Beard D A, Bassingthwaighte J B
Center for Bioengineering, University of Washington, Seattle 98195-7962, USA.
Ann Biomed Eng. 1998 Sep-Oct;26(5):775-9. doi: 10.1114/1.105.
Recent studies suggest that the tail of the washout of tracer-labeled substances from physiological systems can exhibit power-law behavior. In this work we develop a theoretical interpretation of the power-law behavior of the flow-limited washout of tracer-labeled water from the myocardium. Using minimal assumptions concerning the complicated structure of the coronary network we show that the washout from a heterogeneous flow system is given by h(t) approximately equal to A x p1 (V/t)(-beta), where beta is close to 3, p1 is the probability density of flows through the system, V is a constant volume associated with each pathway, and A is a constant. This prediction fits observed power-law washout behavior of tracer water in the heart. This theory is general enough to lead us to speculate that close examination of transport in other heterogeneity-perfused systems is likely to reveal similar power-law behavior.
近期研究表明，示踪剂标记物质从生理系统中清除的尾部可能呈现幂律行为。在这项工作中，我们对示踪剂标记水从心肌中以流量限制方式清除的幂律行为进行了理论解释。通过对冠状动脉网络复杂结构做出最少假设，我们表明异质流系统的清除情况由(h(t)\approx A\times p1(V/t)^{-\beta})给出，其中(\beta)接近3，(p1)是流经该系统的流量的概率密度，(V)是与每条路径相关的恒定体积，(A)是一个常数。这一预测符合在心脏中观察到的示踪剂水的幂律清除行为。该理论具有足够的普遍性，使我们推测对其他异质灌注系统中的传输进行仔细研究可能会揭示类似的幂律行为。
