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Article

# Determination of Microvessel Permeability and Tissue Diffusion Coefficient of Solutes by Laser Scanning Confocal Microscopy

[+] Author and Article Information
Bingmei M. Fu1

Department of Mechanical Engineering, Cancer Institute,  University of Nevada, Las Vegas, 4505 Maryland Parkway, Box 454027, Las Vegas, NV 89154fu@ccny.cuny.edu

Roger H. Adamson, Fitz-Roy E. Curry

Department of Human Physiology, School of Medicine,  University of California at Davis, Davis, CA 95616

1

Corresponding author. Current address: Department of Biomedical Engineering, The City College of the City University of New York, 138th Street at Convent Avenue, New York, NY 10031.

J Biomech Eng 127(2), 270-278 (Sep 18, 2004) (9 pages) doi:10.1115/1.1865186 History: Received May 22, 2003; Revised September 18, 2004

## Abstract

Interstitium contains a matrix of fibrous molecules that creates considerable resistance to water and solutes in series with the microvessel wall. On the basis of our preliminary studies (Adamson, 1994, Microcirculation1(4), pp. 251–265; Fu, 1995Am. J. Physiol.269(38), pp. H2124–H2140), by using laser-scanning confocal microscopy and a theoretical model for interstitial transport, we determined both microvessel solute permeability $(P)$ and solute tissue diffusion coefficient $(Dt)$ of $α$-lactalbumin (Stokes radius $2.01nm$) from the rate of tissue solute accumulation and the radial concentration gradient around individually perfused microvessel in frog mesentery. $Pα‐lactalbumin$ is $1.7±0.7(SD)×10−6cm∕s(n=6)$. $Dt∕Dfree$ for $α$-lactalbumin is $27%±5%(SD)(n=6)$. This value of $Dt∕Dfree$ is comparable to that for small solute sodium fluorescein (Stokes radius $0.45nm$), while $Pα‐lactalbumin$ is only 3.4% of $Psodiumfluorescein$. Our results suggest that frog mesenteric tissue is much less selective to solutes than the microvessel wall.

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## Figures

Figure 1

Schematic of double-barreled θ pipette (b) and its holder (a) (modified from Refs. 14-15). Each lumen of the θ pipette is connected to a water manometer that allows alternate perfusion of the downstream microvessel with a washout solution containing no fluorescent solute or the test solution containing the fluorescent solute. This arrangement also enables perfusion at known pressures.

Figure 2

(a) Illustration of the orientation and the dimension of the x–z optical section transverse to the capillary in the mesentery. The mesentery is arranged horizontally on the surface of the coverslip that forms the base of the observation stage. The optical section is composed of multiple line scans of the laser along the x axis, collected as the objective is lowered along the z axis. (b) When the fluorescein-dyed α-lactalbumin is perfused into the vessel lumen, the dye will travel across the vessel wall and accumulate in the tissue space surrounding the vessel. (c) An x–z confocal image after 13s perfusion of FITC-α-lactalbumin. It shows that the fluorescence dye fills the microvessel lumen and spreads in the surrounding tissue [schematic in (b)].

Figure 3

Total fluorescence intensity in the tissue surrounding a microvessel as a function of perfusion time. Fluorescence intensity in this figure is proportional to the total mass of solute accumulated in the measuring region surrounding the microvessel. Data are from images taken every 12to13s. The slope of regression line over the initial linear accumulation is used for the estimation of permeability in Eq. 1. For this run the permeability to α-lactalbumin is 1.4×10−6cm∕s.

Figure 4

Temporal and spatial fluorescence intensity profiles in the tissue surrounding a microvessel. Noisy lines are experimental results at perfusion time=13,26,39,52s. Values are averaged over three measurements along the centerline of the tissue sample in the x direction. Smooth lines are the best-fitting theoretical model predictions when the appropriate value of the effective solute diffusion coefficient Dt is chosen. Dt∕Dfree=0.35 in this experiment.

Figure 5

In vitro calibration of fluorescence intensity versus concentration under two gain settings. High gain of the averaged value 5 is used to record the detailed fluorescence intensity profiles in the tissue surrounding the perfused microvessel when the fluorescence intensity is saturated in the vessel lumen, where the highest tracer concentration is. Low gain of the averaged value 3.6 is used to measure the lumen intensity when it is not saturated. The ratio of the slopes of the regression lines for those measurements under two gain settings gives the scaling factor F described in the text.

Figure 6

Accumulation of fluorescence intensity in tissue during Ringer superfusion (filled circles) compared with accumulation during mineral oil superfusion (filled squares). The two runs on one vessel recorded about 12min apart are superimposed by aligning the time base with respect to the initiation of perfusion with FITC-α-lactalbumin. The initial rate of accumulation is not different, indicating that a nonsignificant amount of solutes escaped through the mesothelial surface.

Figure 7

Fluorescence intensity profiles along the horizontal centerline of the tissue sample around a noncannulated vessel during 2mg∕ml FITC-α-lactalbumin superfusion on the mesentery surface at time=26,77,128,179s. This mesentery has minor mesothelium damage on the left-hand side of the vessel and no damage on the other side. The damaged site is about 150μm from the edge of the vessel on the left. Fluorescence intensity shown here is expressed as the ratio to the intensity of the superfusate.

Figure 8

Tissue concentration profile (solid noisy line) at time t=52s. Tissue concentration Ct(xt,t) is expressed as the ratio to the vessel wall concentration Ca(t). (a) Effect of permeability P on the determination of effective solute diffusion coefficient in tissue Dt when P has three values: measured P=2.3×10−6cm∕s (long-dashed line), corrected Pc=1.1P (short-dashed line) and 10P (dash-dot-dash line). The long-dashed line overlaps with the short-dashed line. (b) Fitting curves when the ratio of effective diffusion coefficient in the tissue to free-diffusion coefficient Dt∕Dfree=0.5 (dotted line), 0.35 (dashed line), and 0.2 (dash-dot-dot-dash line).

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