A fractional approach to 3D artery simulation under a regular pulse load

Juan Palomares-Ruiz; Efrén Ruelas; Flavio Muñoz; José Castro; Angel Rodríguez; Juan Palomares-Ruiz; Efrén Ruelas; Flavio Muñoz; José Castro; Angel Rodríguez

doi:10.3934/mbe.2020138

Mathematical Biosciences and Engineering

2020, Volume 17, Issue 3: 2516-2529. doi: 10.3934/mbe.2020138

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A fractional approach to 3D artery simulation under a regular pulse load

1.
Tecnológico Nacional de México/ITS de Cajeme, subdirección de posgrado e investigación, Carretera internacional a Nogales Km. 2 S/N, Ciudad Obregón, Sonora, México
2.
Pontificia Universidad Católica de Valparaíso, Escuela de Ingeniería Mecánica, Chile. Avenida Los Carrera 01567, Quilpué, Valparaíso, Chile

Received: 08 November 2019 Accepted: 19 February 2020 Published: 26 February 2020

For the diagnosis and treatment of many pathologies related to arteries, it is necessary to known their mechanical behavior. Previous investigation implement multi-layer structural models for arterial walls based on a Fung model, which can be problematic with the material stability in the convergence sense for finite element methods, issue avoided with a large number of terms in the prony series and the inclusion of relaxation function. On the other hand, this solution increase significantly the computer cost for the solution finding. In this research was implement a 3D simulation of the aorta artery, composed of three different layers that allow identifying how are distributed the stress-strain state caused by the flow pressure. A vectorized geometry was created based on medical tomography images and a fractional linear-standard viscoelastic constitutive model for solids was developed and validated. For the model adjustment was used creep-relaxation experiment data and a set of parameters, in the frequency domain, from a previous calculated complex modulus. The mechanical simulated behavior of the artery section proof that the fractional model showns an accurate representation of the simulated phenomenon, and a lower convergence time.
- Zener,
- fractional,
- hyperelastic,
- biomechanics,
- soft tissues
Citation: Juan Palomares-Ruiz, Efrén Ruelas, Flavio Muñoz, José Castro, Angel Rodríguez. A fractional approach to 3D artery simulation under a regular pulse load[J]. Mathematical Biosciences and Engineering, 2020, 17(3): 2516-2529. doi: 10.3934/mbe.2020138

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Abstract

For the diagnosis and treatment of many pathologies related to arteries, it is necessary to known their mechanical behavior. Previous investigation implement multi-layer structural models for arterial walls based on a Fung model, which can be problematic with the material stability in the convergence sense for finite element methods, issue avoided with a large number of terms in the prony series and the inclusion of relaxation function. On the other hand, this solution increase significantly the computer cost for the solution finding. In this research was implement a 3D simulation of the aorta artery, composed of three different layers that allow identifying how are distributed the stress-strain state caused by the flow pressure. A vectorized geometry was created based on medical tomography images and a fractional linear-standard viscoelastic constitutive model for solids was developed and validated. For the model adjustment was used creep-relaxation experiment data and a set of parameters, in the frequency domain, from a previous calculated complex modulus. The mechanical simulated behavior of the artery section proof that the fractional model showns an accurate representation of the simulated phenomenon, and a lower convergence time.

References

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