Figure 16
From: A Differential Approach to Form and Site of Peptic Ulcer
Simulation of the influence of a rising mucosal conductivity (ω↗) on blood flow in the terminal vascular bed: Terminal blood flow jω(x,y) in a rectangular limited watershed area of the duodenal wall, which is only collaterally perfused. Considering the localisation of Mayo’s anemic spot such areas with a strictly retrograde flow to the muscle mantle do exist to some extent at the anterior and posterior aspect of the duodenal bulb. In the central 30 × 30 area, which has no direct transmural influx but is supplied by submucosal arteries only, mucosal flow is maintained by collateral flow alone. When local blood flow rises, adapting to an increasing metabolic demand, the effect will be more marked - in strictly collaterally supplied areas a central dip of MBF will develop. Disregarding the initial form of the collaterally supplied area it will produce a nearly circular profile at the bottom. The same effect can be accomplished by increasing wall stress (α↘). In both cases collateral flow will exclude any discontinuity of terminal flow, as long as the mucosa is vital: the effect will not be limited sharply. Initial conditions: in the 50 × 50 matrix considered there is no direct transmural influx to the central 30 × 30 square (α(x,y): = 0.001), while the surrounding (10, 10) 〈(x, y)〉 (41, 41) has a free influx (α(x,y): = 1). A uniform criss-cross-pattern of submucous arteries is assumed: (1, 1) < (x, y) < (50, 50) → λx(x,y) = λy(x,y) = 3.82 × 10−1. Mucosal metabolic demand and conductivity ω(x,y) will rise exponentially from the bottom to the top: ω(x,y): = 1 (bottom), ω(x,y): = 10 (centre), ω(x,y): = 100 (top). Numerical solution by SIMA47.
