Question

(25 pts) You construct an organ-on-a-Chip (OOC) system to model an organ so you can evaluate different drugs for a pharmaceutical company. The chip allows injection of the organ chamber with a constant volumetric flow rate (Q) from one side and leaks through a membrane from the other side with a leak rate constant, k1 to model drug administration and adsorption. Create and solve a single compartment model of the OOC.

a. (5 pts) Sketch a single compartmental model of the chip system. Be sure to show Q (the volumetric flow rate entering the control volume), V (the control volume of the chamber which we are modeling), and k1.

b. (5 pts) Starting with the conservation of mass, derive an equation to describe how the liquidvolume changes and put it into our standard differential equation form. Hint: Since only mass is conserved, you need to represent mass as a the product of volume and another property.

c. (15 pts) Find the integration factor and solve the differential equation. The integration constant can be solved by using an initial OOC volume of Vo. d. (5 pts) Given kl = 0.025/min, Vo = 0.5uL, and Q = 0.5 uL/minute, determine the amount of time until the OOC has reached its maximum volume capacity assuming it can hold up to 15uL of fluid

Answer 1