Cardiac mathematical modeling is becoming an important facet of modern cardiological research. The field of mathematical modeling of the heart encompasses both electrophysiology and mechanics, expressed through differential equations, spans phenomena from the molecular scale, to dynamics of ion currents through the cell membrane, and finally models of propagation and contraction through tissue samples or whole hearts. A main challenge is determining the validity of models and capturing physiological variability, including that among patients.
Kallhovd's thesis cover topics concerning both healthy and diseased hearts, involving the sensitivity of computational results to model parameters.
Modeling can explore the mechanisms of initiation and possible targets for termination of arrhythmias, which are unwanted patterns of tissue activation. Arrhythmogenic Right Ventricle Cardiomyopathy (ARVC) is a disease that affects the connections between myocytes, and eventually causes myocyte cell death so that fibrotic and fatty tissue infiltrate or replace functional myocardium. This thesis include an exploratory study of the influence of several factors related to fatty tissue infiltration, that cannot easily be determined from clinical measurements, such as the role of placement of diseased tissue, and fraction of fatty infiltration, with the ultimate goal of arrhythmia risk evaluation.
The two latter topics involve solving inverse problems to correctly parameterize patient- specific models in general. We investigate the interdependence between the material stiffness parameters, the unloaded geometry of the left ventricle and the stress calculated over a heart beat with the goal of validating patient-specific mechanical models by providing the optimal match between observed patient pressure-volume loops and left ventricular modeling results. In cardiac imaging, the geometry of the heart can be determined during the cardiac cycle, but the heart will always experience some intrinsic loading from both the pressure on the ventricular walls and the state of contraction. In computational mechanics the initial state of the system is assumed to be a stress free state, which necessitates the estimation of an unloaded geometry, which is determined by the chosen material passive stiffness parameters that is investigated.
The last topic involves applying PDE-constrained gradient-based optimisation with the adjoint method to investigate its applicability to estimating timings and dynamics of the initial electrical activation of cardiac tissue. We consider several sources of model observations, and test the system with severe degrees of noise. In future applications, the goal is to find activation from electrocardiography (ECG) data, so we consider the appropriate sampling frequency and test the approach on relatively coarse meshes for computational tractability.
The thesis is written within the field of Scientific Computing. The work has been conducted at Simula Research Laboratory.
Prior to the defense, at 11:15, Siri Kallhovdpresented her trial lecture "Sensitivity analyses and Variability in Electrophysiological Cardiac AP Models".
- Professor Beatriz Ana Trenor Gomis, Universitat Politécnica de València, Spain
- Lecturer Jack Lee, King’s College London, United Kingdom
- Professor Xing Cai, Department of Informatics, University of Oslo
Chair of the disputation
- Professor Fritz Albregsten, University of Oslo, Institute of Informatics
- Associate Professor Joakim Sundnes, Department of Informatics, University of Oslo
- Senior Research Scientist Samuel Wall, Simula Research Lab
- Senior Research ScientistMary M. Maleckar,Simula Research Lab