Non-invasive assessment of the cardiac function: a patient-specific modeling perspective
Simone Pezzuto (USI, Switzerland)
Thursday 23rd July, 2020 14:00-15:00 ZOOM (ID: 953 2392 6772)
Please Note: The ZOOM meeting will be password protected, as per the e-mail you received with subject: "Applied Mathematics Seminar ZOOM password".
All healthy hearts are alike; every unhealthy heart is unhealthy in its own way.” The Anna Karenina principle is perfectly summarizing an emerging paradigm in cardiology, and more generally in medicine: shifting from generic to patient-specific therapeutic interventions.
Mathematical models of the heart, underpinning patient-specific modeling, are well established in the literature. The so-called “virtual heart” has now become a reality, with realistic arrhythmia events routinely simulated. However, most of current patient-specific models are only anatomy-tailored, while many parameters (fibers, electric conductivities, ionic model, strain energy and contractility) are simply population-based. Given the increasing availability of patient data, from the standard 12-lead ECG and cardiac imaging to minimally invasive, high-density catheter mapping, it is tempting to assimilate such data and its associated uncertainty into models for further individualization and, ultimately, improved therapeutic intervention.
In such an exciting landscape, this talk will focus on 3 clinically relevant problems: the reconstruction of the ventricular activation from the 12-lead ECG; the estimate of anisotropic conduction velocity parameters in the atria from electroanatomic maps; the reconstruction of tissue contractility from sparse displacement measurements. A common thread links all the problems, as they all recast to PDE-constrained optimization. Specifically, the objective is to minimize (in some metric) the mismatch between recorded and simulated data, whereas the constraint is the patient-specific model. Despite the similarities, such as the ill-posedness stemming from the inverse procedure, each problem has also its own idiosyncrasies. In the reconstruction of the ventricular activation, special emphasis is given to the identification of earliest activation sites. For the atrial conduction velocity, we aim at estimating the full conductivity tensor—hence deducing the local fiber direction from its eigendecomposition—, yielding a minimization on the manifold of symmetric positive definite tensor fields. Finally, displacement and contractility are linked by a highly non-linear problem.
In the last part of the talk I will briefly discuss some open issues, such as the identifiability of the parameters, the quantification of uncertainty and model selection, all particularly relevant in view of clinical applications.