Mathematical modeling of mass transfer in microvascular wall and interstitial space
Department of Chemical Engineering, Chemistry and Environmental Science
Doctor of Philosophy
Armenante, Piero M.
Knox, Dana E.
Kristol, David S.
Duran, Walter Nunez
The dynamics of macromolecular transport across the microvascular wall and into the adjoining interstitial space was studied in the hamster cheek pouch using intravital fluorescence microscopy in combination with digital image processing. Fluorescein isothiocyanate-labe led dextrans (FITC-Dx) of 70,000 and 150,000 daltons were used as tracers. In each experiment, the time-dependent extravasation of FITC-Dx from a leakage site in a blood vessel was videotaped for about 2 hours. The macromolecular transport from individual microvessels was quantified by digital video-image processing. Histograms of the light intensity distributions for selected fields at various times were obtained and then converted to the interstitial FITC-Dx concentrations using a newly developed in vivo calibration procedure.
A one-dimensional unsteady-state model was developed to describe the dynamics of the macromolecular transport. Both molecular diffusion and convective transport in the microvascular wall as well as in the interstitial space were accounted for in the model.
The experimental data were correlated using a non-linear regression algorithm incorporating the mathematical model in order to determine the diffusivity coefficients and average fluid velocity terms in the two regions. The diffusivity coefficients for FITC-Dx 70 were found to be 0.90±0.04x10-11 cm2/s in the microvascular wall, and 1.29±0.05x10-8 cm2/s in the interstitial space. The average fluid velocity term in both regions was found to be 2.05±0.05x10-8 cm/s. The corresponding transport parameters for FITC-Dx 150 were 0.27±0.02x10-11 cm2/s, 0.55±0.0SX10-8 cm2/s, and 1.71±0.48x10-8 cm/s, respectively.
Using a similar experimental procedures, the extravasation of FITC-Dx 70 and FITC-Dx 150 was experimentally determined after a 5-minute topical application of calcium ionophore A23187 (7x10 7 M) which produced a transient increases in the rate of blood-tissue transport of large molecules. In this case, the diffusivity coefficients and average fluid velocity terms were found to be approximately two times and eight times higher, respectively, than the corresponding parameters obtained in the absence of the calcium ionophore A23187.
The diffusivity coefficients and average fluid velocity terms so obtained were then used to quantify the role of the diffusive and convective mechanisms in the total solute flux through the microvascular wall and into the adjoining interstitial space. The macromolecular transport in the microvascular wall was found to be the limiting transport mechanism for the entire process. Within the microvascular wall, it appeared that the molecular diffusion mechanism dominated over convective transport in all the cases considered. However, in the presence of the calcium ionophore A23187 the convection term increased about three times if compared with the corresponding value in the absence of it. Within the interstitial space, diffusion appeared to be the dominating transport mechanism for all cases.
It is expected that the proposed model and calibration procedure will be used in the future to describe the dynamics of macromolecular transfer across the microvascular wall and into the interstitial space on the basis of both molecular diffusion and convective transport mechanisms, thus contributing to the solution of the controversy regarding the nature of the transfer mechanism controlling the transport of macromolecules in living systems.
njit-etd1991-024 (157 pages ~ 6,750 KB pdf)
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Created May 7, 2004