Absorption rate constants

Remember that Equations 7.25 and 7.26 are valid only for the elimination phase of an oral dose. The y-intercept of the line described in Equation 7.26 (In Cpy int) contains a number of factors. If F has already been determined from AUC data (Equation 7.22), the formula for Cpy int (Equation 7.27) can be rearranged to Equation 7.28 for calculation of kah. 

A particularly significant Cp-time point for an oral drug is Cpmax and tmax. Cpmax occurs during a transition between the absorption and elimination phases. At Cpmax, dCp/dt is 0, and the rate of absorption is balanced by the rate of elimination (Equation 7.29). Through analysis and rearrangement of the first derivative of Equation 7.21 with respect to time, Equation 7.30 can be obtained and used for simple calculation of tmax. Substitution of tmax into Equation 7.21 then provides Cpmax. 

While tmax can be directly calculated with Equation 7.30, tmax can also be estimated from a set of clinical Cp-time data points. With both el and an estimated tmax, one may 

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After oral dosing, the bi-exponential Bateman function holds true with the absorption rate constant (Ka). 

A special case for reduced bioavailabilty results from first-pass extraction that sometimes might be subjected to saturable Michaelis-Menten absorption kinetics. The lower the hepatic drug clearance is (Clhep) in relation to liver blood flow (Ql), or the faster the drug absorption rate constant (Ka), and the higher the dose (D) are, the more bioavailable is the drug (F). 

Apparent first-order absorption rate constant (min 1) ... 

Fig. 16 (A) Absorption rate constant of sulfaethidole in dogs as a function of mesenteric blood flow. (Based on data from Ref. 108.) (B) Absorption rate of several compounds in rats as a function of intestinal blood flow. (Based on data from Ref. 107.)...

The most common extravascular route is oral. When a solution or a rapidly dissolving solid dosage form is given orally, the absorption process often obeys first-order kinetics. In these cases, absorption can be characterized by evaluating the absorption rate constant, ka, using plasma concentration versus time data. 

Db = drug in the body De = eliminated drug ka = first-order absorption rate constant kei = overall elimination rate constant... 

Often it is unnecessary to calculate an exact value for an absorption rate constant. For example, when several oral tablets containing the same drug substance are all found to be completely absorbed, it may be sufficient to merely determine if the absorption rates are similar to conclude that the products would be therapeutically equivalent. In another instance, it would be possible to choose between an elixir and a sustained-release tablet for a specific therapeutic need without assigning accurate numbers to the absorption rate constant for the two dosage forms. 

The time of the peak can also be used to roughly estimate the absorption rate constant. If it is assumed that ka is at least 5 x kei, then it can be assumed that absorption is at least 95% complete at the peak time that is, the peak time represents approximately five absorption half-lives (see Table 1). The absorption half-life can then be calculated by dividing the time of the peak by 5, and the absorption rate constant can be calculated by dividing the absorption half-life into 0.693. 

Example. Inspection of Fig. 10 gives a peak time of about 2.5 hours. The absorption half-life can be estimated to be 0.5 h and the absorption rate constant, to be 1.4h-1. 

In these cases it is not necessary to determine the absolute bioavailability or the absorption rate constant for the product under study. It is only necessary to prove that the plasma concentration versus time curve is not significantly different from the reference product s curve. This is done by comparing the means and standard deviations of the plasma concentrations for the two products at each sampling time using an appropriate statistical test. 

Other applications of the previously described optimization techniques are beginning to appear regularly in the pharmaceutical literature. A literature search in Chemical Abstracts on process optimization in pharmaceuticals yielded 17 articles in the 1990-1993 time-frame. An additional 18 articles were found between 1985 and 1990 for the same narrow subject. This simple literature search indicates a resurgence in the use of optimization techniques in the pharmaceutical industry. In addition, these same techniques have been applied not only to the physical properties of a tablet formulation, but also to the biological properties and the in-vivo performance of the product [30,31]. In addition to the usual tablet properties the authors studied the following pharmacokinetic parameters (a) time of the peak plasma concentration, (b) lag time, (c) absorption rate constant, and (d) elimination rate constant. The graphs in Fig. 15 show that for the drug hydrochlorothiazide, the time of the plasma peak and the absorption rate constant could, indeed, be... 

Fig. 15 Computer plots for (a) absorption rate constant and (b) time of plasma peak. (From Ref. 31.)... 

These ideas appear to merit careful consideration. Similarly, the use of nomograms to evaluate the intrinsic absorption rate constants for drugs that may be formulated into oral prolonged-release products may be of value [5],... 

S. C. Dyer and R. E. Notari, A nomogram to evaluate intrinsic absorption rate constants of potential oral prolonged release candidates, Pharm. Dev. Tech., 4, 305 (1999). 

H Yuasa, T Iga, M Hanano, J Watanabe. Relationship between in vivo first-order intestinal absorption rate constant and the membrane permeability clearance. J Pharm Sci 78 922-924, 1989. 

Figure 8 Schematic of mixing tank model with volume V0 and flow rate Q. M, is the amount of drug (liquid) and Ma is the amount of drug absorbed. Ka is the intrinsic absorption rate constant.

The absorption rate constant Ka can be estimated from the effective permeability ... 

The pharmacokinetics of nalidixic and hydroxy-nalidixic acids have been studied by several different groups. Takasugi ejt al studied in-situ and in-vitro absorption of nalidixic acid from the gastrointestinal tracts of rats as a function of pH. They reported that the absorption of non-ionized nalidixic acid was faster than the ionized form, with the maximum absorption rate constant found when the drug was administered from a pH=3 buffer solution. The absorption in-sltu was found to be ten times the rate in-vitro, but this was dependent on several factors.(13)... 

P = octanol-buffer partition coefficient k,A = absorption rate constant t = time... 

Brown, H.S., Ito, K., Galetin, A. and Houston, J.B. (2005) Prediction of in vivo drug—drug interactions from in vitro data impact of incorporating parallel pathways of drug elimination and inhibitor absorption rate constant British Journal of Clinical Pharmacology, 60 (5), 508-518. 

Figure 2.3 Schematic diagram of the method approach in optimising the drug design for passive absorption by determining the additional hpophihcity required to raise the absorption rate constant of the lead candidate in dilute solution to >90% of the maximum (Adapted from Ho et al. [5]).

The first-order absorption rate constant introduced above may be directly related to the effective permeability coefficient (Peff) using... 

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