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

Muhammad Akram Randhawa

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 Nigella sativa, in mice and rats
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.
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 LD50 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 LD50
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 7.33
The 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 1.76
and LD50= 57.54 mg/kg.
Calculation of Standard Error (SE) of LD50
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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