Monocyte and T-lymphocyte trans-endothelial migration in relation to cardiovascular disease: some alternative boundary conditions in a model recently proposed by Little et al. (PLoS Comput Biol 2009 5(10) e1000539)

where are the monocyte concentrations in the lumen and intima, respectively, and are the T-lymphocyte concentrations in the lumen and intima, respectively. The fundamentally linear form of these is inspired by data in Takaku et al. (2) and Klouche et al. (3). If we set , then in the context of the experimental system studied by Takaku et al. (2), with a fixed monocyte population, a proportion of which transmigrates, this leads to the differential equation:

Setting we have that:

With the initial condition this has solution:

(5) We fit this by least squares to the data in Figure 4

(35.8 10.4) 1.17 x 10 M ml s (47.2 11.9)

, using values given in Figure 4 of .] Some of the differences = , which we do because of evidence that the total number of cells does not appear to be constant.

As the results of the paper of Little et al. (1) assumed zero boundary flux of monocytes and T-lymphocytes, these possible changes in the form of the model, and to the derived coefficients, have no implications for the results and conclusions of that paper.