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Pressure-flow relationship in the canine left coronary artery: Study of linearity and stationarity using a time-domain representation and estimation methods

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Abstract

Linearity and stationarity of pressure-flow relationship in the circumflex coronary artery are fundamental properties which rule any mathematical description of this system. They are studied by evaluating through a quantitative criterion the error done in a linear approximation. Parameters of two different impulse response models are estimated, from data measured in the dog, with a recursive algorithm minimising a structural distance. Quantitative comparison between system and models behaviours shows that it is possible to represent the circumflex coronary functioning with a single-input/single-output linear stationary finite-memory model with a relative quadratic error less than 5% for a wide range of working conditions.

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Abbreviations

p C :

pressure at the entrance of the circumflex artery

p v :

left intra-ventricular pressure

p A :

aortic pressure

q :

flow at the entrance of the circumflex artery

h 0 :

impulse response with respect to the input (p A −p V )

h 1 :

impulse response with respect to the inputp A

h 2 :

impulse response with respect to the inputp V

h s :

structural vector of the actual system

h k :

estimate ofh s at thekth iteration

ĥ:

final estimate ofh s

p(n) :

information vector at instantn

\(\hat q\) :

model output

W i :

estimation window

W 0 :

observation window

R :

number of sampled data onW i

DW i :

relative quadratic state distance onW i

DW 0 :

relative quadratic state distance onW o

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Authors and Affiliations

  1. Laboratoire des Signaux et Systèmes (C.N.R.S.-E.S.E.), Plateau du Moulon, 91190, Gif-sur-Yvette, France

    D. Saint-Felix & G. Demoment

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  1. D. Saint-Felix
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  2. G. Demoment
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Saint-Felix, D., Demoment, G. Pressure-flow relationship in the canine left coronary artery: Study of linearity and stationarity using a time-domain representation and estimation methods. Med. Biol. Eng. Comput. 20, 231–239 (1982). https://doi.org/10.1007/BF02441360

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