UNIT 3 ELIMINATION RATE FROM URINARY DATA S.SANGEETHA., M.PHARM., (Ph.d) DEPARTMENT OF PHARMACEUTICS SRM COLLEGE OF PHARMACY SRM UNIVERSITY
Calculation of k el from Urinary Excretion Data after I.V. Injection k el can be calculated from urinary excretion data. The excretion rate of the drug is assumed to be first order. k e is the renal excretion rate constant. D u is the amount of drug excreted unchanged in the urine. 2
Elimination k el = k e + k m 3
For a single i.v. dose, Scheme of the Model IV Dose D B = C p V d k e D u k m dd u /dt = k e D B 4
Rate of Drug Excretion in the Urine Equations But D B = D B0 e k el t dd u = k e D B dt dd dt u = k e D o B e k el t Therefore, ln dd dt u = ln k e D o B k el t 5
Plotting on a Semilog Paper Plot dd u /dt vs. Time k e D B ddu/dt Slope= -k el Time 6
Example Time D u (mg) D u /t mg/hr t* (hr) 0.25 160 160/0.25 640 0.125 0.5 140 140/0.25 560 0.375 1.0 200 200/0.5 400 0.750 2.0 250 250/1 250 1.50 4.0 188 188/2 94 3.0 6.0 46 46/2 23 5.0 7
Difference between t and t* t is the time interval for collection of urine sample. t* is the midpoint of collection period. Assuming renal clearance is constant, D u /t is proportional to plasma drug conc, and plotting D u /t vs. t* is like plotting C p vs. time. The measured urinary excretion rate reflects the average plasma concentration during the collection interval. 8
Why t*? Because the drug urinary excretion rate (dd u /dt) cannot be determined experimentally at any given instant. In practice, urine is collected over a specified time interval, and the urine specimen is analyzed for drug. An average urinary excretion rate is then calculated for that collection period. The average ddu/dt is then plotted against the average time (t*). 9
Determination of the non-renal rate constant (k nr ) k nr = is the elimination rate constant for any route of elimination other than renal excretion. k el k e = k nr Since drug elimination occurs mainly through renal excretion and metabolism, k nr k m k el = k e + k m 10
Determination of renal clearance Renal clearance, Cl R, is defined as the volume of plasma that is cleared of drug per unit of time through the kidney Cl = k V T el d Cl = k R e V d 11
Sigma-Minus Method Also called the Amount of Drug Remaining to be Excreted Method. It is an alternative method for the calculation of k el from urinary excretion data. It is more accurate than the previous method. k e /k el is the fraction of drug excreted unchanged in the urine. (k e /k el )*Dose= total amount of drug excreted unchanged in the urine. 12
Sigma-Minus Method (cont) Equations D u = k e k D 0 k t (1 Where, o D u is the cumulative amount of drug excreted unchanged in the urine until time t. o (1 e k elt ) is the fraction of drug lost from the body. el e el ) 13
Sigma-Minus Method (cont) The amount of drug that is ultimately excreted at time infinity will be equal to D u D u = k e /k el (D 0 ) (2) By substituting in the previous equation (1) D u D u = D u e k elt (3) To obtain a linear equation: Ln (D u D u ) = ln D u k el t (4) Where, (D u D u ) is the amount of drug remaining to be excreted. 14
Sigma Minus Plot On a semilog paper: D u D u -Du Slope= -k el Time 15
Example Use these data to calculate k el Time (hr) D u (mg) D u (cum) D u -D u 0.25 160 160 824 0.5 140 300 684 1.0 200 500 484 2.0 250 750 234 4.0 188 938 46 6.0 46 984 0 16
Cumulative Amount of Drug Excreted in the Urine Plot Cumulative amount excreted D u One needs to collect urine samples for a minimum of 7-10 half-lives of the drug to assure all the drug is excreted into the urine. Time 17
Renal clearance Renal clearance can be determined from model independent equation Cl R = D u [AUC ] 0 18
Fraction of drug excreted The fraction of drug excreted unchanged in the urine (f e ) can be calculated as follows: u D f = = e Dose k k e el k e Cl R = ClT = kel f e Cl T 19
Comparison between the Rate and the Sigma-Minus Method 1 In the rate method, D u need not be known, and the loss of one urine specimen does not invalidate the entire study. 2 The sigma minus method needs accurate determination of D u which requires urine collection until drug excretion is complete. 3 Fluctuations in the rate of drug elimination and experimental errors (such as incomplete bladder emptying) cause considerable departure from linearity in the rate method. 20
Comparison (cont) 4 The sigma minus is less affected by fluctuations in the rate of drug elimination. 5 The rate method is applicable to zero order elimination process, while sigma minus method is not. 6 The k e can be obtained from the rate method but not from the sigma minus method. 21
Problems in Obtaining Valid Urinary Excretion Data 1 A significant fraction of unchanged drug must be excreted in the urine( at least 20 % ). 2 The assay technique must be specific. 3 Frequent sampling is necessary for a good curve description. 4 Urine samples should be collected until almost all drug is excreted(7 t half) 5 Variation in urinary ph and volume cause significant variation in urinary excretion rates. 6 Subjects should be instructed to the importance of complete bladder emptying. 22