Three Computational Mathematics Techniques: Comparative Determination of Area under Curve

Authors: Khalid Pervaiz Akhter, Mahmood Ahmad, Ghulam Murtaza, Ishrat Shafi, Zafar Javed

Abstract:

The objective of this manuscript is to find area under the plasma concentration- time curve (AUC) for multiple doses of salbutamol sulphate sustained release tablets (Ventolin® oral tablets SR 8 mg, GSK, Pakistan) in the group of 18 healthy adults by using computational mathematics techniques. Following the administration of 4 doses of Ventolin® tablets 12 hourly to 24 healthy human subjects and bioanalysis of obtained plasma samples, plasma drug concentration-time profile was constructed. AUC, an important pharmacokinetic parameter, was measured using integrated equation of multiple oral dose regimens. The approximated AUC was also calculated by using computational mathematics techniques such as repeated rectangular, repeated trapezium and repeated Simpson's rule and compared with exact value of AUC calculated by using integrated equation of multiple oral dose regimens to find best computational mathematics method that gives AUC values closest to exact. The exact values of AUC for four consecutive doses of Ventolin® oral tablets were 150.5819473, 157.8131756, 164.4178231 and 162.78 ng.h/ml while the closest values approximated AUC values were 149.245962, 157.336171, 164.2585768 and 162.289224 ng.h/ml, respectively as found by repeated rectangular rule. The errors in the approximated values of AUC were negligible. It is concluded that all computational tools approximated values of AUC accurately but the repeated rectangular rule gives slightly better approximated values of AUC as compared to repeated trapezium and repeated Simpson's rules.

Keywords: Salbutamol sulphate, Area under curve (AUC), repeated rectangular rule, repeated trapezium rule, repeated Simpson's rule.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1080910

References:

[1] C. Rudy, B.A. Coda, S.M. Archer and D.P. Wermeling. (2004, November). Multiple-Dose Phase I Study of Intranasal Hydromorphone Hydrochloride in Healthy Volunteers. Anesth Analg. (Online). 99: 1379-1386. Available: http:// www.anesthesia-analgesia.org/cgi/content /abstract/99/5/1379.
[2] J. Buvanendran, S. Kroin, K.J. Tuman, T.R. Lubenow, D. Elmofty and P. Luk. (2005, May). Cerebrospinal fluid and plasma pharmacokinetics of the cyclooxygenase 2 inhibitor rofecoxib in humans: single and multiple oral drug administration. Anest Analg. (Online). 100: 1320- 1324. Available: http:// www.anesthesia-analgesia.org/cgi/ content/full/100/5/1320
[3] A.K. Nakagawa, M. Kitano, H. Ikematsu, K. Nakamura, S. Yokota, Y. Tominaga, N. Arai and T. Mae. (2007, June). Clinical safety of licorice flavonoid oil (LFO) and pharmacokinetics of glabridin in healthy humans. The American College of Nutrition. (Online). 26: 209-218. Available: http:// www.jacn.org/cgi/content/abstract/26/3/2 09
[4] F. Traunmuller, T.M. Zeitlinger, P. Zeleny, M. Muller and C. Joukhadar. (2007, September). Pharmacokinetics of Single- and Multiple-Dose Oral Clarithromycin in Soft Tissues Determined by Microdialysis, Antimicrobial Agents and Chemotherapy. (Online). 51: 3185-3189. Available: http://www.aac.asm.org/cgi/content/abstract/51/9/3185
[5] L.G. Howes, J.B. Howes, J.L. Huang and C. Walker. (2008, March). Phase Ib Single- and multiple-dose pharmacokinetic study of oral NV- 52 in healthy volunteers. Drugs R D. (Online). 9: 159-166. Available: http:// www.ncbi.nlm.nih.gov/ pubmed/18457468
[6] B.K. Soo, W.K. Jin, K.H. Young, K.G. Yoon, K. Gsang and L.G. Myung. (2005, March). Hepatic and intestinal first-pass effects of oltipraz in rats. Biopharmaceutics & Drug Disposition. (Online). 26: 129-134. Available: http:// cat.inist.fr/?aModele=afficheN&cpsidt=16737056
[7] G. Murtaza, M. Ahmad, M.A. Madni and M.W. Asghar. (2009, April). A new reverse phase HPLC method with fluorescent detection for the determination of salbutamol sulfate in human plasma. Bull. Chem. Soc. Ethiop. (Online). 22: 1-8. Available: http:// ajol.info/index.php /bcse/article/view/21292
[8] G. Murtaza, M. Ahmad and N. Akhtar. (2009, August). Biowaiver study of oral tabletted ethylcellulose microcapsules of a BCS class I drug. Bull. Chem. Soc. Ethiop. (Online). 23: 1-16. Available: http:// ajol.info /index.php/bcse/article/view/44959
[9] E.A. Kolbrich, A. Erin, A. Goodwin, S. Robert, A. Elliot, T. Huestis and G. Marilyn. (2008, June). Plasma Pharmacokinetics of 3, 4- methylenedioxymethamphet- amine after controlled oral administration to young adults. Vvvvvvvv. (Online). 30: 320-332. Available: http:// www.ncbi.nlm.nih.gov/pmc/articles/PMC2663855/
[10] K.P. Akhter and M. Ahmad. (2002, February). Estimation of area under the plasma concentration time curve using a combination of numerical methods. (Not Online). Journal of Pure and Applied Sciences. 21: 63- 77. Available: http://
[11] H.N. Coldham, A. Gielbert, N. Kuhnert, M.J. Sauer, L.J. King and C. Ioannides. (2007, July). Absolute bioavailability and dose-dependent pharmacokinetic behaviour of dietary doses of the chemopreventive isothiocyanate sulforaphane in rat. (Online). British Journal of Nutrition. 99: 559-564. Available: http://www. journals.cambridge.org/production/action/cjoGetFulltext?fulltextid