Model two-compartment

In a two-compartment model, /3 is equivalent to k in the one-compartment model. Therefore, the terminal half-life for the elimination of a chemical compound following two-compartment model elimination can be calculated from the equation (i = 0.693/ti/i ... 

Physiologically based toxicokinetic models are nowadays used increasingly for toxicological risk assessment. These models are based on human physiology, and thus take into consideration the actual toxicokinetic processes more accurately than the one- or two-compartment models. In these models, all of the relevant information regarding absorption, distribution, biotransformarion, and elimination of a compound is utilized. The principles of physiologically based pharmaco/ toxicokinetic models are depicted in Fig. 5.41a and h. The... 

Hill, B.D. and Schaalje, G.B. (1985). A two compartment model for the dissipation of delta-methrin in soil. Journal of Agriculture and Food Chemistry 33, 1001-1006. 

Simkins S, R Mukherjee, M Alexander (1986) Two approaches to modeling kinetics of biodegradation by growing cells and application of a two-compartment model for mineralization kinetics in sewage. Appl Environ Microbiol 51 1153-1160. 

In the previous discussion of the one- and two-compartment models we have loaded the system with a single-dose D at time zero, and subsequently we observed its transient response until a steady state was reached. It has been shown that an analysis of the response in the central plasma compartment allows to estimate the transfer constants of the system. Once the transfer constants have been established, it is possible to study the behaviour of the model with different types of input functions. The case when the input is delivered at a constant rate during a certain time interval is of special importance. It applies when a drug is delivered by continuous intravenous infusion. We assume that an amount Z) of a drug is delivered during the time of infusion x at a constant rate (Fig. 39.10). The first part of the mass balance differential equation for this one-compartment open system, for times t between 0 and x, is given by ... 

To conclude this section on two-compartment models we note that the hybrid constants a and p in the exponential function are eigenvalues of the matrix of coefficients of the system of linear differential equations ... 

The inverse transform Xp(t) in the time domain can be obtained by means of the method of indeterminate coefficients, which was presented above in Section 39.1.6. In this case the solution is the same as the one which was derived by conventional methods in Section 39.1.2 (eq. (39.16)). The solution of the two-compartment model in the Laplace domain (eq. (39.77)) can now be used in the analysis of more complex systems, as will be shown below. 

In the previous section we found that the hybrid transfer constants of a two-compartment model are eigenvalues of the transfer constant matrix K. This can be generalized to the multi-compartment model. Hence the characteristic equation can be written by means of the determinant A ... 

This general approach for solving linear pharmacokinetic problems is referred to as the y-method. It is a generalization of the approach by means of the Laplace transform, which has been applied in the previous Section 39.1.6 to the case of a two-compartment model. 

Our pharmacokinetic data indicate that detectable PCP levels may remain in the urine for 4 to 5 weeks after the last use, similar to previous reports (Khajawall and Simpson 1983). The observed elimination kinetics were equally consistent with a one- or two-compartment model, but methodological problems with our data make... 

Azacitidine, a cytidine analog, causes hypomethylation of DNA, which normalizes the function of genes that control cell differentiation to promote normal cell maturation. The suspension is administered as a subcutaneous injection daily for 7 days for the treatment of myelodysplastic syndrome, a preleukemia disease. The pharmacokinetics of azacitidine are best described by a two-compartment model, with a terminal half life of 3.4 to 6.2 hours, whereas peak concentrations are achieved 30 minutes after a subcutaneous injection.7 Azacitidine has been shown to be clinically active in the treatment of myelodysplastic syndromes. The side effects include myelosuppression, renal tubular acidosis, renal dysfunction, and injection-site reactions. 

Etoposide causes multiple DNA double-strand breaks by inhibiting topoisomerase II. The pharmacokinetics of etoposide are described by a two-compartment model, with an a half-life of 0.5 to 1 hour and a (5 half-life of 3.4 to 8.3 hours. Approximately 30% of the dose is excreted unchanged by the kidney.16 Etoposide has shown activity in the treatment of several types of lymphoma, testicular and lung cancer, retinoblastoma, and carcinoma of unknown primary. The intravenous preparation has limited stability, so final concentrations should be 0.4 mg/mL. Intravenous administration needs to be slow to prevent hypotension. Oral bioavailability is approximately 50%, so oral dosages are approximate two times those of intravenous doses however, relatively low oral daily dosages are used for 1 to 2 weeks. Side effects include mucositis, myelosuppression, alopecia, phlebitis, hypersensitivity reactions, and secondary leukemias. 

Topotecan inhibits topoisomerase I to cause single-strand breaks in DNA. The pharmacokinetics of topotecan can be described by a two-compartment model, with a terminal half-life of 80 to 180 minutes, with renal clearance accounting for approximately 70% of the clearance.19 Topotecan has shown clinical activity in the treatment of ovarian and lung cancer, myelodysplastic syndromes, and acute myelogenous leukemia. The intravenous infusion may be daily for 5 days or once weekly. Side effects include myelosuppression, mucositis, and diarrhea. 

Daunorubicin is an anthracycline that is sometimes referred to as an antitumor antibiotic. Daunorubicin inserts between base pairs of DNA to cause structural changes in DNA however, the primary mechanism of cytotoxicity is the inhibition of topoisomerase II. The pharmacokinetics are best described by a two-compartment model, with a terminal half-life of about 20 hours. The predominant route of elimination of daunorubicin and hydroxylated metabolites is hepatobiliary... 

Liposomal doxorubicin is an irritant, not a vesicant, and is dosed differently from doxorubicin, so clinicians need to be very careful when prescribing these two drugs. The pharmacokinetics of liposomal doxorubicin are best described by a two-compartment model, with a terminal half-life of 30 to 90 hours.20 Liposomal doxorubicin has shown significant activity in the treatment of breast and ovarian cancer, along with multiple myeloma and Kaposi s sarcoma. Side effects include mucositis, myelosuppression, alopecia, and palmar-plantar erythrodysesthesia. The liposomal doxorubicin may be less cardiotoxic than doxorubicin. 

While carboplatin has the same mechanism of action as cisplatin, it has a much less toxic side-effect profile than cisplatin. The pharmacokinetics of carboplatin are best described by a two-compartment model, with an a half-life of 90 minutes and a terminal half-life of 180 minutes. Carboplatin is eliminated almost entirely by the kidney by glomerular filtration and tubular secretion. Many chemotherapy regimens dose carboplatin based on an area under the curve (AUC), which is referred to... 

Mitomycin C is an alkylating agent that forms cross-links with DNA to inhibit DNA and RNA synthesis. The pharmacokinetics of mitomycin C are best described by a two-compartment model, with an a half-life of 8 minutes and a terminal half-life of 48 minutes.31 Liver metabolism is the primary route of elimination. Mitomycin C has shown clinical activity in the treatment of anal, bladder, cervix, gallbladder, esophageal, and stomach cancer. Side effects consist of myelosuppression and mucositis, and it is a vesicant. 

Denileukin diftitox is a combination of the active sections of interleukin 2 and diphtheria toxin. It binds to high-affinity interleukin 2 receptors on the cancer cell (and other cells), and the toxin portion of the molecule inhibits protein synthesis to result in cell death. The pharmacokinetics of denileukin diftitox are best described by a two-compartment model, with an a half-life of 2 to 5 minutes and a terminal half-life of 70 to 80 minutes. Denileukin diftitox is used for the treatment of persistent or recurrent cutaneous T-cell lymphoma whose cells express the CD25 receptor. Side effects include vascular leak syndrome, fevers/chills, hypersensitivity reactions, hypotension, anorexia, diarrhea, and nausea and vomiting. 

Rituximab is a monoclonal antibody to the CD20 receptor expressed on the surface of B lymphocytes the presence of the antibody is determined during flow cytometry of the tumor cells. Cell death results from antibody-dependent cellular cytotoxicity. The pharmacokinetics of rituximab are best described by a two-compartment model, with a terminal half-life of 76 hours after the first infusion and a terminal half-life of 205 hours after the fourth dose.36 Rituximab has shown clinical activity in the treatment of B-cell lymphomas that are CD20+. Side effects include hypersensitivity reactions, hypotension, fevers, chills, rash, headache, and mild nausea and vomiting. 

Toremifene is an estrogen receptor antagonist. The pharmacokinetics of toremifene are best described by a two-compartment model, with an a half-life of 4 hours and an elimination half-life of 5 days. Peak plasma concentrations are achieved approximately 3 hours after an oral dose. Toremifene is metabolized extensively, with metabolites found primarily in the feces. Toremifene is used for the treatment of metastatic breast cancer in postmenopausal women with estrogen-receptor-positive or unknown tumors. Toremifene causes hot flashes, vaginal bleeding, thromboembolism, and visual acuity changes. 

Analysis of data using simple mammillary, compartmental models allows the estimation of all of the basic parameters mentioned here, if data for individual tissues are analyzed with one or two compartment models, and combined with results from... 

The equation is compiled in the same way as that for a two-compartment model B.e-/3f continues to represent the terminal elimination phase and the term C.e 7f is added to represent slowly equilibrating compartments. 

C(t) modeled according to two-compartment model with zero-order and first-order absorption Pharmacokinetic/pharmacodynamic relationship modeled using Hill model with first-order absorption. Modeled parameters matched experimental parameters when bicompartmental model with zero-order input was used. Linear PKs, anticlockwise hysteresis loop established for all doses studied. Apomorphine and growth hormone concentration predicted with good accuracy... 

A four-compartment model consisting of a two-compartment model for each enantiomer, with elimination from both compartments, connected by rate constants for chiral inversion was fitted to the concentration data, whereas the sedative effects were correlated with the blood concentrations of R- and S-thalidomide by means of logistic regression. PK modeling predicted that varying the infusion time of a fixed dose of S-thalidomide between 10 min and 6 h would have little influence on the maximal blood concentration of formed R-thaKdomide. These effects may chiefly be exerted by S-thalidomide, but the enantiomers are interconverted in vim... 

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