A simulation of three dimensional oxygen transport in brain tissue with a single neuron-single capillary system by the Williford-Bruley technique.

Despite the importance of biological mass transfer, its mathematical models have been difficult to develop because of the complexity of biological systems and the lack of sufficient and efficient computational techniques to solve the resulting equations. The Williford-Bruley (W-B) Technique is a probabilistic numerical method which is found to be a better method to solve this kind of problems because of following advantages. In computation of the solution, this technique takes only mean distances of the probability distribution function instead of performing actual random walks which require enormous computation time. This property makes it simple to apply and reduces the computation time. The W-B technique can solve three dimensional time dependent diffusion-convection-reaction problems, which are very difficult to solve by other methods. The first objective of this simulation is the application of the W-B technique for solving a three dimensional time dependent bio-mass transport problem in a heterogeneous system (2, 21, 22).