Assessment of wall stresses and mechanical heart power in the left ventricle: Finite element modeling versus Laplace analysis

Figures

• 

  Figure 1. (A) Geometric setup, (B) sperical coordinate system and (C) displacement boundary conditions

• 

  Figure 2. Image‐based patient‐specific left ventricle (LV) anatomy models. (A) Shown are the finite element model setup with Dirichlet (solid triangles) and Neumann boundary conditions controlled by a three‐element Windkessel model of afterload, and fiber architecture (bottom panel). (B) Patient‐specific anatomical models LV A, LV B, LV C, and LV D of LV and aorta constructed from a 3DWH MRI scan in end‐diastolic configuration

• 

  Figure 3. Fitting of the afterload model. Measured input data comprise V cav(t) (top panel), derived flow q LV = d V cav/d t (mid panel), p^LV and pressure drop Δp=p^LV−p^ao along with simulated pressure traces p LV and p ao (bottom panel), with annotations of onset of ejection, t 0,ej, instant of peak pressure in the left ventricle (LV), tp^, cardiac contraction time, T sct, and the instant of peak flow, tq^

• 

  Figure 4. Determination of input parameters radius r¯ and wall width h¯ for Laplace analysis. (A) Automated left ventricle slicing along long‐axis z. (B) Sampling of variations in r, R, and h within a slice, z i. (C) Averaged parameters r¯ and h¯ as a function of p

• 

  Figure 5. (A) EDPVRs for isotropic spherical shell models of varying wall thickness h. (B) Comparison of FE‐based mean circumferential and radial stresses, σ‾circ and σ‾rr, with Laplace‐based estimations σ L,h and σ L,H

• 

  Figure 6. (A) Loading protocol. (B) Stresses, power and work for anisotropic model. Data are shown for model LV D

• 

  Figure 7. Fitting of EM LV models (red traces) using Cine‐MRI‐based volume data (blue traces) and estimated LV peak pressures, p^LV, as input. Top panels show LV anatomy in end‐diastolic (transparent blue) and end‐systolic (solid blue) configuration

• 

  Figure 8. Comparison of FE‐based computation of stresses ( σ‾ϕϕ, σ‾θθ, σ‾circ and σ‾rr) and power P int with Laplace‐based estimates of stress, σ L,h, σ L,H and σ L,V, and power P int,h, P int,H and P int,V. Top panels show the time course of pressure p in the LV endocardium. The solid black vertical line indicates the instant, tp^, when peak pressure in the LV, p^LV, occurs

• 

  Figure 9. Statistical analysis of the circumferential stress σ circ at the instant of peak pressure. The top row shows σ circ averaged over the corresponding LV segment and the bottom row shows the variation of σ circ in each LV segment