Revisiting the pressure-area relation for the flow in elastic tubes: Application to arterial vessels

R. Absi

Abstract: For the description of the flow behaviour in elastic tubes as arterial vessels, we need a relationship between the transmural (internal minus external) pressure p_tm and the variation in the cross-sectional area A (or diameter), i.e., the pressure-area p-A constitutive relation. However, a literature review shows different relations. In this study, the method based on the linear theory of elasticity is revisited. A new pressure-area p-A relation is proposed. Results for the variation of cross-sectional area, arterial compliance C_c and distensibility D_i are presented. To define a unique threshold value for the applicability of the former equations, all results are presented in dimensionless form using the parameter β_1= E h_0/R_0 (where E is Young’s Modulus, h_0 and R_0 are respectively the vessel wall thickness and the internal radius at p_tm=0). Comparisons with the so-called linear and non-linear p-A equations show that all results are similar for p_tm/β_1 < 0.05. Our results indicate that the former equations could be used with an accepted gap until p_tm/β_1=0.1. However, the inaccuracy increases with p_tm and at p_tm/β_1=0.2, the difference is of 26.7% and 24.6% respectively for the linear and non-linear relations. Proposed equations were applied to arterial vessels with p_tm=150mmHg for radius from 0.8 to 6 mm. Results show an increase in the diameter of 4% for R_0=0.8mm while it is of 30% for R_0=6mm.

Series on Biomechanics, Vol.32, No.1 (2018), 47-59

Series on Biomechanics, Vol.32, No.1 (2018), 47-59

Keywords: arterial vessels; compliance; elastic tubes; Pressure-area relation; transmural pressure

Date published: 2018-05-18

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