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Quasi-Newton for Multi-Physics Projekt

Quasi-Newton Methods for Coupled Multi-Physics Problems
Gefördert durch Haushalt
Beginn 01.06.2015
Leiter Prof. Dr. rer. nat. habil. Miriam Mehl
M.Sc. Klaudius Scheufele
Mitarbeiter Scheufele, Klaudius
Ansprechpartner Scheufele, Klaudius
Kooperationspartner George Biros, ICES, UT Austin

SIBIA big pictureFig.1: Schematic illustration of joint biophysical brain tumor models and medical image registration.

In scientific computing, an increasing need for ever more detailed insights and optimization leads
to improved models often including several effects / components described by different types of
equations. In most applications, we have a strong coupling between all involved effects, such that
neglecting the coupling would lead to inaccurate or wrong results. My primary focus of research are
strongly coupled multi-component problems that are inherently hard to solve as different equations
might require different kinds of approaches while the dependencies amongst the equations (coupling
conditions) need to be fulfilled at all times. Those systems have a natural need for high performance
computing, since the smaller modeling error we get when switching from a single-component to a
multi-component model is useless if we cannot sustain a high resolution. The complexity of the
corresponding solver algorithms and implementations typically can be tackled with so-called parti-
tioned simulations reusing existing and established software codes for different components. This
approach profits from decades of experience and development in terms of models, numerical meth-
ods and parallel scalability of the single components. Ensuring the fulfillment of coupling conditions
and overall stability requires sophisticated coupling numerics. Quasi-Newton approaches are a par-
ticularly promising numerical approach for the outer coupling iterations as they require only input
and output values of each component in order to estimate the underlying Jacobian or their inverses
and execute an approximate Newton iteration for the coupled system.

Reconstruction from real patient MR data.Fig.2: Hard segmentation of joint biophysical inversion and medical registration reconstruction for real patient MR data.

Two exemplary applications are addressed in this project: surface coupled multi-physics problems such as fluid-structure interactions and a volume-coupling between brain tumor growth and image registration with the final task to identify growth parameters based on an adjoint approach. The SIBIA (Scalable Integrated Biophysics-based Image Analysis) framework is developed to provide methods and algorithms for the joint image registration and biophysical inversion. Its application is in analysing MR images of glioblastomas (primary brain tumors). Given the segmentation of a normal brain MRI and the segmentation of a cancer patient MRI, we wish to determine tumor growth parameters and a registration map so that if we grow a tumor (using our tumor model) in the normal segmented image and then register it to the segmented patient image, then the registration mismatch is as small as possible. We call this the coupled problembecause it two-way couples the biophysical inversion and registration problems. In the image registration step we solve a large-deformation diffeomorphic registration problem parameterized by an Eulerian velocity field. In the biophysical inversion step we estimate parameters in a reaction-diffusion tumor growth model that is formulated as a partial differential equation (PDE). In SIBIA, we couple these two steps in an iterative manner.

Selected Publications

  • Scheufele, K., Mang, A., Gholami, A., Davatzikos, C., Biros, G., & Mehl, M. Coupling Brain-Tumor Biophysical Models and Diffeomorphic Image Registration. submitted to CMAME arXiv preprint externer Link   arXiv:1710.06420 .
  • Gholami, A., Mang, A., Scheufele, K., Davatzikos, C., Mehl, M., & Biros, G. externer Link  A framework for scalable biophysics-based image analysis. In Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis (p. 19). ACM. DOI: 10.1145/3126908.3126930 Best Student Paper Award