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 of 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 (actually longer as does not take into account endogenous production rate and even longer if impaired renal function, concomitant alcohol or a larger intake)