Three-compartment pharmacokinetic model

Fig. 7 A three-compartment pharmacokinetic model describing targeted drug delivery. (From Ref. 46.)...

Figure 2.12 Three-compartment pharmacokinetic model with a linked effect compartment.

As discussed, a number of studies have examined the effect of vasoactive drugs on percutaneons absorption. We therefore limit this discnssion to the more detailed investigations. Mnch of this early work was undertaken nsing both the IPPSF (Riviere and Williams, 1991) and anesthetized weanling pig model (Riviere etal., 1992). They reported that the vasodilator tolazoline significantly increased lidocaine flux compared to that observed in vitro, whereas norepinephrine (a vasoconstrictor) sigruficantly decreased lidocaine flux in the IPPSF (Riviere and Williams, 1991). Tolazoline shortened and norepinephrine increased the mean absorption time. Neither of these effects conld be replicated in the in vitro model. Their subsequent work in the anesthetized pig model showed that, in tissue samples taken 4 h after a 1-h iontophoretic treatment period, tolazoline had decreased underlying tissue concentrations of lidocaine, and norepinephrine had increased tissue levels compared to those observed when lidocaine was administered alone (Riviere etal., 1992). Subsequently, Williams and Riviere (1993) used a three-compartment pharmacokinetic model to describe these results. 

Three distinct regions are observed in the clearance curves. It begins with a region where data is gathered pre-bolus injection, and represents the baseline value for the subsequent experiments. The ICG plasma concentration rapidly peaks within a few seconds, followed by rapid exponential decay as the liver eliminates the dye from blood. Visually, the decay rates are similar for all three, and well within biological variability. After 15 minutes, approximately 90% of the initial signal is lost. The ICG elimination from blood follows the single compartment pharmacokinetics model described by Eq. (3). After several experi-... 

Wall et al.9 administered 1.3 pg/kg of 3H-PCP intravenously to human volunteers and collected blood samples for 72 h. Data from this study suggested a two-compartment pharmacokinetic model with a plasma half-life for PCP of 7 to 16 h. Domino et al.10 further analyzed the data from Wall et al. and developed a more complex three-compartment PK model. The reported half-lives for... 

FIGURE 4-4 Influence of biologic half-life relationship between exposure level (E, upper left) and biomarker level (BM). Daily exposure levels were created by Monte Carlo sampling from auto-correlated lognormal distribution. Observation time is 400 days. Biomarker levels were calculated for three half-lives—1 day (upper right), 1 month (lower left), and 1 year (lower right)—with one-compartment pharmacokinetic model. 

Pharmacokinetic analysis indicated that two-compartment open models best characterized the disposition of 2,4-DNP and 2-amino- 4-nitrophenol from plasma, whereas a three-compartment open model best characterized the disposition of 4-amino-2-nitrophenol from plasma. The elimination half-lives (tV2) for the terminal phase were estimated at 10.3 hours for 2,4-DNP, 46.2 hours for 2-amino-4-nitrophenol, and 25.7 hours for 4-amino-2-nitrophenol. 

An ideal pharmacokinetic model of the percutaneous absorption process should be capable of describing not only the time course of penetration through skin and Into blood (or receptor fluid In a diffusion cell), but also the time course of disappearance from the skin surface and accumulation (reservoir effect) of penetrant within the skin membrane. Neither Pick s Plrst Law of Diffusion nor a simple kinetic model considering skin as a rate limiting membrane only Is satisfactory, since neither can account for an accumulation of penetrant within skin. To resolve this dilemma, we have analyzed the In vitro time course of absorption of radiolabeled benzoic acid (a rapid penetrant) and paraquat (a poor penetrant) through hairless mouse skin using a linear three compartment kinetic model (Figure 5). The three compartments correspond to the skin surface (where the Initial dose Is deposited), the skin Itself (considered as a separate compartment), and the receptor fluid In the diffusion cell. The Initial amount deposited on the skin surface Is symbolized by XIO, and K12 and K23 are first order rate constants. 

Vinblastine is another vesicant vinca alkaloid that causes myelo-suppression and less neurotoxicity than vincristine. The pharmacokinetics of vinblastine are best described by a three-compartment model, with an a half-life of 25 minutes, a 3 half-life of 53 minutes, and a terminal half-life of 19 to 25 hours.12 Vinblastine has shown activity in the treatment of bladder, breast, and kidney cancer, as well as some lymphomas. The doses of vinblastine tend to be higher on a milligram per meter squared basis than vincristine. Nausea and vomiting are minimal with vinblastine. Other side effects include mild alopecia, rash, photosensitivity, and stomatitis. 

The vesicant vinorelbine is structurally similar to vincristine and may cause many of the same side effects as vincristine. While this vesicant is administered intravenously over 6 to 10 minutes, patients should be counseled about neuropathy, ileus, and myelosuppression. The pharmacokinetics of vinorelbine are best described by a three-compartment model, with an a half-life of 2 to 6 minutes, a 3 half-life of 1.9 hours, and a y half-life of 40 hours. Vinorelbine has shown efficacy in the treatment of breast cancer and non-small cell lung cancer. Additional side effects include myelosuppression, paresthesias, and mild nausea and vomiting. 

Docetaxel, another taxane, binds to tubulin to promote microtubule assembly. The pharmacokinetics of docetaxel are best described by a three-compartment model, with an a half-life of 0.08 hours, a 3 half-life of 1.6 to 1.8 hours, and a terminal half-life of 65 to 73 hours.14 Docetaxel has activity in the treatment of breast, non-small cell lung, prostate, bladder, esophageal, stomach, ovary, and head and neck cancers. Dexamethasone, 8 mg twice daily for 3 days starting the day before treatment, is used to prevent the fluid retention syndrome associated with docetaxel and possible hypersensitivity reactions. The fluid... 

Teniposide, a topoisomerase II inhibitor, is administered as an infusion over 30 to 60 minutes to prevent hypotension. The pharmacokinetics are described by a three-compartment model, with an a half-life of 0.75 hours, a (5 half-life of 4 hours, and a terminal half-life of 20 hours. Considerable variability in clearance of teniposide in children has been reported.17 Teniposide has shown activity in the treatment of acute lymphocytic leukemia, neuroblastoma, and non-Hodgkin s lymphoma. Side effects include myelosuppression, nausea, vomiting, mucositis, and venous irritation. Hypersensitivity reactions may be life-threatening. 

Epirubicin inhibits both DNA and RNA polymerases and thus inhibits nucleic acid synthesis and topoisomerase II enzymes. Epirubicin pharmacokinetics are best described by a three-compartment model, with an a half-life of 4 to 5 minutes, a... 

Idarubicin inhibits both DNA and RNA polymerase, as well as topoisomerase II. The pharmacokinetics of idarubicin can best be described by a three-compartment model, with an a half-life of 13 minutes, a (3 half-life of 2.4 hours, and a terminal half-life of 16 hours.22 Idarubicin is metabolized to an active metabolite, idarubicinol, which has a half-life of 41 to 69 hours. Idarubicin and idarubicinol are eliminated by the liver and through the bile. Idarubicin has shown clinical activity in the treatment of acute leukemias, chronic myelogenous leukemia, and myelodysplastic syndromes. Idarubicin causes cardiomyopathy at cumulative doses of greater than 150 mg/m2 and produces cumulative cardiotoxic effects with other anthracyclines. Idarubicin is a vesicant and causes red-orange urine, mucositis, mild to moderate nausea and vomiting, and bone marrow suppression. 

This royal-blue-colored drug is an anthracenedione that inhibits DNA topoisomerase II. The pharmacokinetics of mitoxantrone may best be described by a three-compartment model, with an a half-life of 3 to 10 minutes, a 3 half life of 0.3 to 3 hours, and a median terminal half-life of 12 days. Biliary elimination appears to be the primary route of elimination, with less than 10% of the drug eliminated by the kidney.23 Mitoxantrone has shown clinical activity in the treatment of acute leukemias, breast and prostate cancer, and non-Hodgkin s lymphomas. Myelosuppression, mucositis, nausea and vomiting, and cardiac toxicity are side effects of this drug. The total cumulative dose limit is 160 mg/m2 for patients who have not received prior anthracycline or mediastinal radiation. Patients who have received prior doxorubicin or daunorubicin therapy should not receive a cumulative dose greater than 120 mg/m2 of mitoxantrone. Patients should be counseled that their urine will turn a blue-green color. 

Another method of predicting human pharmacokinetics is physiologically based pharmacokinetics (PB-PK). The normal pharmacokinetic approach is to try to fit the plasma concentration-time curve to a mathematical function with one, two or three compartments, which are really mathematical constructs necessary for curve fitting, and do not necessarily have any physiological correlates. In PB-PK, the model consists of a series of compartments that are taken to actually represent different tissues [75-77] (Fig. 6.3). In order to build the model it is necessary to know the size and perfusion rate of each tissue, the partition coefficient of the compound between each tissue and blood, and the rate of clearance of the compound in each tissue. Although different sources of errors in the models have been... 

Models may contain any number of compartments but single-compartment models are generally inaccurate for studying pharmacokinetics. A three-compartment model allows fairly accurate modelling with only limited complexity. 

X2° = X30 = 0 assumed to be known exactly. The only observed variable is = x. Jennrich and Bright (ref. 31) used the indirect approach to parameter estimation and solved the equations (5.72) numerically in each iteration of a Gauss-Newton type procedure exploiting the linearity of (5.72) only in the sensitivity calculation. They used relative weighting. Although a similar procedure is too time consuming on most personal computers, this does not mean that we are not able to solve the problem. In fact, linear differential equations can be solved by analytical methods, and solutions of most important linear compartmental models are listed in pharmacokinetics textbooks (see e.g., ref. 33). For the three compartment model of Fig. 5.7 the solution is of the form... 

The classical three-compartment model describes pharmacokinetics of 5-HT1A receptor agonists. By means of a sigmoidal function E (c), the 5-HT1A agonist concentration c (t) influences the set-point signal that dynamically interacts with the body temperature. By using x (t) and y (t) as dimensionless state variables for the set-point and temperature, respectively, the model is expressed by the set of two nonlinear differential equations ... 

Butorphanol, an analog of buprenorphine, showed a nasal bioavailability of 70% and also a much lower Tmax after nasal absorption as compared with the sublingual and buccal routes [115]. Lindhardt et al. [106] compared buprenorphine formulated in 30% PEG-300 in sheep with that of the 5% dextrose formulation mentioned earlier. A unit-dose Pfeiffer device was again used to administer the formulation. It was found that nasal bioavailability in sheep was about 70% when buprenorphine was formulated in PEG-300 and approximately 89% when it was formulated with 5% dextrose. The rate of absorption was reported to be very fast, with a Tmax of 10 min the Cmax was found to be 37 and 48ng/mL for PEG-300 and dextrose, respectively. In sheep, the pharmacokinetics of buprenorphine showed a two-compartment model as compared to a three-compartment model in humans. 

These techniques also can be applied to develop equations for three-compartment and other commonly used pharmacokinetic models. 

Two commonly used three-compartment models are shown in Figures 8.6D and E. Of the two peripheral compartments, one exchanges rapidly and one changes slowly with the central compartment. Model D is (7 priori identifiable while model E is not. Model E will have two different compartmental matrices that will produce the same fit of the data. The reason is that the loss is from a peripheral compartment. Finally, model F, a model very commonly used to describe the pharmacokinetics of drug absorption, is not a priori identifiable. Again, there are two values for the compartmental K matrix that will produce the same fit to the data. 

The pharmacokinetics of aminoglycosides ascribes to an interrelated two or three compartment model. The three compartment model comprises three phases, an a or distributive phase, and two elimination phases, P and Y- After administration of an intravenous dose in the three compartment model, the aminoglycoside first enters the a or distributive phase [33]. During this initial phase, the aminoglycoside is transported from the vascular to the extracellular compartment. The p or elimination phase represents the elimination of the aminoglycoside from the plasma and extravascular compartments [33]. The third or y phase corresponds to the protracted elimination of the aminoglycoside... 

Vancomycin is approximately 30 to 55% bound to plasma proteins. Its distribution after intravenous administration proceeds as a biphasic process and is consistent with a two or three compartment model. The half-life of the first distributive phase is approximately 0.4 hour in patients with normal renal function the second distributive phase is approximately 1.6 hours [172]. Consistent with its multicompartment pharmacokinetic modeling, vancomycin is widely distributed and penetrates into many different body fluids and... 

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