Fig 1.
Leftmost side: Schematic of the experiment setup.
LA: left atrium, MV: Mitral valve, AV: Aortic valve, Ao: aorta. Flow and pressure sensors are indicated in blue and red respectively. The body lumped system is afterwards characterised with a three element Windkessel model with parameters Rp, Rs and Cp. Center: variables extracted from the benchtop experiment to create the simulation and address the uncertainty quantification (UQ). Rightmost side: Schematic of the simulation, including the lumped models for the boundary conditions. The measured PLA is imposed in the mitral valve. The measured Rp, Rs and Cp are used in a three element Windkessel boundary condition at the Aortic valve output. The H-Q curve retrieved and measured is used as a dynamic boundary condition in the LVAD outflow. The benchtop piston dynamics is used as boundary condition for the deformable LV geometry.
Table 1.
Fitting coefficients (aVAD, bVAD, and cVAD) and fitting errors ϵ of the H-Q performance curves.
The pump speed is measured in [rpm]. The units are aVAD[Pa], bVAD[Pa ⋅ s/m3], and cVAD[Pa ⋅ s2/m6].
Fig 2.
Scheme of DARE building blocks.
Table 2.
Adapted from [46].
Table 3.
ASME V&V40 credibility factors [11] analysed on the risk-based assessment.
The table shows the maximum possible score (“Max.” column), the desired goal (“Goal” column) and the obtained score (“Obt.” column). The goal column also includes the description of the activity to achieve that gradation.
Table 4.
Table of model inputs and their uncertainty characterisation.
Fig 3.
Scatter plots and total Sobol indices tornado plots for the 8 input variables and the 6 QoIs.
The scatter plot also shows the Pearson’s linear correlation number ρ in the top left corner. Units are intentionally avoided in the Y-axis of the total Sobol indices tornado plot to ease its legibility.
Table 5.
The six validation points used for the UQ analysis.
Table 6.
Range of H-Q curve coefficients used for the UQ analysis.
The range is obtained as 2ϵnum + ϵfit where ϵfit is 10% of the measured value.
Fig 4.
Qualitative surface results for the condition 22[%]@68.42[bpm].
Pump speed is 0k[rpm], 8k[rpm], and 11k[rpm] in the first, second, and third rows respectively. The columns indicate different time frames in the simulation. t = 0.42[s] show results for the plateau previous to systole, t = 0.58[s] show the atrial kick, t = 0.77[s] show systole, and t = 1.03[s] shows diastole. Videos of the simulations can be found in the S1 Video.
Fig 5.
Summary for the condition 22[%]@68.42[bpm] and 0k[rpm].
(a): aortic valve and LVAD flows. (b): validation metrics. (c): scatter plot showing the experimental and simulation data. (d): ECDF for the simulation, experimental data limits and the constructed uniform distribution.
Fig 6.
Summary for the condition 22[%]@68.42[bpm] and 8k[rpm].
(a): aortic valve and LVAD flows. (b): validation metrics. (c): scatter plot showing the simulation and experimental data. (d): ECDF for the simulation, experimental data limits and the constructed uniform distribution.
Fig 7.
Summary for the condition 22[%]@68.42[bpm] and 11k[rpm].
(a): aortic valve and LVAD flows. (b): validation metrics. (c): scatter plot showing the simulation and experimental data. (d): ECDF for the simulation, experimental data limits and the constructed uniform distribution.
Fig 8.
Qualitative surface results for the condition 17[%]@61.18[bpm].
Pump speed is 0k[rpm], 8k[rpm], and 11k[rpm] in the first, second, and third rows respectively. The columns indicate different time frames in the simulation. t = 0.42[s] show results for the plateau previous to systole, t = 0.64[s] show the atrial kick, t = 0.85[s] show systole, and t = 1.16[s] shows the diastolic filling. Videos of the simulations can be found in the S1 Video.
Fig 9.
Summary for the condition 17[%]@61.18[bpm] and 0k[rpm].
(a): aortic valve and LVAD flows. (b): validation metrics. (c): scatter plot showing the simulation and experimental data. (d): ECDF for the simulation, experimental data limits and the constructed uniform distributions.
Fig 10.
Summary for the condition 17[%]@61.18[bpm] and 8k[rpm].
(a): aortic valve and LVAD flows. (b): validation metrics. (c): scatter plot showing the simulation and experimental data. (d): ECDF for the simulation, experimental data limits and the constructed uniform distribution.
Fig 11.
Summary for the condition 17[%]@61.18[bpm] and 11k[rpm].
(a): aortic valve and LVAD flows. (b): validation metrics. (c): scatter plot showing the simulation aned experimental data. (d): ECDF for the simulation, experimental data limits and the constructed uniform distributions.
Fig 12.
Aortic valve flow and total flow
as a function of the HR and EF.
Data is shown for both, 8k[rpm] and 11k[rpm]. The grey hatched region represents the minimum limit for both and
.