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Technische Wetenschappen

3D Numerical Simulation of Bone Ingrowth for Glenoid Component Design of ShoulderProstheses

Applicants

Dr.ir. C.W. Oosterlee(1) (Project coordinator),

Prof.dr.ir. P. Wesseling(1) and Prof.dr.ir. F. van Keulen(2)

Addresses: TU Delft

(1) Numerical Analysis group (NA)Faculty of Electrical Engineering, Mathematics and Computer ScienceDepartment of Applied Mathematical AnalysisMekelweg 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: 015-2788283E-mail: c.w.oosterlee@ewi.tudelft.nlInternet: http://ta.twi.tudelft.nl/people/C.W.Oosterlee

v. Keulen: Tel: 015-278 65 15E-mail: F.vanKeulen@wbmt.tudelft.nlInternet: http://socm.wbmt.tudelft.nl/˜wbtmavk/

Secretary: D. Steeneken, Tel: 015-27 87221, Fax: 015-2787245

Framework:

Recently, Delft University of Technology (DUT) has reorganized research efforts in a numberof “spearheads” and “platforms”. This has led to the initiation of the “Platform Computa-tional Science and Engineering”, consisting of eighteen research groups from five differentfaculties. The present cooperation originates from two participating groups from differentfaculties, namely the Numerical Analysis group (NA) and the Structural Optimization andComputational Mechanics group (SOCM). The project in this proposal will be embeddedwithin the platform.Furthermore, at Delft University of Technology, an interfaculty-research programme aimingat improving the state-of-the-art in shoulder joint replacement surgery was initiated in 1999.The programme is entitled: “Development of Improved endoProstheses for the upper Extrem-ities” (DIPEX). The DIPEX programme involves six PhD students and four postdocs, whocollaborate intensively with Leiden University Medical Center (LUMC), Free University Am-sterdam and “Erasmus” University Medical Center Rotterdam (UMCR). The SOCM-groupis 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 outwithin the DIPEX programme.

Keywords shoulder prosthesis, bone ingrowth, multi-model multi-scale application, ho-mogenization, poroelasticity, mechanobiology, modeling of bone tissue differentiation, bone-implant interface, efficient numerical solution

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1 Project Description

1 Summary

1.1. Background

The goal of this project is to improve the understanding and simulation of bone ingrowthin a prosthesis for the replacement of the socket (glenoid) of the shoulder joint. A jointreplacement restores the functional use of limbs and relieves pain. In the lower extremities,joint replacement is a commonly used and successful surgical procedure nowadays. Roughly300,000 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 theshoulder blade has relatively little bone mass. One of the complicating geometrical aspectsis a shallow cavity in the glenoid. Alignment of the replacement glenoid is important tomaintain 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, havebeen observed in up to 96 % of replacements. The consequences of prosthetic loosening canbe dramatic, as the prosthesis cannot always be replaced due to bone deficiencies. Thereforethere is a great clinical need to improve fixation of glenoid components.Previously, many designs have been introduced to overcome the problem of loosening. Sofar, 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 specialcementless 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 avoidtime consuming trial-and-error approaches involving many clinical tests, a systematic processcan be established using mathematical models for design and optimization. For this accuratesimulation tools for bone ingrowth processes are absolutely mandatory.Two-dimensional (2D) finite element simulation models have already been set up in theStructural Optimization and Computational Mechanics (SOCM) group. However, the boneingrowth concept used is rather phenomenological. In order to reliably estimate successof a specific design, a full 3D model that more faithfully accounts for the complexity of theunderlying biological processes is needed. Furthermore, the present models require substantialcomputing 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 shoulderprostheses by means of a 3D numerical model with more realistic biological modeling. The3D model will give a more detailed insight in the bone ingrowth process, as the physicalgeometry is genuinely three-dimensional. To achieve this we need further research from thepresent status along two lines, by two researchers.First of all, the generalization of the 2D application to 3D is a major task in numericalmathematics. It is absolutely necessary to accelerate or reformulate the numerical algorithmsunderlying 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 andbiochemical processes need to be carefully reconsidered. After a multi-scale analysis, inwhich the biomechanical processes at the bone-prosthesis interface are first considered onmicro levels, coefficients and parameters in a continuous macro model will be determined byhomogenization. The resulting, more realistic, macro model will be incorporated in the 3Dsolution method.

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In a close cooperation between the SOCM group and the Numerical Analysis group, we expectto find the required synergy in the pursuit of this target.

1.3 Utilization

Within the clinical-driven research programme DIPEX, the computer-aided pre-operativeshoulder replacement planning tool DSCAS is being developed. This software environment isdeveloped in close collaboration with clinicians, particularly from the LUMC. DSCAS will em-bed image processing, visualization, functional analysis and fixation analysis tools. Moreover,interfaces to patient-dependent operation guidance tool production and computer naviga-tion are currently developed. The computational techniques as developed within the projectproposed will be integrated in DSCAS as well. In this manner, the simulation techniqueswill be used for pilot studies of new prosthesis designs. These studies will be carried out incollaboration with (academic) clinical partners and endoprosthesis manufactures, e.g. Isotis,Ortomed, Zimmer, Stryker Howmedica Osteonics or Implex. Isotis is suggested as a possiblemember of the users committee. Moreover, DSCAS is intended as a tool which will be usedparticularly by clinicians. Thus, the new techniques developed in the course of the presentproject will automatically become available in clinics.The results of the project can also be implemented in commercial simulation software pack-ages. Typical examples are ABAQUS and MSC-MARC. The latter company is suggested asa possible member of the users committee.The utilization will be primarily focused on shoulder prostheses. However, there is no reasonwhy the techniques developed cannot be applied to other implants. Therefore, we will activelyseek collaboration with both clinical and industrial partners who can use the techniques intheir field of application. The people interested in participation in a users committee regardingthe 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 hetwiskundig modelleren van bot-ingroei bij een prothese voor het zogeheten glenoid gedeeltevan het schoudergewricht. Onderarm- en beenprothesen, die het gebruik van armen en benenherstellen en pijn wegnemen, zijn tegenwoordig zeer succesvolle chirurgische ingrepen. In deEU worden jaarlijks ongeveer 300.000 heup- en 250.000 knieprothesen ingebracht. Echter,succesvolle schouderblad-prothesen zijn moeilijker te ontwikkelen, vanwege de complexe geo-metrie en omdat het schouderblad relatief weinig botmassa bezit. Een van de geometrischecomplicaties is de vlakke caviteit in het glenoid. Een geometrisch goed passende prothese iserg belangrijk voor de stabiliteit van het gewricht en om een zo groot mogelijke vrijheid inde armbeweging te garanderen.Een groot probleem in schouderchirurgie is het herhaaldelijk loslaten van de glenoide prothese-componenten. Terwijl voor heup en knieprothesen in slechts 5 tot 10 procent van de gevallenproblemen met loslating gerapporteerd worden, is dit bij glenoid componenten tot 44 procentvan de patienten. Rontgenstralen, die een indicatie geven van loslating op de lange termijn,duiden op problemen in wel 96 procent van de prothesen. De consequenties van loslatingkunnen dramatisch zijn, omdat prothesen door het verdwijnen van botstructuur niet altijdvervangen kunnen worden. Derhalve is verbetering van de fixatie van de glenoid compo-nenten erg belangrijk. Vele poly-ethyleen of met metaal versterkte componenten zijn reeds

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geıntroduceerd om de fixatie te verbeteren. Tot nu toe heeft geen van de ontwerpen signifi-cant succes bij de lange termijn fixatie. Prothesen gefixeerd met cement hebben problemendoor bezwijken van de cementlaag; cementvrije, metaalversterkte prothesen hebben proble-men 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 com-ponent de ingroei bevordert. Om tijdrovend experimenteren te vermijden, stellen we eenontwerpproces voor op basis van wiskundige modellen en optimalisatie van de geometrie.De wiskundige bot-ingroei modellen, partiele differentiaalvergelijkingen, dienen doorgerekendte worden met numerieke technieken. Twee-dimensionale eindige-elementen modellen zijnreeds aanwezig in de SOCM groep bij werktuigbouwkunde. Zij kosten echter veel reken-tijd (meerdere dagen voor een simulatie) om de numerieke oplossingen te verkrijgen. Het isverder noodzakelijk de biologische en mechanisch-mathematische modellen voor bot-ingroeite verbeteren.

Doel (Nederlands)

In dit project willen we drie-dimensionale geometrieen simuleren met realistische wiskundigemodellen voor de biologische processen die aan bot-ingroei gerelateerd zijn. Een 3D modelgeeft een veel gedetailleerder inzicht in bot-ingroei dan een 2D model, omdat de werkelijkegeometrie drie-dimensionaal is. Er zijn geen symmetrieen, die de dimensie van het modelkunnen reduceren. Om dit ambitieuze doel te bereiken willen we het onderzoek langs tweelijnen voortzetten. Allereerst is het generaliseren van het 2D model naar 3D een belangrijkenumeriek wiskundige opgave. Het is absoluut noodzakelijk om de reeds bestaande oplostech-nieken voor het 2D model aan te passen (te versnellen) met nieuwe methoden uit de numeriekewiskunde en parallelisatie.Verder moeten de gekozen wiskundige modellen voor de mechanische en biologische as-pecten onder de loep genomen worden. Met behulp van een “meer-schalen” analyse, waarinde biologische processen worden geanalyseerd en gemodelleerd op micro-niveau, moetenmet behulp van homogenisatie-technieken, coeffienten en andere parameters in het con-tinue mechanica/diffusie model ingebracht worden. Dit is nodig, omdat bot-ingroei modellenop micro-niveau niet in redelijke rekentijd doorgerekend kunnen worden voor een complete,realistische prothese configuratie. De meer-schalen analyse zal een realistischer wiskundigmodel opleveren voor het complexe bot-ingroei proces. In een samenwerking van de werk-tuigbouwkundige SOCM groep en de wiskundige NA groep verwachten wij een synergie effectvoor het bereiken van deze doelstelling.

Utilisatie (Nederlands)

In het door medische klinieken aangestuurde onderzoeksprogramma DIPEX wordt operatieplanningssoftware voor schouderprothesen, genaamd DSCAS, opgezet. Deze software omge-ving wordt in nauwe samenwerking met ziekenhuisartsen, in het bijzonder van het LUMContwikkeld. DSCAS zal medische beeldverwerking, visualisatie en analysemogelijkheden om-vatten. Verder wordt een interface voor patientafhankelijke operatieondersteuning en com-puternavigatie ingebouwd. De numerieke simulaties die in het voorgestelde project opgezetworden zullen deel uitmaken van DSCAS, zodat de ontwikkelde numerieke methoden gebruiktkunnen worden voor de ontwikkeling van nieuwe prothesen. Deze studies worden doorgevoerdin samenwerking met de (academische) partners uit de ziekenhuizen en met industrien dieprothesen ontwikkelen, zoals Isotis, Ortomed, Zimmer, Stryker Howmedia Osteonics of Im-plex. Isotis wordt voorgesteld als mogelijk lid van een gebruikerscommissie. Het instrumentDSCAS is in het bijzonder voor gebruik in medische klinieken ontwikkeld. Daarom zullende nieuwe numerieke modellen automatisch beschikbaar zijn in klinieken. De resultaten vanhet hier voorgestelde project kunnen ook eenvoudig in commerciele softwarepakketten alsABAQUS en MSC-MARC ingebouwd worden. De laatstgenoemde is een potentieel lid van

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de gebruikercommissie. Dit deel van de utilisatie focusseert vooral op de schouderprothesen.Echter, de te ontwikkelen inzichten en technieken kunnen ook voor andere implantaten inhet menselijk lichaam gebruikt worden. In de loop van dit project zal er daarom ook actiefnaar andere toepassingsgebieden voor de numeriek modellen gezocht worden. Geinteresseerdepartners voor dit voorstel zijn:

� Firma Isotis, www.isotis.com.

� 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 / yearDr.ir. C.W. Oosterlee UHD DUT (NA) 0.1Prof.dr.ir. F. van Keulen HL DUT (SOCM) 0.1Dr.ir. F.J. Vermolen UD DUT (NA) 0.1Prof.dr.ir. P. Wesseling HL DUT (NA) 0.1Dr.ir. J. van der Linden UD UMCR/DUT (SOCM) 0.1Dr. E. Valstar UD LUMC/DUT (SOCM) 0.1Ir. P. Broomans PhD (4 years) STW 1.0Ir. A. Andreykiv postdoc (2 years) STW 1.0

The daily supervision of the PhD student Broomans is in the hands of Oosterlee, Vermolenand van Keulen.The project is carried out as a cooperation between the Numerical Analysis group (NA) andthe Structural Optimization and Computational Mechanics group (SOCM), both at the DelftUniversity of Technology. The NA group has built up thorough knowledge of applicablemathematics and develops expertise in applying the methods and tools of mathematics toproblems in science and engineering. Development of novel solution methods, and the analysisof existing numerical methods with the purpose to accelerate the convergence of iterativemethods in complicated multidisciplinary applications is a major effort within the group thathas 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 collabora-tion with Dr. F.J. Gaspar from the University of Zaragoza, Spain and Dr. R. Wienands fromthe University of Cologne, Germany [9, 10]. Vermolen has worked with advanced FE dis-cretizations and fast solution methods for porous media and diffusion applications for severalyears [11–13].The Structural Optimization and Computational Mechanics group (SOCM) has great ex-pertise in numerical techniques for optimization methods applied to real-life engineering ap-plications. The group is part of the Department Mechantronics and Control, in which allongoing biomedical research activities at the faculty of Design, Engineering and Productionare concentrated. In the field of bone mechanics, the attention has been on models usedfor pre-operative numerical studies for shoulder endoprosthesis designs. In this context, theapplication of micro-polar continuum models was studied, including material parameter es-timation. Bone ingrowth modeling was initiated a few years ago. This research serves asthe starting point for the present research proposal. Finally, a study is ongoing on the globalmodeling of the shoulder, which includes a unique study on material inhomogeneity and

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anisotropy in the glenoid of the shoulder. Important publications from the SOCM group inthe 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 thedirections of the research in this project. Moreover, they ensure embedding and collaborationwith 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 existingmodels by inclusion of biological and chemical aspects. The PhD student will initially work onthe computational aspects in the project, like the acceleration/reformulation of the solutionmethods, the improved coupling of the different models and the generalization to threedimensions. In addition, the accuracy of the models will be addressed. For the PhD positionwe 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 supervisionof profs. Wesseling and van Keulen on July 10th 2003 with initial funding by DUT in theframework of the Platform for Computational Science and Engineering.For the postdoc position we have a suitable candidate among the PhD students working inthe DIPEX project in the SOCM group. Ir. A. Andreykiv is finalizing his PhD thesis on thecomputational model for bone ingrowth. In his PhD thesis (concept should be ready by July2004) he will present a pilot interface model which is based on homogenization. We wouldlike him to stay for two more years to work on the subject as a postdoc. The PhD studentwill benefit greatly from the knowledge gathered by the postdoc and from his computationalmodels. A cooperation between the postdoc and the PhD student is a crucial prerequisitefor the success of the project. They share the same office. The Curriculum Vitae of the PhDstudent 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. Twofixation techniques for the prosthesis are cement and bone ingrowth fixation. Often additionalscrews or pegs are used to ensure initial stability. Although cemented fixation performs verywell initially, damage accumulation, that progresses within the cement mantle with timecauses fixation failure. Some studies show that this failure can already occur two yearspost operatively. Bone ingrowth fixation, on the contrary, may last practically forever. Forbone ingrowth, use has been made, for example, of porous tantalum, titanium mesh, porousceramics, 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-implantinterface may result in the appearance of fibrous tissue that inhibits bone ingrowth. Accurateand 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 forrepresentative geometries and under realistic loading conditions. The latter will be availableusing a musculo-skeletal model (Delft Shoulder Model [29, 30]), as available within theDIPEX programme. Factors that are particularly important for fixation by bone ingrowthare the appropriate structure, bio-compatibility of the material at the bone-implant interfaceand the initial stability of the implant. A stable immediate fixation is a requirement for asuccessful secondary fixation by bone ingrowth. In fact, the entire biomechanical-chemicalstatus near and in the porous prosthesis determines whether or not fixation through ingrowth

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takes place. Numerical simulation methods may help to predict this status as a functionof time and loading. In this way a prediction on the occurrence of bone ingrowth can bemade. Moreover, the availability of these methods opens the route towards model-basedoptimization.

3.1.1. Work of the Postdoc

The recent research carried out by Andreykiv in the SOCM group will soon crystallize in a PhDthesis. 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 modelis based on a poroelastic analysis, including contact analysis and a diffusion model. Thelatter is used to evaluate the concentration of mesenchymal cells. The series of picturesdepicts the formation of bone (blue) and cartilage (red) as a function of time. The presentmodel 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 ingrowthfor only a small part of a bone-implant interface. The work to be carried out by the postdocwill be a direct continuation of this work. The 2D simulation for different design configurationstudies the influence of the initial fixation (pegs in Figure 1) and material properties of theimplant on bone ingrowth. A 3D simulation of tibial bone fracture healing enables accuratevalidation of tissue differentiation models to be developed. A 3D micro-model of the interfacetissue enables a detailed study on local bone ingrowth as a function of the mechanical loadingconditions, local topology of the implant, imperfections of the interface, among many otheraspects. For this reason, the first task will be to carry out a detailed study on differentaspects that influence on local bone ingrowth. Figure 2 shows part of the bone-implantinterface 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. Thenumerical observation is, see Figure 3, compared, as far as possible, with experimental andclinical observations. This data [15, 16] will become available through literature and the

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collaboration with experimentally-oriented groups, e.g. the Division of Biomechanics andEngineering Design at the KU in Leuven (KUL), Belgium and clinicians at LUMC. The 3Dmicro-model study will result in a review of the different (design) aspects in relation tolocal bone ingrowth. The results will be communicated and/or made available to clinicalresearchers and/or prosthesis manufacturers.A second task is to refine the 3D model for a limited part of the interface, see Fig. 3. Theserefinements 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 anticipatedthat refinements of the model particularly involve the biological aspects in the model andthe biomechanical models used for cell distribution and cell differentiation. The results ofthis second task will be reported in the literature. A third task will be the construction of asimplified interface model. The basis for such a simplified model will be the detailed 3D modelof 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. Thismodel should be a compromise between accuracy and computational efficiency and shouldbe applicable in the context of design and automated optimization studies of protheses. Theconstruction of this interface model has similarity with homogenization tasks. However, herethe 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 andpitfalls, 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 effectiveinterface models can be formulated, the step towards 3D models will be made. The 3D-interface model will be integrated in the DSCAS software. In this manner, it may becomeavailable for clinicians and prosthesis design manufacturers. In a future step, the 3D-interfacemodel will be used in (re)design studies of existing and new prostheses. This will be done incollaboration with clinicians and prosthesis design manufacturers.

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Figure 3: Preliminary results: Prediction of interface tissue phenotype according tocalculated 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 interfacemodel. The latter can, because of its computational efficiency, easily be integrated intoa macroscopic computational model. This macroscopic model is a tool for pre-clinicaldesign studies in the DSCAS software environment.

3.1.2. Work of the PhD Student

The numerical model is based on the assumption that a patient is able to move his armonly to some extent after the glenoid replacement. This arm movement is modeled as afluctuating 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 porousprosthesis. Strain and fluid velocity are then computed using poroelastic equations, i.e., theequilibrium equations in combination with a mass balance for the bone fluid. The strain andfluid 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 accountcell 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 poroelasticityproblem, and the solution of diffusion equations, can be clearly identified.The PhD student will initially work on the improvement of the numerical algorithms in atwo-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-

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cal diffusion models of tissue differentiation (e.g. [27, 28]). Secondly, he will develop anefficient numerical technique for the solution of the poroelastic problem, that is used to sim-ulate deformation of the soft interface tissue, which precedes the bone. It is not trivial tofind a stable finite element for the poroelasticity equations (with standard finite elementsoscillating solutions are reported in the literature). It is further a challenging task to de-velop efficient iterative solution methods for the coupled poroelasticity/tissue differentiationproblem, especially in 3D.These two stages of the solution process need to be coupled with the contact analysis, inwhich 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 ofunknowns/elements.The PhD student will develop efficient iterative solution methods for the implicit systemsappearing. As the matrix from the finite element discretization is nonsymmetric and notstructured, the design of an appropriate iterative solver is state-of-the-art research. Anotherimportant concept for the reduction of the total turn-around time of 3D computations isparallelization. The successful ingredients will be used for the 3D target bone ingrowthmodel to be developed.Furthermore, the student will interact closely with the postdoc on improved biological andbiochemical models for bone ingrowth, and on the detailed models of the behavior of porousstructures (mentioned above).

3.2.1 Personnel

We request one PhD student for four years, and a postdoc for two years.

3.2.2 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 needlicenses for the commercial software for pre- and post-processing. In total, we request 7k

�

for computer hardware and 13k�

for software.

3.3. Planning

The planning for the work of the postdoc is:Year 1:

� Detailed study of the bone-implant interface

� Refinement of the interface model

Year 2:

� 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 struc-tural, bone mechanics and biological modeling

� Acceleration of the convergence of the 2D model (space, time discretization)

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Year 2:

� Study of the biological/chemical and mechanical aspects

� Improvement of the model (with advanced biochemical models)

Year 3:

� Generalization of 2D model to 3D (incorporate a grid generator, . . . )

� Implementation in DSCAS.

� Solving a realistic configuration (3D grid)

� Presentations on conferences

Year 4:

� Finishing the research work, preparing publications for scientific journals, presentationsfor conferences. Preparation of the PhD thesis.

There are many important conferences in the field of biomechanical engineering, scientificcomputing, and numerical mathematics to attend. Important conferences are:

� The conferences of the European Society of Biomechanics, every second year.

� ASME (American Society of Mechanical Engineers) Summer Bioengineering confer-ence, annually, organized by ASME BioEngineering Division (BED).

� World Congress on Computational Mechanics, held every second year.

� The annual MIT conference on fluid and solid mechanics in Boston, USA.

� ECCM - European Conference on Computational Mechanics (Solids, Structures andCoupled Problems in Engineering).

High standing journals in the field of this proposal are:

� Journal of Biomechanics (Elsevier)

� Journal of Clinical Biomechanics (Elsevier)

� Journal of Biomechanical Engineering (American Soc. Mechanical Engin.)

� Journal of Orthopaedic Research (Elsevier)

During and after the research regularly informal contacts with target users will be maintained,which will speed up the research and point towards the appropriate direction.

3.4. Infrastructure

The project will be executed at Delft University of Technology. Infrastructure, computingbudget and salaries of other project members are provided by the DUT (LUMC and UMCR).The local infrastructure consists of local area networks of workstations and PCs, with parallel(cluster) computing facilities. Application will be made to the Dutch supercomputing facilitySARA for computing time on the national parallel computer.We will combine the experience of the members in the Numerical Analysis group on accuratediscretization for partial differential equations, iterative solution methods and parallel com-puting with the expertise on structural and bone mechanics, biomechanical modeling andoptimization methods of the members for the Structural Optimization and ComputationalMechanics Group.

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Both the PhD student and the postdoc will benefit from the infrastructure of DIPEX. Indetail, realistic loading conditions can be provided using the Delft Shoulder Model. Imageprocessing is an important item in DIPEX. Patient dependent images based on MRI, CT andDEXA may be used, for example, for realistic 3D geometry modeling. A 3D grid generatorhas been developed for the meshing of shoulder geometries in the pre-processing phase.Finally, visualization tools are available within DIPEX. These software tools are currentlybeing integrated in the DSCAS tool which becomes available to clinicians. For several yearsthe SOCM group members have developed an in-house finite element software package. Thegroup has also in-house developed optimization software. Furthermore, licenses are availablefor a commercial finite element package as well as for commercial pre- and post-processing.

3.5. Relation to other research programmes

Nationally, the research group of Prof.dr.ir H.W.J. Huiskes, Techn. University Eindhoven,is one of the leading groups in the simulation of bone mechanics. Currently, a well-knownguest, Dr. K. Ito, is visiting the Eindhoven group.Advanced mathematical modeling of fracture healing processes is currently a topic of highinterest worldwide. Renowned research groups include the Center for Bioengineering of theTrinity College in Dublin, Ireland, headed by Prof. Prendergast. These people are experts inthe mechanical aspects of numerical bone simulation. Dr. D. Lacroix, Technical University ofCatalonia, Barcelona develops advanced fracture healing models that include biological andmechanical aspects. The group headed by Prof. M. van der Meulen at Cornell University,USA deals with the biological aspects of fracture healing. At the KU in Leuven, Belgium thegroup of Prof. J. van der Sloten has a research direction in bone mechanics with similaritiesto our research program.Fast solvers for the poroelasticity equations are developed at the University of Zaragoza,Spain by Dr. F.J. Gaspar and Prof. F.J. Lisbona. In the engineering department of thatuniversity Prof. J-M. Garcia and Prof. M. Doblare have developed new models for bonemechanics simulations.Researchers dealing experimentally with bone mechanics include Prof. A. Goodship and J.Kenwright, University of Bristol, UK. They perform animal experiments on fracture healing.Further, Prof. J.D. Bobyn, Montreal General Hospital and McGill University, Canada doesanimal studies on bone ingrowth into porous tantalum (commercially called Hedrocell). Prof.L.E. Claes and Prof. C.A. Heigele at the University of Ulm, Germany gather experimentalresults and compare them within their group with 2D finite element computations.

4. Utilization

4.1 Utilization

Within the clinical-driven research programme DIPEX, the computer-aided pre-operativeshoulder replacement planning tool DSCAS is being developed. This software environment isdeveloped in close collaboration with clinicians, particularly from the LUMC. DSCAS will em-bed image processing, visualization, functional analysis and fixation analysis tools. Moreover,interfaces to patient-dependent operation guidance tool production and computer naviga-tion are currently developed. The computational techniques as developed within the presentproject will be integrated in DSCAS as well. In this manner, the simulation techniques willbe used for pilot studies of new endoprosthesis designs. These studies will be carried out incollaboration with (academic) clinical partners and endoprosthesis manufactures, e.g. Isotis(possible member of a users committee), Ortomed, Zimmer, Stryker Howmedica Osteonicsand Implex.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 becomeavailable in clinics.

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The results of the present project can also be implemented easily in commercial simula-tion software packages. Typical examples are ABAQUS and MSC-MARC, the latter beingsuggested as a possible users committee member for this project.The utilization will be primarily focused on shoulder endoprostheses. However, there is noreason why the developed techniques cannot be applied to other implants. Therefore, wewill actively seek collaboration with both clinical and industrial partners who can use thetechniques in their field of application. We will use the proven strategy of interaction withtarget users.

4.2 Users

Interested partners and users of the obtained knowledge and software who have agreed tofollow the project closely, possibly as members of a users committee are

� Dr. J.R. de Wijn,Company Isotis (www.isotis.com),Prof. Bronkhorstlaan 10-D, 3723MB Bilthoven,T+31 30 229 5 247.Isotis provides biological information from clinical experiments with prostheses, whichis important in the multi-scale modeling of bone ingrowth.

� Dr.ir. B. Knops,MSC Software BV,Groningenweg 6, 2803 PV Gouda,Tel 0182-543700, Bert.Knops@mscsoftware.com.MSC will closely follow the work in this project aiming to standardize parts of the (finiteelement) software for the poroelastic parts of the shoulder prosthesis in their commercialbiomechanical software. Further, they will consult on future implementations of themodel in their software.

� Prof.dr. P.M. Rozing,Leiden University Medical Center, Fac. GeneeskundeOrthopedie, Divisie 1, Postbus 9600, 2300 RC Leiden.Tel. 071 5263606, P.M.ROZING@LUMC.NLProf. Rozing is the clinical partner regarding the Delft Shoulder Model. He is veryinterested in the applicability of the results from this project in the context of thatmodel.

� Ir. A.W.A. Konter,Netherlands Institute for Metals Research (NIMR)Postbus 2350, 3430DT Nieuwegein,030-6075383, konter@nimr.nl.As a former member of the advisory board of the DIPEX programme, Ir. Konter isan important advisor for our project from the metallurgy field. The target of NIMRis to upgrade industrial know-how and to generate new technologies in the industrialcompetition.

4.3 Implementation

Utilization of the research results will follow the strategy that has been successfully used inprevious projects at DUT. Application will be made to realistic examples, chosen in consul-tation with the experts. Together, we will test them in a realistic clinical setting. For theresearch this is advantageous, as it provides a direct feedback on how well the techniquesfunction in practice. This direct involvement will improve later dissemination of the results.

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4.4 Past performance

Development of novel parallel solution methods, and the analysis of existing numerical meth-ods with the purpose to accelerate the convergence of iterative methods in complicatedmultidisciplinary applications is a major effort within the Numerical Analysis group. In recentyears, the group has developed the DeFT CFD code with support from STW. Four licenseshave been issued to outside users under contract with STW and DUT.The SOCM-group has its background in computational mechanics, particularly the modelingof thin-walled structures undergoing large rotations. This research resulted in unique shellelements suited for extremely large rotational increments. At a later stage, also researchon optimization was initiated, including comprehensive research on semi-analytical designsensitivities and multi-point approximation concepts. The SOCM group is now coordinatingthe Bsik Microned programme (funding of 28M

�). In the field of bone mechanics, the

focus has mainly been on models to be used for pre-operative numerical studies for shoulderendoprosthesis designs. In this context, the application of micro-polar continuum models wasstudied, including the material parameter estimation. These models have the advantage ofincluding a material length scale. Then, a bone ingrowth modeling research line was initiated.This research serves as the starting point for the present research proposal. Finally, a studyis ongoing on the global modeling of the shoulder, which includes a unique study on materialinhomogeneity and anisotropy in the glenoid of the shoulder.

5. Knowledge management

5.1 Contracts We are not bounded by any contracts in the field of this project.

5.2 Patents Not applicable.

6. Budget

6.1 Personnel

1 PhD researcher for 4 years, 1 postdoc for 2 years.

6.2 Travel Abroad

To visit conferences and other research groups: 20k�

for 4 years. 5 trips for the PhD, 3 forthe postdoc, 3 for the other project members.

6.3 Support of Users

6.4 Material excluding VAT

Computer Hardware and Software 7k�

and 13k�

, respectively.

6.5 Budget Summary

Year 1 Year 2 Year 3 Year 4 TotalPersonnel: 1 PhD 1 fte 1 fte 1 fte 1 fte 1 fte for 4 years

1 postdoc 1 fte 1 fte 1 fte for 2 yearsTravel 7.5 7.5 2.5 2.5 20k

�

Material 20 20k�

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7. Publications by the team

References

Publications NA Group (relevant for the proposal):

[1] P. Sonneveld, CGS, a fast Lanczos-type solver for nonsymmetric linear systems, SIAM J. Sci.

Comput., 10:36-52, 1989.

[2] U. Trottenberg, C.W. Oosterlee and A. Schuller, Multigrid, Academic Press, Lon-don, 2001.

[3] H.A. van der Vorst, Bi-CGSTAB: a fast and smoothly converging variant of Bi-CG forsolution of non-symmetric linear systems, SIAM J. Sci. Comput.,13: 631–644, 1992.

[4] H.A. van der Vorst and C. Vuik, GMRESR: a family of nested GMRES methods, Num.

Lin. Alg. Appl., 1:369-386, 1994.

[5] C. Vuik, A. Segal and J.A. Meijerink, An efficient preconditioned CG method for thesolution of a class of layered problems with extreme contrasts in the coefficients, J. Comp.

Phys., 152: 385-403, 1999.

[6] C. Vuik and J. Frank, Coarse grid acceleration of a parallel block preconditioner, Future

Generation Computer Systems, 17:933-940, 2001.

[7] P. Wesseling, An introduction to multigrid methods. Wiley, Chicester, 1991.

[8] P. Wesseling and C.W. Oosterlee, Geometric multigrid with applications to computationalfluid dynamics, J. Comp. Appl. Math., 128: 311-334, 2001.

[9] F.J. Gaspar, F.J. Lisbona, R. Wienands and C.W. Oosterlee, A systematic comparisonof coupled and distributive smoothing in multigrid for the poroelasticity system. Num. Lin. Alg.

Appl., to appear.

[10] R. Wienands, F.J. Gaspar, F.J. Lisbona, and C.W. Oosterlee, An efficient multigridsolver based on distributive smoothing for poroelasticity equations. Submitted for publication.

[11] F.J. Vermolen, J. Bruining and C.J. van Duijn, Gel placement in porous media: con-stant injection rate, Transport in porous media, 44: 247-266, 2001.

[12] F.J. Vermolen, P.L.J. Zitha and J. Bruining, A model for a viscous preflush prior togelation in a porous medium, Comput. Vis. Sc., 4: 205-212, 2002.

[13] C. Vuik, A. Segal and F.J. Vermolen, A conserving discretization for a Stefan problemwith an interface reaction at the free boundary, Comput. Vis. Sc., 3:109-114, 2000.

⇒ Other publications by Oosterlee et al. athttp://ta.twi.tudelft.nl/users/oosterlee/oosterlee/oosterlee_pub.html.

Publications SOCM Group (relevant for the proposal):

[14] A.Andreykiv, P.J. Prendergast, F. van Keulen, W. Swieszkowski, Modelling ofbone ingrowth into a porous tantalum mesh of a glenoid component. Proc. 13th conf. of EuropeanSociety of Biomechanics, Wroclaw, Poland, 2002.

[15] A. Andreykiv, P.J. Prendergast, F. van Keulen, W. Swieczkowski, P.M. Rozing,

Bone Ingrowth Simulation for a Concept Glenoid Component Design. Submitted for publicationJ. Biomechanics.

[16] A. Andreykiv and F. van Keulen, The effect of micromotions and interface thicknesson biophysical stimuli at the bone-implant interface: A finite element study. Proc. 6th Intern.Symposium Comp. Methods in Biomechanics & Biomedical Eng., 25-28 Feb. 2004, Madrid,Spain.

16

[17] J. Fatemi, P.R. Onck, G. Poort and F. van Keulen, Cosserat Moduli of AnisotropicCancellous Bone: A Micromechanical Analysis. In S. Cescotto, Proceedings of the 6th Eu-rop. Mech. Materials Conference (EMMC6), Nonlinear Mechanics of Anisotropic Materials,Euromech-Mecamat, Liege, Belgium, Sept. 9-12, 2002, ISBN 2-87047-028-2, 2002.

[18] J. Fatemi, F. van Keulen and P.R. Onck, Generalized Continuum Theories: Applicationto Stress Analysis in Bone. Meccanica 37: 385-396, 2002.

[19] J. Fatemi, P.R. Onck, G. Poort and F. van Keulen, Cosserat moduli of anistropiccancellous bone: a micromechanical analysis, J. Phys. IV France 105: 273-280, 2002.

[20] J. Fatemi, F. van Keulen, P.R. Onck, C. Tekoglu, On micropolar modeling of cancellousbone, Proceedings of the ASME Bioengineering Conference, Key Biscayne, Florida, June 25-29,2003. ISBN 0-9742492-0-3.

[21] L. Geris, A. Andreykiv, H. van Oosterwyck, J. Vander Sloten, F. van Keulen, J.

Duyck and I. Naert, Numerical Simulation of Tissue Differentiation Around Loaded TitaniumImplants in a Bone Chamber; To appear in J. Biomechanics.

[22] S.Gupta, F.C.T. van der Helm, F. van Keulen, Stress Analysis of Cemented GlenoidProstheses in Total Shoulder Arthroplasty, To appear J. Biomechanics.

[23] S. Gupta, F.C.T. van der Helm, F. van Keulen, The Possibilities of Uncemented GlenoidComponent - a Finite Element Study, To appear Clinical Biomechanics.

[24] S.Gupta, F.C.T van der Helm, J.C. Sterk, F. van Keulen and B.L. Kaptein,

Development and experimental validation of a three-dimensional model of the huma scapula, Toappear J. of Eng. Medicine, I. Mech E.

[25] Oosterom R., van Keulen F., Rozing P.M., Design considerations of the glenohumeralprosthesis. In: E.K.J. Chadwick, H.E.J. Veeger, F.C.T. van der Helm and J. Nagels (eds.)Proceedings of the third conference of the international shoulder group, 4-6 September 2000,Newcastle upon Tyne, UK, 72-76, ISBN 90-407-2268-4, 2000.

⇒ Other publications by van Keulen et al. athttp://socm.wbmt.tudelft.nl/~wbtmavk/publications.html

Publications by others

[26] Ch. Ament and E. P. Hofer, A fuzzy logic model of fracture healing, J. Biomechanics

33(8): 961-968, 2000.

[27] A. Bailon-Plaza and M.C.H. van der Meulen, A mathematical framework to study theeffects of growth factors infuences on fracture healing. J. Theoret. Biology 212: 191-209, 2001.

[28] A. Bailon-Plaza and M.C.H. van der Meulen, Beneficial effects of moderate, earlyloading and adverse effects of delayed or excessive loading on bone healing. J. Biomechanics

36(8): 1069-1077, 2003.

[29] F.C.T. van der Helm, Analysis of the kinematic and dynamic behavior of the shouldermechanism. J. Biomechanics, 27(5): 527-550, 1994.

[30] F.C.T. van der Helm, A finite element musculoskeletal model of the shoulder mechanism.J. Biomechanics, 27(5): 551-569, 1994.

[31] D. Lacroix and P.J. Prendergast, A mechano-regulation model for tissue differentiationduring fracture healing: analysis of gap size and loading. J. Biomechanics 35(9): 1163 -1171,2002.

[32] P.J. Prendergast, R. Huiskes and K. Soballe, Biophysical stimuli on cells during tissuedifferentiation at implant interfaces. J. Biomechanics 30(6): 539-548, 1997.

17

Curriculum Vitae van P. Broomans

Persoonsgegevens

Naam: Peterjan BroomansAdres: Van Hasseltlaan 470

2625 JE DELFTTelefoon: 015 - 262 55 34

Geboortedatum: 10 oktober 1977Geboorteplaats: RotterdamBurgerlijke staat: ongehuwd

Opleiding

VWO te Rotterdam (diploma 1996)

Technische Universiteit DelftOpleiding Technische Wiskunde, vakgroep Numerieke Wiskunde (1996 - 2003)

Studiereis Verenigde Staten en Canada

Deelnemer, onderwerp: risicoanalyse.Casestudie voor Rijkswaterstaat, onderwerp: onzekerheidsanalyse met betrekking tot derekenmethode voor het afschuiven van dijken.Periode: januari t/m juli 1999.

Stage aan de University of Portsmouth

Onderzoeken van de parallelle capaciteiten van de schematische programmeertaal Clarity.Periode: juli en augustus 2000.

Stage bij GeoDelft

Ontwerp en implementatie van trekpaalberekeningen voor het softwarepakket MFoundation.Periode: april en mei 2001.

Afstudeerstage bij WL | Delft Hydraulics

Numerical Accuracy in the Solutions of the Shallow-Water Equations.Periode: maart 2002 – februari 2003.

Cursus “Bone, Cell and Tissue Mechanics”

Plaats: CISM, Udine, ItaliePeriode: 14-18 juli 2003.

Aanvullende opleiding

Cursussen: Schriftelijk rapporterenComputertalen: Pascal, Delphi, Fortran 77Systemen: DOS, Windows, MatlabTalen: Engels:

mondeling: redelijk; schriftelijk: goed

Werkervaring

� Student-assistent vakgroep Algemene Wiskunde: evaluatie van de nieuwe dicaten vooranalyse en lineaire algebra (1998 – 1999: 6 maanden parttime).

� Student-assistent vakgroep Technology Assessment: verzamelen van artikelen uit demedia voor het opstellen van opdrachten; begeleiden van studenten (1999 – 2000: 12maanden parttime).

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� Student-assistent vakgroep Numerieke Analyse: instructie en begeleiding van tweede-en derdejaars studenten; meewerken aan de ontwikkeling van nieuwe opgaven (1999 –2001: 18 maanden parttime).

Overige activiteiten

� Werk als secretaris van de jeugdcommissie van een volleybalvereniging; trainer en coachvan jeugdteams (1997 - 2000: 2 jaar).

� Belangrijkste hobby: volleyballen (in competitieverband).

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Curriculum Vitae for A. Andreykiv

Personal dataName: Andriy AndreykivAddress: Arthur van Schendelplein 12

2624 CM DELFTTelephone: 015 - 2786818E-mail: a.andreykiv@wbmt.tudelft.nlBirthdate: 28 January 1977Birthplace: Lviv, UkraineCitizenship: Ukrainian

(Dutch resident since 2000, permitted to work in The Netherlands)Marital Status: marriedMilitary Service: an officer in reserve (specialization: overall military intelligence)

Education

High School with specialization in mathematics (Lviv, 1993)

Franko Lviv National University

Faculty of Mechanics and Mathematics, specialization in mechanics. Combined Bachelor andMaster program (1993 - 1998).

Lviv National Polytechnical University

Faculty of Computer Science, specialization in software engineering. Master program (1999-2000).

Institute of Physics and Mechanics (Lviv, Ukraine)Internship during Master thesis preparation. Subject of research: Investigation of crackpropagation subjected to high cycle loading (1998).

Additional qualifications

Courses: Micro-mechanics of materials (Ireland 2000),Nonlinear Dynamics and Acoustics (2001, The Netherlands),Nonlinear Computational Mechanics (2002, The Netherlands),Homogenization theory (2001, Belgium),Bone Cell Mechanics (2003, Italy),Optimization of Structures (2003, The Netherlands)

Computer languages: Visual C++, Java, Visual Prolog, Fortran 77

Systems: DOS, Windows, Linux

Foreign languages (native Ukrainian): English (TOEFL result 201),Russian (as native),Polish (spoken good, written intermediate),Dutch (spoken and written lower intermediate)

Working experience

� An Engineer at Institute of Physics and Mechanics, Lviv, Ukraine: Mathematical mod-eling and experimental investigation of short fatigue crack propagation. 1999-2000(2000 Part-time)

� A Ph.D. student at Delft University of Technology (The Netherlands): Numerical mod-eling of bone ingrowth into the porous surface of a glenoid component. (2000-presenttime)

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Publications

� Journal publications: 2 journal publications on fatigue crack propagation, 1 publicationon tissue differentiation inside a bone chamber (2nd author )

� Conference publications: 1 publication on fatigue crack propagation, 4 publications onbone ingrowth into the porous backing of glenoid component

Honors and prizes

� Franko Lviv National University: Graduation with honors (1998)

� Lviv National Polytechnical University: Graduation with honors (2000)

� Ukrainian Academy of Sciences: Prize for the young scientists (2000)

� Engineering Mechanics Symposium: 3rd poster prize (2003)

General Activities

� Member of Ukrainian Scout Organization since 1990

� Junior Music School: Classic Guitar (1991-1997)

� University Boxing team (1993-1998)

Hobbies

� Playing guitar

� Racing bike

� Windsurfing