# PDE-constrained optimization in medical image analysis

@article{Mang2018PDEconstrainedOI, title={PDE-constrained optimization in medical image analysis}, author={Andreas Mang and Amir Gholami and Christos Davatzikos and George Biros}, journal={Optimization and Engineering}, year={2018}, volume={19}, pages={765-812} }

PDE-constrained optimization problems find many applications in medical image analysis, for example, neuroimaging, cardiovascular imaging, and oncologic imaging. We review the related literature and give examples of the formulation, discretization, and numerical solution of PDE-constrained optimization problems for medical imaging. We discuss three examples. The first is image registration, the second is data assimilation for brain tumor patients, and the third is data assimilation in… Expand

#### Figures, Tables, and Topics from this paper

#### 20 Citations

Stuttgart Efficient Algorithms for Geodesic Shooting in Diffeomorphic Image Registration

- 2019

Diffeomorphic image registration is a common problem in medical image analysis. Here, one searches for a diffeomorphic deformation that maps one image (the moving or template image) onto another… Expand

Coupling brain-tumor biophysical models and diffeomorphic image registration.

- Computer Science, Medicine
- Computer methods in applied mechanics and engineering
- 2019

The introduction of a PDE-constrained optimization formulation of the coupled problem, and the derivation of a Picard iterative solution scheme are introduced. Expand

Image-Driven Biophysical Tumor Growth Model Calibration

- Computer Science, Mathematics
- SIAM J. Sci. Comput.
- 2020

A novel formulation for the calibration of a biophysical tumor growth model from a single-time snapshot, multiparametric magnetic resonance imaging (MRI) scan of a glioblastoma patient, using a PDE-constrained optimization framework and a modified Picard-iteration-type solution strategy. Expand

An introduction to partial differential equations constrained optimization

- Optimization and Engineering
- 2018

Partial differential equation (PDE) constrained optimization is designed to solve control, design, and inverse problems with underlying physics. A distinguishing challenge of this technique is the… Expand

CLAIRE: A distributed-memory solver for constrained large deformation diffeomorphic image registration

- Medicine, Computer Science
- SIAM J. Sci. Comput.
- 2019

This work releases CLAIRE, a distributed-memory implementation of an effective solver for constrained large deformation diifeomorphic image registration problems in three dimensions, and introduces an improved preconditioner for the reduced space Hessian to speed up the convergence of the solver. Expand

Analyzing the role of the Inf-Sup condition for parameter identification in saddle point problems with application in elasticity imaging

- Mathematics
- 2020

We study the inverse problem of parameter identification in general saddle point problems. For saddle point problems, the use of elliptic regularization is an essential component. Saddle point… Expand

CLAIRE: Constrained Large Deformation Diffeomorphic Image Registration on Parallel Computing Architectures

- Computer Science
- J. Open Source Softw.
- 2021

CLAIRE (Mang & Biros, 2019) is a computational framework for Constrained LArge deformation diffeomorphic Image REgistration that supports highly-optimized, parallel computational kernels for (multi-node) CPU and multi-GPU architectures and a Newton–Krylov solver for numerical optimization. Expand

Physics-aware registration based auto-encoder for convection dominated PDEs

- Mathematics, Computer Science
- ArXiv
- 2020

A physics-aware auto-encoder to specifically reduce the dimensionality of solutions arising from convection-dominated nonlinear physical systems and demonstrates the efficacy and interpretability of the approach to separate convection/advection from diffusion/scaling on various manufactured and physical systems. Expand

A solution for fractional PDE constrained optimization problems using reduced basis method

- Mathematics
- 2019

In this paper, we employ a reduced basis method for solving PDE constrained optimization problem governed by a fractional parabolic equation with the fractional derivative in time. The fractional… Expand

On Some Features of the Numerical Solving of Coefficient Inverse Problems for an Equation of the Reaction-Diffusion-Advection-Type with Data on the Position of a Reaction Front

- Mathematics
- 2021

The work continues a series of articles devoted to the peculiarities of solving coefficient inverse problems for nonlinear singularly perturbed equations of the reaction-diffusion-advection-type with… Expand

#### References

SHOWING 1-10 OF 232 REFERENCES

Brain--Tumor Interaction Biophysical Models for Medical Image Registration

- Mathematics, Computer Science
- SIAM J. Sci. Comput.
- 2008

This article uses a constrained optimization formulation in which the image similarity functional is coupled to a biophysical model, and presents an approximate model that couples tumor growth with the mechanical deformations of the surrounding brain tissue. Expand

Coupling brain-tumor biophysical models and diffeomorphic image registration.

- Computer Science, Medicine
- Computer methods in applied mechanics and engineering
- 2019

The introduction of a PDE-constrained optimization formulation of the coupled problem, and the derivation of a Picard iterative solution scheme are introduced. Expand

Adjoint method for a tumor growth PDE-constrained optimization problem

- Computer Science, Mathematics
- Comput. Math. Appl.
- 2013

A method for estimating unknown parameters that appear on an avascular, spheric tumor growth model by fitting the numerical solution with real data, obtained via in vitro experiments and medical imaging is presented. Expand

A framework for scalable biophysics-based image analysis

- Computer Science
- SC
- 2017

SIBIA (Scalable Integrated Biophysics-based Image Analysis), a framework for coupling biophysical models with medical image analysis, provides solvers for an image-driven inverse brain tumor growth model and an image registration problem that can eventually help in diagnosis and prognosis of brain tumors. Expand

An image-driven parameter estimation problem for a reaction–diffusion glioma growth model with mass effects

- Computer Science, Medicine
- Journal of mathematical biology
- 2008

The two main goals are 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 to develop predictive capabilities for glioma growth, after the model parameters are estimated for a given patient. Expand

Biophysical modeling of brain tumor progression: from unconditionally stable explicit time integration to an inverse problem with parabolic PDE constraints for model calibration.

- Medicine
- Medical physics
- 2012

PURPOSE
A novel unconditionally stable, explicit numerical method is introduced to the field of modeling brain cancer progression on a tissue level together with an inverse problem (IP) based on… Expand

Algorithms for PDE‐constrained optimization

- Mathematics
- 2010

Some first and second order algorithmic approaches for the solution of PDE-constrained optimization problems are reviewed. An optimal control problem for the stationary Navier-Stokes system with… Expand

Three-dimensional Image-based Mechanical Modeling for Predicting the Response of Breast Cancer to Neoadjuvant Therapy.

- Computer Science, Medicine
- Computer methods in applied mechanics and engineering
- 2017

A data-driven framework for prediction of residual tumor burden following neoadjuvant therapy in breast cancer that uses a biophysical mathematical model combining reaction-diffusion growth/therapy dynamics and biomechanical effects driven by early time point imaging data is demonstrated. Expand

An inexact Newton-Krylov algorithm for constrained diffeomorphic image registration

- Mathematics, Computer Science
- SIAM J. Imaging Sci.
- 2015

Overall, the reported results demonstrate excellent numerical accuracy, guaranteed local deformation regularity, and computational efficiency with an optional control on local mass conservation with a black-box solver that exploits computational tools that are precisely tailored for solving the optimality system. Expand

Adjoint method for a tumor invasion PDE-constrained optimization problem in 2D using adaptive finite element method

- Mathematics, Computer Science
- Appl. Math. Comput.
- 2015

A method for estimating an unknown parameter that appears in a two dimensional non-linear reaction-diffusion model of cancer invasion, which considers that tumor-induced alteration of micro-environmental pH provides a mechanism for cancer invasion. Expand