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TECHNICAL PAPERS: Fluids/Heat/Transport

# Lumped Parameter Model for Computing the Minimum Pressure During Mechanical Heart Valve Closure

[+] Author and Article Information
Brant H. Maines

CarboMedics,  A Sorin Group Company, Austin, Texas 78752

Christopher E. Brennen

California Institute of Technology, Pasadena, California 91125

J Biomech Eng 127(4), 648-655 (Mar 09, 2005) (8 pages) doi:10.1115/1.1934164 History: Received May 24, 2004; Revised March 09, 2005

## Abstract

The cavitation inception threshold of mechanical heart valves has been shown to be highly variable. This is in part due to the random distribution of the initial and final conditions that characterize leaflet closure. While numerous hypotheses exist explaining the mechanisms of inception, no consistent scaling laws have been developed to describe this phenomenon due to the complex nature of these dynamic conditions. Thus in order to isolate and assess the impact of these varied conditions and mechanisms on inception, a system of ordinary differential equations is developed to describe each system component and solved numerically to predict the minimum pressure generated during valve closure. In addition, an experiment was conducted in a mock circulatory loop using an optically transparent size 29 bileaflet valve over a range of conditions to calibrate and validate this model under physiological conditions. High-speed video and high-response pressure measurements were obtained simultaneously to characterize the relationship between the valve motion, fluid motion, and negative pressure transients during closure. The simulation model was calibrated using data from a single closure cycle and then compared to other experimental flow conditions and to results found in the literature. The simulation showed good agreement with the closing dynamics and with the minimum pressure trends in the current experiment. Additionally, the simulation suggests that the variability observed experimentally (when using $dP∕dt$ alone as the primary measure of cavitation inception) is predictable. Overall, results from the current form of this lumped parameter model indicate that it is a good engineering assessment tool.

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## Figures

Figure 1

Bileaflet mechanical heart valve model

Figure 2

Enlargement of jet region

Figure 3

Horizontal mock circulatory loop

Figure 4

Details of the acrylic valve model

Figure 5

Typical loading rates during valve closure. Symbols represent the closure time of each leaflet. (Open=leaflet proximal to pressure transducer; solid=distal leaflet).

Figure 6

Typical pressure wave forms (P2) measured ∼2mm downstream of the leaflet surface. Symbols represent the closure time of each leaflet. Open=leaflet proximal to pressure transducer; solid=distal leaflet.

Figure 7

Comparison of the predicted minimum pressure to experiment at a low flow condition

Figure 8

Comparison of the predicted minimum pressure to experiment at a high flow condition

Figure 9

Comparison of the predicted closing time to experiment

Figure 10

Comparison of the predicted minimum pressure (P2) to experiment

Figure 11

Comparison of the predicted angular position to experiment

Figure 12

Predicted angular rates at closure match experimental trends

Figure 13

Predicted minimum pressure is significantly affected by a change in initial or final conditions for a constant dP∕dt=200mmHg∕s

Figure 14

Simulation suggests that cavitation inception trends developed using the loading rate are likely to produce inconsistent results due to the variability in initial or final conditions and waveform shape. Solid=simulation; open=experimental.

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