Authors : I.S. Ike, L.E. Aneke and G.O. Mbah
Abstract: Models describing the variation of concentration of solute in the bloodstream over distance, x and time, t as blood solution moves at constant velocity through the blood vessel were formulated from first principle. The models are solved both analytically and numerically. The models were used to simulate the diffusion process in human bloodstream, determine the parameters that affect the flux density and how the system responds to unit change in these parameters. It was discovered that the concentration gradient between the bloodstream and its surrounding fluid decreases exponentially as the blood solution flows through the vessel at a constant velocity, v. Hence, concentration of solute in the bloodstream approaches that of the solute in its surrounding fluid as the distance, x travelled becomes very large. The concentration of the solute in the bloodstream also decreases with an increase in time, t and approaches that in the surrounding fluid as time spent gets large. The flux density (the time rate at which solute diffuses per unit area) decreases with distance, x since the concentration gradient decreases with distance, x and approach zero (no diffusion) as the concentration gradient approach zero. The flux density becomes zero (an equilibrium state) when the concentration of solute in bloodstream is equal to the concentration in the surrounding fluid. It was, also noticed that the flux density decreases with an increase in the velocity of the solution in the blood vessel. Hence, the flux density depends majorly on the solute concentration gradient between the bloodstream and its surrounding fluid, the distance, x travelled by the blood solution in the vessel, time, t spent and the velocity of the blood solution. The usefulness of this research have been identified to include but not limited to nutrient uptake from the blood, infections by pathogenic secretions, dialysis, drug action, gaseous exchange, etc.
I.S. Ike, L.E. Aneke and G.O. Mbah, 2013. Mathematical Modeling and Simulation of a Diffusion Process in the Human Bloodstream. Journal of Engineering and Applied Sciences, 8: 260-268.