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].
 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.
 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.
 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.