Andreas Buttenschoen

Andreas Buttenschoen

Department of Mathematics and Statistics
LGRT 1525
710 North Pleasant Street
Amherst, MA 01003

andreas.buttenschoen@umass.edu
www.umass.edu/mathematics-statistics/about/directory/andreas-buttenschoen

Assistant Professor of Mathematics and Statistics

I am an applied mathematician, building bridges between the mathematical, computational, and biological sciences. My strong foundations in each, allow me to identify key biological problems, draw on and contribute to theoretical mathematical foundations, and develop advanced computational tools. Swarms, flocks, and human societies all exhibit complex collective behaviours. I am interested in collective cell behaviours, which I view as swarms with a twist: 

  1. Cells are not simply point-like particles but have spatial extent;
  2. Interactions between cells go beyond simple attraction-repulsion; and 
  3. Cells “live” in a regime where friction dominates over inertia. 

Examples include: wound healing, embryogenesis (normal development), the immune response, and cancer metastasis. I use mathematical modelling and computational biology to uncover the universal principles how biological, physical, and chemical factors shape biological tissues. 

Interactions in tissues range over several orders of magnitude in time and spatial scales. Distinct mathematical frameworks are appropriate for specific levels of detail. For instance, differential equations (DEs), tracking changes in cell (or protein) densities, are suitable for describing large populations. I use dynamical systems, bifurcation theory, and group theory to analyse nonlocal DEs. On the other hand, to track the motion, behaviour, or forces produced by individual cells, a more detailed cell-cell-based computational framework is needed. I refer to such models as cell-based models (CBMs).

Current Research

One specific current focus of my research is a mathematical characterization of collective cell migration and invasion, whether by single cells, strands of cells, detached clusters or whole tissue fronts (as in wound healing) (see Friedl et. al. 2012). The primary significance is to foster a deeper understanding of metastatic cancer. My role would be to describe using rigorous mathematics the biological, physical and chemical forces at play in tissue dynamics. In more detail, I am interested in three particular research directions: 

  1. Development of digital-twins for in-vitro and in-vivo experiments; 
  2. Development of the next generation continuum limits of cell-based models; and 
  3. Statistical methods to compare experimental data, cell-based models, and continuum models.

Learn more at Buttenschoen Research Group 

Academic Background

Bs (2012) Physics and Mathematics at University of Alberta
BsH (2013) Applied Mathematics at University of Alberta
PhD (2017) Applied Mathematics at University of Alberta
Post doctoral fellow at University of British Columbia Department of Mathematics (2018-2022)

  • Models to Medicine Center