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Journal of Computing and Information Technology - CIT 14, 2006, 1, 53–64 53 Computer-Assisted Planning in Cranio-Maxillofacial Surgery Stefan Zachow 1 , Hans-Christian Hege 1 and Peter Deuhard 12 1 Zuse-Institute Berlin (ZIB) 2 Free University of Berlin, Mathematics and Scientic Computing In cranio-maxillofacial surgery physicians are often faced with the reconstruction of massively destroyed or rad- ically resected tissue structures caused by trauma or tumours. Also corrections of dislocated bone fragments up to the complete modeling of facial regions in cases of complex congenital malformations are common tasks of plastic and reconstructive surgeons. With regard to the individual anatomy and physiology, such procedures have to be planned and executed thoroughly in order to achieve the best functional as well as an optimal aesthetic rehabilitation. On this account a computer-assisted mod- eling, planning and simulation approach is presented that allows for preoperative assessment of different therapeu- tic strategies on the basis of three-dimensional patient models. Bone structures can be mobilized and relocated under consideration of anatomical and functional con- straints. The resulting facial appearance is simulated via finite-element methods on the basis of a biomechanical tissue model, and visualized using high quality rendering techniques. Such an approach is not only important for preoperative mental preparation, but also for vivid patient information, documentation, quality assurance as well as for surgical education and training. Keywords: cranio-maxillofacial surgery, computer-as- sisted surgery planning, osteotomies, bone relocation, soft tissue prediction, finite-element simulation, visual- ization 1. Introduction A constantly increasing public mobility with always faster transportation systems, as well as an increasing level of sport activities with all accidents that might result thereof lead to a growing number of complex fractures in the cranio-maxillofacial region. A surgeon’s pri- mary concern is to reconstruct the original sit- uation as close as possible. For that purpose photographs or any other source of information that documents the previous state is used. The Fig. 1. Complex congenital skull deformities. functional and aesthetic rehabilitation of con- genital malformations, however, is much more difficult to achieve, since any individual recon- struction template is missing Fig. 1 . Especially for children or youths, the psychoso- cial consequences of an appearance, that is deviating from the respective standards, are of extremely high relevance for their personal development and the later social acceptance. Therefore, a surgeon has to model a functional anatomy under consideration of a harmonious facial appearance. Such a modeling task re- quires a high level of surgical expertise, a dis- tinct sense of aesthetics, artistic skills, and ex- tensive communication with the patients and their relatives. Due to the individuality of pa- tients, the complexity of anatomy and physiol- ogy of the human organism, as well as the de- mand for optimal functional and aesthetic reha- bilitation, cranio-maxillofacial surgery must be Medical Planning Systems, Visualization & Data Analysis, [email protected],

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Journal of Computing and Information Technology - CIT 14, 2006, 1, 53–64 53

Computer-Assisted Planningin Cranio-Maxillofacial Surgery

Stefan Zachow1�, Hans-Christian Hege1 and Peter Deuflhard1�2

1Zuse-Institute Berlin (ZIB)2Free University of Berlin, Mathematics and Scientific Computing

In cranio-maxillofacial surgery physicians are often facedwith the reconstruction of massively destroyed or rad-ically resected tissue structures caused by trauma ortumours. Also corrections of dislocated bone fragmentsup to the complete modeling of facial regions in casesof complex congenital malformations are common tasksof plastic and reconstructive surgeons. With regard tothe individual anatomy and physiology, such procedureshave to be planned and executed thoroughly in order toachieve the best functional as well as an optimal aestheticrehabilitation. On this account a computer-assisted mod-eling, planning and simulation approach is presented thatallows for preoperative assessment of different therapeu-tic strategies on the basis of three-dimensional patientmodels. Bone structures can be mobilized and relocatedunder consideration of anatomical and functional con-straints. The resulting facial appearance is simulated viafinite-element methods on the basis of a biomechanicaltissue model, and visualized using high quality renderingtechniques. Such an approach is not only importantfor preoperative mental preparation, but also for vividpatient information, documentation, quality assurance aswell as for surgical education and training.

Keywords: cranio-maxillofacial surgery, computer-as-sisted surgery planning, osteotomies, bone relocation,soft tissue prediction, finite-element simulation, visual-ization

1. Introduction

A constantly increasing public mobility withalways faster transportation systems, as wellas an increasing level of sport activities withall accidents that might result thereof lead toa growing number of complex fractures in thecranio-maxillofacial region. A surgeon’s pri-mary concern is to reconstruct the original sit-uation as close as possible. For that purposephotographs or any other source of informationthat documents the previous state is used. The

Fig. 1. Complex congenital skull deformities.

functional and aesthetic rehabilitation of con-genital malformations, however, is much moredifficult to achieve, since any individual recon-struction template is missing �Fig. 1�.

Especially for children or youths, the psychoso-cial consequences of an appearance, that isdeviating from the respective standards, areof extremely high relevance for their personaldevelopment and the later social acceptance.Therefore, a surgeon has to model a functionalanatomy under consideration of a harmoniousfacial appearance. Such a modeling task re-quires a high level of surgical expertise, a dis-tinct sense of aesthetics, artistic skills, and ex-tensive communication with the patients andtheir relatives. Due to the individuality of pa-tients, the complexity of anatomy and physiol-ogy of the human organism, as well as the de-mand for optimal functional and aesthetic reha-bilitation, cranio-maxillofacial surgery must be

�Medical Planning Systems, Visualization & Data Analysis, [email protected], www�zib�de�visual�medical�projects

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54 Computer-Assisted Planning in Cranio-Maxillofacial Surgery

carefully planned under utilization of all avail-able planning aids. Reliable methods and toolsare needed to prejudge the overall result of facialsurgery to its full extent.

2. Surgery Planning

The surgical correction of facial disproportionsrequires profound knowledge of a normally de-veloped anatomy. Among many physiognomicinvestigations, Albrecht Durer and Leonardo daVinci already did accomplish elaborate studieson facial proportions and the characterizationof harmonious faces, that even today still haveits validity �1�. Meanwhile a comprehensivedatabase of healthy or pathologic proportionsas a result of anthropometric or cephalometricstudies provide sufficient information for thecharacterization of anomalies �2, 3�. To as-sess an individual situation, anthropometric andcephalometric landmarks are identified on theskin surface as well as on X-ray images, and areset in relation to each other for a comparison tothe normal range.

Starting from anatomic landmarks and lateralor frontal X-ray images, cephalometric analysisis typically performed on 2D projections of 3Danatomy. Traditionally, contours, landmarks,distances, and angles were manually traced onradiographs using acetate overlays, and thesetracings were copied, cut and rearranged. Lateron, in the 1970’s, this process was adapted toa computer using a digitizer tablet and 2D im-age processing software �4� �Fig. 2�. That wayprofile corrections could be planned, however,without any possibility to reliably assess impli-cations on the facial soft tissue.

Fig. 2. 2D Planning of orthognathic surgery.

From the 1980’s on, computer-assisted planningmethods have been developed that allow for acombined use of anthropometric and cephalo-metric landmarks to predict soft tissue profiles

on the basis of heuristic ratios that have beenobserved over time �5�. Advanced image pro-cessing tools distort digital 2D profile imagesaccording to the estimated profile changes, lead-ing to a rough, but often grotesque approxima-tion of a patient’s postoperative appearance. Forcomplex facial dysplasia, 2D planning meth-ods with profile analysis are generally not suffi-cient. Especially symmetry aspects, as in casesof hemifacial microsomia �cf. Fig. 1, center�,are only assessable in a frontal view. Thus,the goal should be to plan any complex facialsurgery on a 3D model of a patient’s head, and toassess any changes in a 3D view from arbitraryperspectives.

Fig. 3. 3D planning of maxillofacial surgery.

The prerequisites for a 3D planning are 3Dimaging techniques, as available with computedtomography. Due to the high X-ray absorp-tion rate of bone, skeletal structures can almostautomatically be reconstructed from a consec-utive set of CT slices. This layered, three-dimensional information can be converted to alife-size replica of a patient’s skull via so calledrapid prototyping techniques �Fig. 3�. On suchmodels, surgeons are able to practically performbone cuts �osteotomies� and bone relocations topreoperatively assess functional rehabilitation�6, 7�. However, rapid prototyping techniquesare rather expensive, especially when differenttherapeutic concepts are to be evaluated. Fur-thermore, neither the impact of an osteotomyon vulnerable structures, like nerves, vesselsor, for example, the roots of the teeth, nor thefacial soft tissue arrangement resulting frombone relocations, can be assessed. These re-quirements are additional important reasons forcomputer-assisted planning methods in cranio-maxillofacial surgery.

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Computer-Assisted Planning in Cranio-Maxillofacial Surgery 55

3. Computer-Assisted 3D Planning

From the late 1980’s on, computer-assisted 3Dplanning of cranio-maxillofacial surgery becamea topic of interest �8, 9, 10, 11, 12�. Besides the3D reconstruction of individual anatomy fromtomographic data, a major focus was on predict-ing soft tissue changes due to bone relocations�13, 14, 15, 16, 17, 18, 19, 20�. Only a fewresearch groups did focus on an integrated 3Dplanning approach �21, 22, 23, 24�.

In the following we present such an integratedapproach for 3D surgery planning on virtual pa-tient models, addressing three major problems:i� authentic reconstruction of adequate 3D pa-tientmodels from tomographic data, ii� intuitivesurgery planning of bone cuts and bone reloca-tions, and iii� reliable and fast simulation ofthe resulting facial appearance. Our planningenvironment is based on the 3D modeling andvisualization system AMIRA �25�, that has beendeveloped at Zuse-Institute Berlin �ZIB�.

3.1. 3D Patient Models

Advanced visualization techniques like directrendering of scalar fields �e.g. stacks of tomo-graphic images containing HOUNSFIELD values�using texture hardware or polygon renderingof automatically generated iso-surfaces allowfor an immediate display of anatomic structureswithin 3D image data. These techniques arewell suited for diagnostic purposes, but cannotcompensate for imaging or reconstruction arti-facts that might occur due to metal shadowingor partial volume effects �cf. Fig. 4�.

Fig. 4. 3D visualization of tomographic data: left�iso-surfaces, right� volume rendering.

For a meaningful planning of surgical proce-dures, reliable patient models are the basic re-quirement. Such models, reconstructed fromstacks of tomographic slices, must represent all

relevant details of an individual anatomy, i.e.the correct surfaces of bony structures and teeth,as well as of all soft tissue boundaries. There-fore, advanced segmentation tools are needed,as, for instance, provided with AMIRA.

In view of a functional rehabilitation, the 3Dmodel of bony structures and teeth is the foun-dation for an interactive three-dimensional plan-ning of osteotomies and subsequent relocationsof mobilized bone segments. The bone-tissue,interface is needed to peg bone relocations tosurrounding soft tissue whose volume is de-fined by its boundaries to hard tissue and air.A volumetric representation of soft tissue is theprerequisite for a reliable 3D simulation of softtissue deformation and hence for a preoperativeassessment of an aesthetic rehabilitation.

All tissue boundaries are initially reconstructedfrom a sequence of tomographic images withsubvoxel accuracy �26, 27�. A resulting sur-face model typically consists of several milliontriangles �Fig. 5�, depending on the amount ofslices and the voxel size, i.e. the inner-slice res-olution and the inter-slice distance. Since highresolution surface models are very demandingin view of interactive visualization and manip-ulation, and also lead to very high resolutionvolumetric grids, being far too large for fastfinite element simulations, a mesh simplifica-tion based on error quadrics is applied �28�.That way, planning models with a resolution of75 000 to 250 000 triangles are constructed �Fig.5, center�. The simplification error, measuredas deviation between initial and reduced surface

Fig. 5. left� high resolution surface model consisting ofapprox. 5 million triangles, center� simplified model

with 250000 triangles, right� volumetric soft tissue gridconsisting of 650000 tetrahedrons.

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56 Computer-Assisted Planning in Cranio-Maxillofacial Surgery

models, depends on the voxel size and in ourimplementation amounts to a few tenths of amillimeter, thus being rather negligible.

To locally control the mesh resolution, i.e. tomake sure thin tissue layers can be filled witha sufficient amount of undistorted volume el-ements, the original algorithm of Garland andHeckbert �28� has been extended to consider amaximum edge length information per triangleas an additional cost value. Such maximum val-ues can be specified for certain tissue regionsand are automatically adjusted with regard tolocal soft tissue thickness. During simplifica-tion, the triangulated surfacemodel is optimizedwith regard to triangle distortion. That way,suitable surface meshes of finite-element com-patible triangles are generated �Fig. 6�. Theseclosed triangle meshes are the basis for the gen-eration of unstructured tetrahedral grids. Forgrid generation a modified Advancing Front al-gorithm is used �29, 30�. Since a major re-quirement for fast finite-element analysis is acoarse mesh with optimally shaped elements,the placement of inner nodes is controlled viaa 3D scalar field of edge length information,which is computed from the resolution of thesimplified surface model up to a given maxi-mum inner element size. The resulting soft tis-sue grids typically consist of 175 000 to 750 000tetrahedrons, leading to computing times of 1 to10 minutes on a standard PC for a linear elasticmodeling approach �see Sect. 3.4.�.

Fig. 6. 3D patient model for surgery planning.

Anatomically and topologically correct patientmodels, which not only represent tissue sur-faces, but also mixed tissue volumes in a con-sistent manner, are the first major requirementsof our integrated planning and simulation ap-proach. With such a combined representa-tion of individual anatomy, where tissue inter-faces �polygonal boundary surfaces� and tis-sue volumes �tetrahedral grids� are generatedand optimized concerning spatial resolution andmesh quality, we are able to perform interactivesurgery planning as well as fast finite-elementanalysis.

3.2. Cephalometric Analysis

Authentic three-dimensional models of individ-ual anatomy �so called virtual patient mod-els� and tomographic images, in combinationwith interactive 3D visualization techniques,have a tremendous diagnostic value for cranio-maxillofacial surgeons. Anomalies or asym-metries are immediately apparent and can bequantified by measuring distances and anglesbetween characteristic points. Such measure-ments are very common in anthropometric stud-ies as well as in two-dimensional cephalomet-ric analysis, where lateral X-ray images are ac-quired in a standardized way �31, 32�. Refer-ence points are either located on the facial skinsurface or on cephalograms. An individual ar-rangement of these points is compared to a sta-tistical reference for the assessment of dysplasia�cf. Fig. 7, left�.

Fig. 7. Cephalometric reference frames: a� 2Daccording to �32�, 3D with sagittal median and

b� Sella-Nasion, resp. c� Frankfort Horizontal plane.

Projective techniques, thoughwidely-used, haveobvious drawbacks in cases where asymmetricmalformations have to be assessed. En-Faceanalysis is also rather difficult to achieve using2D cephalometry. Thus, for complex cranio-maxillofacial dysplasia, a 3D analysis based ontomographic data and virtual patient models isgoing to become the method of choice �33�.Cephalographic projections can still be com-puted from tomographic data, and 2D mea-surements can be performed on such projec-tion images or on any other arbitrarily reformat-ted slice. In addition, 3D measurements alongcurved slices or between different slices, as wellas on the reconstructed 3D surface model itselfare possible. Characteristic points can either belocated within the image data �e.g. the centerof the hypophyseal fossa — sella turcica�, oron the skull and the skin surface respectively.Reference points, or even reference planes, canbe constructed from two or more points, as for

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Computer-Assisted Planning in Cranio-Maxillofacial Surgery 57

Fig. 8. En-Face symmetry and profile analysis.

instance the Frankfort Horizontal, the median,or an orthogonal plane through the sella pointand the nasion �cf. Figs. 7, right and 8�.

For a standardized three-dimensional cephalom-etry, patient models must be aligned within acommon reference frame. Such a coordinatesystem can be easily constructed from referencepoints and planes. In our case, all models arecentered using the sella point, and aligned viathe sagittal median and the Frankfort Horizon-tal plane. Within such a cephalometric coordi-nate system, measurements can be performed ina standardized way, anomalies or asymmetriescan be quantified, and useful guidelines for therelocation of bone segments can be given. Afacial profile analysis can also be performed,since extreme values can be uniquely defined�cf. Figs. 7, left and 8, right�. In addition, theassessment of dysplasia can be further enhancedusing statistical 3D shape models of normallydeveloped anatomy. By comparing an individ-ual skull shape with a statistical reference, de-viations might even lead to automatically ge-nerated reconstruction proposals �34�.

3.3. Osteotomy Planning

Facial regions that deviate from a bilateral sym-metry or that show a functional impairmentcan be identified by cephalometric and func-tional analysis. The correction of facial dyspla-sia typically requires relocation, removal, aug-mentation or even a total replacement of bonystructures. Therefore, bone has to be cut �os-teotomized� — a procedure that, without anydoubt, must be thoroughly planned. In com-plex cases, such osteotomies are planned onlife size replicas of the skull, as shown in Fig.3. Osteotomy lines are drawn onto the modeland cuts are performed accordingly. Mobilizedbone segments are rearranged to achieve skele-tal symmetry and to re-establish a functionalanatomy. However, the assessment of different

therapeutic concepts necessitates a set of plan-ning models. Due to increasing costs in healthcare and a decreasing cost recovery by the gov-ernmental health insurance, such approach isnot practicable at large.

Our goal was to develop an integrated soft-ware system that enables a surgeon to preoper-atively plan complex osteotomies and bone re-locations on virtual patient models. That way,different strategies can be evaluated at almostno additional costs. The computer-assisted os-teotomy planning is oriented on the aforemen-tioned ‘draw and cut’ principle �35�. Linescan be drawn onto the polygonal surface modelof the skull. For a very intuitive specifica-tion of such lines, a pen tablet with integratedgraphic display can be used, as shown in Fig. 9.Line drawings on a two-dimensional displayscreen are immediately projected onto the three-dimensional surface, thus giving a surgeon theimpression of drawing directly on the planningmodel. During line specification, the model canbe rotated or zoomed at will.

Fig. 9. Intuitive 3D Osteotomy Planning.

After osteotomy lines have been specified, aprocess that usually takes no longer than a fewminutes, cut surfaces are computed from a paththe cutting tool must follow to adhere to theselines. To reveal transections of vulnerable in-ner structures, like nerves, vessels or for ex-ample the roots of the teeth, tomographic im-age data can be mapped onto the cut surfaces

Fig. 10. Osteotomy planning: left� sagittal split of amandible, right� three variants of a Le Fort-I osteotomy.Assessment with regard to vulnerable inner structures.

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58 Computer-Assisted Planning in Cranio-Maxillofacial Surgery

�cf. Fig. 10�. In case osteotomies have beenspecified with regard to surgical guidelines anddo not harm any structures of risk, the modelwill be cut, i.e. bone segments are separated.

Mobilized parts of the model can be inter-actively translated and rotated into the desig-nated positions. Transformations can also berestricted to single degrees of freedom and ap-plied successively for easier control. A center ofrotation can be specified as well as a rotationalaxis �Fig. 11�. The latter is especially useful forfunctional analysis of lower jaw movements. Inaddition, collision detection and collision avoid-ance facilitate the planning of bone relocations.In orthognathic surgery, for instance, collisiondetection is helpful for orthodontic treatmentplanning, where tooth positions have to be ad-justed according to the new relationship of thejaws. Collision avoidance is even more restric-tive but very helpful for the re-establishment of acorrect dental occlusion. Besides a visual plan-ning of bone relocations, to each bone segmentthe transformation parameters can be exportedfor intraoperative navigation techniques �36�.

Fig. 11. Interactive bone relocations.

3.4. Soft Tissue Prediction

Functional rehabilitation is the priority objec-tive of osteotomy planning with bone reloca-tions. In cases where multiple bone segmentsare to be relocated simultaneously and in rela-tion to each other, or different therapeutic con-cepts are conceivable, facial soft tissue predic-tion becomes an additional important — for apatient most often the essential — criterion insurgery planning. The possibility to preoper-atively assess the implications of bone reloca-tions on the facial soft tissue, and thus to con-sider aesthetic rehabilitation as well, is highlydemanded by cranio-maxillofacial surgeons �5�.In view of an improved surgical preparation andpatient information, a reliable simulation of a

patient’s postoperative appearance is addressedwith our integrated planning approach.

The foundation of a reliable simulation of softtissue deformation is an adequate geometricmodel of a patient’s individual tissue volume�Sect. 3.1.�, as well as a mechanical model thatdescribes deformation of biological tissues in agood approximation �37�. The latter is basedon the theory of 3D elasticity, that has its ap-plications in many different engineering fields,as for example in construction design and stressanalysis �38�.

Soft tissue deformation is caused by the relo-cation of bone segments. Since bone and sur-rounding soft tissue share boundaries that areeither fixed or transformed, the resulting tis-sue configuration can be computed from thegiven boundary displacementsujΓD , in conjunc-tion with properly assigned boundary types, byminimizing the deformation energy W.

W:�Z

V

12ε :σ dV�

ZV

fext�u dV�Z

A�σ �n��u dA

�1�In �1�, the first integral term describes the in-ternal energy, being induced by strains and re-sulting stresses, represented by the two tensorsε and σ respectively. The second term com-prises external volume forces, like gravity, act-ing on the body, and the third contains normalstresses acting on the free part of the body’ssurface. In a stable static equilibrium, internaland external forces are in balance, and defor-mation energy attains a local minimum. Sincewe only prescribe boundary displacements andneglect gravity, the latter two integrals in �1�vanish. Thus, tissue prediction can be reducedto numerically finding the minimum of the firstintegral �2� as a function of the displacements uwithin the computational domain Ω, e.g. usinga finite element method. Ω is represented by avolumetric grid of the soft tissue and ΓΩ by thetissue’s boundaries �Fig. 12�.

W�u� :�12

ZΩε : σ dV �� min �2�

Stresses σ are related to strains ε via a constitu-tive law. In a first attempt, soft tissue is modeledas an isotropic and linear elastic ST. VENANT-KIRCHHOFF material, characterized by only twoindependent elastic coefficients, POISSON’s ra-tio ν and YOUNG’s modulus E. Strains are de-scribed by the linearized CAUCHY strain tensor

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Computer-Assisted Planning in Cranio-Maxillofacial Surgery 59

ε�u� � 12�ru � �ru�T� �18�. Based on these

assumptions, the following system of partialdifferential equations �3�, the so called LAME-NAVIER equation �42�, is solved for the givenboundary value problem �4� using fast finite-element methods �43, 44, 45�.

Fig. 12. Boundary displacements.

E2�1�ν�

�1

1�2νr�r�u�x�� � Δu�x�

��0 in Ω

�3�u�x� � uD0�x�� x � ΓD0 � �Ωu�x� � uD�x�� x � ΓD � �Ωσ�x� � n � 0� x � ΓN � �Ω

�4�

Such a rigorous physics-based approach repre-sents a well established method for deformationmodeling in continuum mechanics. In combi-nation with an adequate model of a patient’sanatomy, resp. soft tissue, the simulation ap-proach in general can be regarded as approvedand well suited for that class of problems. Thesimulation results depend on the choice of ap-propriate boundary conditions, as well as ofsuitable mechanical properties of living tissues,that are taken from literature �40,41�. Soft tissuecan be modeled as a homogeneous or inhomo-geneous material by assigning tissue-dependentelastic coefficients to individual volume ele-ments. Anisotropic tissue properties, non-linearelasticity and more sophisticated tissue modelsare currently investigated �45�, and are to beintegrated into our planning system as well.

An example of a three-dimensional soft tissueprediction is depicted in Fig. 13. The top rowdemonstrates the planing of a bimaxillary os-teotomy, where both maxilla and mandible areto be relocated to achieve a correct dental oc-clusion. The first image shows the preoper-ative situation with a mandibular prognathism

Fig. 13. Planning of a bimaxillary osteotomy with softtissue simulation.

and a maxillary retrognathism. The middle im-age shows a correction by maxillary advance-ment only, and the right image an alternativeby mandibular setback. Obviously there aremany combinations of bignathic relocations inbetween, that also lead to a functional rehabil-itation. The computer-assisted planning allowsfor an assessment of all possibilities, by contin-uous variation of bone positions under consid-eration of the resulting soft tissue arrangement.In the bottom row, the preoperative state is com-pared to the planned postoperative state, wherea maxillary advancement of approx. 8 mm anda mandibular setback of 3.5mm are simulated.Simulation results can be presented with photo-realistic quality as single images from differentperspectives or even as animated sequences.2

The latter is extremely well suited for indicat-ing subtle changes and leads to a vivid patientinformation �46�.

4. Results

Up to now, more than 30 clinical cases wereplanned using the previously described approach.All plannings were performed in close collab-oration with different clinical partners in Eu-rope. CT data in DICOM format were trans-ferred either with CD or via secure FTP to ZIB,where the 3D patient models were built. The re-construction process is still the most time con-suming task taking up to several hours. Af-terwards, the virtual patient models were pre-sented to the surgeons and appropriate strate-gies for osteotomies and bone reloactions werediscussed. In most of the cases, the osteotomyplanning, including bone relocation, was per-formed together with the surgeon in a video

2 http���www�zib�de�visual�projects�cas�cas�gallery�html

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60 Computer-Assisted Planning in Cranio-Maxillofacial Surgery

conference setting, using remotely controlledplanning tools. Such a planning typically takesno longer than 15 to 30 minutes. In all othercases an iterative approach was chosen, ex-changing all necessary information via e-mailand a series of annotated 2D images. For eachvariant the tissue deformation was computedwithin a few minutes, depending on the sizeand the quality of the soft tissue mesh. Staticimages of the simulation, results from differentperspectives, were visualized to and assessedby the surgeons, thus getting an impression ofthe implication of bone relocations on the facialsoft tissue.

A qualitative comparison of our soft tissue pre-dictions with postoperative results, that havebeen documented with profile photographs, al-ready yields a good correspondence. Fig. 14shows a pre- and a postoperative image as wellas an overlay view of the predicted 3D facialtissue �semitransparent� with relocated bonystructures �opaque� and the photograph of thetrue outcome, both rendered in a common co-ordinate system with the photograph positionedat the midsagittal plane. Such an evaluationallows for a comparison of the tissue profilein cases where the bone relocations have beendocumented with lateral cephalograms.

In order to determine the three-dimensionalprediction accuracy and thus the reliability ofour modeling approach, a quantitative analy-

Fig. 14. 2D assessment of tissue prediction using profilephotographs and 3D visualization techniques,

right� overlay of the postoperative photograph and thealtered planning model with predicted facial soft tissue.

sis based on postoperative CT data was per-formed �47�. For four patients with distinctmidfacial hypoplasia and class III dysgnathiaa maxillary advancement of up to 15mm wasplanned and performed �cf. Fig. 15�. With thepostoperative CT data the actual results, i.e. theexact courses of the osteotomy lines and the newpositions of mobilized bone segments are doc-umented, thus enabling us to exactly reproducethe surgical procedure. Therefore, the pre- andthe postoperative models were aligned via theneurocranium, that was not affected by the sur-gical procedure, using an iterative closest pointmethod �49�. The mean registration error was inthe order of 1–2 tenths of a millimeter. Mobilebone segments like the mandible, the hyoid andthe spine, as well as the osteotomized maxillawere rigidly aligned via anatomic landmarks.The overall registration error of the bone sur-face was below 0.5mm. That way we were ableto compare our soft tissue simulations with thepostoperative results, as it is described in �48�.

Fig. 15. 3D assessment of soft tissue prediction usingpostop. CT data: grey� simulation, magenta� actual

result.

Among others, the prediction accuracy dependson an appropriately chosen biomechanic modelof living soft tissues. Therefore, the histome-chanic parameters of soft tissues are required.However, these parameters vary individuallyand are difficult to obtain in-vivo. In the firstassumption, soft tissue was modeled as a ho-mogeneous, isotropic and linear elastic mate-rial. In a homogeneous tissue model, YOUNG’smodulus E has no influence at all on the LAME-NAVIER-equation �3�. Hence, only the value ofPOISSON’s ratio ν was varied within the rangeof �0 � � �0�5�, where a value of 0�5 stands forincompressibility. For all of the four patients

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Computer-Assisted Planning in Cranio-Maxillofacial Surgery 61

the HAUSDORFF-distance H � max�d�S1� S2�,d�S2� S1�� between the retrospectively simu-lated and the postoperative facial skin surfacewas computed �39�. A minimum deviationH�ν�min was expected to yield a representa-tive mean value ν for soft tissue compressibil-ity �Fig. 16�.

Fig. 16. Prediction quality of a homogeneous tissuemodel with varying POISSON’s ratio ν.

Considering soft tissue as an inhomogeneousmaterial, not only compressibility, but also elas-ticity of each tissue type has to be taken intoaccount. In another study an inhomogeneoustissue model was investigated, where to eachtissue element individual histomechanic param-eters were attributed. Unfortunately, there isno unique relationship between HOUNSFIELDunits and mechanical properties. Determina-tion of appropriate values for different tissuetypes is still the subject of ongoing research inbiomechanics and elastography. Thus, litera-ture values derived from ex-vivo experimentswere used �47�.

In order to preserve the original tissue grid forcomparison, tissue elements were relabeled ac-cording to the mean HOUNSFIELD values, usinga barycentric sampling with selectable refine-ment of up to 512 sample points per tetrahe-dron. At first we differentiated between muscleand embedding tissue, since muscle can be eas-ily segmented within a range of ��30� 100�HU.As a result, the tissue grid consists of two differ-ent tissue types that can be assigned individualvalues for ν and E. For each tissue, the POISSONratio ν was varied within the range of �0 � � �0�5�and YOUNG’s modulus E within �50� 450� kPa.Again, a parameter study with approx. 2 500FE simulations of the tissue deformation re-sulting from maxillary advancement was con-ducted, and for each simulation the deviation of

the predicted and the postoperative soft tissueconfiguration H�νs� Es� νm� Em� was computedusing a closest points distance. The best corre-spondence was found with 0�43 � νm � 0�45and Em � 300 kPa for muscle and with 0�44 �νs � 0�47 and Es � 50 kPa for the embeddingtissue �Fig. 17�.

Fig. 17. Prediction quality of an inhomogeneous tissuemodel with varying POISSON’s ratio ν and YOUNG’s

modulus E with regard to muscle and embedding tissue.

For approximately 70% of the facial skin sur-face3, the prediction error was below 1 mm,and only 5 – 10% showed a deviation largerthan 3, up to 4mm. These areas were mainlysubject to postoperative swelling. However, amean prediction error of about 1 – 1.5mm al-ready seemed to be an acceptable result for ahomogeneous, linear-elastic tissue model. Theinhomogeneous model performed slightly bet-ter, though the differences were rather marginal.The net improvement of using an inhomoge-neous tissue model, or of fine tuning the elasticparameters does not seem to significantly influ-ence the prediction of the skin surface �47�.

In conclusion we would like to point out thatcomputer-assisted planning with soft tissue pre-diction contributes to an improved surgical pre-paration. Different therapeutic concepts canbe evaluated, thus giving a surgeon more cer-tainty in cases of complex cranio-maxillofacialsurgery. The next consequential step is an ex-act transfer of the planning into the operatingroom by using innovative navigation techniquesthat will definitely find their way into cranio-maxillofacial surgery �36�.

Besides an improved mental preparation, an in-tegrated computer-assisted approach also con-tributes to a demonstrative patient information.This in turn enhances the motivation �patientcompliance� that again typically leads to better

3 only the facial region and not the entire head was evaluated

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62 Computer-Assisted Planning in Cranio-Maxillofacial Surgery

Fig. 18. Improved patient information using advanced3D visualization techniques.

therapeutic results. In some cases patients didactively participate by using our planning andvisualization system themselves �cf. Fig. 18�,and in one case a patient even insisted on a softtissue prediction for an intended genioplasty.A reliable simulation with photo-realistic visu-alization also contributes to an improved doc-umentation and quality assurance. The sim-ulation of the effects of different therapeuticconcepts can even be leveraged for surgical ed-ucation and training. New or unconventionalosteotomy techniques, for instance, can be sim-ulated on virtual patient models, and the impacton the soft tissue can be studied.

5. Future Work

There is still a lot of work to be done. At first,the modeling of soft tissue deformation can befurther enhanced. On that account, anisotropydue to tendons, muscle fibers and skin ten-sion lines are to be investigated, as well asnon-linear, or even visco-elastic material prop-erties �45�. Since computational costs are in-creasing with advanced modeling approaches,concepts for multigrid methods as well as par-allelization must be considered as well Tissueremodeling and histogenesis is another impor-tant topic that must be taken into account forlarge deformations. Also, the transfer of bound-ary displacements from bone relocations to thesoft tissue can be improved since tissue regionsare detached from bone and lifted off duringsurgery, and bone segments are re-covered afterbone relocations have been accomplished. Forsuch regions, the direct coupling of tissue andbone must be replaced by sliding contact or ob-stacle modeling. With all these improvements aprediction error of below 1mm might be attain-able, an accuracy that seems quite acceptablefor surgery planning.

6. Acknowledgements

We are very grateful to our cooperating sur-geons: Prof. Dr. Dr. Zeilhofer, University Hos-pital Basel, Switzerland; Prof. Dr. Dr. Sader,University Hospital Frankfurt, Germany; Priv.-Doz. Dr. Dr. Hierl, University Hospital Leipzig,Germany; Dr. Westermark, Karolinska InsituteStockholm, Sweden; Dr. Dr. Nkenke, Univer-sityHospital Erlangen-Nurnberg,Germany, andDr. Dr. Gert Wittwer, University Hospital Vi-enna, Austria. Many thanks to all support-ing clinicians for their valuable remarks and inparticular to the patients for their trust in oursurgery planning and soft tissue prediction. Fi-nally, we would like to thank the reviewers ofthis article for their valuable comments.

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Received: December, 2005Accepted: February, 2006

Contact address:

Stefan ZachowDept. Medical Planning Systems

Zuse-Institute Berlin �ZIB�Germany

e-mail: zachow�zib�de

STEFAN ZACHOW is a senior researcher at ZIB, heading the MedicalPlanning Systems group. He earned degrees in computer engineering�University of Applied Sciences Berlin�, computer science �Universityof Technology Berlin�, and finished a postgraduate study on medicalphysics �Humboldt and Free University Berlin�. Stefan received hisPh.D. in 2005 and is a member of the ACM, the IEEE computer society,ISCAS, curac, and the GI working group of medical visualization.

HANS-CHRISTIAN HEGE is the head of the department Visualization &Data Analysis at ZIB, where the 3D visualization and volume modellingsoftware Amira has been developed. He graduated in physics �FreeUniversity Berlin� and was cofounder of mental images as well as ofIndeed Visual Concepts, Berlin. He has edited books on mathematicalvisualization and acts as member of the editorial boards of the book se-ries Mathematics �Visualization and the video�dvd series VideoMath�Springer Verlag�. He served as program committee member for IEEEVisualization, IEEE Eurographics Symposium on Visualization, andWSCG. Mr. Hege is a honorary professor at the German Film Schoolin Potsdam and a member of the ACM, IEEE, GI, and curac.

PETER DEUFLHARD is founder and president of the Zuse-InstituteBerlin.He has a full professorship in mathematics and scientific computing atthe Free University of Berlin. He studied physics at the TechnicalUniversity of Munich, where he obtained his diploma degree in PurePhysics in 1968. He then turned to mathematics and received his Ph.D.in mathematics in 1972 from the University of Cologne. In 1977, hecompleted his postdoctoral thesis in mathematics at the University ofMunich. From 1978 to 1986 he held the chair of numerical analysis atthe University of Heidelberg. Prof. Deuflhard is co-editor of a numberof scientific journals. His research interests are modelling, simulation,inverse problems, and optimization in all kinds of differential equations.