Mostly Biomathematics Lunchtime Seminar

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Construction of a hyperelastic immersed boundary model of the human heart

Speaker: Charles Puelz, Courant Institute of Mathematical Sciences, New York University

Location: Warren Weaver Hall 1314

Date: Tuesday, September 18, 2018, 12:30 p.m.

Synopsis:

The focus of this talk is the construction of a computer model of the human heart, which includes the four valves, ascending aorta, and pulmonary artery.  The equations of motion are approximated with the immersed boundary finite element method.  The fluid is discretized on a fixed Cartesian grid and the solid displacements and forces are represented using nodal finite elements.  In addition to discussing implementation of the numerical methods, we describe in detail the model construction process, beginning with the creation of a finite element mesh from medical images.  Since the solid models are hyperelastic, another important component is the specification of a strain energy density for each part of the heart.  In particular, the constitutive models for the myocardium and valve leaflets require fiber vector fields, which are created using Poisson interpolation techniques.  At the end of the talk we give some preliminary simulations with physiologically reasonable pressure sources and boundary conditions.