An adjoint-based method for a linear mechanically-coupled tumor model

application to estimate the spatial variation of murine glioma growth based on diffusion weighted magnetic resonance imaging

Xinzeng Feng, David A. Hormuth, Thomas Yankeelov

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

We present an efficient numerical method to quantify the spatial variation of glioma growth based on subject-specific medical images using a mechanically-coupled tumor model. The method is illustrated in a murine model of glioma in which we consider the tumor as a growing elastic mass that continuously deforms the surrounding healthy-appearing brain tissue. As an inverse parameter identification problem, we quantify the volumetric growth of glioma and the growth component of deformation by fitting the model predicted cell density to the cell density estimated using the diffusion-weighted magnetic resonance imaging data. Numerically, we developed an adjoint-based approach to solve the optimization problem. Results on a set of experimentally measured, in vivo rat glioma data indicate good agreement between the fitted and measured tumor area and suggest a wide variation of in-plane glioma growth with the growth-induced Jacobian ranging from 1.0 to 6.0.

Original languageEnglish (US)
Pages (from-to)159-180
Number of pages22
JournalComputational Mechanics
Volume63
Issue number2
DOIs
StatePublished - Feb 15 2019

Fingerprint

Magnetic Resonance Imaging
Magnetic resonance
Tumors
Tumor
Imaging techniques
Estimate
Quantify
Model
Cell
Identification Problem
Parameter Identification
Medical Image
Rats
Brain
Numerical methods
Identification (control systems)
Numerical Methods
Tissue
Optimization Problem

Keywords

  • Adjoint-state method
  • Finite element
  • Glioma growth
  • Inverse problem
  • Mass effect
  • Mechanically-coupled

ASJC Scopus subject areas

  • Computational Mechanics
  • Ocean Engineering
  • Mechanical Engineering
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics

Cite this

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title = "An adjoint-based method for a linear mechanically-coupled tumor model: application to estimate the spatial variation of murine glioma growth based on diffusion weighted magnetic resonance imaging",
abstract = "We present an efficient numerical method to quantify the spatial variation of glioma growth based on subject-specific medical images using a mechanically-coupled tumor model. The method is illustrated in a murine model of glioma in which we consider the tumor as a growing elastic mass that continuously deforms the surrounding healthy-appearing brain tissue. As an inverse parameter identification problem, we quantify the volumetric growth of glioma and the growth component of deformation by fitting the model predicted cell density to the cell density estimated using the diffusion-weighted magnetic resonance imaging data. Numerically, we developed an adjoint-based approach to solve the optimization problem. Results on a set of experimentally measured, in vivo rat glioma data indicate good agreement between the fitted and measured tumor area and suggest a wide variation of in-plane glioma growth with the growth-induced Jacobian ranging from 1.0 to 6.0.",
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AU - Yankeelov, Thomas

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N2 - We present an efficient numerical method to quantify the spatial variation of glioma growth based on subject-specific medical images using a mechanically-coupled tumor model. The method is illustrated in a murine model of glioma in which we consider the tumor as a growing elastic mass that continuously deforms the surrounding healthy-appearing brain tissue. As an inverse parameter identification problem, we quantify the volumetric growth of glioma and the growth component of deformation by fitting the model predicted cell density to the cell density estimated using the diffusion-weighted magnetic resonance imaging data. Numerically, we developed an adjoint-based approach to solve the optimization problem. Results on a set of experimentally measured, in vivo rat glioma data indicate good agreement between the fitted and measured tumor area and suggest a wide variation of in-plane glioma growth with the growth-induced Jacobian ranging from 1.0 to 6.0.

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