Modeling & Simulation


We develop mathematical models and numerical simulations of biophysical and biomedical processes for clinical use. In close collaboration with other areas of medical image computing, we support diagnosis and therapy.

By complementing medical imaging with computational modeling, our approaches reveal information that is not directly visible, thus enabling radiology beyond the eye.

With a portfolio of patient-specific biophysical models, simulations, and mathematical optimization techniques, we predict and optimize treatment and therapy outcome. We pave the way for clinical translation by verification, validation and uncertainty quantification following FDA standards and quality assurance according to ISO13485.


Multiphysics and Multiscale Models

We develop mathematically sound models involving various biophysical processes such as fluid dynamics, tissue deformations, and radiofrequency and microwave ablation. Separating phenomena according to the appropriate physiological scales, we build modular and efficient multiscale models. Applications include pharmacodynamics or biomechanics.

Efficient GPU Implementations

We exploit modern hardware architectures like multi-core or many-core processors and GPUs. Efficient parallel implementations mitigate the computational cost of patient-individualized simulation and optimization, thus enabling applications in clinical practice. For example, pre-interventional planning of HIFU treatment is enabled by GPU parallelization of the simulation of thermal damage.

Accurate Simulations

We simulate hemodynamic alterations in major arteries after a virtual intervention and thereby support deciding on an optimal treatment plan. For this purpose, we perform computationally efficient blood flow simulations in complex vascular structures using the Lattice Boltzmann method. We also employ Finite Difference and Finite Element methods to simulate deformations of soft tissues or trabecular bones in biomechanics, for instance.

Uncertainty Quantification

Personalized medicine requires running bio-medical simulations with individual parameters and data, which are often not precisely known. In order to quantify uncertainty in the solution and to select solutions which are robust against uncertain input, we model such data as random variables. By these stochastic PDEs, we model RFA simulation, optimization, and parameter identification, and perform PDE-based image processing.

Model Approximations

Besides parallelization, we develop model approximations for real-time simulations. By a combination of pre-computed results and image-based geometry information, this provides sufficient accuracy for individualized interactive planning of interventions like RFA. Employing numerical homogenization techniques, we determine effective tissue parameters for use in multiscale models.


Planning patient-individual thermal treatment benefits from optimization, for example, finding the best probe position and identifying material parameters from temperature measurements. Modeling the underlying bio-physical effects with PDEs, we apply optimization techniques such as CG or SQP methods or shape derivatives.

Application Highlights

GPU-based Software Assistant for Liver High-Intensity Focused Ultrasound

Modeling, Simulation, Optimization, Uncertainty Quantification in RFA

Spatially Resolved Liver Blood Flow and Pharmacokinetics Simulations

Blood Flow Simulation for Cardiovascular Intervention Planning

Model-Based Position Correlation for the Breast