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One-dimensional model for propagation of a pressure wave in a model of the human arterial network: comparison of theoretical and experimental results.
J Biomech Eng 2011; 133(12):121005JB

Abstract

Pulse wave evaluation is an effective method for arteriosclerosis screening. In a previous study, we verified that pulse waveforms change markedly due to arterial stiffness. However, a pulse wave consists of two components, the incident wave and multireflected waves. Clarification of the complicated propagation of these waves is necessary to gain an understanding of the nature of pulse waves in vivo. In this study, we built a one-dimensional theoretical model of a pressure wave propagating in a flexible tube. To evaluate the applicability of the model, we compared theoretical estimations with measured data obtained from basic tube models and a simple arterial model. We constructed different viscoelastic tube set-ups: two straight tubes; one tube connected to two tubes of different elasticity; a single bifurcation tube; and a simple arterial network with four bifurcations. Soft polyurethane tubes were used and the configuration was based on a realistic human arterial network. The tensile modulus of the material was similar to the elasticity of arteries. A pulsatile flow with ejection time 0.3 s was applied using a controlled pump. Inner pressure waves and flow velocity were then measured using a pressure sensor and an ultrasonic diagnostic system. We formulated a 1D model derived from the Navier-Stokes equations and a continuity equation to characterize pressure propagation in flexible tubes. The theoretical model includes nonlinearity and attenuation terms due to the tube wall, and flow viscosity derived from a steady Hagen-Poiseuille profile. Under the same configuration as for experiments, the governing equations were computed using the MacCormack scheme. The theoretical pressure waves for each case showed a good fit to the experimental waves. The square sum of residuals (difference between theoretical and experimental wave-forms) for each case was <10.0%. A possible explanation for the increase in the square sum of residuals is the approximation error for flow viscosity. However, the comparatively small values prove the validity of the approach and indicate the usefulness of the model for understanding pressure propagation in the human arterial network.

Authors+Show Affiliations

Laboratory of Ultrasonic Electronics, Doshisha University, 1-3 Tatara-Miyakodani, Kyotanabeshi, Kyoto, 610-0321, Japan.No affiliation info availableNo affiliation info availableNo affiliation info availableNo affiliation info availableNo affiliation info available

Pub Type(s)

Comparative Study
Journal Article

Language

eng

PubMed ID

22206422

Citation

Saito, Masashi, et al. "One-dimensional Model for Propagation of a Pressure Wave in a Model of the Human Arterial Network: Comparison of Theoretical and Experimental Results." Journal of Biomechanical Engineering, vol. 133, no. 12, 2011, p. 121005.
Saito M, Ikenaga Y, Matsukawa M, et al. One-dimensional model for propagation of a pressure wave in a model of the human arterial network: comparison of theoretical and experimental results. J Biomech Eng. 2011;133(12):121005.
Saito, M., Ikenaga, Y., Matsukawa, M., Watanabe, Y., Asada, T., & Lagrée, P. Y. (2011). One-dimensional model for propagation of a pressure wave in a model of the human arterial network: comparison of theoretical and experimental results. Journal of Biomechanical Engineering, 133(12), p. 121005. doi:10.1115/1.4005472.
Saito M, et al. One-dimensional Model for Propagation of a Pressure Wave in a Model of the Human Arterial Network: Comparison of Theoretical and Experimental Results. J Biomech Eng. 2011;133(12):121005. PubMed PMID: 22206422.
* Article titles in AMA citation format should be in sentence-case
TY - JOUR T1 - One-dimensional model for propagation of a pressure wave in a model of the human arterial network: comparison of theoretical and experimental results. AU - Saito,Masashi, AU - Ikenaga,Yuki, AU - Matsukawa,Mami, AU - Watanabe,Yoshiaki, AU - Asada,Takaaki, AU - Lagrée,Pierre-Yves, PY - 2011/12/31/entrez PY - 2011/12/31/pubmed PY - 2012/5/12/medline SP - 121005 EP - 121005 JF - Journal of biomechanical engineering JO - J Biomech Eng VL - 133 IS - 12 N2 - Pulse wave evaluation is an effective method for arteriosclerosis screening. In a previous study, we verified that pulse waveforms change markedly due to arterial stiffness. However, a pulse wave consists of two components, the incident wave and multireflected waves. Clarification of the complicated propagation of these waves is necessary to gain an understanding of the nature of pulse waves in vivo. In this study, we built a one-dimensional theoretical model of a pressure wave propagating in a flexible tube. To evaluate the applicability of the model, we compared theoretical estimations with measured data obtained from basic tube models and a simple arterial model. We constructed different viscoelastic tube set-ups: two straight tubes; one tube connected to two tubes of different elasticity; a single bifurcation tube; and a simple arterial network with four bifurcations. Soft polyurethane tubes were used and the configuration was based on a realistic human arterial network. The tensile modulus of the material was similar to the elasticity of arteries. A pulsatile flow with ejection time 0.3 s was applied using a controlled pump. Inner pressure waves and flow velocity were then measured using a pressure sensor and an ultrasonic diagnostic system. We formulated a 1D model derived from the Navier-Stokes equations and a continuity equation to characterize pressure propagation in flexible tubes. The theoretical model includes nonlinearity and attenuation terms due to the tube wall, and flow viscosity derived from a steady Hagen-Poiseuille profile. Under the same configuration as for experiments, the governing equations were computed using the MacCormack scheme. The theoretical pressure waves for each case showed a good fit to the experimental waves. The square sum of residuals (difference between theoretical and experimental wave-forms) for each case was <10.0%. A possible explanation for the increase in the square sum of residuals is the approximation error for flow viscosity. However, the comparatively small values prove the validity of the approach and indicate the usefulness of the model for understanding pressure propagation in the human arterial network. SN - 1528-8951 UR - https://www.unboundmedicine.com/medline/citation/22206422/One_dimensional_model_for_propagation_of_a_pressure_wave_in_a_model_of_the_human_arterial_network:_comparison_of_theoretical_and_experimental_results_ L2 - http://biomechanical.asmedigitalcollection.asme.org/article.aspx?doi=10.1115/1.4005472 DB - PRIME DP - Unbound Medicine ER -