Modeling blood flow heterogeneity.
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Journal: 1996/October - Annals of Biomedical Engineering
ISSN: 0090-6964
PUBMED: 8734057
Abstract:
It has been known for some time that regional blood flows within an organ are not uniform. Useful measures of heterogeneity of regional blood flows are the standard deviation and coefficient of variation or relative dispersion of the probability density function (PDF) of regional flows obtained from the regional concentrations of tracers that are deposited in proportion to blood flow. When a mathematical model is used to analyze dilution curves after tracer solute administration, for many solutes it is important to account for flow heterogeneity and the wide range of transit times through multiple pathways in parallel. Failure to do so leads to bias in the estimates of volumes of distribution and membrane conductances. Since in practice the number of paths used should be relatively small, the analysis is sensitive to the choice of the individual elements used to approximate the distribution of flows or transit times. Presented here is a method for modeling heterogeneous flow through an organ using a scheme that covers both the high flow and long transit time extremes of the flow distribution. With this method, numerical experiments are performed to determine the errors made in estimating parameters when flow heterogeneity is ignored, in both the absence and presence of noise. The magnitude of the errors in the estimates depends upon the system parameters, the amount of flow heterogeneity present, and whether the shape of the input function is known. In some cases, some parameters may be estimated to within 10% when heterogeneity is ignored (homogeneous model), but errors of 15-20% may result, even when the level of heterogeneity is modest. In repeated trials in the presence of 5% noise, the mean of the estimates was always closer to the true value with the heterogeneous model than when heterogeneity was ignored, but the distributions of the estimates from the homogeneous and heterogeneous models overlapped for some parameters when outflow dilution curves were analyzed. The separation between the distributions was further reduced when tissue content curves were analyzed. It is concluded that multipath models accounting for flow heterogeneity are a vehicle for assessing the effects of flow heterogeneity under the conditions applicable to specific laboratory protocols, that efforts should be made to assess the actual level of flow heterogeneity in the organ being studied, and that the errors in parameter estimates are generally smaller when the input function is known rather than estimated by deconvolution.
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Ann Biomed Eng 24(3): 352-372
PMID: 8734057

Modeling Blood Flow Heterogeneity

Center for Bioengineering, University of Washington, Seattle, WA
Address correspondence to James B. Bassingthwaighte, M.D., Ph.D., Center for Bioengineering, University of Washington, Box 357962, Seattle, WA 98195-7962, U.S.A
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Abstract

It has been known for some time that regional blood flows within an organ are not uniform. Useful measures of heterogeneity of regional blood flows are the standard deviation and coefficient of variation or relative dispersion of the probability density function (PDF) of regional flows obtained from the regional concentrations of tracers that are deposited in proportion to blood flow. When a mathematical model is used to analyze dilution curves after tracer solute administration, for many solutes it is important to account for flow heterogeneity and the wide range of transit times through multiple pathways in parallel. Failure to do so leads to bias in the estimates of volumes of distribution and membrane conductances. Since in practice the number of paths used should be relatively small, the analysis is sensitive to the choice of the individual elements used to approximate the distribution of flows or transit times. Presented here is a method for modeling heterogeneous flow through an organ using a scheme that covers both the high flow and long transit time extremes of the flow distribution. With this method, numerical experiments are performed to determine the errors made in estimating parameters when flow heterogeneity is ignored, in both the absence and presence of noise. The magnitude of the errors in the estimates depends upon the system parameters, the amount of flow heterogeneity present, and whether the shape of the input function is known. In some cases, some parameters may be estimated to within 10% when heterogeneity is ignored (homogeneous model), but errors of 15–20% may result, even when the level of heterogeneity is modest. In repeated trials in the presence of 5% noise, the mean of the estimates was always closer to the true value with the heterogeneous model than when heterogeneity was ignored, but the distributions of the estimates from the homogeneous and heterogeneous models overlapped for some parameters when outflow dilution curves were analyzed. The separation between the distributions was further reduced when tissue content curves were analyzed. It is concluded that multipath models accounting for flow heterogeneity are a vehicle for assessing the effects of flow heterogeneity under the conditions applicable to specific laboratory protocols, that efforts should be made to assess the actual level of flow heterogeneity in the organ being studied, and that the errors in parameter estimates are generally smaller when the input function is known rather than estimated by deconvolution.

Keywords: Heterogeneity, Circulatory transport, Vascular dispersion, Capillary permeability–surface area products, Blood–tissue exchange kinetics, Indicator dilution
Abstract

Footnotes

Year of publication: 1996

Footnotes

References

  • 1. Abounader R, Vogel J, Kuschinsky WPatterns of capillary plasma perfusion in brains of conscious rats during normocapnia and hypercapnia. Circ Res. 1995;76:120–126.[PubMed][Google Scholar]
  • 2. Audi SH, Krenz GS, Linehan JH, Rickaby DA, Dawson CAPulmonary capillary transport function from flow-limited indicators. J Appl Physiol. 1994;77:332–351.[PubMed][Google Scholar]
  • 3. Audi SH, Linehan JH, Krenz GS, Dawson CA, Ahlf SB, Roerig DLEstimation of the pulmonary capillary transport function in isolated rabbit lungs. J Appl Physiol. 1995;78:1004–1014.[PubMed][Google Scholar]
  • 4. Bassingthwaighte JB, Ackerman FH, Wood EHApplications of the lagged normal density curve as a model for arterial dilution curves. Circ Res. 1966;18:398–415.[Google Scholar]
  • 5. Bassingthwaighte JBPlasma indicator dispersion in arteries of the human leg. Circ Res. 1966;19:332–346.[Google Scholar]
  • 6. Bassingthwaighte JB, Levin MAnalysis of coronary outflow dilution curves for the estimation of cellular uptake rates in the presence of heterogeneous regional flows. Basic Res Cardiol. 1981;76:404–410.[Google Scholar]
  • 7. Bassingthwaighte JB, Goresky CA. Modeling in the analysis of solute and water exchange in the microvasculature. In: Renkin EM, Michel CC, editors. Handbook of Physiology, Section 2, The Cardiovascular System, vol. 4, The Microcirculation. Bethesda, MD: American Physiological Society; 1984. pp. 549–626. [PubMed]
  • 8. Bassingthwaighte JB, Malone MA, Moffett TC, King RB, Little SE, Link JM, Krohn KAValidity of microsphere depositions for regional myocardial flows. Am J Physiol. 253Heart Circ Physiol. 1987;22:H184–H193.[Google Scholar]
  • 9. Bassingthwaighte JB, King RB, Roger SAFractal nature of regional myocardial blood flow heterogeneity. Circ Res. 1989;65:578–590.[Google Scholar]
  • 10. Bassingthwaighte JB, I, Chan S, Wang CYComputationally efficient algorithms for capillary convection-permeation-diffusion models for blood-tissue exchange. Ann Biomed Eng. 1992;20:687–725.[PubMed][Google Scholar]
  • 11. Bronikowski TA, Dawson CA, Linehan JH, Rickaby DAA mathematical model of indicator extraction by the pulmonary endothelium via saturation kinetics. Math Biosci. 1982;61:237–266.[PubMed][Google Scholar]
  • 12. Bronikowski TA, Dawson CA, Linehan JHOn indicator dilution and perfusion heterogeneity: A stochastic model. Math Biosci. 1987;83:199–225.[PubMed][Google Scholar]
  • 13. Chan IS, Goldstein AA, Bassingthwaighte JBSENSOP: A derivative-free solver for non-linear least squares with sensitivity scaling. Ann Biomed Eng. 1993;21:621–631.[Google Scholar]
  • 14. Clough AV, Al-Tinawi A, Linehan JH, Dawson CARegional transit time estimation from image residue curves. Ann Biomed Eng. 1994;22:128–143.[PubMed][Google Scholar]
  • 15. Cobelli C, Saccomani MP, Ferrannini E, Defronzo RA, Gelfand R, Bonadonna RA compartmental model to quantitate in vivo glucose transport in the human forearm. Am J Physiol. 257Endocril Metab. 1989;20:E943–E958.[PubMed][Google Scholar]
  • 16. Cousineau DF, Goresky CA, Rouleau JR, Rose CPMicrosphere and dilution measurements of flow and interstitial space in dog heart. J Appl Physiol. 1994;77:113–120.[PubMed][Google Scholar]
  • 17. Duling BR, Damon DHAn examination of the measurement of flow heterogeneity in striated muscle. Circ Res. 1987;60:1–13.[PubMed][Google Scholar]
  • 18. Glenny RW, Robertson HTFractal modeling of pulmonary blood flow heterogeneity. J Appl Physiol. 1991;70:1024–1030.[PubMed][Google Scholar]
  • 19. Gonzalez F, Bassingthwaighte JBHeterogeneities in regional volumes of distribution and flows in the rabbit heart. Am J Physiol. 258Heart Circ Physiol. 1990;27:H1012–H1024.[Google Scholar]
  • 20. Haselton FR, Parker RE, Roselli RJ, Harris TRAnalysis of lung multiple indicator data with an effective diffusivity model of capillary exchange. J Appl Physiol. 1984;57:98–109.[PubMed][Google Scholar]
  • 21. Hoedt-Rasmussen K, Sveinsdottir E, Lassen NARegional cerebral blood flow in man determined by intraarterial injection of radioactive inert gas. Circ Res. 1966;18:237–247.[PubMed][Google Scholar]
  • 22. King RB, Bassingthwaighte JB, Hales JRS, Rowell LBStability of heterogeneity of myocardial blood flow in normal awake baboons. Circ Res. 1985;57:285–295.[Google Scholar]
  • 23. King RB, Deussen A, Raymond GR, Bassingthwaighte JBA vascular transport operator. Am J Physiol. 265Heart Circ Physiol. 1993;34:H2196–H2208.[Google Scholar]
  • 24. Kirkebo A, Haugan A, Tyssebotn IBlood flow heterogeneity in the renal cortex during bum shock in dogs. Acta Physiol Scand. 1985;123:205–213.[PubMed][Google Scholar]
  • 25. Knopp TJ, Dobbs WA, Greenleaf JF, Bassingthwaighte JBTranscoronary intravascular transport functions obtained via a stable deconvolution technique. Ann Biomed Eng. 1976;4:44–59.[Google Scholar]
  • 26. Kroll K, Stepp DWAdenosine kinetics in the canine coronary circulation. Am J Physiol. 269Heart Circ Physiol. 1996;38[PubMed][Google Scholar]
  • 27. Rose CP, Goresky CAVasomotor control of capillary transit time heterogeneity in the canine coronary circulation. Circ Res. 1976;39:541–554.[PubMed][Google Scholar]
  • 28. Rowlett RD, Harris TRA comparative study of organs models and numerical techniques for the evaluation of capillary permeability from multiple-indicator data. Math Biosci. 1976;29:273–298.[PubMed][Google Scholar]
  • 29. Stapleton DD, Moffett TC, Baskin DG, Bassingthwaighte JBAutoradiographic assessment of blood flow heterogeneity in the hamster heart. Microcirculation. 1995;2:277–282.[Google Scholar]
  • 30. van Beek JHGM, Bassingthwaighte JB, Roger SAFractal networks explain regional myocardial flow heterogeneity. Adv Exp Med Biol. 1989;248:249–257.[Google Scholar]
  • 31. Wolpers HG, Geppert V, Hoeft A, Korb H, Schrader R, Hellige GEstimation of myocardial blood flow heterogeneity by transorgan helium transport functions. Pflugers Arch. 1984;401:217–222.[PubMed][Google Scholar]
  • 32. Yipintsoi T, Dobbs WA, Jr, Scanlon PD, Knopp TJ, Bassingthwaighte JBRegional distribution of diffusible tracers and carbonized microspheres in the left ventricle of isolated dog hearts. Circ Res. 1973;33:573–587.[Google Scholar]
  • 33. Zierler KLA critique of compartmental analysis. Annu Rev Biophys Bioeng. 1981;10:531–562.[PubMed][Google Scholar]
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