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Research Papers

Inertance Estimation in a Lumped-Parameter Hydraulic Simulator of Human Circulation

[+] Author and Article Information
Ettore Lanzarone

e-mail: ettore.lanzarone@cnr.it

Fabrizio Ruggeri

Istituto di Matematica Applicata e Tecnologie Informatiche (IMATI),
Italian National Research Council (CNR),
Via Bassini 15,
Milan20133, Italy

1Corresponding author.

Contributed by the Bioengineering Division of ASME for publication in the JOURNAL OF BIOMECHANICAL ENGINEERING. Manuscript received January 4, 2013; final manuscript received March 22, 2013; accepted manuscript posted April 4, 2013; published online May 10, 2013. Assoc. Editor: Tim David.

J Biomech Eng 135(6), 061012 (May 10, 2013) (17 pages) Paper No: BIO-13-1005; doi: 10.1115/1.4024138 History: Received January 04, 2013; Revised March 22, 2013; Accepted April 04, 2013

Pulsatile mock loop systems are largely used to investigate the cardiovascular system in vitro. They consist of a pump, which replicates the heart, coupled with a lumped-parameter hydraulic afterload, which simulates vasculature. An accurate dimensioning of components is required for a reliable mimicking of the physiopathological behavior of the system. However, it is not possible to create a component for the afterload inertance, and inertance contributions are present in the entire circuit. Hence, in the literature, inertance is neglected or qualitatively evaluated. In this paper, we propose two quantitative methods (Maximum-likelihood estimation (MLE) and Bayesian estimation) for estimating afterload inertance based on observed pressure and flow waveforms. These methods are also applied to a real mock loop system. Results show that the system has an inertance comparable with the literature reference value of the entire systemic circulation, and that the expected variations over inlet average flow and pulse frequency are in general confirmed. Comparing the methods, the Bayesian approach results in higher and more stable estimations than the classical MLE.

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Figures

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Fig. 1

Sketch of the mock loop system: main components (pumping system and hydraulic afterload) with an atrial reservoir downstream the afterload to manage volumes (a). Lumped parameter model of the systemic circulation in the RCR configuration without inertance (b) and in the RLRC configuration with the inertance L in series to the aortic resistance Rc (c).

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Fig. 2

Photography of the analyzed afterload, with indicated the inlet and the outlet of flow, together with the position of the three lumped parameters [33]

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Fig. 3

Pressure drop per unit length (ΔP/l) in function of mean fluid velocity over section (v) measured on the test resistance under continuous flow (a), and corresponding values of specific resistance ρ (b)

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Fig. 4

Averaged data profiles of flow and pressure adopted for the estimations in the five considered experimental conditions: data profiles without moving average (dotted line) and data filtered with a five-points moving average (continuous line)

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Fig. 6

MCMC samples of λ2 as function of the corresponding sample L0 in the same iteration, obtained from JAGS. Plots refer to the five configurations with five-point average.

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Fig. 7

Pressure waveform simulation for the configuration at 5 L/min and 60 bpm, with five-point average: fixed parameters L0 and λ equal to their MLE estimator L∧0 and λ∧ (a), values extracted from their Bayesian posterior density at each time instant ti (b), and fixed parameters L0 and λ equal to L∧0 × 10 and λ∧ (c)

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Fig. 5

Traces and posterior densities of L0 and λ2 obtained from JAGS in the five configurations with five-point average

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