Mathematical Modelling and Numerical Simulation in Medicine
This page contains the talks given as part of the CIMPA Summer School on Mathematical Modelling and Numerical Simulation in Medicine.
The talks were given under the theme “Examples and principles of mathematical modelling in medicine”
Microwave Ablation
The first lecture introduces the basic principles of mathematical modelling in medicine and the typical clinical workflow for image-guided therapies.
The curl-curl form of Maxwell’s equations are presented and the challenges in tractably computing the dose delivered in needle-based microwave ablation therapy presented.
The slides can be found [here].
Cryoablation
The second lecture presents cryoablation, and the requirements for computing the damage by cryotherapy. The challenges of model validation on clinical data are presented.
The slides can be found [here].
Ultrasound
The third lecture introduces the numerical challenges in modelling high-intensity focused ultrasound therapy, specifically focusing on the challenges posed by frequency-dependent powerlaw absorption for nonlinear wave propagation.
The slides can be found [here].
Exercises
Throughout the lectures a number of problems will be presented.
An set of collated problems can be found [here].
David Sinden is an applied mathematician working as a senior scientist at the Fraunhofer Institute for Digital Medicine MEVIS, in Bremen.
His research interests include ultrasound modelling, thermal ablation and pharmacokinetic models. He works within the modelling and simulation and image-guided therapy groups.