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Research Papers

Design and Subspace System Identification of an Ex Vivo Vascular Perfusion System

[+] Author and Article Information
Mohammed S. El-Kurdi

Department of Surgery, Division of Vascular Surgery, University of Pittsburgh, Suite 200, Bridgeside Point, Pittsburgh, PA 15219; Department of Bioengineering, University of Pittsburgh, Pittsburgh, PA 15219; McGowan Institute for Regenerative Medicine, University of Pittsburgh, 100 Technology Drive, Pittsburgh, PA 15219

Jeffrey S. Vipperman

Department of Mechanical Engineering and Material Science, and Department of Bioengineering, University of Pittsburgh, Pittsburgh, PA 15219

David A. Vorp1

Department of Surgery, Division of Vascular Surgery, University of Pittsburgh, Suite 200, Bridgeside Point, Pittsburgh, PA 15219; Department of Bioengineering, University of Pittsburgh, Pittsburgh, PA 15219; McGowan Institute for Regenerative Medicine, University of Pittsburgh, 100 Technology Drive, Pittsburgh, PA 15219vorpda@upmc.edu

1

Corresponding author.

J Biomech Eng 131(4), 041012 (Feb 12, 2009) (8 pages) doi:10.1115/1.3072895 History: Received November 29, 2007; Revised November 23, 2008; Published February 12, 2009

Abstract

Numerical algorithms for subspace system identification (N4SID) are a powerful tool for generating the state space (SS) representation of any system. The purpose of this work was to use N4SID to generate SS models of the flowrate and pressure generation within an ex vivo vascular perfusion system (EVPS). Accurate SS models were generated and converted to transfer functions (TFs) to be used for proportional integral and derivative (PID) controller design. By prescribing the pressure and flowrate inputs to the pumping components within the EVPS and measuring the resulting pressure and flowrate in the system,_four TFs were estimated;_two for a flowrate controller ($HRP,f$ and $HRPP,f$) and two for a pressure controller ($HRP,p$ and $HRPP,p$). In each controller,_one TF represents a roller pump ($HRP,f$ and $HRP,p$),_and the other represents a roller pump and piston in series ($HRPP,f$ and $HRPP,p$). Experiments to generate the four TFs were repeated five times $(N=5)$ from which average TFs were calculated. The average model fits, computed as the percentage of the output variation (to_the_prescribed_inputs) reproduced by the model, were $94.93±1.05%$ for $HRP,p$, $81.29±0.20%$ for $HRPP,p$, $94.45±0.73%$ for $HRP,f$, and $77.12±0.36%$ for $HRPP,f$. The simulated step, impulse, and frequency responses indicate that the EVPS is a stable system and can respond to signals containing power of up to 70_Hz.

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Figures

Figure 1

Modifications made to render our earlier generation vascular perfusion system more compact (a) so that it fits within a laminar flow hood (b). Note the stacked vessel housing chambers and single laser micrometer in (b), reducing the size of the two independent flow loops in (a). (c) is a photograph of the components within the closed-loop ex vivo perfusion system. The bulk flow was generated using a Masterflex L/S computerized roller pump (c(a)). A pulse dampener (c(b)) was added downstream to remove the very high-frequency perturbations generated by the roller pump. Higher frequency components of the physiologic arterial pressure and flowrate waveforms were generated using a custom-built piston/cylinder device (c(c)). A one-way valve (c(d)), was placed between the pulse dampener and the piston to inhibit the flow or pressure from the piston to be dissipated by the pulse dampener. A fluid reservoir (c(e)) completes the closed-loop system. (d) is a close-up picture of the piston/cylinder assembly. The components are held together with a custom-built frame (d(a)). The voice coil (d(b)) is coupled to a shaft (d(c)) that translates linearly within the bearing (d(d)). At the end of the shaft, a piston head (d(e)) is connected to a water tight rolling diaphragm (d(f)) that allows the piston head to have frictionless motion within the cylinder (d(g)). The voice coil is driven by analog signals sent to its own servo-amplifier (d(h)). Also seen are the pressure monitor (d(i)) and the tubing flowmeter (d(j)) used to process and transmit the pressure and flow transducer signals, respectively, to the data acquisition system.

Figure 2

Physiologic arterial pressure (a) and flowrate (b) waveforms recorded from a pig using a 150 Hz sampling frequency

Figure 3

(a) The step and impulse responses suggest that HRP,p has very slow overdamped and open-loop-stable poles. (b) The frequency response suggests that HRP,p is low frequency and has a bandwidth of approximately 0.1 Hz. (c) The step and impulse responses suggest that HRPP,p appears to have much faster, slightly underdamped, but open-loop-stable poles. (d) The frequency response suggests that HRPP,p has a band pass filter centered at approximately 37.5 Hz.

Figure 4

(a) The step and impulse responses show that HRP,f has overdamped and open-loop-stable poles. (b) The frequency response suggests that HRP,f has a bandwidth of approximately 2 Hz but also responds well from 18 Hz to 30 Hz. (c) The step and impulse responses show that HRPP,f appears to have slightly underdamped, but open-loop-stable poles. (d) The frequency response suggests that HRPP,f has a bandwidth of approximately 15 Hz that is centered about 22 Hz, with good response also observed in the vicinity of 70 Hz.

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