Hypoplastic left heart syndrome (HLHS) is a rare congenital heart defect in which the left ventricle of the heart is severely underdeveloped. It requires intervention within the first few days after birth.1 The Norwood procedure is a first-stage palliation used both to provide unobstructed blood flow to the systemic circulation (Qs) and to maintain a stable source of pulmonary blood flow (Qp) while achieving an acceptable balance (Qp/Qs) using the single functional ventricle. The aorta is reconstructed using the pulmonary artery (PA) root and the autogenous aorta, creating the supply to the systemic circulation.2 The pulmonary circulation is typically established by using a shunt to redirect some portion of the systemic flow to the PAs. Depending on the technique, the systemic shunt to the PA can branch off from various sites, such as the right ventricle, the innominate artery, or the aortic arch.3
The Norwood circulation is complex, and many factors can affect the postoperative hemodynamics.4 The heterogeneous nature of congenital defects makes the patient-specific outcome difficult to predict. The shunt, such as the modified Blalock–Taussig (mBT) shunt from the innominate artery to the PAs, is vulnerable to acute and chronic thrombosis, resulting in a sudden reduction of pulmonary vascular perfusion.4 After the procedure, the pulmonary vascular resistance of an infant will decrease rapidly during the first few months of life as the lungs develop, while the ratio of upper to lower body flow decreases.5 The reconstruction of the congenital aortic arch can lead to a range of possible morphologies from a hypoplastic tubular to a highly dilated arch. Aortic coarctation is a frequent complication after the Norwood procedure, which can influence the flow balance between systemic and pulmonary circulations.4
Biglino et al.6 provide a detailed review of modern engineering tools to study the first-stage palliation of HLHS. Pennati et al.7 provide a comprehensive review regarding the methodology of modeling systemic to pulmonary shunts in newborns with HLHS. Both reviews highlight the advantages of using multiscale models for providing local and system-level hemodynamics. Multiscale models, which couple a lumped parameter (LP) model of the circulation8–10 with a three-dimensional (3D) model of an anastomosis site, have been used previously to account for patient differences in single-ventricle physiologies.8,9,11,12 Such models should be able to demonstrate the system-level effects of different patient pathologic conditions on the surgical outcome.
An in vitro multiscale model of the Norwood circulation was described by Biglino et al.13 The system function was verified using representative clinical data for the LP model and representative 3D aortic test phantoms reconstructed from magnetic resonance imaging (MRI) data. Later, Biglino et al.14 modified the model to study the circulation of a Norwood patient with a Sano shunt. Vukicevic et al.15,16 have validated an in vitro multiscale model of the third-stage palliation or Fontan circulation to recapitulate the effects of respiration on the local and system-level hemodynamics on the caval flows. These studies13–16 each demonstrate the ability of an in vitro multiscale model to capture the major hemodynamics of the single-ventricle circulation. In this article, we build on previous work13 to describe a multiscale mock circulatory system (MCS) of the Norwood circulation and validate its ability to reproduce patient-specific clinical measurements using five different patient physiologic profiles with correspondingly accurate anatomic details. Given the heterogeneous nature of the single-ventricle patient pool and the complexities of this delicate physiology, such a system should be a useful tool to study the physiologic and morphologic differences at the local and system-levels between patients and to study changes occurring within a patient over time with a goal of improved patient management.
Materials and Methods
Patient Selection and Anatomical Models
Five patients were identified and selected from clinical information collected within our single-ventricle research network at three medical centers under appropriate institutional review board approvals (University of Michigan [UM], Great Ormond Street Hospital [GOSH], and Medical University of South Carolina [MUSC]). These five patients are designated as MUSC7, GOSH22, MUSC2, UM5, and UM10. All of the patients underwent a Norwood procedure with mBT shunt. The selected patients each presented a different aortic morphology ranging from a hypoplastic tubular arch to a strongly dilated arch. Clinical measurements included ascending aortic pressure and pulmonary wedge pressure measurements by cardiac catheterization, and mBT shunt flow and ascending aortic flow velocity measurements by either echo Doppler velocimetry or magnetic resonance. Physiologic characterization and clinical measures are given in Table 1.
For each patient, a test section or phantom was created based on segmenting MRI data. Commercial software (Mimics; Materialise NV, Leuven, Belgium) was used to prepare the virtual images for additive manufacture, as previously described.17 The aortic arch, descending aorta, major superior arteries, and shunt-brachiocephalic artery anastomosis were reproduced. The coronary arteries were not modeled. The inlet from the aortic valve root was extended to provide for a connection to an external heart pump. The phantoms were printed by stereolithography using a transparent rigid resin (Watershed XC 11122; DSM Somos, Elgin, IL). The virtual and manufactured phantoms used are shown in Figure 1.
Mock Circulatory System
The MCS coupled an LP network of the Norwood circulation with an anatomically accurate, 3D test phantom of the neoaorta and aortic arch. A detailed multicompartment LP model of the Norwood circulation was described by Hsia et al.9,10 and applied here. This detailed LP model was reduced to fewer elements in its physical realization through Thevenin impedance matching.15,16 The final LP network and circuit design used is shown in Figure 2. The model contains three major circulation branches: upper body, lower body, and pulmonary branch. Each branch compartment was composed of one resistance element, one compliance element, and the inertance of connecting tubing.13,15,18 The system was tuned initially to a particular physiologic state using generic reference values that are scaled using body surface area (BSA) for each impedance element, as previously described,11 and then the appropriate elemental values were adjusted based on available patient-specific clinical information. The MCS in Figure 2 shows the following modifications from the previous study13: each superior artery was coupled with its own compliance element, separate resistance elements were used in the upper body, and each LP setup made use of available clinical data and the test phantom specific to that patient. A photograph of the MCS is shown in Figure 3.
A ventricular-assist device (VAD; Excor, 25 ml, Berlin Heart GmbH, Berlin, Germany) was used to develop pulsatile aortic pressure and cardiac output (CO), providing the role of the single-ventricle heart. The VAD was driven pneumatically under computer control.15 A computer signal controlled alternating air pressure, as provided by proportional pressure regulators (Tecno-plus PS1201 series, Parker-Origa, Richland, MI), to the VAD to simulate the diastolic and systolic functions of the ventricle. The signal was adjusted to control the values of stroke volume, heart rate, systolic ratio, and mean aortic pressure (MAP). The single atrial pressure (SAP) was adjusted to match the mean value for a patient using a constant head tank.
Each resistance element (R) in the LP network was realized using combinations of a tube bundle, tube length, and an adjustable needle pinch valve.13,15 Resistance values were confirmed under steady flow conditions based on flow rate through and pressure drop across each relevant branch so as to include the resistance of connectors and tubing. An air chamber was used for each compliance (C) element, where the compliance is provided by the compressibility of a predetermined volume of trapped air within a rigid cylinder.15,16 To compensate for the rigidity of the aortic phantom, a proximal aortic compliance chamber was inserted between the VAD and the phantom.13 Resistances and compliance values used are given in Table 2. The resistances values are compared with clinical references in Table 2. Vascular compliance values were not measured in our patients. Instead, the compliances values applied in the MCS were taken from previous multiscale models of the Norwood circulation and scaled for the patient BSA.10,12
Measurement points for pressure (P) and flow rate (Q) are indicated in Figure 2. Pressures were measured using either catheters (MikroTip, Millar Inc., Houston, TX) for time-based measurements or wall taps connected to liquid-filled transducers (DTXplus, BD Medical Systems, Sandy, UT). Flow rates were measured with electromagnetic probes (Carolina Medical Electronics, King, NC). System operation was controlled using a data acquisition/control board (USB 6211, Labview 8.6; National Instruments, Austin, TX) at a sampling rate of 160 Hz. A saline–glycerin blood analog was used (1,060 kg/m3, 3.3 × 10–6 m2/s at 22°C).
For each patient case, compliance and resistance values were set, and then mean aortic and atrial pressures, heart rate, and systolic ratio were set to the clinical values (Table 2). The aortic proximal compliance was adjusted to minimize overshoot in the systolic pressure signal from the VAD. System-level measurements were then recorded for each test case, and statistical values were determined more than 25 contiguous cardiac cycles, a number deemed sufficient to achieve stationary values. For each time-based signal comparison, a scatter plot was made of the experimental data magnitudes versus the clinical data magnitudes at corresponding time points. Regression analysis was then used to quantify the time-based agreement, and an R2 value was computed. Corresponding experimental and clinical mean values were compared using a paired t test with a value of p < 0.05 judged to indicate a statistically significant difference. A percent root-mean-square (rms) error, σ, was calculated as a point-by-point comparison between experimental and clinical data and divided by the mean value. The reported value is the ensemble average of more than 25 contiguous heart cycles. Because of the in vivo nature of the clinical measurements and the associated uncertainties in reported clinical values, clinical significance was judged to be 1 mmHg in pressure and 0.02 lpm in flow rate.
The error sources affecting the stated experimental pressure and flow estimates included zero-point systemic error, instrumental error, data acquisition error, and the random errors found both within and between cardiac cycles. Propagation of the elemental uncertainties to the overall uncertainty estimate were carried out by the perturbation method and confirmed with Monte Carlo analysis.19 The uncertainty in the reported pressure and flow rate measurements were each within 3% at the 95% confidence level.
With the system adjusted to the appropriate patient-specific settings, pressures and flow rates were measured throughout the system for comparison against the clinical pressure and flow rate tracings. The experimentally measured ensemble mean values with their standard error are reported in Table 3 along with the clinical measurements.
The time-based experimental and clinical signals for ascending aortic pressure are shown in Figure 4 over three cardiac cycles for four of the five cases; the GOSH22 clinical aortic pressure signal was not available. Overall, the experimentally measured ascending pressures reproduced the clinical signals well. Subtle differences can be noticed at peak systole and end diastole. The MUSC2 and MUSC7 clinical signals showed a dicrotic notch, which was difficult to reproduce with the VAD.13 Systolic contractility was also evaluated by comparing the time rate of systolic pressure change of the aortic signals. Differences in dp/dt for MUSC7 and UM5 were less than 6.5% between clinical and experimental values, whereas for UM10 and MUSC2, the differences were about 12 and 32%. The pulse pressures compared with within 9% for each case except for UM5 at 16%. However, the coefficient of determination (R2) comparing experimental and clinical signals ranged from 0.77 to 0.90 for the four cases, demonstrating the system’s capability to reproduce the time-based clinical signals for each patient when observed over the full cardiac cycle. As indicated in Figure 4, the percent rms error between the clinical and the experimental signals never exceeded 1.0%. The measured and clinical MAPs were closely matched, and differences were not statistically significant (p > 0.10).
The remaining experimental measurements demonstrated the outcomes of the system tuning. The time-based ascending aortic flow rate signals, shown in Figure 5A, followed the physiologic characteristics of the clinical measurements very well (0.88 < R2 < 0.95) for the five patients. As indicated, the rms error for each signal was under 2%. The corresponding experimental mean values for the aortic flow rate, and listed as the CO, were within 0.01 lpm of the clinical measurements for each of the five patients (Table 3) with no statistical differences (p > 0.37).
System-level measurements were also in good agreement. The experimental and clinical mean pulmonary pressures agreed to within 1 mm Hg, except for MUSC2 and UM10. The differences in these two cases were 1.9 and 1.2 mm Hg, respectively. However, the corresponding time-based pulmonary shunt flow rate values (Qpul) are compared in Figure 5B, and these signals matched well (0.72 < R2 < 0.85). The rms errors for these signals were under 1% for all but patient UM5, which was at 3.4%. Experimental and clinical shunt flow mean values (Table 3) agreed to within 0.02 lpm or 2% for each patient, and differences were neither statistically significant (p > 0.33) nor clinically significant. Experimental and clinical upper body (Qub) and lower body (Qlb) mean flow rates (Table 3) also agreed to within 0.02 lpm (p > 0.18). The balance between the pulmonary to systemic flow rate (Qp/Qs) each agreed to within 6%. The distribution of systemic flow rate (Qub/Qlb) each agreed to within 9%.
This study focuses on the validation of the MCS as a test bench for patient-specific modeling using differing patient aortic morphologies and physiologic conditions. The VAD input condition fixed the mean aortic and the atrial pressures. The hemodynamic system-level response, determined in terms of upper and lower body pressures and flow rates, and the aortic and shunt flow rates in five patients were replicated with reasonable fidelity in terms of both mean values and time-based behavior. The advantages of this system are its compact nature, its ease of tuning, and its inclusion of relevant circulation branches to achieve realistic system-level information. Test phantoms can be produced quickly, from imaging to realization within days. Patient-specific tuning does require more clinical pressure, and flow rate information may be typically available with a given patient, particularly in neonates. In such cases, some elements of the LP model may need to be extracted from available clinical data representative of these patients.10,12
The system was operated open loop for this study, that is, the VAD operating pressures (i.e., MAP and SAP) were set and maintained at the known patient conditions. As designed with proportional pressure regulators, feedback from pressure and flow sensors can be used to regulate the MAP, heart rate, and CO of the VAD, but an algorithm for such response was not tested in this validation study. Further, a different heart model than the one used here could be readily imposed without changing the validated distributed hydraulic features of the MCS described.
When coupled with a rigid anatomically accurate phantom, a proximal aortic compliance must be used between the VAD and aortic phantom to achieve a physiologically realistic ascending aortic pressure waveform and to prevent large amplitude aortic pressure ringing. Vukicevic et al.15 developed a thin-walled, compliant phantom of a total cavopulmonary connection and found that measured system pressures and flow rates were not significantly different from those measured using a rigid phantom when paired with a proximal compliance. We used representative values for the vascular compliance elements in this study.10,12 Although aortic compliance could be extracted from appropriate MRI information, we did not attempt to do this here.
Within these limitations, a patient-specific neoaorta phantom coupled with a LP model tuned to available clinical values produced a physical response throughout the circulation that compared well to corresponding clinical measurements for each of five different patient morphologies and clinical presentations. The multiscale aspect of the MCS that allows flow and pressure measurements throughout the circulation provides a means to study variables in isolation with effects at the system level, as well as locally within the 3D phantom. The system is suited for parametric studies on effects to the flow distributions and pressures within the territories, as well as on single-ventricular power requirements. Examples might include the effects of shunt size, vascular resistance, arch morphology, or the effects of progressing coarctation and the threshold for clinical intervention. As operated here, the MCS provides a means to simulate the postsurgical scenario, the equilibrium condition after a major change to the circulation. The LP model can be adjusted to simulate different conditions of patient stress or stenosis. Such a system will be valuable for recreating the clinical setting so as to evaluate situations that cannot be usually measured or attempted in patients, such as novel surgical procedures, interventional measurements, or effects because of an increasing severity of coarctation.
An in vitro multiscale, patient-specific Norwood circulation model was described. By using separate anatomically accurate phantoms of five patients having differing aortic morphologies, the system was tuned to clinical physiologic parameters. Patient-specific input conditions were achieved, and pressure and flow rate were measured throughout the system and compared against clinical measurements. Results demonstrated that the time-based experimental signals were both physiologic in form and agreed with clinical measurements (0.72 < R2 < 0.95) for each patient with no more than 2.5% rms error. Corresponding mean results for pressure and flow rate matched clinical measurements (p > 0.10). The multiscale model was shown to be capable of replicating the Norwood circulation at a patient-specific level over a range of patient presentations. As described, the system is suitable to conduct further research into the performance of the Norwood circulation to study the physiologic and morphologic differences at the local and system levels between patients and to study changes occurring over time within a patient.
The members of Modeling of Congenital Hearts Alliance (MOCHA) Group are as follows: Andrew Taylor, Alessandro Giardini, Sachin Khambadkone, Silvia Schievano, Marc de Leval, and T. -Y. Hsia (Cardiothoracic and Cardiorespiratory Units, Great Ormond Street Hospital for Children, Institute of Cardiovascular Science, University College of London, London, United Kingdom); Edward Bove and Adam Dorfman (University of Michigan, Ann Arbor, MI); G. Hamilton Baker and Anthony Hlavacek (Medical University of South Carolina, Charleston, SC); Francesco Migliavacca, Giancarlo Pennati, and Gabriele Dubini (Politecnico di Milano, Milan, Italy); Alison Marsden (University of California, San Diego, CA); Jeffrey Feinstein (Stanford University, Stanford, CA); Irene Vignon-Clementel (INRIA, Paris, France); and Richard Figliola and Ethan Kung (Clemson University, Clemson, SC).
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