Invited Session Thu.1.H 0111

Thursday, 10:30 - 12:00 h, Room: H 0111

Cluster 19: PDE-constrained optimization & multi-level/multi-grid methods [...]

PDE optimization in medicine I


Chair: Anton Schiela



Thursday, 10:30 - 10:55 h, Room: H 0111, Talk 1

Luis A. Fernandez
Optimizing a chemotherapy model for brain tumors by using PDE


We study some optimal control problems concerning a reaction-diffusion PDE that describes
the growth of some brain tumors called gliomas, taking into account the pharmacokinetics of the chemotherapy treatment
through its corresponding PDE in different frameworks.



Thursday, 11:00 - 11:25 h, Room: H 0111, Talk 2

Lars Ole Schwen
Modeling flow through realistic, algorithmically generated vascular structures in the liver

Coauthor: Preusser Tobias


The liver is a highly perfused and central metabolic organ. Its main connection to the rest of the organism is the blood flow through two supplying and one draining vascular system. For modeling blood flow through these, a proper geometric model of the vascular systems in the liver is an important building block.
In vivo imaging or imaging of corrosion casts does not provide sufficient details to obtain a geometric representation of the vascular structures down to the sinusoidal scale. The method of Constrained Constructive Optimization [Buxbaum; Schreiner; Karch et al.] is used for this purpose, determining a structure of minimal intravascular volume that provides homogeneous supply/drainage for the perfused volume.
We quantify the similarity of algorithmically generated vascular structures to real human and murine ones, comparing different geometric features, and use these findings to improve the algorithm. For simulating flow in the whole organ as well as for jointly generating supplying and draining vascular systems, the tissue in between is taken into account as a porous medium in a 3D simulation coupled to the vascular flow.



Thursday, 11:30 - 11:55 h, Room: H 0111, Talk 3

Lars Lubkoll
Optimal control in implant shape design

Coauthors: Anton Schiela, Martin Weiser


As in many parts of modern medicine the design of implants is today more dependent on the experience of medical scientists than on technical tools. Especially in the case of heavy fractures or natural deformations of the oral and maxillofacial bone structure it is often difficult to accurately predict the shape of the patients face after the medical treatment. Consequently it would be of advantage if one could delegate the determination of an implant's shape from a given desired shape of the skin to a computer-assisted tool. This would allow to give reliable assistance regarding the training, preparation and verification of implant insertions.
In this context we present an approach that leads to an optimal control problem with an elastic constitutive law as PDE constraint. In the case of linearized elasticity we analyse this problem and will present numerical results. Moreover we will give an outline on our progress on the treatment of more realistic nonlinear material models.


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