Fig 1.
Finite element convergence models.
(A) Epicardial rendering of model with 9 epicardial nodes for applied force application in no load state. (B) Epicardial rendering of refined model with 17 epicardial nodes for applied force application in no load state. (C) Cross-sectional rendering of the finite elements for the 17-node model showing key nodes of the axisymmetric model at which ventricular wall strains and stresses are calculated. The top two nodes are the epicardial (B1a) and endocardial (B1b) nodes at the ventricular base. The center nodes are in the middle of the compression region and are designated C1a (epicardium) and C1b (endocardium. The lowest nodes are at the apical end of the compression zone and are designated C2a (epicardium) and C2b (endocardium).
Table 1.
Lumped parameter circulatory values.
These values are from the baseline HF model at ED of a steady state cardiac cycle and are the initial conditions for. all compression simulations.
Fig 2.
Left ventricular heart failure model.
(A) Applied force at all force application nodes as a function of time employed to compress LV throughout the simulation cardiac cycle of 750ms. Applied forces are zero throughout isovolumic contraction. Force application commences at 154 ms, peaks at 254 ms, and decreases until it returns to zero at 354 ms and remains there for the remainder of the cardiac cycle during filling. The maximum applied force is scaled by the peak value of the sinusoid so that only at 254 ms will the maximum force be applied. Time tracings of (B) left ventricular volume and (C) left ventricular pressure showing rapid equilibration of the simulation. (D)The pressure-volume loop for the baseline heart failure model after equilibration (last cardiac cycle shown in (B) and (C)).
Fig 3.
Convergence test for longitudinal refinement.
(A) Epicardial maximum principal stress plotted at peak compression for both models at applied force nodes. (B) Endocardial maximum principal stress plotted at peak compression for both models at applied force nodes. Note close correspondence of epicardial stresses with small underestimation of stresses using the 9-node model. Also, note very close match of larger endocardial stresses with small overestimation of values by the 9-node model toward the apical part of the compression zone.
Fig 4.
Nominal compression global hemodynamics.
(A) Epicardial and endocardial surface renderings of baseline HF and the nominal compression simulation near end-ejection when peak compression of cVAD model occurs. (B) Pressure-Volume loops for the converged solutions of the baseline heart failure and nominal compression simulations. Note the large increase in the size of the P-V loop with compression and its complete separation from the baseline HF loop.
Fig 5.
Hemodynamic variations as applied forces change magnitudes.
(A) Changes in ejection fraction and peak pressure as functions of applied forces. (B) Changes in end-diastolic and end-systolic volume as functions of applied forces. Note: Value of 1.0 on the abscissas indicates nominal forces at peak compression.
Table 2.
These values are from the baseline HF case, the nominal compression, and the parametric variation of the applied forces. Headings reflect fraction of nominal compression forces used in each compression simulation; note: these correspond with the plots shown in Fig 5 and the strain and stress values shown in Table 3.
Fig 6.
Analysis of myocardial thickening.
Thickening percentage throughout the cardiac cycle for baseline HF (no compression) and compression simulations in the middle of the compression zone (A) and the corresponding hoop stress (B). Corresponding thickening at the apex (C) and the base of the heart (D). This is the percentage change in the entire myocardial wall thickness compared with the end diastolic wall thickness.
Fig 7.
Principal strain rendering and time plots of principal and key contributing strain components in fiber coordinates.
(Top) Maximum and minimum principal strain renderings on the epicardial and endocardial surfaces at nominal peak compression. (A and B) Time series of maximum endocardial and epicardial principal strain and main contributing strain components. (C and D) Time series of minimum endocardial and epicardial principal strain and main contributing strain components. Note: All time renderings come from the middle of the compression. P3 is the maximum principal strain. P1 is the minimum principal strain. Fiber coordinates 1, 2 and 3 correspond to fiber, cross-fiber and transmural directions, respectively, i.e., E11, E22 and E33 are the normal stresses.
Table 3.
Tabluation of maximum and minimum principal stress and strain in parametric analysis.
Comparison of regional wall mechanics between the baseline heart failure case, the nominal compression case and the parametric variation of applied forces corresponding with Table 2 and Fig 5. The maxmimum and minimal principal stresses and strains at the nodes indicated in Fig 1C are shown. B1a and B1b are the epicardial and endocardial nodes at the ventricular base; C1a and C1b are epicardial and endocardial nodes near the center of the compression zone; C2a and C2b are epicardial and endocardial nodes at the apical end of the compression zone.
Fig 8.
Principal stress rendering and time plots of principal and key contributing stress components in fiber coordinates.
(Top) Maximum and minimum principal stress renderings on the epicardial and endocardial surfaces at peak compression. (A and B) Time series of maximum endocardial and epicardial principal stress and main contributing stress components. (C and D) Time series of minimum endocardial and epicardial principal stress and main contributing stress components. Note: All time renderings come from the middle of the compression. P3 is the maximum principal stress. P1 is the minimum principal stress. Fiber coordinates 1, 2 and 3 correspond to fiber, cross-fiber and transmural directions, respectively, i.e., T11, T22 and T33 are the normal stresses.