- Email: [email protected]
Computer assisted osteotomy design for autografts in craniofacial reconstructive surgery
International Congress Series 1230 (2001) 44 – 50
Computer assisted osteotomy design for autografts in craniofacial reconstructive surgery Z. Kro´la, *, P. Zerfassa, B. von Rymon-Lipinskia, T. Jansena, W. Hauckb, R. Saderb, H.-F. Zeilhoferb, E. Keevea a
Surgical Simulation and Navigation Group, Caesar-Center of Advanced European Studies and Research, Bonn, Germany b Department of Oral and Maxillofacial Surgery, Klinikum rechts der Isar, Munich University of Technology, Munich, Germany
Abstract For reconstruction of some craniofacial defects which may be caused by trauma, removal of cancer, or due to congenital absence, the procedure of bone grafting is necessary. In this paper, we propose a method to identify an optimal donor site for autologous grafts. It is done by performing an optimization of appropriate surface based and voxel based similarity measures between donor region and a defined graft template. All generated solutions can be evaluated interactively by the surgeon on the computer display using an efficient graphical interface. By this approach, the operation time can be considerably shortened. D 2001 Elsevier Science B.V. All rights reserved. Keywords: Osteotomy planning; Transplant design; Matching; Haptic interface; Autologous grafts; Donor site
1. Introduction Patients with craniofacial osseous defects must often undergo bone graft surgery. In this operative technique, the defected bone is resected, then the designed graft is harvested from the identified donor site and transplanted into the resected section. The reconstructed bone section is then fixed with bone plates and crews until the healing process is complete. Autologous graft refers to bone taken from one anatomic site and transplanted to another site in the same individual. Such autografts offer complete
*
Corresponding author. Tel.: +49-228-965-6230; fax: +49-228-965-6111. E-mail address: [email protected] (Z. Kro´l).
0531-5131/01/$ – see front matter D 2001 Elsevier Science B.V. All rights reserved. PII: S 0 5 3 1 - 5 1 3 1 ( 0 1 ) 0 0 0 0 9 - 7
Z. Kro´l et al. / International Congress Series 1230 (2001) 44–50
45
histocompatibility and they provide the best osteoinductive and osteoconductive stimuli for bone growth. For these reasons, autologous bone serves as the standard grafting material in the treatment of maxillofacial bone tumors, traumatic defects or loss of substance in growth disorders. The preselection of a donor site depends primarily on the morphological fit of the available bone mass and the shape of the part that is to be transplanted. An optimal fit and structural support, as well as minimal lesion of the donor site, are guidelines in this process. Up to now, the selection of the donor sites for autologous grafts was generally performed by the surgeon according to his experience and intuition. The anatomical solid models or manually superposition of 3D datasets were the only options for the preoperative planning [1,2]. These procedures were costly and time consuming. To improve the surgery planning step, we looked for a semi-automatic way, according to the object’s geometrical properties [3]. This continuing work is concerned with providing improved tools for computer aided selection of optimal donor sites for autologous bone grafts.
2. Methodology The planning of the bone graft surgery is based on three-dimensional CT studies. Given two pre-operative CT data sets of the same patient and the geometry description of both objects of interest, the problem of matching a desired transplant with the donor region can be posed as an optimization problem where the objective is to minimize some misregistration measure between the features defined in the two data sets. Let us define a donor site as a finite set of features in the first data set where the graft should be dissected from, and a template as a finite set of features in the second data volume where the shape of the desired transplant is defined. Our method consists of two main stages: graft design and optimization step. At the initial stage, the surgeon has to define interactively the shape of the template and the geometrical constraints for the optimization task. It is followed by the optimization step, which is fully automatic and permits generation of a set of sub-optimal and optimal donor sites for a given template. In the next section, we formulate the optimization problem and discuss the choice of the misregistration measures. After that, we describe the main stages of our method. 2.1. Statement of the optimization problem The bones are rigid bodies. So we can assume that the transformation, which aligns the designed graft with the donor region, can be modeled by a rigid transformation T :R3 ! R3. The transformation matrix can be parameterized by a six-components vector v = (rx , ry , rz , tx , ty , tz)2R6 , where rx , ry , rz , tx , ty , and tz are rotations around and translations along each of the three principal coordinate axes accordingly. From mathematical point of view, we consider problem of the form vopt ¼ arg min fCðvÞ j v 2 Mg;
ð1Þ
Z. Kro´l et al. / International Congress Series 1230 (2001) 44–50
46
where C(v) is an objective function and M R6 is a set of permissible parameter vectors which satisfy some constraints. The goal of the optimization is to find the parameter vector vopt defining a 3D rigid transformation, which minimizes the misregistration measure between the template and the donor site. Two kinds of restrictions can be put on the transformation parameters. Geometrical constraints are defined according to the geometrical properties of the template and the donor region surfaces. They restrict the search to the region with shape, size or curvature similar to the desired one. The second kind of constraints incorporates a priori knowledge into the optimization process. The quality and validity of a given solution is then evaluated according to the local morphological and functional information. The problem of matching a desired transplant with the donor region can be interpreted as a special type of the registration task. Like in the registration of the single- and multimodality data of the same subject, two common approaches have been used to determine the optimal alignment. In the surface-similarity approach, the feature space is a set of surface points (voxels) whose extraction is done in a segmentation step (normally nonautomatic). In the voxel-similarity approach, the feature space is composed of all voxels with corresponding grey-values. In the first case, we define the surface-similarity measure for any vector v =(rx , ry , rz , tx , ty , tz)2R6 as follows XN CðvÞ ¼ d 2 ðTvð pi ÞÞ ð2Þ i¼1 where d(Tv(p)) is the Euclidean distance between the position of the template surface point p after being transformed by Tv and the closest point of the donor site surface. N is the number of template voxels (surface points). In our approach the chamfer distance metric [4] has been used to determine the distance between voxels. In the voxel-similarity approach, the mutual information [5] has been used as the misregistration measure. The following formula estimates the mutual information between the donor site and the template CðvÞ ¼
X
X gi 2GT
gj 2GD
Pðgi ; gj Þ log
Pðgi ; gj Þ Pðgi ÞPðgj Þ
ð3Þ
where P( gi , gj) is a probability distribution of the scatter-plot histogram, and the P( gi), P( gj) are the probabilities for each template and donor site grey-value in the intersection volume. GT and GD are the grey-value sets of the template and the donor site volumes. In general, mutual information is a measure of statistical dependency between two data sets. It measures the distance between the probability distribution of the scatter-plot histogram P( gi, gj) and the distribution P( gi)P( gj) of two completely independent signals. The goal is to find such Topt that the transformed template voxels are most relevant for predicting the grey-values of donor site voxels. We can observe that the surface similarity and mutual information measures are taking into account different pieces of the whole morphological information about the bony internal structure. So they derive their optimal donor site on the basis of different features. Applying such different similarity measures enables the surgeon to select the optimal donor site not only in terms of bone surface correlation but also according to the whole volumetric information contained in both data sets. In the final step, the surgeon has to
Z. Kro´l et al. / International Congress Series 1230 (2001) 44–50
47
choose the best parameter vector from among a number of competing sub-optimal vectors according to the local morphological and functional information. 2.2. Graft design At the initial stage, the surgeon has to identify the spatial extent of the pathological finding. In our clinical practice, the patients with cranio- and maxillofacial disorders have often to undergo different imaging modalities as computed tomography, magnetic resonance imaging or positron emission tomography. The registration of these complementary data sets leads to a better view of the critical region, particularly, when the pathological process involves multiple tissue structure. Depending on the applied multimodal combination of data, tumor spreading can be more exactly localized or in amatory processes can be presented in their bony and soft tissue part. Thus, the differentiation between pathological and healthy structures can be done more successfully. Our system provides simple segmentation and marking tools (for example cutting planes) which allow the surgeon to delineate precisely the osteotomy border lines in the template data set as well as to define the set of constraints M in the donor site data set (see Fig. 1 (left)). In cases of loss of large bone parts or large tumor spreading, the defected structure can be reconstructed using mirror techniques from the healthy side. It is critical that the surgeons be able to interact with the virtual patient model during the planning phase in an efficient manner. Unfortunately, the interaction performed by using a standard computer mouse and keyboard is for the surgeons awkward. We are currently developing more intuitive user interfaces using a PHANToM haptic interface [6] (SensAble Technologies, Woburn, MA). It allows the surgeon through tactile force feedback to touch, feel, manipulate and alter the objects within the virtual 3D space (see Fig. 1 (right)). By using the haptic interface, the graft design step can be performed easier and faster than the standard 2D mouse based approach.
Fig. 1. Left: Delineation of the template’s osteotomy lines using the cutting planes controlled by the haptic device. Right: PHANToM haptic interface.
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Z. Kro´l et al. / International Congress Series 1230 (2001) 44–50
2.3. Optimization Estimation of the optimal transformation vector vopt defining a rigid transformation which minimizes the misregistration measure between the template and the donor site is the goal of the optimization process. Because the misregistration measures are nonlinear functions, they can have multiple local minima on the feasible set M. In addition, the topography of search space for the applied objective functions is characterized by high diversity of objective function landscapes. Generally, we are facing a multivariate, continuous, nonlinear and constrained optimization problem. For solving such complex optimization tasks, global optimization methods are required. We have applied a simulated annealing method [7] to obtain numerically the solution of the optimization problem (1). The method belongs to the class of non-deterministic optimization methods. In contrast to the deterministic algorithms deteriorations of the objective function can also be accepted. This allows to avoid being trapped in local minima. We have implemented a several adaptive cooling schedules for the dynamic parameter selection according to progressively discovered features of the objective function landscape.
3. Results We have developed a computer aided surgical planning system for selection of optimal donor sites for autologous grafts. The system provides segmentation and marking tools (e.g. planar cutting tools) which allow the surgeon to delineate precisely the osteotomy border lines in the template data set and to define the geometrical constraints in the donor site data set. Several similarity criteria and an efficient optimization method have been implemented. The system enables the surgeon to generate a set of sub-optimal and optimal donor sites for a given template. All generated solutions can be explored interactively on the computer display using an efficient graphical interface. Besides the various 2D techniques to display matched slices conventional surface rendering techniques have been implemented. The two objects can be also rendered as semi-transparent surfaces (see Fig. 2). Combining these with volume rendering and introducing a dynamical component significantly enhances the perception of three-dimensionality during the examination and offers a valuable tool in comprehension of complex 3D structures. A reconstructive operation with the 3D planning was performed on 28 patients with osseous defects in different areas of the facial bones. All CT data have been acquired on the Siemens and Philips scanners with the high resolution protocols. The grafts were taken from the area of the iliac crest. In the mandibular disorders, the iliac bone is especially suitable for the reconstruction of the lower jaw. Due to the bone volume available, it enables an extremely stable and sturdy continuity and possesses many varied formation possibilities due to its anatomical and morphological characteristics. Fig. 2 shows a superposition of the to be reconstructed part of mandible with the pelvis donor site. Continuous follow-up observations show that there is less loss of transplants, when they are individually designed as well as high improvement of the functional results like
Z. Kro´l et al. / International Congress Series 1230 (2001) 44–50
49
Fig. 2. Semi-transparent rendering of pelvis with the matched mandible (template).
chewing ability by exact reconstruction of dental occlusion. Moreover, by the 3Dpreoperative planning, the operation time was reduced.
4. Conclusions A method for semi-automatic selection of optimal donor sites for autologous grafts in craniofacial surgery has been proposed. The method is generally applicable for various autologous grafts regardless of its shape and the grafting site. The main advantage of the proposed approach is that after determination of the initial conditions and constraints it provides an automatic procedure to find the best fitting position. Several similarity criteria and an efficient optimization method have been implemented in our system. Applying the different similarity measures enables the surgeon to select the optimal donor site not only in terms of bone surface correlation but also according to the whole volumetric information contained in both data sets. Using the haptic device has potential to greatly simplify and improve the interaction with the virtual patient model during the surgery planning. The proposed approach permits more precise planning of the surgical procedure, reducing intraoperative time and improving the postoperative outcome. Our future work will focus on the combining of intraoperative navigation and instrument tracking systems with our system as well as on the extension to more complex graft geometries (i.e. multipart dissections).
References [1] J. Satoh, H. Chiyokura, M. Kobayashi, T. Fujino, Simulation of surgical operations based on solid modeling, in: T.L. Kunii (Ed.), Visual Computing-Integrating Computer Graphics with Computer Vision, Springer Verlag, Berlin, 1992, pp. 907 – 916.
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Z. Kro´l et al. / International Congress Series 1230 (2001) 44–50
[2] H.-F. Zeilhofer, R. Sader, R. Kirsten, M. Lenz, Computer aided individual transplant design for reconstruction of the mandible, in: H.U. Lemke, et al. (Eds.), Computer Assisted Radiology, Springer Verlag, Berlin, 1995, pp. 1353 – 1358. [3] Z. Kro´l, H.-F. Zeilhofer, R. Sader, K.-H. Hoffmann, P. Gerhardt, H.-H. Horch, Computer assisted selection of donor sites for autologous grafts, in: E.A. Hoffman (Ed.), Proceedings of SPIE 3031 (1997) 196 – 202. [4] G. Borgefors, Distance transformations in arbitrary dimensions, Computer Vision, Graphics and Image Processing 27 (1984) 321 – 345. [5] P. Viola, Alignment by maximization of mutual information, PhD thesis, MIT Department Electrical Engineering and Computer Science, Cambridge, MA, 1995. [6] The PHANTOM TM Desktop System, SensAble Technologies, Inc., Woburn, MA, 01801, http://www. sensable.com. [7] P.J.M. van Laarhoven, E.H.J. Aarts, Simulated Annealing: Theory and Applications. Series: Mathematics and its applications, D. Reidel Publishing, Dordrecht, 1987.
Computer assisted osteotomy design for autografts in craniofacial reconstructive surgery Z. Kro´la, *, P. Zerfassa, B. von Rymon-Lipinskia, T. Jansena, W. Hauckb, R. Saderb, H.-F. Zeilhoferb, E. Keevea a
Surgical Simulation and Navigation Group, Caesar-Center of Advanced European Studies and Research, Bonn, Germany b Department of Oral and Maxillofacial Surgery, Klinikum rechts der Isar, Munich University of Technology, Munich, Germany
Abstract For reconstruction of some craniofacial defects which may be caused by trauma, removal of cancer, or due to congenital absence, the procedure of bone grafting is necessary. In this paper, we propose a method to identify an optimal donor site for autologous grafts. It is done by performing an optimization of appropriate surface based and voxel based similarity measures between donor region and a defined graft template. All generated solutions can be evaluated interactively by the surgeon on the computer display using an efficient graphical interface. By this approach, the operation time can be considerably shortened. D 2001 Elsevier Science B.V. All rights reserved. Keywords: Osteotomy planning; Transplant design; Matching; Haptic interface; Autologous grafts; Donor site
1. Introduction Patients with craniofacial osseous defects must often undergo bone graft surgery. In this operative technique, the defected bone is resected, then the designed graft is harvested from the identified donor site and transplanted into the resected section. The reconstructed bone section is then fixed with bone plates and crews until the healing process is complete. Autologous graft refers to bone taken from one anatomic site and transplanted to another site in the same individual. Such autografts offer complete
*
Corresponding author. Tel.: +49-228-965-6230; fax: +49-228-965-6111. E-mail address: [email protected] (Z. Kro´l).
0531-5131/01/$ – see front matter D 2001 Elsevier Science B.V. All rights reserved. PII: S 0 5 3 1 - 5 1 3 1 ( 0 1 ) 0 0 0 0 9 - 7
Z. Kro´l et al. / International Congress Series 1230 (2001) 44–50
45
histocompatibility and they provide the best osteoinductive and osteoconductive stimuli for bone growth. For these reasons, autologous bone serves as the standard grafting material in the treatment of maxillofacial bone tumors, traumatic defects or loss of substance in growth disorders. The preselection of a donor site depends primarily on the morphological fit of the available bone mass and the shape of the part that is to be transplanted. An optimal fit and structural support, as well as minimal lesion of the donor site, are guidelines in this process. Up to now, the selection of the donor sites for autologous grafts was generally performed by the surgeon according to his experience and intuition. The anatomical solid models or manually superposition of 3D datasets were the only options for the preoperative planning [1,2]. These procedures were costly and time consuming. To improve the surgery planning step, we looked for a semi-automatic way, according to the object’s geometrical properties [3]. This continuing work is concerned with providing improved tools for computer aided selection of optimal donor sites for autologous bone grafts.
2. Methodology The planning of the bone graft surgery is based on three-dimensional CT studies. Given two pre-operative CT data sets of the same patient and the geometry description of both objects of interest, the problem of matching a desired transplant with the donor region can be posed as an optimization problem where the objective is to minimize some misregistration measure between the features defined in the two data sets. Let us define a donor site as a finite set of features in the first data set where the graft should be dissected from, and a template as a finite set of features in the second data volume where the shape of the desired transplant is defined. Our method consists of two main stages: graft design and optimization step. At the initial stage, the surgeon has to define interactively the shape of the template and the geometrical constraints for the optimization task. It is followed by the optimization step, which is fully automatic and permits generation of a set of sub-optimal and optimal donor sites for a given template. In the next section, we formulate the optimization problem and discuss the choice of the misregistration measures. After that, we describe the main stages of our method. 2.1. Statement of the optimization problem The bones are rigid bodies. So we can assume that the transformation, which aligns the designed graft with the donor region, can be modeled by a rigid transformation T :R3 ! R3. The transformation matrix can be parameterized by a six-components vector v = (rx , ry , rz , tx , ty , tz)2R6 , where rx , ry , rz , tx , ty , and tz are rotations around and translations along each of the three principal coordinate axes accordingly. From mathematical point of view, we consider problem of the form vopt ¼ arg min fCðvÞ j v 2 Mg;
ð1Þ
Z. Kro´l et al. / International Congress Series 1230 (2001) 44–50
46
where C(v) is an objective function and M R6 is a set of permissible parameter vectors which satisfy some constraints. The goal of the optimization is to find the parameter vector vopt defining a 3D rigid transformation, which minimizes the misregistration measure between the template and the donor site. Two kinds of restrictions can be put on the transformation parameters. Geometrical constraints are defined according to the geometrical properties of the template and the donor region surfaces. They restrict the search to the region with shape, size or curvature similar to the desired one. The second kind of constraints incorporates a priori knowledge into the optimization process. The quality and validity of a given solution is then evaluated according to the local morphological and functional information. The problem of matching a desired transplant with the donor region can be interpreted as a special type of the registration task. Like in the registration of the single- and multimodality data of the same subject, two common approaches have been used to determine the optimal alignment. In the surface-similarity approach, the feature space is a set of surface points (voxels) whose extraction is done in a segmentation step (normally nonautomatic). In the voxel-similarity approach, the feature space is composed of all voxels with corresponding grey-values. In the first case, we define the surface-similarity measure for any vector v =(rx , ry , rz , tx , ty , tz)2R6 as follows XN CðvÞ ¼ d 2 ðTvð pi ÞÞ ð2Þ i¼1 where d(Tv(p)) is the Euclidean distance between the position of the template surface point p after being transformed by Tv and the closest point of the donor site surface. N is the number of template voxels (surface points). In our approach the chamfer distance metric [4] has been used to determine the distance between voxels. In the voxel-similarity approach, the mutual information [5] has been used as the misregistration measure. The following formula estimates the mutual information between the donor site and the template CðvÞ ¼
X
X gi 2GT
gj 2GD
Pðgi ; gj Þ log
Pðgi ; gj Þ Pðgi ÞPðgj Þ
ð3Þ
where P( gi , gj) is a probability distribution of the scatter-plot histogram, and the P( gi), P( gj) are the probabilities for each template and donor site grey-value in the intersection volume. GT and GD are the grey-value sets of the template and the donor site volumes. In general, mutual information is a measure of statistical dependency between two data sets. It measures the distance between the probability distribution of the scatter-plot histogram P( gi, gj) and the distribution P( gi)P( gj) of two completely independent signals. The goal is to find such Topt that the transformed template voxels are most relevant for predicting the grey-values of donor site voxels. We can observe that the surface similarity and mutual information measures are taking into account different pieces of the whole morphological information about the bony internal structure. So they derive their optimal donor site on the basis of different features. Applying such different similarity measures enables the surgeon to select the optimal donor site not only in terms of bone surface correlation but also according to the whole volumetric information contained in both data sets. In the final step, the surgeon has to
Z. Kro´l et al. / International Congress Series 1230 (2001) 44–50
47
choose the best parameter vector from among a number of competing sub-optimal vectors according to the local morphological and functional information. 2.2. Graft design At the initial stage, the surgeon has to identify the spatial extent of the pathological finding. In our clinical practice, the patients with cranio- and maxillofacial disorders have often to undergo different imaging modalities as computed tomography, magnetic resonance imaging or positron emission tomography. The registration of these complementary data sets leads to a better view of the critical region, particularly, when the pathological process involves multiple tissue structure. Depending on the applied multimodal combination of data, tumor spreading can be more exactly localized or in amatory processes can be presented in their bony and soft tissue part. Thus, the differentiation between pathological and healthy structures can be done more successfully. Our system provides simple segmentation and marking tools (for example cutting planes) which allow the surgeon to delineate precisely the osteotomy border lines in the template data set as well as to define the set of constraints M in the donor site data set (see Fig. 1 (left)). In cases of loss of large bone parts or large tumor spreading, the defected structure can be reconstructed using mirror techniques from the healthy side. It is critical that the surgeons be able to interact with the virtual patient model during the planning phase in an efficient manner. Unfortunately, the interaction performed by using a standard computer mouse and keyboard is for the surgeons awkward. We are currently developing more intuitive user interfaces using a PHANToM haptic interface [6] (SensAble Technologies, Woburn, MA). It allows the surgeon through tactile force feedback to touch, feel, manipulate and alter the objects within the virtual 3D space (see Fig. 1 (right)). By using the haptic interface, the graft design step can be performed easier and faster than the standard 2D mouse based approach.
Fig. 1. Left: Delineation of the template’s osteotomy lines using the cutting planes controlled by the haptic device. Right: PHANToM haptic interface.
48
Z. Kro´l et al. / International Congress Series 1230 (2001) 44–50
2.3. Optimization Estimation of the optimal transformation vector vopt defining a rigid transformation which minimizes the misregistration measure between the template and the donor site is the goal of the optimization process. Because the misregistration measures are nonlinear functions, they can have multiple local minima on the feasible set M. In addition, the topography of search space for the applied objective functions is characterized by high diversity of objective function landscapes. Generally, we are facing a multivariate, continuous, nonlinear and constrained optimization problem. For solving such complex optimization tasks, global optimization methods are required. We have applied a simulated annealing method [7] to obtain numerically the solution of the optimization problem (1). The method belongs to the class of non-deterministic optimization methods. In contrast to the deterministic algorithms deteriorations of the objective function can also be accepted. This allows to avoid being trapped in local minima. We have implemented a several adaptive cooling schedules for the dynamic parameter selection according to progressively discovered features of the objective function landscape.
3. Results We have developed a computer aided surgical planning system for selection of optimal donor sites for autologous grafts. The system provides segmentation and marking tools (e.g. planar cutting tools) which allow the surgeon to delineate precisely the osteotomy border lines in the template data set and to define the geometrical constraints in the donor site data set. Several similarity criteria and an efficient optimization method have been implemented. The system enables the surgeon to generate a set of sub-optimal and optimal donor sites for a given template. All generated solutions can be explored interactively on the computer display using an efficient graphical interface. Besides the various 2D techniques to display matched slices conventional surface rendering techniques have been implemented. The two objects can be also rendered as semi-transparent surfaces (see Fig. 2). Combining these with volume rendering and introducing a dynamical component significantly enhances the perception of three-dimensionality during the examination and offers a valuable tool in comprehension of complex 3D structures. A reconstructive operation with the 3D planning was performed on 28 patients with osseous defects in different areas of the facial bones. All CT data have been acquired on the Siemens and Philips scanners with the high resolution protocols. The grafts were taken from the area of the iliac crest. In the mandibular disorders, the iliac bone is especially suitable for the reconstruction of the lower jaw. Due to the bone volume available, it enables an extremely stable and sturdy continuity and possesses many varied formation possibilities due to its anatomical and morphological characteristics. Fig. 2 shows a superposition of the to be reconstructed part of mandible with the pelvis donor site. Continuous follow-up observations show that there is less loss of transplants, when they are individually designed as well as high improvement of the functional results like
Z. Kro´l et al. / International Congress Series 1230 (2001) 44–50
49
Fig. 2. Semi-transparent rendering of pelvis with the matched mandible (template).
chewing ability by exact reconstruction of dental occlusion. Moreover, by the 3Dpreoperative planning, the operation time was reduced.
4. Conclusions A method for semi-automatic selection of optimal donor sites for autologous grafts in craniofacial surgery has been proposed. The method is generally applicable for various autologous grafts regardless of its shape and the grafting site. The main advantage of the proposed approach is that after determination of the initial conditions and constraints it provides an automatic procedure to find the best fitting position. Several similarity criteria and an efficient optimization method have been implemented in our system. Applying the different similarity measures enables the surgeon to select the optimal donor site not only in terms of bone surface correlation but also according to the whole volumetric information contained in both data sets. Using the haptic device has potential to greatly simplify and improve the interaction with the virtual patient model during the surgery planning. The proposed approach permits more precise planning of the surgical procedure, reducing intraoperative time and improving the postoperative outcome. Our future work will focus on the combining of intraoperative navigation and instrument tracking systems with our system as well as on the extension to more complex graft geometries (i.e. multipart dissections).
References [1] J. Satoh, H. Chiyokura, M. Kobayashi, T. Fujino, Simulation of surgical operations based on solid modeling, in: T.L. Kunii (Ed.), Visual Computing-Integrating Computer Graphics with Computer Vision, Springer Verlag, Berlin, 1992, pp. 907 – 916.
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Z. Kro´l et al. / International Congress Series 1230 (2001) 44–50
[2] H.-F. Zeilhofer, R. Sader, R. Kirsten, M. Lenz, Computer aided individual transplant design for reconstruction of the mandible, in: H.U. Lemke, et al. (Eds.), Computer Assisted Radiology, Springer Verlag, Berlin, 1995, pp. 1353 – 1358. [3] Z. Kro´l, H.-F. Zeilhofer, R. Sader, K.-H. Hoffmann, P. Gerhardt, H.-H. Horch, Computer assisted selection of donor sites for autologous grafts, in: E.A. Hoffman (Ed.), Proceedings of SPIE 3031 (1997) 196 – 202. [4] G. Borgefors, Distance transformations in arbitrary dimensions, Computer Vision, Graphics and Image Processing 27 (1984) 321 – 345. [5] P. Viola, Alignment by maximization of mutual information, PhD thesis, MIT Department Electrical Engineering and Computer Science, Cambridge, MA, 1995. [6] The PHANTOM TM Desktop System, SensAble Technologies, Inc., Woburn, MA, 01801, http://www. sensable.com. [7] P.J.M. van Laarhoven, E.H.J. Aarts, Simulated Annealing: Theory and Applications. Series: Mathematics and its applications, D. Reidel Publishing, Dordrecht, 1987.