Method and program for predicting plasma concentration transition after intravenous administration from pharmacokinetic parameter

Abstract

To solve the problem that changes other than changes in plasma concentration which can be described with a 1-compartment model cannot be predicted from a measured pharmacokinetic parameter described in an attached document of a drug or a pharmacokinetic parameter predicted from non-clinical tests, and to provide a method for predicting changes in plasma concentration that are described with a 2-compartment model.SOLUTION: A method includes: estimating an optimum drug macro parameter from an input dosage of a drug to be predicted, an area under the concentration-time curve (AUC) and steady-state volume of distribution (Vss), or information on a measured or predicted pharmacokinetics parameter (S-1) in a half-life period (T1 / 2) and a macro parameter or micro parameter analyzed with a 2-compartment model of an existing drug (S-2); and predicting changes in plasma concentration using the 2-compartment model (S-3).SELECTED DRAWING: Figure 1

Description

[Technical Field]

[0001] The present disclosure relates to a method and apparatus for predicting (simulating) the progression of the plasma concentration of a compound, including a drug, using a compartmental model when the compound is intravenously administered to an animal, including a human. [Background technology]

[0002] Administered drugs move to the site of action and exhibit either medicinal or toxic effects. Because the concentration of a drug at the site of action and the duration of its action depend on the plasma concentration, understanding the relationship between efficacy / toxicity and plasma concentration trends is important for the appropriate use of pharmaceuticals. Pharmacokinetic analysis is a method for analyzing the time course of a drug's plasma concentration.

[0003] There are three methods of pharmacokinetic analysis: compartmental model analysis, non-compartmental analysis, and physiological pharmacokinetic analysis. Generally, the pharmacokinetic parameters listed in drug package inserts and academic papers are the results of non-compartmental analysis. Non-compartmental analysis cannot predict plasma concentration trends. Compartmental model analysis and physiological pharmacokinetic analysis are used to predict blood and plasma concentration trends. Physiological pharmacokinetic models are complex models that require many parameters. Furthermore, physiological pharmacokinetic model analysis is limited in its use because it requires dedicated software. Compartmental model analysis is widely used for dosage design, etc., because analytical solutions exist and calculations are simple.

[0004] Predicting plasma concentration trends using compartment models is effective for appropriate drug administration planning. Conventional compartment model analysis applies the obtained plasma concentration to 1-, 2-, or 3-compartment models, and the obtained analysis results can be used to easily predict plasma concentration trends under different administration conditions, such as repeated administration.

[0005] The pharmacokinetic parameters for intravenous administration are the area under the plasma concentration-time curve (AUC) and / or total body clearance (CL), plasma elimination half-life (T1 / 2), and steady-state volume of distribution (Vss) after rapid administration. For continuous administration, the maximum plasma concentration (Cmax) and time to reach maximum plasma concentration (Tmax) may also be listed in addition to the above four parameters.

[0006] During the drug discovery and development stages of pharmaceutical development, pharmacokinetics in humans is predicted from the results of animal and in vitro studies. The pharmacokinetic parameters CL and Vss are predicted using a variety of methods (J Pharm Sci. 2011;100:4090-110). Methods for predicting plasma concentration over time include the Dedric method (Cancer Chemother Rep. 1970;54:95-101) and the Css-MRT method (J Pharm Sci. 2004;93:1890-900, Patent Document 2), which are based on animal studies, and physiologically based pharmacokinetic models (Patent Document 3), which are based on in vitro and / or in silico studies. The only method for predicting plasma concentration over time from the two pharmacokinetic parameters CL and Vss is the one-compartment model.

[0007] Because the amount of information provided by pharmacokinetic parameters actually obtained in humans and those predicted from non-clinical studies is insufficient, a two-compartment model cannot be used to predict the plasma concentration profile, and only a one-compartment model can be used. When plasma concentration profiles described by a two-compartment model are predicted using a one-compartment model, the prediction error is large. Most plasma concentration profiles following oral administration are described using a two-compartment model. (Patent Document 1)

[0008] The two-compartment model consists of two compartments: compartment 1 (the central compartment), which represents the systemic circulation containing plasma, and compartment 2, which takes time to equilibrate with plasma. The two-compartment model requires four microparameters: the distribution volume of compartment 1 (V1), the two intercompartment rate constants (K12, K21), and the elimination rate constant (Ke). Analytical solutions for plasma concentration profiles are complicated when expressed using microparameters, so they are expressed using four macroparameters: A and B, which represent concentrations, and α and β, which represent rate constants. Analysis and prediction are usually performed using analytical solutions. Pharmacokinetic parameters published in package inserts and academic papers often contain insufficient information, making it impossible to calculate the parameters required for a two-compartment model. Human CL and Vss are predicted from nonclinical studies, but these are also two parameters, making the two-compartment model ineffective at predicting plasma concentration profiles.

[0009] Although not directly related to the present invention, an example of an analytical method that compensates for a lack of information is shown below. Population analysis is a method for predicting the plasma concentration over time of a patient based on limited blood sampling from that patient. Although compartmental analysis is not possible with only a few plasma concentrations per patient, data from many patients, even a few samples per patient, can be analyzed as a group to evaluate the mean and variance of parameters. These mean and variance data can then be used as prior information for Bayesian estimation in combination with the blood sampling from several samples, thereby estimating the individual's parameters and predicting the plasma concentration over time (Non-Patent Document 2).

[0010] Here is another example. In physiological pharmacokinetic models, there are too many parameters to identify from observable data, so it can be difficult to obtain the parameters. One solution to this problem is the cluster Gauss-Newton method. This method efficiently searches for unknown parameters from a wide parameter space (Non-Patent Document 3). Just as in population analysis, where the parameter range is specified by the mean and variance, this method also specifies the parameter range and then estimates it. [Prior art documents] [Patent documents]

[0011] [Patent Document 1] Patent application 2024-35378 [Patent Document 2] Patent Publication No. 2021-63689 [Patent Document 2] Patent Publication No. 2022-106330 [Non-patent literature]

[0012] [Non-Patent Document 1] Motohiro Kato 30P-pm482 The 144th Annual Meeting of the Pharmaceutical Society of Japan (2024) [Non-patent document 2] Introduction to Population Pharmacokinetics for Drug Blood Concentration Monitoring, Yakugyo Jihosha, 1988. [Non-patent document 3] CPT Pharmacometrics Syst Pharmacol.2023;00:1-14. [Non-patent document 4] J Pharm Sci.2004;93:1890-900 Summary of the Invention [Problem to be solved by the invention]

[0013] In view of the above problems, the present invention provides a method and program for predicting the plasma concentration profile of a drug after intravenous administration using a two-compartment model, which could not be predicted from pharmacokinetic parameters using the conventional one-compartment model. [Means for solving the problem]

[0014] The present inventors have devised the following method for predicting the plasma concentration profile of a target drug by estimating parameters in a two-compartment model of the target drug from two pieces of information: measured pharmacokinetic parameters described in drug package inserts or academic papers, or pharmacokinetic parameters predicted from non-clinical studies, and parameter information obtained by two-compartment model analysis of existing drugs.

[0015] In a first exemplary embodiment of the present invention, there is provided a method for predicting the plasma concentration profile of a drug using a computer. The prediction method includes the steps of estimating macroparameters or microparameters of an optimal 2-compartment model of the target drug from two or three pharmacokinetic parameters, namely AUC or CL at a certain dose of the drug to be predicted, Vss and / or T1 / 2, and prior information on existing drugs, and predicting the plasma concentration profile using the compartment model. In the present invention, the AUC or CL at a certain dose of the drug is used, but since AUC can be calculated by dividing the dose by CL, the pharmacokinetic parameter used for prediction is AUC at a certain dose.

[0016] In a second exemplary aspect of the present invention, there is provided a program for executing the prediction method of the first aspect.

[0017] In a third exemplary aspect of the present invention, there is provided a simulation device comprising a memory storing the program of the first aspect and a control circuit which is a computer, and which executes the computer program to estimate parameters in a compartment model and predict the plasma concentration transition using the parameters. [Effects of the Invention]

[0018] Of the AUC, Vss, T1 / 2, and Cmax measured or predicted at a certain dose of the drug to be predicted, the macro or micro parameters of the optimal 2-compartment model for the target drug can be estimated from two pharmacokinetic parameters, AUC and Vss or T1 / 2, and prior information on existing drugs, to predict the plasma concentration profile. [Brief explanation of the drawings]

[0019] [Figure 1] FIG. 1 is a flowchart showing the procedure of a system for predicting the progression of plasma drug concentration according to an embodiment of the present invention. [Figure 2] FIG. 1 is a diagram showing an example of a system for predicting the transition of plasma concentration of a drug according to an embodiment of the present invention. [Figure 3] FIG. 1 shows the correlation of micro parameters obtained by two-compartment model analysis of existing drugs. [Figure 4] FIG. 1 shows a comparison of the plasma concentration trends of midazolam, alfentanil, alogliptin, esaxerenone, and lorlatinib predicted by the conventional method and the method of the present invention (macro method and micro method) using two parameters, AUC and Vss. DETAILED DESCRIPTION OF THE INVENTION

[0020] The prediction method and apparatus of this embodiment will be described below with reference to the accompanying drawings as appropriate.

[0021] <Parameter definition> The parameters used in the following disclosure are defined as follows: D: Dosage C: Plasma concentration K0: Administration rate Cmax: maximum plasma concentration Tmax: Time to reach maximum plasma concentration AUC: Area under the plasma concentration time curve T1 / 2: Half-life T: Continuous administration time Vd: Volume of distribution in a one-compartment model Ke: Elimination rate constant V1: Volume of distribution of compartment 1 in a two-compartment model K12: Transfer rate constant from compartment 1 to compartment 2 K21: Transfer rate constant from compartment 2 to compartment 1 A / D: Constant of concentration standardized by the dose in the α phase. B / D: Constant of concentration standardized by the dose in the β phase. α: Elimination rate constant in the α phase β: Elimination rate constant in the β phase

[0022] The flowcharts and systems of the prediction method of the present invention are shown in FIGS. 1 and 2. The data input unit 10 inputs the dose, the pharmacokinetic parameters at the time of that dose, and the simulation conditions (S-1). The simulation conditions are the dose, the administration rate, the duration of continuous administration, and the time for calculating the concentration.

[0023] The two-compartment model calculation unit 20 estimates the macroparameters (S-2).

[0024] The equations of the two-compartment model describing the plasma concentration changes during intravenous rapid administration and continuous administration are shown in Equations (1) and (2). Usually, the plasma concentration changes are applied to these equations to estimate the optimal parameters. Also, the plasma concentration changes can be predicted from the obtained parameters.

Equation

Equation

[0025] The pharmacokinetic parameter range control section specifies the possible difference (error) between the measured pharmacokinetic parameters and the estimated pharmacokinetic parameters. Using equation (1) or (2), the plasma concentration time course of existing drugs is applied to find the optimal macroparameters (A, B, α, β) for each drug. The predicted pharmacokinetic parameters are calculated using the obtained macroparameters using equations (3)-(6) below, and the ratios to the measured pharmacokinetic parameters are calculated. The mean and standard deviation of the ratios are used as the range parameters for the pharmacokinetic parameter range control section.

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[0026] <Provided from macro parameters> For existing drug macroparameters, A and B are standardized by dosage. The parameters are logarithmically transformed, and the range, mean value, standard deviation, and correlation coefficient between parameters for each logarithmically transformed macroparameter are calculated. The macroparameter range control section associates the obtained macroparameter information using an estimation method (multiple regression analysis, neural network, etc.) that takes correlation into account and has a high probability of existence of parameters, thereby limiting the parameter range.

[0027] <Providing macro parameters from micro parameters> The microparameters (V1, K12, K21, Ke) are calculated from the macroparameters obtained by fitting existing drugs using equations (7)-(10). The parameters are logarithmically transformed, and the range, mean value, standard deviation, and correlation coefficient between each logarithmically transformed microparameter are calculated. The microparameter range control unit associates the obtained macroparameter information with an estimation method (multiple regression analysis, neural network, etc.) that takes correlation into account and has a high probability of existence of parameters, thereby limiting the parameter range.

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[0028] <Provided from macro parameters> The macro parameter calculation unit estimates parameters for predicting plasma concentrations from the range information provided by the macro parameter range control unit and the pharmacokinetic parameters of the target drug. The Bayesian method is shown as an example of a parameter estimation method. The optimal parameters are estimated using equation (11). The measured or predicted pharmacokinetic parameter is Y. The square of the difference between the estimated macro parameter and the value calculated using equations (3)-(6) is taken as the residual square. This is calculated for all parameters used in the calculation, and the sum is taken as the residual sum of squares. The logarithmically transformed macro parameter of the existing drug is P. The square of the difference between this and the estimated logarithmically transformed parameter is taken as the residual square. This is calculated for all parameters, and the sum is taken as the residual sum of squares. The optimal macro parameters are estimated so that the sum of squares of the pharmacokinetic parameter term and the sum of squares of the logarithmically transformed macro parameter term (SS) are minimized. However, if T1 / 2 is used, the residual of β is not calculated.

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[0029] <Providing macro parameters from micro parameters> The conversion formula from micro parameters to macro parameters is shown below.

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[0030] One method for providing macro parameters to the macro parameter range control unit is to provide them from micro parameters. The estimated pharmacokinetic parameters are calculated from the micro parameters using equations (12)-(16), and then calculated from equations (3)-(6). A / D and B / D are values ​​standardized by the dose, and in the calculation, A and B are used as A and B at the desired dose.

[0031] Let Y be the measured or predicted pharmacokinetic parameter. The square of the difference between the estimated macroparameter and the value calculated using equations (3)-(6) is the residual sum. The sum is calculated for all parameters used in the calculation and is the sum of squared residuals. Using equation (11), the optimal microparameters are estimated so that the sum of squared residuals of the pharmacokinetic parameter terms and the sum of squared residuals (SS) of the logarithmically transformed microparameter terms are minimized. Let Y1 = AUC, Y2 = Vss, Y3 = T1 / 2, and Y4 = Cmax. The uppercase Y is the pharmacokinetic parameter of the input target drug, and the lowercase y is the estimated pharmacokinetic parameter. Let P1 = log(V1), P2 = log(K21), P3 = log(Ke), and P4 = log(K12). The uppercase P represents the average value of the parameter for the existing drug, and the lowercase p represents the estimated value of the corresponding parameter for the target drug. The weight of parameter Y is the variance of parameter Y (the square of the value obtained by multiplying the average value by the standard deviation σ), and the weight of parameter P is the variance of parameter P.

[0032] The macroparameters are calculated from the estimated microparameters using equations (12)-(16). A / D and B / D are values ​​normalized by the dose, and in the calculation, A and B are used as the values ​​at the target dose.

[0033] The plasma concentration calculation unit 30 uses the parameters estimated by the 2-compartment model calculation unit 20 to predict the plasma concentration transition using equation (1) or (2) under the set simulation conditions (dosage, administration time). [Example]

[0034] The present invention will be specifically described below with reference to examples, but the present invention is not limited to these examples.

[0035] Application summaries for oral drugs approved as new active ingredients in Japan from 2010 to 2016 (Pharmaceuticals and Medical Devices Agency website; https: / / www.pmda.go.jp / The plasma concentration was read from the graph showing the plasma concentration profile after intravenous administration described in the FDA's FDA Approval Document. The pharmacokinetic parameters used were those described in the application summary. The plasma concentration profile was analyzed using a two-compartment model.

[0036] The data ranges of the pharmacokinetic parameter range control section are shown as examples of analysis results for 23 drugs. The ratios of the measured and predicted values ​​of the pharmacokinetic parameters are AUCR, T1 / 2R, VssR, and CmaxR, and the mean values, standard deviations, maximum values, minimum values, and number of subjects are shown in Table 1. The values ​​shown in published figures and tables are mean values, and the values ​​in the figures and tables do not necessarily agree. The variance calculated from the standard deviations of the parameters listed in Table 1 is used as the variance of the relative error of the pharmacokinetic parameters. [Table 1]

[0037] The data ranges of the macro parameter range control section are shown as examples of analysis results for 23 drugs. The mean values, standard deviations, maximum values, and minimum values ​​of the logarithmically transformed macro parameters are shown in Table 2. The correlation coefficients between parameters are shown in Table 3. [Table 2] [Table 3]

[0038] Table 4 shows the mean, standard deviation, maximum and minimum values ​​of the logarithmically transformed microparameters calculated from the macroparameters of the 23 drugs, and Table 5 shows the correlation coefficients between the parameters. [Table 4] [Table 5]

[0039] The plasma concentration transition was predicted using two methods for providing macro parameters for the macro parameter range control section: one was provided from macro parameters, and the other was provided from micro parameters.

[0040] In the method of providing macro parameters, there is a correlation between log(A / D) and log(B / D), and log(α) and log(β), and these are related by using log(B / A) and log(α / β). The values ​​in Table 2 were used for the average value and standard deviation. Although the average value is used as a method of providing macro parameters, this is not limited to these methods.

[0041] In the method of providing micro parameters, there is a correlation between log(K21) and log(K12), and log(K21) and log(Ke), and these are related by log(Ke / K21) and log(K12 / K21). The average values ​​and standard deviations used are those in Table 2. Although average values ​​are used as a method of providing macro parameters, this is not limited to these methods.

[0042] <Example of plasma concentration transition prediction> The pharmacokinetic parameters of alfentanil, midazolam, esaxerenone, and lorlatinib obtained from literature sources are shown in Table 4. T is the duration of administration. Alfentanil and midazolam are administered bolus-time, while esaxerenone and lorlatinib are administered continuously. [Table 6]

[0043] Macroparameters were estimated in the 2-compartment model calculation section from the AUC and one to three pharmacokinetic parameters other than AUC for alfentanil, midazolam, esaxerenone, and lorlatinib in Table 6. The macroparameter range control section used the macro method and micro method to provide macroparameters. Using the two pharmacokinetic parameters, AUC and Vss, the plasma concentration trends were predicted from the obtained parameters for the four drugs, and the actual measured values ​​read from the figures published in the paper are shown in Figure 4. The conventional method is a prediction using a 1-compartment model. The actual measured values ​​were biphasic, whereas the conventional method was monophasic. The present invention reproduced this biphasic elimination. <Comparison of prediction methods>

[0044] The macro- or micro-parameters of the optimal 2-compartment model for the target drug were estimated from three combinations of pharmacokinetic parameters (AUC and Vss, AUC and T1 / 2, AUC, Vss, T1 / 2 and Cmax) at a certain dose of the drug to be predicted, as well as prior information on existing drugs, and the prediction accuracy of the plasma concentration profile was compared with that of conventional methods using absolute average fold error (AAFE).

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[0045] Cpred and Cobs are the predicted and measured values, respectively. Table 5 shows the AAFE for four drugs. Compared to the conventional method using a one-compartment model, the prediction method of the present invention using AUC and T1 / 2 or Vss had higher prediction accuracy. In the case of continuous administration, prediction using all four parameters was most accurate. The prediction accuracy of the macro method and the micro method was similar. [Table 5] [Industrial Applicability]

[0046] This invention makes it possible to correlate plasma concentration trends with pharmacokinetic parameters, allowing them to be handled on a computer as compartment model parameters. In clinical practice, this is expected to play a major role in optimal patient administration and predicting drug-drug interactions. It is now possible to predict plasma concentration trends with higher accuracy from CL and Vss predicted from non-clinical trials compared to the conventional one-compartment model, which will be useful for efficient drug development. [Explanation of symbols]

[0047] 10 Data input section 20 2-compartment model calculation section 30 Plasma concentration calculation section

Claims

1. A method for predicting the plasma concentration profile of a compound after intravenous administration using a computer, comprising: providing two-compartment model parameters for the compound of interest; and calculating the plasma concentration profile of the target compound using a two-compartment model.

2. The method for providing model parameters according to claim 1, wherein optimal parameters of a two-compartment model are estimated from the pharmacokinetic parameters of a target drug after intravenous administration, the ranges of parameters of multiple drugs analyzed by the two-compartment model, and the error ranges of the pharmacokinetic parameters of the target compound. The parameter ranges here specify the possible ranges of parameters, such as the mean value and standard deviation of the parameters as prior information, the maximum value, the initial value, and values ​​estimated by regression analysis or machine learning.

3. A method for providing model parameters that estimates optimal parameters of a two-compartment model using Bayesian estimation based on the pharmacokinetic parameters of a target drug after intravenous administration, the ranges of parameters of multiple drugs analyzed using the two-compartment model, and the error ranges of the pharmacokinetic parameters of the target compound. The parameter ranges here specify the ranges that can be taken by parameters such as the mean and standard deviation of the parameters as prior information, the maximum value, the initial value, and values ​​estimated by regression analysis and machine learning.

4. A database of macro- and micro-parameters of a two-compartment model of a compound obtained by the method of claims 2-3.

5. A simulation device that executes the prediction method according to any one of claims 1 to 3.

6. A computer program for carrying out the prediction method according to any one of claims 1 to 3.

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