AN ANALYSIS OF THE EFFECT OF SYNOVIAL CAPILLARY DISTRIBUTION UPON TRANS-SYNOVIAL CONCENTRATION PROFILES AND EXCHANGE

¹ Department of Physiology, St George's Hospital Medical School, London, SW17 ORE

Recent morphometric studies of synovium lining the rabbit knee showed that capillaries extend to 200 µm below the synovial surface; that a proportion of the superficial capillaries are fenestrated; and that the numerical density of the capillaries varies with depth (Knight & Levick, 1983, 1984). Such observations raised the question ‘Down to what depth do capillaries contribute significantly to the diffusional flux of a small extracellular solute (e.g. sulphate) into the joint cavity?’ This problem was addressed by a mathematical model of trans-synovial diffusion. The periarticular tissue was considered as a stack of thin slices (x = 2-5 µm), each of known depth and capillary population. An expression for interstitial concentration normal to the surface was derived from the Fick diffusion equations and the mass-balance equation for each slice. Morphometric values were substituted into the area and distance terms of the Fick equation. A range of values was explored for two permeability terms, namely D_t/D_i (diffusivity across unit fenestral matrix relative to that across unit interstitial matrix) and PS/Q (permeability-surface area product/blood flow for synovial fenestrated capillaries); the ranges lay between the estimated extreme values. Steady-state concentrations and transcapillary fluxes at each depth were obtained by iterative calculation on a microcomputer. The thickness of tissue from which 80% of the joint influx arose (T_0·8) was 7-13 µm for diffusion-limited transcapillary exchange (PS/Q = 0·05; D_t/D_i = 1-0·03); or 9-17, µm for flow-limited exchange (PS/Q = 5; D_t/D_i = 1-0·03) in areolar synovium, which is the most extensive tissue. The relative independence of the results from the permeability conditions was due to the dominant effect of a peak in capillary density just below the synovial surface. The resistance of the capillary endothelial wall as a fraction of total blood-joint barrier resistance was calculated to be 0·18-0·80 in areolar synovium under conditions of diffusion-limited exchange.