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Transcript
LEARNING OBJECTIVES Understand the plasma concentration-time profiles of single-dose orally administered drugs Estimate relevant kinetic parameters of oral drug alone or in conjunction with IV kinetics Know the major differences in the kinetics of oral drugs and IV bolus injections Review the factors influencing the drug accumulation or disappearance rate in the body after the oral administration Appreciate the relative changes in the absorption and elimination rates after oral administration Know the major kinetic parameters that can be calculated from the oral data Know the equations for Plasma concentration-time profiles after oral administration Plasma concentration-time curve when absorption is over Explain the following concepts and methods Residual method Lag and onset time Flip-flop phenomenon Calculate the following kinetic parameters for oral drugs: Maximum plasma concentration (𝐶𝑚𝑎𝑥 ) and time to reach 𝐶𝑚𝑎𝑥 (𝑡𝑚𝑎𝑥 ) Elimination half-life Absorption and elimination rate-constants Clearance Distribution-volume Fraction-dose un-excreted DIFFERENCES BETWEEN ORAL AND IV ADMINISTRATIONS Oral dosing is one of the extravascular methods of administration Other extravascular routes: Intramuscular Subcutaneous Transdermal Inhalation Drugs administered via the extra-vascular routes are first absorbed before entering the systemic circulation Dosage forms must disintegrate and drugs must dissolve for absorption to occur The absorbed drugs pass through the liver before reaching the systemic circulation The fraction-dose that survives the first-pass loss enters the systemic circulation Once in the blood, our body treats all drugs equally regardless of their entry into the system KINETIC MODEL FOR ORAL DOSING We will only focus on drugs that are not subject to active efflux In case of one-compartment model for an oral drug without active efflux The absorption process is either zero or firstorder Drug enters the systemic circulation after absorption Rapidly distributes in the body Undergoes first-order elimination A typical plasma concentration-time curve consists of rise and fall of drug levels (the plot on the right) ABSORPTION AND ELIMINATION OF ORAL DRUGS After oral administration, the drug amount changes as a function of absorption (input) and elimination (output) processes: 𝑅𝑎𝑡𝑒 𝑜𝑓 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑡ℎ𝑒 𝑏𝑜𝑑𝑦 = 𝑑𝐴𝐵 𝑑𝑡 𝑑𝐴𝐵 𝑑𝑡 = 𝑖𝑛𝑝𝑢𝑡 − 𝑜𝑢𝑡𝑝𝑢𝑡 = 𝑟𝑎𝑡𝑒 𝑜𝑓 𝑎𝑏𝑠𝑜𝑟𝑝𝑡𝑖𝑜𝑛 − 𝑟𝑎𝑡𝑒 𝑜𝑓 𝑒𝑙𝑖𝑚𝑖𝑛𝑎𝑡𝑖𝑜𝑛 When both absorption and elimination processes are firstorder: The absorption-rate depends on the drug amount in the GIT (𝐴𝐺𝐼 ) The elimination-rate depends on the drug amount in the body (𝐴𝐵 ) 𝑑𝐴𝐵 𝑑𝑡 = 𝑎𝑏𝑠𝑜𝑟𝑝𝑡𝑖𝑜𝑛 𝑟𝑎𝑡𝑒 − 𝑒𝑙𝑖𝑚𝑖𝑛𝑎𝑡𝑖𝑜𝑛 𝑟𝑎𝑡𝑒 = 𝑘𝑎 𝐴𝐺𝐼 − 𝑘𝐴𝐵 ORAL PLASMA CONCENTRATION-TIME CURVE After oral administration, the drugamount in the GIT and the absorption rate (𝑘𝑎 𝐴𝐺𝐼 ) are maximum With the increase in drug-amount, plasma-concentration increases With the fall in the drug-amount, absorption-rate falls The drug-amount continues to rise until the absorption-rate equals the The drug absorption continues after 𝑡𝑚𝑎𝑥 but at a elimination-rate rate slower than the The time-point when absorptionelimination-rate rate equals the elimination-rate is The 𝐶𝑚𝑎𝑥 of oral drugs is called 𝒕𝒎𝒂𝒙 smaller than the 𝐶𝑚𝑎𝑥 of IV After 𝑡𝑚𝑎𝑥 , the elimination-rate drugs administered at the surpasses the absorption-rate, the same dose plasma-concentration starts falling EQUATION FOR ORAL PLASMA CONCENTRATIONTIME DATA The plasma-concentration of orally administered drug at any time is expressed by: 𝐶 = 𝐹𝐷𝑜𝑠𝑒𝑘 𝑉 𝑘𝑎 −𝑘 (𝑒 −𝑘𝑡 − 𝑒 −𝑘𝑎 𝑡 ) F=fraction-dose in the systemic circulation V= distribution-volume 𝑒 −𝑘𝑎 𝑡 =absorption process 𝑒 −𝑘𝑡 =elimination process The plasma concentration-time on loggraphs exhibits a terminal linear relation or a linear-segment The linear-segment represents the presence of one-exponential term: The end of absorption and start of elimination EQUATION FOR THE ELIMINATION PHASE OF ORAL ABSORPTION The equation below describe the elimination phase 𝐶= 𝐹𝐷𝑜𝑠𝑒𝑘𝑎 −𝑘𝑡 𝑒 𝑉 𝑘𝑎 −𝑘 This equation is a complex version of the equation for IV bolus plasma-concentration data: 𝐶 = 𝐶0 𝑒 −𝑘𝑡 Taking log converts the equation into a straight-line equation 𝑙𝑛𝐶 = ln 𝐹𝐷𝑜𝑠𝑒𝑘𝑎 𝑉 𝑘𝑎 −𝑘 − 𝑘𝑡 The intercept of the line is ln 𝐹𝐷𝑜𝑠𝑒𝑘𝑎 𝑉 𝑘𝑎 −𝑘 and slope is -k The slope of the terminal phase of the oral plasma concentration-time data is the same as the slope of the straight-line for IV plasma concentration-time data ELIMINATION RATE CONSTANT CALCULATION For most drugs, the absorptionrate is faster than eliminationrate 𝑘𝑎 >>k When the absorption process stops, the plasma concentration is defined by the single exponential term related to the elimination with a slope of –k and a half-life. You can calculate the elimination rate-constant and half-life from the terminal linear segment of the oral plasma concentrationtime curve LAG AND ONSET TIMES Lag time Some drugs do not exhibit absorption phase immediately after administration This delay in absorption is called lag time Drug formulation and physiologic factors such as gastric emptying time may be responsible for lag-time The lag-time can be a few minutes to hours. Long lag- times are observed for enteric-coated tablets Onset Time The time required for the pharmacologic effects to start Depends on how fast the plasma concentrations reach the minimum effective concentration GENERAL ASSUMPTIONS FOR ORAL ABSORPTION Majority of the orally administered drugs and drug formulations meet the following assumptions: The absorption rate-constant (𝑘𝑎 ) is much larger than the elimination rate-constant (𝑘𝑎 >>k) The terminal rate-constant and half-life represent elimination rate-constant and half-life, respectively The half-life calculated from the terminal linear-segment of the oral data is equal to the half-life for the IV data Both lines (terminal segment of oral data and IV data) represent elimination and produce the same slope FLIP-FLOP PHENOMENON Some orally administered drugs’ absorption is very slow or the elimination is very fast For these drugs, the absorption rate constant is smaller than elimination rate constant (k>> 𝑘𝑎 ) When absorption rate constant is smaller than that of elimination, the terminal phase of plasma concentration-time profile represents the absorption process instead of the elimination process, a phenomenon called flip-flop, or reversal of the assumption that ka >> k Flip-flop (ka<<k) occurs when Drug absorption is inherently slow Drug formulation is controlled or sustained release type Drug elimination half-life is short Flip-flop causes the following changes The half-life (elimination 𝑡1/2 ) for IV data does not match the half-life from the terminal linear-segment of oral plasma-concentrationtime data (absorption 𝑡1/2 ) Drugs exhibits absorption-rate limited elimination IDENTIFICATION OF THE FLIP-FLOP PHENOMENON Flip-flop phenomenon can be identified by Using IV data Using data from different dosage forms administered via the same route Using data from different routes administration USING IV DATA When the half-lives for oral and IV data are very similar (IV-𝑡1/2 ≅ Oral-𝑡1/2 ), then the terminal oral half-life is related to the elimination If the IV half-life is shorter than that of oral (IV-𝑡1/2 < Oral-𝑡1/2 ), then the terminal oral half-life is related to the absorption process DIFFERENT DOSAGE FORMS ADMINISTERED VIA THE SAME ROUTE In the absence of IV data, different dosage forms of a drug with different absorption profiles can be used to determine whether the terminal half-life is related to elimination or absorption A drug may have different absorption profiles when administered in the solution or tablet form Solutions exhibit faster absorption and shorter half-lives but tablets show slower absorption, or longer absorption halflives When tablets and solutions are administered at different occasions to a subject, we may observe two scenarios: Case I and Case II In both cases, the absorption of the solution is faster than tablet, resulting in higher 𝐶𝑚𝑎𝑥 and earlier 𝑡𝑚𝑎𝑥 values for the solution CASE I: SAME HALF-LIVES FOR SOLUTION AND TABLET Both the solution and tablet exhibit the same terminal half-lives This terminal phase halflife cannot represent absorption because solution exhibits a shorter absorption halflife Thus, this half-life is the elimination half-life CASE II: DIFFERENT HALF-LIVES FOR SOLUTION AND TABLETS A change in the half-life reflects the terminal halflives The terminal half-life of the tablet is related to the absorption process DATA FOR DIFFERENT ROUTES OF ADMINISTRATION For two different routes, the absorption half-life will be different, but the elimination half-life will be the same When a drug is administered via IM and oral routes, the terminal half-lives are going to be the same CALCULATION OF KINETIC PARAMETERS USING ORAL PLASMA DATA Cmax and tmax Elimination half-life Clearance Distribution-volume Oral bio-availability CALCULATION OF 𝐶𝑚𝑎𝑥 and 𝑡𝑚𝑎𝑥 𝒕𝒎𝒂𝒙 If you know the absorption (𝑘𝑎 ) and elimination (k) rate constants, use the following equation to calculate 𝑡𝑚𝑎𝑥 𝑘 𝑡𝑚𝑎𝑥 = ln( 𝑘𝑎 ) 𝑘𝑎 −𝑘 𝑪𝒎𝒂𝒙 To calculate 𝐶𝑚𝑎𝑥 , use plasma concentration equation and 𝑡𝑚𝑎𝑥 obtained using the above equation But the estimation of absorption rate-constant is not usually accurate By taking enough samples around 𝑡𝑚𝑎𝑥 , both 𝐶𝑚𝑎𝑥 and 𝑡𝑚𝑎𝑥 can be estimated from the plasma concentration-time curve 𝑘𝑎 and k can affect 𝑡𝑚𝑎𝑥 , a larger 𝑘𝑎 or k reduces 𝑡𝑚𝑎𝑥 and vice versa. k a , k, F, dose and V influence Cmax ELIMINATION HALF-LIFE You can use the data points that fall on the linear section of the curve to calculate the half-life and rate-constant of the linear-segment of the plasma-concentration-time But to confirm whether the data obtained from the linear segment of the terminal phase belong to elimination phase, you need additional information like IV data CLEARANCE FROM ORAL DATA The equation for the clearance after oral dosing 𝐹𝐷𝑜𝑠𝑒 𝐶𝑙 = 𝐴𝑈𝐶 You have to know F (oral bioavailability) to calculate Cl after oral administration Calculate AUC using the trapezoidal rule 𝐶𝑙𝑎𝑠𝑡 Calculate 𝐴𝑈𝐶𝑡𝑙𝑎𝑠𝑡−∞ using 𝑘𝑡𝑒𝑟𝑚𝑖𝑛𝑎𝑙 You must calculate 𝐴𝑈𝐶𝑡𝑙𝑎𝑠𝑡−∞ regardless whether 𝑘𝑡𝑒𝑟𝑚𝑖𝑛𝑎𝑙 is related to absorption or elimination Oral clearance (𝐶𝑙0 ) A clearance term obtained by dividing the oral dose with the oral AUC, without considering F Oral clearance is defined by 𝐶𝑙0 = 𝐷𝑜𝑠𝑒𝑝𝑜 𝐴𝑈𝐶𝑝𝑜 = 𝐶𝑙 𝐹 CALCULATION OF DISTRIBUTIONVOLUME The equation for the distribution-volume 𝑉= 𝐶𝑙 𝑘 Use this equation to calculate Cl and k You need IV data to calculate Cl and k In the above equation k is the elimination rate constant If the drug-disposition is absorption-rate limited, the terminal rate constant from oral-plasma concentration time cannot be used to calculate V Use the rate-constant from IV data When only oral data is available and F is unknown, you can calculate V/F, instead of V 𝑉 𝐹 = 𝐶𝑙𝑜 𝑘 ORAL BIOAVAILABILITY (F) F is calculated from the AUC for oral and IV data at the same dose: 𝐹= 𝐴𝑈𝐶𝑝𝑜 𝐴𝑈𝐶𝐼𝑉 In case of different doses, the AUC ratios are corrected for the dose: •𝐹= 𝐴𝑈𝐶𝑝𝑜 𝐴𝑈𝐶𝐼𝑉 × 𝐷𝑜𝑠𝑒𝐼𝑉 𝐷𝑜𝑠𝑒𝑝𝑜 CALCULATION OF KINETIC PARAMETERS USING ORAL URINE DATA Half-life Fraction-excreted unchanged Renal clearance Oral bio-availability HALF-LIFE FROM ORAL URINE DATA The urinary drug excretion-rate is proportional to the amount of drug in the body (AB), regardless of the route of drug administration 𝑑𝐴𝑢 𝑑𝑡 = 𝑘𝑟 × 𝐴𝐵 A plot of urinary drug excretion-rate against the midpoint of sample collection interval would parallel the plot of the drugamount in the body or plasma drug concentration against time The terminal half-life and rate-constant of the rate plot would be similar to that of the plasma drug concentrationtime curve But the terminal rate constant or half-life may stem from either absorption or elimination FRACTION EXCRETED UNCHANGED ( 𝑓𝑒 ) To calculate 𝑓𝑒 for oral administration, use the fraction-dose in the systemic circulation (F Dose) instead of Dose used to calculate 𝑓𝑒 for IV bolus 𝑓𝑒 = 𝐴∞ 𝑢 𝐹∙𝑑𝑜𝑠𝑒 You must know F from a previous study to calculate 𝑓𝑒 for oral administration RENAL CLEARANCE You need both plasma and urine data to calculate the renal clearance for oral administration The renal clearance can be calculated directly from oral data without any IV data 𝐶𝑙𝑟 = 𝐴∞ 𝑢 𝐴𝑈𝐶0−∞