A hydraulic constitutive closure for reduced haemodynamic models with generalised-Newtonian rheology
Abstract
Blood is shear thinning, yet reduced haemodynamic models coupled to resolved three-dimensional domains typically represent their resistive elements using fixed-viscosity Poiseuille relations, leaving the rheology inconsistent across the coupling interface. A constitutive-to-resistance closure is introduced that carries a generalised-Newtonian rheology consistently into a reduced hydraulic model. Combining the constitutive law with the Weissenberg–Rabinowitsch–Mooney–Schofield relation for steady tube flow, the nonlinear pressure–flow response is written in Poiseuille form through an effective hydraulic viscosity depending only on the wall shear stress. Because the wall shear stress follows from the pressure drop, radius and path length through the axial momentum balance, the constitutive map is independent of vessel radius and effective path length: morphometry sets the operating wall stress, rheology the flow sustained at that stress. This separation gives a direct route from a constitutive law to a nonlinear reduced resistance, and permits the rheological state to be estimated before solving the coupled problem. Closed-form mappings are obtained for the power-law, Cross, Carreau–Yasuda and Quemada laws, with an analytical tangent for implicit coupling. In a coupled 0D–3D coronary model, the rheological correction is small near the high-shear plateau but appreciable under systolic compression: constant-viscosity resistances underestimate the cycle-averaged proximal effective viscosity by 7–24% and alter mean coronary inflow by 3.6–8.5%. Pressure in the resolved domain remains within 0.05% of the constant-viscosity result, whereas wall-shear-stress and viscous-dissipation fields differ by up to 28% and 79% in relative norm. Pressure agreement can therefore conceal substantial differences in local haemodynamics, and the reduced closure alone can materially alter predicted coronary flow and wall quantities.
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BibTeX
@misc{britopacheco2026hydraulic,
title = {{A hydraulic constitutive closure for reduced haemodynamic models with generalised-Newtonian rheology}},
author = {Carlos Brito-Pacheco and Milenko Espinosa and Ernesto Castillo and Scarlett Espinoza and Alfredo Parra-Lucares and Luis Berr and Oscar Ruz},
howpublished = {HAL},
year = {2026},
month = sep,
url = {https://hal.science/hal-05749403v1},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A hydraulic constitutive closure for reduced haemodynamic models with generalised-Newtonian rheology
AU - Carlos Brito-Pacheco
AU - Milenko Espinosa
AU - Ernesto Castillo
AU - Scarlett Espinoza
AU - Alfredo Parra-Lucares
AU - Luis Berr
AU - Oscar Ruz
PY - 2026
DA - 2026/09/14
PB - HAL
UR - https://hal.science/hal-05749403v1
AB - Blood is shear thinning, yet reduced haemodynamic models coupled to resolved three-dimensional domains typically represent their resistive elements using fixed-viscosity Poiseuille relations, leaving the rheology inconsistent across the coupling interface. A constitutive-to-resistance closure is introduced that carries a generalised-Newtonian rheology consistently into a reduced hydraulic model. Combining the constitutive law with the Weissenberg–Rabinowitsch–Mooney–Schofield relation for steady tube flow, the nonlinear pressure–flow response is written in Poiseuille form through an effective hydraulic viscosity depending only on the wall shear stress. Because the wall shear stress follows from the pressure drop, radius and path length through the axial momentum balance, the constitutive map is independent of vessel radius and effective path length: morphometry sets the operating wall stress, rheology the flow sustained at that stress. This separation gives a direct route from a constitutive law to a nonlinear reduced resistance, and permits the rheological state to be estimated before solving the coupled problem. Closed-form mappings are obtained for the power-law, Cross, Carreau–Yasuda and Quemada laws, with an analytical tangent for implicit coupling. In a coupled 0D–3D coronary model, the rheological correction is small near the high-shear plateau but appreciable under systolic compression: constant-viscosity resistances underestimate the cycle-averaged proximal effective viscosity by 7–24% and alter mean coronary inflow by 3.6–8.5%. Pressure in the resolved domain remains within 0.05% of the constant-viscosity result, whereas wall-shear-stress and viscous-dissipation fields differ by up to 28% and 79% in relative norm. Pressure agreement can therefore conceal substantial differences in local haemodynamics, and the reduced closure alone can materially alter predicted coronary flow and wall quantities.
ER -