A flexible framework for sequential estimation of model parameters in computational hemodynamics

Advanced Modeling and Simulation in Engineering Sciences

Table 1 Final estimated Windkessel parameters

Outlet	1	2	3	4	5	6	7	8	9
C (\(\hbox {mm}^3\)/Pa)
True values	0.783	0.409	0.324	0.464	0.464	0.660	0.761	0.293	0.296
A (no P)	0.844	0.432	0.358	0.500	0.480	0.693	0.775	0.302	0.308
% error	7.83%	5.64%	10.31%	7.78%	3.38%	4.96%	1.84%	2.98%	4.16%
B (1 P)	0.843	0.431	0.354	0.498	0.475	0.690	0.765	0.302	0.308
% error	7.73%	5.38%	9.26%	7.23%	2.44%	4.54%	0.50%	2.91%	4.13%
C (all P)	0.829	0.425	0.340	0.480	0.463	0.679	0.739	0.302	0.308
% error	5.88%	3.76%	4.73%	3.40%	− 0.12%	2.97%	− 2.87%	2.85%	4.02%
\(R_2\) (Pa s/\(\hbox {mm}^3\))
True values	0.629	1.202	1.517	1.060	1.061	0.746	0.647	1.679	1.664
A (no P)	0.598	1.157	1.444	1.018	1.034	0.714	0.629	1.652	1.627
% error	− textbf4.93%	− 3.76%	− 4.83%	− 3.94%	− 2.55%	− 4.29%	− 2.78%	− 1.57%	− 2.22%
B (1 P)	0.615	1.194	1.507	1.055	1.073	0.736	0.650	1.706	1.680
% error	− 2.17%	− 0.65%	− 0.70%	− 0.47%	1.18%	− 1.34%	0.47%	1.61%	0.97%
C (all P)	0.625	1.219	1.539	1.079	1.096	0.748	0.659	1.733	1.708
% error	− 0.59%	1.38%	1.46%	1.77%	3.31%	0.29%	1.83%	3.27%	2.67%
\(R_1\) (Pa s/\(\hbox {mm}^3\))
True values	0.137	0.137	0.269	0.279	0.279	0.147	0.246	0.107	0.122
A (no P)	0.137	0.144	0.306	0.290	0.288	0.147	0.253	0.114	0.128
% error	0.32%	5.21%	14.05%	3.89%	3.28%	0.05%	2.62%	6.25%	4.71%
B (1 P)	0.137	0.144	0.306	0.290	0.288	0.148	0.252	0.114	0.127
% error	0.04%	4.67%	14.00%	3.83%	3.28%	0.40%	2.43%	5.90%	4.42%
C (all P)	0.135	0.141	0.302	0.287	0.286	0.148	0.248	0.111	0.125
% error	− 1.27%	2.77%	12.31%	2.59%	2.56%	0.68%	0.83%	3.69%	2.56%

Case A has no pressure data, Case B has pressure data only in the left carotid artery, and Case C has pressure data at all nine outlets of the model (c.f. Fig. 8). See Fig. 9 for the parameter evolution in each case. Errors less than 5% in absolute value are highlighted in bold; those less than 2.5% are shown in italic