Pharmacokinetic equation

Yamaoka K, Nakagawa T, Uno T (1978) Application of Akaike s Information criterion (AIC) in the evaluation of linear pharmacokinetic equations. J Pharmacokinet Biopharm 6 165-175. 

Wagner, J.G. 1976. Linear pharmacokinetic equations allowing direct calculation of many needed pharmacokinetic parameters from the coefficients and exponents of polyexponential equations which have been fitted to the data. 

Since there is a directly proportionate relationship between administered drug dose and steady-state plasma levels Equations 2.2 and 2.3 provide a straightforward guide to dose adjustment for drugs that are eliminated by first-order kinetics. Thus, to double the plasma levels the dose simply should be doubled. Con-versely to halve the plasma level, the dose should be halved. It is for this reason that Equations 2.2 and 2.3 are the most clinically important pharmacokinetic equations. Note that, as is apparent from Eigure 2.6, these equations also stipulate that the steady-state level is determined only by the maintenance dose and elimination clearance. The loading dose does not appear in the equations and does not influence the eventual steady-state level. 

The term (D PC/FP) is compound dependent, and it is termed the permeability coefficient (Kp), reducing the determination of flux to Kp AX or Kp C, a first-order pharmacokinetic equation (dxldt = kX). Rearrangement of this... 

For example, LK is a 50-year-old, 75-kg, 5-ft, 11-in male renal transplant recipient who is receiving oral cyclosporine 400 mg every 12 hours. The current steady-state blood cyclosporine concentration is 375 ng/mL. To compute a cyclosporine dose that will provide a steady-state concentration of 200 ng/mL, linear pharmacokinetic equations can be used. The new dose to attain the desired concentration should be proportional to the old dose that produced the measured concentration (total daily dose = 400 mg/dose x 2 doses/day = 800 mg/day) ... 

Allometry is the study of size and its consequences. It is often of interest to predict pharmacokinetic behavior in humans based on data in animals. - The simplest allometric pharmacokinetic equation that is often used is the power relationship,... 

Figure 6.1 illustrates that, if drug levels are measured before steady state is achieved, therapeutic adjustments could result in concentrations much higher than desired. Dosage adjustments can be made from non-steady-state levels, but the pharmacokineticist must make sure that the appropriate pharmacokinetic equations are chosen that include accumulation factors and that it is known how many doses have been given, and the timing of those doses. Many clinicians choose to wait until steady state is achieved before drug levels are measured to assess the current therapy so that simplified steady-state equations can be used. 

It is also very important to take note of the units in which assay results are reported. When the concentration information is used in the pharmacokinetic equations, it is important that the proper concentration units be used to obtain the correct units for volume of distribution and half-life. Once again, as individual drugs are reviewed, take note of the preferred assay technique, the proper sampling matrix, and the units of concentration reported. 

Angiotensin-converting enzyme (ACE) inhibitors, angiotensin-11 receptor blockers (ARBs), P-blockers, and calcium channel blockers are not dosed in the clinical setting using pharmacokinetic equations. The clinical use and selection of a drug within a class of medications is determined, in part, on differences in pharmacokinetic parameters. Eor example, metoprolol is commonly used in patients with renal disease because it is metabolized in the liver. Atenolol is avoided because it is renally eliminated. Select pharmacokinetic parameters for ACE inhibitors, ARBs, P-blockers, and calcium channel blockers are listed in Tables 8.11 through 8.13. 

Similar findings suggesting presystemic GI inversion with ibuprofen have been described by Avgerinos and Hutt [92]. However, a C ax S/R ratio alone does not unequivocally demonstrate inversion this is only demonstrated through an increase in ratio with an increase in 7) ax- Other laboratories have also shown a similar trend of increasing C ax S/R ratio with prolongation of T ax [93]. After administration of racemic ibuprofen to humans, the Tmax values for the enantiomers were found to be identical, but the mean Cmax for the S-ibuprofen exceeded that of the R-isomer [94]. Absorption rate dependency of ibuprofen inversion has also been demonstrated in the rat [95]. Theoretical proof of this presystemic inversion was put forward employing newly developed pharmacokinetic equations [96]. Furthermore, food-induced reduction of the rate of ibuprofen delivery may mimic the effect of a sustained release preparation and also supports the concept of presystemic GI inversion [97]. 

Unlike intravascular dosage forms, in which a solution of drug is injected (usually by the intravenous route) into the systemic circulation, extravascular dosage forms are not immediately delivered into the systemic circulation. Extravascular dosage forms such as oral, intramuscular, subcutaneous and transdermal patches are meant to deliver dmg to the systemic circulation however, this systemic delivery is not instantaneous. Therefore, the pharmacokinetic equations require a term reflecting an absorption process. In order to understand multiple oral dosing, one... 

The (AUC)g has been shown above to be the 0th statistical moment. It can be calculated for plasma drug concentration data that are not describable by an explicit pharmacokinetic equation, even in cases when the curve has an irregular shape. If the assumption is made that all the underlying processes of absorption, distribution, and elimination follow linear kinetics (are monoexponential functions), (AUC)o can provide us with the most important parameter in all pharmacokinetics, the systemic clearance of drug (CIJ. Here is the relationship ... 

PHARMACOKINETICS AND BIOPHARMACEUnCS COUTSeS have been included in phannacy curricula across the USA and in many other countries for the past several years. At present, there are a number of textbooks available for use by students and other readers. Most of these textbooks, although valuable and well written, concentrate on presenting the material in substantial mathematical depth, with much less emphasis needed on explanations that will facilitate rmderstanding and the abiUty to use the pharmacokinetic equations which are introduced. Furthermore, also evident in currently available textbooks is a paucity of adequate explanation regarding factors influencing pharmacokinetic parameters present in these equations. 

This technique will be useful In the pharmacokinetic evaluation of drugs which cannot be given by a single quick bolus injection, because of potential toxicity, irritation or limited solubility. These authors utilized Laplace, transform input functions In deriving their equations, a rapid and easy method for deriving pharmacokinetic equations which should find expanded use in the next year. 

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