TP1: Separating Dynamics and Motion in Medical 4D Image Data
Subproject leaders
Prof. Dr J. Modersitzki, Dr Stefan Heldmann
Project researcher
Dr Benjamin Wacker
Project partner
Prof. Dr Jörg Barkhausen, University Medical Center Schleswig-Holstein
Contact
Objectives
This subproject aims to develop mathematically sound and validated models for describing and separating dynamics and motion in medical 4D image data. We use the following models for dynamics and motion:
$\begin{align} \operatorname{dynamic}(D,M)&:=\operatorname{modelFit}(D,M)+\operatorname{smoothness}(M)\\ \operatorname{motion}(D,y)&:=\operatorname{dataFit}(A,D,y)+\operatorname{regularity}(y) \end{align}$
The process (data) is represented by a 4D intensity function $D:\mathbb R^3\times [0,T]\mapsto \mathbb R$, dynamics by a model $M:\mathbb R^3\times [0,T]\mapsto \mathbb R$, baseline anatomy by a function $A:\mathbb R^3 \mapsto \mathbb R$, and motion by a vector field $y:\mathbb R^3\times [0,T]\mapsto \mathbb R^3$. The models are specified in subprojects TP1.1–TP1.4; TP4 addresses the general data setting and evaluation of the results.
Input (from other subprojects)
Eulerian motion-correction model (TP2)
Optimisation methods (TP2)
Selection of regularisation parameters and uncertainty quantification (TP3)
Problem definitions (TP4)
Output (to other subprojects)
Approaches for separating dynamics and motion in 4D image data (TP2–TP4)
Lagrangian motion-correction model (TP2)
Motion correction with constraints (TP2)
Motion-correction algorithms (TP4)
Pharmacokinetic models and algorithms (TP4)
Previous work
The applicants have an extensive body of work on image registration (motion compensation), including more than 100 publications and two textbooks. This provides a well-structured variational mathematical approach to image registration. The applicants have also developed freely available software implementing state-of-the-art variational registration methods numerically in a modular, extensible framework [36]. This provides an excellent computational foundation.
Previous work with the University of Bergen in Norway addressed motion correction for DCE-MRI data, although the mathematical coupling of dynamics and motion was not yet implemented. The applicants have maintained a strong collaboration with the Institute of Mathematics and Computer Science at the University of Münster, resulting in two joint doctoral researchers. Bachelor’s and master’s theses have already studied the coupling of dynamics and motion by implementing and comparing basic compartment models. These models provide a strong starting point for the pharmacokinetic models to be developed.