Commun. Comput. Phys.,
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Volume 4.


Lumped Parameter Outflow Models for 1-D Blood Flow Simulations: Effect on Pulse Waves and Parameter Estimation

J. Alastruey 1*, K. H. Parker 2, J. Peiro 3, S. J. Sherwin 3

1 Department of Aeronautics, Imperial College London, South Kensington Campus, London SW7 2AZ, U.K; and Department of Bioengineering, Imperial College London, South Kensington Campus, London SW7 2AZ, U.K.
2 Department of Aeronautics, Imperial College London, South Kensington Campus, London SW7 2AZ, U.K.
3 Department of Bioengineering, Imperial College London, South Kensington Campus, London SW7 2AZ, U.K.

Received 19 October 2007; Accepted (in revised version) 10 December 2007
Available online 18 March 2008

Abstract

Several lumped parameter, or zero-dimensional (\mbox{0-D}), models of the micro-circulation are coupled in the time domain to the nonlinear, one-dimensional (\mbox{1-D}) equations of blood flow in large arteries. A linear analysis of the coupled system, together with \emph{in vivo} observations, shows that: (i) an inflow resistance that matches the characteristic impedance of the terminal arteries is required to avoid non-physiological wave reflections; (ii) periodic mean pressures and flow distributions in large arteries depend on arterial and peripheral resistances, but not on the compliances and inertias of the system, which only affect instantaneous pressure and flow waveforms; (iii) peripheral inertias have a minor effect on pulse waveforms under normal conditions; and (iv) the time constant of the diastolic pressure decay is the same in any 1-D model artery, if viscous dissipation can be neglected in these arteries, and it depends on all the peripheral compliances and resistances of the system. Following this analysis, we propose an algorithm to accurately estimate peripheral resistances and compliances from \emph{in vivo} data. This algorithm is verified against numerical data simulated using a \mbox{1-D} model network of the 55 largest human arteries, in which the parameters of the peripheral windkessel outflow models are known \emph{a priori}. Pressure and flow waveforms in the aorta and the first generation of bifurcations are reproduced with relative root-mean-square errors smaller than 3\%.

AMS subject classifications: 92C35, 35L45

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Key words: Pulse wave propagation, one-dimensional modelling, lumped parameter outflow models, time-domain coupling, arterial compliance, peripheral compliance, peripheral resistance, multiscale modelling.

*Corresponding author.
Email: jordi.alastruey-arimon@imperial.ac.uk (J. Alastruey), k.parker@imperial.ac.uk (K. H. Parker), j.peiro@imperial.ac.uk (J. Peiro), s.sherwin@imperial.ac.uk (S. J. Sherwin)
 

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