Investigating Fontan Failure Using Mathematical Modeling

Babies born with a single functioning heart ventricle instead of two require a series of surgeries during the first few years of life to redirect their blood flow, resulting in a Fontan circulation. Patients with Fontan circulations have excellent early survival; however, over time, their circulations begin to fail, ultimately resulting in their death. Currently, the only treatment for failing Fontan circulation is a heart transplant; however, many Fontan patients do not survive long enough to receive a donor heart. One of the reasons for this is a lack of understanding of the Fontan failure cascade. Often patients are identified as failing when they do not have enough time left to receive a heart transplant. The objective of this problem is to develop mathematical models of healthy and failing Fontan circulations to i) improve our understanding of Fontan failure from a hemodynamic perspective, and ii) identify physiologically-relevant ranges of parameters.

In silico and in vitro conductivity models of the left heart ventricle

Ventricular Assist Devices (VADs) are used to treat patients with cardiogenic shock. As the heart is unable to supply the organs with sufficient oxygenated blood and nutrients, a VAD maintains the circulation to keep the patient alive. The observation of the patient's hemodynamics is crucial for an individual treatment; therefore, sensors to measure quantifiable hemodynmaic parameters are desirable.In addition to pressure measurement, the volume of the left ventricle and the progress of muscle recovery seem to be promising parameters. Ongoing research aims to estimate ventricular volume and changes in electrical properties of cardiac muscle tissue by applying bioimpedance measurement. In the case where ventricular insufficiency is treated by a catheter-based VAD, this very catheter could be used to conduct bioimpedance measurement inside the assisted heart. However, the simultaneous measurement of bioimpedance and VAD support has not yet been realized, although this would allow the determination of various loading conditions of the ventricle. For this purpose, it is necessary to develop models to validate and quantify bioimpedance measurement during VAD support.In this study, we present an in silico and an in vitro conductivity model of a left ventricle to study the application of bioimpedance measurement in the context of VAD therapy. The in vitro model is developed from casting two anatomical silicone phantoms: One phantom of pure silicone, and one phantom enriched with carbon, to obtain a conductive behavior close to the properties of heart muscle tissue. Additionally, a measurement device to record the impedance inside the ventricle is presented. Equivalent to the in vitro model, the in silico model was designed. This finite element model offers changes in material properties for myocardium and the blood cavity.The measurements in the in vitro models show a strong correlation with the results of the simulation of the in silico model. The measurements and the simulation demonstrate a decrease in impedance, when conductive muscle properties are applied and higher impedances correspond to smaller ventricle cross sections.The in silico and in vitro models are used to further investigate the application of bioimpedance measurement inside the left heart ventricle during VAD support. We are confident that the models presented will allow for future evaluation of hemodynamic monitoring during VAD therapy at an early stage of research and development.