Construction of an Artificial Heart Pump Performance Test System

Abstract

A hydraulic loop, which simulates pressure/flow response of the human circulatory system, is needed to bench test the various versions of rotary left ventricular assist devices (LVADs). This article describes the design of such a loop and the simulated response of different physiological states, such as a healthy person in sleep, rest, and mild physical activity, and in different pathological states. The loop consists of: (1) pulsatile left and right cardiac simulators; (2) air/water tanks to model the venous and arterial compliances; (3) tygon tubes to model the venous, arterial, and other system flow resistances; and (4) a tuning clamp to model the variation in system resistance characteristics under different cardiac pressure/flow conditions. The simulated responses were compared to the data found in the literature to validate the loop performance prior to LVAD testing.

Appendix

Derivation of compliance of air tight tank

$$V_{\rm air} +V_{\rm fluid}=V_{\rm tank}=\hbox{const}$$

(2)

$$P_{\rm air} \times V_{\rm air}=nRT=\hbox{const}$$

(3)

$$ P_{\rm air}+\rho g\times h_{\rm fluid}=P_{\rm fluid}$$

(4)

Taking derivative on (2), (3) and (4), we can get

$$ \hbox{d}V_{\rm fluid}+\hbox{d}V_{\rm air}=0\Rightarrow \hbox{d}V_{\rm fluid}=-\hbox{d}V_{\rm air}$$

(5)

$$ \hbox{d}P_{\rm air}\times V_{\rm air}+P_{\rm air} \times \hbox{d}V_{\rm air}=0\Rightarrow \frac{\hbox{d}P_{\rm air}}{\hbox{d}V_{\rm air} }=-\frac{P_{\rm air} }{V_{\rm air}}$$

(6)

$$ \hbox{d}P_{\rm air} +\rho g\times \hbox{d}h_{\rm fluid}=\hbox{d}P_{\rm fluid}$$

(7)

where ρ is the density of fluid, g is the gravity acceleration, P _fluid is the pressure of fluid at the bottom of tank, and h _fluid is the height of the fluid in the tank.

Combining (5), (6) and (7), the elasticity (E) of a tank, which is the reciprocal of compliance (C), is given in Eq. (8):

$$ E=\frac{1}{C}=\frac{\hbox{d}P_{\rm fluid} }{\hbox{d}V_{\rm fluid} }=-\frac{\hbox{d}P_{\rm air}}{\hbox{d}V_{\rm air} }+\frac{\rho g}{A}=\frac{P_{\rm air}}{V_{\rm air} }+\frac{\rho g}{A}$$

(8)

where E is the elasticity of the tank, C is the compliance of the tank, P _air is the pressure of air in the tank, V _air is the volume of air in the tank, ρ is the density of the fluid in the tank, A is the area of the tank, g is the gravity acceleration. The numerical value of ${\rho g/A}$ is less than 5% of total elastance of artery or vein, thus can be neglected. The formula to calculate the compliance of an airtight tank can finally be simplified as:

$$ C=\frac{1}{E}=\frac{V_{\rm air} }{P_{\rm air} }=\frac{V_{\rm tank}-A_{\rm tank} h_{\rm fluid} }{P_{\rm fluid}-\rho gh_{\rm fluid}}.$$

(9)