An image-driven parameter estimation problem for a reaction-diffusion glioma growth model with mass effects.
We present a framework for modeling gliomas growth and their mechanical impact on the surrounding brain tissue (the so-called, mass-effect). We employ an Eulerian continuum approach that results in a strongly coupled system of nonlinear Partial Differential Equations (PDEs): a reaction-diffusion model for the tumor growth and a piecewise linearly elastic material for the background tissue. To estimate unknown model parameters and enable patient-specific simulations we formulate and solve a PDE-constrained optimization problem. Our two main goals are the following: (1) to improve the deformable registration from images of brain tumor patients to a common stereotactic space, thereby assisting in the construction of statistical anatomical atlases; and (2) to develop predictive capabilities for glioma growth, after the model parameters are estimated for a given patient. To our knowledge, this is the first attempt in the literature to introduce an adjoint-based, PDE-constrained optimization formulation in the context of image-driven modeling spatio-temporal tumor evolution. In this paper, we present the formulation, and the solution method and we conduct 1D numerical experiments for preliminary evaluation of the overall formulation/methodology.
Hogea
Cosmina
C
Section of Biomedical Image Analysis, Department of Radiology, University of Pennsylvania, Philadelphia, PA 19104, USA. hogeac@uphs.upenn.edu
Davatzikos
Christos
C
Biros
George
G
D001185:Artificial Intelligence; D001696:Biomechanical Phenomena; D001921:Brain / Q000473:pathology; D001932:Brain Neoplasms / Q000473:pathology*; D004058:Diffusion; D005910:Glioma / Q000473:pathology*; D006128:Growth; D006801:Humans; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D007091:Image Processing, Computer-Assisted; D008279:Magnetic Resonance Imaging; D008954:Models, Biological; D009361:Neoplasm Invasiveness; D009716:Numerical Analysis, Computer-Assisted; D010363:Pattern Recognition, Automated; D013382:Subtraction Technique