An analysis of the effect of synovial capillary distribution upon trans-synovial concentration profiles and exchange

Recent morphometric studies of synovium lining the rabbit knee showed that capillaries extend to greater than 200 microns 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 (delta chi = 2.5 microns), 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 Df/Di (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 (T0.8) was 7-13 microns for diffusion-limited transcapillary exchange (PS/Q = 0.05; Df/Di = 1-0.3); or 9-17 microns for flow-limited exchange (PS/Q = 5; Df/Di = 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.