Finite element analysis of blood flow through biological tissue

Vankan, W.J.; Huyghe, Jmrj Jacques; Janssen, JD Jan; Huson, A.; Hacking, Wim J.G.; Schreiner, Wolfgang

doi:10.1016/s0020-7225(96)00108-5

Cited by 49 publications

(27 citation statements)

References 16 publications

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“…Blood flow is described by spatial components and a hierarchical component. The latter corresponds to the physiological quantity of regional perfusion (ml/(s 100 g)) (Huyghe et al, 1989, Vankan et al, 1997b. Equations for conservation of solid mass, conservation of fluid mass per unit of x , and conservation of momentum for the mixture have been formulated (Vankan et al, 1997a):…”

Section: The Fe Modelmentioning

confidence: 99%

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Mechanical blood-tissue interaction in contracting muscles

Vankan

Huyghe

Donkelaar

et al. 1998

Journal of Biomechanics

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A finite element (FE) model of blood perfused biological tissue has been developed. Blood perfusion is described by fluid flow through a series of 5 intercommunicating vascular compartments that are embedded in the tissue. Each compartment is characterized by a blood flow permeability tensor, blood volume fraction and vessel compliance. Local non-linear relationships between intra-extra vascular pressure difference and blood volume fraction, and between blood volume fraction and the permeability tensor, are included in the FE model. To test the implementation of these non-linear relations, FE results of blood perfusion in a piece of tissue that is subject to increased intramuscular pressure, are compared to results that are calculated with a lumped parameter (LP) model of blood perfusion. FE simulation of blood flow through a contracting rat calf muscle is performed. The FE model used in this simulation contains a transversely isotropic, non-linearly elastic description of deforming muscle tissue, in which local contraction stress is prescribed as a function of time. FE results of muscle tension, total arterial inflow and total venous outflow of the muscle during contraction, correspond to experimental results of an isometrically and tetanically contracting rat calf muscle.

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Section: The Fe Modelmentioning

confidence: 99%

“…If, as an approximation, Poiseuillian flow is assumed on the level of the individual vessels (e.g., Huyghe and van Campen, 1995;Vankan et al, 1997b), the permeability tensor is related to the fourth power of the vessel diameters. Hence, the following relation is used:…”

Section: The Fe Modelmentioning

confidence: 99%

Mechanical blood-tissue interaction in contracting muscles

Vankan

Huyghe

Donkelaar

et al. 1998

Journal of Biomechanics

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“…Various studies using this model have been presented in the context of porous media heat transfer, as described by Pop and Ingham (2001). Significant works include those by Preziosi and Farina (2002) who studied mass exchange using an extended Darcy model, Vankan et al (1997) who considered non-Darcy transport in blood perfused tissue and Sorek and Sideman (1986) who analyzed blood flow in cardiac vessels using a Darcy-Forchheimer model. Recently, Bhargava et al (2007) used the Darcy-Forchheimer model to analyze pulsating magnetohydrodynamic blood flow and species diffusion in a porous medium channel.…”

Section: Introductionmentioning

confidence: 99%

Mathematical Modeling of Magneto Pulsatile Blood Flow Through a Porous Medium with a Heat Source

Sharma¹,

Sharma²,

Gaur³

et al. 2015

International Journal of Applied Mechanics and Engineering

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In the present study a mathematical model for the hydro-magnetic non-Newtonian blood flow in the non-Darcy porous medium with a heat source and Joule effect is proposed. A uniform magnetic field acts perpendicular to the porous surface. The governing non-linear partial differential equations have been solved numerically by applying the explicit finite difference Method (FDM). The effects of various parameters such as the Reynolds number, hydro-magnetic parameter, Forchheimer parameter, Darcian parameter, Prandtl number, Eckert number, heat source parameter, Schmidt number on the velocity, temperature and concentration have been examined with the help of graphs. The present study finds its applications in surgical operations, industrial material processing and various heat transfer operations.

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“…Concerning biological applications, averaging techniques have been employed in different contexts. For instance, mixture theory has been used to model blood flow in a hierarchy of vessels [6]; and volume averaging techniques have been successfully applied in several problems related to biofluids and bioheat exchanges [7], not to mention the contributions of asymptotic analysis to biomechanics. Yet, the topic of interface conditions between heterogeneous subregions, such as those between microvascular networks and parent large vessels still needs further investigations.…”

Section: Introductionmentioning

confidence: 99%

Asymptotic-numerical derivation of the Robin type coupling conditions for the macroscopic pressure at a reservoir–capillaries interface

D’Angelo¹,

Panasenko²,

Quarteroni³

2013

Applicable Analysis

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In this article the Stokes equations are considered in a domain simulating a capillary bed system. The capillaries are supposed to be thin, parallel and periodic. An asymptotic approximation is constructed. The macroscopic pressure satisfies a Robin interface condition whose coefficients are calculated numerically through a finite element approximation of a boundary layer problem, which is inspired to a domain decomposition technique

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Finite element analysis of blood flow through biological tissue

Cited by 49 publications

References 16 publications

Mechanical blood-tissue interaction in contracting muscles

Mechanical blood-tissue interaction in contracting muscles

Mathematical Modeling of Magneto Pulsatile Blood Flow Through a Porous Medium with a Heat Source

Asymptotic-numerical derivation of the Robin type coupling conditions for the macroscopic pressure at a reservoir–capillaries interface

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