### CALCULATION OF LD50 VALUES FROM THE METHOD OF MILLER AND TAINTER, 1944

#### Abstract

Dear Editor,

Acute toxicity of a drug can be determined by the calculation of LD50, i.e., the dose that will kill 50% of animals of a

particular species. Recently, we reported the LD50 of thymoquinone, an active principle of

by the method described by Miller and Tainter, 1944.1,2 Since then some post-graduate students and investigators have

asked us to explain the details of calculation of LD50 by this method, as the original article, being very old, is not easily

available in the literature. We also faced problem in the calculations, however, we found some details for the calculation of

LD50 in the Fundamentals of Experimental Pharmacology by Ghosh3, which also is not easy to obtain in many parts of the

world. Therefore, few lines are written, on behalf of the other authors, to elaborate the calculation of LD50 by the method

of Miller and Tainter for the benefit of young researchers.

An approximate LD50 can be initially determined as a

pilot study by a so called ‘staircase method’ using a

small number of animals (2 each dose) and increasing

the doses of the drug. Five doses can be chosen for

determination of LD50 starting from no death to 100%

mortality. In our study for estimation of LD50 of

thymoquinone, 5 doses were given intraperitoneally to 5

groups of rats, 10 in each group (Table-1).

The animals were observed for first 2 hours

and then at 6th and 24th hour for any toxic symptoms.

After 24 hours, the number of deceased rats was

counted in each group and percentage of mortality

calculated.

1 25 1.4 0 2.5 3.04

2 50 1.7 40 40 4.75

3 75 1.88 70 70 5.52

4 100 2 90 90 6.28

5 150 2.18 100 97.5 6.96

*Corrected % Formula for 0 and 100 is given in the text.

The percentage of animals that had died at each dose

level is then transformed to probit (Table-2).

The percentage dead for 0 and 100 are corrected before

the determination of probits as under:

For 0% dead: 100(0.25/n)

For 100% dead: 100(n-0.25/n)

The probit values are plotted against log-doses and then

the dose corresponding to probit 5, i.e., 50%, is found

out (

and LD50= 57.54 mg/kg.

The SE of LD50 can be calculated from the following

formula:3

Approx. SE of LD50= (Log LD84-Log LD16) … (a)

where N is number of animals in each group.

The probits of 84 and 16 from Table-1 are 5.99

and 4.01 (Approx. 6 and 4), respectively. The log-LD

values for the probits 6 and 4 are obtained from the line

on the graph in Figure-1, which in the present case are

1.96 and 1.58 and their antilog are 91.2 and 38.02.

Using these values in formula (a) the SE of LD50 is 11.9.

Therefore, LD50 of thymoquinone when given

intraperitoneally is 57.54±11.9, with 95% confidence

interval of 45.64–69.44.

Acute toxicity of a drug can be determined by the calculation of LD50, i.e., the dose that will kill 50% of animals of a

particular species. Recently, we reported the LD50 of thymoquinone, an active principle of

*Nigella sativa*, in mice and ratsby the method described by Miller and Tainter, 1944.1,2 Since then some post-graduate students and investigators have

asked us to explain the details of calculation of LD50 by this method, as the original article, being very old, is not easily

available in the literature. We also faced problem in the calculations, however, we found some details for the calculation of

LD50 in the Fundamentals of Experimental Pharmacology by Ghosh3, which also is not easy to obtain in many parts of the

world. Therefore, few lines are written, on behalf of the other authors, to elaborate the calculation of LD50 by the method

of Miller and Tainter for the benefit of young researchers.

**Estimation of the dose range and percentage of****mortality**An approximate LD50 can be initially determined as a

pilot study by a so called ‘staircase method’ using a

small number of animals (2 each dose) and increasing

the doses of the drug. Five doses can be chosen for

determination of LD50 starting from no death to 100%

mortality. In our study for estimation of LD50 of

thymoquinone, 5 doses were given intraperitoneally to 5

groups of rats, 10 in each group (Table-1).

The animals were observed for first 2 hours

and then at 6th and 24th hour for any toxic symptoms.

After 24 hours, the number of deceased rats was

counted in each group and percentage of mortality

calculated.

**Table-1: Results of the lethal doses of****thymoquinone for the determination of LD****50****after****intraperitoneal injection in rats (n=10)****Group****Dose****(mg/kg)****Log****dose****%****Dead*****Corrected****% Probits**1 25 1.4 0 2.5 3.04

2 50 1.7 40 40 4.75

3 75 1.88 70 70 5.52

4 100 2 90 90 6.28

5 150 2.18 100 97.5 6.96

*Corrected % Formula for 0 and 100 is given in the text.

**Conversion of percentage mortalities to probits****and calculation of LD****50**The percentage of animals that had died at each dose

level is then transformed to probit (Table-2).

**Table-2: Transformation of percentage mortalities to probits****% 0 1 2 3 4 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**20**4.16 4.19 4.23 4.26 4.29 4.33 4.36 4.39 4.42 4.45**30**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 4.92 4.95 4.97**50**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**5.84 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 7.33The percentage dead for 0 and 100 are corrected before

the determination of probits as under:

**Corrected % Formula**for 0 and 100% mortality3:For 0% dead: 100(0.25/n)

For 100% dead: 100(n-0.25/n)

The probit values are plotted against log-doses and then

the dose corresponding to probit 5, i.e., 50%, is found

out (

**Figure-1**). In the present case the Log LD50 is 1.76and LD50= 57.54 mg/kg.

**Calculation of Standard Error (SE) of LD****50**The SE of LD50 can be calculated from the following

formula:3

Approx. SE of LD50= (Log LD84-Log LD16) … (a)

where N is number of animals in each group.

The probits of 84 and 16 from Table-1 are 5.99

and 4.01 (Approx. 6 and 4), respectively. The log-LD

values for the probits 6 and 4 are obtained from the line

on the graph in Figure-1, which in the present case are

1.96 and 1.58 and their antilog are 91.2 and 38.02.

Using these values in formula (a) the SE of LD50 is 11.9.

Therefore, LD50 of thymoquinone when given

intraperitoneally is 57.54±11.9, with 95% confidence

interval of 45.64–69.44.

#### References

Al-Ali A, Alkhawajah A, Randhawa MA, Shaikh NA. Oral

and intraperitoneal LD50 of thymoquinone, an active

principle of Nigella sativa, in mice and rats. J Ayub Med Coll

Abbotabad 2008;20(2):25–7.

Miller LC, Tainter ML. Estimation of LD50 and its error by

means of log-probit graph paper. Proc Soc Exp Bio Med

;57:261.

Ghosh MN. In Statistical Analysis, Fundamentals of

Experimental Pharmacology, 2nd ed, Scientific Book Agency

Calcutta, 1984. pp187–9.

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