Gel walled cylindrical channels as models for the microcirculation: dynamics of flow

Vessels in the microcirculation have been compared to channels in a gel. A method has been developed whereby a geometrically well defined section of a flow system was composed of a cylindrical gel mantle of outer radius R(G), surrounding a cylindrical channel of radius R. Both the channel and the mantle were of length L and were contained in a rigid transparent support or inner radius R(G). Hence R(G) and L were fixed (R(G) = 1.3 or 4.5 mm; L = 40 mm) and the radius R approx. 0.14 mm could be measured by mounting the whole system on the stage of a microscope fitted with an eye piece micrometer. The gel was crosslinked polyacrylamide swollen with water. Water also served as the flow medium. It was found that R increased with absolute pressure applied statically to the system under no flow conditions. In flow the channel tended to expand upstream and contract downstream. Flow rate Q through the system and pressure drop ΔP were measured and the radius of the channel was monitored as a function of distance x along its length. At low pressure gradients flow rates Q agreed with the theoretically predicted flow rates Q₀ but dropped below Q₀ at higher pressure gradients even though allowance was made for changes in R in calculating Q₀ and flow was shown to be laminar. The extent of deviation decreased with gel rigidity G' and increased with thickness of the gel wall R(G)-R. The results expressed as Q/Q₀ could be correlated when plotted as a function of (R(G)/2LG')ΔP, and corresponded approximately to the function Q/Q₀ = (1-α)⁴. The relevance of these results for the microcirculation is discussed.