Mechanical circulatory support (MCS) devices are widely used to treat end-stage heart failure. According to a report from the Interagency Registry for Mechanically Assisted Circulatory Support (INTERMACS), nearly 20,000 patients who had received an MCS device approved by the US Food and Drug Administration were entered into the INTERMACS database.1 The rate of patient enrollment has continued at a pace exceeding 2,500 patients per year. Continuous-flow left ventricular assist devices (CF LVADs) are the most commonly implanted type of device, with clinical results improving greatly over the last several decades. However, many complications are still encountered, such as device failure, bleeding, thromboembolism, infection, and right ventricular failure. Thus, heart transplantation is still considered to be the best treatment for end-stage heart failure.
To evaluate or develop MCS devices, a simulation model of the cardiovascular system can play an important role, in addition to that of clinical research and animal experiments. Bench testing with mock loops that mimic the human circulatory system is essential to evaluate the hemodynamic performance of MCS devices. Mock loops can simulate the interaction of the MCS device with the human cardiovascular system to an extent, but the range of physiologic conditions and disease states is limited to the design of the mock loop and the availability of the MCS device, which may be in an early phase of design and development.
Numerical simulation modeling has emerged as a useful research tool, and several researchers have reproduced various aspects of the human cardiovascular system.1–15 We have developed the Virtual Mock Loop (VML) to support the development of MCS devices at our institution: LVAD, right ventricular assist device (RVAD), advanced ventricular assist device, biventricular assist device (BiVAD), and CF total artificial heart (CFTAH). The purpose of this study was to simulate the hemodynamic performance of Cleveland Clinic’s self-regulating CFTAH with the VML and to evaluate the accuracy of this model compared with bench data from the mock loop.
Materials and Methods
Continuous-Flow Total Artificial Heart
The CFTAH is small at 6 cm in diameter and 10 cm in body length, with a priming volume of 37 ml (Figure 1). As previously described in detail,16 this single-piece design is self-regulating and allows for a degree of free axial movement of one moving part (rotating assembly) in the direction of differential forces across the rotating assembly, caused primarily by atrial pressure differences. This axial movement changes the size of the right pump aperture, affecting relative left/right performance in a direction to correct the atrial pressure imbalance. In this way, the performance of the right pump is passively controlled by the aperture opening, whereas the left pump’s performance is largely unaffected. When the left inlet pressure is higher than the right inlet pressure (caused by right overpumping, left underpumping, or right atrial suction), the rotating assembly is shifted by hydraulic forces to the right, thereby narrowing the right pump aperture and decreasing the right pump’s performance. Similarly, when the right inlet pressure is higher than the left (caused by left overpumping, right underpumping, or left atrial suction), the rotating assembly moves to the left, thereby opening the aperture and increasing the right pump’s performance.
Bench Mock Loop
The CFTAH system performance was evaluated using the CFTAH bench mock circulatory loop (MCL; Figure 2).16,17 A glycerin/water mixture (specific gravity 1.060) was used as the working fluid. Vascular resistances were modeled with manual valves, arterial compliances were modeled with closed pneumatic reservoirs, and the pump inlets were fed from open reservoirs. The amount of air in the pneumatic reservoirs was adjusted to give systemic and pulmonary compliances of 1 ml/mm Hg and 5 ml/mm Hg, respectively. Pressures were monitored at four of the pump ports. In each CFTAH characterization test, data were recorded across the full range of operation (left pump flow of 3–9 L/min, aortic pressure of 70–130 mm Hg, and pulmonary arterial pressure of 20–40 mm Hg) controlling flow (±0.05 L/min) and pressures (±3 mm Hg) to provide power data in both fixed speed and sinusoid speed pulsatility (80 bpm, ±25% speed modulation of the average pump speed) modes.16,17 Normalized pump performance curves were plotted, in which flow was normalized by dividing by speed, and pressure rise was normalized by dividing by speed squared.18
Virtual Mock Loop
The VML’s software, developed in MATLAB (MathWorks, Inc., Natick, MA), simulates the hemodynamics of the cardiovascular system with a lumped-parameter model, including systemic and pulmonary circulation and cardiac four-chamber and valve characteristics.3,10 Lumped parameters representing the systemic and pulmonary vasculatures are modeled with resistors, capacitors, and inductors (Figure 3). Inputs include a distribution of impedances, systolic and diastolic ventricular compliances, beat rate, and blood volume. The system’s output includes pressure, volume, and flow values throughout the cardiovascular system/pump environment. An input user interface allows selection of a variety of single or multiple disease conditions, including stenosis or regurgitation in each of the four valves, and scaling of the simulation based on the weight of the subject.
Settings in the Virtual Mock Loop
Detailed circulatory system settings for the VML are shown in Supplemental Table 1 (Supplemental Digital Content, http://links.lww.com/ASAIO/A312). Regarding parameters of the heart, the VML was created to simulate MCS interaction with the native system, including valves and a beating heart. However, for the CFTAH, because both ventricles with four valves are resected during implantation and the simulation uses constant-speed pumps, the compliance and inertance inputs did not affect the solution. To eliminate the action of the atria and ventricles, the systolic and diastolic compliances were set to be equal.
For bench-test data, the resistances were input by manual valve settings on the test loop. The values for resistance were also inputs to the VML model and were linearized from the test data by dividing mean pressure difference by mean flow. To set the desired systemic vascular resistance (SVR) and pulmonary vascular resistance (PVR), the resistances in capillaries were changed, simulating the valve adjustments on the bench mock loop. The bronchial shunt was shut off using a high resistance value (1,000) because the mock loop being simulated did not use a bronchial shunt. Vascular compliance and inertances were referenced from other literature.3,10
The VML CFTAH pump parameters are shown in Table 1. The design point of this pump was set at 7.7 L/min flow and 86 mm Hg pressure on 2,800 rpm in the left pump and 6.5 L/min flow and 25 mm Hg pressure in the right pump. The left pump and mean right pump performance models were based on similitude properties of rotodynamic pumps. A family of head curves (pressure rise versus flow) at different speeds can be calculated, based on the shape of the head curve and the specified design point in terms of flow, pressure rise, and speed. The shape of the head curve for a specific pump is input as an equation, normalized with the design point ratios (flow/design point flow, pressure rise/design point pressure rise), and mapped to the values of (1,1). Pressure rise for all flows and pump speeds can be scaled from there (Figure 4). The constants that govern left/right pump interaction for self-regulation (C1, C2, and C3) are set empirically, as shown in Equations 1 and 2. The mechanism of self-regulation of this pump has been discussed in detail separately.17 Axial movement of the rotor is affected by pressure differences between the four pump ports and by rotational speed. This empirical relationship allows the definition of a differential pressure-gradient term that can be normalized by dividing by speed squared.
where LAP is left atrial pressure (mm Hg), RAP is right atrial pressure (mm Hg), AoP is aortic pressure (mm Hg), PAP is pulmonary arterial pressure (mm Hg), N is pump speed (krpm), and C1 is empirical weighting factor.
A scale factor for right pump flow simulates the effect of the automatic opening and closing of the right aperture in response to variation in pressure differences. This scale factor is a simple linearized approximation and varies with the normalized gradient difference, as shown in Equation 2.
where NGD is normalized gradient difference, C3 is empirical slope, and C2 is empirical y intercept.
From the CFTAH characterization test, a total of 23 hemodynamic conditions at constant speed were selected to reproduce in the VML (Table 2). SVR, PVR, and pump rotational speed were set according to the bench test; we compared the outputs (pump flow, left and right pump pressure rise, normalized pump performance, and atrial pressure difference) between results from bench testing and the VML.
Figure 5 shows the comparisons of VML and bench testing. Pump flow and left pump pressure rise were comparable (flow: y = 0.9417x + 0.3786, R2 = 0.9957; left pump pressure rise: y = 0.9335x + 3.0005, R2 = 0.996) (Figure 5A, B). The values for right pump pressure rise showed some scatter between VML and bench data (y = 0.6724x + 8.5445, R2 = 0.7084) (Figure 5C), indicating that further improvements need to be made in the right pump algorithm.
In the bench test without bronchial shunt, the left and right pumps generated the same flow rate under various conditions (Figure 6, y = 1.0062x + 0.0039, R2 = 0.997).
Figure 7 shows the normalized pump performance of the bench test (Figure 7A) and the VML (Figure 7B). As the left pump characteristic remained constant and independent of atrial pressure, the normalized pump performance curves were not changed by rotational speed or pressure differences. On the other hand, the right pump characteristic was self-regulated depending on the atrial pressure differences, so normalized right pump performance varied with the aperture opening to adjust the pump flow and the atrial pressure difference. In comparing the bench-test and VML results, the left pump showed similar pump performance curves (bench test: y = −0.67x2 + 0.05x + 14.00, R2 = 0.95 and VML: y = −0.6714x2 − 0.4601x + 14.885, R2 = 0.9992). In the right pump, VML results were within the same range of performance indicated by bench testing. This result showed that the self-regulation property of this pump was acceptably reproduced in the VML condition. Figure 8 shows the plot of atrial pressure differences from the VML and bench testing, indicating similar results, but with a difference of several millimeters of mercury in the midrange of the systemic/pulmonary gradients.
The VML was developed to simulate the interaction between the human circulatory system and a variety of MCS devices under development at our institution. Bench testing of the CFTAH by our standard mock loop was successfully reproduced by the new VML. Hemodynamic outputs were very similar in pump flow and left pump pressure rise and comparable in right pump pressure rise. The VML also reproduced the self-regulation system of this CFTAH; right pump function and atrial pressure differences were within the expected regulation range.
Mock circulatory loops are traditionally used for in vitro testing, and many institutions have developed their specific mock loop for bench testing. Koenig et al.19 made an MCL that mimics the Starling response for both normal and failing ventricles. Pantalos et al.20 also demonstrated the ability of mock circulation to produce the Frank-Starling response with physiologic hemodynamic parameters and pressure-volume relationships. Jhun et al.21 investigated effective LV unloading at different stages of heart failure over LVAD speed by using the Penn State University MCS system. Timms et al.22 made a mock loop with emerging autoregulatory features, and Ruiz et al.23 made a multichamber mock loop including the heart model, pulmonary and systemic circulation, and control, measurement, and monitoring systems. Wang et al.24 constructed a mock loop to mimic congenital heart circulation. They have developed and shown several types of mock loop and have succeeded in simulating specific physiologic conditions with them.
Numerical simulation modeling is another way to mimic human circulation under various conditions, including heart failure, Valsalva maneuver, or ventricular assist device (VAD) support. Thomas et al.9 reported findings from the lumped-parameter numerical model they used to analyze pulmonary venous flow in various hemodynamic conditions. Lu et al.16 developed a cardiovascular model to encompass human heart mechanics, a circulatory loop, baroreflex control of arterial pressure, airway mechanics, and gas transport at the alveolar-capillary membrane and simulated Valsalva maneuver. Hassani et al.12 advanced existing electrical models by increasing more segments and parameters, adding more detail to the arterial model. Korakianitis and Shi10 made an innovative numerical simulation model for heart valve dynamics. Colacino et al.8 conducted studies using numerical and experimental models, with the aim of showing that the elastance model of mock ventricles behaves according to the Starling mechanism. Currently, the numerical simulation approach is developing rapidly with increasing detail, as it is easy to share and researchers can add in the required features.
This model is also applied to MCS conditions. Mitsui et al.5 simulated the effect of an LVAD on the circulation in a numerical simulation model and showed physiologic results. Zhou et al.6 simulated the interaction with their developing LVAD and heart failure. Vollkron et al.2 applied the numerical simulation model to the rotary blood pump. Shi et al.3 simulated various type of VADs to this model, including impeller, displacement, and reciprocating pumps. Gregory et al.13 made a mathematical simulation of an existing mock loop. They showed the feasibility of designing an improved physical mock loop system. Bonnemain et al.7 developed their numerical model with an LVAD to assess possible differences in flow rates and pressure patterns depending on the location of the anastomosis and on the rotational speed of the device. Bozkurt and Safak4 developed a numerical model for describing the pressure-flow rate relationship of a new CF LVAD to evaluate the hemodynamic response of a model of dilated cardiomyopathy. Gohean et al.14 made the simulation model of the TORVAD (a toroidal design by Windmill Cardiovascular Systems, Inc., Austin, TX) and a CF VAD and compared the hemodynamic effects in a computational model of the cardiovascular system. In this report, we have shared results from our new numerical simulation model, the VML, which enables us to evaluate various hemodynamic conditions, e.g., valve dysfunction, right and left heart failure, and MCS conditions, including support from a CF VAD, BiVAD, or CFTAH.
The first report to show numerical simulation of a CFTAH was provided by Khalil et al.,25 describing the control system as a multivariable feedback unit using a mathematical model. They showed the effectiveness of the flow control system of a CFTAH with an MCL. The control system was designed to work in conjunction with the autoregulating features of the CFTAH. Cuenca-Navalon et al.26 described the design of a new hybrid MCL with electrically adjustable elements and an integrated numerical model of the baroreflex autoregulatory mechanism. Their MCL was divided into a hydraulic model, with hardware in the loop system, a control unit, and a sensor system. The ReinHeart total artificial heart system (ReinHeart TAH GmbH, Aachen, Germany) was connected to a hybrid MCL to replicate the pumping heart. Nestler et al.27 also developed a hybrid mock loop, specifically for a total artificial heart configuration, that can be used for hydraulic design, control development, and durability testing. Our CFTAH has a self-regulating mechanism; right pump performance is automatically adjusted with pressure difference and pump speed. It can therefore be reproduced in a numerical model by applying an empiric self-regulation strategy.
There were some limitations to our study. First, the VML cannot currently reproduce the speed modulation mode of the CFTAH. The CFTAH will be operated with speed modulation to provide pulsatile blood flow.28 By using the speed modulation mode, we can also obtain information regarding the hemodynamic environment of the pump, detecting incipient suction and estimating the SVR and PVR.29 We plan to add some features to the VML to the control patient monitoring. The VML enables us to obtain data including flow rate of the pump, pressure differences between pump inlets and outlets, and pressure differences between left and right atria. A second limitation is that right pump performance was not completely reproduced in the VML. We calculated right pump performance according to a self-regulation mechanism17 from the bench data in this study, but the resulting scatter indicates that we still need to improve the correlation. More data will be evaluated between in vivo experiments and the VML, and then we will find the way to reproduce right pump performance. A third limitation is that this VML study simulated an MCL run with a glycerin/water mixture. Human blood shows a different viscosity from this glycerin/water mixture depending on the hematocrit, and blood is a non-Newtonian fluid. In our experience, in a computational fluid dynamics study comparing glycerin/water with non-Newtonian blood properties, the viscosity effect on the relationship between flow, pressure rise, and speed is small because the pumping elements operate in the turbulent regime, where the inertial forces far outweigh the viscous forces (data not shown).
We successfully reproduced bench testing with an MCL of our CFTAH in the VML numerical simulation. Using this model, the self-regulation feature of right pump performance of the CFTAH was calculated effectively. We can further develop this model for future use in simulating a wide range of physiologic conditions seen in patients with MCS devices, in patient monitoring, and as an aid in MCS training.
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Keywords:Copyright © 2018 by the ASAIO
blood pumps; mechanical circulatory support; cardiovascular models; mathematical models; numerical simulation