A mathematical approach to hemodialysis

¹ Tulane Bio-Medical Computing System, Tulane University, New Orleans, Louisiana

Hemodialysis may be investigated by utilizing a laboratory system composed of a reservoir, hemodialysis unit, and bath solution. The effect of the Kolff-type dialysis unit is to permit diffusion of solute and to filter solvent and solute while pressure decreases along the length of its tubing. Kinetic equations in which the length of the dialysis tubing is the independent variable describe these processes in terms of the gradients of pressure, solvent flow rate, and solute concentration. Changes of volume and solvent concentration in the wash and reservoir solutions are functions of time and of the net effect of the dialysis unit at a given time. The complete set of general equations describes the behavior of the system. Functions for the equations of the wash and reservoir solutions are easily derived. An inflatable ellipse is selected as an appropriate geometric shape for the cross section of the dialysis tubing and functions are derived for the equations of the dialysis unit.