Evaluation of the concentric-circles method for estimating capillary-tissue diffusion distances

The concentric-circles method for estimating the complete distribution of distances from any point in the tissue of animals to the nearest capillary was evaluated. Models representing capillaries in transverse sections of muscle tissue were devised, using dots at various densities in ordered, random, or contagious (clustered) arrays. The distribution of distances from random points to the nearest capillary in each model was derived mathematically. These values were compared to values estimated by a method using sets of concentric circles placed over the models. In each set of circles, the smallest circle containing a capillary was recorded. The concentric-circles method generated estimates of median and maximal distances to the nearest capillary, and provided complete distributions of distances that were statistically similar to predictions, and deviated from predictions by an average of less than 10%.