The state of health and functioning of the liver is often assessed with dye-tracer techniques. The dye used most frequently is bromosulfophthalein (abbreviated BSP). With normal function liver, the dye will be removed from circulation after it is conjugated with cysteine or glutathione (which happens in the liver) following a first order kinetics k=0.5 hr-1 at 37°C. The usual clinical procedure is to have a single injection to the blood and then to measure the amount remaining in the liver after a certain period of time. Liver function is assessed by comparing the experimental value with the range of normal values. Assuming the flow of the dye from the blood stream to liver is donor control and of linear relationship (k12= 1 hr-1 ).1) Identify the engineering principles needed to solve this problem.2) Develop the differential equations to describe the amount of drug in each compartment 3) Clearly state your assumptions 4) Find the amount of the dye in the liver 1 hours after an injection of 10 mg of the dye into the blood stream 5) If the amount of the dye in the liver is determined to be 4.0 mg after 1 hour of injection. What can potentially go wrong with this patient?