Visiting Researcher: Tomoki Kitawaki Article List>> Introduction Various numerical computation models have been constructed for use as a biomechanical simulation model to analyze the cardiovascular system[1]. In particular, a one-dimensional-distributed constant model that expresses the flow conditions along the vascular axis has been useful in understanding vascular phenomena qualitatively [2], [3], and [4]. Recently, the usefulness of biomechanical simulation using the one-dimensional-distributed constant model has regained recognition. Since this simulation can quantitatively analyze blood flow, it is used for preoperative investigation during bypass grafting [5]. Moreover, the necessity of constructing an integrated model combining a three-dimensional model that is used to calculate the localized flow distribution and the one-dimensional model of the entire vascular system has been emphasized [6]. Although present-day computers exhibit a high performance, it is almost impossible to construct a three-dimensional simulation model of the entire circulatory system. Therefore, it is practical to analyze only a specific region of interest by using a localized three-dimensional model and analyze the behavior of the entire vascular system by using a one-dimensional model. If a one-dimensional model is used for such an analysis, it must be more accurate and quantitative with lesser approximate errors than the conventional model. In this project, in order to achieve the “Improve the accuracy of the cardiovascular system by using a one-dimensional numerical simulation model” theme, a one-dimensional model with high accuracy was constructed. Summary of this study The following 5 items are essential to improve the accuracy of the one-dimensional model. (1) Vascular structure (taper, branching, etc.) (2) Unsteadiness of blood flow (fluid viscosity) (3) Movement of the vascular wall (viscoelasticity of the blood vessels) (4) Non-Newtonian property of blood (5) Boundary conditions Among these items, three items were considered for constructing new models; these items were selected since the influences of the branching angle, unsteady viscosity, and viscoelastic property of the vascular wall on the error in the biomechanical simulation model was considered to be greater than that of the other items. (1) Influence of the branching angle The law of conservation of momentum with two axes was established while considering the radial ratio and branching angle at the vascular branch, and a new branch model was constructed. Then, the influence of the branching angle was evaluated (--> download pages (1) and (2)), (--> a list of related papers (2)). (2) Influence of unsteady viscosity A viscosity-resistance model of unsteadily oscillating blood flow in the elastic vessel was extended to construct a viscoelasticity model; subsequently, this model was imported into a one-dimensional model together with a high-speed computational method. Then, the influence of unsteady viscosity was evaluated (--> a list of papers (3) and (4)). (3) Influence of vascular wall viscoelasticity The tube law was derived from a generalized viscoelasticity model and a high-speed computational method was newly developed to compute this tube law. Then, the computed results obtained using this high-speed method were compared with the experimental results to evaluate the approximate errors of various numerical models and confirm the usefulness of the new method (--> a list of papers (5) and (6)). The abovementioned results demonstrated that the accuracy of the newly constructed models was sufficiently high, and these models could be used for vascular simulation (--> a list of papers (7)). Future implications After this study, a model of the entire circulatory simulation was constructed based on the models constructed in this study (--> a list of papers (8) and (9)); the intravital phenomena of the circulatory system are expected to be elucidated. Moreover, a study that combines the models constructed in this study with a three-dimensional model will be performed. [1] ****** [2] Snyder, M. F., Rideout, V. C. and Hillestad, R. J., Computer modeling of the human systemic arterial tree, J. Biomechanics, 1(1968), 341-53. [3] Avolio A. P., Multi-branched model of the human arterial system, Medical and Biological Engineering and Computing, 18-6 (1980), 709-18. [4] Schaaf, B. W., Abbrecht, P.H., Digital computer simulation of human systemic arterial pulse wave transmission: a nonlinear model, J. Biomechanics, 5 (1972), 345-364. [5] Wan, J., Steele, B., Spicer, S. A., Strohband, S., Feijoo, G. R., Hughes, T. J.R., and Taylor, C. A., A One-Dimensional Finite Element Method For Simulation-Based Medical Planning For Cardiovascular Disease, Computer Methods in Biomechanics and Biomedical Engineering, 5(3) (2002), 195-206. [6] Kamm, R. D., Shim, E-B., Shirai, A., Bathe, M., Younis, H., Kaazaempur-Mofrad, M. R., and Hwang, W., Multi-scale simulation in biological systems, Proceedings of the First Internation Symposium on Advanced Fluid Information, (2001), 121-124.