A Mathematical Model of Arteries in the Active State. Incorporation of Active Stress and Activation Parameter.

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  • 平滑筋活性状態での動脈壁の力学的挙動のモデル化　　能動的応力と活性化パラメータの導入
  • ヘイカツキン カッセイ ジョウタイ デ ノ ドウミャクヘキ ノ リキガクテキ

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Abstract

A mathematical model is proposed for various types of arteries in the active state on the loading process with an incorporation of an activation parameter, an inelastic strain and stiffening of elasticity. In this model the total stress, which is defined between the unloaded configuration and the current configuration, is divided into a passive stress and an active stress. The passive part is expressed by an incompressible isotropic strain energy density function. The active part is expressed as a fiber stress of smooth muscles whose stress-strain relationship is determined by an isometric force-length relationship with a use of the activation parameter. The inelastic strain corresponds to the deformation between the reference configuration and the unloaded configuration. Stiffening of the elastic property is considered mainly for elastic-type arteries. The simulation results for pressure-diameter relationship of arteries in the passive and active states show that the model describes the relationships in the physiological pressure range well. The stress analyses of the arterial walls show that the circumferential stress changes to a compressive one in the active state with a strong contraction and lower transmural pressure of the vessel.

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