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A model of fluid, erythrocyte, and solute transport in the lung

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Abstract

A mathematical model of fluid, solute, and red cell transport in the lung has been developed that includes the effects of simultaneous changes in lung vascular and interstitial volumes. The model provides separate arterial, microvascular, and venous pulmonary regions and a systemic vascular region in addition to a pulmonary interstitial compartment. Pressure, volume, hematocrit, flow, and concentration of up to 12 solutes and tracers can be computed in each compartment. Computer code is written in the C programming language, with Microsoft Excel serving as a user interface. Implementation is currently on PC-486 microcomputer systems, but the core program can easily be moved to other computer systems. The user can select different models for the blood-interstitial barrier (e.g. multiple pore, nonlinear Patlak equation), osmotic pressure-concentration relationships (e.g., Nitta, Navar-Navar), solute reflection coefficients, interstitial macromolecule exclusion, or lymph barrier characteristics. Each model parameter or a combination of parameters can be altered with time in a predetermined fashion. The model is particularly useful in interpreting lung experimental data where simultaneous changes occur in vascular and extravascular compartments. Several applications are presented and discussed, including interpretation of optical filtration experiments, venous occlusion experiments, external detection of macromolecular exchange, and blood-lymph studies that use exogenous tracers. A number of limitations of the model are identified and improvements are proposed. A major strength of the model is that it is specifically designed to incorporate newly discovered relationships as the field of lung physiology expands.

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References

  1. Abernathy, V. J., N. A. Pou, T. L. Wilson, R. E. Parker, S. N. Mason, J. A. Clanton, L. J. Baudendistel, and R. J. Roselli. Noninvasive measures of radiolabeled dextran transport in in situ rabbit lung.J. Nucl. Med. 36:1436–1441, 1995.

    PubMed  CAS  Google Scholar 

  2. Arturson, G., and G. Wallenius. The intravascular persistence of dextran of different molecular sizes in normal humans.Scand. J. Clin. Lab. Invest. 1:76–80, 1964.

    Google Scholar 

  3. Barman, S. A., and A. E. Taylor. Histamine’s effect on pulmonary vascular resistance and compliance at elevated tone.Am. J. Physiol. 257:H618-H625, 1989.

    PubMed  CAS  Google Scholar 

  4. Bert, J. L., and R. H. Pearce. The interstitium and microvascular exchange. In:Handbook of Physiology. The Cardiovascular System. IV. Microcirculation, edited by E. M. Renkin and C. C. Michel. Bethesda, MD: American Physiological Society, 1984, pp. 521–547.

    Google Scholar 

  5. Blake, L., and N. Staub. Pulmonary vascular transport in sheep: a mathematical model.Microvasc Res. 12:197–220, 1976.

    Article  PubMed  CAS  Google Scholar 

  6. Cope, D. K., F. Grimbert, J. M. Downey, and A. E. Taylor. Pulmonary capillary pressure: a review.Crit. Care Med. 20:1043–1056, 1992.

    Article  PubMed  CAS  Google Scholar 

  7. Curry, F. R., and C. C. Michel. A fiber matrix model of capillary permeability.Microvasc. Res. 20:96–99, 1980.

    Article  PubMed  CAS  Google Scholar 

  8. Dawson, C. A., J. H. Linehan, D. A. Rickaby, and G. S. Krenz. Effect of vasoconstriction on longitudinal distribution of pulmonary vascular pressure and volume.J. Appl. Physiol. 70:1607–1616, 1991.

    PubMed  CAS  Google Scholar 

  9. Dawson, C. A., D. A. Rickaby, J. H. Linehan, and T. A. Bronikowsky. Distributions of vascular volume and complicance in the lung.J. Appl. Physiol. 64:266–273, 1988.

    PubMed  CAS  Google Scholar 

  10. Fung, Y. C., and H. T. Tang. Solute distribution in the flow in a channel bounded by porous layers: a model of the lung.J. Appl. Mech. 42:531–535, 1975.

    Google Scholar 

  11. Fung, Y. C., and R. T. Yen. A new theory of pulmonary blood flow in zone 2 condition.J. Appl. Physiol. 60:1638–1650, 1986.

    PubMed  CAS  Google Scholar 

  12. Gallenger, H., D. Garewal, R. E. Drake, and J. C. Gabel. Estimation of lymph flow by relating lymphatic pump function to passive flow curves.Lymphology 26:56–60, 1993.

    Google Scholar 

  13. Gorin, A. B., W. J. Weidner, R. Demling, and N. C. Staub. Noninvasive measurement of pulmonary transvascular protein flux in sheep.J. Appl. Physiol. 45:225–233, 1978.

    PubMed  CAS  Google Scholar 

  14. Harris, N. R., R. E. Parker, N. A. Pou, and R. J. Roselli. Canine pulmonary filtration coefficient calculated from optical, radioisotope, and weight measurements.J. Appl. Physiol. 73:2648–2661, 1992.

    PubMed  CAS  Google Scholar 

  15. Harris, T. R., and R. J. Roselli. A theoretical model of protein, fluid, and small molecule transport in the lung.J. Appl. Physiol. 50:1–14, 1981.

    PubMed  Google Scholar 

  16. Lanken, P. N., J. H. Hansen-Flaschen, P. M. Sampson, G. G. Pietra, F. R. Haselton, and A. P. Fishman. Passage of uncharged dextrans from blood to lung lymph in awake sheep.J. Appl. Physiol. 59:580–591, 1985.

    PubMed  CAS  Google Scholar 

  17. Levick, J. R. An analysis of the interaction between interstitial plasma protein, interstitial flow, and fenestral filtration and its application to synovium.Microvasc. Res. 47:90–125, 1994.

    Article  PubMed  CAS  Google Scholar 

  18. Linehan, J. H., and C. A. Dawson. A three compartment model of the pulmonary vasculature: effects of vasoconstriction.J. Appl. Physiol. 55:923–928, 1983.

    PubMed  CAS  Google Scholar 

  19. Linehan, J. H., C. A. Dawson, and D. A. Rickaby. Distribution of vascular resistance and compliance in a dog lung lobe.J. Appl. Physiol. 53:158–168, 1982.

    PubMed  CAS  Google Scholar 

  20. Linehan, J. H., C. A. Dawson, D. A. Rickaby, and T. A. Bronikowski. Pulmonary vascular compliance and viscoelasticity.J. Appl. Physiol. 61:1802–1814, 1986.

    PubMed  CAS  Google Scholar 

  21. Linehan, J. H., S. T. Haworth, L. D. Nelin, G. S. Krenz, and C. A. Dawson. A simple distensible vessel model for interpreting pulmonary vascular pressure-flow curves.J. Appl. Physiol. 73:987–994, 1992.

    PubMed  CAS  Google Scholar 

  22. McNamee, J. E. Restricted dextran transport in the sheep lung lymph preparation.J. Appl. Physiol. 52:585–590, 1982.

    PubMed  CAS  Google Scholar 

  23. McNamee, J. E., and N. C. Staub. Pore models of sheep lung microvascular barrier using new data on protein tracers.Microvasc. Res. 18:229–244, 1979.

    Article  PubMed  CAS  Google Scholar 

  24. Ogston, A. G., B. N. Preston, and J. D. Wells. On the transport of compact molecules through solutions of chainpolymers.Proc. R. Soc. Lond. (A) 333:317–336, 1973.

    Article  Google Scholar 

  25. Paine, P. L., and P. Scherr. Drag coefficients for movements of rigid spheres through liquid filled pores.Biophys. J. 15:1087–1091, 1975.

    Article  PubMed  CAS  Google Scholar 

  26. Pappenheimer, J. R., E. M. Renkin, and L. M. Borrero. Filtration, diffusion and molecular sieving through peripheral capillary membranes.Am. J. Physiol. 167:13, 1951.

    PubMed  CAS  Google Scholar 

  27. Parker, J. C., M. I. Townsley, and J. T. Cartledge. Lung edema increases transvascular filtration rate but not filtration coefficient.J. Appl. Physiol. 66:1553–1560, 1989.

    PubMed  CAS  Google Scholar 

  28. Patlak, C. S., D. A. Goldstein, and J. F. Hoffman. The flow of solute and solvent across a two-membrane system.J. Theor. Biol. 5:426–442, 1963.

    Article  PubMed  CAS  Google Scholar 

  29. Pou, N. A., R. J. Roselli, R. E. Parker, J. A. Clanton, and T. R. Harris. Measurement of fluid volumes and albumin exclusion in sheep lungs.J. Appl. Physiol. 67:1323–1330, 1989.

    PubMed  CAS  Google Scholar 

  30. Reddy, N. P., T. A. Krouskrop, and P. H. Newell, {jrJr.} A note on the mechanisms of lymph flow through the terminal lymphatics.Microvasc. Res. 10:2104–2106, 1975.

    Article  Google Scholar 

  31. Rippe, B., J. C. Parker, M. I. Townsley, N. A. Mortillaro, and E. E. Taylor. Segmental vascular resistances and compliances in dog lung.J. Appl. Physiol. 62:1206–1215, 1987.

    PubMed  CAS  Google Scholar 

  32. Roselli, R. J., S. R. Coy, and T. R. Harris. Models of lung transvascular fluid and protein transport.Ann. Biomed. Eng. 15:127–138, 1987.

    Article  PubMed  CAS  Google Scholar 

  33. Roselli, R. J., and T. R. Harris. Lung fluid and macromolecular transport. In:Respiration Physiology: An Analytical Approach, edited by H. K. Chang and M. Paiva. New York: Marcel Dekker, 1989, pp. 633–735.

    Google Scholar 

  34. Roselli, R. J., R. E. Parker, and T. R. Harris. A model of unsteady-state transvascular fluid and protein transport in the lung.J. Appl. Physiol. Respir. Environ. Exercise Physiol. 56:1389–1402, 1984.

    CAS  Google Scholar 

  35. Roselli, R. J., and W. R. Riddle. Analysis of non-invasive microvascular macromolecular transport measurements in the lung.J. Appl. Physiol. 67:2343–2350, 1989.

    PubMed  CAS  Google Scholar 

  36. Schnitzer, J. E. Fiber matrix model reanalysis: matrix exclusion limits define effective pore radius describing capillary and glomerular permselectivity.Microvasc. Res. 43:342–346, 1992.

    Article  PubMed  CAS  Google Scholar 

  37. Tack, G., R. J. Roselli, K. A. Overholser, and T. R. Harris. The use of Microsoft Excel as a user interface for biological simulations.Comp. Biomed. Res. 28:24–37, 1995.

    Article  CAS  Google Scholar 

  38. Weinbaum, S., R. Tsay, and F. E. Curry. A three-dimensional junction-pore-matrix model for capillary permeability.Microvasc. Res. 44:85–111, 1992.

    Article  PubMed  CAS  Google Scholar 

  39. Wolf, M. B., P. D. Watson, and D. R. C. Scott, {jrII}. The integral mass balance method for determination of the solvent drag reflection coefficient.Am. J. Physiol. 253:H194-H204, 1987.

    PubMed  CAS  Google Scholar 

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Authors and Affiliations

  1. Department of Biomedical Engineering, Vanderbilt University, School of Engineering, Box 36, Station B, 37235, Nashville, TN, USA

    Robert J. Roselli, Gyerae Tack & Thomas R. Harris

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  1. Robert J. Roselli
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  2. Gyerae Tack
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Roselli, R.J., Tack, G. & Harris, T.R. A model of fluid, erythrocyte, and solute transport in the lung. Ann Biomed Eng 25, 46–61 (1997). https://doi.org/10.1007/BF02738537

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  • DOI: https://doi.org/10.1007/BF02738537

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