A new one-dimensional model of collapsible-tube flow taking three-dimensional flow profile into account

摘要

Most theoretical analyses on biological collapsible tubes conveying a flow represented by blood vessels have been performed using one-dimensional models (e.g., Cancelli and Pedley, 1985; Matsuzaki and Matsumoto, 1989; Ikeda and Matsuzaki, 1998). Especially, Matsuzaki et al. have used a mathematical model of a two-dimensional channel conveying a one-dimensional flow derived from an idea of a two-dimensional flow. In the two-dimensional model deformation of the channel and a flow profile in the lateral direction are assumed uniform as shown in FIg. la. However, a real tube deforms three-dimensionally to have a complicated shape and a flow through it also has a three-dimensional complicated profile (e.g., Bertram and Godbole, 1997) as drawn schematically in Fig. lb. Accrdingly, one may doubt if the two-dimensional models are either a simple model of the real tube flow or a model completely different from it.