An inverse problem formulation for parameter estimation of a reaction-diffusion model of low grade gliomas
From MaRDI portal
Publication:907131
DOI10.1007/s00285-015-0888-xzbMath1333.92032arXiv1408.6221OpenAlexW1723524309WikidataQ40950674 ScholiaQ40950674MaRDI QIDQ907131
George Biros, Amir Gholami, Andreas Mang
Publication date: 2 February 2016
Published in: Journal of Mathematical Biology (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1408.6221
Medical applications (general) (92C50) Numerical solution of inverse problems involving ordinary differential equations (65L09) Preconditioners for iterative methods (65F08)
Related Items (27)
On convex modified output least-squares for elliptic inverse problems: stability, regularization, applications, and numerics ⋮ Dispersion–current adjoint functions for monitoring accidental sources in 3D transport equations ⋮ Learning physics-based models from data: perspectives from inverse problems and model reduction ⋮ Inverse problem approaches for mutation laws in heterogeneous tumours with local and nonlocal dynamics ⋮ Features of numerical reconstruction of a boundary condition in an inverse problem for a reaction-diffusion-advection equation with data on the position of a reaction front ⋮ Numerical simulation of front dynamics in a nonlinear singularly perturbed reaction-diffusion problem ⋮ Constrained $H^1$-Regularization Schemes for Diffeomorphic Image Registration ⋮ Some features of solving an inverse backward problem for a generalized Burgers' equation ⋮ Convergence rates for nonlinear inverse problems of parameter identification using Bregman distances ⋮ A Semi-Lagrangian Two-Level Preconditioned Newton--Krylov Solver for Constrained Diffeomorphic Image Registration ⋮ Data driven modeling of pseudopalisade pattern formation ⋮ Image-Driven Biophysical Tumor Growth Model Calibration ⋮ On the features of numerical solution of coefficient inverse problems for nonlinear equations of the reaction-diffusion-advection type with data of various types ⋮ A convex inversion framework for identifying parameters in saddle point problems with applications to inverse incompressible elasticity ⋮ A Data Scalable Augmented Lagrangian KKT Preconditioner for Large-Scale Inverse Problems ⋮ 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 ⋮ Analyzing the role of the Inf-Sup condition for parameter identification in saddle point problems with application in elasticity imaging ⋮ Coupling brain-tumor biophysical models and diffeomorphic image registration ⋮ Asymptotic analysis of solving an inverse boundary value problem for a nonlinear singularly perturbed time-periodic reaction-diffusion-advection equation ⋮ Solving coefficient inverse problems for nonlinear singularly perturbed equations of the reaction-diffusion-advection type with data on the position of a reaction front ⋮ Contingent derivatives and regularization for noncoercive inverse problems ⋮ Simulation of glioblastoma growth using a 3D multispecies tumor model with mass effect ⋮ PDE-constrained optimization in medical image analysis ⋮ Numerical reconstruction of brain tumours ⋮ CLAIRE: A Distributed-Memory Solver for Constrained Large Deformation Diffeomorphic Image Registration ⋮ Where did the tumor start? An inverse solver with sparse localization for tumor growth models ⋮ Numerical simulations in 3-dimensions of reaction–diffusion models for brain tumour growth
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Glioma follow white matter tracts: a multiscale DTI-based model
- \(M^5\) mesoscopic and macroscopic models for mesenchymal motion
- An image-driven parameter estimation problem for a reaction-diffusion glioma growth model with mass effects
- Stability of operator splitting methods for systems with indefinite operators: Advection-diffusion-reaction systems
- Complex dynamics of tumors: modeling an emerging brain tumor system with coupled reaction-diffusion equations
- A mathematical model for brain tumor response to radiation therapy
- Mathematical modelling of glioma growth: the use of diffusion tensor imaging (DTI) data to predict the anisotropic pathways of cancer invasion
- A hybrid ten-species phase-field model of tumor growth
- Time-domain hybrid formulations for wave simulations in three-dimensional PML-truncated heterogeneous media
- Adaptive finite element methods for the solution of inverse problems in optical tomography
- ON THE FOUNDATIONS OF CANCER MODELLING: SELECTED TOPICS, SPECULATIONS, AND PERSPECTIVES
- Brain–Tumor Interaction Biophysical Models for Medical Image Registration
- Analysis of Discrete Ill-Posed Problems by Means of the L-Curve
- Parallel Lagrange--Newton--Krylov--Schur Methods for PDE-Constrained Optimization. Part I: The Krylov--Schur Solver
- Parallel Lagrange--Newton--Krylov--Schur Methods for PDE-Constrained Optimization. Part II: The Lagrange--Newton Solver and Its Application to Optimal Control of Steady Viscous Flows
- On the Construction and Comparison of Difference Schemes
This page was built for publication: An inverse problem formulation for parameter estimation of a reaction-diffusion model of low grade gliomas