Mathias Davids, PhD, is currently an Instructor in Radiology at Harvard Medical School. He received a BSc in Biomedical Engineering at University of Luebeck in 2011, and an MSc and Ph.D. in Biomedical Physics at Heidelberg University in 2014 and 2018, respectively. Dr. Davids has a strong background in mathematical modeling of biomedical and biophysical processes.

His work specializes on developing tools to understand, predict, and control peripheral nerve stimulations, PNS, in the human body induced by magnetostimulation (coils) and electrostimulation (electrodes) devices.

For example, PNS has become a significant limitation on using powerful Magnetic Resonance Imaging (MRI) gradient systems in human subjects, and potentially limits the translation of Magnetic Particle Imaging (MPI) to humans. The PNS modeling tool developed by Dr. Davids (together with Dr. Wald and Dr. Guerin) combines electromagnetic simulations in detailed anatomical body model meshes and neurodynamic simulations of the peripheral nervous system embedded in the body models. As such, the PNS tool includes various state-of-the-art components, including large-scale finite element modeling (FEM) to predict the electric fields induced in the body (solving Maxwell’s equations), generation and optimization of computational meshes, and prediction of the nervous system responses using linear and non-linear nerve membrane models. This tool is the first of its kind, as it reproduces experimental PNS thresholds and locations obtained in stimulation studies on healthy human subjects.

Having a comprehensive PNS modeling tool helps fostering our understanding of how PNS is generated, and how it can be avoided in MRI and MPI. For example, a linear version of the PNS tool can be included in the standard approach for the numeric winding optimization of gradient coils (called boundary element method stream function approach, BEM-SF). The knowledge of how the gradient coil’s magnetic field interact with peripheral nerves allows the winding optimizer to “design around” the human body, by identifying winding solutions that interact minimally with the nerves. The goal will be faster and safer MRI and MPI machines with superior spatial and temporal image resolution. Other goals of Dr. Davids’ PNS work include utilization of coil and electrode arrays to selectively stimulate nerves or manipulate the nerve’s ion dynamics for therapeutic purposes, and an extension to modeling stimulation of excitable cardiac tissue.


PhD in Biomedical Physics, Heidelberg University

Select Publications

Davids, Mathias, et al. “Optimization of MRI Gradient Coils with Explicit Peripheral Nerve Stimulation Constraints.” IEEE Transactions on Medical Imaging (2020), DOI: 10.1109/TMI.2020.3023329

Davids, Mathias et al. “Optimizing selective stimulation of peripheral nerves with arrays of coils or surface electrodes using a linear peripheral nerve stimulation metric.” Journal of neural engineering vol. 17,1 016029. 14 Jan. 2020, doi:10.1088/1741-2552/ab52bd

Davids, Mathias et al. “Prediction of peripheral nerve stimulation thresholds of MRI gradient coils using coupled electromagnetic and neurodynamic simulations.” Magnetic resonance in medicine vol. 81,1 (2019): 686-701. doi:10.1002/mrm.27382

Davids, Mathias et al. “Fast three-dimensional inner volume excitations using parallel transmission and optimized k-space trajectories.” Magnetic resonance in medicine vol. 76,4 (2016): 1170-82. doi:10.1002/mrm.26021

Full publication list:


2019: I.I. Rabi Young Investigator Award Winner, ISMRM

2013: Medical Physics “Best Student” Scholarship, Heidelberg University