KR20110119409A - Combination analysis system for pharmacokinetic and pharmacodynamic modeling of drug - Google Patents

Abstract

PURPOSE: A combination analysis system for performing the pharmacodynamic modeling of drugs is provided to rapidly offer customized pharmacodynamic modeling to a user by changing drug delivery information according to drug delivery environment. CONSTITUTION: An input unit(110) receives drug delivery information and the metameter of blood drug content according to a time about a patient who receives drugs. A modeling unit(120) performs modeling through the metameter of the blood drug content. A control unit(130) determines optimized pharmacokinetic parameter which constitutes the modeling by applying the metameter of the blood drug content and drug delivery information to a model fitness algorithm.

Description

COMBINATION ANALYSIS SYSTEM FOR Pharmacokinetic AND Pharmacodynamic MODELING OF DRUG

The present invention relates to an integrated analytical system for pharmacokinetic-pharmacodynamic modeling of drugs, and more particularly to the pharmacokinetic-pharmacodynamics of drugs that determine optimized pharmacokinetic parameters that constitute pharmacokinetic-pharmacodynamic modeling of drugs injected into a patient. To provide a modeling method.

Pharmacokinetic is a field for studying the absorption, distribution, in vivo changes and excretion of drugs, and Pharmacodynamic is a field for studying the biological response of drugs in the body. In other words, pharmacokinetics model changes in blood concentrations with time after drug administration, and pharmacodynamics model changes in drug efficacy according to concentrations of effects.

After the drug enters the human body, it undergoes a process of absorption, distribution, metabolism, and excretion, which varies from person to person, especially depending on demographic and pathological characteristics such as age, sex, and race. The action of drugs differs from person to person because of the different pharmacokinetic mechanisms that humans exhibit for drugs, rather than the pharmacodynamic mechanisms that appear in humans.

The fields of pharmacokinetic and pharmacodynamic analysis have evolved significantly over the last few decades to understand the pharmacokinetics, distribution, and biological action of drugs at both quantitative and qualitative levels. PK / PD modeling helps drug developers and clinicians to more accurately determine the most effective and cost-effective use of drugs, and helps in planning for the creation of drugs with the desired characteristics. .

Acquiring statistical modeling as well as pharmacokinetic / pharmacodynamic modeling at the same time is not easy and has been one of the biggest challenges for software development in biology and medicine.

In characterizing the drug-body interactions, it is important to understand not only the differences between individuals but also the range of pharmacokinetic / pharmacodynamic profiles that can be expected from each group of individuals. Therefore, a program for pharmacokinetic / pharmacodynamic analysis must have adequate statistical capacity to account for measurement errors and be able to account for the distribution of measured pharmacodynamic / pharmacodynamic parameters among patients.

In addition, for pharmacokinetic / pharmacodynamic analysis, a complex numerical method that can explain irregular dosage methods is required, and a powerful and flexible analysis environment is needed to deal with it.

Accordingly, an object of the present invention is to provide a pharmacokinetic-pharmacodynamic modeling method of a drug for determining an optimized pharmacokinetic parameter constituting the pharmacokinetic-pharmacodynamic modeling of a drug injected into a patient.

According to an embodiment of the present invention, a pharmacokinetic-pharmacodynamic modeling method of a drug may include: receiving a measurement of blood drug concentration over time for each patient to which the drug is administered; Performing modeling through the measurement values, receiving the administration information of the administered drug, and applying the input measurement value of the blood drug concentration and the administration information of the drug to a model fit algorithm to configure the modeling. Determining the pharmacokinetic parameters.

The modeling represents a change in blood concentration over time, and may be expressed by the following equation.

Where C (t) is the blood concentration over time t, D is the dose, V is the distribution volume, Ka is the absorption rate constant, and K is the loss rate constant.

The administration information of the drug may include at least one of an absorption section of the drug, an administration method of the drug, a loss method of the drug, and an error handling method.

The model fit algorithm can obtain the conditional expected value of the log likelihood function for the pharmacokinetic parameters using Monte Carlo simulation.

The pharmacokinetic parameter may include at least one of the distribution volume (V), absorption rate constant (Ka), and disappearance rate constant (K).

An integrated analysis system for pharmacokinetic-pharmacodynamic modeling of a drug according to another embodiment of the present invention receives a measurement of blood drug concentration over time for each patient to which the drug is administered, and receives the administration information of the administered drug. Optimized pharmacokinetics constituting the modeling by applying an input unit, a modeling unit performing modeling through the measurement of the blood drug concentration, and the input measurement value of the blood drug concentration and the drug administration information to a model fit algorithm It includes a control unit for determining the parameters.

As described above, according to the present invention, the optimal value of the pharmacokinetic parameters expressed as a nonlinear function can be accurately obtained through the integrated analysis system for pharmacokinetic-pharmacodynamic modeling of the drug. In addition, modeling can be performed while changing the drug administration information according to the drug administration environment, and thus, pharmacokinetic-pharmacodynamic modeling can be obtained conveniently and quickly.

1 is a view for explaining an integrated analysis system for pharmacokinetic-pharmacodynamic modeling of a drug according to an embodiment of the present invention.
2 is a flowchart illustrating a method for pharmacokinetic-pharmacodynamic modeling of an integrated analysis system according to an exemplary embodiment of the present invention.
3A to 3C are exemplary views showing input analysis data.
4A is a diagram for explaining a one-part primary absorption model.
4B to 4D are exemplary views illustrating an analysis process of input analysis data.
5 is a basic screen for performing modeling according to an embodiment of the present invention.
6A to 6D are screens illustrating modeling output results generated using FIG. 5.
7A to 7D are screens for verifying a candidate model.
8A to 8C are diagrams illustrating screens showing covariates with respect to the disappearance rate constant K, the absorption rate constant Ka, and the distribution volume V, respectively.

DETAILED DESCRIPTION Hereinafter, exemplary embodiments of the present invention will be described in detail with reference to the accompanying drawings so that those skilled in the art may easily implement the present invention.

1 is a view for explaining an integrated analysis system for pharmacokinetic-pharmacodynamic modeling of a drug according to an embodiment of the present invention. The integrated analysis system 100 for pharmacokinetic-pharmacodynamic modeling of a drug according to FIG. 1 displays an input unit 110, a modeling unit 120, a controller 130, and a display unit 140.

The input unit 110 receives a measurement of blood drug concentration over time for each patient injected with the drug, and receives administration information of the injected drug. In addition, the modeling unit 120 performs modeling through the measurement of the input blood drug concentration.

The controller 130 determines the optimized pharmacokinetic parameters constituting the modeling by applying the input blood drug concentration and drug administration information to the model fit algorithm. The display unit 140 serves as an interface for receiving drug administration information or outputting a modeled result.

2 is a flowchart illustrating a method for pharmacokinetic-pharmacodynamic modeling of an integrated analysis system according to an exemplary embodiment of the present invention. As shown in Figure 2, the pharmacokinetic-pharmacodynamic modeling method of the integrated analysis system is a data input step (S210), exploratory data analysis step (S220), model fitting step (S230), model verification step (S240) and covariate analysis Step S250 is included.

First, in the data input step S210, the integrated analysis system 100 receives various analysis data.

3A to 3C are exemplary views showing input analysis data. 3A and 3B are data on administration information of a drug administered to a patient, and FIG. 3C is measurement data of blood concentration of a drug over time.

The input data according to FIG. 3A includes a dose (AMT), a rate of administration (RATE), an administration time (TIME), etc. of the drug administered to the patient ID. , AMT and RATE can be selected. In addition, the input data according to FIG. 3B represents a drug dose and time according to the subject, and the user may select Subject, Dose, and Time as shown in the right figure of FIG. 3B.

The drug administration information data according to FIGS. 3A and 3B record the drug dosage information according to each patient (ID, subject) .-- In case of persistent dwelling, the dosage (AMT) and the dosage rate (as shown in FIG. 3A) RATE), and in the case of oral administration or bolus, the dose and time are recorded as shown in FIG. 3b.

In addition, the location or name of each variable ("ID", "TIME", "Dose", etc.) can be specified by the user arbitrarily. When reading from the GUI, the name corresponding to ID and name corresponding to Dose can be specified. Is devised.

Blood concentration (dependent variable, DV) measurement data of the drug according to Figure 3c is a measurement data showing the blood concentration (conc.) Over time for the drug administered to the individual (Subject) having a certain weight (Wt). That is, according to FIG. 3c, the drug was administered to the first patient having a weight of 79.6 kg at different dose concentrations, and the drug was administered to the second patient having a weight of 72.4 kg at different dose concentrations over time. Indicates that one did. Similarly, the user can select ID, Wt, Time, and conc as shown in the right figure of FIG. 3C.

As such, in the data input step (S210), the integrated analysis system 100 may receive the administration information data of the drug and the blood concentration measurement data of the drug, thereby increasing the convenience of data input by having two different input structures. .

Then, in the exploratory data analysis step (S220), the user may analyze the data input in the data input step (S210) through the integrated analysis system.

Before explaining the data analysis step (S220), a structural model of pharmacokinetics will be described. When the structural model of pharmacokinetics is represented by the dosing method, it is assumed that the one-compartmental model is distributed evenly in all parts of the body immediately after the drug is administered. The two-compartmental model divides body tissue and body fluid into two compartments, the central compartment and another secondary compartment, which takes time to distribute the drug evenly across all parts of the body. Assume

4A is a diagram for explaining a one-part primary absorption model. According to Figure 4a shows that the drug (Dose) is absorbed by the body at the rate of Ka is lost at the rate of K. In the figure on the right, the vertical axis represents the blood concentration (conc), the horizontal axis represents the time (time), and the change in blood concentration over time in the one-segment primary absorption model can be expressed as a curve in the right figure of FIG. 4A. . If this is formulated, it can be expressed as Equation 1 below.

Equation 1 shows the change in blood concentration (C (t)) with time (t), and the given volume (D) and distribution volume (V), absorption rate constant (Ka) and loss rate constant ( Is represented by K). The distribution volume (V) is the apparent volume in which the drug is distributed, and the large distribution volume means that the dose of the drug must be large in order to reach an optimal concentration.

4B to 4D are exemplary views illustrating an analysis process of input analysis data.

In particular, FIG. 4B is a result plot showing analysis results of all patients (ID 1 to ID 12) on one screen, FIG. 4C is an analysis result plot of some patients (ID 4) among all patients, and FIG. 4D is a whole This is a result plot of the analysis results of patients (ID 1 to ID 12) displayed on each screen.

Therefore, according to the integrated analysis system 100 according to an exemplary embodiment of the present invention, the GUI is configured to enable not only a plot for searching the entire profile but also a profile search for each individual, and additionally, the number of individual If not many, it is possible to compare the individual profiles at the same time as shown in Figure 4d.

Next, in the model fitting step (S230), the integrated analysis system 100 performs pharmacokinetic-pharmacodynamic modeling of the drug using the analysis results obtained in the exploratory data analysis step (S220).

First, the structural model and the statistical model of group pharmacokinetics can be expressed as Equation 2 below.

Where y _i is the measurement vector for the i patient, D _i is the dose of the i patient, t _i is the measurement time vector, x _i is the covariate, θ _i is the individual pharmacokinetic parameter, and θ is the group pharmacokinetic parameter Indicates. In particular, θ can be expressed as a function of distribution volume (V), absorption rate constant (Ka) and disappearance rate constant (K).

Then, the pharmacokinetic parameters θ, Ω and σ ² are obtained to maximize the parameter functions L (θ, Ω, σ ² ) as shown in Equation 3 below. Where Ω is a parameter representing the difference between the individual patients, and σ ² is a parameter representing the difference within the individual.

Here, in the nonlinear mixed effect model, the likelihood function is not only a complex nonlinear form for the parameters but also includes an integral for the random effects, so it is not easy to obtain the maximum likelihood estimate. Most pharmacokinetic / pharmacodynamic model estimation software uses a linear approximation of likelihood functions such as FO / FOCE / Laplacian, but this has the disadvantage that the estimate can be inconsistent, especially when the number of subjects is small. . In order to solve this problem, the integrated analysis system 100 according to an exemplary embodiment of the present invention uses a model fitting algorithm, which is a modified EM algorithm, to obtain an estimate using an accurate likelihood function.

The classical EM algorithm estimates the maximum likelihood by repeating the expectation (E) step of obtaining the conditional expected value of the log likelihood function for a random effect given a parameter and the maximization (M) step of finding the parameter that maximizes the obtained conditional expected value. Integral methods were used to find conditional expected values in step E. In this case, in the nonlinear mixed effect model, the conditional expected value of the log likelihood function is not expressed in a closed form, and thus, a modification of step E is required.

According to an embodiment of the present invention, the expected value of step E is calculated by using monte carlo simulation.

That is, according to the model fit algorithm according to an embodiment of the present invention, first i posterior distribution with respect to the second person _{p (Φ i | y i,} Ω (k), σ 2 (k)) for Φ _i m dog (Φ from _{i, 1} ,..., Φ _{i, m} ) is sampled and updated θ, Ω, σ ² calculated by the following equation (4).

And, if the same process as in Equation 4 is repeated, the kth may be represented as Equation 5 below.

As described above, according to the model fitting algorithm, the maximum likelihood estimation value at which the equation 3 becomes the maximum at the k th iteration can be obtained, and the pharmacokinetic parameters θ, Ω, and σ ² can be obtained.

Hereinafter, a process of performing pharmacokinetic-pharmacodynamic modeling of the drug through the integrated analysis system 100 will be described with reference to FIGS. 5 to 6D. FIG. 5 is a basic screen for performing modeling according to an embodiment of the present invention, and FIGS. 6A to 6D are screens showing modeling output results generated using FIG. 5.

First, in the basic screen as shown in FIG. 5, the user selects the corresponding items from the items of Compartment, Administration, Elimination, and Error. That is, the user selects a compartment representing a stage in which the drug is injected and reacts to the human body based on the experimental result, and the administration method of the drug is IV bolus, IV infusion, First order absorption after oral administration, or zero order absorption after oral administration.

In addition, the user selects the linear or Michaelis Menten method to model the amount of drug disappearance, and the error is processed by selecting one of the constant error model, proportional error model, combined error model, combined error model with power. The user also inputs the number of simulations and the number of samples through the lower right of the basic screen.

As such, when the user inputs the modeling method to the experimental result, the integrated analysis system 100 models the equation 1 and the model fitting algorithm and outputs the parameter estimation result as shown in FIGS. 6A to 6D.

FIG. 6A shows the results of parameter estimates (THETA (θ), SIGMA (σ), OMEGA (Ω)) calculated by the integrated analysis system 100 when the One comp / First Order absorption / linear elimination / constant error method is selected. . In addition, FIG. 6B illustrates a parameter estimation result calculated through the integrated analysis system 100 when the proportional error method is selected instead of the constant error method when compared with FIG. 6A.

In addition, FIG. 6C illustrates a parameter estimation result calculated through the integrated analysis system 100 when the two comp / first order absorption / linear elimination / constant error method is selected, and FIG. 6D shows a constant error method in comparison with FIG. 6C. If the proportional error method is selected, the parameter estimation result calculated by the integrated analysis system 100 is shown.

As described above, in the model fitting step S230, various candidate modelings may be generated according to a user's selection, and the user may obtain an optimized model by verifying the candidate model through the model verification step S240.

7A to 7D are screens for verifying a candidate model. In particular, FIG. 7A shows the results of the blood concentration (DV) measured through the experiment and the blood concentration (PRED) of the estimated patient population, and FIG. 7B shows the blood concentration (DV) measured through the experiment and the blood of the specific patient estimated. The result of concentration (PRED) is shown.

In FIG. 7A, the horizontal axis represents the blood concentration (conc) of the patient population measured as a result of the experiment, and the vertical axis represents the blood concentration (y.pop) of the patient population estimated through candidate modeling. The closer it is, the better the model. Here, the candidate model may be verified using the entire experimental data of the patient population, or the candidate model may be verified by extracting an average value or a specific value of the experimental data.

Likewise, in FIG. 7B, the horizontal axis represents the blood concentration (conc) of the specific patient measured as a result of the experiment, and the vertical axis represents the blood concentration (y.ind) of the specific patient estimated through candidate modeling.

FIG. 7C shows the measured blood concentration (DV) of the patient and the estimated residual concentration (RES) value. The graph on the left shows the residual (RES) value of the patient population, and the graph on the right shows the residual of the specific patient. (WRES) value. As shown in FIG. 7C, the more the residual value converges to 0, the better the model is.

7D is a graph illustrating a change in a residual RES value over time. In addition, FIG. 7E is a graph showing the change in blood concentration (DV) measured with time for the patient population (assuming 12 persons in the embodiment of the present invention), and FIG. 7F is an individual patient ( ID 3 "as an example) is a graph showing the change in the measurement of blood concentration (Conc) with time. FIG. 7G is a graph illustrating a comparison of measured changes of blood concentration Conc with time of all patients ID 1 to ID 12.

The user may modify the model by modifying the drug administration information when the estimated blood concentration obtained through the modeling is greater than the measured value and the difference value of the blood drug concentration.

Finally, in the covariate analysis step S250, the integrated analysis system 100 provides a GUI for searching for a valid covariate in the model. 8A to 8C are diagrams illustrating screens showing covariates with respect to the disappearance rate constant K, the absorption rate constant Ka, and the distribution volume V, respectively. Therefore, the user can know the individual differences of the pharmacokinetic parameters through the covariate graphs shown in FIGS. 8A to 8C.

As described above, according to the exemplary embodiment of the present invention, an optimal analysis of pharmacokinetic parameters expressed as a nonlinear function can be accurately obtained through an integrated analysis system for pharmacokinetic-pharmacodynamic modeling of a drug. In addition, modeling can be performed while changing the drug administration information according to the drug administration environment, and thus, pharmacokinetic-pharmacodynamic modeling can be obtained conveniently and quickly.

Embodiments of the invention include a computer readable recording medium containing program instructions for performing various computer-implemented operations. The recording medium records a program for executing the method of performing pharmacokinetic-pharmacodynamic modeling of the drug described so far. The media may include, alone or in combination with the program instructions, data files, data structures, and the like. Examples of such media include magnetic media such as hard disks, floppy disks and magnetic tape, optical recording media such as CDs and DVDs, floppy disks and program commands such as magnetic-optical media, ROM, RAM, flash memory, and the like. Hardware devices configured to store and perform such operations. Alternatively, the medium may be a transmission medium such as an optical or metal wire, a waveguide, or the like including a carrier wave for transmitting a signal specifying a program command, a data structure, and the like. Examples of program instructions include not only machine code generated by a compiler, but also high-level language code that can be executed by a computer using an interpreter or the like.

While the present invention has been described with reference to exemplary embodiments, it is to be understood that the invention is not limited to the disclosed exemplary embodiments, but, on the contrary, is intended to cover various modifications and equivalent arrangements included within the spirit and scope of the appended claims. Therefore, the true technical protection scope of the present invention will be defined by the technical spirit of the appended claims.

100: integrated analysis system, 110: input unit,
120: modeling unit, 130: control unit,
140: display unit

Claims (10)

Receiving a measurement of blood drug concentration over time for each patient administered the drug,
Performing modeling through the measurement of the blood drug concentration,
Receiving the administration information of the administered drug, and
Determining the optimized pharmacokinetic parameters constituting the modeling by applying the input measurement of the drug concentration in the blood and the administration information of the drug to a model fit algorithm. The method of claim 1,
The modeling represents a change in blood concentration over time, and the pharmacokinetic-pharmacodynamic modeling method of a drug represented by the following equation:

Where C (t) is the blood concentration over time t, D is the dose, V is the distribution volume, Ka is the absorption rate constant, and K is the loss rate constant. The method of claim 2,
Administration information of the drug,
A pharmacokinetic-pharmacodynamic modeling method of a drug comprising at least one of an absorption compartment of the drug, a mode of administration of the drug, a mode of loss of the drug, and an error handling mode. The method of claim 2,
The model fit algorithm is a pharmacokinetic-pharmacodynamic modeling method of a drug that obtains conditional expected values of log likelihood functions for pharmacokinetic parameters using Monte Carlo simulation. The method of claim 4, wherein
The pharmacokinetic parameter is a pharmacokinetic-pharmacodynamic modeling method of a drug comprising at least one of the distribution volume (V), absorption rate constant (Ka) and loss rate constant (K). An input unit for receiving a measurement of blood drug concentration over time for each patient to which the drug is administered, and inputting administration information of the drug to be administered;
A modeling unit performing modeling through the measurement of the blood drug concentration, and
An integrated analysis system for pharmacokinetic-pharmacodynamic modeling of a drug comprising a control unit for determining the optimized pharmacokinetic parameters constituting the modeling by applying the input measurement value of the blood drug concentration and the drug administration information to a model fit algorithm. . The method of claim 6,
The modeling represents a change in blood concentration over time, and an integrated analysis system for pharmacokinetic-pharmacodynamic modeling of a drug represented by the following equation:

Where C (t) is the blood concentration over time t, D is the dose, V is the distribution volume, Ka is the absorption rate constant, and K is the loss rate constant. The method of claim 7, wherein
Administration information of the drug,
An integrated analysis system for pharmacokinetic-pharmacodynamic modeling of a drug comprising at least one of an absorption compartment of the drug, a mode of administration of the drug, a mode of loss of the drug, and an error handling mode. The method of claim 8,
The model fit algorithm is an integrated analysis system for pharmacokinetic-pharmacodynamic modeling of drugs that obtains conditional expected values of log-likelihood functions for pharmacokinetic parameters using Monte Carlo simulations. A computer-readable recording medium having recorded thereon a program for executing the method of claim 1 on a computer.

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