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Analyzing inter-individual shape variations of the middle ear cavity by developing a common shape model based on medial representation
International Congress Series 1268 (2004) 243 – 248
www.ics-elsevier.com
Analyzing inter-individual shape variations of the middle ear cavity by developing a common shape model based on medial representation K.D. Fritscher a,*, R. Pilgram a, R. Leuwer b, C. Habermann c, A. Mu¨ller b, R. Schubert a a
Institute for Medical Knowledge Representation and Visualization, University for Medical Informatics and Technology Tyrol, Innrain 98, Innsbruck 6020, Austria b Department of Ear, Nose and Throat Surgery, University Hospital Hamburg-Eppendorf, Germany c Department of Interventional and Diagnostic Radiology, University Hospital Hamburg-Eppendorf, Germany
Abstract. Analysis of shape variability of anatomical structures is a widespread problem on one hand and an essential fundament for the analysis of biological processes and the diagnosis of a large spectrum of pathologies on the other hand. Many diseases affecting the middle ear result from morphological alterations and provoke morphological changes of the middle ear cavity. Therefore, it was our goal to analyze shape and shape variations of a population of this anatomical structure. By segmenting and modeling 10 middle ear cavities using a medial-based representation, which provides inter-individual correspondence, a common shape model of the tympanic cavity has been generated. The results show that medial-based representation is suitable to generate a common shape model of the tympanic cavity and to provide a facility to analyze the complex shape of the anatomical structure and the physiological variations. D 2004 CARS and Elsevier B.V. All rights reserved. Keywords: Middle ear cavity; Common shape model; Statistical shape analysis; Medial representation
1. Introduction Statistical shape analysis is a well-known approach to study diseases (patients vs. normal controls) or variations of an anatomical structure among a population. Proper usage of anatomical shape information can significantly improve our understanding of evolutionary processes and anatomical changes due to pathological disorders. Most pathologies affecting the middle ear cavity are very likely to result from morphological alterations and consequently also change the anatomical form of the cavity. Moreover, the tympanic cavity is a hollow space within the tympanic bone. Therefore, it is * Corresponding author. Tel.: 43-50-8648-3825; fax: +43-50-8648-3830. E-mail address: [email protected] (K.D. Fritscher). URL: http://imwv.umit.at. 0531-5131/ D 2004 CARS and Elsevier B.V. All rights reserved. doi:10.1016/j.ics.2004.03.190
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K.D. Fritscher et al. / International Congress Series 1268 (2004) 243–248
not a grown organ in a common sense, but its form is constrained by the shape and growth process of the surrounding tympanic bone. These circumstances and the fact that high resolution CT-scans depict the bony abnormalities associated with cholesteatoma in great detail [1] motivated our approach to generate three-dimensional shape models that represent inter-individual and population-specific shape variations, as a meaningful tool for future diagnosis and surgical planning. There are different surface and volume-based methods as well as approaches based on finite element methods [2], active shape models (ASM) [3] and harmonic maps [4], which are used for shape modeling. Pizer et al. [5,6] introduced a medial-based approach [5,6] which provides a straight forward method to establish geometric correspondence between the individuals of a population without altering the individual shape. Up to now, FEM models have been used to analyze the mechanical aspects of the middle ear [7], but to our knowledge, none of the methods mentioned above have ever been applied to analyze the shape variations of the middle ear cavity. Based on previous experiences with medial-based shape representation [8], the objective of the presented work was to build a control model based on a healthy population using m-reps in order to answer two questions: 1. Does the method succeed in generating a common shape model of the tympanic cavity? 2. Does this model allow analyzing specific and characteristic shape features and variations useful for clinical applications? 2. Methods For the presented study, we used CT scans of 10 anatomical specimens of tympanic bones, which are considered not to be morphologically changed in a pathological way. After some pre-processing steps required to get isotropic data sets, the middle ear cavity in these scans has been segmented semi-automatically (Fig. 1). In the epitympanon, the junction between the epitympanic recess and mastoid antrum was chosen as a boundary to separate the tympanic cavity from the mastoid cells. As a boundary line between tuba auditiva and hypotympanon, we used the connecting line between processus cochleariformis and the edge at the crossover between tympanic cavity and auditory tube (f Ostium tympanicum). The labeled objects have been modeled using a medial-based representation method (m-rep) introduced by Pizer et al. This method is based on the idea of using a discrete n m grid of predefined points in the interior of the object, called atoms, to form a medial sheet. Each of these atoms holds a tupel of parameters describing the characteristics of the local shape of the model. The same grid of atoms is used as a base model for each individual object. Refining this model in an iterative process for each object results in atom grids with different individual shapes, representing inter-individual variations. Correspondence can be established by correlating the particular atoms of subjects. This fact allows to generate a common shape model of anatomical structures. The inter-individual shape variations have been analyzed and quantified using principal geodesic analysis (PGA) derived by Fletcher el al. [10], which is an
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245
Fig. 1. The medial wall and part of the posterior and anterior walls of the right tympanic cavity, lateral view (from Spalteholz [9]). White lines indicate defined boundaries to auditory tube and mastoid cells.
extension of principal component analysis (PCA) in order to be able to use PCA in figural space. 3. Results Using the medial representation method with an atom grid containing 15 (5 3) atoms, a common shape model of the population has been generated (Fig. 2). All individuals are lying within a Gaussian distribution—no outliers among these 10 subjects have been identified. Application of principal geodesic analysis has shown that the first three main components cover a shape space of 77% and the first six components, a shape space of 93%. All the major variations of shape among the population are covered within a range of max. F 2.2r for each single mode (Fig. 3).
Fig. 2. Common shape model of 10 tympanic cavities. Left: surface view of paries membranacea. Right: corresponding wire frame model with atom grid + parameter vectors.
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Fig. 3. First (I) and second (II) main principal geodesic components of the tympanic cavity (left); second (II) and third (III) main principal geodesic components of the tympanic cavity (right).
Although the model is yet based on a rather low number of subjects, first analysis of the common shape model reveals characteristic directions of variations within the population and enabled us to identify areas in the tympanic cavity, where variations
Fig. 4. Shape variability of the common shape model showing the first two modes within F 2 standard deviations including their percentage impact to the shape space (left: 2r model (solid) + mean model (wire frame), middle: mean model, right: + 2r model (wire frame) + mean model (solid)).
K.D. Fritscher et al. / International Congress Series 1268 (2004) 243–248
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in shape are quite distinct in contrast to other parts, in which form is more constant throughout the population: The first mode—covering a space of 47%—reveals that the major variation among the population is a stretching and compression along the longitudinal axis of the cavity going through paries jugularis and paries tegmentalis. The major part of this variation is caused by differences in size of the meso- and especially the hypotympanon and only to a lower portion by variations of the epitympanon. In contrast to this, changes along the axis through paries caroticus and paries mastoideum are mainly represented by the second main component—covering a shape of only 15%—and are much more distinct. Least changes in size can be observed along the axis through paries membranacea and paries labyrinthica. Additionally, it turned out that the regions in which the borders have been set according to subjective guidelines (antrum mastoideum and entry to auditory tube) are not showing morphological variations above average (Fig. 4). 4. Discussion Our results demonstrate the suitability of the medial-based approach to generate a common shape model of the middle ear cavity. This model is providing a facility to analyze the complex shape of the anatomical structure and the physiological variations in a quantitative way. Although the number of subjects is still rather low, the model and its statistical interpretations are very promising and provide a basis for further research. The problem of missing delimitable anatomical structures in some parts of the middle ear cavity could be reduced by manual interaction during the segmentation process and by strictly abiding to anatomical definitions. In addition, the influence of these artificial variations will not affect the space of Prusak, which is the area that is mainly affected by cholesteatomas. In order to improve the accuracy of the model near the border between middle ear cavity and tuba auditiva, it turned out that it is recommendable to create an additional model of the auditory tube. This will also give us the possibility to analyze correlations between the shape of the auditory tube and the tympanic cavity. For this purpose, it will be reasonable to redefine the anatomical landmarks which act as a border between the two models. One possibility would be to use the onset and tendon of the M. tensor tympani as such a landmark. Modeling the auditory tube as well will bring another improvement in terms of objectiveness of the model. Moreover, this should make it possible to model the structures close to the border between auditory tube and tympanic cavity, which are important for the aeration of the middle ear, in more detail. The next targets of this project will be refining our results by increasing the number of subjects and comparing our population of not pathologically changed middle ears with a population of middle ear cavities of patients suffering from cholesteatoma. Acknowledgements We thank the Medical Image Display and Analysis Group, from the UNC Chapel Hill for providing the software tool Pablo used for generating m-rep models. The preprocessing
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K.D. Fritscher et al. / International Congress Series 1268 (2004) 243–248
and segmentation tools used in this work were partly developed in a project, supported by the Forschungsfo¨rderungsfonds fu¨r die gewerbliche Wirtschaft (FFF-Austria). References [1] N.W.C. Chee, T.Y. Tan, The value of pre-operative high resolution CT scans in cholesteatoma surgery, Singapore Medical Journal 42 (4) (2001) 155 – 159. [2] D. Terzopoulos, D. Metaxas, Dynamic 3D models with local and global deformation: deformable superquadratics, IEEE Transaction on Pattern Analysis and Machine Intelligence 13 (1991) 703 – 714. [3] T.F. Cootes, et al., The use of active shape models for locating structures in medical images, in: H.H. Barret, A.F. Gmitro (Eds.), Information Processing in Medical Imaging, Springer-Verlag, Heidelberg, 1993, pp. 33 – 47. [4] A.P. Fordy, J.C. Wood, Harmonic Maps and Integrable Systems, Aspects of Mathematics, vol. E23, Vieweg, Braunschweig, 1994. [5] S.M. Pizer, et al., Segmentation, registration, and measurement of shape variation via image object shape, IEEE Transactions on Medical Imaging 18 (1999) 851 – 865. [6] S. Joshi, et al., Multiscale deformable model segmentation and statistical shape analysis using medial descriptions, IEEE Transactions on Medical Imaging 21 (2002) 538 – 550. [7] T. Koike, H. Wada, T. Kobayashi, Modeling of the human middle ear using finite-element method, Journal of the Acoustical Society of America 111 (2002) 1306 – 1317. [8] R. Pilgram, et al., Common shape modeling of the multiobject organ heart, accepted forBioMED (2004 Feb.). [9] W. Spalteholz, Handatlas der Anatomie des Mensche in III Ba¨nden, Hirzel-Verlag, Leipzig. [10] P.T. Fletcher, C. Lu, S. Joshi, Statistics of shape via principal geodesic analysis on lie groups, CVPR, (2003).
www.ics-elsevier.com
Analyzing inter-individual shape variations of the middle ear cavity by developing a common shape model based on medial representation K.D. Fritscher a,*, R. Pilgram a, R. Leuwer b, C. Habermann c, A. Mu¨ller b, R. Schubert a a
Institute for Medical Knowledge Representation and Visualization, University for Medical Informatics and Technology Tyrol, Innrain 98, Innsbruck 6020, Austria b Department of Ear, Nose and Throat Surgery, University Hospital Hamburg-Eppendorf, Germany c Department of Interventional and Diagnostic Radiology, University Hospital Hamburg-Eppendorf, Germany
Abstract. Analysis of shape variability of anatomical structures is a widespread problem on one hand and an essential fundament for the analysis of biological processes and the diagnosis of a large spectrum of pathologies on the other hand. Many diseases affecting the middle ear result from morphological alterations and provoke morphological changes of the middle ear cavity. Therefore, it was our goal to analyze shape and shape variations of a population of this anatomical structure. By segmenting and modeling 10 middle ear cavities using a medial-based representation, which provides inter-individual correspondence, a common shape model of the tympanic cavity has been generated. The results show that medial-based representation is suitable to generate a common shape model of the tympanic cavity and to provide a facility to analyze the complex shape of the anatomical structure and the physiological variations. D 2004 CARS and Elsevier B.V. All rights reserved. Keywords: Middle ear cavity; Common shape model; Statistical shape analysis; Medial representation
1. Introduction Statistical shape analysis is a well-known approach to study diseases (patients vs. normal controls) or variations of an anatomical structure among a population. Proper usage of anatomical shape information can significantly improve our understanding of evolutionary processes and anatomical changes due to pathological disorders. Most pathologies affecting the middle ear cavity are very likely to result from morphological alterations and consequently also change the anatomical form of the cavity. Moreover, the tympanic cavity is a hollow space within the tympanic bone. Therefore, it is * Corresponding author. Tel.: 43-50-8648-3825; fax: +43-50-8648-3830. E-mail address: [email protected] (K.D. Fritscher). URL: http://imwv.umit.at. 0531-5131/ D 2004 CARS and Elsevier B.V. All rights reserved. doi:10.1016/j.ics.2004.03.190
244
K.D. Fritscher et al. / International Congress Series 1268 (2004) 243–248
not a grown organ in a common sense, but its form is constrained by the shape and growth process of the surrounding tympanic bone. These circumstances and the fact that high resolution CT-scans depict the bony abnormalities associated with cholesteatoma in great detail [1] motivated our approach to generate three-dimensional shape models that represent inter-individual and population-specific shape variations, as a meaningful tool for future diagnosis and surgical planning. There are different surface and volume-based methods as well as approaches based on finite element methods [2], active shape models (ASM) [3] and harmonic maps [4], which are used for shape modeling. Pizer et al. [5,6] introduced a medial-based approach [5,6] which provides a straight forward method to establish geometric correspondence between the individuals of a population without altering the individual shape. Up to now, FEM models have been used to analyze the mechanical aspects of the middle ear [7], but to our knowledge, none of the methods mentioned above have ever been applied to analyze the shape variations of the middle ear cavity. Based on previous experiences with medial-based shape representation [8], the objective of the presented work was to build a control model based on a healthy population using m-reps in order to answer two questions: 1. Does the method succeed in generating a common shape model of the tympanic cavity? 2. Does this model allow analyzing specific and characteristic shape features and variations useful for clinical applications? 2. Methods For the presented study, we used CT scans of 10 anatomical specimens of tympanic bones, which are considered not to be morphologically changed in a pathological way. After some pre-processing steps required to get isotropic data sets, the middle ear cavity in these scans has been segmented semi-automatically (Fig. 1). In the epitympanon, the junction between the epitympanic recess and mastoid antrum was chosen as a boundary to separate the tympanic cavity from the mastoid cells. As a boundary line between tuba auditiva and hypotympanon, we used the connecting line between processus cochleariformis and the edge at the crossover between tympanic cavity and auditory tube (f Ostium tympanicum). The labeled objects have been modeled using a medial-based representation method (m-rep) introduced by Pizer et al. This method is based on the idea of using a discrete n m grid of predefined points in the interior of the object, called atoms, to form a medial sheet. Each of these atoms holds a tupel of parameters describing the characteristics of the local shape of the model. The same grid of atoms is used as a base model for each individual object. Refining this model in an iterative process for each object results in atom grids with different individual shapes, representing inter-individual variations. Correspondence can be established by correlating the particular atoms of subjects. This fact allows to generate a common shape model of anatomical structures. The inter-individual shape variations have been analyzed and quantified using principal geodesic analysis (PGA) derived by Fletcher el al. [10], which is an
K.D. Fritscher et al. / International Congress Series 1268 (2004) 243–248
245
Fig. 1. The medial wall and part of the posterior and anterior walls of the right tympanic cavity, lateral view (from Spalteholz [9]). White lines indicate defined boundaries to auditory tube and mastoid cells.
extension of principal component analysis (PCA) in order to be able to use PCA in figural space. 3. Results Using the medial representation method with an atom grid containing 15 (5 3) atoms, a common shape model of the population has been generated (Fig. 2). All individuals are lying within a Gaussian distribution—no outliers among these 10 subjects have been identified. Application of principal geodesic analysis has shown that the first three main components cover a shape space of 77% and the first six components, a shape space of 93%. All the major variations of shape among the population are covered within a range of max. F 2.2r for each single mode (Fig. 3).
Fig. 2. Common shape model of 10 tympanic cavities. Left: surface view of paries membranacea. Right: corresponding wire frame model with atom grid + parameter vectors.
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K.D. Fritscher et al. / International Congress Series 1268 (2004) 243–248
Fig. 3. First (I) and second (II) main principal geodesic components of the tympanic cavity (left); second (II) and third (III) main principal geodesic components of the tympanic cavity (right).
Although the model is yet based on a rather low number of subjects, first analysis of the common shape model reveals characteristic directions of variations within the population and enabled us to identify areas in the tympanic cavity, where variations
Fig. 4. Shape variability of the common shape model showing the first two modes within F 2 standard deviations including their percentage impact to the shape space (left: 2r model (solid) + mean model (wire frame), middle: mean model, right: + 2r model (wire frame) + mean model (solid)).
K.D. Fritscher et al. / International Congress Series 1268 (2004) 243–248
247
in shape are quite distinct in contrast to other parts, in which form is more constant throughout the population: The first mode—covering a space of 47%—reveals that the major variation among the population is a stretching and compression along the longitudinal axis of the cavity going through paries jugularis and paries tegmentalis. The major part of this variation is caused by differences in size of the meso- and especially the hypotympanon and only to a lower portion by variations of the epitympanon. In contrast to this, changes along the axis through paries caroticus and paries mastoideum are mainly represented by the second main component—covering a shape of only 15%—and are much more distinct. Least changes in size can be observed along the axis through paries membranacea and paries labyrinthica. Additionally, it turned out that the regions in which the borders have been set according to subjective guidelines (antrum mastoideum and entry to auditory tube) are not showing morphological variations above average (Fig. 4). 4. Discussion Our results demonstrate the suitability of the medial-based approach to generate a common shape model of the middle ear cavity. This model is providing a facility to analyze the complex shape of the anatomical structure and the physiological variations in a quantitative way. Although the number of subjects is still rather low, the model and its statistical interpretations are very promising and provide a basis for further research. The problem of missing delimitable anatomical structures in some parts of the middle ear cavity could be reduced by manual interaction during the segmentation process and by strictly abiding to anatomical definitions. In addition, the influence of these artificial variations will not affect the space of Prusak, which is the area that is mainly affected by cholesteatomas. In order to improve the accuracy of the model near the border between middle ear cavity and tuba auditiva, it turned out that it is recommendable to create an additional model of the auditory tube. This will also give us the possibility to analyze correlations between the shape of the auditory tube and the tympanic cavity. For this purpose, it will be reasonable to redefine the anatomical landmarks which act as a border between the two models. One possibility would be to use the onset and tendon of the M. tensor tympani as such a landmark. Modeling the auditory tube as well will bring another improvement in terms of objectiveness of the model. Moreover, this should make it possible to model the structures close to the border between auditory tube and tympanic cavity, which are important for the aeration of the middle ear, in more detail. The next targets of this project will be refining our results by increasing the number of subjects and comparing our population of not pathologically changed middle ears with a population of middle ear cavities of patients suffering from cholesteatoma. Acknowledgements We thank the Medical Image Display and Analysis Group, from the UNC Chapel Hill for providing the software tool Pablo used for generating m-rep models. The preprocessing
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K.D. Fritscher et al. / International Congress Series 1268 (2004) 243–248
and segmentation tools used in this work were partly developed in a project, supported by the Forschungsfo¨rderungsfonds fu¨r die gewerbliche Wirtschaft (FFF-Austria). References [1] N.W.C. Chee, T.Y. Tan, The value of pre-operative high resolution CT scans in cholesteatoma surgery, Singapore Medical Journal 42 (4) (2001) 155 – 159. [2] D. Terzopoulos, D. Metaxas, Dynamic 3D models with local and global deformation: deformable superquadratics, IEEE Transaction on Pattern Analysis and Machine Intelligence 13 (1991) 703 – 714. [3] T.F. Cootes, et al., The use of active shape models for locating structures in medical images, in: H.H. Barret, A.F. Gmitro (Eds.), Information Processing in Medical Imaging, Springer-Verlag, Heidelberg, 1993, pp. 33 – 47. [4] A.P. Fordy, J.C. Wood, Harmonic Maps and Integrable Systems, Aspects of Mathematics, vol. E23, Vieweg, Braunschweig, 1994. [5] S.M. Pizer, et al., Segmentation, registration, and measurement of shape variation via image object shape, IEEE Transactions on Medical Imaging 18 (1999) 851 – 865. [6] S. Joshi, et al., Multiscale deformable model segmentation and statistical shape analysis using medial descriptions, IEEE Transactions on Medical Imaging 21 (2002) 538 – 550. [7] T. Koike, H. Wada, T. Kobayashi, Modeling of the human middle ear using finite-element method, Journal of the Acoustical Society of America 111 (2002) 1306 – 1317. [8] R. Pilgram, et al., Common shape modeling of the multiobject organ heart, accepted forBioMED (2004 Feb.). [9] W. Spalteholz, Handatlas der Anatomie des Mensche in III Ba¨nden, Hirzel-Verlag, Leipzig. [10] P.T. Fletcher, C. Lu, S. Joshi, Statistics of shape via principal geodesic analysis on lie groups, CVPR, (2003).