# Estimate Renal Clearance from Urine versus Time Data

## with suggestions from Sukyung Woo, PhD

A dose of 300 mg was administered intravenously to a healthy volunteer. Total urine samples were collected after 2, 4, 6, 8, 10, 12, 18 and 24 hours. Samples were well mixed and analyzed for drug concentration. The volume of each sample was also recorded. During the study, plasma sample were collected at the midpoint (Tmid) of each collection period. The collected data are shown in the table below.

 Urine Data Plasma Data Time (hr) Urine Volume (ml) Cu (mg/ml) Tmid (hr) Cp (mg/L) 2 127 0.492 1 12.7 4 151 0.255 3 7.82 6 133 0.179 5 4.83 8 164 0.09 7 2.98 10 186 0.049 9 1.84 12 139 0.04 11 1.14 18 410 0.017 15 0.433 24 425 0.004 21 0.102

The table above provides a set of data for you to analyze. Using the plasma data, plot the Cp-time data on a semi-log graph and estimate the overall elimination rate constant, volume of distribution, and total clearance for the drug. Using the urine data, first calculate the amount of unchanged drug excreted during each time interval and then the cumulative amount excreted upto that time point, U. Calculate the rate of excretion during each interval. A plot of the rate of excretion against the corresponding plasma concentration in a linear graph yields a straight line with a slope equal to renal clearance.

Your objective is to estimate kel, total CL, fe, CLr, CLm and ke.

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### Some Equations:

Equation 12.3.1 Total Clearance

Equation 12.3.2 Renal Clearance

Equation 12.3.3 Fraction Excreted Unchanged

Equation 12.3.4 Renal Clearance and Excretion Rate Constant

Equation 12.3.5 Metabolic Clearance

Equation 12.3.6 Metabolic Rate Constant

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