Am J Physiol Renal Physiol 306: F284–F285, 2014; doi:10.1152/ajprenal.00560.2013.
Editorial Focus
Advancement in integrated models of renal function: closing the gap between simulation and real life Branko Braam Division of Nephrology and Immunology, Department of Medicine, and Department of Physiology, University of Alberta, Edmonton, Alberta, Canada
Address for reprint requests and other correspondence: B. Braam, Div. of Nephrology and Immunology, Dept. Medicine, 11-107 CSB, Edmonton, Alberta, Canada T6G 2G3 (e-mail: [email protected]). F284
cular 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 data about transporters and the cellular biology of transport mechanisms, such as trafficking of transporters in microvilli. Why is the model by Moss and Thomas (12a) of interest? First, few or no attempts have been reported to describe the differences in behavior of cortical vs. medullary parts of the kidney, yet some physiological theories rely heavily on the differential function of the locations in the kidney, as illustrated beautifully by the hypothesis about vascular renal regulation in the kidney in the context of heart/kidney coupling by Ito (5). Second, few reports include the simulation of major neurohumoral modulators of renal function. The authors simulate the actions of ANG II and AVP, and even simulate the response to inhibition of early and late distal reabsorption (“thiazide” and “amiloride” simulations). Thereby, they move gradually toward simulation of real life physiology and pharmacology. Besides this applause, a few considerations regarding their model can be formulated. Tubuloglomerular feedback (TGF) is modeled by a piece-wise linear function, and not by a sigmoidal relationship. This has interesting consequences: how does one model the combined effects of ANG II to enhance the maximum of the TGF response and to decrease the threshold of the loop distal delivery-single-nephron GFR relationship? The authors have partly run their model with a sigmoidal relationship and report that it performs similarly, but this does not exclude the possibility that it might be important for overall sodium excretion related to blood pressure under some (extreme) circumstances. Angiotensin can clearly and strongly enhance proximal tubular reabsorption (2, 12). In the current model, the actions of ANG II on proximal and distal reabsorption are simplified, likely due to the lack of sufficient data. For example, the additive, linear, and very strong independent distal effects of aldosterone and ANG II are based on one study (17). Furthermore, the statement that “external hormone levels appear to be chiefly responsible for the intra-renal hormone levels,” following Ichikawa’s thoughts, is likely invalid during hypertensive states or renal diseases, and may indeed also be invalid during nonpathological states. The dispute about the source of proximal tubular ANG II is ongoing, but angiotensinogen is also present in the proximal tubule (8). When one looks at the simulations of arterial pressure variations on GFR, not all the curves are intuitive (slope-plateau-slope), and might also indicate imperfections. At any rate, beauty, but also imperfection, is in the eye of the beholder, so that experts on renal tubular transport may well view other points where the model could be refined.
1931-857X/14 Copyright © 2014 the American Physiological Society
http://www.ajprenal.org
Downloaded from http://ajprenal.physiology.org/ by 10.220.33.2 on September 8, 2017
IN A RECENT ISSUE OF THE AMERICAN Journal of Physiology-Renal Physiology, 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 vas-
Editorial Focus F285
DISCLOSURES No conflicts of interest financial or otherwise, are declared by the author. AUTHOR CONTRIBUTIONS B.B. drafted manuscript; B.B. edited and revised manuscript; B.B. approved final version of manuscript. REFERENCES 1. Braam B, Cupples WA, Joles JA, Gaillard C. Systemic arterial and venous determinants of renal hemodynamics in congestive heart failure. Heart Fail Rev 17: 161–175, 2012. 2. Cogan MG. Angiotensin II: a powerful controller of sodium transport in the early proximal tubule. Hypertension 15: 451–458, 1990. 3. Deen WM, Robertson CR, Brenner BM. A model of glomerular ultrafiltration in the rat. Am J Physiol 223: 1178 –1183, 1972. 4. Holstein-Rathlou NH, Sosnovtseva OV, Pavlov AN, Cupples WA, Sorensen CM, Marsh DJ. Nephron blood flow dynamics measured by laser speckle contrast imaging. Am J Physiol Renal Physiol 300: F319 – F329, 2011. 5. Ito S. Cardiorenal syndrome: an evolutionary point of view. Hypertension 60: 589 –595, 2012.
6. Jensen PK, Christensen O, Steven K. A mathematical model of fluid transport in the kidney. Acta Physiol Scand 112: 373–385, 1981. 7. Kainer R. A functional model of the rat kidney. J Math Biol 7: 57–94, 1979. 8. Kobori H, Ozawa Y, Suzaki Y, Prieto-Carrasquero MC, Nishiyama A, Shoji T, Cohen EP, Navar LG. Young Scholars Award Lecture: Intratubular angiotensinogen in hypertension and kidney diseases. Am J Hypertens 19: 541–550, 2006. 9. Layton AT, Dantzler WH, Pannabecker TL. Urine concentrating mechanism: impact of vascular and tubular architecture and a proposed descending limb urea-Na⫹ cotransporter. Am J Physiol Renal Physiol 302: F591–F605, 2012. 10. Marsh DJ, Wexler AS, Brazhe A, Postnov DE, Sosnovtseva OV, Holstein-Rathlou NH. Multinephron dynamics on the renal vascular network. Am J Physiol Renal Physiol 304: F88 –F102, 2013. 11. Marxen M, Sled JG, Henkelman RM. Volume ordering for analysis and modeling of vascular systems. Ann Biomed Eng 37: 542–551, 2009. 12. Mitchell KD, Navar LG. Superficial nephron responses to peritubular capillary infusions of angiotensins I and II. Am J Physiol Renal Fluid Electrolyte Physiol 252: F818 –F824, 1987. 12a.Moss R, Thomas SR. Hormonal regulation of salt and water excretion: a mathematical model of whole kidney function and pressure natriuresis. Am J Physiol Renal Physiol (First published October 9, 2013). doi:10.1152/ ajprenal.00089.2013. 13. Oien AH, Aukland K. A mathematical analysis of the myogenic hypothesis with special reference to autoregulation of renal blood flow. Circ Res 52: 241–252, 1983. 14. Ryu H, Layton AT. Effect of tubular inhomogeneities on feedbackmediated dynamics of a model of a thick ascending limb. Math Med Biol 30: 191–212, 2013. 15. Stephenson JL. Concentration of urine in a central core model of the renal counterflow system. Kidney Int 2: 85–94, 1972. 16. Uttamsingh RJ, Leaning MS, Bushman JA, Carson ER, Finkelstein L. Mathematical model of the human renal system. Med Biol Eng Comput 23: 525–535, 1985. 17. van der Lubbe N, Lim CH, Fenton RA, Meima ME, Jan Danser AH, Zietse R, Hoorn EJ. Angiotensin II induces phosphorylation of the thiazide-sensitive sodium chloride cotransporter independent of aldosterone. Kidney Int 79: 66 –76, 2011. 18. Weinstein AM. A mathematical model of rat ascending Henle limb. I. Cotransporter function. Am J Physiol Renal Physiol 298: F512–F524, 2010.
AJP-Renal Physiol • doi:10.1152/ajprenal.00560.2013 • www.ajprenal.org
Downloaded from http://ajprenal.physiology.org/ by 10.220.33.2 on September 8, 2017
What avenues could be further explored with respect to whole kidney modeling? The current model is static and to be able to simulate complex pathophysiological states, it should be developed to become dynamic. This is certainly not a trivial undertaking for a sufficiently complex model. It would be very attractive to apply the model to simulate clinical conditions. A fashionable example would be the consequences of arterial and venous hemodynamic changes and neurohumoral modulation in cardiorenal failure, the complexity of which reaches beyond what can be captured by the human mind (1). In such a case, mechanisms should be developed to calibrate model parameters to information available from humans and from animal experiments. Altogether, Moss and Thomas (12a) push the agenda further with their model and hopefully trigger both discussion and enthusiasm in the renal physiological and nephrological community.
Editorial Focus
Advancement in integrated models of renal function: closing the gap between simulation and real life Branko Braam Division of Nephrology and Immunology, Department of Medicine, and Department of Physiology, University of Alberta, Edmonton, Alberta, Canada
Address for reprint requests and other correspondence: B. Braam, Div. of Nephrology and Immunology, Dept. Medicine, 11-107 CSB, Edmonton, Alberta, Canada T6G 2G3 (e-mail: [email protected]). F284
cular 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 data about transporters and the cellular biology of transport mechanisms, such as trafficking of transporters in microvilli. Why is the model by Moss and Thomas (12a) of interest? First, few or no attempts have been reported to describe the differences in behavior of cortical vs. medullary parts of the kidney, yet some physiological theories rely heavily on the differential function of the locations in the kidney, as illustrated beautifully by the hypothesis about vascular renal regulation in the kidney in the context of heart/kidney coupling by Ito (5). Second, few reports include the simulation of major neurohumoral modulators of renal function. The authors simulate the actions of ANG II and AVP, and even simulate the response to inhibition of early and late distal reabsorption (“thiazide” and “amiloride” simulations). Thereby, they move gradually toward simulation of real life physiology and pharmacology. Besides this applause, a few considerations regarding their model can be formulated. Tubuloglomerular feedback (TGF) is modeled by a piece-wise linear function, and not by a sigmoidal relationship. This has interesting consequences: how does one model the combined effects of ANG II to enhance the maximum of the TGF response and to decrease the threshold of the loop distal delivery-single-nephron GFR relationship? The authors have partly run their model with a sigmoidal relationship and report that it performs similarly, but this does not exclude the possibility that it might be important for overall sodium excretion related to blood pressure under some (extreme) circumstances. Angiotensin can clearly and strongly enhance proximal tubular reabsorption (2, 12). In the current model, the actions of ANG II on proximal and distal reabsorption are simplified, likely due to the lack of sufficient data. For example, the additive, linear, and very strong independent distal effects of aldosterone and ANG II are based on one study (17). Furthermore, the statement that “external hormone levels appear to be chiefly responsible for the intra-renal hormone levels,” following Ichikawa’s thoughts, is likely invalid during hypertensive states or renal diseases, and may indeed also be invalid during nonpathological states. The dispute about the source of proximal tubular ANG II is ongoing, but angiotensinogen is also present in the proximal tubule (8). When one looks at the simulations of arterial pressure variations on GFR, not all the curves are intuitive (slope-plateau-slope), and might also indicate imperfections. At any rate, beauty, but also imperfection, is in the eye of the beholder, so that experts on renal tubular transport may well view other points where the model could be refined.
1931-857X/14 Copyright © 2014 the American Physiological Society
http://www.ajprenal.org
Downloaded from http://ajprenal.physiology.org/ by 10.220.33.2 on September 8, 2017
IN A RECENT ISSUE OF THE AMERICAN Journal of Physiology-Renal Physiology, 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 vas-
Editorial Focus F285
DISCLOSURES No conflicts of interest financial or otherwise, are declared by the author. AUTHOR CONTRIBUTIONS B.B. drafted manuscript; B.B. edited and revised manuscript; B.B. approved final version of manuscript. REFERENCES 1. Braam B, Cupples WA, Joles JA, Gaillard C. Systemic arterial and venous determinants of renal hemodynamics in congestive heart failure. Heart Fail Rev 17: 161–175, 2012. 2. Cogan MG. Angiotensin II: a powerful controller of sodium transport in the early proximal tubule. Hypertension 15: 451–458, 1990. 3. Deen WM, Robertson CR, Brenner BM. A model of glomerular ultrafiltration in the rat. Am J Physiol 223: 1178 –1183, 1972. 4. Holstein-Rathlou NH, Sosnovtseva OV, Pavlov AN, Cupples WA, Sorensen CM, Marsh DJ. Nephron blood flow dynamics measured by laser speckle contrast imaging. Am J Physiol Renal Physiol 300: F319 – F329, 2011. 5. Ito S. Cardiorenal syndrome: an evolutionary point of view. Hypertension 60: 589 –595, 2012.
6. Jensen PK, Christensen O, Steven K. A mathematical model of fluid transport in the kidney. Acta Physiol Scand 112: 373–385, 1981. 7. Kainer R. A functional model of the rat kidney. J Math Biol 7: 57–94, 1979. 8. Kobori H, Ozawa Y, Suzaki Y, Prieto-Carrasquero MC, Nishiyama A, Shoji T, Cohen EP, Navar LG. Young Scholars Award Lecture: Intratubular angiotensinogen in hypertension and kidney diseases. Am J Hypertens 19: 541–550, 2006. 9. Layton AT, Dantzler WH, Pannabecker TL. Urine concentrating mechanism: impact of vascular and tubular architecture and a proposed descending limb urea-Na⫹ cotransporter. Am J Physiol Renal Physiol 302: F591–F605, 2012. 10. Marsh DJ, Wexler AS, Brazhe A, Postnov DE, Sosnovtseva OV, Holstein-Rathlou NH. Multinephron dynamics on the renal vascular network. Am J Physiol Renal Physiol 304: F88 –F102, 2013. 11. Marxen M, Sled JG, Henkelman RM. Volume ordering for analysis and modeling of vascular systems. Ann Biomed Eng 37: 542–551, 2009. 12. Mitchell KD, Navar LG. Superficial nephron responses to peritubular capillary infusions of angiotensins I and II. Am J Physiol Renal Fluid Electrolyte Physiol 252: F818 –F824, 1987. 12a.Moss R, Thomas SR. Hormonal regulation of salt and water excretion: a mathematical model of whole kidney function and pressure natriuresis. Am J Physiol Renal Physiol (First published October 9, 2013). doi:10.1152/ ajprenal.00089.2013. 13. Oien AH, Aukland K. A mathematical analysis of the myogenic hypothesis with special reference to autoregulation of renal blood flow. Circ Res 52: 241–252, 1983. 14. Ryu H, Layton AT. Effect of tubular inhomogeneities on feedbackmediated dynamics of a model of a thick ascending limb. Math Med Biol 30: 191–212, 2013. 15. Stephenson JL. Concentration of urine in a central core model of the renal counterflow system. Kidney Int 2: 85–94, 1972. 16. Uttamsingh RJ, Leaning MS, Bushman JA, Carson ER, Finkelstein L. Mathematical model of the human renal system. Med Biol Eng Comput 23: 525–535, 1985. 17. van der Lubbe N, Lim CH, Fenton RA, Meima ME, Jan Danser AH, Zietse R, Hoorn EJ. Angiotensin II induces phosphorylation of the thiazide-sensitive sodium chloride cotransporter independent of aldosterone. Kidney Int 79: 66 –76, 2011. 18. Weinstein AM. A mathematical model of rat ascending Henle limb. I. Cotransporter function. Am J Physiol Renal Physiol 298: F512–F524, 2010.
AJP-Renal Physiol • doi:10.1152/ajprenal.00560.2013 • www.ajprenal.org
Downloaded from http://ajprenal.physiology.org/ by 10.220.33.2 on September 8, 2017
What avenues could be further explored with respect to whole kidney modeling? The current model is static and to be able to simulate complex pathophysiological states, it should be developed to become dynamic. This is certainly not a trivial undertaking for a sufficiently complex model. It would be very attractive to apply the model to simulate clinical conditions. A fashionable example would be the consequences of arterial and venous hemodynamic changes and neurohumoral modulation in cardiorenal failure, the complexity of which reaches beyond what can be captured by the human mind (1). In such a case, mechanisms should be developed to calibrate model parameters to information available from humans and from animal experiments. Altogether, Moss and Thomas (12a) push the agenda further with their model and hopefully trigger both discussion and enthusiasm in the renal physiological and nephrological community.
