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1 1 Technische Wetenschappen 3D Numerical Simulation of Bone Ingrowth for Glenoid Component Design of Shoulder Prostheses Applicants Addresses: Dr.ir. C.W. Oosterlee (1) (Project coordinator), Prof.dr.ir. P. Wesseling (1) and Prof.dr.ir. F. van Keulen (2) TU Delft (1) Numerical Analysis group (NA) Faculty of Electrical Engineering, Mathematics and Computer Science Department of Applied Mathematical Analysis Mekelweg 4, 2628 CD Delft (2) Structural Optimization and Computational Mechanics group (SOCM) Faculty of Mechanical Engineering and Marine Technology, Mekelweg 2, 2628 CD Delft Oosterlee: Tel: Internet: v. Keulen: Tel: Internet: wbtmavk/ Secretary: D. Steeneken, Tel: , Fax: Framework: Recently, Delft University of Technology (DUT) has reorganized research efforts in a number of spearheads and platforms. This has led to the initiation of the Platform Computational Science and Engineering, consisting of eighteen research groups from five different faculties. The present cooperation originates from two participating groups from different faculties, namely the Numerical Analysis group (NA) and the Structural Optimization and Computational Mechanics group (SOCM). The project in this proposal will be embedded within the platform. Furthermore, at Delft University of Technology, an interfaculty-research programme aiming at improving the state-of-the-art in shoulder joint replacement surgery was initiated in The programme is entitled: Development of Improved endoprostheses for the upper Extremities (DIPEX). The DIPEX programme involves six PhD students and four postdocs, who collaborate intensively with Leiden University Medical Center (LUMC), Free University Amsterdam and Erasmus University Medical Center Rotterdam (UMCR). The SOCM-group is responsible for the research on the mechanical aspects of shoulder endoprosthesis fixation. The present research proposal is building on and integrates with the research carried out within the DIPEX programme. Keywords shoulder prosthesis, bone ingrowth, multi-model multi-scale application, homogenization, poroelasticity, mechanobiology, modeling of bone tissue differentiation, boneimplant interface, efficient numerical solution

2 2 1 Project Description 1 Summary 1.1. Background The goal of this project is to improve the understanding and simulation of bone ingrowth in a prosthesis for the replacement of the socket (glenoid) of the shoulder joint. A joint replacement restores the functional use of limbs and relieves pain. In the lower extremities, joint replacement is a commonly used and successful surgical procedure nowadays. Roughly 300,000 hip joint and 250,000 knee joint replacements are performed in the EU annually. Glenoid prostheses, however, are difficult to design as the geometry is complex and the shoulder blade has relatively little bone mass. One of the complicating geometrical aspects is a shallow cavity in the glenoid. Alignment of the replacement glenoid is important to maintain stability and as much freedom of arm movement as possible. Loosening of glenoid components is one of the major problems in shoulder arthroplasty. Whereas the loosening rate in hip joint and knee joint replacements is about 5 10%, glenoid loosening in total shoulder replacement has been reported in up to 44 % of the cases. Radiolucent lines, which give an indication of mid- and longterm prosthetic loosening, have been observed in up to 96 % of replacements. The consequences of prosthetic loosening can be dramatic, as the prosthesis cannot always be replaced due to bone deficiencies. Therefore there is a great clinical need to improve fixation of glenoid components. Previously, many designs have been introduced to overcome the problem of loosening. So far, however, none of these designs fully succeeded in improving results of long-term fixation. Cemented glenoid components loosen mostly due to mechanical failure of the cement layer; certain cementless metal-backed components show problems with rapid polyethylene wear. Better performance may be expected of fixation realized through bone ingrowth in special cementless prosthesis layers. In that case, the design of the prosthesis should be well-adapted. The question arises of how ingrowth into glenoid components can be improved. To avoid time consuming trial-and-error approaches involving many clinical tests, a systematic process can be established using mathematical models for design and optimization. For this accurate simulation tools for bone ingrowth processes are absolutely mandatory. Two-dimensional (2D) finite element simulation models have already been set up in the Structural Optimization and Computational Mechanics (SOCM) group. However, the bone ingrowth concept used is rather phenomenological. In order to reliably estimate success of a specific design, a full 3D model that more faithfully accounts for the complexity of the underlying biological processes is needed. Furthermore, the present models require substantial computing time (several days for a run); this needs to be reduced. 1.2 Research In this project, we aim at improving an existing computational model for the design of shoulder prostheses by means of a 3D numerical model with more realistic biological modeling. The 3D model will give a more detailed insight in the bone ingrowth process, as the physical geometry is genuinely three-dimensional. To achieve this we need further research from the present status along two lines, by two researchers. First of all, the generalization of the 2D application to 3D is a major task in numerical mathematics. It is absolutely necessary to accelerate or reformulate the numerical algorithms underlying the 2D model in order to obtain 3D results within reasonable computing time. Furthermore, the assumptions in the present model concerning some of the mechanical and biochemical processes need to be carefully reconsidered. After a multi-scale analysis, in which the biomechanical processes at the bone-prosthesis interface are first considered on micro levels, coefficients and parameters in a continuous macro model will be determined by homogenization. The resulting, more realistic, macro model will be incorporated in the 3D solution method.

3 3 In a close cooperation between the SOCM group and the Numerical Analysis group, we expect to find the required synergy in the pursuit of this target. 1.3 Utilization Within the clinical-driven research programme DIPEX, the computer-aided pre-operative shoulder replacement planning tool DSCAS is being developed. This software environment is developed in close collaboration with clinicians, particularly from the LUMC. DSCAS will embed image processing, visualization, functional analysis and fixation analysis tools. Moreover, interfaces to patient-dependent operation guidance tool production and computer navigation are currently developed. The computational techniques as developed within the project proposed will be integrated in DSCAS as well. In this manner, the simulation techniques will be used for pilot studies of new prosthesis designs. These studies will be carried out in collaboration with (academic) clinical partners and endoprosthesis manufactures, e.g. Isotis, Ortomed, Zimmer, Stryker Howmedica Osteonics or Implex. Isotis is suggested as a possible member of the users committee. Moreover, DSCAS is intended as a tool which will be used particularly by clinicians. Thus, the new techniques developed in the course of the present project will automatically become available in clinics. The results of the project can also be implemented in commercial simulation software packages. Typical examples are ABAQUS and MSC-MARC. The latter company is suggested as a possible member of the users committee. The utilization will be primarily focused on shoulder prostheses. However, there is no reason why the techniques developed cannot be applied to other implants. Therefore, we will actively seek collaboration with both clinical and industrial partners who can use the techniques in their field of application. The people interested in participation in a users committee regarding the project proposed are from the following companies/institutes: Company Isotis (www.isotis.com). Company MSC Software BV. LUMC, Leiden. Netherlands Institute for Metals Research (NIMR). Samenvatting (Nederlands) Het doel van dit project is een verbeterd inzicht in bot-ingroei processen door middel van het wiskundig modelleren van bot-ingroei bij een prothese voor het zogeheten glenoid gedeelte van het schoudergewricht. Onderarm- en beenprothesen, die het gebruik van armen en benen herstellen en pijn wegnemen, zijn tegenwoordig zeer succesvolle chirurgische ingrepen. In de EU worden jaarlijks ongeveer heup- en knieprothesen ingebracht. Echter, succesvolle schouderblad-prothesen zijn moeilijker te ontwikkelen, vanwege de complexe geometrie en omdat het schouderblad relatief weinig botmassa bezit. Een van de geometrische complicaties is de vlakke caviteit in het glenoid. Een geometrisch goed passende prothese is erg belangrijk voor de stabiliteit van het gewricht en om een zo groot mogelijke vrijheid in de armbeweging te garanderen. Een groot probleem in schouderchirurgie is het herhaaldelijk loslaten van de glenoide prothesecomponenten. Terwijl voor heup en knieprothesen in slechts 5 tot 10 procent van de gevallen problemen met loslating gerapporteerd worden, is dit bij glenoid componenten tot 44 procent van de patiënten. Röntgenstralen, die een indicatie geven van loslating op de lange termijn, duiden op problemen in wel 96 procent van de prothesen. De consequenties van loslating kunnen dramatisch zijn, omdat prothesen door het verdwijnen van botstructuur niet altijd vervangen kunnen worden. Derhalve is verbetering van de fixatie van de glenoid componenten erg belangrijk. Vele poly-ethyleen of met metaal versterkte componenten zijn reeds

4 4 geïntroduceerd om de fixatie te verbeteren. Tot nu toe heeft geen van de ontwerpen significant succes bij de lange termijn fixatie. Prothesen gefixeerd met cement hebben problemen door bezwijken van de cementlaag; cementvrije, metaalversterkte prothesen hebben problemen met poly-ethyleenslijtage. Een betere fixatie wordt verwacht met behulp van bot-ingroei. In dit laatste geval moet de prothese zo ontwikkeld worden dat de ingroei optimaal verloopt. De vraag dient zich aan hoe een prothese ontwerp eruit moet zien, zodat de glenoid component de ingroei bevordert. Om tijdrovend experimenteren te vermijden, stellen we een ontwerpproces voor op basis van wiskundige modellen en optimalisatie van de geometrie. De wiskundige bot-ingroei modellen, partiële differentiaalvergelijkingen, dienen doorgerekend te worden met numerieke technieken. Twee-dimensionale eindige-elementen modellen zijn reeds aanwezig in de SOCM groep bij werktuigbouwkunde. Zij kosten echter veel rekentijd (meerdere dagen voor één simulatie) om de numerieke oplossingen te verkrijgen. Het is verder noodzakelijk de biologische en mechanisch-mathematische modellen voor bot-ingroei te verbeteren. Doel (Nederlands) In dit project willen we drie-dimensionale geometrieën simuleren met realistische wiskundige modellen voor de biologische processen die aan bot-ingroei gerelateerd zijn. Een 3D model geeft een veel gedetailleerder inzicht in bot-ingroei dan een 2D model, omdat de werkelijke geometrie drie-dimensionaal is. Er zijn geen symmetrieën, die de dimensie van het model kunnen reduceren. Om dit ambitieuze doel te bereiken willen we het onderzoek langs twee lijnen voortzetten. Allereerst is het generaliseren van het 2D model naar 3D een belangrijke numeriek wiskundige opgave. Het is absoluut noodzakelijk om de reeds bestaande oplostechnieken voor het 2D model aan te passen (te versnellen) met nieuwe methoden uit de numerieke wiskunde en parallelisatie. Verder moeten de gekozen wiskundige modellen voor de mechanische en biologische aspecten onder de loep genomen worden. Met behulp van een meer-schalen analyse, waarin de biologische processen worden geanalyseerd en gemodelleerd op micro-niveau, moeten met behulp van homogenisatie-technieken, coëffiënten en andere parameters in het continue mechanica/diffusie model ingebracht worden. Dit is nodig, omdat bot-ingroei modellen op micro-niveau niet in redelijke rekentijd doorgerekend kunnen worden voor een complete, realistische prothese configuratie. De meer-schalen analyse zal een realistischer wiskundig model opleveren voor het complexe bot-ingroei proces. In een samenwerking van de werktuigbouwkundige SOCM groep en de wiskundige NA groep verwachten wij een synergie effect voor het bereiken van deze doelstelling. Utilisatie (Nederlands) In het door medische klinieken aangestuurde onderzoeksprogramma DIPEX wordt operatie planningssoftware voor schouderprothesen, genaamd DSCAS, opgezet. Deze software omgeving wordt in nauwe samenwerking met ziekenhuisartsen, in het bijzonder van het LUMC ontwikkeld. DSCAS zal medische beeldverwerking, visualisatie en analysemogelijkheden omvatten. Verder wordt een interface voor patientafhankelijke operatieondersteuning en computernavigatie ingebouwd. De numerieke simulaties die in het voorgestelde project opgezet worden zullen deel uitmaken van DSCAS, zodat de ontwikkelde numerieke methoden gebruikt kunnen worden voor de ontwikkeling van nieuwe prothesen. Deze studies worden doorgevoerd in samenwerking met de (academische) partners uit de ziekenhuizen en met industriën die prothesen ontwikkelen, zoals Isotis, Ortomed, Zimmer, Stryker Howmedia Osteonics of Implex. Isotis wordt voorgesteld als mogelijk lid van een gebruikerscommissie. Het instrument DSCAS is in het bijzonder voor gebruik in medische klinieken ontwikkeld. Daarom zullen de nieuwe numerieke modellen automatisch beschikbaar zijn in klinieken. De resultaten van het hier voorgestelde project kunnen ook eenvoudig in commerciële softwarepakketten als ABAQUS en MSC-MARC ingebouwd worden. De laatstgenoemde is een potentieël lid van

5 5 de gebruikercommissie. Dit deel van de utilisatie focusseert vooral op de schouderprothesen. Echter, de te ontwikkelen inzichten en technieken kunnen ook voor andere implantaten in het menselijk lichaam gebruikt worden. In de loop van dit project zal er daarom ook actief naar andere toepassingsgebieden voor de numeriek modellen gezocht worden. Geinteresseerde partners voor dit voorstel zijn: Firma Isotis, Firma MSC Software BV. LUMC, Leiden. Netherlands Institute for Metals Research (NIMR). 2. Composition of the Research Team 2.1 The Team The team is composed as follows: Name: Rank Funding fte / year Dr.ir. C.W. Oosterlee UHD DUT (NA) 0.1 Prof.dr.ir. F. van Keulen HL DUT (SOCM) 0.1 Dr.ir. F.J. Vermolen UD DUT (NA) 0.1 Prof.dr.ir. P. Wesseling HL DUT (NA) 0.1 Dr.ir. J. van der Linden UD UMCR/DUT (SOCM) 0.1 Dr. E. Valstar UD LUMC/DUT (SOCM) 0.1 Ir. P. Broomans PhD (4 years) STW 1.0 Ir. A. Andreykiv postdoc (2 years) STW 1.0 The daily supervision of the PhD student Broomans is in the hands of Oosterlee, Vermolen and van Keulen. The project is carried out as a cooperation between the Numerical Analysis group (NA) and the Structural Optimization and Computational Mechanics group (SOCM), both at the Delft University of Technology. The NA group has built up thorough knowledge of applicable mathematics and develops expertise in applying the methods and tools of mathematics to problems in science and engineering. Development of novel solution methods, and the analysis of existing numerical methods with the purpose to accelerate the convergence of iterative methods in complicated multidisciplinary applications is a major effort within the group that has received worldwide recognition. Key contributions by members of the group have been [1 8]. Oosterlee has developed fast iterative solvers for the poroelasticity equations in a collaboration with Dr. F.J. Gaspar from the University of Zaragoza, Spain and Dr. R. Wienands from the University of Cologne, Germany [9, 10]. Vermolen has worked with advanced FE discretizations and fast solution methods for porous media and diffusion applications for several years [11 13]. The Structural Optimization and Computational Mechanics group (SOCM) has great expertise in numerical techniques for optimization methods applied to real-life engineering applications. The group is part of the Department Mechantronics and Control, in which all ongoing biomedical research activities at the faculty of Design, Engineering and Production are concentrated. In the field of bone mechanics, the attention has been on models used for pre-operative numerical studies for shoulder endoprosthesis designs. In this context, the application of micro-polar continuum models was studied, including material parameter estimation. Bone ingrowth modeling was initiated a few years ago. This research serves as the starting point for the present research proposal. Finally, a study is ongoing on the global modeling of the shoulder, which includes a unique study on material inhomogeneity and

6 6 anisotropy in the glenoid of the shoulder. Important publications from the SOCM group in the direction of the present proposal are [14 25]. From DIPEX, two experts on biomechanical modeling have part-time positions at DUT, Dr.ir. J. van der Linden and Dr. E. Valstar. Their expertise is extremely important regarding the directions of the research in this project. Moreover, they ensure embedding and collaboration with the academic clinical partners (LUMC and UMCR). 2.2 Candidates We request funding from STW for one PhD student and one postdoc (two years) position. The postdoc will work on novel interface elements and the micro-modeling of the interface. Both the PhD student and the postdoc will study routes for improvement of the existing models by inclusion of biological and chemical aspects. The PhD student will initially work on the computational aspects in the project, like the acceleration/reformulation of the solution methods, the improved coupling of the different models and the generalization to three dimensions. In addition, the accuracy of the models will be addressed. For the PhD position we have a suitable candidate among the Master s students of the Numerical Analysis group. Ir. P. Broomans graduated in August 2003 under supervision of Dr. C. Vuik and Prof. P. Wesseling, and he has started on the project as PhD student under the joint supervision of profs. Wesseling and van Keulen on July 10th 2003 with initial funding by DUT in the framework of the Platform for Computational Science and Engineering. For the postdoc position we have a suitable candidate among the PhD students working in the DIPEX project in the SOCM group. Ir. A. Andreykiv is finalizing his PhD thesis on the computational model for bone ingrowth. In his PhD thesis (concept should be ready by July 2004) he will present a pilot interface model which is based on homogenization. We would like him to stay for two more years to work on the subject as a postdoc. The PhD student will benefit greatly from the knowledge gathered by the postdoc and from his computational models. A cooperation between the postdoc and the PhD student is a crucial prerequisite for the success of the project. They share the same office. The Curriculum Vitae of the PhD student and the postdoc are added in an appendix to this proposal. 3. Scientific Description 3.1 Summary of Research Loosening of glenoid components is a major complication for shoulder arthroplasty. Two fixation techniques for the prosthesis are cement and bone ingrowth fixation. Often additional screws or pegs are used to ensure initial stability. Although cemented fixation performs very well initially, damage accumulation, that progresses within the cement mantle with time causes fixation failure. Some studies show that this failure can already occur two years post operatively. Bone ingrowth fixation, on the contrary, may last practically forever. For bone ingrowth, use has been made, for example, of porous tantalum, titanium mesh, porous ceramics, cintered bids etc. However, success of the surgery is achieved only if full-scale bone ingrowth has taken place. In some cases mechanical instabilities on the bone-implant interface may result in the appearance of fibrous tissue that inhibits bone ingrowth. Accurate and time efficient numerical models are the tools of choice for pre-clinical design and testing. The present proposal aims at accurate and efficient numerical modeling of bone ingrowth for representative geometries and under realistic loading conditions. The latter will be available using a musculo-skeletal model (Delft Shoulder Model [29, 30]), as available within the DIPEX programme. Factors that are particularly important for fixation by bone ingrowth are the appropriate structure, bio-compatibility of the material at the bone-implant interface and the initial stability of the implant. A stable immediate fixation is a requirement for a successful secondary fixation by bone ingrowth. In fact, the entire biomechanical-chemical status near and in the porous prosthesis determines whether or not fixation through ingrowth

7 7 takes place. Numerical simulation methods may help to predict this status as a function of time and loading. In this way a prediction on the occurrence of bone ingrowth can be made. Moreover, the availability of these methods opens the route towards model-based optimization Work of the Postdoc The recent research carried out by Andreykiv in the SOCM group will soon crystallize in a PhD thesis. The thesis will report on 2D simulations for different prosthesis design configurations Figure 1: Bone ingrowth into the porous backing of a 2D glenoid prosthesis. The model is based on a poroelastic analysis, including contact analysis and a diffusion model. The latter is used to evaluate the concentration of mesenchymal cells. The series of pictures depicts the formation of bone (blue) and cartilage (red) as a function of time. The present model is restricted to two dimensions because of the computing time involved. (see Figure 1) but also on initial 3D simulations of bone fracture healing and bone ingrowth for only a small part of a bone-implant interface. The work to be carried out by the postdoc will be a direct continuation of this work. The 2D simulation for different design configuration studies the influence of the initial fixation (pegs in Figure 1) and material properties of the implant on bone ingrowth. A 3D simulation of tibial bone fracture healing enables accurate validation of tissue differentiation models to be developed. A 3D micro-model of the interface tissue enables a detailed study on local bone ingrowth as a function of the mechanical loading conditions, local topology of the implant, imperfections of the interface, among many other aspects. For this reason, the first task will be to carry out a detailed study on different aspects that influence on local bone ingrowth. Figure 2 shows part of the bone-implant interface with porous backing of the implant, soft tissue at the interface and adjacent bone. It indicates that the interface between tantalum and bone will be modeled in detail. The numerical observation is, see Figure 3, compared, as far as possible, with experimental and clinical observations. This data [15, 16] will become available through literature and the

8 8 collaboration with experimentally-oriented groups, e.g. the Division of Biomechanics and Engineering Design at the KU in Leuven (KUL), Belgium and clinicians at LUMC. The 3D micro-model study will result in a review of the different (design) aspects in relation to local bone ingrowth. The results will be communicated and/or made available to clinical researchers and/or prosthesis manufacturers. A second task is to refine the 3D model for a limited part of the interface, see Fig. 3. These refinements will be based on: (i) recent work on bone-healing models (see [26-28,31,32]) and (ii) clinical and experimental observations (e.g., KUL and LUMC). It is anticipated that refinements of the model particularly involve the biological aspects in the model and the biomechanical models used for cell distribution and cell differentiation. The results of this second task will be reported in the literature. A third task will be the construction of a simplified interface model. The basis for such a simplified model will be the detailed 3D model of a limited part of the interface (Fig. 3). The goal here (presented schematically in Fig. 4) is Figure 2: Glenoid with a prosthesis (top), schematic representation of the interface (left) and mesh of the interface tissue (right) to be used for the study of the interface. to construct an inexpensive computational tool which sufficiently models the interface. This model should be a compromise between accuracy and computational efficiency and should be applicable in the context of design and automated optimization studies of protheses. The construction of this interface model has similarity with homogenization tasks. However, here the purpose is not to construct a continuum model but to formulate an interface model. This study will start with 2D cases. The 2D study should easily reveal principal problems and pitfalls, as the comparison with high-resolution 2D-models can be done relatively easily, i.e. without overwhelming computational cost. Once the 2D study has indicated that effective interface models can be formulated, the step towards 3D models will be made. The 3Dinterface model will be integrated in the DSCAS software. In this manner, it may become available for clinicians and prosthesis design manufacturers. In a future step, the 3D-interface model will be used in (re)design studies of existing and new prostheses. This will be done in collaboration with clinicians and prosthesis design manufacturers.

9 9 Figure 3: Preliminary results: Prediction of interface tissue phenotype according to calculated osteogenic index [16] (blue-bone, red-cartilage, yellow-fibrous tissue). Figure 4: Detailed micro-scale porous medium model to be used as a basis for an interface model. The latter can, because of its computational efficiency, easily be integrated into a macroscopic computational model. This macroscopic model is a tool for pre-clinical design studies in the DSCAS software environment Work of the PhD Student The numerical model is based on the assumption that a patient is able to move his arm only to some extent after the glenoid replacement. This arm movement is modeled as a fluctuating distributed load on the prosthesis. It is used in a contact analysis which provides, among other aspects, the micromotions at the interface and the deformations of the porous prosthesis. Strain and fluid velocity are then computed using poroelastic equations, i.e., the equilibrium equations in combination with a mass balance for the bone fluid. The strain and fluid velocity determine whether or not mesenchymal cells may differentiate into fibrous tissue, cartilage or bone. The concentration of mesenchymal cells is modeled by taking into account cell migration, proliferation and apoptosis. These aspects are modeled by an augmented diffusion model. In the overall algorithm the three stages, contact analysis, the solution of a poroelasticity problem, and the solution of diffusion equations, can be clearly identified. The PhD student will initially work on the improvement of the numerical algorithms in a two-dimensional bone ingrowth model. His work will focus on the following aspects. Firstly, the development of an accurate finite element formulation for recently introduced biologi-

10 10 cal diffusion models of tissue differentiation (e.g. [27, 28]). Secondly, he will develop an efficient numerical technique for the solution of the poroelastic problem, that is used to simulate deformation of the soft interface tissue, which precedes the bone. It is not trivial to find a stable finite element for the poroelasticity equations (with standard finite elements oscillating solutions are reported in the literature). It is further a challenging task to develop efficient iterative solution methods for the coupled poroelasticity/tissue differentiation problem, especially in 3D. These two stages of the solution process need to be coupled with the contact analysis, in which about 200 computations are performed with different boundary conditions. At present, the time dependence in all stages is handled by means of fully implicit time integration. The cost of solution by direct solution methods increases quadratically with the number of unknowns/elements. The PhD student will develop efficient iterative solution methods for the implicit systems appearing. As the matrix from the finite element discretization is nonsymmetric and not structured, the design of an appropriate iterative solver is state-of-the-art research. Another important concept for the reduction of the total turn-around time of 3D computations is parallelization. The successful ingredients will be used for the 3D target bone ingrowth model to be developed. Furthermore, the student will interact closely with the postdoc on improved biological and biochemical models for bone ingrowth, and on the detailed models of the behavior of porous structures (mentioned above) Personnel We request one PhD student for four years, and a postdoc for two years Material/ Cost For travel abroad we request a budget of 20 k for the researchers. For the 3D simulations, we need 4 new computer nodes for an already existing Linux cluster in the group. We need licenses for the commercial software for pre- and post-processing. In total, we request 7k for computer hardware and 13k for software Planning The planning for the work of the postdoc is: Year 1: Year 2: Detailed study of the bone-implant interface Refinement of the interface model Construction of computationally efficient interface model Implementation in DSCAS Documentation and writing publications The project planning for the PhD student is the following. Year 1: Getting acquainted with the setting, study of the partial differential equations in structural, bone mechanics and biological modeling Acceleration of the convergence of the 2D model (space, time discretization)

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