renal clearance / excretion
Introduction
Absolute renal clearance
absolute clearance (mL/min) = urine concentration of substance x urine output rate (mL/min) / plasma concentration of substance
Excretion rate
the calculated rate of excretion via the kidneys for a substance
eg. for uric acid with a clearance of 12mL/min and a serum concentration of 8.0 mg/dL, ~57mg would be excreted each hour
excretion rate (mg/hr) = absolute clearance (ml/min) x 60 x serum concentration of substance (mg/dL)
Elimination Rate Constant (k<sub>e</sub>)
ke(percent per hour) = absolute clearance (L/hr) / volume of distribution (Vd) (L)
volume of distribution (Vd) (L) = fractional Vd/kg x lean body weight (kg)
Elimination half life
elimination half-Life in hours = 0.693 / ke(percent per hour)
Fractional clearance or fractional excretion
fractional clearance (%) = (urine concentration of substance x serum concentration of creatinine) / (urine concentration of creatinine x serum concentration of substance)
Other renal equations
Filtration fraction
filtration fraction = glomerular filtration rate (GFR) / renal plasma flow rate (RPF)
Example - how long does it take to excrete a meal's worth or uric acid?
normal serum concentrations generally range from 3.4 to 7.2 mg/dL (0.20–0.43 mmol/L) in men
uric acid poorly crosses cell membranes hence volume of distribution (Vd) = 0.2-0.3L/lean body weight in kg = 14-21L for an average 70kg adult
GIT bioavailability of purines is ~60%
every 1mg of base purines yields roughly 1.2mg of uric acid
a 300g steak plus a beer gives ~450mg purines of which ~270mg is absorbed and metabolized which gives about 324mg uric acid
assuming 324mg uric acid is absorbed, the expected rise in serum levels would be = 324mg / 17L = 19mg/L = 1.9mg/dL
a renal clearance of 12mL/min for uric acid (upper limit normal range) with serum levels of 10mg/dL would give a uric acid excretion rate of 72mg/hr and thus take the kidneys several hours to reduce serum uric acid levels back to normal after this spike (even longer if impaired renal function, concomitant alcohol or a larger intake)