Cardiac and renal function interactions in heart failure with reduced ejection fraction: A mathematical modeling analysis

Hongtao Yu, Sanchita Basu, K. Melissa Hallow


Congestive heart failure is characterized by suppressed cardiac output and arterial filling pressure, leading to renal retention of salt and water, contributing to further volume overload. Mathematical modeling provides a means to investigate the integrated function and dysfunction of heart and kidney in heart failure. This study updates our previously reported integrated model of cardiac and renal functions to account for the fluid exchange between the blood and interstitium across the capillary membrane, allowing the simulation of edema. A state of heart failure with reduced ejection fraction (HF-rEF) was then produced by altering cardiac parameters reflecting cardiac injury and cardiovascular disease, including heart contractility, myocyte hypertrophy, arterial stiffness, and systemic resistance. After matching baseline characteristics of the SOLVD clinical study, parameters governing rates of cardiac remodeling were calibrated to describe the progression of cardiac hemodynamic variables observed over one year in the placebo arm of the SOLVD clinical study. The model was then validated by reproducing improvements in cardiac function in the enalapril arm of SOLVD.


Chronic heart failure (HF) is a condition in which the heart is incapable of preserving a sufficient cardiac output (CO) to reach the metabolic requirements of peripheral organs [1]. HF with reduced ejection fraction (HF-rEF) is characterized by a left ventricle ejection fraction (LVEF) less than 40%, suppressed CO, elevated cardiac filling pressure, and progressive eccentric remodeling of the heart. HF-rEF is often a consequence of ischemic damage to the cardiac muscle, although HF-rEF may also result from valvular disease, hypertension, or idiopathic causes [2–6]. Inadequate organ perfusion due to depressed CO activates neurohormonal mechanisms, such as the renin-angiotensin-aldosterone-system (RAAS). However, excessive volume retention increases both preload and afterload on the heart, causing detrimental cardiac remodeling. Excessive preload also leads to elevated venous pressure and the development of peripheral edema and pulmonary congestion [7,8]. These factors contribute to the progressive worsening of HF over time, usually with repeated and costly hospitalizations [9].


In this study, an integrated model of cardiorenal function was updated and utilized to simulate states of HF-rEF. After matching an HF-rEF virtual patient to the baseline hemodynamic characteristics in the SOLVD clinical trial [42], the model was able to describe the rightward progression of the P-V loop in the placebo arm, as well as the leftward shift in the enalapril arm, providing validation that the model adequately describes the progression of cardiac remodeling in response to hemodynamic overload in HF, as well as improvements with renally acting therapies. The model was then applied to investigate cardiac hemodynamic and systemic volume responses that may explain clinical observed improvements in HF outcomes with SGLT2i. The model predicts that SGLT2i reduces LVEDP in both diabetic and non-diabetic HF-rEF (although reductions are larger in diabetics), and that this preload reduction slows cardiac remodeling and progression over one year. It further predicts that SGLT2i will reduce interstitial congestion without inducing large reductions in blood volume.

Citation: Yu H, Basu S, Hallow KM (2020) Cardiac and renal function interactions in heart failure with reduced ejection fraction: A mathematical modeling analysis. PLoS Comput Biol 16(8): e1008074.

Editor: Daniel A. Beard, University of Michigan, UNITED STATES

Received: March 20, 2020; Accepted: June 18, 2020; Published: August 17, 2020

Copyright: © 2020 Yu et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Data Availability: All relevant data are within the manuscript and its Supporting Information files.

Funding: This research was funded by AstraZeneca. In this work, the funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

Competing interests: No authors have competing interests.

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