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Statistical moment method of pharmacokinetics
Linear differential equations are used to describe the regularity of these processes in vivo. When the dosage of the drug with the characteristics of single-chamber or double-chamber model changes, the corresponding blood concentration changes in direct proportion to the dosage change, the biological half-life of the drug has nothing to do with the dosage, and the total area under the blood concentration-time curve is in direct proportion to the dosage.

Nonlinear dynamics is produced when the drug concentration exceeds a certain limit and the enzymes involved in drug metabolism are saturated. The famous Michaelis equation can be used to describe the kinetic equation of enzyme.

The equation is based on the formation of another chemical substance with the participation of enzymes or carriers. Because this process needs to be carried out with the participation of specific enzymes or vectors, these processes have strong specificity. Enzymes are involved in biotransformation of drugs, secretion of renal tubules and bile secretion of some drugs, so they have nonlinear kinetic characteristics. Bioavailability refers to the relative quantity and speed of drugs entering the systemic circulation in the preparation, that is, bioavailability includes two aspects: absorption speed and absorption degree of drugs.

The bioavailability of pharmaceutical preparations is one of the important indexes to evaluate the quality of pharmaceutical preparations, and it is also an important content of new drug research. Generally, the bioavailability of the following drugs should be studied: drugs used to prevent and treat serious diseases, especially drugs with a therapeutic dose close to poisoning; Drugs with steep dose-response curve or adverse reactions; Drugs with slow dissolution rate; Some drugs are relatively insoluble or become insoluble in the gastrointestinal tract; Drug preparation, its dissolution rate is affected by particle size and polymorphism; The auxiliary materials in the preparation can change the characteristics of the main drug.

Absorption speed

① The absorption rate can be expressed by the time to peak (tmax) on the plasma concentration-time curve.

② Ka can be obtained by residue method.

(3) ③Wagner-Nelson method (absorption percentage plotted against time) is suitable for single cavity model.

(4) Loo-Reigeiman method is suitable for two-compartment model.

Degree of absorption

The absorption degree can be determined by the total area (AUC) under the plasma concentration-time curve of the test preparation and the reference preparation.

1. Absolute bioavailability

AUCiv is the area under the plasma concentration-time curve of intravenous administration.

2. Relative bioavailability.

AUC test is the area under the blood concentration-time curve of the test sample, and the AUC reference ratio is the area under the blood concentration-time curve of the standard preparation.

The solution of AUC: 1 Basic requirements of biological sample analysis methods

① strong specificity; ② High sensitivity; ③ Good accuracy; ④ High accuracy; ⑤ The standard curve shall cover the whole concentration range to be measured and shall not be extrapolated.

2. Common preparations

1) The bioavailability and bioequivalence of the subjects are generally conducted in human body, and normal and healthy volunteers should be selected. The selection conditions are: the age is generally 16~40 years old, male, and the weight is 10% of the standard weight. The subjects should have liver, renal function and electrocardiogram examinations, and all drugs should be stopped two weeks before the experiment. Smoking, drinking and caffeinated drinks should be prohibited during the experiment. Subjects must have enough cases, requiring at least 18~24 cases.

2) reference preparation research must have reference preparation as control. Its safety and effectiveness should be qualified. In the study of ethics, we should consider choosing the same dosage form and market-leading preparations that have been listed at home and abroad as standard reference preparations. Only when there is no corresponding preparation at home and abroad will other similar preparations be considered as reference preparations.

3) The safety of the preparation to be tested should meet the requirements, and data such as dissolution, stability, content or titer should be provided. The sample to be tested should be a pilot scale-up sample.

4) Experimental design For the double-agent test of a test preparation and a standard control preparation, a double-period crossover randomized trial design is usually adopted, and the interval between two test periods is at least 7~ 10 half-life of the active substance, usually 1 week.

The complete plasma concentration-time curve should include absorption period, equilibrium period and elimination period. There are enough sampling points for each, and the total sampling points shall not be less than 1 1. Generally, there are 2-3 points in the absorption stage, 2-3 points in the equilibrium stage and 6-8 points in the elimination stage. For sustained and controlled release preparations, the sampling points should be increased accordingly. The whole sampling period should be at least 3~5 half-lives, or the sampling should continue until the blood concentration reaches110 ~1/20 of Cmax.

5) Determination of drug dosage In the study of bioavailability, the drug dosage should generally be consistent with clinical medication. If the sensitivity of the blood concentration determination method is limited, the dose can be increased appropriately, but the dose should not exceed the maximum clinical dose on the premise of ensuring safety. The standard participating preparation of the test preparation is preferably an equal dose.

6) During the study, the subjects fasted for the test preparation or the standard reference preparation overnight, took it with 200~250ml warm boiled water, and unified diet after 2~4 hours.

7) The main pharmacokinetic parameters in pharmacokinetic analysis are biological half-life (t 1/2), peak concentration (Cmax), time to peak (tmax) and AUC under the plasma concentration-time curve. Cmax and tmax shall be measured values and shall not be extrapolated.

8) Calculation of bioavailability Calculate the bioavailability f through AUC0~∞ of each subject, and get its mean SD.

9) Evaluation of bioavailability and bioequivalence The 95% confidence limit of the parameter AUC of the test preparation falls within the range of 80%~ 125% of the standard reference preparation, the acceptable range of Cmax is 70%~ 145%, and the relative bioavailability of the test preparation should be 80%~ 120%.

3. Sustained-release and controlled-release preparations

1) single dose, double cycle crossover test

2) Multi-dose dual-cycle steady-state study