Question 11.1: Calculate the time rate of change of proteoglycans within th...
Calculate the time rate of change of proteoglycans within the synovial fluid, if their diffusion is only restricted by the presence of glycosaminoglycans (GAGs) within the synovial space. Assume that the molecular weight for the proteoglycan of interest is 300 kDa and its density is 1.45 g/mL. The effective radius for the GAGs is 0.5 nm and the volume fraction is 0.008. The free diffusion of proteoglycan in water is 1.1E – 7 cm²/s. The permeability of the proteoglycan through the synovial membrane is 1E – 6 cm/s. Assume that the degradation of the proteoglycan is negligible. The formation rate of proteoglycans within the synovial membrane and the cartilage are 6E – 9 mg/(cm²s) and 3E – 7 mg/(cm²s), respectively. The cross-sectional areas of the synovial membrane and the cartilage are 29.5 mm² and 13.5 mm², respectively. The concentration gradient of the proteoglycan is 0.13 mg/mL.
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