Figure 5
Spatial variation of transforming growth factor beta (TGF-β) concentration within a fed-batch culture. The numerical solutions of Equations (10) and (11) in Additional file 1 are shown for a 24-well-plate well of initial media height h 0 = 5 mm (corresponding to 1 ml culture) for (a) 1 day, (b) 2 days, (c) 4 days, and (d) 8 days. The diffusivity is D = 6.5 × 10−11 m2/second, the cell population is assumed constant at X = 105, and the secretion rate is r ϕ  = 1.94 × 10−6 pg/cell/day. Solid black line indicates the free surface of the cell culture medium, and dashed line indicates the height at which the concentration is 5% of the concentration at the bottom of the culture.