and quantitative measurements despite having calibrated clinical faculty members. In order to make the three categories more distinct, mild periodontitis with 1-2mm CAL was omitted from the study. Many subjects in the severe periodontal group had guarded to hopeless prognosis. Despite these distinctions, our results showed that there is no statistical difference between 80 the two periodontitis groups. A larger sample size may be required to validate the positive trend with statistical significance. In the present study, the region of interest (ROI) was selected below the apex of the mandibular anterior teeth. Fractal analysis required a large uninterrupted trabecular bone area for computation. In both moderate and severe periodontitis groups, tissue destruction is happening near our cropped ROIs and it was reasonable to expect trabecular pattern changes. Because of the difference in individual anatomy, different amounts of bone were available and this made it difficult to select ROIs with the same size. Despite the appeal of a fixed ROI size, in the end the authors chose to retain as much useful information as possible, rather than cropping to the smallest common size. In the future with higher resolution radiographs, we expect to obtain more data from each image and gain the ability to unify ROI size. This study did not detect statistically significant differences in fractal dimension between genders in either the anterior or posterior mandibular regions. While gender-dependent differences in iliac and vertebra cancellous bone have been reported, other studies have not detected any significant differences(19). Individual variances in mandibular size, shape, medical background, and dynamics of bone metabolism can negate gender specific factors. A larger sample size is needed to conduct a separate experiment for studying the effects of gender on trabecular bone architecture. 81 On average our periodontal groups were older than the controlled healthy group. However, when we studied the effect of age on trabecular bone pattern, age could only account for a minor percentage of the variance in fractal dimension. The differences found between healthy and periodontal groups in the mandibular anterior region in our study could not be attributed to the differences in age alone. It would be difficult to do a longitudinal study of the same individual with our fractal protocols. Since it is hard to select the same ROI in two images of the same anatomical region over a period of years, this is a limitation of our study. Techniques in image registration could solve this problem and make it possible to analyze trabecular bone in the same region. Optimizations to some of the image processing stages may still be possible: in order to correct for lighting irregularity, a Guassian filter with a sigma of 10 pixels was applied to each image. Although this filter was selected based on White’s paper in 2005 (White et al. 2005), this might not be the most ideal filter for correcting lighting irregularity. Moreover, when the images were changed to binary format in ImageJ, the grayscale images were converted into binary based on a threshold value provided by the program. Alternate thresholding techniques may provide more consistent results. 82 Finally, the extension of the fractal analysis technique to define a test for increased systemic risks or for monitoring periodontal condition is still limited by the difficulty of applying quantitative imaging to bones; there is a disconnect between correct application at superficial bone and unreliable application to deep bones. The future evolution and validity not only depend upon better fractal methods but upon detailed and repeatable imaging of the bones in clinical conditions. Future Directions In our present study, the clinical information we considered was limited by what was collected from patients’ dental charts. The addition of clinical information should improve the predictive power of the model for systemic risks with trabecular changes caused by periodontal diseases. Variables such as age, history of diabetes, heart problems, body mass index, smoker status, pack years smoking, attitude score, supplemental vitamin dose, and other radiographic information such as mandibular bone density, thickness of mandibular inferior border, or alveolar bone height, may improve the correlation of oral findings with systemic risks of other medical diseases. In White’s paper in 2005 (White et al. 2005), he uses other computational techniques to analyze changes in mandibular trabecular pattern. Struct analysis, run-length 83 analysis, and Fourier analysis were made in the same lower anterior region as our study. These techniques could be used to complement fractal index and provide a more thorough analysis of the trabecular arrangement. With all these analyses, it may be possible to quantify trabecular bone such that a number would be used to follow an individual’s periodontal condition and to compare an individual’s bone health with that of a large population, similar to the way doctors monitor a patient’s cholesterol level. This value could also be used to monitor changes in an individual’s bone quality over a period of time to study the effects of aging, disease processes, and other factors. Our study focused on alterations of trabecular architecture seen on periapical radiographs. We measured radiographic characteristics on a two-dimensional projected image of a three-dimensional structure. While it is preferable to work with 3D image data such as that obtained from the NewTom machine, this technology is not widely available to many clinicians currently and it is therefore difficult to use as a mass screening tool. 3D image analysis may become much more important in the future as the technology improves. The regions of interest were selected from the periapical films of lower anterior teeth because it provides the largest possible area for fractal analysis without too much overlapping anatomical structure. However, other regions of the mouth, such as 84 apices to the upper anterior teeth or posterior teeth, should be investigated to find the best correlation between fractal index and periodontal condition. The biomechanics of cancellous bone has come under renewed focus. The ability to more accurately describe the morphological complexity of trabecular bone with respect to its three-dimensional structure will facilitate this process. Several biomechanical measurements such as the removal torque test and resonance frequency analysis could be examined to see if there is any correlation between these measurements and fractal dimensions. Removal torque has been a widely used research method for assessing implant stability and osseointegreation (Johansson et al. 1991). The technique measures the peak torque necessary to shear the interface between the implant surface and the surrounding bone. This is a destructive test method in which the application of shear stress at the implant interface leads to failure and as such the use of removal torque in the clinical assessment of osseointegration appears to have some limitation. Resonance frequency analysis is a non-invasive test also used to measure implant stability. This technique measures the resonance frequency of a small transducer which may be attached to an implant fixture or abutment. Changes in the stiffness of an implant in bone and the height of the marginal bone can be monitored and measured. Since bone quality plays an essential role in the stability of an implant, it would be interesting to correlate the stability of the implant through either resonance frequency analysis or a removal 85 torque test with the fractal index on dental radiographs. Fractal analysis could become an even less invasive technique for studies on bone quality. 86 Chapter 5: Conclusion The principal aim of this thesis was to develop a technique that is able to describe the complexity of trabecular bone architecture through the use of fractal geometry and to differentiate the bone pattern in subjects with different periodontal conditions. It was hypoth esized that fractal dimensions may identify changes in the cancellous bone structure in moderate and severe periodontal subjects compared to healthy individuals. The literature review discusses the basis of periodontal disease, bone biology, and the imaging technology. It also highlights the application of fractal analysis as a novel technique in medical research that required a rigorous validation of the methodology. To the present, there have been relatively few investigations that use fractal analysis for the description of the complexity of trabecular bone structure on dental radiographs. The preliminary nature of these studies indicates that ad hoc protocols based on the box-counting method were employed to obtain the fractal dimension. Fractal analysis has been shown to detect morphological differences in the trabecular bone between subjects with healthy gingiva and subjects with moderate and severe periodontitis at the lower anterior regions. This indicates that subjects affected by 87 severe periodontitis have trabeculae that are significantly less complex in shape than the normal and moderate periodontal subjects. This may be due to the loss of perforation of trabeculae which leads to less interconnection between trabeculae, increased spatial separation between the trabeculae, loss of branching and more rounded trabeculae. This has enabled new understanding of how changes to cancellous bone structure may occur as a result of a disease process. 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Asset Metadata

Creator Xiang, Sophia Sy-Hann (author)

Core Title Fractal analysis on dental radiographs to detect trabecular patterns in patients affected by periodontitis

School School of Dentistry

Degree Master of Science

Degree Program Craniofacial Biology

Degree Conferral Date 2007-05

Publication Date 04/02/2007

Defense Date 02/01/2007

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag fractal analysis,OAI-PMH Harvest,periodontitis

Language English

Advisor Nowzari, Hessam (committee chair), Rich, Sandra (committee member), Sameshima, Glenn T. (committee member)

Creator Email sxiang@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-m341

Unique identifier UC1159108

Identifier etd-Xiang-20070402 (filename),usctheses-m40 (legacy collection record id),usctheses-c127-321997 (legacy record id),usctheses-m341 (legacy record id)

Legacy Identifier etd-Xiang-20070402.pdf

Dmrecord 321997

Document Type Thesis

Rights Xiang, Sophia Sy-Hann

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Repository Name Libraries, University of Southern California

Repository Location Los Angeles, California

Repository Email uscdl@usc.edu

Abstract (if available)

Abstract Objective: To evaluate fractal analysis as a tool to quantitatively measure the impact of periodontal disease on surrounding bone.