Advertisement

A Mechanistic Analysis of Possible Blood Transfusion Failure to Increase Circulatory Oxygen Delivery in Anemic Patients

  • Robert A. Zimmerman
  • Amy G. Tsai
  • Marcos Intaglietta
  • Daniel M. TartakovskyEmail author
Article
  • 50 Downloads

Abstract

The effects of changing hematocrit (Hct) on the rate of circulatory oxygen (\(\hbox {O}_2\)) delivery were modeled analytically to describe transfusion of 0.5–3.0 units of packed red blood cells (pRBC, 300 mL/unit, 60% Hct) to anemic patients. In our model, Hct affects \(\hbox {O}_2\) delivery to the microcirculation by changing blood \(\hbox {O}_2\) carrying capacity and blood viscosity, which in turn affects blood flow velocity and, therefore, \(\hbox {O}_2\) delivery. Changing blood velocity impacts the \(\hbox {O}_2\) delivery by affecting the oxygen diffusive losses as blood transits through the arteriolar vasculature. An increase in Hct has two opposite effects: it increases the blood \(\hbox {O}_2\) carrying capacity and decreases the flow velocity. This suggests the existence of an optimal Hct that maximizes \(\hbox {O}_2\) delivery. Our results show that maximal \(\hbox {O}_2\) delivery occurs in the anemic range, where \(\text {Hct} < 39\)%. Optimal blood management is associated with transfusing enough units up to reaching maximal \(\hbox {O}_2\) delivery. Although somewhat complex to implement, this practice would result in both substantial blood savings and improved \(\hbox {O}_2\) delivery.

Keywords

Oxygen delivery Oxygen carrying capacity Blood transfusion 

Notes

Acknowledgments

This research was supported in part by National Science Foundation under Grant DMS-1802189.

References

  1. 1.
    Aberman, A., J. M. Cavanilles, J. Trotter, D. Erbeck, M. H. Weil, and H. Shubin. An equation for the oxygen hemoglobin dissociation curve. J. Appl. Physiol. 35(4):570–571, 1973.Google Scholar
  2. 2.
    Adair, G. S. The hemoglobin system. VI. The oxygen dissociation curve of hemoglobin. J. Biol. Chem. 63(2):529–545, 1925.Google Scholar
  3. 3.
    Adam, J. A. Blood vessel branching: beyond the standard calculus problem. Math. Mag. 84(3):196–207, 2011.Google Scholar
  4. 4.
    Aris, R. On the dispersion of a solute in a fluid flowing through a tube. Proc. Roy. Soc. London A 235(1200):67–77, 1956.Google Scholar
  5. 5.
    Beard, D. A., and J. B. Bassingthwaighte. Advection and diffusion of substances in biological tissues with complex vascular networks. Ann. Biomed. Engrg. 28(3):253–268, 2000.Google Scholar
  6. 6.
    Beard, D. A., and J. B. Bassingthwaighte. Modeling advection and diffusion of oxygen in complex vascular networks. Ann. Biomed. Engrg. 29(4):298–310, 2001.Google Scholar
  7. 7.
    Buerk, D. G., R. D. Shonat, C. E. Riva, and S. D. Cranstoun. $\text{ O }_2$ gradients and countercurrent exchange in the cat vitreous humor near retinal arterioles and venules. Microvasc. Res. 45(2):134–148, 1993.Google Scholar
  8. 8.
    Carson, J. L. Risk of anemia and transfusion triggers: implications for bloodless care. Surg. Infect. 6(S1):S17–S21, 2005.Google Scholar
  9. 9.
    Crowell, J. W., R. G. Ford, and V. M. Lewis. Oxygen transport in hemorrhagic shock as a function of the hematocrit ratio. Am. J. Physiol. 196(5):1033–1038, 1959.Google Scholar
  10. 10.
    Crowell, J. W., and E. E. Smith. Determinant of the optimal hematocrit. J. Appl. Physiol. 22(3):501–504, 1967.Google Scholar
  11. 11.
    Daland, G. A., and R. Isaacs. Cell respiration studies: II. A comparative study of the oxygen consumption of blood from normal individuals and patients with increased leucocyte counts (sepsis; chronic myelogenous leucemia). J. Exp. Med. 46(1):53, 1927.Google Scholar
  12. 12.
    Duling, B. R., and R. M. Berne. Longitudinal gradients in periarteriolar oxygen tension. A possible mechanism for the participation of oxygen in local regulation of blood flow. Circ. Res. 27(5):669–678, 1970.Google Scholar
  13. 13.
    Forbes, R. M., A. R. Cooper, and H. H. Mitchell. The composition of the adult human body as determined by chemical analysis. J. Biol. Chem. 203(1):359–366, 1953.Google Scholar
  14. 14.
    Goldman, D. Theoretical models of microvascular oxygen transport to tissue. Microcirculation. 15(8):795–811, 2008.Google Scholar
  15. 15.
    Goldstick, T. K., V. T. Ciuryla, and L. Zuckerman. Diffusion of oxygen in plasma and blood. In Oxygen Transport to Tissue – II. Advances in Experimental Medicine and Biology, volume 75, edited by J. Grote, D. Reneau, and G. Thews. Springer, Boston, MA, 1976, p. 183.Google Scholar
  16. 16.
    Gore, R. W. Wall stress: a determinant of regional differences in response of frog microvessels to norepinephrine. Am. J. Physiol. 222(1):82–91, 1972.Google Scholar
  17. 17.
    Green, H. D. Circulation: physical principles. Med. Phys. 1:208–232, 1944.Google Scholar
  18. 18.
    Harris, K. R., and L. A. Woolf. Pressure and temperature dependence of the self diffusion coefficient of water and oxygen-18 water. Faraday Trans. 1: Phys. Chem. Cond. Phases 76:377–385, 1980.Google Scholar
  19. 19.
    Hellums, J. D., P. K. Nair, N. S. Huang, and N. Ohshima. Simulation of intraluminal gas transport processes in the microcirculation. Ann. Biomed. Engrg. 24(1):1–24, 1995.Google Scholar
  20. 20.
    Hershey, D., and T. Karhan. Diffusion coefficients for oxygen transport in whole blood. AIChE J. 14(6):969–972, 1968.Google Scholar
  21. 21.
    Hill, A. V. The possible effects of the aggregation of the molecules of haemoglobin on its dissociation curves. J. Physiol. (Lond.) 40:4–7, 1910.Google Scholar
  22. 22.
    Intaglietta, M. Whitaker lecture 1996: Microcirculation, biomedical engineering, and artificial blood. Ann. Biomed. Eng. 25(4):593–603, 1997.Google Scholar
  23. 23.
    Intaglietta, M., P. C. Johnson, and R. M. Winslow. Microvascular and tissue oxygen distribution. Cardiovasc. Res. 32(4):632–643, 1996.Google Scholar
  24. 24.
    Ivanov, K. P., A. N. Derry, E. P. Vovenko, M. O. Samoilov, and D. G. Semionov. Direct measurements of oxygen tension at the surface of arterioles, capillaries and venules of the cerebral cortex. Pflügers Arch. 393(1):118–120, 1982.Google Scholar
  25. 25.
    Klein, H. G., D. R. Spahn, and J. L. Carson. Red blood cell transfusion in clinical practice. Lancet 370(9585):415–426, 2007.Google Scholar
  26. 26.
    Krogh, A. The rate of diffusion of gases through animal tissues, with some remarks on the coefficient of invasion. J. Physiol. 52(6):391, 1919.Google Scholar
  27. 27.
    Lee, J.-S., and Y.-C. Fung. Flow in nonuniform small blood vessels. Microvasc. Res. 3(3):272–287, 1971.Google Scholar
  28. 28.
    MacDougall, J. D. B., and M. McCabe. Diffusion coefficient of oxygen through tissues. Nature 215:1173–1174, 1967.Google Scholar
  29. 29.
    Martini, J., A. G. Tsai, P. Cabrales, P. C. Johnson, and M. Intaglietta. Increased cardiac output and microvascular blood flow during mild hemoconcentration in hamster window model. Am. J. Physiol. Heart Circ. Physiol. 291(1):H310–H317, 2006.Google Scholar
  30. 30.
    Mirhashemi, S., S. Ertefai, K. Messmer, and M. Intaglietta. Model analysis of the enhancement of tissue oxygenation by hemodilution due to increased microvascular flow velocity. Microvasc. Res. 34(3):290–301, 1987.Google Scholar
  31. 31.
    Mori, K., H. Arai, K. Nakajima, A. Tajima, and M. Maeda. Hemorheological and hemodynamic analysis of hypervolemic hemodilution therapy for cerebral vasospasm after aneurysmal subarachnoid hemorrhage. Stroke 26(9):1620–1626, 1995.Google Scholar
  32. 32.
    Nair, P. K., J. D. Hellums, and J. S. Olson. Prediction of oxygen transport rates in blood flowing in large capillaries. Microvasc. Res. 38(3):269–285, 1989.Google Scholar
  33. 33.
    Nair, P. K., N. S. Huang, J. D. Hellums, and J. S. Olson. A simple model for prediction of oxygen transport rates by flowing blood in large capillaries. Microvasc. Res. 39(2):203–211, 1990.Google Scholar
  34. 34.
    Pasipoularides, A. Optimal hematocrit: a Procrustean bed for maximum oxygen transport rate? J. Appl. Physiol. 113(3):353–354, 2012.Google Scholar
  35. 35.
    Popel, A. S., and J. F. Gross. Analysis of oxygen diffusion from arteriolar networks. Am. J. Physiol. Heart Circ. Physiol. 237(6):H681–H689, 1979.Google Scholar
  36. 36.
    Popel, A. S., and J. D. Hellums. Theory of oxygen transport to tissue. Crit. Rev. Biomed. Eng. 17(3):257, 1989.Google Scholar
  37. 37.
    Popel, A. S., R. N. Pittman, and M. L. Ellsworth. Rate of oxygen loss from arterioles is an order of magnitude higher than expected. Am. J. Physiol. Heart Circ. Physiol. 256(3):H921–H924, 1989.Google Scholar
  38. 38.
    Qiu, Y., and J. M. Tarbell. Numerical simulation of oxygen mass transfer in a compliant curved tube model of a coronary artery. Ann. Biomed. Eng. 28:26–38, 2000.Google Scholar
  39. 39.
    Quintó, L., J. J. Aponte, C. Menéndez, J. Sacarlal, P. Aide, M. Espasa, I. Mandomando, C. Guinovart, E. Macete, and R. Hirt. Relationship between haemoglobin and haematocrit in the definition of anaemia. Trop. Med. Int. Health 11(8):1295–1302, 2006.Google Scholar
  40. 40.
    Ress, D., J. K. Thompson, B. Rokers, R. K. Khan, and A. C. Huk. A model for transient oxygen delivery in cerebral cortex. Front. Neuroenerget. 1:3, 2009.Google Scholar
  41. 41.
    Richardson, T. Q., and A. C. Guyton. Effects of polycythemia and anemia on cardiac output and other circulatory factors. Am. J. Physiol. 197(6):1167–1170, 1959.Google Scholar
  42. 42.
    Sarpkaya, T. Experimental determination of the critical Reynolds number for pulsating Poiseuille flow. J. Basic Eng. 88(3):589–598, 1966.Google Scholar
  43. 43.
    Shepherd, A. P., and G .L. Riedel. Optimal hematocrit for oxygenation of canine intestine. Circ. Res. 51(2):233–239, 1982.Google Scholar
  44. 44.
    Sobin, S. S., Y.-C. Fung, R. G. Lindal, H. M. Tremer, and L. Clark. Topology of pulmonary arterioles, capillaries, and venules in the cat. Microvasc. Res. 19(2):217–233, 1980.Google Scholar
  45. 45.
    Sriram, K., M. Intaglietta, and D. M. Tartakovsky. Hematocrit dispersion in asymmetrically bifurcating vascular networks. Am. J. Physiol. Heart Circ. Physiol. 307(11):H1576–H1586, 2014.Google Scholar
  46. 46.
    Sriram, K., B. Y. Salazar Vazquez, O. Yalcin, P. C. Johnson, M. Intaglietta, and D. M. Tartakovsky. The effect of small changes in hematocrit on nitric oxide transport in arterioles. Antioxid. Redox Signal. 14(2):175–185, 2011.Google Scholar
  47. 47.
    Sriram, K., A. G. Tsai, P. Cabrales, F. Meng, S. A. Acharya, D. M. Tartakovsky, and M. Intaglietta. PEG-Albumin supra plasma expansion is due to increased vessel wall shear stress induced by blood viscosity shear thinning. Am. J. Physiol. Heart Circ. Physiol. 302(12):H2489–H2497, 2012.Google Scholar
  48. 48.
    Sriram, K., B. Y. Vázquez Salazar, A. G. Tsai, P. Cabrales, M. Intaglietta, and D. M. Tartakovsky. Autoregulation and mechanotransduction control the arteriolar response to small changes in hematocrit. Am. J. Physiol. Heart Circ. Physiol. 303(9):H1096–H1106, 2012.Google Scholar
  49. 49.
    Takahashi, G. H., I. Fatt, and T. K. Goldstick. Oxygen consumption rate of tissue measured by a micropolarographic method. J. General Physiol. 50(2):317–335, 1966.Google Scholar
  50. 50.
    Tangelder, G. J., D. W. Slaaf, A. M. Muijtjens, T. Arts, M. G. Oude Egbrink, and R. S. Reneman. Velocity profiles of blood platelets and red blood cells flowing in arterioles of the rabbit mesentery. Circ. Res. 59(5):505–514, 1986.Google Scholar
  51. 51.
    Taylor, A. E. Capillary fluid filtration. Starling forces and lymph flow. Circ. Res. 49:557–575, 1981.Google Scholar
  52. 52.
    Taylor, G. I. Dispersion of soluble matter in solvent flowing slowly through a tube. Proc. R. Soc. London A 219(1137):186–203, 1953.Google Scholar
  53. 53.
    Torres Filho, I. P., H. Kerger, and M. Intaglietta. $\text{ pO }_2$ measurements in arteriolar networks. Microvas. Res. 51(2):202–212, 1996.Google Scholar
  54. 54.
    Tsai, A. G., B. Friesenecker, M. C. Mazzoni, H. Kerger, D. G. Buerk, P. C. Johnson, and M. Intaglietta. Microvascular and tissue oxygen gradients in the rat mesentery. Proc. Natl. Acad. Sci. 95(12):6590–6595, 1998.Google Scholar
  55. 55.
    Winslow, R. M., M. Samaja, N. J. Winslow, L. Rossi-Bernardi, and R. I. Shrager. Simulation of continuous blood O2 equilibrium curve over physiological pH, DPG, and PCO2 range. J. Appl. Physiol. 54(2):524–529, 1983.Google Scholar
  56. 56.
    Womersley, J. R.. Method for the calculation of velocity, rate of flow and viscous drag in arteries when the pressure gradient is known. J. Physiol. 127(3):553, 1955.Google Scholar
  57. 57.
    Zamir, M. The branching structure of arterial trees. Comments Theor. Biol. 1:15–37, 1988.Google Scholar
  58. 58.
    Zimmerman, R. A., G. Severino, and D. M. Tartakovsky. Hydrodynamic dispersion in a tube with diffusive losses through its walls. J. Fluid Mech. 837:546–561, 2018.Google Scholar
  59. 59.
    Zimmerman, R. A., A. Tsai, B. Y. Salazar Vazquez, P. Cabrales, A. Hoffman, J. Meier, A. Shander, D. R. Spahn, J. M. Friedman, D. M. Tartakovsky, and M. Intaglietta. Post-transfusion increase of hematocrit per se does not improve circulatory oxygen delivery due to increased blood viscosity. Anesth. Analg. 124(5):1547–1554, 2017.Google Scholar

Copyright information

© Biomedical Engineering Society 2019

Authors and Affiliations

  1. 1.Los Alamos National LaboratoryLos AlamosUSA
  2. 2.Department of BioengineeringUniversity of California, San DiegoLa JollaUSA
  3. 3.Department of Energy Resources EngineeringStanford UniversityStanfordUSA

Personalised recommendations