Fig. 4. Oxygen transfer across a compartment interface with additional diffusion barrier (cuticle). The grid point referenced by the indices i and j is located on an infinitesimal thin diffusion barrier separating the tissue from the medium compartment. This grid point is characterized by two variables, and , which represent the oxygen partial pressure at the inner and the outer side of the circular diffusion barrier, respectively. To calculate the temporal changes in and (see equations 4, 5), the following geometrical parameters are required: the cylindrical wall areas B_i-0.5, B_i and B_i+0.5, the areas of the hollow-cylindrical bases and , and the hollow-cylindrical volumes and . Three example equations for calculating these parameters are given. v_M, flow velocity in the medium compartment; P_j,i-1, P_j,i+1, , oxygen partial pressures of the neighbouring grid points; h and r, distance between two grid points in axial and radial direction.