A flat (not spherical) tissue engineered skin (thickness 2.5 mm) is attached to the bottom of a dish and cultured with cell media atop it (which has an oxygen concentration of 0.15 mol/m3). The diffusivity of oxygen in the skin is 3.4 E-9 m2/s, and according to experiments that you’ve performed, you want to make sure that the concentration of oxygen in the device doesn’t fall below 0.06 mol/m3. (Below that concentration harms the cells.) The rate of oxygen consumption is -5.9 E-17 mol/[cell◦s]. What is the maximum cellularity (in cells/mL, three significant digits) that this tissue engineered skin can support?

A flat (not spherical) tissue engineered skin (thickness 2.5 mm) is attached to the bottom of a dish and cultured with cell media atop it (which has an oxygen concentration of 0.15 mol/m3). The diffusivity of oxygen in the skin is 3.4 E-9 m2/s, and according to experiments that you’ve performed, you want to make sure that the concentration of oxygen in the device doesn’t fall below 0.06 mol/m3. (Below that concentration harms the cells.) The rate of oxygen consumption is -5.9 E-17 mol/[cell◦s]. What is the maximum cellularity (in cells/mL, three significant digits) that this tissue engineered skin can support?