A multiple-nephron inner medullary model is extended to include the ou
ter medulla. The number of solutes modeled is also increased to includ
e osmolyte in the central compartment. Two efficient parallel algorith
ms are described for solving the systems of differential and algebraic
equations arising in mathematical models of solute and water flow alo
ng the tubules with permeable walls. We show that both algorithms appr
oach a perfect speedup rate when modeling a large number of nephrons.