Adv Dent Res 17:61-64, December, 2003
© 2003 International and American Associations for Dental Research
Computational Models of Oral and Craniofacial Development, Growth, and Repair
P. Hammond*,
T. Hutton,
S. Maheswaran, and
S. Modgil
Biomedical Informatics Unit, Eastman Dental Institute for Oral Health Care Sciences, University College London, 256 Gray’s Inn Road, London WC1X 8LD, UK;
Correspondence: * corresponding author, p.hammond@eastman.ucl.ac.uk
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Abstract
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This paper illustrates how biological and clinical problems stimulate research in biomedical informatics and how such research contributes to their solution. The computational models described use techniques from Logic Programming, Machine Learning, Computer Vision, and Biomathematics. They address problems in the development, growth, and repair of oral and craniofacial tissues arising in cell biology, clinical genetics, and dentistry. At the micro-level, the dynamic interaction of cells in the oral epithelium is modeled. At the macro-level, models are constructed of either the craniofacial shape of an individual or the craniofacial shape differences within and between healthy and congenitally abnormal populations. In between, in terms of scale, there are models of normal dentition and the use of computerized expert knowledge to guide the design of dental prostheses used to restore function in partially edentulous patients.
KEY WORDS: Computer • pathology • dentistry • dysmorphology
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Background and Motivation
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The oral and craniofacial complexes undergo major change in form during development and subsequent growth. In this paper, we demonstrate how computational models can illustrate aspects of the underlying cell biology and changes in shape during growth. The models are used to analyze normal growth, to help detect disease and growth abnormalities, and to assist in treatment planning.
Changes in face shape over time are very familiar, and it is straightforward to differentiate between young and older faces, or those of a different gender. Typically, ethnic differences in face shape are easily discernible, and during puberty there are major changes in face shape—especially in male faces. Some individuals are pre-programmed to have a different face shape. For example, a child with Noonan syndrome, a condition associated with an abnormality of chromosome 12, is likely to have a heart malformation and growth problems. In addition, for such a child, the eyes can be farther apart than usual, the eyelids may droop, the eye opening may slant downwards at the outer edges, and the ears may be set lower on the head. Such face shape differences usually do not require surgical intervention, and often disappear or become less pronounced with age. However, they do contribute significantly to a clinical geneticist’s diagnosis of Noonan syndrome, and of many other dysmorphic syndromes for which there is no definitive genetic test. Computer analysis of face shape in 3-D can detect subtle differences in face shape and hence support the diagnosis of such congenital abnormalities.
Some individuals with a very short or long face desire its shape to be altered surgically. This may be for aesthetic reasons or because of speech or eating difficulties. They undergo as many as two years of combined orthodontic treatment and orthognathic surgery. Of course, many individuals need receive only orthodontic treatment to achieve a more acceptable occlusion or relative positioning of their teeth. Such interventions require an analysis of occlusion and craniofacial shape in treatment planning and also in its audit. Two- and 3-D models of craniofacial shape, of both soft and hard tissues, can be combined to facilitate the analysis, treatment, and auditing stages.
With the burgeoning elderly population, the loss of teeth continues to be a major dental health problem. The restoration of missing teeth with an implant or customized prosthesis requires both clinical expertise as well as design skills in the configuration of components customized to the individual patient. The design knowledge of recognized expert prosthodontists can be provided in the form of a knowledge-based system to guide the less-experienced dentist to a more acceptable design.
Within the oral cavity, potentially serious conditions arise from time to time, such as oral cancer. Their diagnosis requires the inspection of histopathology images by an oral pathologist who looks for changes in the shapes of cells or their proliferation and position relative to the boundary between the epithelium and extracellular matrix. Models of normal epithelial tissue can be constructed and then perturbed to illustrate abnormal cell division with the potential to form a tumor or other pathological conditions.
In the remainder of the paper, we describe how these biological and medical problems have inspired our research and how the results have been used clinically or experimentally to address the original problem.
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Individual-based Model of the Oral Epithelium
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A cross-section of the oral epithelium (Fig. 1
) shows stratified layers of cells, from keratinized or dead cells at the surface, down to basal cells on the basement membrane. The tips of the finger-like protuberances, rete pegs, are where the progenitor or stem cells are located. The shape of the rete pegs alters in oral disease, as do the numbers, positions, and shapes of the basal cells. We are building a simulation model of the normal equilibrium state of epithelial cell production so that we can subsequently perturb it to simulate abnormal behavior. This individual-based model has cells in 3 stages of differentiation from stem to dead cell. Each cell type has different properties in terms of its influence on the motion and mitosis of other cells. In the model, stem cells divide infinitely, often into a copy and a basal cell. Basal cells produce two clones for a finite number of occasions before they differentiate terminally. Physical forces, due to overlap, result in cells pushing against each other. Other behaviors modeled include cell signaling, cell aging, and probabilistic properties of movement and mitosis. Currently, the model successfully reproduces aspects of epithelial cell behavior. For example, if the model is started with 5 stem cells in a row, the number and juxtaposition of cells after 115 iterations is shown in Fig. 2a. This can be compared with a section of real epithelium (Fig. 2b). Currently, there are 10 parameters affecting model output. The aim is to make the model available to oral pathologists and cell biologists so that, by choosing values for particular model parameters, they can carry out in silico experiments that would otherwise take significantly longer and incur major expense. Interesting model behavior may then stimulate in vitro experiments that in turn suggest improvements to the model (Maheswaran et al., 2003).
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Logic-based Model of Removable Partial Denture Design
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Several surveys have shown removable partial dentures to be badly designed by dentists, resulting in adverse effects on the health and finances of patients (Basker et al., 1991). We developed RaPiD, a computer-aided design (CAD) tool enhanced with the knowledge of expert prosthodontists, to guide dentists to more acceptable designs. RaPiD has the usual CAD style interface with a drawing area and set of tools with which to place and manipulate prosthesis components (Fig. 3). The dentist begins by removing teeth icons to match the patient’s dentition. Surfaces on which artificial teeth are to be placed are generated, and rests are placed to transfer biting forces from soft tissues to dental surfaces. If an incorrect location is chosen, a critique appears, suggesting corrective action.
Behind the scenes, RaPiD generates descriptions of the RPD components as Horn clauses in a logic database (Hammond et al., 1993) defining inter alia which teeth are absent/present, those to be replaced by artificial teeth; which teeth have rests on them, and which have clasps to retain the prosthesis in the mouth. The expert knowledge, expressed as rules in Horn clauses, is used to validate the dentist’s design. If a rule is contravened, a critiquing error message suggests a more acceptable way to proceed. A survey of 70 expert prosthetic dentists was undertaken to validate over 100 design rules.
The RaPiD users were initially pleased with the software but became discontented at having to use a mouse to draw the major connector, the cross-hatched central component in Fig. 3
. Observation of how the expert drew major connectors, following a sequence of teeth, sometimes linking and sometimes avoiding components, suggested a sequential parsing of an iconic representation of teeth and RPD components. This is similar to using a grammar to parse and understand the structure of natural language. We invented a special grammar, a "path grammar", to parse the component sequence and translate it into a series of points describing the outer edge of the major connector. This gives an initial shape that can subsequently be altered. So, with just a few mouse clicks, a clinician can generate a draft design semi-automatically (Modgil et al., 2002).
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Point Distribution Models of Dentition and Craniofacial Shape
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Subsequently, the RaPiD users asked for the design to be overlaid on a digital image of a dental cast, so that the position and shape of RPD components could be tailored to the precise position and shape of the patient’s teeth. This required the shape of individual teeth to be recognized within the image of the scanned dental model. The solution involved two stages. First, we used Point Distribution Models to determine the variation in dentition in a large number of digitized dental cast images. Each image is overlaid with a shape template made up of points that capture an individual’s dentition (Fig. 4). The collection of templates is then aligned and the mean shape determined. Finally, a principal component analysis (PCA) is performed on the set of differences between the mean and the individual dentitions in terms of co-ordinates of the points in the template. This generates a set of modes of shape variation, known as a point distribution model (PDM). The first mode captures variation in arch width and the second differences between triangular and square arches—the two most common variations. To find the teeth shapes in a particular image, we overlay it with the mean template and adjust it iteratively until it best matches the structures therein. The deformations are limited so that the shape remains within the variation found, i.e., is synthesizable from, modes in the PDM.
Although this was a fairly simple application of shape modeling, it introduced a new technique of widespread application. For instance, it is only a minor development to look for hard-tissue structures in a lateral head radiograph. Once the template converges to the correct anatomical structures, angles and distances between anatomical landmarks can be computed (Fig. 5). Thus, semi-automated cephalometric analysis is possible, reducing the time taken to prepare an orthodontic/orthognathic treatment plan (Hutton et al., 2000).
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3-D Dense Surface Models of Face Shape
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Shortly after tackling the 2-D cephalometric analysis problem, we worked on the identification of soft-tissue features from 2-D images to delineate face shape differences of children with dysmorphic syndromes. But pose was a significant problem, in that it distorted the real position of some features—for example, the position of the ears. Fortunately, a new technology, 3-D digital photography, arrived, and we were able to apply similar shape modeling techniques.
In 3-D photogrammetry, multiple cameras capture different views of the face that are then used to compute stereo points and hence a 3-D surface. Additional cameras produce left/right semi-portraits to capture appearance. With such 3-D images of the soft tissues of the face, many new applications are possible. For example, standard anthropometric analyses can be performed on soft tissues by identifying anatomical landmarks and automatically computing measurements of interest. However, parts of the face that are between these landmarks also contain useful shape information, and so we interpolate a dense correspondence across the entire face. From the corresponding points, an average face can be computed, and then a PCA of the differences between individual faces and the average face results in a set of shape variation modes, or a dense surface model (DSM) (Hutton et al., 2001). In a mixed set of images of children and adults, variation in face size is typically the first mode of the corresponding DSM. Similarly, mode 2 is usually a variation from long, oval face to short, squarer face. Typically, as few as 50 modes cover 98% of all face shape variations in the dataset. Since each face surface may have 8000 3-D points, we potentially have 24,000 variables. The dense surface model, therefore, provides a very compact set of building blocks with which to synthesize faces from the original collection. The faces can now be modeled in a 50-dimensional "shape space".
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Auditing Soft-tissue Changes Following Orthognathic Surgery
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One immediate application of a dense surface model of face shape is in tracking soft-tissue changes accompanying orthognathic surgery (Hutton et al., 2002). Each diamond in the scatter plot (Fig. 6) represents an individual face in a collection of patients and controls. The arrows link a patient’s pre-/post-surgery pair of images. The vertical axis measures the shortness/longness of the face as the distance in mm between nasion and gnathion. A senior orthodontist classified each of the faces in terms of retro/prognathicism. The horizontal axis is a line in shape space between the averages of the Class II and Class III subgroups. The vertical, dotted lines separate faces into the usual three orthodontic classes. Class I would be considered "normal". Now we can see how "normal" the faces of patients have become following surgery. Patient B has moved from extremely prognathic to class I. The same is true of patient E. Patient F, though, is still a little retrognathic. By morphing dynamically between the pre- and post-scans, we can give the surgeon a 3-D impression of the face shape changes that have occurred. Our ultimate goal is to analyze the correlations between soft- and hard-tissue shapes, both before and after surgery, and to produce software that can "simulate" soft-tissue change from the pre-surgery hard and soft images and a desired hard-tissue change. This would be used for patient education and to aid in surgery planning. The two- to three-year lead time on completion of treatment means that the data collection, and hence the model, is not yet complete.
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Delineating and Discriminating Differences in Facial Shape
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As was mentioned earlier, the first mode in a face shape DSM typically captures variation in overall size and hence is highly correlated with age, at least as far as late puberty. Such a plot can be used to make a simple ‘face size-age’ comparison based on gender. A better approach is to use kernel smoothing. This involves computing a weighted average of a mode value over time, so that an average value for a 10-year-old face may be computed from faces between 0 and 20 years, combined with an appropriately shaped weighting function. Average growth trajectories can then be computed, for example, to make a male-female comparison (Hutton et al., 2003) or to compare groups of individuals with a dysmorphic syndrome where growth may be quite different.
Average faces can be computed for any set of faces. We can compare the average of a control group with that of an age-matched syndromic group. We can compare a static or rotatable pair of average faces or we can morph dynamically between the two averages (Fig. 7). Both visualize important differences in face shape. Such images and animations could form an educational tool for trainee geneticists. It is useful to be able to discriminate between individuals with a syndrome and controls or between individuals with different syndromes. This may assist in earlier diagnosis or at least suggest more focused genetic testing. In the scatter plot of Fig. 8, the horizontal axis joins the averages of a group of children with Noonan syndrome and a group of controls. The vertical axis measures mode 1, overall face size. When the two groups are plotted, there is good horizontal separation. Of course, this only discriminates within the set used to compute the averages that determine the classification. What is needed is unseen testing. We performed this using 10-fold cross-validation—that is, training on 90% and testing 10% blind for 10 different randomized splits. Classifying an individual according to the nearest mean face gives an average sensitivity of 88% and average specificity of 86% for 60 children with Noonan syndrome and 160 age-matched controls. The best classification results, 92% sensitivity and 93% specificity, were for a state-of-the-art pattern-matching technique called "support vector machines" (Hammond et al., 2004).
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Summary
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The applications described above have stimulated our research or at least have required the judicious application of state-of-the-art research by others working in related fields. To gain maximum benefit from biomedical informatics in terms of improved scientific understanding or improvements in healthcare, we must at least be aware of, if not contributing to, the latest research and technological developments. It is insufficient to consider biomedical informatics simply as a supporting technology. It is a discipline in its own right with an independent research agenda but with the potential to make significant contributions to biomedicine.
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Acknowledgments
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We acknowledge the many collaborating clinicians, computer scientists, and statisticians who have contributed to this work: Judith Allanson, Philip Beales, Bernard Buxton, Susan Cunningham, John Davenport, Raoul Hennekam, Kieran Murphy, Mike Patton, Henry Potts, Adam Shaw, Ann Smith, Paul Speight, and Robin Winter. Sponsors of the research include the Birth Defects Foundation, EPSRC, the Teaching Company Directorate, and the Wellcome Trust.
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Footnotes
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Publication supported by Software of Excellence (Auckland, NZ)
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References
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Basker RM, Davenport JC, Harrison A (1991). Designing removable partial dentures in general dental practice. In: Proceedings, 38th Annual Conference of British Society for the Study of Prosthetic Dentistry (unpublished).
Hammond P, Davenport JC, Fitzpatrick FJ (1993). Logic-based integrity constraints and the design of dental prostheses. Artif Intell Med 5:431–446.[Medline]
Hammond P, Hutton TJ, Allanson JE, Campbell LE, Hennekam RCM, Holden S, et al. (2004). 3D analysis of facial morphology. Am J Med Genet (in press).
Hutton TJ, Cunningham S, Hammond P (2000). An evaluation of active shape models for the automatic identification of cephalometric landmarks. Eur J Orthod 22:499–508.[Abstract/Free Full Text]
Hutton TJ, Buxton BF, Hammond P (2001). Dense surface point distribution models of the human face. In: Proceedings, IEEE Workshop "Mathematical Methods in Biomedical Image Analysis, Computer Vision and Pattern Recognition" (CVPR01), Kauai, Hawaii. pp. 153–160. http://csdl.computer.org/comp/proceedings/mmbia/2001/1336/00/13360153abs.htm
Hutton TJ, Cunningham S, Winchester L, Ward-Booth P, Hammond P (2002). Assessing surgery outcome using surface shape analysis. In: Proceedings, British Orthodontic Society Conference, Glasgow, 22–25th September 2002. http://www.eastman.ucl.ac.uk/ndmi/Papers/no_faces_bos_2002.pdf
Hutton TJ, Buxton BF, Hammond P, Potts HWW (2003). Estimating average growth trajectories in shape-space using kernel smoothing. IEEE Trans Med Im 22:747–753.
Maheswaran S, Hammond P, Speight P (2003). Towards computer based models for classification of normal and dysplastic tissue structures. In: Proceedings, "Linking mathematical and biological models in cancer research", Magdeburg, Germany. http://www.eastman.ucl.ac.uk/ndmi/Papers/dysplastic.pdf
Modgil S, Hutton TJ, Hammond P, Davenport JC (2002). Combining biometric and symbolic models for customized, automated prosthesis design. Artif Intell Med 25:227–245.[Medline]
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Abstract
Background and Motivation
