Quantitative Assessment of Proximal and Distal Vascular Properties Using iCMR and Windkessel Model in Congenital Heart Disease

Background: In patients with congenital heart disease understanding mechanical properties of the circulatory system can be of prognostic significance. This work employs the Windkessel (WK) model to quantitatively compare proximal and distal mechanical properties of the systemic circulation in patients with single-ventricle (SV) circulation, and both systemic and pulmonary circulations in repaired tetralogy of Fallot left and right ventricles (rTOF-LV/-RV).

Methods: This study included 30 patients with SV circulation undergoing assessment via interventional cardiac magnetic resonance (iCMR) and 19 patients rTOF undergoing percutaneous pulmonary valve replacement, with CMR data collected sequentially with fluid-filled catheterization pre-PVR. The rTOF group provided 16 LV and 19 RV datasets. Median (IQR) BSA was 1.08 (0.73) and 1.29 (0.59) m^2, and age was 8.4 (6.5) and 11(6.5) years in SV and rTOF groups, respectively. In the SV group 22 patients had hypoplastic left heart syndrome (HLHS).

All phase contrast flow data were acquired over 40 cardiac phases, TE/TR=2.7/4.4 ms, with two signal averages during free breathing, 2x2x8 mm resolution, SENSE factor 2, velocity encoding gradient at 25% above the maximum expected velocity in aorta and pulmonary arteries.

Patient-specific two-stage WK models1 (Figure 1) were constructed for 46 systemic and 19 pulmonary circulations (Figure 2). Measured forward arterial phase contrast flow was imposed to adjust distal resistance (R_d) and capacitance (C_d) to fit arterial diastolic pressure decay, and proximal resistance (R_p) was adjusted so that simulated peak pressure matched the measured peak². Venous pressure (P_vs) was imposed from measured data2. Proximal capacitance (C_p) was prescribed a nominal value and held constant throughout the simulations. The diastolic arterial pressure decay constant (τ) was calculated as R_d * C_d.

Results: As expected, systemic R_p, R_d, and τ were significantly higher in both SV and rTOF-LV groups compared to the pulmonary circulation in the rTOF-RV group (Table 1). No significant differences in C_d were observed between the groups. No differences were noted amongst SV patients regardless of prior aortic arch reconstruction. These findings suggest that SV and rTOF-LV groups exhibit quantitively similar mechanical properties of the systemic circulation. These preliminary findings taken modeled with CMR flow and invasive pressure are contrary to numerous purely non-invasive reports suggesting increased proximal stiffness and total distal resistance in patients with SV circulation. The framework allows larger scale studies to separate the contributions from central arterial stiffening and distal vascular health in these patients.

Conclusion: Windkessel modeling enables patient-specific quantification of vascular mechanics and, when applied to larger cohorts, may reveal adaptations to various hemodynamic conditions.

Table 1. Windkessel model-derived parameters of circulatory systems in single-ventricle systemic circulation, repaired tetralogy of Fallot left ventricle (rTOF-LV) systemic circulation, and rTOF right ventricle (rTOF-RV) pulmonary circulations. Single-venricle group was divided into hypoplastic left heart syndrome (HLHS) subgroup 1a, and all non-HLHS subgroup 1b. Data are presented as median (interquartile range). * is significant difference between single-ventricle (all patients) and rTOF-LV; ** is significant difference between single-ventricle (all patients) and rTOF-RV; *** significant difference between rTOF-LV and rTOF-RV; all significance were of Kruskal-Wallis test at p<0.05.

	N	Rp	Rd	Cd	τ
		Pa*s*m-3	Pa*s*m-3	m-3/Pa	s
1. Single-vent. (all)	30	1.85 (0.87) x1e7 **	1.14 (0.66) x1e8 **	1.30 (1.83) x1e-8	1.60 (1.30) **
1a. HPLH	22	1.83 (0.59) x1e7	1.14 (0.62) x1e8	1.30 (1.28) x1e-8	1.66 (0.94)
1b. non-HPLH	8	2.00 (1.65) x1e7	1.12 (1.00) x1e8	1.28 (3.10) x1e-8	1.62 (2.13)
2. rTOF-LV	16	1.13 (0.74) x1e7 ***	1.20 (0.50) x1e8 ***	1.50 (1.03) x1e-8	1.80 (0.55) ***
3. rTOF-RV	19	3.00 (4.00) x1e6	1.30 (1.05) x1e7	3.00 (2.50) x1e-8	0.32 (0.44)

Figure 1. Two-stage Windkessel model of circulation system. Q is an imposed phase contrast forward arterial flow. Par, 𝑃𝑑 and 𝑃𝑣𝑠 are pressures artery, distal circulation, and venous system, respectively. Rp and Cp are resistance and capacitance of the proximal circulation, respectively. Rd and Cd are resistance and capacitance of the distal circulation, respectively.
Figure 2. Example of calibrated Windkessel model for a single-ventricle patient, repaired tetralogy of Fallot left ventricle (rTOF-LV), and rTOF right ventricle (RV). Left column demonstrates the phase contrast arterial flow waveforms that were imposed to calibrate corresponding arterial pressure Windkessel (WK) models.