The Journal of Physiological Sciences

, Volume 68, Issue 4, pp 355–367 | Cite as

Regulation of the glucose supply from capillary to tissue examined by developing a capillary model

  • Akitoshi Maeda
  • Yukiko Himeno
  • Masayuki Ikebuchi
  • Akinori NomaEmail author
  • Akira Amano
Original Paper


A new glucose transport model relying upon diffusion and convection across the capillary membrane was developed, and supplemented with tissue space and lymph flow. The rate of glucose utilization (J util) in the tissue space was described as a saturation function of glucose concentration in the interstitial fluid (C glu,isf), and was varied by applying a scaling factor f to J max. With f = 0, the glucose diffusion ceased within ~20 min. While, with increasing f, the diffusion was accelerated through a decrease in C glu,isf, but the convective flux remained close to resting level. When the glucose supplying capacity of the capillary was measured with a criterion of J util /J max = 0.5, the capacity increased in proportion to the number of perfused capillaries. A consistent profile of declining C glu,isf along the capillary axis was observed at the criterion of 0.5 irrespective of the capillary number. Increasing blood flow scarcely improved the supplying capacity.


Mathematical capillary model Glucose supplying capacity Diffusion across the capillary membrane Convective glucose flux Reflection coefficient 



We thank colleagues in the laboratory of Regulation of Tissue Functions at the Department of life Sciences, Ritsumeikan University, for very fruitful discussions.

Compliance with ethical standards

No experimental measurements were carried out in the present study.

Conflict of interest

The authors declare that they have no conflict of interest.


  1. 1.
    Goldstein MS, Mullick V, Huddlestun B, Levine R (1953) Action of muscular work on transfer of sugars across cell barriers; comparison with action of insulin. Am J Physiol 173:212–216CrossRefGoogle Scholar
  2. 2.
    Hansen P, Gulve E, Gao J, Schluter J, Mueckler M, Holloszy J (1995) Kinetics of 2-deoxyglucose transport in skeletal muscle: effects of insulin and contractions. Am J Physiol 268:C30–C35CrossRefGoogle Scholar
  3. 3.
    Desvigne N, Barthelemy JC, Bertholon F, Gay-Montchamp JP, Freyssenet D, Costes F (2004) Validation of a new calibration method for human muscle microdialysis at rest and during exercise. Eur J Appl Physiol 92:312–320CrossRefGoogle Scholar
  4. 4.
    Rosdahl H, Ungerstedt U, Jorfeldt L, Henriksson J (1993) Interstitial glucose and lactate balance in human skeletal muscle and adipose tissue studied by microdialysis. J Physiol 471:637–657CrossRefGoogle Scholar
  5. 5.
    Henriksson J, Knol M (2005) A single bout of exercise is followed by a prolonged decrease in the interstitial glucose concentration in skeletal muscle. Acta Physiol Scand 185:313–320CrossRefGoogle Scholar
  6. 6.
    Hamrin K, Henriksson J (2008) Interstitial glucose concentration in insulin-resistant human skeletal muscle: influence of one bout of exercise and of local perfusion with insulin or vanadate. Eur J Appl Physiol 103:595–603CrossRefGoogle Scholar
  7. 7.
    Curry FE (1974) A hydrodynamic description of the osmotic reflection coefficient with application to the pore theory of transcapillary exchange. Microvasc Res 8:236–252CrossRefGoogle Scholar
  8. 8.
    Renkin EM (1977) Multiple pathways of capillary permeability. Circ Res 41:735–743CrossRefGoogle Scholar
  9. 9.
    Rippe B, Haraldsson B (1986) Capillary permeability in rat hindquarters as determined by estimations of capillary reflection coefficients. Acta Physiol Scand 127:289–303CrossRefGoogle Scholar
  10. 10.
    Wolf MB (2002) A three-pathway pore model describes extensive transport data from mammalian microvascular beds and frog microvessels. Microcirculation 9:497–511CrossRefGoogle Scholar
  11. 11.
    Michel CC (1980) Filtration coefficients and osmotic reflexion coefficients of the walls of single frog mesenteric capillaries. J Physiol 309:341–355CrossRefGoogle Scholar
  12. 12.
    Pappenheimer JR, Renkin EM, Borrero LM (1951) Filtration, diffusion and molecular sieving through peripheral capillary membranes; a contribution to the pore theory of capillary permeability. Am J Physiol 167:13–46CrossRefGoogle Scholar
  13. 13.
    Diana JN, Long SC, Yao H (1972) Effect of histamine on equivalent pore radius in capillaries of isolated dog hindlimb. Microvasc Res 4:413–437CrossRefGoogle Scholar
  14. 14.
    Taylor AE, Gibson WH, Granger HJ, Guyton AC (1973) The interaction between intracapillary and tissue forces in the overall regulation of interstitial fluid volume. Lymphology 6:192–208PubMedGoogle Scholar
  15. 15.
    Miserocchi G, Negrini D, Mukenge S, Turconi P, Del Fabbro M (1989) Liquid drainage through the peritoneal diaphragmatic surface. J Appl Physiol (1985) 66:1579–1585CrossRefGoogle Scholar
  16. 16.
    Kellen MR, Bassingthwaighte JB (2003) An integrative model of coupled water and solute exchange in the heart. Am J Physiol Heart Circ Physiol 285:H1303–H1316CrossRefGoogle Scholar
  17. 17.
    Kellen MR, Bassingthwaighte JB (2003) Transient transcapillary exchange of water driven by osmotic forces in the heart. Am J Physiol Heart Circ Physiol 285:H1317–H1331CrossRefGoogle Scholar
  18. 18.
    Bassingthwaighte JB, Raymond GM, Ploger JD, Schwartz LM, Bukowski TR (2006) GENTEX, a general multiscale model for in vivo tissue exchanges and intraorgan metabolism. Philos Trans A Math Phys Eng Sci 364:1423–1442CrossRefGoogle Scholar
  19. 19.
    Li Y, Dash RK, Kim J, Saidel GM, Cabrera ME (2009) Role of NADH/NAD + transport activity and glycogen store on skeletal muscle energy metabolism during exercise: in silico studies. Am J Physiol Cell Physiol 296:C25–C46CrossRefGoogle Scholar
  20. 20.
    Himeno Y, Ikebuchi M, Maeda A, Noma A, Amano A (2016) Mechanisms underlying the volume regulation of interstitial fluid by capillaries: a simulation study. Integr Med Res 5:11–21CrossRefGoogle Scholar
  21. 21.
    Krogh A (1919) The number and distribution of capillaries in muscles with calculations of the oxygen pressure head necessary for supplying the tissue. J Physiol 52:409–415CrossRefGoogle Scholar
  22. 22.
    Levick JR (2013) An introduction to cardiovascular physiology, chapter 10, 5th edn. CRC Press, Boca Raton, FLGoogle Scholar
  23. 23.
    Holloszy JO, Narahara HT (1965) Studies of tissue permeability. X. Changes in permeability to 3-methylglucose associated with contraction of isolated frog muscle. J Biol Chem 240:3493–3500PubMedGoogle Scholar
  24. 24.
    Park CR, Crofford OB, Kono T (1968) Mediated (nonactive) transport of glucose in mammalian cells and its regulation. J Gen Physiol 52:296–318CrossRefGoogle Scholar
  25. 25.
    Furler SM, Jenkins AB, Storlien LH, Kraegen EW (1991) In vivo location of the rate-limiting step of hexose uptake in muscle and brain tissue of rats. Am J Physiol 261:E337–E347PubMedGoogle Scholar
  26. 26.
    Ziel FH, Venkatesan N, Davidson MB (1988) Glucose transport is rate limiting for skeletal muscle glucose metabolism in normal and STZ-induced diabetic rats. Diabetes 37:885–890CrossRefGoogle Scholar
  27. 27.
    Glatz JF, Luiken JJ, Bonen A (2010) Membrane fatty acid transporters as regulators of lipid metabolism: implications for metabolic disease. Physiol Rev 90:367–417CrossRefGoogle Scholar
  28. 28.
    Wallberg-Henriksson H, Holloszy JO (1984) Contractile activity increases glucose uptake by muscle in severely diabetic rats. J Appl Physiol Respir Environ Exerc Physiol 57:1045–1049PubMedGoogle Scholar
  29. 29.
    Karnieli E, Armoni M (2008) Transcriptional regulation of the insulin-responsive glucose transporter GLUT4 gene: from physiology to pathology. Am J Physiol Endocrinol Metab 295:E38–E45CrossRefGoogle Scholar
  30. 30.
    Whitesell RR, Gliemann J (1979) Kinetic parameters of transport of 3-O-methylglucose and glucose in adipocytes. J Biol Chem 254:5276–5283PubMedGoogle Scholar
  31. 31.
    Guyton AC (1963) A concept of negative interstitial pressure based on pressures in implanted perforated capsules. Circ Res 12:399–414CrossRefGoogle Scholar
  32. 32.
    Guyton AC (1965) Unterstitial fluid presure. II. Pressure-volume curves of interstitial space. Circ Res 16:452–460CrossRefGoogle Scholar
  33. 33.
    Hamilton WF, Dow P (1963) Circulation. Handbook of physiology, Section 2. America Physiological Society, Washington, pp 961–1034Google Scholar
  34. 34.
    Hall JE (2015) Guyton and Hall textbook of medical physiology, chapter16. Elsevier Health Sciences, PhiladelphiaGoogle Scholar
  35. 35.
    Michel CC, Phillips ME (1987) Steady-state fluid filtration at different capillary pressures in perfused frog mesenteric capillaries. J Physiol 388:421–435CrossRefGoogle Scholar
  36. 36.
    Landis EM (1934) Capillary pressure and capillary permeability. Physiol Rev 14:404–481CrossRefGoogle Scholar
  37. 37.
    Renkin EM (1954) Filtration, diffusion, and molecular sieving through porous cellulose membranes. J Gen Physiol 38:225–243PubMedPubMedCentralGoogle Scholar
  38. 38.
    Oberg CM, Rippe B (2014) A distributed two-pore model: theoretical implications and practical application to the glomerular sieving of Ficoll. Am J Physiol Renal Physiol 306:F844–F854CrossRefGoogle Scholar
  39. 39.
    Renkin EM (ed) (1987) Handbook of physiology: Section 2. The cardiovascular system. Microcirculation: pt. 2, vol 4. American Physiological Society, Bethesda, MD, p 431Google Scholar
  40. 40.
    Korth U, Merkel G, Fernandez FF, Jandewerth O, Dogan G, Koch T, van Ackern K, Weichel O, Klein J (2000) Tourniquet-induced changes of energy metabolism in human skeletal muscle monitored by microdialysis. Anesthesiology 93:1407–1412CrossRefGoogle Scholar
  41. 41.
    McDonald JN, Levick JR (1993) Effect of extravascular plasma protein on pressure-flow relations across synovium in anaesthetized rabbits. J Physiol 465:539–559CrossRefGoogle Scholar
  42. 42.
    Michel CC (1997) Starling: the formulation of his hypothesis of microvascular fluid exchange and its significance after 100 years. Exp Physiol 82:1–30CrossRefGoogle Scholar
  43. 43.
    Weinbaum S (1998) 1997 Whitaker Distinguished Lecture: models to solve mysteries in biomechanics at the cellular level; a new view of fiber matrix layers. Ann Biomed Eng 26:627–643CrossRefGoogle Scholar
  44. 44.
    Adamson RH, Lenz JF, Zhang X, Adamson GN, Weinbaum S, Curry FE (2004) Oncotic pressures opposing filtration across non-fenestrated rat microvessels. J Physiol 557:889–907CrossRefGoogle Scholar
  45. 45.
    Levick JR (1991) Capillary filtration-absorption balance reconsidered in light of dynamic extravascular factors. Exp Physiol 76:825–857CrossRefGoogle Scholar
  46. 46.
    Michel CC, Kendall S (1997) Differing effects of histamine and serotonin on microvascular permeability in anaesthetized rats. J Physiol 501(Pt 3):657–662CrossRefGoogle Scholar

Copyright information

© The Physiological Society of Japan and Springer Japan 2017

Authors and Affiliations

  1. 1.Department of Life SciencesRitsumeikan UniversityShigaJapan

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