不均一性を考慮した血管の一次元格子モデルによる脈波の周期的挙動の数理的解析

摘要

A theoretical analysis for pulsatile behaviors of a blood vessel with an inhomogeneous part has been conducted by using a one-dimensional lattice model associated with the material nonlinearity of the arterial vessel wall. In the present study, from the viewpoint of mechanics, a certain part of blood vessel, which has the different configuration and mechanical properties of the arterial vessel wall, is regarded as the inhomogeneous part by a generalization. The soliton theory is applied in order to analyze the nonlinear system which describes the pulsatile behaviors of a blood vessel with an inhomogeneous part. As a result, the behaviors of the pulse wave which propagates periodically through the inhomogeneous part in the blood vessel are shown analytically. The factor which has the effects on the propagation of the pulse wave is revealed clearly. Moreover, the relations between the recurrence and the homeostatic behavior of the pulse wave are discussed theoretically.%血管壁の一部において，形態や力学的性質などとrnいった力学的性状の異変は，動脈硬化や動脈癌などのrn血管系疾患の要因ともなり，大変，深刻な問題となっrnている．それゆえ，これまでに血管壁の力学的性状rnに着目をして，血管壁の形態や力学的性質が異なる部rn位が，血管を伝播する圧力脈波に及ぼす影響を明らかrnにするために，血管の一次元格子モデルを応用した研rn究がなされている．