JPH0769328B2 - Metabolism analysis method - Google Patents

Description

Detailed Description of the Invention

[0001]

FIELD OF THE INVENTION The present invention relates to a method for analyzing the kinetics of drugs, substrates, etc.
The present invention relates to a kinetic analysis method for drugs, substrates, etc., which can obtain quantitative information on the metabolic capacity and the metabolic rate as well as the size of the metabolic pool that is the rate-determining step of the metabolic pathway.

[0002]

2. Description of the Related Art Drugs, toxins, or substrates labeled with a suitable radioisotope such as carbon, hydrogen, sulfur, or phosphorus are administered to animals by intravenous injection, intraperitoneal injection, oral administration, etc. By measuring the change in radioactivity concentration over time,
Metabolism in animals can be analyzed. Alternatively,
Metabolism in the body is analyzed by administering a drug labeled with an appropriate stable (non-radioactive) isotope, such as nitrogen, to animals by intravenous injection, etc., and measuring the time-dependent change in labeled concentration in blood. can do.

When a radiolabeled substance is intravenously injected, the time-dependent change in the radioactivity concentration in the blood is often the true number of the time after administration on the horizontal axis of the graph, and the logarithm of the blood radioactivity concentration on the vertical axis. When plotted on an axis, it was analyzed by utilizing the fact that it is approximately represented by a straight line or a curve containing two or more straight line portions.

In the former case, that is, when the temporal change in the radioactivity concentration in the blood is approximated to a straight line on a semilogarithmic graph, the temporal change in the radioactivity concentration in the blood Cp is Cp = Co exp (-λt). (T is the time after administration, Co and λ are constants), and it is estimated that there is no metabolic pool involved in the metabolism of the labeled substance. On the other hand, in the latter case, that is, when the graph consists of two or more straight lines, the blood radioactivity concentration Cp
The change over time of Cp ＝ C ₁ exp (-λ ₁ t) ＋ C ₂ exp (-λ ₂ t) ＋ C ₃ exp (-λ ₃ t) ＋ ・ ・ ・ (1) (C ₁ , C ₂ , C ₃ ; λ ₁ , λ ₂ , λ ₃ etc. are constants), and the existence of some metabolic pool is estimated.

From the corresponding combination of Cp, t values, C ₁ ,
Calculation programs for obtaining optimum values of parameters such as C ₂ and C ₃ and λ ₁ , λ ₂ and λ ₃ are also commercially available.

However, on the graph, a region where t is sufficiently small (for C ₁ , λ ₁ ) and a region where t is sufficiently large (C ₂ ,
λ ₂ etc.) to C ₁ , C ₂ , C ₃ etc. and λ ₁ , λ ₂ , λ ₃
If the constant (parameter) is sufficiently greater than ,, lambda ₁ being asked accurately has lambda _2, etc. etc., or lambda ₂
Is limited to the case where is sufficiently larger than λ ₃ etc. If the difference between λ ₁ and λ ₂ etc. is relatively small, the proportion occupied by the straight line part will be small and the accuracy of C ₁ , C ₂ and λ ₂ etc. obtained from the graph will be poor, and the measured data of the obtained graph The conformity with is extremely poor. In such a case, the accuracy of calculation by an arithmetic program that calculates each parameter without using a graph becomes extremely poor.

Even when the accuracy of parameters such as C ₁ and C ₂ and λ ₁ and λ ₂ is relatively good, the values of those parameters are used as the pool volume and blood flow velocity in the estimated metabolic model. It was difficult to connect directly.

The conventional method (1) (the sum of simple exponential functions) is applied when the blood concentration Cp is constantly decreased, and the slope of the decrease is midway. When the value increases with (in this case, an inflection point appears), especially the density
It was difficult to apply Cp when it showed a marked maximum with time.

[0009]

Therefore, it is possible to accurately express the temporal change of the concentration in body fluid such as blood by a function of a relatively simple form, and to estimate the metabolic model and There is an urgent need for a method for analyzing the kinetics of drugs, toxins, substrates, etc., which enables at least semi-quantitative estimation of the size of the metabolic pool of E. coli. Even if the time-dependent change in concentration Cp shows a complicated profile, such as the decrease gradient increases in the middle or shows a remarkable maximum, the time-dependent change in concentration can be accurately expressed with a relatively simple function. Therefore, a method for analyzing the in vivo kinetics of drugs and the like has been earnestly desired.

The object of the present invention is, firstly, to obtain a function of the time-dependent change in the concentration of a drug or the like and a metabolite thereof in a body fluid such as blood in a relatively simple form even if the profile is complicated. It is to realize a dynamic analysis method for drugs and the like that can be accurately expressed by.

Secondly, the object of the present invention is to estimate the in vivo metabolism model of a drug or the like, and at least semi-quantitatively estimate the size of the metabolic pool therein, the pharmacokinetics of the drug or the like. It is to realize the analysis method.

[0012]

In the present invention, in order to achieve the above-mentioned object, the time change of the concentration Cp in a body fluid after administration of a labeled substance such as a drug administered to an organism is treated as a function Y = A. exp (-k ₁ t) + B {1−exp (-k ₁ t)} {1−exp (-k ₂ t ')} exp (-k ₃ t) (2) Time after administration, A, B, k ₁ , k ₂ ,
k ₃ represents a constant, t 'is equal to t-d, d is 0 or a positive real number, when t is not greater than d t' is 0). When d is 0, the equation (2) is Y = A exp (-k ₁ t) + B {1−exp (-k ₁ t)} {1−exp (-k ₂ t)} exp (-k ₃ t) (2a), which can also be written as (where b
= B / A). Y ＝ A [exp (-k ₁ t) ＋ b {1−exp (-k ₁ t)} {1−exp (-k ₂ t)} exp (-k ₃ t)] (3)

The time t after administration is plotted on the horizontal axis (logarithm) of the semilogarithmic graph, and the blood labeled substance concentration Cp is plotted on the vertical axis (logarithm). For the time being, each point is connected to form a line graph and the line is drawn. Draw a curve that smooths and passes near each point on the graph. The tangent slope of the steepest part of this curve near t = 0 is tentative k ₁ , and the ordinate Y at the intersection of the tangent extension and the ordinate is the tentative A value. Let the tangent slope of the portion where the tangent slope of the curve is small in the region of large t be the temporary value of k ₃ . Next, to determine the approximate value of k ₂ , suppose k ₃ = k ₂ , k ₃ = 2k ₂ , k ₃ = 3k ₂ , k ₃ = 4k ₂ , 2k ₃ = k ₂ , 3k ₃ =
Let k ₂ , 4k ₃ = k _2, etc. In each case, the L = {1-exp (-k 2 t)} exp a (-k ₃ t) is maximum t _m (t present measured value for Cp in the vicinity
t _m ), {Cp−A exp (-k ₁ t _m )} / {1−exp (-k ₁ t _m )} {1−exp (-k
₂ t _m )} exp (-k ₃ t _m ) ＝ {Cp−A exp (-k ₁ t _m )} / {1−exp (-k
_{The value of 1} t _m )} L (t _m ) is calculated (Cp means the measured value, and the temporary values calculated from the above graph are used as A, k ₁ , and k ₃ ). Using it as a temporary approximation to B, Y ＝ A exp (-k ₁ t) + B {1−exp (-k ₁ t)} {1−exp (-k ₂ t)} ex
Find the value of k ₂ (relative relationship with k ₃ ) such that the value of p (-k ₃ t) gives the closest value to the measured value of Cp. This k ₂ and the previously obtained A
, K ₁ , k ₃ , and B using the temporary values Y = A exp (-k ₁ t) + B {1−exp (-k ₁ t)} {1−exp (-k ₂ t)} ex
Let p (-k ₃ t) be the function of the first approximation that represents the temporal change in the concentration Cp of the labeled substance in blood.

When the provisional value of B is obtained, if the value of k ₁ is relatively large, {1−exp (−k ₁ t _m )} can be approximated to 1, and the expression B = {Cp−A You may use exp (-k ₁ t _m )} / {1-exp (-k ₂ t _m )} exp (-k ₃ t _m ).

In the above calculation, b = B / A
It is easier to obtain b by rewriting (2a) as follows. Y ＝ A [exp (-k ₁ t) ＋ b {1−exp (-k ₁ t)} {1−exp (-k ₂ t)} exp (-k ₃ t)] (3) b is 1 It never grows.

In order to simplify the calculation when setting the temporary value of k ₂ and obtaining the approximate value of B or b, the following relation can be used. When k ₂ = mk ₃ (m is a positive real number), the maximum t of L ＝ {1−exp (-k ₂ t)} exp (-k ₃ t) is obtained.
(T _m ) is t _m = {ln (m + 1)} / mk ₃ and the above obtained at t _m = {ln (m + 1)} / mk ₃
The maximum value of L is {1-1 / (m + 1)} / {(m + 1) / m} = m ² / (m + 1) ² (for example, when k ₂ = k _{3 t m = ln2 / k 3 =} 0.
It is 69 / k ₃ , and the maximum of L is 1/2 ² = 1/4 at this time.
When a _{k 2 = 2k 3, t m} = ln3 / (2k 3) = a 0.55 / k _3, the maximum value of L is 2 ^{2/3 2} = 4/9 or about 0.44 (m> 1 In some cases, the maximum value of L is always larger than the maximum value 1/4 when m = 1 (k ₂ = k ₃ ).

When there is a relation of k ₃ = nk ₂ , L = {1−exp
(-k ₂ t)} exp (-k ₃ t) is the maximum tm is t _m = {ln (n + 1) −ln (n)} / k ₂ = {ln (n + 1) −ln ( n)} / (k ₃ / n)
= N {ln (n + 1) −ln (n)} / k ₃ and the value of L (maximum value) obtained at t _m is [1− {n
/ (N + 1)}] {n / (n + 1)} ⁿ = {1 / (n + 1)} {1-1 / (n + 1)} ⁿ . For example, if k ₃ = 2k ₂ , t _m = 2 {ln (3) −ln
(2)} / k ₃ = 0.814 / k ₃ , and the maximum value of L is (1/3) (2/3) ² or about 0.15. If k ₃ = 4 k ₂ , then t _m = 4 {ln (5)
−ln (4)} / k ₃ = 0.89 / k ₃ , the maximum value of L is (1/5) (4/5) ⁴ or about 0.08 (when n> 1, the maximum value of L is
It is always smaller than 1/4 of the maximum value when n = 1 (k ₂ = k ₃ ).

By using such a relationship, the optimum value of k ₂ can be easily found. For example, assuming that k ₂ = k ₃ , first, at t _m = 0.69 / k ₃ where L is a maximum, {Cp / A −exp (-k ₁ t _m )} / [{1−exp (-k ₁ t _m )} / 4] ＝ 4 {Cp / A−
Since exp (-0.69k ₁ / k ₃ )} / {1−exp (-0.69k ₁ / k ₃ )} is given as a provisional value of b, the previously defined A,
using measured values of k _1, temporary value of k ₃ and Cp of t _m, t function (3) at various t other than _m i.e. _{Y = AY 0 = A [exp} (-k 1 t) + b {1−exp (-k ₁ t)} {1−exp (-k ₂
t)} exp (-k ₃ t)] (Y ₀ = exp (-k ₁ t) ＋ b {1−exp (-k ₁ t)} {1−exp (-k ₂ t)} e
Calculate the value of xp (-k ₃ t) = Y / A). The value is compared with the measured value of Cp. Next, assuming that k ₂ = 2k ₃ , t _m = 0.55 /
At k ₃ , {Cp / A− exp (-k ₁ t _m )} / {1−exp (-k ₁ t _m )} = 9/4 {Cp / A−ex
Since p (-0.55k ₁ / k ₃ )} / {1−exp (-0.55k ₁ / k ₃ )} is the tentative value of b, similar to the above, for various t, the function (3) of Obtain the value and compare it to the measured value of Cp. From this comparison, when k ₂ = 2k ₃ , the function (3)
It is determined whether the difference between the value of Cp and the measured value of Cp decreases compared with the case of k ₂ = k ₃ . k ₂ = Write in the case of the k ₂ = 2k ₃ than in the case of k ₃ is the difference between the measured value of the value and Cp of the function (3) | Y -Cp
If | tends to decrease over the entire region of t, then m
= K ₂ / k ₃ is further increased to 3 or 4 or sequentially, and | Y-Cp | is minimized m = k ₂ / k ₃
Find the value of.

When k ₂ = 2k _3, it is considered that if the difference | Y −Cp | from the measured value increases when k ₂ = k ₃ , then k ₂ must be smaller than k _3. , K ₃ = nk ₂ (n =
2,3,4 etc.) and find the optimal n by the same procedure as above. For example, assuming that k ₃ = 2k ₂ , t _{m at} which L becomes a maximum
= 0.814 / k ₃ {Cp / A−exp (-0.814k ₁ / k ₃ )} / 0.15 {1−exp (-0.814k ₁ /
k ₃ )} is given as a temporary value of b. Using this, various t
Calculate the value (Y) of the function (3) with and compare it with the measured value of Cp. If the difference between the calculated value Y and the measured value Cp is smaller than when n = 1 (k ₂ = k ₃ ), try increasing n further to 3 or 4, or sequentially, and obtain | Y − Cp | The smallest
Find the value of n. Since it takes a lot of time and effort to start m or n from 1 and make them larger,
If a maximum or an inflection point is found on the semi-logarithmic graph created earlier, m or n can be easily obtained by the following method. When a maximum or inflection point is found on the semilog graph, t _{m at} which L is a maximum is in the vicinity of
When the time t of the maximum or inflection point is t _m , the above-mentioned relation t _m = {ln (m + 1)} / mk ₃ or t _m = n {ln (n + 1) −ln (n)}
It is possible to easily find m or n corresponding to the optimum k ₂ by using / k ₃ . That is, if a table of values of {ln (m + 1)} / m as shown below is created for _m , {ln (m + 1)} / which is almost equal to the product k ₃ t _m It is possible to determine m from the value of m. [Table 01] m ln (m + 1) / m 2 ln3 / 2 = 0.55 3 ln4 / 3 = 0.46 4 ln5 / 4 = 0.40 5 ln6 / 5 = 0.36 6 ln7 / 6 = 0.32 10 ln11 / 10 = 0.24415 ln16 / 15 = 0.185 For example, if the product of k ₃ and t _m obtained from the graph is 0.4,
Since ln5 / 4 = 0.40, 4 is selected as m, and k ₂ is 4k ₃ . For n, n {ln (n + 1) −ln (n)}
If you make a table of the values of, from that value that matches the product k ₃ t _m
n = k ₃ / k ₂ is required. [Table 02] nn {ln (n + 1) -ln (n)} 2 2 {ln3-ln2} = 0.81 3 3 {ln4-ln3} = 0.86 5 5 {ln6-ln5} = 0.91 1010 {ln11- ln10} = 0.95 15 15 {ln16−ln15} = 0.97

The difference between the value of the function (3) and the measured value of Cp (for example, expressed as the sum of standard deviations) is calculated with respect to the value of b obtained by using the value of m or n thus obtained. Then, the values of b and k ₂ and, if necessary, the values of A, k ₁ , and k ₃ are modified little by little to determine the optimum function (2a) or (3). The method of determining A, b, k ₁ , k ₂ , k ₃ described above is summarized as follows. 1) Time after administration on semi-logarithmic graph
Plot t on the horizontal axis (antilogarithm) and the blood concentration Cp of labeled substances on the vertical axis (logarithm), and connect the points to form a line graph. 2) Smooth the polygonal line and draw a curve that passes near each point on the graph. 3) The tangent slope of the steepest part of this curve near t = 0 is tentative k ₁ , and the value of the vertical axis Y at the intersection of the extension of this tangent and the vertical axis is the temporary A value. To do. 4) The tangent slope of the part where the tangent slope of the curve becomes small in the region where t is large is taken as the provisional value of k ₃ . 5) When a maximum or inflection point is found on the semilog graph, the time t at that point is defined as t _m (L is a maximum), and the following relation t _m = {ln (m + 1)} / Mk ₃ or t _m = n {ln (n + 1) −ln (n)}
Using / k ₃ , m or n that satisfies these relationships is calculated from the product k ₃ t _{m of} the tentative value of k ₃ and t _m obtained earlier. 6) Obtain k ₂ from m and k ₃ by the equation k ₂ = mk ₃ or from n and k ₃ by the equation k ₃ = nk ₂ . 7) Measured values of this k ₂ and Cp and previously obtained
A, k _1, using the value of the temporary k _3, t = t _m as {Cp / A-exp (-k 1 t)} / {1-exp (-k 1 t)} {1-exp (- k ₂ t)} exp
(-k ₃ t) ＝ {Cp / A−exp (-k ₁ t)} / {1−exp (-k ₁ t)} Find the value of L and use it as a temporary approximation of b (k _{When 1} is relatively large, b = {Cp / A−exp (-k ₁ t)} / L. 8) This b and the previously obtained A, k ₁ , k ₂ ,
using the value of the temporary _{k 3 Y = AY 0 = A} [exp (-k 1 t) + b {1-exp (-k 1 t)} {1-exp (-k 2
Let t)} exp (-k ₃ t)] be a function of the first approximation that represents the change over time in the concentration Cp of the labeled substance in blood. 9) If there is no maximum or inflection point on the semilog graph, k ₃ = k ₂ , k ₃ = 2k ₂ , k ₃ = 3k ₂ , k ₃
＝ 4k ₂ , 2k ₃ ＝ k ₂ , 3k ₃ ＝ k ₂ , 4k ₃ ＝ k _2, etc. In each case, L ＝ {1−exp (-k ₂ t)} exp (-k ₃ t) is At the maximum t _m (the maximum of t _m and L is m = k ₂
/ k ₃ or n ＝ k ₃ / k ₂ can be easily obtained by a simple relational expression) {Cp−A exp (-k ₁ t _m )} / {1−exp (-k ₁ t _m )} L ( The value of t _m ) is calculated (Cp is the measured value, and A, k ₁ , and k ₃ are temporary values calculated from the graph). Let it be a temporary approximation of B, Y ＝ A exp (-k ₁ t) + B {1−exp (-k ₁ t)} {1−exp (-k ₂ t)} ex
Find the value of k ₂ (relation m or n with k ₃ ) that gives the value of p (-k ₃ t) closest to the measured value of Cp. Using this k ₂ and the tentative values of A, k ₁ , k ₃ , and B previously obtained, Y ＝ A exp (-k ₁ t) ＋ B {1−exp (-k ₁ t)} {1−exp (-k ₂ t)} ex
Let p (-k ₃ t) be the function of the first approximation that represents the temporal change in the concentration Cp of the labeled substance in blood. 10) The value of b or B and k ₂ , and if necessary
The values of A, k ₁ and k ₃ are modified little by little to determine the optimum function (2a) or (3).

In the increasing region of the function Y, if the value of │Y-Cp│ does not become sufficiently small even if the value of k ₂ is modified, instead of t, when t is larger than the positive constant d, t -D
The accuracy of the approximation of the function can be improved by using a variable t'which is equal to and which is 0 when t is not greater than d and choosing a suitable value for d.

The above calculation can be easily performed by using an electronic calculator. The electronic computer, for example, has significant digits 1 to 9.999 for A, decimal digits 0.01 to 1000,
Significant digits 1 to 9.9 or 9. for b, k ₁ , k ₂ , k ₃ .
If the numerical signals up to 99 and the decimal digits from 0.001 to 10 can be sequentially and selectively output to the arithmetic unit, the purpose of obtaining a function suitable for the measured value of Cp can be achieved.

The metabolic analysis method of the present invention can be applied to various administration methods such as intravenous injection, intraperitoneal injection, and oral administration, but is particularly useful when administered by intravenous injection. When the radiolabel is administered by intravenous injection and the time change of the radioactivity concentration in blood is measured, the function used in the present invention agrees very well with the measured value of the time change of the radioactivity concentration in blood. . The same applies when a compound labeled with a stable isotope is used instead of the radiolabel. It is also effective when tracing at least a part of the compound itself and its metabolites by using a microanalysis method (liquid chromatography, gas chromatography, etc.) without using a labeled substance.

The metabolic analysis method of the present invention is extremely useful in clarifying its pharmacokinetics in the development of new drugs.

[0025]

EXAMPLES The following examples are given to further illustrate the present invention. [Example 1] 0.05 cc of a solution containing 2.3 μmol of inulin labeled at the methoxy position with 34 Cq / mmol of ¹⁴ C was injected into the portal vein of a Wistar male rat weighing 220 g for 15 seconds, 75 seconds, 3 seconds.
Minutes, 5 minutes, 10 minutes, 20 minutes, 30 minutes, 40 minutes, 50 minutes, and 60 minutes later, about 100 microliters of blood was collected from the hepatic vein, plasma was obtained by a conventional method, and its radioactivity was counted by liquid scintillation counting. It was measured by the method. The measurement results are shown in Table 1.

[0026]

A graph was prepared by plotting the true number of the time t after administration on the horizontal axis and the logarithm of the relative radioactivity intensity Cp on the vertical axis,
A straight line passing through the nearest point corresponding to t = 15 seconds, 75 seconds, and 3 minutes was drawn, and the slope and the intercept of the vertical axis (t = 0) were obtained.
The slope was -0.6 and the intercept was 1530. Further, when the gradient of the straight line passing through the nearest points of t = 20, 30, 40, 50, 60 minutes was calculated on the above graph, it was -0.05.

Then, suppose that 1530 is used as A and 0.6 is used as k _1.
Is selected as k ₃ , 0.05, and then the value of k ₂ is determined. In order to select m in k ₂ = mk ₃ , first estimate t _m that gives the maximum value of L (L = {1−exp (-k ₂ t)} e
xp (-k ₃ t)). When k ₃ = 0.05, t _m is between m and
Have the relationship shown in.

[0029]

20, 10 and 2 are selected as m corresponding to the values 3.04, 4.80 and 11.0 of t _{m which} are close to 3 minutes, 5 minutes and 10 minutes where the measured values are, and the value of L at t _m is set to these values. I calculated. Table 3 shows the calculation process of the value of L. L has the relationship of L = {1−exp (-mk ₃ t _m )} exp (-k ₃ t _m ) between m, k ₃ and t _m , but 1−exp (-mk ₃ t _m ) = 1-exp {-ln (m + 1)} = 1-1 / (m + 1) holds, so L is L = {1-1 / (m + 1)} exp (-k ₃ t _m ). Therefore, for m = 20, 10, 2
The values are shown in the right column of.

Table 3 m 1 / (m + 1) 1-1 / (m + 1) k ₃ t _m exp (-k ₃ t _m ) L 20 0.0476 0.952 0.152 0.854 0.818 10 0.0909 0.909 0.240 0.787 0.715 2 0.333 0.667 0.549 0.578 0.386

On the other hand, Cp / A -exp (-k for t _m triplicate
The value of ₁ t _m ) was calculated using the measured value of Cp. The calculation process and results are shown in Table 4.

Table 4 mt _m exp (-k ₁ t _m ) t Cp / A Cp / A −exp (-k ₁ t _m ) 20 3.04 0.142 3 0.258 0.116 10 4.80 0.050 5 0.182 0.132 2 11.0 0.0025 10 0.101 0.0985

For m = 20, 10, 2, the ratio {Cp / A-exp
The value of (-k ₁ t _m )} / L is m = 20 t = 3 0.116 / 0.818 = 0.141 m = 10 t = 5 0.132 / 0.715 = 0.185 m = 2 t = 10 0.0985 / 0.386 = 0.255 It was The value of this ratio can be used as a temporary value for b.

Therefore, as the values of k ₂ and b, _{three combinations} of k ₂ = 20k ₃ = 1.0 b = 0.14 k ₂ = 10k ₃ = 0.5 b = 0.18 k ₂ = 2k ₃ = 0.1 b = 0.25 are selected. , Y was calculated (as described above, A was 1530, k ₁ was 0.6, and k ₃ was 0.0.
5 were used respectively). As a result, it was the combination of k ₂ = 10k ₃ = 0.5 b = 0.18 that had the smallest difference from the actually measured value. However, this combination gives Y that is about 10% larger than the measured value of Cp at t ≥ 20, so if the value of b is reduced to 0.16, the error between the value of Y and the measured value of Cp at t ≥ 20 becomes extremely small. Moreover, the error at t <20 was sufficiently small.

After all, a function that approximately represents the temporal change of Cp
As Y Y = 1530 [exp (-0.6t) ＋0.16 {1−exp (-0.6t)} {1−exp (-
0.5t)} exp (-0.05t)] was obtained. Table 5 compares the Y value and the measured Cp value at each measurement time. Further, it is shown as a graph in FIG. In FIG. 1, the abscissa represents the true number of the time t 1 after administration, and the ordinate represents the logarithm of the relative radioactivity intensity Cp.

[0037]

The excretion rate of inulin the initial concentration of the labeled inulin value 1530 in plasma of A, the value 0.6 of k ₁ is the rate of migration to the tissues such as the liver of the inulin, the value 0.05 of k ₃ is urine It is considered that k ₂ represents the resupply rate of inulin from tissues such as liver to blood, and b represents the magnitude of its contribution.

[Embodiment 2] The above calculation may be performed by using a personal computer, and the calculation can be performed in a short time without any trouble. In advance on the personal computer
Significant digits 1 to 9.999 for A in function (3) above
Up to 10 decimal digits from 0.1 to 1000, b, k ₁ , k ₂ , k ₃ significant digits from 1 to 9.99 and decimal digits from 0.001 to 10 can be selectively output to the arithmetic unit. Keep it. The same result as above can be obtained by inputting the measurement result of radioactivity into a personal computer and performing calculation according to a preset program.

[Third Embodiment] In the first embodiment, exp (-k ₂ t _m ) is negligible as compared with 1 when t is 20 minutes or more. Hence t
The average value of the ratios of Cp / A and (exp-k ₃ t) was calculated for the measured Cp values for ≧ 20, and 0.16 was set as the temporary value of b. Similar to the first embodiment, the value of L is calculated for m = 20, 10, 2, and {C
The ratio of p / A-exp (-k ₁ t _m )} / L is m = 20 t = 3 0.116 / 0.818 = 0.141 m = 10 t = 5 0.132 / 0.715 = 0.185. Although there is no measurement point between 3 minutes and 5 minutes, it is estimated by interpolation that m = 16 is optimal, so if k ₂ is 0.8,
Table 6 shows the relationship between the Y value and the measured Cp value for each measurement time up to 10 minutes.

[0041]

From this result, the function y at 15 and 75 seconds
Value increases the error of + to Cp Found, as k ₂
0.8 was too large, and rather 0.6 was judged appropriate.

Example 4 Sprague Dawley rats were administered 20 mg / kg body weight of inaperisone (muscle relaxant) from the portal vein, serum was obtained from the collected venous blood, and separated by gas chromatography and mass spectrometry. The concentrations were as shown in Table 7.

[0044]

When a function approximating the concentration Cp of inaperisone was determined according to the present invention, the following function was obtained. Y = 4.7 [exp (-0.115t) +0.6 {1−exp (-0.115t)} {1−exp
(-0.02t)} exp (-0.028t)] The relationship between the Y value and the measured Cp value is shown in Table 8.

[0046]

The function Y = 5.0 [exp (-0.115t) +0.6 {1−exp (-0.115t)} {1−exp
(-0.018t ')} exp (-0.028t)] t' = t−5, the value of Y becomes as shown in Table 9, 30 minutes or
The accuracy of the 45-minute region approximation is improved.

[0048]

[0049]

EFFECTS OF THE INVENTION According to the method for analyzing the kinetics of drugs, toxic substances, substrates, etc. of the present invention, the temporal change in the concentration of the labeled substance in the body fluid such as blood can be accurately expressed with a relatively simple function. be able to. In particular, a change having a complicated profile, such as showing a maximum or an inflection point, is difficult to be expressed by the conventional compartment model, but according to the present invention, a comparison is performed without performing a complicated calculation such as convolution. Can be expressed accurately with a simple function.

Further, according to the present invention, the size of the metabolic pool in the in vivo estimated metabolic model of drugs, poisons, substrates, etc. can be estimated at least semi-quantitatively. Not only that, but the relative relationship between the size of the metabolic pool and the body fluid flow rate or tissue uptake rate can be estimated,
If there is information about one, it can be estimated about the other.

[Brief description of drawings]

FIG. 1 is a graph showing a function showing a temporal change in radioactivity intensity and an actually measured value.

Claims (10)

[Claims] 1. Administering a drug, toxin or substrate to an animal,
In a method of analyzing the metabolism in an animal body by measuring the time-dependent change in the concentration of an administered substance and its metabolites or any of them in blood or other blood, the time of the concentration Cp in the body fluid Change Y = A exp (-k ₁ t) ＋ B {1−exp (-k ₁ t)} {1−exp (-k ₂ t)} ex
p (-k ₃ t) or Y ＝ A [exp (-k ₁ t) ＋ b {1−exp (-k ₁ t)} {1
−exp (-k ₂ t)} exp (-k ₃ t)] (t is the time after administration, A, B, b, k ₁ , k ₂ , k ₃ are constants) Metabolic analysis method. 2. The drug, toxin or substrate is labeled with a radioisotope or a stable isotope, and the metabolism in the animal body is analyzed by measuring the time change of the concentration of the labeled substance in the body fluid. The method for metabolic analysis according to claim 1, which comprises: 3. The metabolic analysis method according to claim 2, wherein the drug, toxin or substrate is labeled with a radioisotope. 4. The metabolic analysis method according to claim 1, wherein the drug, toxin or substrate is administered to an animal by intravenous injection. 5. The metabolic analysis method according to claim 1, wherein the body fluid is blood. 6. The true number of the time t after administration is plotted on the abscissa of the graph, and the logarithm of the measured value Cp of the concentration of the specific substance and its metabolite or one of the metabolites in the body fluid is plotted on the ordinate. , Approximate value of k ₁ is obtained from the gradient of the tangent line at or near t = 0 of the curve on this graph, and approximate value of A is obtained from the intercept of the vertical axis, and t is larger than the area where the approximate value of k ₁ is obtained. In the area,
From the tangent slope where the slope of the curve is approximately constant
obtains an approximate value of k _3, if _{k 3 = mk 2 (m =} 1,2,3,4, ····) or nk ₃ = k ₂ (n =
1,2,3,4, ...)), for k ₂ corresponding to at least one of m or n, {1−exp (-k ₂ t)} exp (-k ₃ t) is Find the maximum t, or the t that is close to the measured value
t _m, and at t _m {Cp−A exp (-k ₁ t _m )} / {1−exp (-k ₁ t _m )} {1−exp (-k
₂ t _m )} exp (-k ₃ t _m ), and use it as the temporary value of B, or {Cp / A −exp (-k ₁ t _m )} / {1−exp (-k ₁ t _m )} {1−exp (-k ₂
t _m )} exp (-k ₃ t _m ), and the temporary value of b is obtained, and the temporary value of B or b, the approximate value of A, the approximate value of k ₁ , and k ₃ The function Y ＝ A exp (-k ₁ t) + B {1−exp (-k ₁ t)} {1−exp (-k ₂ t)} ex
p (-k ₃ t) or Y ＝ A [exp (-k ₁ t) ＋ b {1−exp (-k ₁ t)} {1−
exp (-k ₂ t)} exp (-k ₃ t)] chooses k ₂ so that the value of exp gives the closest value to Cp, and modifies the value of B or b as necessary to make the total of t The difference between Y and Cp is reduced over the region, and the approximate value of A, k ₁ and k ₃ , the value of B or b, and the value of k ₂ , or the difference between them is reduced to Y and Cp. Function Y = A exp (-k ₁ t) + B {1−exp (-k ₁ t)} {1−exp (-k ₂ t)} ex
p (-k ₃ t) or Y ＝ A [exp (-k ₁ t) ＋ b {1−exp (-k ₁ t)} {1−
exp (-k ₂ t)} exp (-k ₃ t)] is a function representing the temporal change of the concentration Cp in the body fluid,
The metabolic analysis method according to claim 1. 7. The time change of the concentration Cp is expressed by a function Y = A [exp (-k ₁ t) + b {1−exp (-k ₁ t)} {1−exp (-k ₂ t)} ex
The method of metabolic analysis according to claim 6, which is approximately represented by p (−k ₃ t)]. 8. The time change of the concentration Cp is approximately represented by the function Y, the true number of the time t after administration is on the horizontal axis of the graph, and the logarithm of the measured value Cp of the concentration is on the vertical axis. plotted on the approximation of k ₁ from the slope of a tangent on the curve of the t = 0 or near on the graph, determine the approximate value of a from the intercept, t is sufficiently than the area of obtaining the approximate values of k ₁ In a large region, the approximate value of k ₃ is obtained from the tangent slope of the part where the slope of the curve is approximately constant, and exp (-k ₁ t) is compared to 1 and selected from the region that can be ignored.
For t {Cp−A exp (-k ₁ t)} / exp (-k ₃ t) or Cp / exp (-k ₃ t
t) to obtain a temporary value for B, or {Cp / A−exp (-k ₁ t)} / exp (-k ₃ t) or Cp / A exp
Calculate the value of (-k ₃ t) and use it as a temporary value of b, and temporarily assume that k ₂ = mk ₃ (m = 1,2,3, ...) Or k ₃ = nk ₂
When (n = 1,2,3, ...), for k ₂ corresponding to at least one of m or n, {1−exp (-k ₂ t)} exp (-k ₃ t) At or near t, at which the measured value Cp of the concentration gives a maximum or an inflection point, k ₂ is tentatively selected, and the temporary value of B or b, the approximate value of A, the k _Using the approximate value of _1, the approximate value of k ₃ , and the temporary value of k ₂ , the function Y = A exp (-k ₁ t) + B {1−exp (-k ₁ t)} {1−exp (-k ₂ t)} ex
p (-k ₃ t) or Y ＝ A [exp (-k ₁ t) ＋ b {1−exp (-k ₁ t)} {1−
exp (-k ₂ t)} exp (-k ₃ t)], modify k ₂ so that the value of Y gives the value closest to Cp, and change the value of B or b as needed. Modify so that the difference between Y and Cp is small over the whole area of t, and the value of k ₂ , the approximate value of A, k ₁ , k _{3 and} the value of B or b, or those 6. The function Y 1 is defined as a function representing the temporal change of the concentration Cp in the body fluid by using a value corrected so that the difference between Cp and Cp becomes small.
The metabolic analysis method according to any one of 1. 9. The time change of the concentration Cp is approximately represented by the function Y, the true number of the time t after administration is on the horizontal axis of the graph, and the logarithm of the measured value Cp of the concentration is on the vertical axis. , And the approximate value of k ₁ is calculated from the tangent slope of the curve on this graph at or near t = 0, and the approximate value of A is calculated from the intercept, and t is larger than the area where the approximate value of k ₁ is calculated. In the area,
From the tangent slope where the slope of the curve is approximately constant
obtains an approximate value of k _3, if _{k 3 = mk 2 (m =} 1,2,3,4, ····) or _{nk 3 = k 2 (n =} 1,2,3,4, ···・), The t that gives the maximum of {1−exp (-k ₂ t)} exp (-k ₃ t) for k ₂ corresponding to at least one of m or n is the measured value of the concentration. Temporarily select k ₂ so as to correspond to the maximum of Cp or the inflection point or its vicinity, and for the temporary k ₂ , {1−exp (-k ₂ t)} exp (-k ₃ t) is the maximum. And t close to that having a measured value is defined as t _m, and at t _m , {Cp−A exp (-k ₁ t _m )} / {1−exp (-k ₂ t _m )} exp (-k ₃ t _m ), and use it as a temporary value for B, or {Cp / A −exp (-k ₁ t _m )} / {1−exp (-k ₂ t _m )} exp (-k ₃ t _m ) to obtain a temporary value of b, and using the approximate value of A, the approximate value of k ₁ , the approximate value of k ₃ , and the temporary value of B or b, the function Y = A exp (-k ₁ t) + B {1−exp (-k ₁ t)} {1−exp (-k ₂ t)} ex
p (-k ₃ t) or Y ＝ A [exp (-k ₁ t) ＋ b {1−exp (-k ₁ t)} {1−
exp (-k ₂ t)} exp (-k ₃ t)], modify k ₂ so that the value of Y gives the value closest to Cp, and change the value of B or b as needed. Modify so that the difference between y and Cp is small over the entire region of t, and the value of k ₂ , the approximation of A, k ₁ , k _{3 and} the value of B or b, or their 6. The value Y modified so that the difference between Cp and Cp becomes small is used as the function Y, which is a function representing the temporal change of the concentration Cp of the labeled substance in the blood. Metabolic analysis method. 10. The metabolism in an animal body is analyzed by administering a specific substance to an animal and measuring the time-dependent change in the concentration of the substance and its metabolite or any one of them in body fluid such as blood. In the method, the time change of the concentration Cp in the body fluid is calculated by a function Y = A exp (-k ₁ t) + B {1−exp (-k ₁ t)} {1−exp (-k ₂ t ') } e
xp (-k ₃ t) or Y ＝ A [exp (-k ₁ t) ＋ b {1−exp (-k ₁ t)} {1−exp (-k ₂ t ')} e
xp (-k ₃ t)] (t is the time after administration, A, B, B, k ₁ , k ₂ , k ₃ are constants, t ′ is equal to t−d, and d is 0 or positive. A metabolic analysis method, which represents a real number, but t'is approximately 0 when t is not greater than d).