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Updated: May 18, 2026
Three-Dimensional Shape Modeling and Analysis of Brain Structures
Published on: November 14, 2019
A generic framework for modeling brain deformation as a constrained parametric optimization problem to aid
1Institute of Medical Engineering, University of Luebeck, Ratzeburger Allee, 23562 Luebeck, Germany.
Objectives:
In the present paper a novel computational framework for modeling tumor induced brain deformation as a biophysical prior for non-rigid image registration is described. More precisely, we aim at providing a generic building block for non-rigid image registration that can be used to resolve inherent irregularities in non-diffeomorphic registration problems that naturally arise in serial and cross-population brain tumor imaging studies due to the presence (or progression) of pathology.
Methods:
The model for the description of brain cancer dynamics on a tissue level is based on an initial boundary value problem (IBVP). The IBVP follows the accepted assumption that the progression of primary brain tumors on a tissue level is governed by proliferation and migration of cancerous cells into surrounding healthy tissue. The model of tumor induced brain deformation is phrased as a parametric, constrained optimization problem. As a basis of comparison and to demonstrate generalizability additional soft constraints (penalties) are considered. A back-tracking line search is implemented in conjunction with a limited memory Broyden-Fletcher-Goldfarb-Shanno (LBFGS) method in order to handle the numerically delicate log-barrier strategy for confining volume change.
Results:
Numerical experiments are performed to test the flexible control of the computed deformation patterns in terms of varying model parameters. The results are qualitatively and quantitatively related to patterns in patient individual magnetic resonance imaging data.
Conclusions:
Numerical experiments demonstrate the flexible control of the computed deformation patterns. This in turn strongly suggests that the model can be adapted to patient individual imaging patterns of brain tumors. Qualitative and quantitative comparison of the computed cancer profiles to patterns in medical imaging data of an exemplary patient demonstrates plausibility. The designed optimization problem is based on computational tools widely used in non-rigid image registration, which in turn makes the model generally applicable for integration into non-rigid image registration algorithms.
