Evaluating the B-cell density with various activation functions using White Noise Path Integral Approach

摘要

A The White Noise Path Integral Approach is used in evaluating the B-cell density or the number of B-cell per unit volume for a basic type of immune system response based on the modeling done by Perelson and Wiegel. From the scaling principles of Perelson [1], the B-cell density is obtained where antigens and antibodies mutates and activation function f(S-S_A) is defined describing the interaction between a specific antigen and a B-cell. If the activation function f(S-S_A) is held constant, the major form of the B-cell density evaluated using white noise analysis is similar to the form of the B-cell density obtained by Perelson and Wiegel using a differential approach.A piecewise linear functionis also used to describe the activation f(S-S_A). If f(S-S_A) is zero, the density decreases exponentially. If f(S-S_A)= S-S_A-S_B, the B-cell density increases exponentially until it reaches a certain maximum value. Forf(S-S_A)= 2S_A-S_B-S, the behavior of B-cell density is oscillating and remains to be in small values.