title: Modeling Transport and Flow Regulatory Mechanisms of the Kidney.
abstract: The kidney plays an indispensable role in the regulation of whole-organism water balance, electrolyte balance, and acid-base balance, and in the excretion of metabolic wastes and toxins. In this paper, we review representative mathematical models that have been developed to better understand kidney physiology and pathophysiology, including the regulation of glomerular filtration, the regulation of renal blood flow by means of the tubuloglomerular feedback mechanisms and of the myogenic mechanism, the urine concentrating mechanism, and regulation of renal oxygen transport. We discuss how such modeling efforts have significantly expanded our understanding of renal function in both health and disease.
authors.affiliation: Department of Mathematics, Duke University, P.O. Box 90320, Durham, NC 27708-0320, USA.
authors.forename: Anita T
authors.initials: AT
authors.lastname: Layton
references.citation: Am J Physiol Renal Physiol. 2008 Jun;294(6):F1306-14
references.pmid: 18417543
references.citation: Am J Physiol Regul Integr Comp Physiol. 2005 May;288(5):R1143-59
references.pmid: 15677526
references.citation: Am J Physiol Renal Physiol. 2011 Mar;300(3):F669-81
references.pmid: 21190949
references.citation: Am J Physiol Renal Physiol. 2011 Nov;301(5):F1047-56
references.pmid: 21753076
references.citation: Am J Physiol Renal Physiol. 2004 Jan;286(1):F38-45
references.pmid: 14519595
references.citation: Am J Physiol Renal Physiol. 2000 Feb;278(2):F287-301
references.pmid: 10662733
references.citation: Biophys J. 1986 Nov;50(5):805-13
references.pmid: 3790686
references.citation: Am J Physiol Regul Integr Comp Physiol. 2008 Nov;295(5):R1502-11
references.pmid: 18685073
references.citation: J Physiol. 1997 Dec 1;505 ( Pt 2):493-501
references.pmid: 9423188
references.citation: Am J Physiol Renal Physiol. 2000 Dec;279(6):F1139-60
references.pmid: 11097634
references.citation: Biophys J. 1975 Sep;15(9):861-86
references.pmid: 1237326
references.citation: Biophys J. 1976 Nov;16(11):1273-86
references.pmid: 974220
references.citation: Am J Physiol Renal Physiol. 2010 Apr;298(4):F962-72
references.pmid: 20042460
references.citation: Am J Physiol. 1982 Aug;243(2):F167-72
references.pmid: 6287850
references.citation: Am J Physiol Renal Physiol. 2012 Jul 15;303(2):F229-39
references.pmid: 22496414
references.citation: Kidney Int Suppl. 1987 May;20:S25-39
references.pmid: 3298801
references.citation: Am J Physiol Renal Physiol. 2004 Oct;287(4):F767-74
references.pmid: 15187004
references.citation: Am J Physiol Renal Physiol. 2006 Jun;290(6):F1355-66
references.pmid: 16380456
references.citation: Math Biosci. 1994 Feb;119(2):127-67
references.pmid: 8142694
references.citation: Am J Physiol Renal Physiol. 2006 Jul;291(1):F79-97
references.pmid: 16204416
references.citation: Am J Physiol Renal Physiol. 2011 Jun;300(6):F1339-52
references.pmid: 21367922
references.citation: Am J Physiol. 1997 Oct;273(4):F635-49
references.pmid: 9362341
references.citation: Bull Math Biol. 2006 Oct;68(7):1625-60
references.pmid: 16967257
references.citation: Am J Physiol Renal Physiol. 2010 Sep;299(3):F616-33
references.pmid: 20534869
references.citation: J Clin Invest. 1974 Feb;53(2):393-402
references.pmid: 11344552
references.citation: Am J Physiol. 1984 Jul;247(1 Pt 2):R89-99
references.pmid: 6331210
references.citation: Am J Physiol. 1994 Jan;266(1 Pt 2):F1-12
references.pmid: 8304474
references.citation: Am J Physiol. 1991 Nov;261(5 Pt 2):F904-19
references.pmid: 1951721
references.citation: Am J Physiol Renal Physiol. 2009 Aug;297(2):F517-36
references.pmid: 19403646
references.citation: Acta Physiol (Oxf). 2011 Jul;202(3):361-78
references.pmid: 21054810
references.citation: Am J Physiol Renal Physiol. 2003 Nov;285(5):F972-89
references.pmid: 12837687
references.citation: Circ Res. 2002 Jun 28;90(12):1316-24
references.pmid: 12089070
references.citation: Am J Physiol Renal Physiol. 2010 Sep;299(3):F634-47
references.pmid: 20519375
references.citation: Am J Physiol. 1996 Jan;270(1 Pt 2):F9-20
references.pmid: 8769818
references.citation: Am J Physiol Renal Physiol. 2009 Aug;297(2):F537-48
references.pmid: 19403645
references.citation: Am J Physiol. 1981 May;240(5):F446-58
references.pmid: 7235019
references.citation: Am J Physiol. 1985 Sep;249(3 Pt 2):F374-89
references.pmid: 4037090
references.citation: J Clin Invest. 1993 Nov;92(5):2274-82
references.pmid: 8227342
references.citation: Am J Physiol. 1995 Aug;269(2 Pt 2):F159-71
references.pmid: 7653590
references.citation: Math Med Biol. 2013 Sep;30(3):191-212
references.pmid: 22511507
references.citation: Biophys J. 1997 Jan;72(1):214-22
references.pmid: 8994606
references.citation: Am J Physiol. 1990 May;258(5 Pt 2):F1448-59
references.pmid: 2337158
references.citation: Am J Physiol Heart Circ Physiol. 2008 Oct;295(4):H1562-71
references.pmid: 18689501
references.citation: Kidney Int. 1987 Feb;31(2):629-33
references.pmid: 3550233
references.citation: Biophys J. 1973 Jun;13(6):546-67
references.pmid: 4714447
references.citation: Math Biosci. 2010 Dec;228(2):185-94
references.pmid: 20934438
references.citation: Am J Physiol. 1996 Jul;271(1 Pt 2):R157-79
references.pmid: 8760217
references.citation: Kidney Int. 1972 Oct;2(4):214-23
references.pmid: 4657922
references.citation: Am J Physiol. 1965 Jun;208:1119-28
references.pmid: 14301367
references.citation: Am J Physiol Heart Circ Physiol. 2008 Oct;295(4):H1572-9
references.pmid: 18723769
references.citation: Bull Math Biol. 2009 Apr;71(3):515-55
references.pmid: 19205808
references.citation: Am J Physiol Renal Physiol. 2001 Oct;281(4):F579-96
references.pmid: 11553505
references.citation: J Math Biol. 2014 Mar;68(4):1023-49
references.pmid: 23529284
references.citation: Am J Physiol. 1990 Jul;259(1 Pt 2):F60-4
references.pmid: 2375393
references.citation: Am J Physiol. 1992 Jun;262(6 Pt 2):F980-8
references.pmid: 1621821
references.citation: Am J Physiol Heart Circ Physiol. 2002 Sep;283(3):H1042-55
references.pmid: 12181134
references.citation: Am J Physiol Renal Physiol. 2005 Dec;289(6):F1346-66
references.pmid: 15914776
references.citation: Am J Physiol Renal Physiol. 2011 Feb;300(2):F356-71
references.pmid: 21068086
references.citation: Am J Physiol Renal Physiol. 2012 Mar 1;302(5):F591-605
references.pmid: 22088433
references.citation: Am J Physiol Renal Physiol. 2005 Dec;289(6):F1367-81
references.pmid: 15914775
references.citation: Am J Physiol Renal Physiol. 2011 Feb;300(2):F372-84
references.pmid: 21068088
references.citation: Am J Physiol. 1985 Dec;249(6 Pt 2):R643-66
references.pmid: 3934988
references.citation: Am J Physiol. 1999 Jun;276(6):F892-902
references.pmid: 10362778
references.citation: Am J Physiol Renal Physiol. 2012 May 1;302(9):F1188-202
references.pmid: 22262482
references.citation: Kidney Int. 1972 Aug;2(2):85-94
references.pmid: 4671532
references.citation: Pflugers Arch. 1987 May;408(5):438-43
references.pmid: 3601634
references.citation: Annu Rev Physiol. 2005;67:531-55
references.pmid: 15709969
references.citation: Am J Physiol. 1998 Feb;274(2):F413-24
references.pmid: 9486237
references.citation: Am J Physiol. 1987 Mar;252(3 Pt 2):F560-72
references.pmid: 3826393
references.citation: Am J Physiol Renal Physiol. 2003 May;284(5):F871-84
references.pmid: 12676732
references.citation: Chaos. 1996 Sep;6(3):280-287
references.pmid: 12780257
references.citation: Bull Math Biol. 2004 Nov;66(6):1463-92
references.pmid: 15522342
references.citation: Bull Math Biol. 2003 Jul;65(4):665-91
references.pmid: 12875338
references.citation: Physiology (Bethesda). 2009 Aug;24:250-6
references.pmid: 19675356
references.citation: Chaos. 2007 Mar;17(1):015114
references.pmid: 17411271
references.citation: Am Heart J. 1969 Jul;78(1):101-18
references.pmid: 4240194
references.citation: Hypertension. 1995 Apr;25(4 Pt 2):663-73
references.pmid: 7721413
references.citation: Kidney Int. 1987 Feb;31(2):538-48
references.pmid: 3550222
references.citation: Z Anat Entwicklungsgesch. 1974;144(2):137-63
references.pmid: 4472393
references.citation: Acta Physiol Scand. 1983 Mar;117(3):415-9
references.pmid: 6880803
references.citation: Z Zellforsch Mikrosk Anat. 1967;82(4):495-535
references.pmid: 4881295
references.citation: Med Biol Eng. 1976 Jul;14(4):408-26
references.pmid: 967175
references.citation: Am J Physiol Renal Physiol. 2008 Nov;295(5):F1259-70
references.pmid: 18550645
references.citation: Biophys J. 1973 Jun;13(6):512-45
references.pmid: 4714446
references.citation: Am J Physiol. 1991 Mar;260(3 Pt 2):F384-94
references.pmid: 2000955
references.citation: Am J Physiol. 1972 Nov;223(5):1178-83
references.pmid: 4654350
references.citation: Am J Physiol. 1989 Sep;257(3 Pt 2):F399-413
references.pmid: 2782422
references.citation: Chaos. 2011 Sep;21(3):033128
references.pmid: 21974663
references.citation: Z Anat Entwicklungsgesch. 1972;138(3):301-19
references.pmid: 4659112
references.citation: Am J Physiol. 1991 Mar;260(3 Pt 2):F368-83
references.pmid: 2000954
references.citation: Am J Physiol. 1981 Jul;241(1):R3-16
references.pmid: 7018270
references.citation: Am J Physiol. 1997 Oct;273(4):F625-34
references.pmid: 9362340
references.citation: Am J Physiol Renal Physiol. 2010 Jun;298(6):F1369-83
references.pmid: 20335320
references.citation: Am J Physiol. 1975 Jan;228(1):71-9
references.pmid: 1147030
references.citation: Am J Physiol. 1998 Nov;275(5):F671-90
references.pmid: 9815126
references.citation: Am J Physiol Renal Physiol. 2010 Apr;298(4):F973-87
references.pmid: 20053796
references.citation: Am J Physiol Renal Physiol. 2004 Oct;287(4):F816-39
references.pmid: 15213067