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Calculations of the oxygen distribution in resting and contracting skeletal muscle are presented, based on a mathematical model and experimental data obtained on the hamster cremaster muscle [Klitzman et al., Microvasc. Res. 25:108-131 (1983)]. The model considers a slab of tissue penetrated by a regular square array of capillaries with concurrent flow. The intracapillary resistance to oxygen transport is neglected. The capillary red blood cell flux and capillary inlet oxygen tension are assumed random variables following certain probability distributions. The sensitivity of the tissue and intracapillary PO 2 to variations of these probability distributions are investigated. The mean tissue PO 2 decreases as the dispersion of the random variables increases, provided that their mean values remain constant. Hypoxic regions appear gradually, especially in the case of contracting muscle, as the dispersion increases. The effect of the number of capillaries in the sample on the resultant distribution of oxygen is studied systematically. The calculated tissue PO 2 histograms are compared with previously reported PO 2 distributions obtained experimentally for resting and contracting skeletal muscle.

A general numerical scheme for solution of two-dimensional Stokes equations in a multiconnected domain of arbitrary shape [1,2] is applied to the motion of a rigid circular cylinder between plane parallel boundaries. Numerically generated boundary-conforming coordinates are used to transform the flow domain into a domain with rectilinear boundaries. The transformed Stokes equations in vorticity-stream function form are then solved on a uniform grid using an iterative algorithm. In Part I coefficients of the resistance matrix representing the forces and torque on the cylinder due to its translational motion parallel or perpendicular to the boundaries or due to rotation about its axis are calculated. The solutions are obtained for a wide range of particle radii and positions across the channel. It is found that the force on a particle translating parallel to the boundaries without rotation exhibits a minimum at a position between the channel centerline and the wall and a local maximum on the centerline.The resistance matrix is utilized to calculate translational and angular velocities of a free particle settling under gravity in a vertical channel. It is found that the translational velocity has a maximum at some lateral position and a minimum on the centerline; the particle angular velocity is opposite in sign to that of a particle rolling along the nearer channel wall except when the gap between the particle and the wall is very small. These results are compared with existing analytical solutions for a small cylindrical particle situated on the channel centerline, and with solutions of related 3-D problems for a spherical particle in a circular tube and in a plane channel. It is shown that the behavior of cylindrical and spherical particles in a channel in many cases is qualitatively different. This is attributed to different flow patterns in these two cases. The motion of a spherical particle in a circular tube has qualitative and quantitative features similar to those for a cylindrical particle in a plane channel.