Key result
The proposed mathematical model adequately describes pressure-diameter relationships in the physiological range and shows that circumferential stress changes to compressive stress in the active state.
A proposed mathematical model of arteries in the active state adequately describes pressure-diameter relationships in the physiological range.
A mathematical model for various types of arteries in the active state is proposed with the incorporation of an activation parameter, an inelastic strain and stiffening of elasticity. The total stress is divided into a passive stress and an active stress. The passive stress is expressed by an incompressible isotropic strain energy density function. The active stress is expressed as a fiber stress of smooth muscles with the use of the activation parameter and an isometric force-length relationship. The inelastic strain corresponds to the deformation between the reference configuration and the unloaded configuration. Stiffening of elasticity is considered mainly for elastic-type arteries. The simulation results show that the model adequately describes the pressure-diameter relationships in the physiological range. The stress analyses of the arterial walls show that the circumferential stress changes to compressive stress in the active state with a strong contraction and a lower transmural pressure of the vessel.
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Hiroshi Yamada (1999) studied this question. Mathematical model of arteries was evaluated on Pressure-diameter relationships and stress analyses. The proposed mathematical model adequately describes pressure-diameter relationships in the physiological range and shows that circumferential stress changes to compressive stress in the active state.
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