The overall goal of this continuing project is to develop efficient algorithms which will permit the construction of realistic and comprehensive mathematical models that relate normal and pathological renal function to the underlying membrane transport and flow processes in the renal tubules and their associated vasculature. The primary thrust of our research during the next period will be: 1. To use our present inner medullary models to develop fairly detailed architectural models of the inner stripe of the outer medulla and then integrate these new models with our present central core and vasa recta n- nephron inner medullary models. 2. To include additional solutes and osmolytes and investigate the role of osmolyte production in the inner medulla. 3. To incorporate a more detailed representation of transmural movement of water and solutes that takes into account both cellular and paracellular pathways and also the exchange of electrolytes and water between red blood cells and plasma in the vasa recta. 4. Adapt current algorithms for serial computers, - if necessary, develop new ones based on our split system solvers - to fully exploit the parallel and vector processing capabilities of supercomputers. This is necessary to handle the size and complexity of our current and future n-nephron models. 5. If necessary - for parallel and/or vector algorithms - (a) improve stability and accuracy of numerical methods, (b) develop hierarchal solution strategies, and (c) incorporate continuation and smoothing methods. 6. To make the non-linear Schur Complement type methods developed by us readily available to other biomedical modelers, for use on minicomputers and/or workstations. These include: (a) reduced models of the whole kidney and medulla, (b) models of epithelia and isolated perfused tubules, (c) tubuloglomerular feedback response models, and (d) neural network models.