Brain-tumor interaction biophysical models for medical image registration

Cosmina Hogea, Christos Davatzikos, George Biros

Research output: Contribution to journalArticle

Abstract

State-of-the art algorithms for deformable image registration are based on the minimization of an image similarity functional that is regularized by adding a penalty term on the deformation map. The penalty function typically represents a smoothness regularization. In this article, we use a constrained optimization formulation in which the image similarity functional is coupled to a biophysical model. This formulation is pertinent when the data have been generated by imaging tissue that undergoes deformations due to an actual biophysical phenomenon. Such is the case of coregistering tumor-bearing brain images from the same individual. We present an approximate model that couples tumor growth with the mechanical deformations of the surrounding brain tissue. We consider primary brain tumors - in particular, gliomas. Glioma growth is modeled by a reaction-advection-diffusion PDE, with a two-way coupling with the underlying tissue elastic deformation. Tumor bulk, infiltration, and subsequent mass effects are not regarded separately but are captured by the model itself in the course of its evolution. Our formulation allows for updating the tumor diffusion coefficient following structural displacements caused by tumor growth/infiltration. Our forward problem implementation builds on the PETSc library of Argonne National Laboratory. Our reformulation results in a very small parameter space, and we use the derivative-free optimization library APPSPACK of Sandia National Laboratories. We test the forward model and the optimization framework by using landmark-based similarity functions and by applying it to brain tumor data from clinical and animal studies. State-of-the-art registration algorithms fail in such problems due to excessive deformations. We compare our results with previous work in our group, and we observed up to 50% improvement in landmark deformation prediction. We present preliminary validation results in which we were able to reconstruct deformation fields using four degrees of freedom. Our study demonstrates the validity of our formulation and points to the need for richer datasets and fast optimization algorithms.

Original languageEnglish (US)
Pages (from-to)3050-3072
Number of pages23
JournalSIAM Journal on Scientific Computing
Volume30
Issue number6
DOIs
StatePublished - 2008
Externally publishedYes

Fingerprint

Brain Tumor
Image registration
Image Registration
Medical Image
Tumors
Brain
Interaction
Tumor
Infiltration
Tumor Growth
Formulation
Landmarks
Tissue
Derivative-free Optimization
Model
Bearings (structural)
Forward Problem
Advection-diffusion
Elastic Deformation
Approximate Model

Keywords

  • Deformable registration
  • Medical image registration
  • Soft-tissue simulations
  • Tumor growth

ASJC Scopus subject areas

  • Applied Mathematics
  • Computational Mathematics

Cite this

Brain-tumor interaction biophysical models for medical image registration. / Hogea, Cosmina; Davatzikos, Christos; Biros, George.

In: SIAM Journal on Scientific Computing, Vol. 30, No. 6, 2008, p. 3050-3072.

Research output: Contribution to journalArticle

Hogea, Cosmina ; Davatzikos, Christos ; Biros, George. / Brain-tumor interaction biophysical models for medical image registration. In: SIAM Journal on Scientific Computing. 2008 ; Vol. 30, No. 6. pp. 3050-3072.
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