Individualized therapies, in particular surgical interventions, require detailed preoperative planning. We address two such areas: bone implant design and osteotomic surgery.

Congenital malformations or trauma-related defects of facial bones are often corrected by patient-specific implants to substitute or complement bone structures. The implant's shape and position affects the soft tissue and hence the visual appearance of the patient. Thus, implant formation and placement are of utmost importance for the final outcome of rehabilitative facial surgery. The shape of an implant is typically customized individually during the operation, which is a tedious and time consuming process. A preoperative design of implants using CAD methods has the potential to shorten operation time, and is becoming more and more relevant.

Congenital or trauma-related deformations of the lower extremities can frequently be corrected by osteotomic surgery. There, a long bone is cut and reset at an angle. Such a change to the mechanical functioning of the musculoskeletal system can have detrimental long-term effects, which need to be assessed beforehand. The choice of surgical procedure today still relies largely on the experience of the surgeon. A simulation of the mechanics of the musculoskeletal system would provide valuable additional information.

Publications

2021
Performance Evaluation and Improvements of the PoCL Open-Source OpenCL Implementation on Intel CPUs IWOCL'21: International Workshop on OpenCL, 2021 Tobias Baumann, Matthias Noack, Thomas Steinke BibTeX
DOI
Computational Surgery Planning
2017
An affine covariant composite step method for optimization with PDEs as equality constraints Optimization Methods and Software, 32(5), pp. 1132-1161, 2017 (preprint available as ZIB-Report 15-09) Lars Lubkoll, Anton Schiela, Martin Weiser PDF (ZIB-Report)
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DOI
Computational Surgery Planning
2015
An Optimal Control Approach to Implant Shape Design : Modeling, Analysis and Numerics Doctoral thesis, Universität Bayreuth, Anton Schiela (Advisor), 2015 Lars Lubkoll BibTeX
Computational Surgery Planning
2014
An optimal control problem in polyconvex hyperelasticity SIAM J. Control Opt., 52(3), pp. 1403-1422, 2014 (preprint available as ZIB-Report 12-08) Lars Lubkoll, Anton Schiela, Martin Weiser PDF (ZIB-Report)
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DOI
Computational Surgery Planning
Mathematics cures virtual patients MATHEON-Mathematics for Key Technologies, Vol.1, pp. 7-25, Peter Deuflhard, Martin Grötschel, Dietmar Hömberg, Ulrich Horst, Jürg Kramer, Volker Mehrmann, Konrad Polthier, Frank Schmidt, Christof Schütte, Martin Skutella, Jürgen Sprekels (Eds.), European Mathematical Society, 2014 Peter Deuflhard, Ralf Kornhuber, Oliver Sander, Anton Schiela, Martin Weiser BibTeX
Computational Surgery Planning
2013
Inexaktheit in Newton-Lagrange-Verfahren für Optimierungsprobleme mit Elliptischen PDGL-Nebenbedingungen Master's thesis, Freie Universität Berlin, Martin Weiser (Advisor), 2013 (preprint available as ZIB-Report 13-37) Felix Lehmann PDF (ZIB-Report)
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Computational Surgery Planning
On goal-oriented adaptivity for elliptic optimal control problems Opt. Meth. Softw., 28(13), pp. 969-992, 2013 (preprint available as ZIB-Report 09-08) Martin Weiser PDF (ZIB-Report)
BibTeX
Computational Surgery Planning
2012
Adaptive numerical integration for dynamical contact problems Doctoral thesis, Freie Universität Berlin, 2012 Corinna Klapproth BibTeX
Computational Surgery Planning
Mathematical Cancer Therapy Planning in Deep Regional Hyperthermia Acta Numerica, Vol.21, pp. 307-378, 2012 (preprint available as ZIB-Report 11-39) Peter Deuflhard, Anton Schiela, Martin Weiser PDF (ZIB-Report)
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Computational Surgery Planning
The Contact-Stabilized Newmark Method - Consistency Error of a Spatiotemporal Discretization ZIB-Report 12-18 Corinna Klapproth PDF
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URN
Computational Surgery Planning
Towards an Efficient Numerical Simulation of Complex 3D Knee Joint Motion ZIB-Report 12-06 Oliver Sander, Corinna Klapproth, Jonathan Youett, Ralf Kornhuber, Peter Deuflhard PDF
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URN
Computational Surgery Planning
2010
Barrier methods for a control problem from hyperthermia treatment planning Recent Advances in Optimization and its Applications in Engineering (Proceedings of 14th Belgian-French-German Conference on Optimization 2009), pp. 419-428, M. Diehl, F. Glineur, E. Jarlebring, W. Michiels (Eds.), Springer, 2010 (preprint available as ZIB-Report 09-36) Anton Schiela, Martin Weiser PDF (ZIB-Report)
BibTeX
Computational Surgery Planning
2009
Optimization and Identification in Regional Hyperthermia Int. J. Appl. Electromagn. and Mech., Vol.30, pp. 265-275, 2009 (preprint available as ZIB-Report 08-40) Martin Weiser PDF (ZIB-Report)
BibTeX
Computational Surgery Planning
2008
A control reduced primal interior point method for a class of control constrained optimal control problems Comput. Optim. Appl., 41(1), pp. 127-145, 2008 (preprint available as ZIB-Report 04-38) Martin Weiser, Tobias Gänzler, Anton Schiela PDF (ZIB-Report)
BibTeX
Computational Surgery Planning
Inertia Revealing Preconditioning For Large-Scale Nonconvex Constrained Optimization SIAM J. Sci. Comp., 31(2), pp. 939-960, 2008 (preprint available as ZIB-Report 07-32) O. Schenk, Andreas Wächter, Martin Weiser PDF (ZIB-Report)
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Computational Surgery Planning
On the Interplay Between Interior Point Approximation and Parametric Sensitivities in Optimal Control Journal of Mathematical Analysis and Applications, pp. 771-793, 2008 (preprint available as ZIB-Report 05-44) Roland Griesse, Martin Weiser PDF (ZIB-Report)
BibTeX
Computational Surgery Planning
Superlinear convergence of the Control Reduced Interior Point Method for PDE Constrained Optimization Computational Optimization and Applications, 39(3), pp. 369-393, 2008 (preprint available as ZIB-Report 05-15) Anton Schiela, Martin Weiser PDF (ZIB-Report)
BibTeX
Computational Surgery Planning
The convergence of an interior point method for an elliptic control problem with mixed control-state constraints Comput. Optim. Appl., 39(2), pp. 183-218, 2008 (preprint available as ZIB-Report 04-47) Uwe Prüfert, Fredi Tröltzsch, Martin Weiser PDF
PDF (ZIB-Report)
BibTeX
Computational Surgery Planning