Understanding heterogeneous mechanisms of heart failure with preserved ejection fraction through cardiorenal mathematical modeling

Fig 1. Schematic of the integrated cardiorenal model. Model links cardiac mechanics (A) and ventricle remodeling (B), a lumped parameter description of cardiovascular circulation (C), whole body Na+ and fluid homeostasis (E), renal hemodynamics (D), renal filtration and reabsorption (F), and neurohormonal and intrinsic feedbacks including the renin-angiotensin-aldosterone system (RAAS) (G). Adapted from Yu et al. (2020) [42].

Fig 2. Slowed relaxation modeled as an elongation of the falling arm of the contraction signal.

Fig 3. Sobol sensitivity of (A) LVEDP and (B) LV EF to changes in each potential HFpEF mechanism (Error bars: 95% confidence interval).

Fig 4. Effect of changing LV stiffness, LV contractility, hypertension, arterial compliance, and outward dilatation, alone and in combination LV EDP and EF. A) LVEDP, B) EF. C) HF state produced by each region of the parameter space: HFpEF (EF>50% and LVEDP > 20mmHg), HF-mEF (40%<EF<50% and LVEDP > 20mmHg), HFrEF (EF<40% and LVEDP > 20mmHg), and non-HF (LVEDP < 20 mmHg).

Fig 5. Effect of changing LV stiffness, LV contractility, hypertension, and arterial compliance, alone and in combination, on A) interstitial fluid volume (IFV) and B) cardiac output (CO). For these simulations, outward dilatation was zero.

Fig 6. Effect of HFpEF mechanisms on changes in LV end diastolic stress (A) vs. strain (B). Reduced contractility, increased outward dilatation, and reduced arterial compliance caused both stress and strain to increase. However, increased LV stiffness caused them to change in opposite directions–stress increased while strain decreased.

Fig 7. Effect of increased LV stiffness or reduced contractility (representative of HFpEF and HFrEF, respectively) over time under two different models of remodeling–strain-driven and stress-driven. With both models, reduced contractility caused EF to decline into the HFrEF range. However, only the strain-driven model allowed EF to remain in the normal range over time with increased LV stiffness. Gray dashed lines are threshold levels of stress/strain above which outward remodeling occurs.

Fig 8. Effects of collage stiffness, myocyte stiffness, collagen volume fraction, and LV contractility on LV mechanical state.

Fig 9. The deleterious consequences of arterial stiffening and/or hypertension in a stiffened myocardium. A) LV stiffness shifts the diastolic pressure curve upward; decreased arterial compliance shifts the end systolic pressure upward, thus increasing end systolic elastance (Ees); hypertension increases both end systolic and peak systolic pressure; Reduced arterial compliance alone increases arterial pulse pressure (B), but has minimal effect on stressed blood volume (C), MAP (D), mean capillary pressure (E), or mean venous pressure (F). However, it has a strong exacerbating effect on stressed blood volume and capillary and venous pressures when combined with a stiff myocardium. Hypertension has a similar exacerbating effect.