A Mathematical Model of Two Phases Newtonian Layer Renal Blood Flow in Capillaries

Authors

  • Tarunika Sharma  Department of Basic science and Humanities, New Horizon College of Engineering, Bangalore,Karnataka, India
  • Rashi khubnani  Department of Basic science and Humanities, New Horizon College of Engineering, Bangalore,Karnataka, India
  • Dr. Harish Chandra  Director Kautilya Academy,Satna, Madhya Pradesh, India

Keywords:

Pressure Drop, Hematocrit, Renal Circulation, Glomerular Capillary, Diabeties, Peritubular Capillary.

Abstract

In this paper we have formulated the mathematical modelling for the renal blood flow along the capillaries in case of renal disease Diabetes, considering the nature of renal circulatory system in human body. Here we have considered the blood flow has two phases, one of which is red blood cell and other is plasma. Further analysis of a clinical data in case of a Diabetic patient for Hematocrit v/s Blood pressure is shown. The graphical presentation for particular parametric value is much closer to the clinical observation. The overall presentation is in tensorial form and solution technique adapted is analytical as well as numerical.

References

  1. Structure and Function of the Kidney Essay. Submitted by: ppaul11 on March 14, 2015
  2. Reddi AS. Structure and function of the kidney. In: Reddi AS. Essentials of Renal Physiology. New Jersey: College Book Publishers, 1999:21-43.
  3. Madsen KM , Tisher CC . Anotomy of kidney . In Brenner BM ,ed. Brenner and Rector’s .The kidney , 7th ed. Vol.- 1Pheladelphia :Saunders, 2004,3-72
  4. Kriz W ,Elgar M Renal anatomy .In Johnson RJ, Feehally J, eds. Comprehenshive clinical nephrology ,2nd ed. Edinburgh Mosby ; 2003;1-11
  5. Cotran , RS S ; Kumar , Cotran, RS S.; Kumar, Vinay; Fausto, Nelson; Robbins, Stanley L.;Abbas, Abul K. (2005). Robbins and Cotran pathologic basis of disease. St. Louis, MO: Elsevier Saunders.ISBN 0-7216-0187-1
  6. Nutrition and Health ; Nutrition Kidney disease ; edited by LD Byham -Grey , JD . Burrowes and GM Chertow Humana Press ;Totowa ; NJ
  7. Essential of Clinical Nephrology ; 1st edition ; Published by ; Dar EI Shorouk, 8 Sebawieh Al masry,Nasr City , Cairo, Egypt ; post box : 33 Pnorama : [email protected]
  8. Renal physiology and Body Fluids ; chapter-22 Kidney Function ;George A Tanner ; Ph.D. ,pp-393
  9. Review of Medical physiology ; 23 edition , Kim Barrett ,Headwen , Brooks Scott Boitano Susan Baman ; pp-644
  10. Kapur J.N., Mathematical Models in Biology & Medicine, EWP New Delhi, 354, 1992.
  11. Shmukler , Michael (2004) " Density of the blood " The physics Factbook . Retrieved October 4 2006
  12. Physiology and maintenance ; Vol-III ;Hemorheology and hemodynamics-oguz k Buskurt, Herburt.J Meiselman
  13. " Human Kidney . Diagram, with nephron ," Pearson publishing .Lab Art Library .96L,12001. wwwlabartlibrary.com/symbiosis/96/96L12001.pdf.juli7, 2003
  14. International journal of Engineering Research and development e-ISSN:227 067X,p-ISSN :2278-800X , www.ijerd.com Vol-5 Issue 5 (Dec.2012) pp-23-30
  15. ISO 9001:2008 Certified International Journal of Engineering and Innovative Technology (IJEIT) Volume 4, Issue 4, November 2014
  16. Journal of physiology and pathophysiology ) ; DOI; 10.5897/JPAP2013.0075 ISSN 2141-260X Academic Journal vol-4(2) pp 23-28 march 2013 www.academic journals.org/JPAP
  17. Journal of Global Research in Computer Science ISSN- 2229-37IX; (www.jgrcs.info)
  18. Vol -2 ; No.-4 April 2011
  19. J Blood Disord Transfus; ISSN2155-9864 JDBT ; open access journal ; vol. 3 Issue -2 http//dx .doi.org /10 .4172/2155-9864.1000118
  20. Aubuchnon JP , Kruskall MS (1997) Transfusion safely ;Realigning efforts with risk . Transfusion 37: 1211-1216
  21. J Blood Disord Transfus; ISSN2155-9864 JDBT ; open access journal ; vol. 3 Issue -2 http//dx .doi.org /10 .4172/2155-9864.1000119
  22. Metz J. MacGrath KM Copperchini ML, Haeusler M, Haysom HE , et al.(1995) Appropriateness of transfusion of red blood cells , platelets and fresh frozen plasma . An audit in a teritarycare teaching hospital , MedJ Aust 162;572-577
  23. A.C.Guyton; Medical Physiology; Chapter 26; Urine Formation by the kidneys; I. Glomerular Filtration, Renal Blood flow and their control; PP 283-285
  24. Shmukler, Michael ; Density of Blood ; The Physics Factbook ; Retrived 4 October 2006
  25. Physiology and Anatomy . Elixir Physio. & Anatomy 89 (2015) 36723-36729
  26. Shoback, edited by David G Garner , Dolores (2011) " chapter 17" . Greenspan’s basic and clinical endocrinology (9th Edit.) . Newyork : McGraw-Hill Medical . ISBN 0-07 -162243-8
  27. Walter F. Boron (2004) . Medical physiology : A cellular and Molecular Aproach . Elsevier / Saunders. ISBN1-4160-2328
  28. Sloop GD. A Unifying Theory of Atherogenesis. Med Hypothesis. 1996;47:321-5
  29. Cokelet GR, Meiselman HJ. Blood rheology. In : Baskurt OK, et al.Handbook of Hemorheology and Hemodynamics. IOS Press, 200; 45-71
  30. ISSN: 2277-3754 ISO 9001:2008 Certified International Journal of Engineering and Innovative Technology (IJEIT) Volume 4, Issue 4, November 2014
  31. Sherman, I.W. & Sherman, V.G.; Biology- a human approach oxford univ. press New York, oxford; 276-277; 1989.
  32. Sapna Ratan Shah; Mathematical analysis of blood flow throw atherosclerotic arterial segment having non-symmetric and mild stenosis; International journal of research in pure & applied physics; 21 april, 2011.
  33. Purves, William K.; Sadava, David; Orians, Gordon H.; Heller, H. Craig (2004). Life: The Science of Biology (7th ed.). Sunderland, Mass: Sinauer Associates. p. 954. ISBN 0-7167-98565.
  34. Stuart J, Kenny MW: Blood rheology. J din Pathol 19803:417-429
  35. Chien S: Blood rheology in hypertension and cardiovascular disease. Cardiovasc Med 1977;2:356-360 [35] Berkow, Robert, ed. Merck Manual of Medical Information. Whitehouse Station, NJ: Merck Research Laboratories, 1997
  36. Fogelson, A.L.; A mathematical model and numerical method for studying platelet adhesion and aggregation during blood clotting; J.comput. physics; 56; 1984.
  37. Singh P. and Upadhyay K.S. ; A New approach for the shock propagation in two phases system; Nat.Acad.Sci.Letters, Vol 8, No 2, 1985
  38. Compbell, I.J. and Pitcher, A.S.; Shock waves in a liquid containing gas bubbles, proc.Roy.Soc; A 243, 1958.
  39. Kapur,J.N; and Gupta, R.c ; Power-law fluid flow in the inlet length of a circular pipe; The math, seminar; 3, 55-67; 1963.
  40. Ruch, T.C. and H.D., Patton, (Eds); Physiology and Biophysics-volsii and iii, W.B.S.; 1973.
  41. Taylor, M.G. ; Hemodynamics. Ann.Rev. Physiol; 35; 87,1973.
  42. Kapur J.N., Mathematical Models in Biology & Medicine, EWP New Delhi, 353, 1992.
  43. Kapur J.N., Mathematical Models in Biology & Medicine, EWP New Delhi, 354, 1992.

IInternational Journal of Scientific Research in Computer Science, Engineering and Information Technology

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Published

2018-06-30

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Volume 3, Issue 5, May-June-2018

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Research Articles

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How to Cite

[1]
Tarunika Sharma, Rashi khubnani, Dr. Harish Chandra, " A Mathematical Model of Two Phases Newtonian Layer Renal Blood Flow in Capillaries, IInternational Journal of Scientific Research in Computer Science, Engineering and Information Technology(IJSRCSEIT), ISSN : 2456-3307, Volume 3, Issue 5, pp.871-880, May-June-2018.