Question

2. Renal Function and Dialysis Metabolism of protein in your diet produces urea as a byproduct. The rate of urea production (r_u) depends on how much protein you eat and how big you are (measured by your body fluid volume, V). A realistic urea production rate for an average person (\/=40 L) is about r_u= 15 mg/min. Urea produced in the liver is rapidly distributed throughout the body's fluid volume V; the average urea concentration in the body's fluids is rho_u. The kidneys remove urea from the body's fluids (via the blood), leading to excretion in urine. The mass flow rate of urea excreted by the kidneys as urine is proportional to the urea concentration in the body fluids and is given by m^dot_u, urine = K_R rho_u The constant K_R, known as the "renal clearance" (units mL/min), depends on how well your kidneys are functioning. Consider the case of homeostasis (biomedical jargon for "steady state"). For an individual with a urea production rate of r_u=15 mg/min and good kidneys with K_R=75 mL/min, what is the steady state urea concentration in the body fluid? Express your answer in mg/dL. Also multiply this value by 0.48 to convert rho_u to blood urea nitrogen (BUN; typical values 6-24 mg/dL). Assuming homeostasis, a blood test for this individual indicates a BUN value of 60 mg/dL. What is the value of renal clearance (K_R) in this situation (known as uremia, an indication of renal insufficiency)? Suppose this individual experiences kidney failure (K_R=0). Develop and solve an unsteady state urea mass balance to determine the urea concentration in the body fluids (rho_u) as a function of time. How long will it take for the urea concentration to increase from 0 to a dangerous level (rho_u = 300 mg/dL)? You may assume homeostasis in the water balance (V=40 L is constant). Renal failure may be treated through dialysis: an external, artificial kidney (dialyzer) removes urea from the blood. An intravenous drip replaces lost water, so V=40 L is again constant. The dialyzer produces an output mass flow of urea given by M^dot_u, dial = K_D rho_u with K_D (units mL/min) denoting the dialyzer clearance. Suppose that for a good dialyzer, K_D =250 mL/min. Develop and solve an unsteady state urea mass balance to determine the urea concentration in the body fluids (rho_u) as a function of time. How long will it take for the urea concentration (rho_u) to decrease from 300 mg/dL to 30 mg/dL?

Answer 1

Ru = 15 mg/min

Kr = 75 mL /min

a) Steady state of urea concentration in body fluid = Ƥ = mu / Kr ( From given equation)

substituting the values = ( 15 mg/min ) / 75 ml/min

= 0.2 mg /mL

= 20 mg / dL

BUN = 20 x 0.48 = 9.6 mg / dL

b) BUN = 60 mg /dL, Kr =?

BUN = Ƥ x 0.48

60 = Mu/Kr x 0.48

Kr= (15 /60 ) x 0.48

Kr = 0.12dL/min

c) Production of urea is 15 mg/min

Total volume = 40

So total production = 15/40 = 0.33 mg /L

0.033 mg /dL /min

Toxic level = 300 mg /dL

Therefore time required to reach toxic level = 300 / 0.033

= 10000 min

= 166 h

= 7 days