A laplace transform-based technique for solving multiscale and multidomain problems: Application to a countercurrent hemodialyzer model

An integral-based method was employed to evaluate the behavior of a countercurrent hemodialyzer model. Solute transfer from the blood into the dialysate was described by writing mass balance equations over a section of the device. The approach provided Laplace transform concentration profiles on both sides of the membrane. Applications of the final value theorem led to the development of the effective time constants and steady-state concentrations in the exit streams. Transient responses were derived by a numerical inversion algorithm. Simulations show that the period elapsed, before reaching equilibrium in the effluents, decreased when the blood flow rate increased from 0.25 to 0.30 ml/s. The performance index decreased from 0.80 to 0.71 when the blood-to-dialysate flow ratio increased by 20% and increased from 0.80 to 0.85 when this fraction was reduced by 17%. The analytical solution predicted methadone removal in patients undergoing dialysis. Clinicians can use these findings to predict the time required to achieve a target extraction ratio.