메뉴 건너뛰기




Volumn 45, Issue 6, 2002, Pages 549-567

A numerical method for renal models that represent tubules with abrupt changes in membrane properties

Author keywords

Differential equations; Kidney; Mathematical biology; Mathematical models; Renal medulla; Semi Lagrangian semi implicit

Indexed keywords

AVES; MAMMALIA;

EID: 0043176171     PISSN: 03036812     EISSN: 14321416     Source Type: Journal    
DOI: 10.1007/s00285-002-0166-6     Document Type: Article
Times cited : (12)

References (35)
  • 2
    • 0017905208 scopus 로고
    • Efficient numerical method for solving differential equation of renal counterflow systems
    • Farahzad, P., Tewarson, R.P.: Efficient numerical method for solving differential equation of renal counterflow systems. Comput. Biol. Med. 8, 57-64 (1978)
    • (1978) Comput. Biol. Med. , vol.8 , pp. 57-64
    • Farahzad, P.1    Tewarson, R.P.2
  • 3
    • 33746900492 scopus 로고
    • Diffusion and convection in a family of tubes
    • Garner, J.B., Kellogg, R.B.: Diffusion and convection in a family of tubes. J. Math. Anal. Appl. 85, 461-472 (1982)
    • (1982) J. Math. Anal. Appl. , vol.85 , pp. 461-472
    • Garner, J.B.1    Kellogg, R.B.2
  • 4
    • 0020783617 scopus 로고
    • Mathematical analysis of a model for the renal concentrating mechanism
    • Garner, J.B., Kellogg, R.B., Stephenson, J.L.: Mathematical analysis of a model for the renal concentrating mechanism. Math. Biosci. 65, 125-150 (1983)
    • (1983) Math. Biosci. , vol.65 , pp. 125-150
    • Garner, J.B.1    Kellogg, R.B.2    Stephenson, J.L.3
  • 5
    • 38249033709 scopus 로고
    • Some singular perturbation problems in renal models
    • Kellogg, R.B.: Some singular perturbation problems in renal models. J. Math. Anal. Apps. 128, 214-240 (1987)
    • (1987) J. Math. Anal. Apps. , vol.128 , pp. 214-240
    • Kellogg, R.B.1
  • 6
    • 0036982856 scopus 로고    scopus 로고
    • A semi-Lagrangian semi-implicit numerical method for models of the urine concentrating mechanism
    • Layton, A.T., Layton, H.E.: A semi-Lagrangian semi-implicit numerical method for models of the urine concentrating mechanism. SIAM J. Sci. Comput. 23, 1528-1548 (2002)
    • (2002) SIAM J. Sci. Comput. , vol.23 , pp. 1528-1548
    • Layton, A.T.1    Layton, H.E.2
  • 7
    • 0037298722 scopus 로고    scopus 로고
    • An efficient numerical method for distributed-loop models of the urine concentrating mechanism
    • Submitted
    • Layton, A.T., Layton, H.E.: An efficient numerical method for distributed-loop models of the urine concentrating mechanism. Submitted, Math. Biosci.
    • Math. Biosci.
    • Layton, A.T.1    Layton, H.E.2
  • 8
    • 0022540201 scopus 로고
    • Distribution of Henle's loops may enhance urine concentrating capability
    • Layton, H.E.: Distribution of Henle's loops may enhance urine concentrating capability. Biophys. J. 49, 1033-1040 (1986)
    • (1986) Biophys. J. , vol.49 , pp. 1033-1040
    • Layton, H.E.1
  • 9
    • 0027234747 scopus 로고
    • Distributed solute and water reabsorption in a central core model of the renal medulla
    • Layton, H.E., Davis, J.M.: Distributed solute and water reabsorption in a central core model of the renal medulla. Math. Biosci. 116, 169-196 (1993)
    • (1993) Math. Biosci. , vol.116 , pp. 169-196
    • Layton, H.E.1    Davis, J.M.2
  • 10
    • 0028435104 scopus 로고
    • A dynamic numerical method for models of renal tubules
    • Layton, H.E., Pitman, E.B.: A dynamic numerical method for models of renal tubules. Bull. Math. Biol. 56(3), 547-565 (1994)
    • (1994) Bull. Math. Biol. , vol.56 , Issue.3 , pp. 547-565
    • Layton, H.E.1    Pitman, E.B.2
  • 11
    • 0029391784 scopus 로고
    • A dynamic numerical method for models of the urine concentrating mechanism
    • Layton, H.E., Pitman, E.B., Knepper, M.A.: A dynamic numerical method for models of the urine concentrating mechanism. SIAM J. Appl. Math. 55, 1390-1418 (1995)
    • (1995) SIAM J. Appl. Math. , vol.55 , pp. 1390-1418
    • Layton, H.E.1    Pitman, E.B.2    Knepper, M.A.3
  • 12
    • 0030020602 scopus 로고    scopus 로고
    • Permeability criteria for effective function of passive countercurrent multipler
    • Layton, H.E., Knepper, M.A., Chou, C.-L.: Permeability criteria for effective function of passive countercurrent multipler. Am. J. Physiol. 270
    • Am. J. Physiol. , vol.270
    • Layton, H.E.1    Knepper, M.A.2    Chou, C.-L.3
  • 15
    • 0019044410 scopus 로고
    • Numerical solution of a kidney model by multiple shooting
    • Lory, P.: Numerical solution of a kidney model by multiple shooting. Math. Biosci. 50, 117-128 (1980)
    • (1980) Math. Biosci. , vol.50 , pp. 117-128
    • Lory, P.1
  • 16
    • 0018941574 scopus 로고    scopus 로고
    • How descending limb of Henle's loop permeability affects hypertonic urine formation
    • Moore, L.C., Marsh, D.J.: How descending limb of Henle's loop permeability affects hypertonic urine formation. Am. J. Physiol. 239
    • Am. J. Physiol. , vol.239
    • Moore, L.C.1    Marsh, D.J.2
  • 18
    • 85088319899 scopus 로고    scopus 로고
    • Sodium chloride and water transport in the thin descending limb of Henle of the quail
    • Nishimura, H., Koseki, C., Braun, E.J.: Sodium chloride and water transport in the thin descending limb of Henle of the quail. Am. J. Physiol., 257
    • Am. J. Physiol. , vol.257
    • Nishimura, H.1    Koseki, C.2    Braun, E.J.3
  • 20
    • 0034058493 scopus 로고    scopus 로고
    • Mixed descending- and ascending-type thin limbs of Henle's loop in mammalian renal inner medulla
    • Pannabecker, T.L., Dahlmann, A., Brokl, O.H., Dantzler, W.H.: Mixed descending- and ascending-type thin limbs of Henle's loop in mammalian renal inner medulla. Am. J. Physiol. Renal Physiol. 278, F202-F208 (2000)
    • (2000) Am. J. Physiol. Renal Physiol. , vol.278
    • Pannabecker, T.L.1    Dahlmann, A.2    Brokl, O.H.3    Dantzler, W.H.4
  • 21
    • 0001976785 scopus 로고    scopus 로고
    • Urine concentrating mechanism and its regulation
    • edited by D. W. Seldin and G. Giebisch. Philadelphia: Lippincott Williams & Wilkins
    • Sands, J.M., Layton, H.E.: Urine concentrating mechanism and its regulation. In: The Kidney: Physiology and Pathophysiology (3d ed.), edited by D. W. Seldin and G. Giebisch. Philadelphia: Lippincott Williams & Wilkins, 1175-1216 (2000)
    • (2000) The Kidney: Physiology and Pathophysiology (3d Ed.) , pp. 1175-1216
    • Sands, J.M.1    Layton, H.E.2
  • 22
    • 0026291228 scopus 로고
    • Semi-Lagrangian integration schemes for atmospheric models - A review
    • Staniforth, A., Côté, J.: Semi-Lagrangian integration schemes for atmospheric models - a review. Mon. Wea. Rev. 119, 2206-2223 (1991)
    • (1991) Mon. Wea. Rev. , vol.119 , pp. 2206-2223
    • Staniforth, A.1    Côté, J.2
  • 23
    • 0015385254 scopus 로고
    • Central core model of the renal counterflow system
    • Stephenson, J.L.: Central core model of the renal counterflow system. Kidney Int. 2, 85-94 (1972)
    • (1972) Kidney Int. , vol.2 , pp. 85-94
    • Stephenson, J.L.1
  • 24
    • 0040309173 scopus 로고
    • Quantitative analysis of mass and energy balance in non-ideal models of the renal counterflow system
    • Stephenson, J.L., Tewarson, R.P., Mejia, R.: Quantitative analysis of mass and energy balance in non-ideal models of the renal counterflow system. Proc. Nat. Acad. Sci. USA 71, 1618-1622 (1974)
    • (1974) Proc. Nat. Acad. Sci. USA , vol.71 , pp. 1618-1622
    • Stephenson, J.L.1    Tewarson, R.P.2    Mejia, R.3
  • 25
    • 0000715961 scopus 로고
    • Urinary concentration and dilution: Models
    • edited by E. E. Windhager, published for the American Physiological Society by Oxford University Press, New York, sect. 8
    • Stephenson, J.L.: Urinary concentration and dilution: models. In: Handbook of Physiology: Renal Physiology, edited by E. E. Windhager, published for the American Physiological Society by Oxford University Press, New York, sect. 8, 2, 1349-1408 (1992)
    • (1992) Handbook of Physiology: Renal Physiology , vol.2 , pp. 1349-1408
    • Stephenson, J.L.1
  • 27
    • 0002746782 scopus 로고
    • An efficient parallel algorithm for solving n-nephron models of the renal inner medulla
    • Wang, H., Stephenson, J.L., Deng, Y.-F., Tewarson, R.P.: An efficient parallel algorithm for solving n-nephron models of the renal inner medulla. Comput. Math. Appl. 28, 1-12 (1994)
    • (1994) Comput. Math. Appl. , vol.28 , pp. 1-12
    • Wang, H.1    Stephenson, J.L.2    Deng, Y.-F.3    Tewarson, R.P.4
  • 28
    • 0031990694 scopus 로고    scopus 로고
    • Outer medullary anatomy and the urine concentrating mechanism
    • Wang, X., Thomas, S.R., Wexler, A.S.: Outer medullary anatomy and the urine concentrating mechanism, Am. J. Physiol. 274
    • Am. J. Physiol. , vol.274
    • Wang, X.1    Thomas, S.R.2    Wexler, A.S.3
  • 32
    • 0025825310 scopus 로고    scopus 로고
    • Three-dimensional anatomy and renal concentrating mechanism. I. Modeling results
    • Wexler, A.S., Kalaba, R.E., Marsh, D.J.: Three-dimensional anatomy and renal concentrating mechanism. I. Modeling results. Am. J. Physiol., 260
    • Am. J. Physiol. , vol.260
    • Wexler, A.S.1    Kalaba, R.E.2    Marsh, D.J.3
  • 34
    • 0025803809 scopus 로고    scopus 로고
    • Three-dimensional anatomy and renal concentrating mechanism. II. Sensitivity results
    • Wexler, A.S., Kalaba, R.E., Marsh, D.J.: Three-dimensional anatomy and renal concentrating mechanism. II. Sensitivity results. Am. J. Physiol., 260
    • Am. J. Physiol. , vol.260
    • Wexler, A.S.1    Kalaba, R.E.2    Marsh, D.J.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.