In-Vitro Validation of Self-Powered Fontan Circulation for Treatment of Single Ventricle Anomaly

Abstract

Around 8% of all newborns with a Congenital Heart Defect (CHD) have only a single functioning ventricle. The Fontan operation has served as palliation for this anomaly for decades, but the surgery entails multiple complications, and the survival rate is less than 50% by adulthood. A rapidly testable novel alternative is proposed by creating a bifurcating graft, or Injection Jet Shunt (IJS), used to “entrain” the pulmonary flow and thus provide assistance while reducing the caval pressure. A dynamically scaled Mock Flow Loop (MFL) has been configured to validate this hypothesis. Three IJS nozzles of varying diameters 2, 3, and 4 mm with three aortic anastomosis angles and pulmonary vascular resistance (PVR) reduction have been tested to validate the hypothesis and optimize the caval pressure reduction. The MFL is based on a Lumped-Parameter Model (LPM) of a non-fenestrated Fontan circulation. The best outcome was achieved with the experimental testing of a 3 mm IJS by producing an average caval pressure reduction of more than 5 mmHg while maintaining the clinically acceptable pulmonary flow rate (Q_p) to systemic flow rate (Q_s) ratio of ~1.5. Furthermore, alteration of the PVR helped in achieving higher caval pressure reduction with the 3 mm IJS at the expense of an increase in Q_p/Q_s ratio.

1. Introduction

A structurally normal heart consists of two separate pumping chambers or ventricles: one ventricle pumps “de-oxygenated” blood returning from the body to the lungs, and the other pumps oxygenated blood to the body. Approximately 1 in 3841 babies is born with hypoplastic left heart syndrome (HLHS). A subset of HLHS is a rare congenital heart defect in which the left ventricle is underdeveloped [1,2,3]. As a result, the remaining viable right ventricle must support both systemic and pulmonary circulations, becoming overloaded [4,5]. These patients do not survive unless a series of palliative operations are performed to establish an adequate flow to both the lungs and body. The Fontan operation has served as palliation for this anomaly for decades, but multiple complications often result in chronic illness, a severe reduction in quality of life, and survival rates of less than 50% to adulthood [6,7,8,9,10,11,12,13,14,15].

The surgery is performed in three sequential stages to establish a viable circulation. In the first stage, the Norwood atrial septectomy is performed, and the hypoplastic aorta is reconstructed and connected to the right ventricle in place of the pulmonary root. A Blalock Taussig (BT) shunt is implanted between the innominate artery and the pulmonary arteries to create a parallel path between the systemic and the pulmonary circulation. The Norwood procedure is performed shortly after birth. In the second stage, the Glenn, the superior vena cava (SVC), is disconnected from the right atrium and connected directly to the right pulmonary artery, and the BT shunt is disconnected. The main purpose of this surgery is to send the de-oxygenated blood flow from the upper systemic circulation to the pulmonary circulation. The Glenn procedure is performed between three and six months following the first surgery [16]. In the third stage, the Fontan, the inferior vena cava (IVC), is disconnected from the right atrium and connected directly to the Glenn (or Hemi-Fontan) through a synthetic graft extending the IVC to form what is known as a Total Cavopulmonary Connection (TCPC) [17].

Ideally, as long as the impedance of the lung vasculature is sufficiently low, the systemic venous return flows “passively” through the lungs without the assistance of a pumping ventricle. However, a substantial proportion of Fontan patients do not do well. The physiological associations with “Fontan failure” are complex, and the mechanisms are incompletely understood. Despite decades of repeated improvements, the Fontan surgery retains numerous complications, leading to less than 50% survival rate to adulthood [17,18] and poor functional outcome in survivors [19,20]. Fontan operation can cause pre-mature death due to intrinsic ventricular dysfunction, elevated pulmonary vascular resistance (PVR) due to pulse pressure loss and blood flow [21,22,23], or elevated IVC pressure leading to liver cirrhosis, protein-losing enteropathy [24], or plastic bronchitis [24,25]. Gewillig et al. [26] provided in-depth knowledge of the Fontan circulation and its failures. The Fontan circulation creates abnormal operating conditions. PVR increases over time, attributed to lack of blood acceleration, flow pulsatility, cardiac output through exercise, and overall pulmonary blood flow. Schmitt et al. [27] also analyzed the response of PVR and collateral blood flow in ten Fontan patients before and after the administration of dobutamine stress, which effectively decreases systemic vascular resistance to increase cardiac output as an alternative method to simulate exercise stress in patients that are unable to perform adequately [28]. Measurements were performed using magnetic resonance imaging (MRI) catheterization techniques during free breathing and during continuous infusion of dobutamine and results showed that the increased cardiac output increased pulmonary flow. This led to a reduction in PVR. Mechanical assistance has been considered using continuous flow pumps to power the pulmonary system [8,29,30]; however, survival rates did not significantly increase (1–2%) [23,24,25,26,29,30,31]. In addition, several computational models have been presented further to improve the Fontan palliation [23,28,32,33].

Various improvements to the Fontan pathway have been experimented. These improvements include changes in the inferior cavopulmonary connection location, shape, and diameter [33,34,35,36,37]. Different in-silico and in-vitro models have been proposed to investigate the hemodynamics of this palliative surgery [38,39,40,41]. To better study mechanical cardiac assist to Fontan circulation, a benchtop Mock flow loop (MFL) can be used to replicate physiological states with realistic hemodynamics to develop a patient-specific circulatory system for Staged Fontan palliation and various in-vitro experiments. Trusty et al. [34] employed MFL to investigate the use of PediMag and CentriMag to improve failing Fontan hemodynamics. Yamada et al. [42] developed MFL to examine a pulmonary circulatory assist device and hemodynamic characteristics of its function, in which they used shape memory alloy fibers for Fontan circulation with total cavopulmonary connection. MFLs have also been constructed to evaluate other Cardiopulmonary Assist Scenarios. Dur et al. [43] studied two different pediatric ventricular assist devices (VADs), Medos and Pediaflow Gen-0, in Fontan circulation. They illustrated that optimal VAD implementation strategies customized for an individual patient are required for the next generation flow loops incorporating more realistic physiological states. MFL was also utilized along with a von Karman viscous impeller pump providing mechanical support to stabilize and augment cavopulmonary flow in the desired pressure range, without venous pathway obstruction [6].

The focus of this experimental study is to present a modified Fontan surgery to alleviate the inferior caval (IVC) pressure by utilizing a dynamically scaled MFL. The problem is approached with a number of constraints on pressure and flow chief among them, the pulmonary (Q_p) to systemic (Q_s) flow ratio, Q_p/Q_s. The ratio of Q_p/Q_s is a vital parameter to influence the performance of IJS, and its value is strongly correlated to systemic oxygen delivery. A novel and rapidly testable alternative solution to power the Fontan circulation by tapping into the reserve mechanical energy of the native heart, a “self-powered Fontan”, is hereby proposed [4]. To achieve this, an injection jet shunt (IJS) is anastomosed from the aorta to the Fontan conduit. This shunt exploits the high-pressure system in the aorta to drive fast-moving blood into the Fontan circulation and entrain the local flow, thereby reducing the IVC pressure. The introduction of this shunt comes with several challenges, such as predicting the physiological response and ensuring the resulting flow field is physiologically viable.

This study aims to experimentally investigate the hemodynamics of the proposed alternative surgical technique and validate the in-silico findings reported by Ni et al. [40]. It is crucial to implement a multi-scale 0D-3D CFD coupling scheme that allows the investigation of surgical planning in a virtual physics-based environment. Ni et al. [40] have implemented a tightly coupled lumped parameter model (LPM) at the time-step level with a full 3D CFD model. With this implementation, the total cavopulmonary connection (TCPC) was no longer modeled by the 0D LPM. CFD could resolve the region of interest, which accounts for momentum transfer and flow directionality that the LPM was unable to capture. In the proof of concept study conducted by Ni et al. [40], the IJS configuration was optimized to cause a maximized pressure drop at the IVC. Steady-state CFD simulations were carried out by simplifying the entire circulation system to rapidly optimize the IJS diameter and placement location in the pulmonary arteries. These optimized IJS parameters were then implemented into a patient-generic model and two patient-specific models. To perform this in-vitro investigation, it is essential to have a robust benchtop setup that can emulate the physiologically consistent flow field. To this end, a dynamically scaled MFL has been developed to integrate the 3-D printed phantoms of Fontan TCPC with IJS. The effects of multiple parameters are analyzed through this study: IJS diameter, IJS anastomosis angle, and PVR effect in decreasing the IVC pressure. To preserve the consistency and compare the in-silico and in-vitro findings, the experimental protocol followed the same sequence of CFD study as mentioned in [40]. At first, the TCPC pressure was elevated to simulate sick conditions for a Fontan circulation. The baseline model was then compared to several optimized IJS configurations, IJS anastomosis angle, and IJS with reduced PVR.

2. Materials and Methods

2.1. Anatomical Model

Ni et al. [40] developed three patient-generic models TCPC configurations that included (an) (1) baseline, (2) IJS, and (3) no entrainment shunt (NES) for carrying out the computational studies. The patient-generic model was built using average patient data mentioned in [36,38,44,45], and the patient-specific models were provided through MRI scans [46,47]. In the model, IJS was placed concentrically to entrain the flow in pulmonary arteries (PA). To isolate the IJS entrainment effects, an NES model was developed to augment pulmonary flow without entrainment.

In the in-vitro study, TCPC phantoms have been modeled on SolidWorks (Dassault Systèmes) using averaged dimensions of 2–4-year-old Fontan patients. Four model configurations were developed, including the baseline (TCPC with no IJS) replicating a “sick Fontan”, IJS prototypes with diameters of 2, 3, and 4 mm. These 3D phantoms were developed by keeping the correlation with in-silico models mentioned in [40]. To accommodate the increase in the pulmonary flow, the cross-sectional flow area of the pulmonary arteries was modeled using the Poiseuille flow equation.

The TCPC was developed by calculating the diameters of the right pulmonary artery (RPA), left pulmonary artery (LPA), superior vena cava (SVC), and inferior vena cava (IVC) as 6, 9, 12, and 18 mm. Their corresponding lengths of RPA and LPA were 40 mm and for SVC and IVC were 23 and 56 mm. A two-part process was carried out to develop the top and the bottom half. The TCPC was developed using Acrylonitrile butadiene styrene (ABS) and manufactured by 3D printing technology. Post manufacturing, the top and bottom half are joined together using a sealant. The IJS was coated with an adhesive sealant to avoid any leaks during the experiment. The ends of the TCPC were clamped with the conduits when connected to the MFL.

The IJS was developed in three pairs having an internal diameter of 2, 3, and 4 mm. The nozzle is placed on top of a coupler with a total length of 135.7 mm. The diameter at the center section is 20 mm at the center and 9 mm at the ends. The IJS is intruded into the LPA and RPA, and the nozzle orient parallels to the flow direction. The role of IJS is to introduce an entrainment jet that flows concentrically to the pulmonary artery flow (PA). The entrainment jet exchanges momentum with the flow in the pulmonary arteries, decreasing the localized vascular resistance in TCPC and decreasing the IVC pressure. Figure 1A shows the IJS prototype placed in MFL, Figure 1B shows the Schematic diagram of IJS, and Figure 1C shows the 2D drawing of various IJS developed along with the 3D printed prototypes. To ensure the concentricity of the flow, the diameter of the IJS increases at the entrainment point.

2.2. Lumped Parameter Model

The LPM is an electric circuit analogy used to replicate the peripheral circulation of the human cardiovascular system. Using this electric analogy, blood flow through various sections in the cardiovascular system can be lumped and represented as electrical circuits that include resistors, inductors, and capacitors. Each of these elements represents vascular resistance, vascular inertance, and vascular compliances. Different LPM setups have been modeled to experimentally replicate various reconstructed cardiovascular anatomies in the last few decades. The main goal of the LPM setup is to couple the fluid dynamic behavior within the 3D phantom to the dynamics of the peripheral circulation.

A specific LPM has been modeled to replicate the proposed reconstructed physiology to achieve the objectives established above. Ideally, a Windkessel compartment in the LPM consists of an arterial bed and venous bed. The arterial bed is developed using an inductor, resistor, and capacitor, while the venous bed is developed using the resistor and capacitor as mentioned in [40]. In these experimental studies, each Windkessel compartment is modeled by lumping the arterial and venous beds together, as shown in Figure 2. Each Windkessel compartment consists of two elements, i.e., a resistor and capacitor.

In this study, a reduced-order LPM has been modeled to develop the MFL test rigs for conducting the experiments. Hence, it is sufficient to control the correct overall resistance and compliance in each branch of the system.

2.2.1. Vascular Resistance

Inlet and outlet pressures are tuned in the MFL. These inlet and outlet pressures generate the pressure differential. This static pressure differential causes the flow to occur in the system. The conduits in the MFL provide a certain amount of resistance, but additional resistance is provided to the system by valves. The pressure drop across each branch is achieved by tuning the resistance in the conduits of MFL. As a result, the blood analog will flow through each conduit across this pressure drop in the MFL setups. In this study, resistance in each conduit of the MFL is achieved by placing a needle valve. Resistances in each compartment of the MFL can be tuned by throttling the respective needle valve. Head loss across a valve is proportional to the velocity, head of fluid as shown in Equation (1) as:

$$\mathsf{\Delta }h=K\frac{{\overline{V}}^2}{g}$$

(1)

where $\mathsf{\Delta }h$ is defined as head loss, $K$ is the loss coefficient that is dictated by the position of the valve, $\overline{V}$ is the average velocity of the fluid, $g$ is the gravitational constant.

The needle valve resistors are manually actuated and precise. These resistors have a range of seven color bands, and each color band has a setting ranging from 0–9. The pressure drop produced across the needle valves is linear, contributing to the successful tuning of the MFL rigs. These are made up of stainless steel with ½” inch national pipe thread (NPT) with female thread size. It has a very accurate flow rate range between 0–22.5 gpm and the pressure range from 0–5000 psi with cracking pressure of 1–2.5 psi.

2.2.2. Vascular Inductance

The pulsatile nature of the blood requires constant change in motion when flowing through the circulatory system. On the mock loop, this can be represented by including an inertance component. This component can be achieved with the correct volume of fluid being flown in each section of the circulatory system and representing these values on the mock loop with pipe lengths and diameters. Inductors affect only non-steady systems. In fluids, inertance is defined as the pressure gradient to accelerate the flow. A parameter describes how rapidly pressure field changes will affect the flow field in the system. The inertance is defined by Equation (2) as:

$$L=\frac{2\rho x}{A}$$

(2)

where $L$ represents the inductance, $\rho$ represents the blood density, and $A$ represents the cross sectional area. In the discussed MFL setup, the length of the vasculature captures the inertance. A specific length for each vasculature cannot be modeled as the arteries and venous network of a human circulation are extremely long.

2.2.3. Vascular Compliance

In biofluid mechanics, vascular compliance refers to the change in stored energy in a vessel for a given change in pressure in the time domain. It is entirely analogous to capacitance in electrical circuits. Like an inductor, this parameter does not affect the behavior of a steady system. This parameter is critical for accurately modeling the effects of distensibility of the arterial and venous beds in MFL.

Specific annular design-based compliance chambers have been developed to produce the desired compliance (C) in this study. These compliance chambers are capable of matching specific compliance in a Windkessel bed by altering the volume of the chambers for a change in dynamic pressure of the fluid generated across that chamber in the MFL. In this setup, a pair of concentric tubes were used to create the annular inner section of the compliance chamber. The outer tube of the compliance chamber was constructed using the clear schedule 40 and 80 pipes, and the inner wall is constructed by using solid Delrin rods, as shown in Figure 3.

To obtain the effective radius, the outer diameter of the compliance chamber was kept constant while the inner diameter varied for simulating different patient-specific cases. Using this volume-controllable approach, no parameter such as entrapped pressure changes during an MFL run reduces the uncertainty of the analysis. Equations (3)–(5) show relationships between the pressure and volume of the compliance chamber with the effective radius as discussed in [48]:

$$Q(t)=\frac{d}{dt}\{C(t)[P(t)-P_g(t)]\}$$

(3)

$$\mathsf{\Delta }P(t)=\frac{1}{C}{\displaystyle \underset{-\infty }{\overset{t}{\int }}Q(t)·dt}$$

(4)

$$C(t)=\frac{V(t)-V_o}{\mathsf{\Delta }P(t)}$$

(5)

To achieve the desired compliance value for the vascular compliance elements, the above equation can be modified to describe the compliance as a function of the compliance element geometry and fluid parameters as seen in (6)–(8)

$$C=\frac{\mathsf{\Delta }V}{\mathsf{\Delta }P}$$

(6)

$$C=\frac{\pi r_e^2\mathsf{\Delta }h}{\rho gh}$$

(7)

$$r_e=\sqrt{\frac{\rho gC}{\pi }}$$

(8)

where r_e is the effective radius of the cylindrical compliance chamber, C represents the vascular compliance, $\mathsf{\Delta }V$ is the change in volume of fluid and change in hemodynamic pressure over a cardiac cycle, and $Q$ represents the blood flowrate.

Ni et al. [40] have developed a detailed full-scale LPM of Fontan circulation. This LPM consists of carotid, subclavian, right pulmonary, left pulmonary, lower body, Fontan TCPC, and coronary compartments. Each compartment contains an arterial and venous bed. In this full-scale LPM model, every arterial bed is modeled with a three-element Windkessel model. As discussed above, a laboratory benchtop realization based on full-scale LPM is not practically feasible. Hence, the MFL setup for the Fontan circulation involved is based on a reduced-order LPM derived from Ni et al. The hydrodynamic variables measured in this study are the flow rates and pressures at the systemic and pulmonary junctions connecting to Fontan TCPC conduits. The reduced-order LPM modeled to develop the MFL consists of four compartments. As mentioned above, every compartment of this model is developed with two elements, i.e., resistance and capacitance, as shown in Figure 4.

This LPM has two systemic and two pulmonary compartments. Two systemic compartments represent upper and lower systemic circulations, and two pulmonary compartments represent right and left pulmonary circulations, respectively. Each branch in the MFL contains a device that corresponds to a circuit element of the reduced LPM. Pulsatility plays a crucial role in the hemodynamic behavior on the arterial side. In addition, the arterial network and capillary system of the systemic circulation provide significant vascular resistance and vascular compliance to the flow field. These arterial networks act as low pass signal conditioning filters to the pulsatile flow field and effectively dampen out most of the pulsatility in the caval blood flow when it reaches the TCPC.

Furthermore, the Fontan circulation is significantly less pulsatile on the venous side due to the absence of the ventricle. In this study, the remaining pulsatility from the cardiac cycle is not modeled. To accurately replicate the infant anatomy while conducting the Fontan experiment, the values of compliance were determined based on physiological values that correspond to body surface area (BSA) of 1.2 m² defined in [41].

Table 1. Vascular compliance of sections.

Lumped Sections	$\mathbf{Compliance}\left(\mathbf{mL}/\mathbf{mmHg}\right)$
Upper compliance (Cupper)	3.12 ± 0.03
TCPC compliance (CTCPC)	0
IVC compliance (CIVC)	1.80 ± 0.055
Liver compliance (Cliver)	4.41 ± 0.14
Lower body compliance (Clower)	3.86 ± 0.06
Right pulmonary artery compliance (Cright)	2.14 ± 0.066
Left pulmonary artery compliance (Cleft)	2.14 ± 0.066

shows the values of vascular compliances corresponding to different anatomical sections.

Due to the relative similarity between the IJS Fontan Mock Flow Loop used in this experiment and the reduced lumped parameter network model utilized, all but the lower systemic compliance could be carried over. To calculate the lower systemic compliance, the liver compliance (C_liver) and lower body (C_lower) compliance are combined in Equation (9) [48] as:

$${\mathrm{C}}_{\mathrm{lower}}={\left(\frac{1}{{\mathrm{C}}_{\mathrm{lb}}}+\frac{1}{{\mathrm{C}}_{\mathrm{liver}}}\right)}^{-1}+{\mathrm{C}}_{\mathrm{ivc}}$$

(9)

Therefore, the resulting compliance values used in this experiment are given below in

Table 2. Compliance values used in in-vitro experiments.

Vascular Branch	Vascular Compliance $\left(\mathbf{ml}/\mathbf{mmHg}\right)$	Effective Radius $\left(\mathbf{in}\right)$
Cupper, Upper Systemic	3.12	0.3365
Clower, Lower Systemic	3.85	0.3742
Cleft, Left Pulmonary Artery	2.14	0.2787
Cright, Right Pulmonary Artery	2.14	0.2787

.

2.3. Pulmonary Vascular Resistance (PVR)

Pulmonary vascular resistance (PVR) is an essential hemodynamic quantity that is very indicative of Fontan surgeries’ outcomes. Abnormal growth of the pulmonary vasculature and significant collateral flow can significantly alter PVR, leading to cardiovascular malfunctions. In particular, elevated PVR can cause pulmonary hypertension, which strongly affects the Fontan patient’s wellbeing. Several studies point to the possibility of a strong correlation between pulmonary flow and PVR. This study attempts to quantify changes in PVR between rest and exercise conditions induced by dobutamine administration, which directly affects the heart rate and stroke volume. The data reveals a negative correlation whereby an increase in pulmonary flow induces a drop in PVR.

This observation becomes of particular importance for this study as implementing an IJS significantly enhances pulmonary flow. In the absence of any PVR response, the additional flow would cause an increase in IVC pressure; however, if PVR reduction could be considered as a parameter, the additional flow would not build up in the Fontan circulation. A PVR drop alone would negate any IVC pressure increase due to fluid build-up as well as potentially be directly responsible for additional pressure reduction.

With the accommodation of the IJS flow, if flow entrainment occurs, the IJS can directly cause a significant pressure drop. Based on the data presented by Schmitt et al. [27], it is possible to derive a curve relating the percent change in PVR with the percent change in pulmonary flow. Out of the ten patients presented in the study, two were considered non-responders as the PVR hardly changed following dobutamine administration, although the observed flowrates reacted accordingly. Due to the low population in this study, an accurate trend cannot be extracted from the statistical analysis, but nonetheless, it can be observed, as shown in Figure 5 for an increasing $Q_p$ the PVR does in fact drop.

The plot suggests that the PVR percent change lies in 30−40% for a maximum. The current in-vitro study will utilize these results to sequentially drop the PVR following IJS activation to observe the outcome to the IVC pressure.

Pulmonary Vascular Resistance Calibration

The relationship between flow rate and needle valve resistance must be determined to implement the PVR drop to increase pulmonary flow. To evaluate the pulmonary resistances, a simple flow loop is set up with a continuous flow pump. The needle valve resistance is calculated by measuring the pressure upstream and downstream of the valve in conjunction with the flow rate as shown in Figure 6A. Ohm’s law relates the scalar valve resistance to the mean pressure gradient ratio to the flow rate. Three different valve settings for the same resistor valve (needle valve) are calibrated for three specific flow rates (1.45 L/min, 1.70 L/min, and 2 L/min) respectively. The calibration procedure is carried out on the right and left pulmonary resistances as shown in Figure 6B. This figure presents the most significant range of valve settings tested for calibration. The plot qualitatively shows that for the same valve setting with the incremental flow rates, the valve resistance grows linearly as expected from the theory of Ohm’s law. This trend remains consistent, as the valve settings are restricted (from green to blue bands). The same calibration study has been performed on both the resistors placed on both LPA and RPA conduits.

2.4. Oxygenation Model for Fontan Physiology

A good source of validation for cardiovascular experiments is to track the projected oxygen transport across the model and evaluate the oxygen saturations in systemic and pulmonary circulations.

The Fontan circulation can typically be considered a circuit in series. However, the addition of a graft shunting flow from the aortic arch to the Fontan circuit generates a pseudo-parallel circuit, as shown in Figure 7. The right ventricle (RV) generates a cardiac output (CO), which splits in the systemic flow $(Q_s$) and the injection jet shunt flow ($Q_{IJS}$). $Q_p$ represents the pulmonary flow. In the systemic circuit, oxygen consumption occurs ($C{\dot{V}}_{O2}$), which depletes systemic oxygen concentration $(C_{AO2}$) to the systemic venous concentration ($C_{SVO2}$), as described in Equation (10). In the pulmonary circuit, the blood gains oxygen ($S{\dot{V}}_{O2}$), increasing the pulmonary arterial blood concentration ($C_{PAO2}$) to the pulmonary concentration ($C_{PVO2}$), as modelled in Equation (11).

$$C_{A{O}_2}{Q}_s-C{\stackrel{.}{V}}_{O_2}=C_{SVO}{}_2·Q_s$$

(10)

$$C_{PAO}{}_{{}_2}·Q_p+S{\stackrel{.}{V}}_O{}_{{}_2}=C_{PVO}{}_{{}_2}{Q}_p$$

(11)

The flow mixing between the systemic venous return and the systemic arterial flow shunted by the IJS can be expressed in Equation (12) as:

$$C_{SVO}{}_2·Q_s+C_{A{O}_2}{Q}_{IJS}=C_{PAO}{}_{{}_2}·Q_p$$

(12)

Based on the circuit schematic, it can be observed that $C_{PVO}{}_{{}_2}{Q}_p=C_{A{O}_2}·CO$ and $CO=Q_p=Q_s+Q_{IJS}$, which suggests that the systemic oxygen saturation matches the pulmonary venous oxygen concentration. The oxygen consumption and assimilation are assumed to occur under “steady” conditions, hence $C{\dot{V}}_{O2}=S{\dot{V}}_{O2}$. Using these observations along with the balance equations derived, the systemic oxygen transport equation can be expressed in Equations (13) and (14) as:

$$C_{A{O}_2}{Q}_s=C_{PVO}{}_{{}_2}CO\frac{1}{1+\frac{Q_{IJS}}{Q_S}}$$

(13)

$$C_{A{O}_2}{Q}_s=C_{PVO}{}_{{}_2}CO\frac{1}{\frac{Q_P}{Q_S}}$$

(14)

These expressions require cycle-average flow rate inputs originating from experimental measurements ($CO$, $Q_s$, and $Q_p$), as well as literature-derived blood oxygen capacity and oxygen consumption data. Pulmonary venous oxygen concentration is calculated from an assumed oxygen saturation (100, 95, 90, 85, and 80%) depending on patient ventilation and a given oxygen capacity (0.22 mLO₂/mLBlood). Oxygen consumption can be determined based on literature derived per-weight oxygen consumption 9 (mL/s)/Kg; hence the user must only know the patient’s weight.

2.5. Uncertainty Model

Uncertainty quantification is the process in which the uncertainties are characterized quantitatively and reduced in an application. Their likelihood of specific outcomes is determined if some aspects of the system are not known. Uncertainty existence is possible in a mathematical and experimental model, which can be categorized into various sources such as parameter, structural, exponential, interpolation, aleatoric, and epistemic.

Experiments mentioned in this report use the sensors to obtain the required output. Uncertainty of sensors can be classified into three types, point, interval, and probabilistic. Type B estimate is used when the statistics of error distribution is done by knowledge of the error in certain quantities. Uncertainty estimates resulting from reference attribute bias, display resolution, operator bias, along with computational and environmental factors, are determined using this technique.

If the measurement error data is normally distributed, the uncertainly is given by Equation (15) [49] as:

$$u=\frac{L}{{\varphi }^{-1}\left(\frac{1+p}{2}\right)}$$

(15)

$\pm L$ is defined as the containment limit, ${\varphi }^{-1}$ the inverse normal distribution function, and the containment probability. Generally, the containment limits are obtained from manufacturer tolerance limits, calibration records, or statistical process control limits. The containment probability is derived from service data from the past. This study aimed to understand the effect of system-level uncertainty on pressure and flow readings obtained during in-vitro simulations.

For the pressure sensors engaged in the MFL setup, errors associated with accuracy that combines errors due to linearity, hysteresis, and repeatability are considered. Other errors that are considered include setting zero offset and span error, the total error band that includes errors due to thermal hysteresis, and thermal errors.

Upon establishing the type of error, the corresponding error limits are defined as a number or as a percent of the full-scale reading. The error limits are to be defined by the confidence interval or by a specified level of probability. All the error sources associated with each individual system are assumed to follow a normal distribution. For calculation purposes, the errors are interpreted as a 95% confidence limit if not mentioned by the manufacturer.

Based on the equation, the uncertainty due to each error is computed based on the error limit. This leads to the development of the standardized error model along with the sensitivity coefficients. The model is further simplified as no correlation exists between the individual error sources. The degree of freedom and confidence limit are considered for the final uncertainty.

2.6. Benchtop Experimentation

As discussed above, MFL setups discussed in this study are based on a reduced LPM. Each R, L, C parameter in the LPM has a specified value derived from clinical measurements. The values for these parameters are physically realized in the MFL setups by replicating components. The key to achieving meaningful results in MFL setups highly depends on the accurate tuning of these individual components and data acquisition. Great precision is maintained during the tuning process. Imprecision of one component can lead to an incorrect response of the whole system. There are various methods by which MFL setups can be devised for conducting different kinds of experiments.

In these in-vitro experiments, MFL setups are systematically tuned by following a bottom-up procedure that involves the sequential execution of the steps mentioned in Appendix A. This in-vitro model replicated a non-fenestrated Fontan. The MFL has been tuned so that the upper systemic circulation receives approximately 30% of the total systemic blood flow while the lower systemic circulation receives approximately 70% of the total systemic blood flow. The left and right branches each receive approximately 50% of the pulmonary blood flow in the pulmonary circulation. The main objective of this preliminary proof of concept study was to experimentally evaluate the efficacy of the IJS mechanism in PAs to satisfy the proposed hypothesis, i.e., reduction in caval pressure. Hence, the water has been used as a working fluid for conducting benchtop experiments. Thus, the vascular resistances are initially tuned to control the flow ratio within systemic and pulmonary lumps of the flow loop. Once the flow ratios had been achieved, the compliance chambers were engaged. Figure 8 and Figure 9 show the type of MFL setup used for conducting the benchtop experiments to validate the proposed hypothesis.

To prove the hypothesis, three different types of experiments were conducted. At first, a failing Fontan case with high IVC pressure was simulated to establish the baseline. Then, three different IJS diameters were tested to identify an optimal operating diameter. Secondly, the optimal IJS is sequentially activated to mimic three proximal aortic anastomotic angles (0°, 45°, and 90°), and then the PVR is reduced. In the experiments, proximal anastomotic angles were replicated by placing a calibrated ball valve on the IJS graft line. Figure 10 shows the comparison of IJS proximal anastomosis angles.

In all these experiments, the Harvard Apparatus medical pump emulates C.O and provides the pulsatile waveform to the whole MFL setup. An RPM decal of the pump determines the frequency of the stroke rate of the piston for a set stroke value. In addition, an output-to-input phase ratio determines the amount of systole to diastole ratio that should be present in each cardiac cycle for the particular stroke and RPM setting. The pulsatile pump was set to produce an output of ~2.4 L/min; this requires pump settings of 80 RPM and 30 cubic centimeters (cc) per stroke. These values were set to match non-dimensional parameters calculated from physiological data. As mentioned in the above modeling section, the vascular inductance was not modeled while developing the LPM for MFL setup. A stock braided vinyl clear hose of ½ inch diameter have been used uniformly to construct the MFL setup. This stock hose has been chosen mainly for ease of coupling with different instruments utilized in the development of MFL setup without creating any artificial obstruction to the flow field. It has been observed that the flow field suffered a proportional amount of noise interference as the key parameters were varied during the experiments. To maintain the brevity in this section, only the performance of the most qualified cases from each of the three parameters (nozzle size, anastomosis angle, PVR %) are shown in Figure 11, Figure 12, Figure 13, Figure 14, Figure 15 and Figure 16.

The spectral analysis on the acquired hemodynamic waveforms for all three parametric studies has been performed using the Fast Fourier Transform (FFT) technique to understand the noise interference pattern, as shown in Figure 17, Figure 18, Figure A1, Figure A2, Figure A3 and Figure A4 (in the Appendix B). Depending on the peak frequency, a cutoff frequency has been selected and applied to develop the filters. A Butterworth filter and the Savitzky-Golay filter were applied to the final post-processed data to filter out these noises. To maintain the brevity in this section, only the performance of the most qualified cases from each of the three parameters (nozzle size, anastomosis angle, PVR %) are discussed here. The filters were applied to the flowrate waveforms for each lump and IVC pressure.

3. Results

3.1. Fontan Hemodynamics

3.1.1. Comparative Study of IJS Nozzle Diameters

The purpose of this study is to determine whether the implementation of an IJS would prove beneficial for Fontan patients. To achieve this goal, the MFL is first tuned to match the physiological conditions of a failing Fontan with elevated caval pressure around 20 mmHg and a systemic flow of 2.03 L/min. Following tuning, the study assesses the IJS viability by altering three parameters (i.e., varying the IJS nozzle diameters, sequential activation of proximal aortic anastomosis angles, and finally, the reduction in PVR). As shown in

Table 3. Pressure and flow measurement for baseline and various IJS diameters.

		IJS Diameters
Hemodynamic Variables	Baseline	2 mm	3 mm	4 mm
$Q_s$ (L/min)	1.51	1.49	1.35	1.24
$Q_p$ (L/min)	1.53	2.05	2.03	2.03
$Q_p$/$Q_s$	1.00	1.36	1.50	1.64
$P_{IVC}$ (mmHg)	20.75	15.40	15.24	16.2
$P_{AO}$ (mmHg)	84.38	97.01	97.01	97.01

, the 3 mm IJS nozzle has proved to be the best candidate in the parametric study on IJS nozzle size. By using the 3 mm IJS nozzle, a caval pressure drop of 5 mmHg is achieved. This caval pressure drop occurs at the expense of $Q_p$/$Q_s$ = 1.5. This in-vitro observation cross-validates the CFD findings by this research group and is reported in Ni et al. [40].

3.1.2. Comparative Study of Aortic Anastomosis Angle with Active IJS

In

Table 4. Pressure and flow measurement for active 3 mm IJS with varying angle.

Active 3 mm IJS
Hemodynamic Variables	Baseline	$90°$	$45°$	$0°$
$Q_s$ (L/min)	1.51	1.32	1.38	1.41
$Q_p$ (L/min)	1.53	2.03	2.03	2.03
$Q_p$/$Q_s$	1.00	1.53	1.47	1.43
$P_{IVC}$ (mmHg)	20.75	17.58	16.38	16.20
$P_{AO}$ (mmHg)	84.38	97.12	97.01	97.01

, the implementation of the IJS clearly results in a significant pressure drop in IVC. Upon tuning, the measured IVC pressure is of 20.75 mmHg with a systemic flow of 1.51 L/min. Following the IJS implementation at a $90°$angle, the pressure drops to 17.58 mmHg, and the systemic flow is 1.03 L/min. At a $45°$angle, the pressure further drops to 16.38 mmHg, and at a $0°$angle, the pressure is found to be 16.20 mmHg. Once the IJS is activated, the $Q_s$ remains mostly constant, however, the IVC pressure sees up to a 1.38 mmHg. This notable pressure drop is due to the kind of pressure the proximal IJS takeoff is subjected to. In the $90°$case, the flow across the IJS is driven solely by the static pressure in the aortic arch. On the other hand, in the $~0°$case, the IJS flow is powered by the combination of the static pressure and, in part, by the dynamic pressure of the moving flow in the arch. For each case, the$Q_p$/$Q_s$ constraint is met at about 1.47. This study does not include a feedback mechanism to maintain homeostatic systemic flow. This results in the observed drop-in $Q_s$following the IJS activation. In Table 4, it can be observed that $Q_p$ increases following IJS activation from the baseline value of 1.53 L/min to 2.03 L/min.

3.1.3. Comparative Study of PVR Reduction by 10 and 30%

As established in the hypothesis, as flow to the pulmonary system increases, PVR drops.

Table 5. Pressure and flow measurements for active IJS and decreasing PVR.

Active 3 mm IJS
Hemodynamic Variables	10% PVR Drop	30% PVR Drop
$Q_s$ (L/min)	1.18	1.00
$Q_p$ (L/min)	2.03	2.03
$Q_p$/$Q_s$	1.71	2.03
$P_{IVC}$ (mmHg)	14.41	13.75
$P_{AO}$ (mmHg)	97.01	97.01

, summarizes results for varying PVR. As PVR decreases, there is not a significant change in either $Q_s$ or $Q_p$. However, IVC pressure is significantly affected. Staring from the most optimal IJS implementation angle of 0$°$, the PVR is first dropped by 10%, resulting in a 14.41 mmHg IVC pressure. A further PVR drop to 30% of baseline decrease IVC pressure to 13.75mmHg. While dropping PVR, the constraint on$Q_p$/$Q_s$ is maintained for each case. Before dropping PVR, the IVC pressure drop totals at 5.5 mmHg for a 3 mm IJS. Once PVR is reduced, the IVC pressure drop increases to 7.00 mmHg. This result qualitatively cross-validates the in-silico results generated by this research group and is reported in Ni et al. [40]. These in-vitro results also suggest that the surgical implementation of an IJS alone can benefit a Fontan patient. The further benefit arises from the hypothetical PVR drop.

3.2. Oxygen Transport

For flow measurements presented in the earlier section, the oxygen transport in the systemic arterial and venous sides can be evaluated.

Due to the lower $CO$ used in these experiments, the oxygen consumption rate per unit weight had to adjust accordingly. As described in the literature, the oxygen consumption rate can have a linear relationship to the cardiac output, hence based on these results, the consumption rate was linearly scaled down to 6.3 mL·s/kg. The results that follow present oxygen saturations for the systemic arterial and venous circuits for different pulmonary venous saturation (representing various degrees of oxygen extraction by the lungs) for each Fontan model explored offers a complete overview of the oxygen saturation calculations. It can be readily observed that, as mentioned in the oxygen model description, the systemic saturation for a non-fenestrated Fontan geometry matches the pulmonary venous saturation. The arterial saturations calculated fall within the acceptable range. Due to the oxygen transport model employed, the systemic venous saturations are highly dependent upon the correct implementation of the consumption rates. As mentioned earlier, the consumption rate found in the literature was scaled down accordingly to match the CO used in these experiments. The resulting systemic venous saturation falls within the expected range, particularly for the baseline case, which can be readily compared to clinical data. This indicates that the consumption rate scaling was performed correctly. Baseline and models implementing the IJS only differ for systemic venous saturations. This difference is due entirely to the strong drop-in $Q_s$ that occurs when the IJS valve is opened. Once the IJS becomes active, proximal shunt anastomosis angle and PVR reduction do not strongly affect oxygen saturation. In general, as the pulmonary venous saturation drops, the systemic arterial and venous saturation follow the same trend.

Figure 19 takes a closer look at the arterial and venous saturations separately. The decreasing trend in oxygen saturation with dropping ventilation is clear. The substantial drop in systemic venous saturation upon IJS activation has been highlighted, as well as the lack of noticeable change in saturation (especially on the venous side) due to model alterations (IJS takeoff angle and PVR). The results presented in this section offer a reasonable degree of validation for the oxygen transport model implemented. The computed quantities match expected trends and can be readily compared to clinical data.

3.3. Uncertainty Analysis

As explained in the methods section, the uncertainty in these experiments is due to the different types of error is computed using the Type B estimate. The noise interference patterns on flow and pressure waveforms through the spectral analysis have also been addressed. The pressure sensor placed on the IVC conduit played a crucial role in validating the proposed hypothesis, hence a preliminary signal-to-noise ratio uncertainty analysis for this particular sensor is performed. This uncertainty analysis has been performed on the analog pressure sensors. The calculated uncertainty due to accuracy was 0.0638 V. The computed uncertainty due to Setting Zero offset, Span, and Total Error Band was 0.051 V. Hence, the total uncertainty in the model was computed as 0.0963 V. Figure 20 shows the cardiac cycle averaged IVC pressure superimposed with the calculated uncertainty value for each experiment.

4. Discussion

A multi-scale model of the Fontan circulation has been constructed. The MFL used in this study experimentally simulates the effect of the IJS implementation in a non-fenestrated Fontan physiology. The benchtop setup was also calibrated to simulate the PVR effect. This in-vitro model combined a reduced 0-D LPM model replicating the patient’s peripheral circulation with a patient-generic 3-D phantom of the Fontan pathway. Various patient-generic TCPC models and IJS prototypes have been developed using stereolithography technology. The outcome of these experimentations has successfully satisfied the hypothesis as established in the objective of the study. A parametric study on IJS nozzle diameter, IJS aortic anastomosis angles, and PVR effect have been conducted in these experiments. The comparative study on the IJS nozzle shows that the 3 mm nozzle is the most efficient for entraining the flow in the PAs. The IJS proximal aortic anastomosis angle study showed that the IJS nozzle could entrain better in the PAs as the angle becomes shallower. Finally, by incorporating the PVR effect along with the 3 mm IJS nozzle, the desired IVC pressure drop of greater than 5 mmHg has been achieved with the commensurate PVR drop. While conducting these experiments, as the IJS nozzles have been introduced to the flow field, pulsatility in the PAs has been increased, and comparatively high-frequency noise was also introduced. This high-frequency noise was filtered by conducting spectral analysis. The main benefits of the proposed IJS reported in [40] and verified in this in-vitro studies include: (1) reduced caval pressure, (2) increased pulmonary flow Q_p and pulse pressure, (3) acceptable even increased systemic Oxygen delivery, and (4) reduced pathological flow in TCPC.

This unique pathophysiology (Fontan circulation) has led to several in-practice or proposed interventions aiming at decreasing caval pressure. The majority of the proposed intracorporeal and extracorporeal interventions focused on either re-modeling TCPC graft (e.g., Y-shaped graft, 2Y-shaped graft) or actively powering the Fontan circuit using various electromechanical pump actuation techniques to augment the blood flow in PAs and while reducing the caval pressure. Many of these proposed interventions have been under laboratory investigations for more than two decades due to various technical problems relating to driveline infection, thromboembolism, hemolysis, cardiac arrhythmias, pump failure, pathological flow conditions. Also, many of the proposed solutions are not feasible to implement clinically, as those involve a major re-modeling of the Fontan conduit. Unlike these, our proposed solution is purely passive in nature and does not involve any significant reconstruction of the native TCPC. Furthermore, since the IJS mechanism involves a simple design concept, it is clinically more feasible to implement and carry out catheter interventions if needed. Additionally, this IJS shunt failure would simply reduce the self-powered Fontan circulation to a regular Fontan circulation, which would be sustainable until the shunt failure is corrected via catheter intervention. Hence our proposed technique is rapidly testable and reconfigurable. As we could observe from the clinical data, the PVR vs. PA flow model is modest [41]. Pharmacological therapies directed at reducing PVR are undergoing steady development, but have yet to show reduced long-term morbidity and mortality. These pharmacological advancements will make our self-powered Fontan circulation more effective.

Through this in-vitro study, our main aim was to experimentally validate the proposed hypothesis investigated in-silico in [40], i.e., the inclusion of an IJS of suitable geometry into the “failing Fontan” circulation involving a normal TCPC can (1) decrease in caval pressure (2) while maintaining acceptable levels of systemic oxygen delivery. Achieving a clinically significant caval pressure drop aims to reduce complications of the failing Fontan circulation, such as protein-losing enteropathy and liver cirrhosis. Also, we have carried out comprehensive in-silico studies investigating alternative IJS configurations coupled to fenestrations aimed at improved caval pressure reduction beyond that reported in [40], even in the context of no PVR reduction. Results from these studies have been presented at professional forums [50,51] and will soon appear elsewhere in the literature. In our upcoming studies, we aim to perform a quantitative analysis of flow energetics between various models of non-powered, actively powered, and self-powered Fontan models.