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

Authors

  • 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 aparticular 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 haveasked us to explain the details of calculation of LD50 by this method, as the original article, being very old, is not easilyavailable in the literature. We also faced problem in the calculations, however, we found some details for the calculation ofLD50 in the Fundamentals of Experimental Pharmacology by Ghosh3, which also is not easy to obtain in many parts of theworld. Therefore, few lines are written, on behalf of the other authors, to elaborate the calculation of LD50 by the methodof Miller and Tainter for the benefit of young researchers.Estimation of the dose range and percentage ofmortalityAn approximate LD50 can be initially determined as apilot study by a so called ‘staircase method’ using asmall number of animals (2 each dose) and increasingthe doses of the drug. Five doses can be chosen fordetermination of LD50 starting from no death to 100%mortality. In our study for estimation of LD50 ofthymoquinone, 5 doses were given intraperitoneally to 5groups of rats, 10 in each group (Table-1).The animals were observed for first 2 hoursand then at 6th and 24th hour for any toxic symptoms.After 24 hours, the number of deceased rats wascounted in each group and percentage of mortalitycalculated.Table-1: Results of the lethal doses ofthymoquinone for the determination of LD50 afterintraperitoneal injection in rats (n=10)GroupDose(mg/kg)Logdose%Dead*Corrected% Probits1 25 1.4 0 2.5 3.042 50 1.7 40 40 4.753 75 1.88 70 70 5.524 100 2 90 90 6.285 150 2.18 100 97.5 6.96*Corrected % Formula for 0 and 100 is given in the text.Conversion of percentage mortalities to probitsand calculation of LD50The percentage of animals that had died at each doselevel is then transformed to probit (Table-2).Table-2: Transformation of percentage mortalities to probits% 0 1 2 3 4 5 6 7 8 90 - 2.67 2.95 3.12 3.25 3.36 3.45 3.52 3.59 3.6610 3.72 3.77 3.82 3.87 3.92 3.96 4.01 4.05 4.08 4.1220 4.16 4.19 4.23 4.26 4.29 4.33 4.36 4.39 4.42 4.4530 4.48 4.50 4.53 4.56 4.59 4.61 4.64 4.67 4.69 4.7240 4.75 4.77 4.80 4.82 4.85 4.87 4.90 4.92 4.95 4.9750 5.00 5.03 5.05 5.08 5.10 5.13 5.15 5.18 5.20 5.2360 5.25 5.28 5.31 5.33 5.36 5.39 5.41 5.44 5.47 5.5070 5.52 5.55 5.58 5.61 5.64 5.67 5.71 5.74 5.77 5.8180 5.84 5.88 5.92 5.95 5.99 6.04 6.08 6.13 6.18 6.2390 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 beforethe 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 thenthe dose corresponding to probit 5, i.e., 50%, is foundout (Figure-1). In the present case the Log LD50 is 1.76and LD50= 57.54 mg/kg.Calculation of Standard Error (SE) of LD50The SE of LD50 can be calculated from the followingformula:3Approx. 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 5.99and 4.01 (Approx. 6 and 4), respectively. The log-LDvalues for the probits 6 and 4 are obtained from the lineon the graph in Figure-1, which in the present case are1.96 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 givenintraperitoneally is 57.54±11.9, with 95% confidenceinterval 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.

Published

2009-09-01