Aspects of the cardiovascular system:(i) coupling between the left ventricle and systemic arteries, and (ii) arterial dissection.

Two topics in mathematical and computational modelling of the systemic arterial circulation will be discussed. First, an immersed boundary model of the left ventricle (LV) is coupled to a structured tree model of the systemic arteries. There is good agreement with clinical observations, and the relationship between active stress in the LV wall, LV pressure and flow rate are studied in cases of pathological cardiovascular function. Secondly, studies of the dissection (tearing) of the wall of the aorta using the HGO constitutive law reveal the role played by collage fibre orientation. Complex buckling patterns of inner wall are shown to be qualitatively similar to those seen in MRI scans.–

Soft tissue mechanics and fluid-structure interaction in the cardiac system

This talk will start with an overview of the invariant-based continuum mechanics approach for anisotropic soft tissues that undergo nonlinear large deformation. I will then report how we model the cardiac system using the invariant-based constitutive laws and a fluid-structure interaction solver. The models will be patient-specific derived from in vivo clinical magnetic resonance images (MRI), with material parameters determined using inverse and statistical approaches so that the model results agree with in vivo observations. We model the cardiac function both in diastole and in systole, and consider agent-based modelling for myocardial infarction, soft tissue changes informed by MRI perfusion measurements, heart-valve, and heart-circulation interactions. Finally, I will briefly introduce the EPSRC funded SofTMech Centre and the ongoing research themes in the Centre.