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Transcript
LEARNING OBJECTIVES Understand the role of renal excretion on the drug elimination Know the routes of drug elimination and relevant elimination rateconstants Identify the equations to estimate kinetic parameters from the urine concentration-time data and plasma concentration-time data after IV bolus Appreciate the reasonable urine collection period to estimate the total amount of drug excreted in urine Review renal clearance Compile the data to determine the renal clearance Understand the pros and cons of cumulative and urinary excretion rate methods used to calculate fraction-dose excreted Calculate the following parameters using the urine data Half-life and elimination rate-constant Total amount of drug excreted in the urine Unchanged fraction-drug excreted in the urine Urinary excretion rate constant ROUTES OF DRUG ELIMINATION The term ‘drug elimination’ encompasses all the processes involved in the removal of a drug from the body Two major processes of drug elimination are Renal excretion Metabolism in the liver (primary) The kidney in conjunction with the liver eliminates over 90% of drugs The excretion of the parent drug into the bile is the third major route of drug elimination that removes <10% of intact drugs Drugs are also excreted in the sweat and exhaled-air RENAL ELIMINATION AND HEPATIC METBAOLISM Renal elimination Drug moves or excreted from the blood to the renal tubule and then eliminated in the urine. Metabolism The parent drug is converted to one or more molecular entities, called, metabolites, via enzymatic action Metabolites may again be metabolized and then excreted in the urine and bile Pharmacokinetics of metabolites When a drug becomes a metabolite, the drug is considered to be eliminated If the metabolite has no pharmacological activity, pharmacokinetics does not evaluate the elimination of inactive metabolites The pharmacokinetics of active-metabolites is often studied DRUG ELIMINATION KINETICS Drug-elimination can be monitored by the elimination rateconstant (k) The slope of the plasma concentration-time plot will give you k Drug elimination rate is composed of two major components Urinary excretion rate-constant (𝑘𝑟 ) Metabolic rate-constant (𝑘𝑚 ) o 𝑘 = 𝑘𝑟 + 𝑘𝑚 The term ‘non-renal rate (𝑘𝑛𝑟 )’ include all possible elimination pathways, although 𝑘𝑛𝑟 equals to 𝑘𝑚 under normal circumstances k can be written as o 𝑘 = 𝑘𝑟 + 𝑘𝑛𝑟 CALCULATION OF ELIMINATION RELATED KINETIC PARAMETERS To calculate kinetic parameters related to elimination, we first have to know how to manipulate urine data I will use the data below to explain the concept Cumulative urinary excretion plot Urinary excretion-rate plot Sampling of urine THE CUMULATIVE URINARY EXCRETION PLOT AND FRACTION-DOSE EXCRETED A plot of total intact drug excreted in the urine, during a certain time-period, against the collection time is called the cumulative urinary excretion plot Consider the urinary data (Table next slide) of a 200 mg IV bolus injection After 96 h, no drug was in the urine The line flattened out after 96 hr The total amount excreted is 144 mg Fraction-dose excreted unchanged is 0.72; 72% of the dose 𝑓𝑒 = 𝐴∞ 𝑢 𝐷𝑜𝑠𝑒 = 144 200 = 0.72 THE CUMULATIVE URINARY EXCRETION PLOT PLASMA HALF-LIFE FROM THE URINE DATA When the plasma data are not available, you can use urine data to calculate the half-life and rate-constant Plasma data may not be available for a number of reasons: No good assay method to quantitate the drug in the plasma To avoid invasive plasma sampling in some patients such as pediatrics A plot of the urinary-excretion-rate vs time is used to calculate plasma half-life from the urine data. URINARY EXCRETION RATE-PLOT The relation between urinary excretion rate ( 𝑑𝐴𝑢 𝑑𝑡 𝑑𝐴𝑢 ) 𝑑𝑡 and time is written as = 𝑘𝑟 × 𝐷 You can rearrange this equation to a straight line equation 𝐴 = 𝐴0 × 𝑒 −𝑘𝑡 = 𝐷𝑜𝑠𝑒 × 𝑒 −𝑘𝑡 𝑑𝐴𝑢 = 𝑑𝑡 𝑑𝐴 ln 𝑢 𝑑𝑡 𝑘𝑟 × 𝐷𝑜𝑠𝑒 × 𝑒 −𝑘𝑡 = l𝑛 𝑘𝑟 × 𝐷𝑜𝑠𝑒 − 𝑘𝑡 A plot of log urinary excretion rate vs time will give a straight-line Slope ‘-k’ of this line is the same as the slope of log plasma concentration-time plot The 𝑡1/2 from the urinary-excretion-rate plot equals the plasma 𝑡1/2 The urinary-excretion-rate cannot be determined at a particular time because the urine is collected over a time-interval (e.g. from 0-2 h). The excretion-rate for an interval is plotted against the midpoint (time) of the collection interval (e.g. 1 h) GRAPHING OF THE URINARY EXCRETION RATE PLOT AND CALCULATIONS OF PLASMA k AND 𝑡1/2 First, you calculate the excretion rates by dividing the drug amount in the urine for every collection period by the duration of time for that interval. The midpoint time is the middle of the collection time The half-life is 8.9 hr and overall rate-constant is 0.0778 hr-1 The slope of this line (-k) is similar to the slope of plasma-concentrationtime on a log-graph Au means Du DURATION FOR URINE SAMPLE COLLECTION To estimate the cumulative amount of urinal drug excretion(𝑨∞ 𝒖 ), you first determine the duration, for collection of urine samples, after which little or no drug will come out in the urine . We have two methods to decide the timespan for urine collection Plasma half-life Fraction-dose un-excreted HALF-LIFE TO DETERMINE THE TIMESPAN FOR URINE COLLECTION U The extent of urinal drug (𝐴∞ 𝑢 ) excretion depends on drug’s halflife The urinal drug excretion represents the fraction-drug eliminated from the plasma by all the methods of elimination Since 50% of the dose is eliminated after one half-life, 50% of total urinal drug excretion (𝐴∞ 𝑢 ) is assumed to be excreted in the urine, although 50% of 𝐴∞ 𝑢 may not represent 50% of the dose because drug elimination also occurs via routes other than urinal elimination After 4 plasma t1/2, 93.7% of the dose will be eliminated that represent 93.7% total urinal excretion (𝐴∞ 𝑢) Urine collection up to ≥4 half-lives gives us a good estimate of 𝐴∞ 𝑢 𝐹𝑟𝑎𝑐𝑡𝑖𝑜𝑛 − 𝑑𝑜𝑠𝑒 𝑟𝑒𝑚𝑎𝑖𝑛𝑖𝑛𝑔 = 1 2 n For data presented in table (slide 10), 36 (4x9) hrs would be an appropriate timespan for sample collection. FRACTION-DOSE UNEXCRETED TO DETERMINE THE TIMESPAN FOR URINE COLLECTION To determine the timespan for urine collection from the fraction-dose un-excreted (the dose remaining in the body), you can use the expression ‘𝑒 −𝑘𝑡 ’ Assume you want to determine the timespan for 95% 𝐴∞ 𝑢 that represent elimination of 95% of the drug Thus the fraction-dose un-excreted (𝑒 −𝑘𝑡 ) is 0.05 (1 − 0.95) 𝑒 −𝑘𝑡 = 0.05; −𝑘𝑡 = ln 0.05; −0.0.0778 𝑡 = −3.0; 𝑡 = 38.6ℎ The timespan of 38.6 hr, for 95% 𝐴∞ 𝑢 , is close to the 4 halflives (36 hr) for estimation of ~93.7% of the drug This expression ′𝑒 −𝑘𝑡′ is used to estimate the timespan to reach any fraction of 𝐴∞ 𝑢 ESTIMATION OF Kr AND K IN THE ABSENCE OF CUMULATIVE URINARY EXCRETION PLOT You may not always be able to construct a cumulative urinary excretion plot for a number of reasons: Missing urine samples for one or more intervals Short sample collection time. You can still construct the urinary excretion-rate plot using available samples You can find the half-life or k from the slope and kr from the intercept fe can be estimated from the urinary excretion rate plot using the following equation: 𝑓𝑒 = 𝑘𝑟 𝑘 CALCULATION OF 𝑘𝑟 FROM EXCRETION RATE PLOT The intercept of the urinary excretion rate plot gives 𝑘𝑟 Intercept on the log-graph= 𝑘𝑟 𝑑𝑜𝑠𝑒 = 11.9 mg/h. If you know the dose (200 mg), you can estimate 𝑘𝑟 𝐷𝑜𝑠𝑒 ∙ 𝑘𝑟 = 11.9𝑚𝑔 𝑜𝑟 ℎ 𝑘𝑟 = 11.9𝑚𝑔/ℎ 200𝑚𝑔 = 0.0595ℎ−1 CALCULATION OF 𝑘𝑟 FROM THE CUMULATIVE AMOUNT EXCRETED The relation among, dose, cumulative amount excreted (𝐴∞ 𝑢 ), 𝑘, 𝑘𝑒 , and fraction-intact-drug excreted 𝑓𝑒 is written as 𝑓𝑒 = 𝐴∞ 𝑢 𝑑𝑜𝑠𝑒 = 𝑘𝑟 𝑘 This equation gives 𝑘𝑟 , when you know other parameters 𝑓𝑒 = 𝐴∞ 𝑢 𝑑𝑜𝑠𝑒 𝑘𝑟 0.0778ℎ −1 = 𝑘𝑟 𝑘 = 0.72 = 0.72 𝑘𝑟 = 0.0560/ℎ𝑟 RENAL CLEARANCE Renal clearance measures the efficiency of the kidneys in excreting the drug Renal clearance relates the urinary excretion-rate with the plasma concentration as follows 𝑑𝐴𝑢 𝑑𝑡 = 𝐶𝑙𝑟 ∙ 𝐶 This equation may be rearranged to estimate 𝐶𝑙𝑟 𝐶𝑙𝑟 = 𝑑𝐴𝑢 /𝑑𝑡 𝐶 You need both plasma-concentration and urinary excretion rate (𝑑𝐴𝑢 /𝑑𝑡) to estimate 𝐶𝑙𝑟 . For this method, you determine 𝑑𝐴𝑢 /𝑑𝑡 using the data from urine samples collected for a period of time (between t1 and t2) You have to collect a plasma sample in the middle of urine collection (between t1 and t2) period. For creatinine clearance, urine is collected for 24 hr and a plasma sample is collected at 12 hr. RENAL CLEARANCE USING AUC The integration of (𝐶𝑙𝑟 = following equation: 𝐶𝐿𝑟 = 𝐴𝑡1−𝑡2 𝑢 𝐴𝑈𝐶𝑡1−𝑡2 = 𝑑𝐴𝑢 /𝑑𝑡 𝐶 ) leads to the 𝐴∞ 𝑢 𝐴𝑈𝐶0−∞ Assume the AUC for this drug is 13.2 mg.hr/L, then 𝐶𝐿𝑟 = 𝐴∞ 𝑢 𝐴𝑈𝐶0−∞ = 144 𝑚𝑔 13.2 𝑚𝑔 ℎ/𝐿 = 10.9 𝐿/ℎ CUMULATIVE METHOD Advantages: Deals with real the time-points (no 𝑡𝑚𝑖𝑑 ) Incomplete bladder emptying does not impact the outcome much Avoid frequent sampling when you want to estimate 𝐴∞ 𝑢 Disadvantages: Sampling should be for at least 4 half-lives in order to estimate 𝐴∞ 𝑢 (problem for drugs with long-half life drugs) 𝐴∞ 𝑢 cannot be estimated in case of accidental sample loss URINARY EXCRETION RATE METHOD Advantages: Sample loss does not impact the outcome One misplaced samples eliminate one data point but the existing data points are still useful Sample collection for ≥ 4 half lives is not required. Disadvantages: Use of 𝑡𝑚𝑖𝑑 instead of sampling time Shorter interval to relate rate to 𝑡𝑚𝑖𝑑 Incomplete bladder emptying affect each data point APPLICATION OF URINE DATA The drug half-life from the urine data can predict the time a drug takes To exit the body To reach a steady plasma profile after multiple dosing. The amount of urinal-excretion of intact drug can determine the relative bioavailability or bioequivalence of two products The fraction-dose excreted in the urine and the renal clearance are used determine the role of kidneys in drug elimination If much of the intact drug is excreted via the kidneys, kidney dysfunction would affect drug excretion If urinal drug excretion is minimal, renal dysfunction does not affect drug elimination