@article{oai:muroran-it.repo.nii.ac.jp:00008167,
 author = {HIRAYAMA, Hirofumi and 平山, 博史 and ONO,  Koichi and 小野, 功一 and YASUDA, Hisakazu and 安田, 寿一},
 journal = {室蘭工業大学研究報告. 理工編, Memoirs of the Muroran Institute of Technology. Science and engineering},
 month = {Nov},
 note = {application/pdf, A theoretical expansion of mathematical models of the cardiovascular system is developed. We established a distributed parameter model of the arterial system. In this paper we have deduced the blood flow velocities in the longitudinal and radical direction based mainly on the Womersley theory. Neglecting the non-liner terms (the convective acceleration terms) in the Navier-Stokes equation and setting linear cyclic solutions, the N-S equations were reduced to the Bessel type ordinary differential equations. By utilizing the Strokes stream function, the equation which input pressure satisfy was proved to be a Bessel type differential equation. Applying the Bessel type pressure function to the linearlyzed N-S equation, a strict form of the solution of the blood flow velocities was obtained. These solutions were confirmed to satisfy the conservative law of mass. To ensure whether these solutions satisfy the Strokes stream function another process was used to obtain the blood flow velocities. Turning to the stream function and differentiating directly of these functions also induced a series of solutions which are identical with the solutions that were obtained by solving the Bessel type N-S equation. By these strict mathematical processes, linear solutions of the blood flow velocities were obtained. To simplify the system and problems we made some assumptions and we have discussed the validity of these assumptions within the range we concern.},
 pages = {107--140},
 title = {A MATHEMATICAL THEORY FOR BLOOD FLOW DYNAMICS IN THE ARTERIAL SYSTEM an induction of blood flow velocity.},
 volume = {41},
 year = {1991},
 yomi = {ヒラヤマ, ヒロフミ and オノ, コウイチ and ヤスダ, ヒサカズ}
}