Advancement in integrated models of renal function: closing the gap between simulation and real life

Abstract

IN A RECENT ISSUE OF THE AMERICAN Journal of Physiology-RenalPhysiology, Moss and Thomas (12a) present a whole kidney lumped mathematical model that incorporates glomerular and tubular function, differentiates cortical and medullary function, and describes vascular and reabsorptive characteristics of the kidney. The model explores regulation of renal function by angiotensin II (ANG II) and antidiuretic hormone (ADH) and simulates actions of a thiazide and of amiloride. This audacious model of integrated renal function altogether is quite successful in simulating renal function, albeit with some caveats. There have been surprisingly few attempts to simulate overall renal function in the literature, yet we are in such strong need of modeling for a variety of reasons. Before returning to this, let us review briefly how mathematical modeling of renal function has developed from the perhaps biased eyes of a clinician/ physiologist.Why is trying to formulate mathematical models important? Transitioning from experimental data addressing a specific hypothesis to induced theories is one step; however, formal description of the theory might reveal inconsistencies. It is exactly at this point that physiology, based on observation and physics, meets mathematics, based on axioms and logic. As a consequence, a mathematical model will challenge the consistency of physiological theories. Modeling can also be used to simulate, with the objective of learning about the behavior of physiological systems, which are too complex to be handled by the human brain. This can be purely out of scientific interest to see how closely the composite system relates to observational real life data, or for education. Last, models may be used in a predictive or prognostic fashion (in fact also a form of simulation). The latter requires intense verification and validation.When one inspects the literature of the last approximately 40 years on modeling and renal function, a number of interesting observations can be made. First, in the initial years of modeling and computer simulations, there was relatively high interest in attempting to simulate the whole kidney (e.g., Refs. 6,7,16). At some point, it became clear that the models needed more detail, and the model of glomerular filtration by Deen et al. (3) is exemplary for this refinement (3). Since then, there have been progressive refinements in models of the concentration mechanism (9, 15), of autoregulation and more specifically of tubuloglomerular feedback (13,14), and of tubular reabsorption of the various parts of the nephron (e.g., Ref. 18). One area that is being developed is the coupling of function between neighboring nephrons or groups of nephrons (10), for which data are currently being generated using new technology (Laser Speckle imaging) (4). Similarly, the relationship between vascular anatomy and hemodynamic function is being investigated by improving the technology of microcomputerized tomography (11). Modeling has not yet been applied with respect to the large amount of molecular d...