RU2576614C1 - Method for searching fractional effect point in determining effective doses of substances by single-point dilution method - Google Patents

Abstract

FIELD: medicine.

SUBSTANCE: determining an alternative dose-response range with the tenfold dose difference requires re-injecting substance solutions into the same animal until a permissible injection limit is exhausted; that is followed by narrowing the alternative dose-response range by successive double reduction through preparing solutions for injections by mixing equal amounts of solutions from extreme points of the alternative dose-response range until the doses falling in extreme points of the range are at least twice different; a reference dose in the produced alternative dose-response range is defined as an average, and the calculated dose is injected into an additional group of four animals. The information referred to six animals received the reference dose are combined in one point; an effect rate is presented as a percentage and converted into probability units - probits according to standard tables; an effective dose for the declared fractional effect is determined by using a known inclination function of a toxicity line, by formula

, wherein D_T is a dose of interest of the test substance having the pre-set effect rate; D_S is a dose of the standard substance; S is the inclination function of the toxicity line for the standard substance; Y_T is a probit corresponding to the preset fractional effect for the test substance; Y_S is a probit corresponding to the fractional effect for the standard substance.

EFFECT: cost-effective toxicological experiment, reduced errors when diluting the substance solutions injected into the animals, higher objectivity ensured by reducing the errors of effective dose determination.

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Description

The invention relates to the study or analysis of materials, namely medical preparations, by special methods. Specifically, the invention relates to toxicometry and can be used to determine doses of substances with an arbitrarily specified frequency of development of the effect.

The “single point” method is used to determine the toxicometric characteristics of a standard substance. In particular, this approach takes place when checking the effectiveness of different batches of the same substance with a reliably known function of the slope of the toxicity line S. When using this method, the following tasks are solved: a) finding a point with a fractional effect; b) to determine the doses of substances with an arbitrarily given frequency of the development of the effect.

Usually the test fractional point, which determines the effective dose with a given fractional toxic effect, is “felt” by sequentially administering to the animal doses of a substance with an n-fold change in its relative amount [Sanotsky I.V. Methods for determination of toxicity and hazard of chemicals (toxicometry) [text] / I.V. Sanotsky, I.P. Ulanova, L.A. Tiunov et al .; under the general. ed. I.V. Sanotsky; USSR Academy of Medical Sciences. - M .: Medicine, - 1970. - 346 p.].

The tactics of a toxicological experiment in the closest of the analogues of the proposed method are described in [Speransky C.V. The tactics of the experiment in determining LD ₅₀ [text] // Gig. and dignity. - No. 1. - 1986. - S. 66-67]. It is proposed to conduct four stages of testing. Stage I - finding a wide (8-fold) fork with the introduction of hypothetical doses (G): 1/8 G, 1 G, 8 G. Stage II - finding a narrow (double) fork with the introduction of: 16 G, 32 G, 1 / 16 G and 1/32 G. III stage - testing of 6 animals at the nearest doses with the development of the effect and without it. Stage IV - depending on the latitude of the zone of toxic effects, a full-fledged experiment is conducted with a different step between doses of 5 animals per point. With this tactic, some doses are retested, which reduces the cost-effectiveness of the experiment; The scheme for preparing the required dilutions of solutions of substances is not optimal, since it requires a preliminary detailed calculation of each dilution and high accuracy when measuring the required quantities of initial solutions.

An algorithm for determining the doses of substances with an arbitrarily specified frequency of the development of the effect from one experimentally determined point is described in [Van der Waerden BL Mathematical statistics [text]: [per. with him.] / B.L. Van der Warden - M.: Ed. in. lit. - 1960. - 435 p.]. The essence of the method consists in plotting an experimentally determined fractional point on a graph with an existing toxicity line, drawing an additional line parallel to the existing line through the resulting point, and graphically determining the effective dose (Fig. 1).

The disadvantages of the presented graphical method are its subjectivity and the need to use a graph. At present, graphical methods are rarely used, dose calculation by the single-point method is carried out mathematically - in accordance with the development of Gaddum (Gaddum), Bliss (Chester I. Bliss), Finney (Finney D.J.) and other authors [Belenky M.L. Elements of a quantitative assessment of the pharmacological effect [text] / M.L. Belenky. - 2nd ed. - L .: State publishing house of medical literature, 1963. - 152 p .; Finney D.J. Statistical method in biological assay [text] / D.J. Finney - 3-rd edit. - London: Charles Griffin & Company LTD. - 1978. - 508 p .; Litchfield J.T., Wilcoxon F.A. The simplified method of evaluating dose-effect experiments [text] // J.T. Litchfield, F.A. Wilcoxon. J. Pharmacol. Exp.Ther., 1949. - No. 2. - P. 99-113]. The approach to determining the average effective dose of substances is described in [Prozorovsky VB, Frumin GT An analytical version of the express "method of one point" to determine the average effective doses [text] // Exp. and wedge. farm. - 1992. - No. 6. - S. 61-63], which shows the application of the "method" for calculating the average effective doses of substances. The equation proposed by the authors for calculating

where Y ₂ and D ₂ - respectively broken down and the dose for the evaluated substance.

Equation (1) is consistent with equation

derived from the basic equation of probit analysis

where D _Y is the dose corresponding to some fractional effect;

Y - probit corresponding to the fractional effect on the dose of D _Y ;

b is the tangent of the angle between the toxic line and the abscissa axis;

and - the distance from zero to the point of intersection of the toxicity line with the ordinate axis.

To use equation (2), a preliminary calculation of the coefficients a and b is necessary.

To calculate the coefficient a , the equation is used:

To calculate the coefficient b, we use the equation

where S is the slope function of the toxicity line for a standard substance obtained earlier on substances of the same class or taken from published data.

The disadvantages of applying the described approach are multi-stage calculations and a decrease in accuracy due to the accumulation of errors in the calculation of each individual element.

The objective of the present invention is to develop the most economical strategy for finding a "test" point with a fractional effect and a convenient scheme for breeding solutions of substances introduced into animals; choosing the most universal algorithm for determining effective doses with a given fractional effect.

The solution of this problem involves a technical result, which consists in the most economical toxicological experiment (it is expected to reduce the number of animals used and reduce the amount of substance needed for research); reduction of errors in dilutions of solutions of substances administered to animals; increasing objectivity by reducing errors in determining effective doses.

The problem is solved in that in the method of finding a point with a fractional effect and determining effective doses of substances by the “single point” method, first, according to the proposed technical solution, when determining the dose interval with an alternative response (IDAO) with a ten-fold difference in doses, re-introduction of solutions of substances to one and the same animal until the limit of the admissible volume of administration has been exhausted; then the IDAO is narrowed by successive two-fold reduction by preparing solutions for administration by mixing the same amounts of solutions from the edges of IDAO until the dose difference at the edges of the interval is less than half; determine the reference dose on the obtained dose range with an alternative response as the average value and enter the calculated dose to an additional group of four animals; combine data on six animals at one point; calculate the frequency of the effect as a percentage and translate it according to standard tables into probability units — broken; determine the effective dose for a given fractional effect using the well-known function of the slope of the toxic line, according to the formula

where D _T is the desired dose of the test substance with a given frequency of effect;

D _S is the dose of the standard substance;

S is the slope of the toxic line for a standard substance;

Y _T - probit corresponding to a given fractional effect for the test substance;

Y _S - probit corresponding to the fractional effect for a standard substance.

The invention is illustrated by drawings, presented in figures 1 and 2.

At the first stage of research on the development of the method, the substantiation of the algorithm for experimental determination of the point with fractional toxic effect was carried out.

In order to save biological material, they initially search for a dose range with an alternative response with a tenfold difference in dose at the edges of the interval using one or two animals. The introduction of substances into the body of an animal begins with a minimum dose that obviously does not cause a given effect (10 or 100 times less than the dose of a standard substance). The next dose is administered to the same animal in an amount 9 times the original dose (so that the total dose is 10 times higher than the previous one). The limitation for the use of only one animal in a rough search for an effective dose is the maximum allowable volume of the introduction of solutions, which is twice the recommended [Karkishchenko N.N. Guide to laboratory animals and alternative models in biomedical technologies [text] / Ed. N.N. Karkishchenko and S.V. Gracheva. Moscow. - 2010. - 344 p.]). When the limit of the admissible volume of administration is exhausted, they transfer to the second animal, to which the dose is administered ten times the total dose for the first animal. The following administration is carried out in the same way as in the first animal, so that the total dose administered is ten times greater than the previous one. Thus, using only two animals, the interval with a thousand-fold difference in doses is overlapped (in the absence of animal deficiency, all doses can be evaluated with a single administration, but this will reduce the cost-effectiveness of the method).

After several “zero” points, a point with the expected effect is obtained and the dose interval with an alternative response (IDAO) of the first approximation is indicated - with no effect at one edge of the interval and with an effect at the other edge - with a tenfold dose difference.

Then, IDAO is narrowed by successive two-fold reduction to a factor of less than two times the difference in alternative doses (overlapping distributions of adjacent doses is observed when they are less than two times different [Popova EB. Planning studies and analysis of the dose-effect relationships of toxic and drug substances [text]: the dissertation of the doctor of medical sciences: 03/14/04, 03/14/06: protected in 2010 / Popova Elena Borisovna - S-Pb., 2010. - 254 s], therefore, two points differing in doses less than two times, theoretically can be combined into one). At this stage, repeated administration of substances to the same animal is excluded. In this case, the dosage schedule is similar to that shown in FIG. 2.

The first dilution is prepared from a working solution, on which the target effect has developed, and a working solution, on which the target effect has not developed - the nearest doses on the scale and which are the boundaries of IDAO. The solutions are mixed in a volume ratio of 1: 1, obtaining a solution with an intermediate ("median") concentration of the substance. The introduction of the substance is based on the standard ratio of the amount of solution to the mass of the animal, ml / kg This is the case with all subsequent contractions of newly formed IDAOs - solutions are always mixed based on an equal volume ratio and animals are given the same amount of solution in relative units (it is unacceptable to change the amount of dose administered by changing the relative volume of administration using this method).

Regardless of the outcome of each administration of a substance to individual animals (absence or presence of an effect), a rapid narrowing of the boundaries of IDAO occurs. When narrowing IDAO from ten to two times the difference in alternative doses spend from 2 to 5 animals. The scheme of double reduction of the interval is consistent with the binary system of counting; therefore, it is the most economical scheme of conducting a toxicological experiment. This scheme has one more positive aspect - all dilutions are prepared by mixing two identical volumes, which reduces the probability of dilution error ¹ ( ¹ For proper organization of work and elimination of errors, it is recommended to use a separate tripod for dilutions, on which the tubes should be arranged in accordance with the location of the doses on the scale: test tubes with working solutions of “zero effect” alternately put on the left, test tubes with working solutions of the “target effect” on the right side).

The administered dose for animals (mg / kg) is determined standardly: by multiplying the concentration of the solution of the substance (mg / ml) by the relative volume of administration (ml / kg).

Next, the average dose, which is administered in a group of four animals, is determined by the boundaries of the minimized IDAO (with less than two dose differences at the interval boundaries). By combining the effects located at the edges and inside the minimized IDAO, an experimental point of six animals is obtained, in which - for any distribution of effects in a group of four animals - the total effect is from 16 to 84% (i.e., the fractional effect is generally accepted the recommended range of penetration from 4 to 6).

The next stage of research to develop the proposed method is devoted to the selection of the most universal algorithm for determining fractional effective doses.

It is proposed to use a simplified algorithm in which there is no need to calculate the coefficients a and b (since the coefficients a and b are calculated using D _Y and S, when calculating doses with fractional toxicological effects, we can limit ourselves to only the indicated values) [I. Mokshanov Optimization of the method for calculating edge doses of toxicants [text]. M., 2011 - 10 s. Dep. at TsVNI of the Ministry of Defense of Russia. Inv. No. B 7263, SRDR, ser. B, no. 94].

Let us consider in detail the algorithm for determining the doses corresponding to fractional toxic effects using the effective dose of the standard substance D _S and the slope of the toxic line S ² ( ² In accordance with paragraph 2.2.1 of the Rules for the Compilation, Filing and Consideration of an Application for a Patent for an Invention ", The presented algorithm for calculating fractional effective doses is not an invention and do not claim legal protection. At the same time, this algorithm is part of the proposed method).

в уравнении (2) преобразовано путем подстановки вместо b правой части уравнения (5)Expression

in equation (2) is transformed by substituting instead of b the right-hand side of equation (5)

By replacing the coefficient a on the right side of equation (4), the expression

where Y _S - probit for the initial dose D _{S of the} substance of the standard;

Y _i - arbitrarily set probit, reflecting the frequency of the effect on the desired dose of the estimated substance.

вставлена результирующая часть уравнения (8) и уравнение (2) приведено к виду, в котором отсутствуют коэффициенты а и bFurther in equation (2) instead of degree

the resulting part of equation (8) is inserted and equation (2) is reduced to a form in which there are no coefficients a and b

Further, taking into account that log a + log b = log ( a b) and 10 ^log x = x, equation (9) is simplified and reduced to a logically complete form (6)

Equation (6) can be used to calculate doses with any frequency of effects for doses of a standard substance with any frequency of effects. As a special case, this approach allows the calculation of doses with fractional effects according to published data, in which the doses are presented as ED ₅₀ together with the slope of the toxicity line S. Given that average effective doses have a probit of 5, the calculation of the main doses with fractional effects is reduced to particular equations:

An example of the method

(³В частности, определение такой дозы необходимо при расчете индексов безопасности. Например, индекс безопасности Брокка - Шнайдера (Brokk - Shneyder) является отношением DL₁₀/DI₉₀ [Беленький М.Л. Элементы количественной оценки фармакологического эффекта [текст] / М.Л. Беленький. - 2-е изд. - Л.: Государственное издательство медицинской литературы, 1963. - 152 с.]; индекс гарантированной защиты (ИГЗ) является отношением DL_10опыт/DL_{99контроль} [Прозоровский В.Б. Индекс гарантированной защиты - новый показатель эффективности антидотов [текст] // В.Б. Прозоровский. - Токсикологический вестник. - 1999. - №4. - С. 10-13].). При этом известно, что доза вещеста-стандарта составляет 20 мг/кг, а функция наклона S вещества-стандарта равна 1,59.Suppose there is a need to determine the dose of a substance $$E{D}_{10}^3$$

( ³ In particular, the determination of such a dose is necessary when calculating safety indices. For example, the Brokk-Shneyder safety index is the ratio DL ₁₀ / DI ₉₀ [Belenky ML Elements for quantifying the pharmacological effect [text] / M. L. Belenky. - 2nd ed. - L.: State Publishing House of Medical Literature, 1963. - 152 p.]; The index of guaranteed protection (ILI) is the ratio DL _10experience / DL _99control [Prozorovsky VB Index of guaranteed protection - a new indicator of the effectiveness of antidotes [text] // VB Prozorovsky. - T ksikologichesky Gazette -. 1999. - №4 -. pp 10-13]).. It is known that the dose of the substance standard is 20 mg / kg, and the slope function S of the standard substance is 1.59.

The first administered (minimum) dose is 0.2 mg / kg (one hundredth of the dose of the standard substance). The next dose, administered to the same animal, is increased 9 times - so that the total dose exceeds the previous 10 times - it is 1.8 mg / kg (total dose will be: 0.2 + 1.8 = 2.0 mg / kg) . The expected effect in the first animal does not develop, the limit of the allowable volume of the introduction of solutions of the substance to the animal is exhausted. To continue the study, a new animal is taken. Suppose, with the introduction of a dose of 20.0 mg / kg to the second animal, the expected effect develops. Thus, the boundaries of the dose interval with an alternative response are determined with a tenfold difference in doses: lower (without effect) - 2.0 mg / kg, upper (with effect) - 20.0 mg / kg.

Next, the dose range is narrowed with an alternative response by successive twofold reduction - to a factor of less than two dose differences. First, the middle of the alternative response interval is determined for doses of 2 and 20 mg / kg: (2 + 20) / 2 = 11 mg / kg. With the introduction of this dose, a negative response is obtained. Further narrowing of the interval with an alternative response is not required, since its boundaries differ in size by less than half (20.0 / 11.0≈1.82).

The reference dose for administration in a group of four animals is defined as the average value of the boundaries of the last dose interval with an alternative response: (20.0 + 11.0) / 2≈15.5 mg / kg (with the indicated proximity of the combined doses, the arithmetic average is slightly different from the geometric mean, generally calculated to take into account the lognormal distribution of the toxicological characteristics of substances).

If in a group of four animals they get a 100% effect, at the combined point the total effect will be 5/6 or 83%. To transfer interest to probit use table 1, taken from [Derelanko M.J. The toxicologist′s pocket handbook [text] / M.J. Derelanko - 2-nd edit. - New York: CRC Press. - 2008. - 394 p.], Or similar presented.

Table 1 Percent to Probit Transfer Interest 0 one 2 3 four 5 6 7 8 9 0 - 2.67 2.95 3.12 3.25 3.36 3.45 3.52 3,59 3.66 10 3.72 3.77 3.82 3.87 3.92 3.96 4.01 4.05 4.08 4.12 twenty 4.16 4.19 4.23 4.26 4.29 4.33 4.36 4.39 4.42 4.45 thirty 4.48 4,50 4,53 4,56 4,59 4.61 4.64 4.67 4.69 4.72 40 4.75 4.77 4.80 4.82 4.85 4.87 4.90 4,912 4.95 4.97 fifty 5.00 5.03 5.05 5.08 5.10 5.13 5.15 5.18 5.20 5.23 60 5.25 5.28 5.31 5.33 5.36 5.39 5.41 5.44 5.47 5.50 70 5.52 5.55 5.58 5.61 5.64 5.67 5.71 5.74 5.77 5.81 80 5.85 5.88 5.92 5.95 5.99 6.04 6.08 6.13 6.18 6.23 90 6.28 6.34 6.41 6.48 6.55 6.64 6.75 6.88 7.05 7.33

The frequency of the effect of 83% corresponds to probit 5.95.

In accordance with the task, given the value, S = 1.59, ED _{10 is} calculated by the formula (6)

ED ₁₀ = ED ₈₃ · S ^(3.72-5.95) = 15.5 · 1.59 ^{(3.72 · 5.95)} = 5.5 mg / kg.

The advantages of the method:

- the method allows you to flexibly conduct a toxicological experiment and minimize the number of animals and the amount of the evaluated substance. Saving animals is more than 50%;

- when narrowing the dose range with an alternative response, working solutions are prepared by mixing two identical volumes, which reduces the likelihood of dilution errors;

- the proposed method is convenient and provides reliability corresponding to the level of express methods. It is universal, since it allows you to determine the dose of the test substance with any fractional effects according to the doses of the standard substance with any fractional effects.

Claims (1)

A way to search for a point with a fractional effect in determining effective doses of substances using the "single point" method, implemented by experimentally determining the test fractional point when animals are injected with an animal with an n-fold change in sequentially administered doses, followed by calculating the dose with a given fractional effect according to the function of the slope of the toxic line, characterized in that when determining the dose range with an alternative response with a ten-fold difference in doses, repeated administration of solutions of substances to the same animal is used until exhaustion of the limit of the admissible volume of administration; then narrow the dose range with an alternative response by successive two-fold reduction by preparing solutions for introducing by mixing the same amounts of solutions from the edges of the dose range with the alternative response to less than two times the dose difference at the edges of the interval; determine the reference dose on the obtained dose range with an alternative response as the average value and enter the calculated dose to an additional group of four animals; combine data on six animals at a reference dose at one point; calculate the frequency of the effect as a percentage and translate it according to standard tables into probability units — broken; determine the effective dose for a given fractional effect using the well-known function of the slope of the toxic line, according to the formula

,
where D _T is the desired dose of the test substance with a given frequency of effect;
D _S is the dose of the standard substance;
S is the slope of the toxic line for a standard substance;
Y _T - probit corresponding to a given fractional effect for the test substance;
Y _S - probit corresponding to the fractional effect for a standard substance.

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