Modeling the cardiac response to hemodynamic changes associated with COVID-19: a computational study

Appraisal of partial anomalous pulmonary venous drainage through a lumped-parameter mathematical model: a new pathophysiological proof of concept

OBJECTIVES

Haemodynamic determinants of the ratio between pulmonary and systemic flow (Qp/Qs) in partial anomalous pulmonary venous return (PAPVR) are still not fully understood. Indeed, among patients with the same number of lung segments draining anomalously, a great variability is observed in terms of right ventricular overload. The aim of this study was to test the hypothesis that the anatomic site of drainage, affecting the total circuit impedance, independently influences the magnitude of shunt estimated by Qp/Qs. A zero-dimensional lumped parameter mathematical model was developed and validated on a sample of patients.

METHODS

We developed a zero-dimensional lumped parameter model, using time-varying elastances for heart chambers, RLC Windkessel circuits for the systemic and pulmonary circulations. Patients were categorized into vena cava (VC) type (including left drainage to anomalous vein) and right atrium (RA) type. The mathematical model is a system of ordinary differential equations that are numerically solved by means of the ode15s solver in the MATLAB environment.

RESULTS

The model showed an increase of Qp/Qs with the increase of the number of anomalous veins. With the same number of anomalous veins, Qp/Qs was lower in patients with anomalous drainage to the VC as compared with RA. The validation sample consisted of 49 patients (27, 55% females). As predicted by the model, patients with PAPVR with VC type displayed a lower invasive and cardiac magnetic resonance Qp/Qs as compared with drainage to RA: 1.4 (1.2-1.7) and 1.45 (1.25-1.6) versus 2 (1.75-2.1) and 1.9 (1.6-2), P < 0.05. After stratifying for number of lung territories, a lower Qp/Qs was measured in patients with VC PAPVR as compared with RA.

CONCLUSIONS

In patients with PAPVR, the site of anomalous drainage modulates the Qp/Qs. According to the model, this effect is mediated by the post-capillary impedance of the circuit and significantly decreases with the increase of pulmonary vascular resistances.

A mathematical model to assess the effects of COVID-19 on the cardiocirculatory system

Impaired cardiac function has been described as a frequent complication of COVID-19-related pneumonia. To investigate possible underlying mechanisms, we represented the cardiovascular system by means of a lumped-parameter 0D mathematical model. The model was calibrated using clinical data, recorded in 58 patients hospitalized for COVID-19-related pneumonia, to make it patient-specific and to compute model outputs of clinical interest related to the cardiocirculatory system. We assessed, for each patient with a successful calibration, the statistical reliability of model outputs estimating the uncertainty intervals. Then, we performed a statistical analysis to compare healthy ranges and mean values (over patients) of reliable model outputs to determine which were significantly altered in COVID-19-related pneumonia. Our results showed significant increases in right ventricular systolic pressure, diastolic and mean pulmonary arterial pressure, and capillary wedge pressure. Instead, physical quantities related to the systemic circulation were not significantly altered. Remarkably, statistical analyses made on raw clinical data, without the support of a mathematical model, were unable to detect the effects of COVID-19-related pneumonia in pulmonary circulation, thus suggesting that the use of a calibrated 0D mathematical model to describe the cardiocirculatory system is an effective tool to investigate the impairments of the cardiocirculatory system associated with COVID-19.

lifex-fiber: an open tool for myofibers generation in cardiac computational models

BACKGROUND

Modeling the whole cardiac function involves the solution of several complex multi-physics and multi-scale models that are highly computationally demanding, which call for simpler yet accurate, high-performance computational tools. Despite the efforts made by several research groups, no software for whole-heart fully-coupled cardiac simulations in the scientific community has reached full maturity yet.

RESULTS

In this work we present [Formula: see text]-fiber, an innovative tool for the generation of myocardial fibers based on Laplace-Dirichlet Rule-Based Methods, which are the essential building blocks for modeling the electrophysiological, mechanical and electromechanical cardiac function, from single-chamber to whole-heart simulations. [Formula: see text]-fiber is the first publicly released module for cardiac simulations based on [Formula: see text], an open-source, high-performance Finite Element solver for multi-physics, multi-scale and multi-domain problems developed in the framework of the iHEART project, which aims at making in silico experiments easily reproducible and accessible to a wide community of users, including those with a background in medicine or bio-engineering.

CONCLUSIONS

The tool presented in this document is intended to provide the scientific community with a computational tool that incorporates general state of the art models and solvers for simulating the cardiac function within a high-performance framework that exposes a user- and developer-friendly interface. This report comes with an extensive technical and mathematical documentation to welcome new users to the core structure of [Formula: see text]-fiber and to provide them with a possible approach to include the generated cardiac fibers into more sophisticated computational pipelines. In the near future, more modules will be successively published either as pre-compiled binaries for x86-64 Linux systems or as open source software.