Critical changes in the lumen of small arterial vessels

Self-sustained peristaltic waves: Explicit asymptotic solutions

“…It should be noted that Eqs. (1) and (2) and their close analogs have appeared together in previous work to calculate the fluid-wall interaction during peristaltic pumping [20][21][22]. Similarly, Eqs.…”

“…It was found that the velocity of the traveling front under conditions described above is given by A unique traveling front solution corresponding to Eq. (22) exists provided that…”

“…Curves "1", "2a", "2b" illustrate the dependences V = V 1 , V = V 2a , V = V ± 2b given by Eqs. (19), (22), and (24), respectively. Note that hysteresis is expected with variation of parameter E in the limit corresponding to V = V ± 2b (curve "2b" parameters of the transporting vessel and the transported fluid are robust, independent of the peculiarities of nonlinear function representation.…”

“…The variables introduced areε = (R − R 0 )/R 0 andp = p i − p e (1 + h 0 /R 0 ) (see Fig. 1 caption).Equation (2) arises from a circumferential stress-strain relationship given by the standard linear solid (SLS) model of the viscoelastic wall material [22,23]. A thin-shell approximation and Laplace's law [20,21] were used to rewrite the stress-strain constitutive equation in terms ofp andε.…”

Mathematical models in urinary system mechanics (review)

“…), which is interpreted as the non-existence of a cylindrical urethra lumen, that is, urethra collapse. For microvessels the approach of [82] was analyzed critically in [83]. It was shown that the existence or non-existence of solutions radically depends on the passive stress behavior for small radii, which is a subject of hypotheses.…”