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Research Papers

A Robust and Subject-Specific Hemodynamic Model of the Lower Limb Based on Noninvasive Arterial Measurements

[+] Author and Article Information
Laurent Dumas

Professor
Lab. de Mathématiques de Versailles,
CNRS,
UVSQ,
Université Paris-Saclay,
Versailles 78035, France
e-mail: laurent.dumas@uvsq.fr

Tamara El Bouti

MINES ParisTech PSL,
Centre D'efficacité Énergétique des Systèmes,
5 rue Léon Blum,
Palaiseau 91120, France
e-mail: tamara.el_bouti@mines-paristech.fr

Didier Lucor

LIMSI,
CNRS,
Université Paris-Saclay,
Campus Universitaire,
bât 508, Rue John von Neumann,
Orsay Cedex F-91405, France
e-mail: didier.lucor@limsi.fr

1Corresponding author.

Manuscript received April 4, 2016; final manuscript received September 19, 2016; published online November 4, 2016. Assoc. Editor: Alison Marsden.

J Biomech Eng 139(1), 011002 (Nov 04, 2016) (11 pages) Paper No: BIO-16-1133; doi: 10.1115/1.4034833 History: Received April 04, 2016; Revised September 19, 2016

Cardiovascular diseases are currently the leading cause of mortality in the population of developed countries, due to the constant increase in cardiovascular risk factors, such as high blood pressure, cholesterol, overweight, tobacco use, lack of physical activity, etc. Numerous prospective and retrospective studies have shown that arterial stiffening is a relevant predictor of these diseases. Unfortunately, the arterial stiffness distribution across the human body is difficult to measure experimentally. We propose a numerical approach to determine the arterial stiffness distribution of an arterial network using a subject-specific one-dimensional model. The proposed approach calibrates the optimal parameters of the reduced-order model, including the arterial stiffness, by solving an inverse problem associated with the noninvasive in vivo measurements. An uncertainty quantification analysis has also been carried out to measure the contribution of the model input parameters variability, alone or by interaction with other inputs, to the variation of clinically relevant hemodynamic indices, here the arterial pulse pressure. The results obtained for a lower limb model, demonstrate that the numerical approach presented here can provide a robust and subject-specific tool to the practitioner, allowing an early and reliable diagnosis of cardiovascular diseases based on a noninvasive clinical examination.

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Figures

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Fig. 1

Simplified schematic of the arterial network of the left lower limb (arterial lengths and diameters are not representative of real scales)

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Fig. 2

Available experimental cross section and velocity profiles for subject P1 and P2: (a) subject P1 and (b) subject P2

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Fig. 3

Layout of a one-dimensional compliant artery

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Fig. 4

Schematic of an arterial bifurcation condition

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Fig. 5

Numerical (solid curves) luminal cross section (top row) and velocity (bottom row) profiles compared to clinical data (dashed curves) for subject P1 with generic parameters

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Fig. 6

Velocity error function: minimizing the amplitude variations and the temporal phase shift between the numerical and measured velocity profiles

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Fig. 7

Evolution of the error function (normalized by its maximum value) with respect to the number of evaluations during a CMA-ES process (subject P1)

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Fig. 8

Numerical luminal cross section and velocity profiles compared to clinical data (dashed curves) for subject P1 with optimal parameters

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Fig. 9

Numerical luminal cross section and velocity profiles compared to clinical data (dashed curves) for subject P1 with optimal parameters obtained with the error function defined by Err1

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Fig. 10

Numerical section and velocity profiles compared to clinical data (dashed curves) for subject P1 with optimal parameters obtained with the error function defined by Err2

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Fig. 11

Numerical section and velocity profiles compared to clinical data (dashed curves) for subject P1 with optimal parameters obtained with the error function defined by Err3

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Fig. 12

Subject P1: first- and second-order Sobol’ coefficients contribution to pulse pressure (PP) for the first UQ study

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Fig. 13

Subject P1: First- and second-order Sobol’ coefficients contribution to pulse pressure (PP) for the second UQ study

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Fig. 14

Subject P1: First- and second-order Sobol’ coefficients contribution to pulse pressure (PP) for the third UQ study

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