Abstract
The Beauchemin model is a simple particle-based description of stochastic lymphocyte migration in tissue, which has been successfully applied to studying immunological questions. In addition to being easy to implement, the model is also to a large extent mathematically tractable. This article provides a comprehensive overview of both existing and new analytical results on the Beauchemin model within a common mathematical framework. Specifically, we derive the motility coefficient, the mean square displacement, and the confinement ratio, and discuss four different methods for simulating biased migration of pre-defined speed. The results provide new insight into published studies and a reference point for future research based on this simple and popular lymphocyte migration model.
Highlights
A unique property of the immune system is that it mainly consists of constantly moving cells
Simulating biased migration For our recent study of the detection limits of twophoton imaging [7], we extended the Beauchemin model for simulating three different types of biased migration, for which we used the term taxis modes [18] to indicate that such biased migration in cells usually occurs in response to an external stimulus
An important practical consequence of these results is that validation of the model against experimentally determined motility coefficient, mean square displacement data, and confinement ratio curves does no longer need to be performed by simulation, because these quantities can be calculated directly from the model parameters
Summary
A unique property of the immune system is that it mainly consists of constantly moving cells. Parameter triplets of the 3D cell random walk model that were found to best fit in vivo data by Beauchemin et al [5] along with their corresponding motility coefficients as per equation (2).
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