Parameter selection and optimization of a computational network model of blood flow in single-ventricle patients

Figure 1.. Comparison of healthy (a) and single-ventricle (b) hearts and vessels. The homographic patch augmentation generated on HLHS patients’ ascending aorta is highlighted in grey in panel (b). DORV patients have a Fontan circulation but do not need aortic reconstruction. The white arrows indicate the direction of blood flow.

Figure 2.. Workflow of the methods implemented in this study. We begin with patient data acquisition, consisting of biometrics, 4D-MRIs and MRAs. We then perform image analysis to obtain patient geometries. We set nominal parameter values for each patient and perform a sensitivity analysis. Once we have determined influential parameters, we use covariance analysis to choose a subset of identifiable parameters estimated using multistart parameter inference. Estimated parameters are used for forward model simulations for each patient.

Figure 3.. Segmentations and centrelines for each patient are shown in their respective pairs.

Figure 4.. Before and after registering the MRA to the 4D-MRI. Panel (a) shows velocities from the 4D-MRI in the unaligned (purple circles) versus the aligned (orange circles) network. Panel (b) shows aligned (orange) MRA segmentation transposed on the unaligned segmentation (pink). The velocities in (a) correspond to the slice through the segmentations in (b). Blue lines denote where flow data were obtained from each patient. The dashed blue line shows where the inflow profile was obtained.

Figure 5.. Network used in the fluids model. (a) Arteries extracted from the MRA images (dark red) and extended vessels outside of the imaged region (cyan). Small vessel networks (black), represented by structured trees are attached to the end of each large terminal vessel. (b) Example structured tree including vessels down to the arteriolar level. Vessel numbers correspond to those given in table 2. The vessel number colours indicate the parameter group used for parameter inference described in §2.4. Red vessel numbers represent group 1, purple group 2, green group 3 and blue group 4.

Figure 6.. Aortic radii for a DORV and an HLHS patient pair. In the HLHS patient, the aortic radius increases along the ascending aorta and then decreases, while in the DORV patient, the aortic radius decreases along its length. Note that the two vessels have similar radii at the distal end. Error bars (one s.d. of radii measurements) are plotted at the inlet of the ascending aorta, aortic arch I, aortic arch II and descending aorta.

Figure 7.. Sensitivity analysis and multistart inference. (a) Local sensitivities, (b) Morris screening and (c) multistart inference on the final identifiable parameter subset. Panels (a) and (b) are boxplots of the relative sensitivities for each patient group. Sensitivities are ranked from most to least influential. Panel (c) shows convergence of the final identifiable parameter subset. For each parameter, CV <0.1 . Note that parameters are scaled from 0 to 1 for easier comparison.

Figure 8.. Model predictions versus patient data. From left to right, the first four panels in each row depict flow waveforms. The five grey lines denote the dynamics for each patient and the averaged dynamics are plotted with a black line. The black error bars represent one standard deviation of the averaged waveform. Model predictions are shown in red. The far-right panel in each row show the systolic (dashed red) and diastolic (dashed blue) cuff pressure measurements. Model predictions are depicted using solid black lines. Shading in the background of each panel denotes the results of simulations sampling the optimized parameters from a uniform distribution. R2 values reporting the quality of model predictions are given in the top right of each panel.

Figure 9.. Box and Whisker comparison of inferred parameter values. Light grey boxes represent the DORV patients, while dark grey represents the HLHS group. Parameters are scaled from 0 to 1 for easier comparison.

Figure 10.. Model predictions. (a) The average systolic and pulse pressure in the aorta and cerebral vessels. Pairwise comparison of the average pulse flow in the aorta (b) and cerebral (c) vessels. Pulse flows are shown relative to total cardiac output. (d) Area deformation over a cardiac cycle, HLHS patients are shown in red and DORV in blue.

Figure 11.. Reflected backward compression waves (BCW) and backward expansion waves (BEW). Incident forward compression waves (FCW) and forward expansion waves (FEW) in the ascending aorta and left/right carotid artery for each patient. The patterns in the other aortic and peripheral vessel segments are similar to the vessels shown here. Each panel also lists the patient's wave-reflection coefficient, IR .

Figure 12.. Wall shear stress in the four aortic vessels for each patient. Shades of blue represent DORV patients, and shades of red represent HLHS patients. The average ± 1 s.d. peak WSS for the DORV and HLHS groups is noted on the graphs. DORV patients' WSS decreases slightly away from the heart, while HLHS patients' WSS increases. For all patients, the WSS is significantly higher in the descending artery. HLHS patient 2 has considerably higher descending aorta WSS than the other patients.