Problem 1.1. Dialysis compartment modeling The purpose of this problem is to derive the equations of a compartment model and solve them numerically. The pool of fluid in the body of a patient undergoing dialysis can be modeled as a one-compartment model as shown diagrammatically in the figure. R is the rate of production of urea by the patient's body, V is the volume of intracellular and extracellular (blood and interstitial) fluids, and C is the concentration of urea in the fluids of the compartment, and k is the clearance rate constant of the dialysis unit. urea urea removed production Total pool by dialysis unit of fluid V, C Derive the unsteady mass balance equation of urea for this one-compartment model. Write a code to solve this equation numerically. For patient X, the following parameters apply for this one-compartment model: litres R 100 V=35litres, k=8 When patient X arrives at the dialysis unit his blood urea nitrogen (BUN) is 150 mg/liter. Integrate the differential equation and plot the solution C(t). Based on your solution, how many hours of dialysis will this patient require in order to reduce the level of BUN to 75 mg/liter? After completion of the treatment, how long will it take for the BUN of this patient to rise back to the initial 150 mg/liter level? c) d) please solve it in details, and consider the fact that I will plot c(t) in MATLAB. thanks Problem 1.1. Dialysis compartment modeling The purpose of this problem is to derive the equations of a compartment model and solve them numerically. The pool of fluid in the body of a patient undergoing dialysis can be modeled as a one-compartment model as shown diagrammatically in the figure. R is the rate of production of urea by the patient's body, V is the volume of intracellular and extracellular (blood and interstitial) fluids, and C is the concentration of urea in the fluids of the compartment, and k is the clearance rate constant of the dialysis unit. urea urea removed production Total pool by dialysis unit of fluid V, C Derive the unsteady mass balance equation of urea for this one-compartment model. Write a code to solve this equation numerically. For patient X, the following parameters apply for this one-compartment model: litres R 100 V=35litres, k=8 When patient X arrives at the dialysis unit his blood urea nitrogen (BUN) is 150 mg/liter. Integrate the differential equation and plot the solution C(t). Based on your solution, how many hours of dialysis will this patient require in order to reduce the level of BUN to 75 mg/liter? After completion of the treatment, how long will it take for the BUN of this patient to rise back to the initial 150 mg/liter level? c) d) please solve it in details, and consider the fact that I will plot c(t) in MATLAB. thanks