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A super short guide to pharmacokinetics and PKAUC.com calculator 1 Pharmacokinetics (PK) Pharmacokinetics studies drug (pharmaco-) movement (-kinetics), mainly drug concentration change with time in the body. PKAUC.com calculator plots a concentration-time curve if two or more data points are typed in. 2 AUC AUC is the area under the concentration-time curve, a main indicator of drug exposure. Drug exposure impacts efficacy of a drug, and also the associated toxicity. AUC is the integration of drug concentrations within a time interval. 3 Route of Administration Medicine can be taken by mouth (oral) or via IV injection. PKAUC.com calculator has two routes to select: (1)IV for IV bolus, and (2)ExV for extravascular administration such as an oral route. 4 NCA Noncompartmental analysis (NCA) has been a traditional and also most widely used method to evaluate PK. PKAUC.com calculator reports key NCA PK parameters such as Tmax , Cmax, AUC, half-life (t1/2), Clearance, and Volume of Distribution (Vss). 5 Cmax Cmax is maximum observed concentration. PKAUC.com calculator reports the first Cmax when more than one Cmax values are present. 6 Tmax Time of Cmax. 7 T0 T0 is zero in PKAUC.com calculator 8 C0 for IV Route If C0 (concentration at time zero) is not typed in, C0 will be back extrapolated in PKAUC.com calculator using the first two concentrations (C1 and C2) by linear regression of logarithm concentrations as follows, provided C2 is lower than C1. C0=e(t2*ln(C1)-t1*ln(C2))/(t2-t1) If C2 is greater than C1, C1 will be assigned as C0. If either C1 or C2 is zero, C0 will be assigned as zero. If back-extrapolated area from C1 to C0 is over 20% of total area, a warning message will be given by PKAUC.com calculator. 9 C0 for ExV Route If C0 is not typed in, C0 will be assigned as zero in PKAUC.com calculator. 10 Trapezoidal Rule AUC is calculated using a linear trapezoidal method in PKAUC.com calculator as follows. AUCt1-t2=(C1+C2)*(t2-t1)/2 11 AUC0-x In PKAUC.com calculator, AUC0-x reports area from time zero to the last time point typed in, regardless of concentration values, zero or non-zero. So, it may not be the same as AUC0-t, which is the area from time zero to the last non-zero time point. In cases where a zero concentration is typed in, AUC0-x calculates (“extrapolates”) the triangle area from the adjacent non-zero concentration to the zero concentration. When comparing exposure within the same time interval across groups, AUC0-x is a more conservative approach to report AUC. If the extrapolated triangle are is more than 20% of total area, a warning message will be given by PKAUC.com calculator. 12 Terminal Phase PKAUC.com calculator evaluates terminal phase if three or more concentration values after Tmax are typed in. Correlation R is calculated with covariance of concentration and time as normalized by the product of standard deviations of concentration and time. Adjusted R2 is calculated as follow (n is number of data points selected for regression), Adjusted R2=1-(1-R2)*(n-1)/(n-2) To determine the slope of the terminal phase, PKAUC.com calculator applies this algorithm: adjusted R2 of the last three, four, … until the maximum data points of the terminal phase. Slope with the largest adjusted R2 will be selected. If two largest adjusted R2 values are within 0.0001, the slope with the larger number of data points will be selected. If the adjusted R2 is less than 0.8, all terminal elimination phase derived parameters will not be reported, and a message will be printed out in PKAUC.com calculator. 13 t1/2 Elimination half-life is the length of time required to reduce 50% of drug in the body. Slope of elimination phase is determined by linear regression of logarithm concentrations in PKAUC.com calculator: covariance of concentration and time divided by variance of time. First order rate constant k is the negative slope, and t1/2is calculated as follows. t1/2=ln(2)/k 14 AUC0-∞ AUC0-∞ is calculated from AUC0-t extrapolated to infinity as follows. AUC0-∞=AUC0-t+AUCextrapolated AUC extrapolation to infinity (AUCextrapolated) after the last measurable concentration (Clast) is calculated with the following equation. AUCextrapolated=Clast/k If AUCextrapolated represents more than 20% of the total area, all terminal elimination phase derived parameters will not be reported. A message will be printed out in PKAUC.com calculator. 15 Clearance Two popular ways to define drug clearance are: (1) rate of drug elimination normalized to the drug concentration in biological fluid (such as plasma), and (2) apparent volume of biological fluid that is cleared of drug per unit time. Simply, clearance is a measurement of rate (not how much drug is removed but the biological fluid from which drug is removed). If this is still too abstract, we may think this way: when we eat chicken soup, instead of calculating how fast we eat chicken, we actually calculate how many bowls of soup we ate per unit time, assuming each bowl contains the same amount of chicken. Clearance is a measure of the body’s efficiency to eliminate drug. To maintain the efficacy of the drug, it shouldn’t be cleared too fast; otherwise patients have to take the drug many times a day. QD and BID should be more convenient than TID and QID. On the other hand, to reduce potential toxicity of the drug, it shouldn’t be cleared too slow. Clearance is determined with the following equation in PKACU.com calculator. It applies to single-dose or the Cycle 1 of multiple-dose PK profiles. Note: for steady-state PK profile, AUC0-∞ should be replaced with AUC0-τ to calculate clearance, which is not a function in this version of calculator. For ExV route, it’s reported as Clearance/F. Clearance=Dose/AUC0-∞ 16 AUMC AUMC is area under the first moment curve, or simply the “concentration*time vs. time curve”. AUMC is calculated in PKAUC.com calculator with a linear trapezoidal method as follows. AUMCt1-t2=(t1*C1+t2*C2)*(t2-t1)/2 AUMC0-∞ is extrapolated with the following equation, which is mainly a mathematic concept introduced to calculate MRT and eventually Vss. AUMC0-∞=AUMC0-t+Clast*tlast/k+Clast/k2 17 MRT MRT (mean residence time) is an intermediate parameter in PKAUC.com calculator to calculate Vss. The concept of MRT is on an individual drug molecule level. Each dose of drug contains numerous molecules of the drug; some of these molecules stay longer in the body than others. MRT is the measurement of average time of these molecules remaining in the body from the administered dose. MRT0-∞ is calculated from the ratio of AUMC and AUC as follows. MRT0-∞=AUMC0-∞/AUC0-∞ 18 Vss Volume of distribution at steady state measures apparent space in the body available to contain the drug. Vss is calculated in PKAUC.com calculator with the following equation. For ExV route, it’s reported as Vss/F. Vss=MRT0-∞*Clearance Vss is different from Vz (or Ve). Vss represents the sum of volume in both central and tissue compartment. However, Vz (or Ve) is calculated as the ratio of clearance to the elimination rate constant k, which varies when k changes. Vss is in general more reliable although the difference between them may not be clinically significant. |