Experimental determination of LD50
The lethal dose (LD50) is an indication of the level of toxicity of drugs, poisons and pathogenic microorganisms. It represents the dose or concentration that kills half of all subjects. Because of the individual variability of organisms, the LD50 needs to be measured with a considerable number of subjects, and the LD50 value of each drug is different for different subjects.
Operation method
Kou's method
Materials and Instruments
White rat Move 1. Preparatory experiments For more product details, please visit Aladdin Scientific website.
Trichlorfon, picric acid
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(1) Finding out the upper and lower limits: i.e., use a small number of animals to gradually find out the minimum dose (Dm) that causes the death of all animals and the maximum dose (Dn) that does not cause the death of even one animal. The method is to set an estimated amount according to experience or literature and observe the death of 2-3 animals. If all animals die, the dose is lowered; if none die, the dose is increased and mapped until a dose is found for which Pm = 100% and Pn = 0%, which are the upper and lower limits, respectively.
(ii) Determine the number of groups, group spacing and dose of each group.
Number of groups: generally 5-8 groups, according to the appropriate group spacing to determine the number of groups, such as the first 5 groups, if the group spacing is too large, you can increase the number of groups to reduce the group spacing. Sometimes the number of groups can be increased or decreased according to the death of animals.
Group distance: refers to the difference between the logarithm of the dose of two adjacent groups, commonly used "d". d should not be too large, because too large can make the standard error increase; should not be too small, because too small will increase the number of groups, the overlap of the mortality rate between the groups resulting in a waste of experimental animals. The size of group spacing mainly depends on the sensitivity of experimental animals to the test factors. If the sensitivity is large, the mortality rate increases (or decreases) with the increase (or decrease) of the dose, the group spacing can be smaller; on the contrary, if the sensitivity is small, the mortality rate changes with the dose is small, then the group spacing should be larger. The distance between the upper and lower limits can be used as an indication of sensitivity. Large distances indicate small sensitivities; small distances indicate large sensitivities. The general requirement is that d should be less than 0.155, mostly between 0.08 and 0.1.
Determine the group distance: Convert the upper and lower dose limits into logarithmic values, set the logarithmic value of the upper limit dose as X k, the logarithmic value of the lower limit dose as X1, and the number of groups as g. Then:
Determine the dose for each group: add X1 by d (or X k by d) to obtain the logarithm of the dose for each group, and then check the logarithm of the number of doses for each group: this gives the dose for each group (in an isoperimetric progression).
(iii) Prepare an isotonic solution and equalize the volume administered to each animal (e.g., 0.5 ml/20 g).
2. Formal experiment
① Selection and grouping of experimental animals Selection principle: Animals can be selected according to different experiments, and animals that are sensitive to the test factors should be selected. The animals should be sensitive to the factors being tested.
LD50 is usually measured by mice. Principle of grouping: The number of animals in each group must be more than the number of groups. If the number of animals in each group is less than the number of groups, the difference in mortality rate of each group cannot be fully reflected. (For example, if there are 8 groups of 10 animals each, the number of deaths in the high-dose group will be 6, 9, and 10, respectively, but if only 6 animals are used in each group, the number of deaths in the high-dose group will probably be 6.) For this experiment, we will divide the animals into 7 groups of 10 mice each.
Grouping Methods: See Appendix, Subject Grouping Methods. First, the animals were separated by sex or mixed half and half, then grouped by body weight, and then randomly grouped so that the average body weight of each group was equal. In this experiment, we directly divided the animals into groups according to body weight and then randomly grouped them.
② Administering drugs, observing the number of deaths, and calculating the mortality rate Route of administration: It can be determined according to the different drugs and animals, and mice are mostly injected intraperitoneally or by gavage; intravenous injection is also possible. In this experiment, we adopt the method of intraperitoneal injection.
Sequence of administration: It is preferable to adopt the method of jumping groups at intervals. For example, if there are 7 groups in total, the drug should be given in the order of groups 2, 4 and 6 first, and then in the order of groups 7, 5, 3 and 1 in the reverse direction. This can avoid the bias error caused by the drug left for too long or animal starvation. Also, when Group 3 is administered, if all animals in Group 2 are dead, Group 1 and Solution 1 can be omitted. If Group 7 is dead, Group 8 can be added to create a group with 0% mortality. The volume of drug to be administered to each animal can be determined according to individual body weight or average body weight. In our experiment, all groups of animals were administered at the same time.
Observation time: Until the animals no longer die due to the effects of the drug. During the observation period, we should pay attention to ensure the living conditions such as food, water, temperature, etc., to prevent the death of non-subject factors, and generally need to observe for one week. In our experiment, the observation time is one hour.
Finally, fill in the following table (4-4) with the deaths and various data.
3. Calculation formula
In order to understand the principles of LD50 determination, it is first necessary to understand the relationship between dose and response. The toxicity of a test factor to an animal is also a response, and its magnitude is often expressed in terms of the amount of lethality it causes. A small lethal dose is indicative of a high toxicity and vice versa. Based on the relationship between dose and response, a dose-response curve (QEC) can be plotted. Figure (4-16) shows the QSR curves in terms of the frequency of deaths and the mortality rate, which have the following characteristics: 
1. Dose versus frequency of death: a curve that is high in the center, low on both sides, and extends farther to the right (Figure 4-16a).
2. log dose versus frequency of death: a normal distribution curve (Figure 4-16b).
3. Dose versus mortality: a long-tailed "S" shaped curve (Figure 4-16d).
4. log dose versus mortality: a positive "S" curve (Figure 4-16c). From the normal distribution of the logarithmic dose versus the frequency of deaths (4-16b), it can be seen that the Lo gLD50 is exactly on the horizontal axis corresponding to the midpoint of the normal curve, and exactly half of the animals died at this dose. Since the midpoint of the normal curve is exactly where the mean is, Lo gLD50 is the arithmetic mean of the logarithm of the minimum lethal dose for all experimental animals (which is also the mean of the number of true doses). From the positive S-shaped curve of the relationship between log dose and mortality (Figure 4-16c), Lo gLD50 is the logarithmic value of the horizontal axis corresponding to the midpoint of the positive S-shaped curve, and therefore the vertical axis (mortality rate) corresponding to the midpoint of the positive S-shaped curve is exactly 50%. This curve is characterized by the following: (1) The slope is greatest when the mortality rate is 50% (i.e., LD50), and the sensitivity is highest because it is located in the center of the curve. The sensitivity is highest because it is located in the center of the curve. ② The curve is flat at both ends and the sensitivity is worst near 0% or 100%, so the dose is not easy to determine, and even if it is determined, it is often unreliable. Therefore, it is appropriate to use the LD50 as an indicator for determining the toxicity of a factor. In summary, the Lo gLD50 and LD50 can be determined by finding the logarithmic value on the horizontal axis corresponding to the midpoint of a normal curve or the logarithmic plant on the horizontal axis corresponding to the midpoint of a positive S-shaped curve.
Derivation of the formula: Based on the logarithmic dose-mortality relationship, the formula can be derived by the area method:
In the figure, the horizontal coordinate is the log dose X, the vertical coordinate is the mortality rate P, and g is the midpoint of the positive S-shaped curve, which corresponds to the vertical coordinate of point H with P = 50%, the horizontal coordinate of point F with X = LogLD50, point A with P = 0% = 0, and point D with P = 100% = 1, and point B with X k is the log dose with P = 100%.
From the figure: rectangle AFED=AF-AD=LogLD50×1=LogLD50.
Also: curved edge ∆X1F g≅ curved edge ∆ gCE (two sides and one angle are equal)
∴ rectangle AFED = curved edge AX1CD = LogLD50
Then LogLD50 = rectangle AXkCD - curved edge X1XkC.
∵ The trapezium X1XkC is equivalent to the sum of the areas of several trapezoids.
∴ curved edge X1XkC = d-Σ(Pi+Pi+1)
Also rectangle AX kCD = AX k-AD = X k-1 = X k
∴ Lo gLD50 = Xk-dΣ(Pi+Pi+1).
The above derivation is represented by the visualization: LgLD50
Equation Evolution:
