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Seminar: Applied/Biomath seminars

Speaker: Daniele Schiavazzi Location: LD002

Stochastic Cardiovascular Modeling: Possibilities and Challenges

Abstract: Stochastic cardiovascular modeling is a particularly rich application field, i.e., forces the analyst to face numerous challenges in both forward and inverse uncertainty analysis. Models can naturally be organized into a hierarchy of fidelities, e.g., from 0-dimensional linearized circuits representations of vascular networks to one-dimensional Navier-Stokes models with axisymmetric vessel deformations, up to state-of-the-art geometrically multi-scale treatment, where a 3D stabilized finite element solver is coupled with a peripheral circuit.

Furthermore, model parameters must be systematically tuned to match specific patient data for personalized medicine. In this context, optimal parameter selection and associated deterministic model results are inadequate to provide a meaningful understanding of the physiology, and one must include multiple sources of uncertainty, e.g., from clinical data, constitutive material model, model segmentation, variability in the surgical outcome and personalized response to treatment. This suggests the need to have a probabilistic description of the parameters whose distributions can be learned from the available data, but model reduction approaches become essential to avoid computationally intractability of repeated model solutions.

I will discuss our approach to stochastic cardiovascular modeling which consists of various tasks: stable model reduction through relevance vector machine regression, investigation of structural and practical identifiability, Bayesian parameter estimation through parallel multi-level MCMC, random field models of material property uncertainty, and multi-resolution uncertainty propagation to local hemodynamics results.

Examples will be presented in the context of coronary artery disease, single-ventricle congenital heart disease and detection of pulmonary hypertension in patients affected by heart failure with preserved ejection fraction.

Bio: Dr. Schiavazzi is an Assistant Professor in the Department of Applied and Computational Mathematics and Statistics at the University of Notre Dame. He graduated with honors and received a Ph.D. in Applied Mathematics from the University of Padova, Italy. He has completed his Ph.D. as a Visiting Researcher at Stanford University, followed by a Postdoctoral position at University of California, San Diego and Stanford University. His main research interests are in stochastic analysis, multi-resolution approximation, numerical modeling and finite element analysis, adaptive Markov chain Monte Carlo estimation and use of computational models to inform clinical decision making under uncertainty. More info can be found at www.nd.edu/~dschiava.

 

Organizer:  Jared Barber and Julia Arciero