BEGIN:VCALENDAR VERSION:2.0 PRODID:-//Talks.cam//talks.cam.ac.uk// X-WR-CALNAME:Talks.cam BEGIN:VEVENT SUMMARY:Enabling high-dimensional uncertainty quantification for cardiac e lectrophysiology via multifidelity techniques - Simone Pezzuto (Universit à della Svizzera italiana) DTSTART:20190605T160000Z DTEND:20190605T163000Z UID:TALK125590@talks.cam.ac.uk CONTACT:INI IT DESCRIPTION: Mathematical modeling of the heart\, as many other models in biomedical sciences\, involves a large number of paramet ers and simplifying approximations. Uncertainties for cardiac models are ubiquitous\, including anatomy\, fiber direction\, and electric and mec hanical properties of the tissue. Hence\, both UQ and parameter sensitiv ity naturally arise during modeling\, and they shall become fundamental in view of clinical applications.

For high-dimensional in put uncertainties\, e.g.\, substrate heterogeneity or cardiac fibers ori entation\, and high-dimensional output quantities of interest\, e.g.\, t he activation map\, the method of choice for UQ is the classic Monte Car lo (MC) method. MC convergence rate does not suffer from the curse of di mensionality\, but it is notoriously slow. While sampling a random field can be done very efficiently via the pivoted Cholesky decomposition\, c omputing the cardiac activation from the bidomain equation is a computat ional demanding task. A single patient-tailored simulation can take seve ral CPU-hours even on a large cluster. This makes uncertainty quantifica tion (UQ) unfeasible\, unless modeling reduction strategies are employed .

One such strategy is represented by multifidelity metho ds [1]. A key ingredient of the multifidelity approach is the choice of low-fidelity models. Typical strategies are projection-based or data-fit surrogates\, which however need to be trained anew for each patient and may become inefficient for a large dimensionality of the input\, as in the case under consideration. Instead\, a more physics-based approach is to take advantage of the natural hierarchy of available models. These i nclude different cellular models for the monodomain equation\, the time- independent eikonal equation\, and the 1D geodesic point activation [2\, 3]. By exploiting statistical correlations in this hierarchy\, we observ ed a reduction of the computational cost by at least two orders of magni tude\, enabling to perform a full analysis within a reasonable time fram e. Moreover\, we incorporate Bayesian techniques\, which provide confidenc e intervals and full probability distributions at selected points\, thus augmenting the information provided by standard frequentist approaches.

References:
[1] Peherstorfer\, B.\, Willcox\, K.\, &\; Gunzburger\, M. (2018). Survey of multifidelity methods in uncertainty propagation\, inference\, and optimization. SIAM Review\, 60 (3)\, 550-591.
[2] Quaglino\, A.\, Pezzuto\, S.\, Koutsourelakis\, P.S.\, Auricchio\, A.\, Krause\, R. (2018). Fast uncertainty quantifica tion of activation sequences in patient-specific cardiac electrophysiolo gy meeting clinical time constraints. Int J Numer Meth Biomed Engng\, e2 985.
[3] Quaglino\, A.\, Pezzuto\, S.\, Krause\, R. (2018). Genera lized Multifidelity Monte Carlo Estimators. Submitted to J Comp Phys. Ar Xiv: 1807.10521 LOCATION:Seminar Room 1\, Newton Institute END:VEVENT END:VCALENDAR