Area Under the Curve from time

AUC((M), the area under the curve from time zero to time t A measure of total systemic exposure. 

An indication of the rate of drug absorption can be obtained from the peak (maximum) plasma concentration (Cmax) and the time taken to reach the peak concentration (fmjx), based on the measured plasma concentration-time data. However, the blood sampling times determine how well the peak is defined and, in particular, fmax. Both Cmax and tm3LX may be influenced by the rate of drug elimination, while Cmax is also affected by the extent of absorption. The term Cmax/ AUC, where AUC is area under the curve from time zero to infinity or to the limit of quantification (LOQ) of the analytical method, provides additional information on the rate of absorption. This term, which is expressed in units of reciprocal time (h ), can easily be calculated. In spite of the imprecision of the estimation provided by Cmax, it generally suffices for clinical purposes. 

The principal parameter used to indicate the rate of drug absorption is Cmax, even though it is also influenced by the extent of absorption the observed fmaX is less reliable. Because of the uncertainty associated with Cmax, it has been suggested (Endrenyi Yan, 1993 Tozer, 1994) that Cmax/AUCo-loq/ where AUCo-loq is the area under the curve from time zero to the LOQ of the acceptable analytical method, may more reliably measure the rate of drug absorption, except when multiexponential decline is extensive. Estimation of the terms should be based on the observed (measured) plasma concentrationtime data and the use of non-compartmental methods rather than compart-mental pharmacokinetic models. MRTs, from time zero to the LOQ of the analytical method, for the test and reference products can be compared, assuming that first-order absorption and disposition of the drug apply (Jackson Chen, 1987). 

The estimated area under the curve from time point zero to infinity (AUC(q j) is calculated using the trapezoidal rule. There are two steps in this process ... 

Figure 7.15 Histogram of observed and simulated dose-normalized area under the curve from time 0 to 24-h postdose based on die observed concentration data (Table 7.4). Concentration data from 25 subjects at each dose (20-640 mg) were simulated using the final parameters estimates in Table 7.5 obtained with FOCE-I.

AUC is the area under the curve or the integral of the plasma levels from zero to infinite time. Conversely, equation 1 may be used to calculate input rates of dmg that would produce steady-state plasma levels that correspond to the occurrence of minor or major side effects of the dmg. 

Radiation heat flux is graphically represented as a function of time in Figure 8.3. The total amount of radiation heat from a surface can be found by integration of the radiation heat flux over the time of flame propagation, that is, the area under the curve. This result is probably an overstatement of realistic values, because the flame will probably not bum as a closed front. Instead, it will consist of several plumes which might reach heights in excess of those assumed in the model but will nevertheless probably produce less flame radiation. Moreover, the flame will not bum as a plane surface but more in the shape of a horseshoe. Finally, wind will have a considerable influence on flame shape and cloud position. None of these eflects has been taken into account. 

Thus, the technique consists of a transformation from the time differential dt to the area differential dQ, and the essential effect of this transformation is a reduction by one of the apparent order of the reaction. The variable 6 is the area under the curve of Cb vs. time from t = 0 to time t. With modem computer techniques for integrating experimental curves, this method should be attractive. 

The effect of hemodialysis can be derived from the removed fraction (FR) that is the relative amount eliminated from the body during the time (/HD) of one dialysis session. This fraction can be derived from the half-life on dialysis (Tl/2on) or from the area under the curve (AUC) on and off dialysis. 

Analysis of most (perhaps 65%) pharmacokinetic data from clinical trials starts and stops with noncompartmental analysis (NCA). NCA usually includes calculating the area under the curve (AUC) of concentration versus time, or under the first-moment curve (AUMC, from a graph of concentration multiplied by time versus time). Calculation of AUC and AUMC facilitates simple calculations for some standard pharmacokinetic parameters and collapses measurements made at several sampling times into a single number representing exposure. The approach makes few assumptions, has few parameters, and allows fairly rigorous statistical description of exposure and how it is affected by dose. An exposure response model may be created. With respect to descriptive dimensions these dose-exposure and exposure-response models... 

Fq values may be calculated either from the area under the curve of a plot of autoclave temperature against time constructed using special chart paper on which the temperature scale is modified to take into account the progressively greater lethality of higher temperatures, or by use of the equation below ... 

The area under the curve AUC is obtained by integrating the plasma concentration function between times 0 and infinity. This integral can be obtained analytically from eq. (39.16) ... 

The simplest non-compartmental parameter that can be obtained from the time course of the plasma concentration is its area under the curve AUC (see also Section 39.1.1) ... 

This parameter can be obtained by numerical integration, for example using the trapezium rule, between time 0 and the time T when the last plasma sample has been taken. The remaining tail of the curve (between T and infinity) must be estimated from an exponential model of the slowest descending part of the observed plasma curve ((3-phase) as shown in Fig. 39.15. The area under the curve AUC can thus be decomposed into a tmncated and extrapolated part ... 

From the mean residence time MRT, the area under the curve AUC and the administered dose D, one can derive the steady-state volume of distribution of... 

Compound (1) suffered from an unfavorable pharmacokinetic profile when studied in rats. It is cleared very rapidly from rat plasma (half-life, t 2 — 0.4/z) and is poorly bioavailable F — 2%), as reflected by the low plasma concentration (area under the plasma concentration-time curve, AUCo oo = 0.2pMh) following a single oral dose of 25mg/kg in rats [42]. The main challenge was to further optimize this series to obtain NS3 protease inhibitors with low-nanomolar cell-based potency (EC5q< 10 nM) and with an adequate pharmacokinetic profile for oral absorption. 

The area under the PCP concentration-time curve (AUC) from the time of antibody administration to the last measured concentration (Cn) was determined by the trapezoidal rule. The remaining area from Cn to time infinity was calculated by dividing Cn by the terminal elimination rate constant. By using dose, AUC, and the terminal elimination rate constant, we were able to calculate the terminal elimination half-life, systemic clearance, and the volume of distribution. Renal clearance was determined from the total amount of PCP appearing in the urine, divided by AUC. Unbound clearances were calculated based on unbound concentrations of PCP. The control values are from studies performed in our laboratory on dogs administered similar radioactive doses (i.e., 2.4 to 6.5 pg of PCP) (Woodworth et al., in press). Only one of the dogs (dog C) was used in both studies. 

Table 6 illustrates the steps involved in carrying out the Wagner-Nelson calculation. The third column (f 0 Cp dt) shows the area under the Cp versus time curve calculated sequentially from t = 0 to each of the time points using the trapezoidal rule (see Sec. VIII.A). The fourth column (kei f 0 Cp di) shows each of the preceding areas multiplied by k.ei (as estimated from the tail )... 

Bioavailability was assessed from measurement of the area under the curve (AUC) of whole blood lead concentration vs time (Blood AUC) or from measurements of the lead concentrations in bone, kidney or liver (the arithmetic mean of the three tissues is shown in the table). Data are from Casteel et al. (1997) and EPA (1996a, 1996b, 1996c). 

Thus, %F is defined as the area under the curve normalized for administered dose. Blood drug concentration is affected by the dynamics of dissolution, solubility, absorption, metabolism, distribution, and elimination. In addition to %F, other pharmacokinetic parameters are derived from the drug concentration versus time plots. These include the terms to describe the compound s absorption, distribution, metabolism and excretion, but they are dependent to some degree on the route of administration of the drug. For instance, if the drug is administered by the intravenous route it will undergo rapid distribution into the tissues, including those tissues that are responsible for its elimination. 

There is no experimental evidence available to assess whether the toxicokinetics of -hexane differ between children and adults. Experiments in the rat model comparing kinetic parameters in weanling and mature animals after exposure to -hexane would be useful. These experiments should be designed to determine the concentration-time dependence (area under the curve) for blood levels of the neurotoxic /7-hcxane metabolite 2,5-hexanedione. w-Hcxanc and its metabolites cross the placenta in the rat (Bus et al. 1979) however, no preferential distribution to the fetus was observed. -Hexane has been detected, but not quantified, in human breast milk (Pellizzari et al. 1982), and a milk/blood partition coefficient of 2.10 has been determined experimentally in humans (Fisher et al. 1997). However, no pharmacokinetic experiments are available to confirm that -hexane or its metabolites are actually transferred to breast milk. Based on studies in humans, it appears unlikely that significant amounts of -hexane would be stored in human tissues at likely levels of exposure, so it is unlikely that maternal stores would be released upon pregnancy or lactation. A PBPK model is available for the transfer of M-hcxanc from milk to a nursing infant (Fisher et al. 1997) the model predicted that -hcxane intake by a nursing infant whose mother was exposed to 50 ppm at work would be well below the EPA advisory level for a 10-kg infant. However, this model cannot be validated without data on -hexane content in milk under known exposure conditions. 

Figure 2.4. In vivo measurement of blood-brain barrier (BBB) permeability, (a) Internal carotid artery perfusion technique (i) in the rat. Other branches of the carotid artery are ligated or electrically coagulated (o, occipital artery p, pterygopalatine artery). The external carotid artery (e) is cannulated and the common carotid artery (c) ligated. Perfusion time may range from 15 s to 10 min, depending on the test substance. It is necessary to subtract the intravascular volume, Vo, from (apparent volume of distribution), to obtain true uptake values and this may be achieved by inclusion of a vascular marker in the perfusate, for example labelled albumin. Time-dependent analysis of results in estimates of the unidirectional brain influx constant Ki (pi min which is equivalent within certain constraints to the PS product. BBB permeability surface area product PS can be calculated from the increase in the apparent volume of distribution Vd over time. Capillary depletion, i.e. separation of the vascular elements from the homogenate by density centrifugation, can discriminate capillary uptake from transcytosis. (b) i.v. bolus kinetics. The PS product is calculated from the brain concentration at the sampling time, T, and the area under the plasma concentration-time curve, AUC.

Absolute systemic bioavailabUity (absorbed fraction of the dose or concentration administered) can only be calculated by comparing the so-called Area Under the Plasma Curve (AUC, the area under the curve in a plot of the concentration of a substance in the plasma against time) after oral, inhalation, or dermal administration with the AUC after direct administration into the systemic circulation, e.g., after intravenous administration. In order to obtain a rehable estimate for AUC after single administration, it is necessary to have blood samples for 3-5 half-hves. In case data are not available for a calculation of the AUC, the absorbed fraction can be indicated from data on the amount of the parent compound and its metabohte(s) excreted in the urine, feces, and exhaled air. It should be noted that the amount excreted in the feces stems from both the unabsorbed fraction as well as from the fraction of the substance following bUiary excretion. 

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