The PDEs of our hearts and minds

Why should we and how can we use mathematical and computational models to study

• tissue fluid flow and waste clearance in the brain?
• the mechanics of a beating human heart?
• collections of pluripotent stem cells?

In this talk, I will present state-of-the-art mathematical models, numerical techniques, and computational tools for addressing the above questions in particular and the role of modelling and simulation in biomedical computing in general. Topics include: modelling electrical signal propagation in tissue, hyperelastic material models including both passive and active forces, generalized poroelasticity models, stability and convergence analysis of mixed finite element methods, pde-constrained optimization and computational frameworks such as the FEniCS and dolfin-adjoint projects [1-3].

References
[1] G. Balaban, M. S. Alnaes, J. Sundnes, and M. E. Rognes. Adjoint multi-start-based estimation of cardiac hyperelastic material parameters using shear data. Biomechanics and modeling in mechanobiology, 15(6):1509-1521, 2016.
[2] G. Balaban, H. Finsberg, H. H. Odland, M. Rognes, S. Ross, J. Sundnes, and S.Wall. High resolution data assimilation of cardiac mechanics applied to a dyssynchronous ventricle. International Journal for Numerical Methods in Biomedical Engineering, 2017.
[3] P. E. Farrell, D. A. Ham, S. W. Funke, and M. E. Rognes. Automated derivation of the adjoint of high-level transient finite element programs. SIAM Journal on Scientific Computing, 35(4):C369-C393, 2013.