Abstract
Large amplitude waves may be generated in the aorta as a result of body impacts, as in traffic accidents. Such phenomenon is analogous, in some respects, to shock waves in a gas flowing through a rigid tube. Here the distensibility of the tube plays the role of the gas compressibility and the problem is one of interaction between the fluid and the wall. So far, most mathematical models that describe nonlinear large wave propagation in distensible tubes employ the method of characteristics. In this method the overall change across the wave can be computed directly with no need for details of the wave front. The constitutive relations of the wall material have been incorporated in this method as a tube cross section — pressure relation that neglects longitudinal stresses [l–7]. Another theory [8] for steady-state shock-structure, based on mathematical analogy with gas-dynamics shock waves, assumes the tube to be axially constrained (complete tethering). In the present study a mathematical model for large amplitude wave propagation is presented. Similar to the above methods the flow is assumed to be quasi-one dimensional. The blood vessel is treated as a membranic shell subjected to biaxial stresses. This model allows such effects as tube geometry, initial loading and boundary conditions to be accounted for as well as different constitutive relation for the wall material.
This research was supported by a grant from the United States-Israel Binational Science Foundation (BSF), Jerusalem, Israel.
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© 1982 Martinus Nijhoff Publishers, The Hague, Boston, London
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Elad, D., Kivity, Y., Foux, A., Lanir, Y. (1982). Nonlinear Wave Propagation in the Aorta with Initial Loading. In: Huiskes, R., van Campen, D.H., de Wijn, J.R. (eds) Biomechanics: Principles and Applications. Developments in Biomechanics, vol 1. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-7678-8_40
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DOI: https://doi.org/10.1007/978-94-009-7678-8_40
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