Preload Sensitivity with TORVAD Counterpulse Support Prevents Suction and Overpumping

Abstract

Purpose

This study compares preload sensitivity of continuous flow (CF) VAD support to counterpulsation using the Windmill toroidal VAD (TORVAD). The TORVAD is a two-piston rotary pump that ejects 30 mL in early diastole, which increases cardiac output while preserving aortic valve flow.

Methods

Preload sensitivity was compared for CF vs. TORVAD counterpulse support using two lumped parameter models of the cardiovascular system: (1) an open-loop model of the systemic circulation was used to obtain ventricular function curves by isolating the systemic circulation and prescribing preload and afterload boundary conditions, and (2) a closed-loop model was used to test the physiological response to changes in pulmonary vascular resistance, systemic vascular resistance, heart rate, inotropic state, and blood volume. In the open-loop model, ventricular function curves (cardiac output vs left ventricular preload) are used to assess preload sensitivity. In the closed-loop model, left ventricular end systolic volume is used to assess the risk of left ventricular suction.

Results

At low preloads of 5 mmHg, CF support overpumps the circulation compared to TORVAD counterpulse support (cardiac output of 3.3 L/min for the healthy heart, 4.7 with CF support, and 3.5 with TORVAD counterpulse support) and has much less sensitivity than counterpulse support (0.342 L/min/mmHg for the healthy heart, 0.092 with CF support, and 0.306 with TORVAD counterpulse support). In the closed-loop model, when PVR is increased beyond 0.035 mmHg s/mL, CF support overpumps the circulation and causes ventricular suction events, but TORVAD counterpulse support maintains sufficient ventricular volume and does not cause suction.

Conclusions

Counterpulse support with the TORVAD preserves aortic valve flow and provides physiological sensitivity across all preload conditions. This should prevent overpumping and minimize the risk of suction.

Appendix

Brief details of the cardiovascular system lumped parameter are provided here. This model is based on previously published work.12,13 Lumped parameter models of the systemic and pulmonary vessels contain two energy storage elements (representing vessel compliance $C$ and fluid inertance $L$), and one passive element (representing viscous fluid resistance $R$).

Energy storage elements can be represented by differential equations, which can be integrated over time to simulate the dynamics of the cardiovascular system. The equation for the rate of change of pressure ($P$) is a function of the compliance ($C$) and the flow in ($Q_{i}$) and out ($Q_{o}$) of the vessel.

$$\dot{P} = \frac{{Q_{i} - Q_{o} }}{C}$$

When fluid inertance elements are present in the model, the differential equation for flow in the element ($Q$) is a function of the viscous resistance ($R$), inertance of the fluid in the tube ($L$), and the pressure at the inlet ($P_{i}$) and outlet ($P_{o}$).

$$\dot{Q} = \frac{{P_{i} - P_{o} - RQ}}{L}$$

When inertial effects are neglected and there is only a passive resistance between two independent pressures, the flow becomes a dependent variable.

$$Q = \frac{{P_{i} - P_{o} }}{R}$$

The volume in the atria and ventricles are modeled following the conservation of mass principle.

$$\dot{V} = Q_{i} - Q_{o}$$

And the heart valves are represented as ideal diodes with a nonlinear orifice model,

$$Q = \left\{ {\begin{array}{*{20}c} {{\raise0.7ex\hbox{${\sqrt {P_{i} - P_{o} } }$} \!\mathord{\left/ {\vphantom {{\sqrt {P_{i} - P_{o} } } R}}\right.\kern-0pt} \!\lower0.7ex\hbox{$R$}} } & {P_{i} > P_{o} } \\ 0 & {P_{i} \le P_{o} } \\ \end{array} } \right.$$

Pressure in the atria and ventricle are defined by active and passive pressures, which are functions of volume that are modulated by the normalized time varying elastance function $e\left( t \right)$.34,38

$$P = \left[ {1 - e\left( t \right)} \right] P_{p} \left( V \right) + e\left( t \right)P_{a} \left( V \right)$$

The passive pressure ($P_{p}$) is also known as the end diastolic pressure volume relationship (EDPVR) and represents the passive elastance of the ventricle during diastole when the ventricle is not contracting and has been modeled several ways. Some studies have opted for a simple linear relationship described by a minimum ventricular elastance, which is clearly not physiologic but may suffice for simulation studies over a very limited range of ventricular preloads.21,37 Logarithmic models have also been proposed to define an initial stiffness at the unstressed volume as well as an asymptotic maximum volume determined by the pericardium and cardiac cytoskeleton.15,36 Most computational models in the literature use exponential relationship.5,20 Exponential coefficients are derived from passive filling curves obtained from excised hearts of human and animals. These curves have been shown to represent the nonlinear aspect of filling relatively well and account for increased stiffness at higher filling volumes.

The approach taken in this study makes use of principles from all models above by superimposing an exponential and linear function.7

$$P_{p} = S_{0} \left[ {r\left( {V - V_{0} } \right) + \left( {1 - r} \right)\frac{{e^{{\alpha \left( {V - V_{0} } \right)}} - 1}}{\alpha }} \right]$$

In this way, one extra term is added to the typical exponential model so that the stiffness ($S_{0}$) at the unstressed volume ($V_{0}$) can be controlled as it is done in the logarithmic model. This can be seen by determining the slope of the curve by evaluating the derivative with respect to volume at the unstressed volume.

$$S_{0} = \left. {\frac{{\partial P_{p} }}{\partial V}} \right|_{{V = V_{0} }}$$

To parameterize the passive pressure, the exponential constant ($\alpha$) is defined as well as the stiffness ($S_{0}$) at the unstressed volume. Then a single operating point through which the passive pressure curve should pass is defined ($P_{op}$ and $V_{op}$). From these, the coefficient $r$ can be found by

$$r = \frac{{\frac{{P_{op} \alpha }}{{S_{0} }} - e^{{\alpha \left( {V_{op} - V_{0} } \right)}} + 1}}{{\alpha \left( {V_{op} - V_{0} } \right) - e^{{\alpha \left( {V_{op} - V_{0} } \right)}} + 1}}$$

Table A1 provides values for healthy and heart failure conditions.

Table A1 Passive pressure (EDPVR) parameters for healthy and heart failure conditions.

The active pressure ($P_{a}$) is also known as the end systolic pressure volume relationship (ESPVR) and is assumed to be a linear function of volume with a maximum elastance $E_{m}$

$$P_{a} = E_{m} \left( {V - V_{0} } \right)$$

The model is parameterized for healthy and heart failure conditions using values described in previous publications.12,13 The ordinary differential equations (ODEs) that represent the time rate of change of the energy storage elements in the model are numerically integrated using an ODE solver in Matlab.