Comparison of Weibull and Probit Analysis in Toxicity Testing of Hunteria umbellata K Schum (Apocynaceae) Extract in Mice

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1 Ezzld & Nahhas Tropcal Joural of Pharmacutcal Rsarch Dcmbr 202; (6): Pharmacothrapy Group, Faculty of Pharmacy, Uvrsty of B, B Cty, Ngra. All rghts rsrvd. Rsarch Artcl Avalabl ol at Comparso of Wbull ad Probt Aalyss Tocty Tstg of Hutra umbllata K Schum (Apocyaca) Etract Mc Suy A Osag, Ighodaro Igb 2* ad Josph E Osmwkha Dpartmt of Mathmatcs, Faculty of Physcal Sccs, 2 Dpartmt of Pharmacology ad Tocology, Faculty of Pharmacy, Uvrsty of B, B Cty, Ngra Abstract Purpos; Hutra umbllata has b foud to hav thraputc pottals th tratmts of dsass such as yaws, pptc ulcrs, dabts, pls ad frtlty Ngra; hc, th statstcal aalyss o th dtrmato of acut tocty of Hutra umbllata was carrd out mc. Mthods; Data o th acut tocty studs of th sd tract of Hutra umbllata admstrd va th traprtoal rout was aalyzd usg th two-paramtr Wbull modl. Rsults; Th mda lthal dos (LD ) was.6 g/kg of body wght. Ths rsult falls th ghbourhood of th mda lthal dos arlr obtad prvous rports. Cocluso; Th rsults show that Hutra umbllata may b slghtly toc wh admstrd traprtoally. Kywords: Hutra umbllata, Wbull modl, Acut tocty, Mda lthal dos (LD ). Rcvd: 7 Novmbr 20 Rvsd accptd: 3 Octobr 202 *Corrspodg author: Emal: gb.ghodaro@ub.du; Tl: Trop J Pharm Rs, Dcmbr 202; (6): 933

2 Osag t al INTRODUCTION May plats hav b usd as substtuts to orthodo mdcs Afrca du to th as of obtag thm bushs ad forsts. Ths hrbal mdcs may b sourcs of substacs wth bttr thraputc pottals tha som currtly usd orthodo mdcs []. Th vromt w lv s flld wth abudat rsourcs ad chmcals dowd to humas by atur for bfcal uss. To plor th bfts of ths rsourcs, thr s d to mak cotact wth thm va ay rout of posur dpdg o th physcal ad chmcal proprts of th substac(s) of trst. Ths could b achvd through halato, sk absorpto, gsto or jcto. Hutra umbllata K. Schum s a small tr of about 5 22 m hght wth a ds vrgr crow [2] of grat mdcal bfts ad s foud Wst ad Ctral Afrca. I Ngra, t s foud th ra forst zo of th southr part of th coutry wth th local ams, osu (Edo), r (Yoruba) ad kpokr (Ibo) [3]. Th plat s also usd for th tratmt of yaws, pptc ulcrs, dabts, pls, dysmoroha, fvrs ad frtlty [4,5,6,7] ad flammato [8,9]. It has b usd th tratmt of varous almts Ngra ad Ghaa, spcally th lavs, roots ad bark [0]. Th statstcal study of th tocty of ths plat s cssary for gag kowldg of ts toc ffct rlato to ts cosumpto by humas. Ths prst study was udrtak to statstcally dtrm th acut tocty of Hutra umbllata tract admstrd to mc through traprtoal rout wth th ad of Wbull modl ad compar wth probt aalyss. Varous mathmatcal modls hav b usd th aalyss of dos-rspos rlatoshps to assss th toc ffcts of chmcal substacs. Ths modls rag from vry smpl modls to trmly complcatd modls for whch th vtual fuctoal forms caot b asly prssd as sgl quatos. Spcfcally, ths modls ar () tolrac dstrbuto modls: log-probt, probt, Wbull, Matl-Brya modls [], () mchastc modls: Ht ad multstag modls [2], () tm-to-tumor modls: Logormal, Wbull, Hatly Sulk ad multstag modls [2,3], (v) physologcally-basd pharmacoktc (PBPK) modls [4,5], ad (v) bologcally- Basd Modls: Moolgavkar-Vzo-Kudso (MVK) modl [6] ad Ellw ad Coh modl [7]. To dtrm th toc ffct of Hutra Umbllata plat, th mda lthal dos (LD ) of th two-paramtr Wbull modl s mployd. Th Wbull modl as a tolracdstrbuto modl has b usd tsvly to prdct tm-to-falur of lctrcal ad mchacal systms ad t s mor wdly appld to dos-rspos rlatoshps. It s capabl of rprstg thrshold ad cocav curvs ad sstv to th shap of th dos-rspos curv. It also has th advatag of bg abl to corporat a tm-to-tumor fucto [3] EXPERIMENTAL Plat matral ad tracto Th rp fruts of Hutra umbllata wr collctd from Egor Local Govrmt Ara B Cty, Ngra. It was frst dtfd by Profssor Macdoald Idu of Dpartmt of Botay, Faculty of Lf Sccs, Uvrsty of B, B Cty, Ngra ad latr authtcatd by Forst Rsarch Isttut of Ngra, Ibada, whr a sampl wth umbr FHI0768 was dpostd. Th frsh rp fruts of Hutra umbllata wr opd ad th pulp rmovd. Th sds wr squzd out of th pulp. Th pulp was drd th su for a wk ad turd to powdr wth th ad of a grdr. Th powdrd matral (400 g) was bold wth,0 ml of dstlld watr for 30 m to obta th aquous tract. Th tract was fltrd, coctratd udr prssur a Trop J Pharm Rs, Dcmbr 202; (6): 934

3 Osag t al rotar vapor at 68 o C ad drd a ov st at 40 o C for 48 h (yld: 2 %). Th drd aquous tract was prsrvd cla glass cotars at 4 o C a rfrgrator utl us. Acut tocty study usg probt aalyss Ovrght-fastd Swss albo mc (7-23 g) of thr s obtad from th Laboratory Amal Ctr, Collg of Mdc, Uvrsty of Lagos, Ngra wr usd for th study. Th amals wr dvdd to fv groups of fv amals ach. Groups A to D rcvd.4,.6,.8 ad 2.0 g/kg of th tract, rspctvly, whl group E rcvd dstlld watr traprtoally. Th umbr of daths that occurrd ach group was dtrmd, ad usg probt aalyss, th LD was dtrmd by had calculato. Mthod of aalyss of acut tocty usg th Wbull modl Suppos X s a rspos data wth data pots, 2,,, th th two paramtr Wbull dstrbuto s dfd as Eq f ( ) = β β whr p β, β > 0 = log (dos) ad dos s th total amout of a substac admstrd or tak up by tst subjct(s). ad β ar shap ad scal paramtrs rspctvly. I stmatg th shap ad scal paramtrs of th Wbull modl gv as Eq 2. p( d) = p ( βd ) It s covt to stmat thm from Eq. Thus, w mployd th mamum lklhood stmato (MLE) mthod for β ad th last squar stmato for rspctvly. Th lklhood fucto of () wth rspct to β s L ( β ) = = = β = β p β β β p Th log-lklhood of (3) s = log L( β ) = log log β β + = β p β Takg partal drvatvs of Eq 4 wth rspct to ad β ad quatg th rsultg drvatvs to zro, w obta ad β = = = [ log = ( log ) log = = = From Eq 6, th stmat of would b dffcult to obta. Hc, th cssty for stmato of va th last squars stmato (LSE) mthod. Ths s do by th cosdrato of th cdf of th two-paramtr Wbull dstrbuto. Th cdf of th two-paramtr Wbull dstrbuto s gv as: F( ) = p whr = log ( dos) ( β ),, β 0 Takg atural logarthm of Eq 7 gvs Eq 8. log { log [ F( ) ]} = log β + log Ths gvs a lar quato of th form y = a + b From Eq 8, th stmat of s Trop J Pharm Rs, Dcmbr 202; (6): 935

4 Osag t al ( log ) ( log { log [ F( )]} ) + ( log ) log { ( log [ F( )])} = = = = 2 ( log ) log = = 2 whr F ) s stmatd as ( (9) rak ( ). + Equatos 5 ad 9 gv th plct mathmatcal formula for th valus of th stmats of ad β [8] from whch th LD of th Wbull modl s calculatd. Also, th mda lthal dos for th Wbull modl s gv as Eq 0. = β (log 2 ) (0) For th purpos of comparso, Rlatv Error s mployd ad dfd as: Err l R. = LD ( wbull) LD ( probt), LD ( probt) whr ER Rl ls bwt 0 ad. For th purpos of th study, w st a bchmark at 0.5 ad mad us of th followg crtra for comparso: Crtro I: If Err Rl. < 0.5, th Wbull modl should b usd to obta th acut tocty,crtro II: If Err Rl. = 0.5, ay of Wbull or probt modl ca b usd, Crtro III: If 0.5 < Err Rl. <, th probt modl should b usd. RESULTS I th dtrmato of LD, Tabl shows th varous doss usd th acut tocty studs ad thr corrspodg log doss, mortalty rato of th amals ad thr corrspodg probt valus ( = 5 pr group). It was obsrvd that th lthal dos at % (LD ) gav.66 g/kg (660 mg/kg) usg probt aalyss. Th stmats of shap ad scal paramtrs of Wbull modl from (5) ad (9) ar obtad as = ad β = Also, = log ( LD ) = It follows that L D = g / kg (64.9 mg / kg) Also, from Eq (), Err Rl. = Tabl : Acut tocty data for H. umbllata sd tract mc Dos Log Mortalty % Probt (g/kg) dos rato Mortalty / / / / Probt Log Dos Fg : Itraprtoal acut tocty of H. umbllata sd tract dcatg th l of rgrsso. Mda lthal dos (LD ) usg probt aalyss s.66 g/kg. DISCUSSION Toc ffcts th bologcal systm ar ot producd by chmcal agts ulss that chmcal agt or ts mtabolc brakdow (botrasformato) rachs approprat st th body at a coctrato ad a lgth of tm suffct ough to produc a toc mafstato. Two major factors that fluc tocty as t rlats to posur stuato for a spcfc chmcal ar th routs of posur, durato ad frqucy of posur. Toc agts grally produc th gratst ffct ad rapd rspos wh Trop J Pharm Rs, Dcmbr 202; (6): 936

5 Osag t al gv travously. A appromatly dscdg ordr of ffctvss for othr routs would b halato, traprtoal, subcutaous, tramuscular, tradrmal, oral ad drmal. Earlr rports hav show that aquous frut pulp tract of Hutra umbllata s ot toc orally [9] hc th d to furthr dtrm ts acut tocty profl va aothr rout of admstrato. Acut tocty study usg th Wbull modl gav a mda lthal dos of.649 g/kg as compard to th probt aalyss mda lthal dos of.66 g/kg. Ths dcats that LD obtad by th wbull modl was comparabl to that of covtoal mthods lk probt aalyss. Th rsults obtad from ths two modls dcat that Hutra umbllata plat s slghtly toc [9]. I addto, th Amrca Socty for Tstg ad Matrals [20], statd that ay chmcal substac wth LD valu lss tha 2 g/kg but gratr tha g/kg could b cosdrd to b slghtly toc. Th rsult obtad th dtrmato of th acut tocty of Hutra umbllata suggsts t s slghtly toc o acut posur traprtoally. CONCLUSION Th Wbull LD valu for Hutra umbllata was.649 g/kg wth rlatv rror of Sc th rlatv rror ls Crtro I, t mpls that th Wbull modl gvs a bttr rsult obtag LD tha probt modl ths study. ACKNOWLEDGEMENT Th authors wsh to thak Dr D Okuogha for hs cotrbutos to th dvlopmt of ths papr. REFERENCES. Wag Y, Wag X, Chg YA. A Computatoal approach to botacal drug dsg by Modllg quattatv compostos actvty rlatoshp, Chm. Bo. Drug Dsg, 2006; 68: Olvr-Bvr B. Mdcal Plats tropcal Wst Afrca. Cambrdg Uvrsty Prss, Cambrdg, 986; Boo MJ. Hutra umbllata (K.Schum) Hallr F.I:Schmlzr GH & Gurb-Fakm A (Edtors) Prota II:Mdcal plats/plats mdcals (CD-Rom).PROTA Wagg. Nthrlad, Rama A, Mallam V. Ehacd vtro actvty of glucokas zym th prsc of Hutra umbllata sds, a tradtoal Ngra tratmt for dabts J. Pharm. Pharmocol., 994; 46: Eluyoba AA. Fmal Ifrtlty th Lads of tradtoal brth attdats South-Wstr Ngra. Ftotrapa, 995; 66: Falodu A, Nworgu ZAM, Ikpomwosa MO. Phytochmcal compots of Hutra umbllata (K.Schum) ad ts ffct o solatd o-prgat rat utrus ostrus. Pak. J. Pharm. Sc., 2006; 9: Igb I, Chg FP, Eromo A. At-Iflammatory actvty of Aquous frut pulp tract of Hutra umbllata K. Schum Acut ad Chroc Iflammato Acta Pol Pharm Drug Rs, 200; 67: Glls LS. Ethomdcal uss of plats Ngra. B Cty. Ub Prss. 992: p Igb I, Ozolua RI, Okpo SO, Obasuy O. Atpyrtc ad Aalgsc ffcts of th Aquous Etract of th Frut Pulp of Hutra umbllata K. Schum (Apocyaca). Trop J Pharm Rs, 200; 8: Ibh IN, Idu M, Atama JE. Tocologcal assssmt of Abr sd (Hutra umbllata K. Schum). J Md Bomd Rs,2005; 4: Chrsts ER. Dos-rspos fuctos Aquatc tocty tstg ad th Wbull modl. Ecol Modllg 984; 22: Hol DG. Mathmatcal dos-rspos modls ad thr applcatos to rsk stmato. I: Mthods for Estmatg Rsk of Chmcal Ijury: Huma ad Nohuma Bota Ad Ecosystms, Scop/SGOMSEC 2. Joh Wly ad Sos, 985; Szymczak W, Szadkowska Staczyk I. Cacr Rsk Assssmt: Prst ad Futur. Itratoal J Occup Mdc Ev Halth 2005; 8: Rddy MB, Yag RSH, Clwll HJ III ad Adrs ME (2005) Physologcally Basd Pharmacoktc (PBPK) Modllg: Scc ad Applcatos Joh Wly ad Sos. pp Chu WA, Barto HA, DWosk RS, Schlossr P. Thompso CM, Soawa B, Lpscomb JC, Krsha K. Rvw: Evaluato of Physologcally Basd Pharmacoktc Modls for us rsk assssmt. J Appld Tocol, 2007; 27: Trop J Pharm Rs, Dcmbr 202; (6): 937

6 Osag t al 6. Moolgavkar SH. A two-stag carcogss modl for rsk assssmt. Joural of Cll Bol. Tocol, 989; 5: Ellw LB, Coh SM. A Cllular Dyamcs modl of prmtal bladdr cacr: Aalyss of th ffct of sodum sacchar th rat. J. Rsk Aalyss, 988; 8: Osmwkha JE, Osag SA. Mathmatcal Modllg of th Gradual Agg of Systms usg th Wbull hazard fucto. J. Ng. Assoc. Math. Phys, 200; 7: Looms TA. Esstals of Tocology. Ed 3, La ad Fbzr, Phladlpha. 978; p Amrca Socty for Tstg ad Matrals. Stadard Tst Mthod for Estmatg Acut Oral Tocty Rats. Amrca Socty for Tstg ad Matrals E63 87, Phladlphd, USA, 987. Trop J Pharm Rs, Dcmbr 202; (6): 938