Release Behaviour of Clozapine Matrix Pellets Based on Percolation Theory

Depósi o de in es igación de la Uni e sidad de Se illa h ps://idus.us.es/ “This is an Accep ed Manusc ip o an a icle published by Else ie in INTERNATIONAL JOURNAL OF PHARMACEUTICS on 14 Feb ua y 2011, a ailable a : h ps://doi.o g/10.1016/j.ijpha m.2010.11.024.” 1 Ti le: Release beha iou o clozapine ma ix pelle s based on pe cola ion heo y. Au ho names and a ilia ions: Ángela Aguila -de-Ley a a . Tahme Sha kawi b Be na d Ba aille b Gilles Baylac b Isido o Ca aballo a a Depa men o Pha macy and Pha maceu ical Technology. Uni e si y o Se ille. P o eso Ga cia González, 2. 41012. Se ille. Spain. b Labo a oi e de Pha macy Galénique e Genie Pha maceu ique. Uni e si é Mon pellie 1. 15 A enue Cha les Flahaul BP 14491 34093 Mon pellie Cedex 5. F ance. Co esponding au ho : Ángela Aguila -de-Ley a. Depa men o Pha macy and Pha maceu ical Technology. Uni e si y o Se ille. P o eso Ga cía González, 2. 41012. Se ille. Spain Telephone numbe : +34676212688 Fax numbe : +34954556085 e-mail add ess: [email p o ec ed]. 2 Abs ac The elease beha iou o clozapine ma ix pelle s was s udied in o de o in es iga e i i is possible o explain i applying he concep s o pe cola ion heo y, p e iously used in he unde s anding o he elease p ocess o ine and hyd ophilic ma ix able s. Thi een ba ches o pelle s wi h di e en p opo ions o clozapine/ mic oc ys alline cellulose (MCC)/ hyd oxyp opylme hyl cellulose (HPMC) and di e en clozapine pa icle size ac ions we e p epa ed by ex usion-sphe onisa ion and he elease p o iles we e s udied. I has been obse ed ha he dis ance o he excipien (HPMC) pe cola ion h eshold is impo an o con ol he elease a e. Fu he mo e, he d ug pe cola ion h eshold has a big in luence in hese sys ems. Ba ches e y close o he d ug pe cola ion h eshold, show a clea e ec o he d ug pa icle size in he elease a e. Howe e , his e ec is much less e iden when he e is a bigge dis ance o he d ug pe cola ion h eshold, so he elease beha iou o clozapine ma ix pelle s is possible o be explained based on he pe cola ion heo y. Keywo ds: Pelle s, Clozapine, Hyd oxyp opylme hyl cellulose, Pe cola ion h eshold. 3 1. In oduc ion The pelle iza ion p ocess in ol es he agglome a ion o ac i e pha maceu ical ing edien s and excipien s in sphe ical uni s o size comp ised be ween 0.5 and 1.5 mm called pelle s (Ba aille e al., 1993). These mul ipa icula e sys ems o e a wide ange o he apeu ic as well as echnological ad an ages compa ed wi h monoli hic sys ems: hey dispe se as indi idualized uni s in he gas oin es inal ac educing high local d ug concen a ion (minimising side e ec s like he i i a ion o he gas ic mucosa), maximising d ug abso p ion and educing peak plasma luc ua ion. Ano he addi ional he apeu ic ad an age is ha hese dosage o ms elimina e he dependence o he d ug e ec on gas ic emp ying, hus educing in a and in e indi idual a iabili y o he d ug plasma concen a ions (Bechgaa d and Hege mann Nielsen, 1978; Bodmeie , 1997). Examples o echnological ad an ages o he pelle s a e hei sphe ical shape, hei na ow pa icle size dis ibu ion and hei low iabili y which p o ide hem e y good low p ope ies and make i easie o coa hem o include hem in o ha d gela in capsules as well as comp ess hem in o able s (Reynolds, 1970). Mo eo e , hese dosage o ms allow combining non-compa ible d ugs o di e en d ug elease p o iles in he same o mula ion (Pin o e al., 2001; Quin a alle e al., 2008). Pelle s can be manu ac u ed in di e en ways. Ne e heless, he mos popula me hod o p oducing pelle s is by an ex usion-sphe onisa ion p ocess which in ol es ou di e en s ages: p epa a ion o he we mass (g anula ion), ex usion o he g anula ed mass o ob ain cylind ical ex uda es, ounding o he ex uda es in o sphe es (sphe onisa ion) and inally, d ying o he sphe es (Reynolds, 1970; Ve ae e al., 1995). The excipien mos used o p oduce pelle s by his echnique is he mic oc ys alline cellulose due o i s a ou able plas ic p ope ies (Cha lapalli and Rohe a, 1998; Delalonde e al., 1997). Clozapine is an a ypical an ipsycho ic which main indica ion is he ea men o esis an schizoph enia, al hough i has also demons a ed e icacy in he ea men o o he condi ions like schizoa ec i e diso de s, bipola dep ession and some neu ological diso de s. One impo an ad an age o his d ug is i s low isk o p oducing side e ec s like ex apy amidal side e ec s, a di e diskynesia o ele a ed p olac ine le els compa ed wi h o he an ipsycho ics (Elizondo, 2008; Iqbal e al., 2003), which makes i one o he mos used d ugs in he ea men o schizoph enia. 4 To ou knowledge, no pelle o mula ion o clozapine has been in es iga ed; we he e o e unde ook o mula ion s udies in o de o ake ad an age o hese dosage o ms o clozapine ea men . The pe cola ion heo y was in oduced in o he pha maceu ical ield by Leuenbe ge and co-wo ke s (Bla ne e al., 1990; Bonny and Leuenbe ge , 1991; Bonny and Leuenbe ge , 1993; Holman and Leuenbe ge , 1988; Leuenbe ge and Leu, 1992; Leuenbe ge e al., 1987), e ie ing p ac ical consequences om he heo e ical p inciples o he pe cola ion heo y. These indings ha e been applied nowadays o he design and op imisa ion o an inc easing numbe o pha maceu ical o mula ions. In ela ion wi h his heo y, a clus e is de ined as a g oup o neighbou ing pa icles o he same componen and is conside ed in ini e o pe cola ing when i ex ends om one side o he o he side o he sys em (S au e and Aha ony, 1992). Pe cola ion h eshold co esponds o he concen a ion o one componen o which he e is a maximum p obabili y o appea ance o an in ini e clus e o i . A his concen a ion poin , i is expec ed ha some p ope ies o he sys em change suddenly. Nume ous s udies applying he concep s o he pe cola ion heo y o he elease beha iou o ine and hyd ophilic ma ix sys ems ha e been ca ied ou . In ine ma ix, he d ug is eleased h ough bo h, he ini ial po es o he ma ix and he po es o med when he d ug has been dissol ed (Ca aballo e al., 1993). The e o e, he ideal o mula ion o an ine ma ix, acco ding o he pe cola ion heo y, would be abo e he d ug pe cola ion h eshold since his ac assu es he elease o he o al d ug dose. The excipien mus also be abo e i s pe cola ion h eshold o a oid he disin eg a ion o he ma ix du ing he elease p ocess and o con ol he d ug elease (Bonny and Leuenbe ge , 1991; Bonny and Leuenbe ge , 1993; Ca aballo e al., 1999; Melgoza e al., 1998). In he case o he hyd ophilic ma ix, he ideal o mula ion is abo e he excipien pe cola ion h eshold, since a ha poin a pe cola ing clus e o he excipien is o med con olling he hyd a ion and he elease a e o he d ug h ough he gel laye o med. Below he excipien pe cola ion h eshold he gel laye is less cohe en esul ing in a as e osion o he ma ix and conduc ing o a apid di usion o he d ug (Ca aballo, 2009). The aim o his s udy is o in es iga e, o he i s ime, i he elease beha iou o ma ix pelle s con aining clozapine can be explained using he concep s o pe cola ion heo y, which ha e been p e iously used in he unde s anding o he elease p ocess o ine and hyd ophilic ma ix able s. 5 2. Ma e ial and Me hods 2.1 Ma e ials The ollowing ma e ials we e used as ma ix o ming ma e ials: hyd oxyp opylme hyl cellulose (Me olose 4.000 and Me olose 100.000, Shin-E su Chemical Co. L d, Japan), mic oc ys alline cellulose (Vi apu 101, J. Re enmaie &Söhne GmbH + Co. KG, Ge many), Magnesium S ea a e (Coope , F ance) and clozapine (Ningbo Yuan ang Biochemicals Co. L d, China). E hanol (Me ck, Ge many) and dis illed wa e we e used as g anula ion liquid. All eagen s and sol en s used we e o analy ical g ade. Wa e was always used in demine alized quali y. 2.2 Me hods 2.2.1 P epa a ion o he pelle s Table 1 desc ibes he s udied o mula ions. Thi een ba ches o 100 g o pelle s wi h di e en p opo ions o clozapine/ MCC/ HPMC we e p epa ed. The ba ches p epa ed con ained 20%, 30% o 40% o clozapine. The d ug pa icle size employed is indica ed in Table 1. The con en o HPMC was 2% o ba ches A, B, C and D, 10% o ba ch 1 and 40% o ba ches 2 o 9. The powde s we e blended in a Tu bula mixe (Willy A. Bacho en, Basle, Swi ze land) o 5 minu es and he we ing was done in a plane a y mixe (Kenwood Majo , U.K.) du ing 20 minu es wi h e hanol-wa e mix u es in di e en p opo ions o ba ches 1 o 9 and dis illed wa e o ba ches A o D. Ex usion was pe o med on a single sc ew axial ex ude (Pha mex 35T Gable Machinenbau, E lingen, Ge many) equipped wi h a 1 mm sc een and ope a ed a 50 pm. Sphe onisa ion was ca ied ou on a Sphae oma SPH 250 MA sphe onise (Gable Machinenbau, E lingen, Ge many) equipped wi h a se a ed pla e o 250 mm diame e and ope a ed a di e en speeds depending on he ba ch. The sphe onisa ion ime also a ied om 2 min o 3 min 30 sec depending on he o mula. An addi ional sphe onisa ion ime a a di e en speed was necessa y o some ba ches ( he speed o his addi ional sphe onisa ion pe iod is exp essed in pa en heses in Table 1). All he ba ches we e d ied in a en ila ed o en (Binde FP400, Ge many) a a empe a u e o 50ºC du ing 20 h . 2.2.2 Analy ical me hods 2.2.2.1. Rheological s udies o he d ug and excipien s Rheological s udies o bo h, d ug and excipien s (clozapine, MCC, HPMC 4000 cp and HPMC 100000 cp) we e ca ied ou acco ding o Eu opean Pha macopoeia (2007). 6 The bulk and apped densi ies we e de e mined in iplica e o he excipien s in a olume e ( ype STAV II, J Engelmann AG, Ge many). The bulk densi y (ρ bulk ) was de e mined by measu ing he bulk olume (V bulk ) occupied by 75 g o sample illed in o a 250 ml g adua ed cylinde eadable o 2 ml. The apped densi y (ρ apped ) was de e mined om he apped olume (V apped ) occupied by he powde a e epea ed aps un il he di e ence be ween successi e measu emen s was less han 2 ml. The alues o densi ies we e calcula ed om he measu ed olumes and i s weigh acco ding o equa ions (1) and (2): (1) bulkbulk Vm /= ρ (2) apped apped Vm /= ρ Ob ained alues o densi ies we e used o calcula ing he comp essibili y index (CI) as indica ed in equa ion (3): (3) ( ) 0 0 100 V VV CI − = The Hausne a io (HR) was calcula ed acco ding o equa ion (4): (4) appedbulk VVHR /= The lowabili y was pe o med also in iplica e in a g anula e low es e (E weka GmbH ype GTB, Heusens amm, Ge many) wi h an ou low opening diame e o 25±0.01 mm, o bo h, clozapine and excipien s. The es angle was also ca ied ou in iplica e in a g anula e low es e (E weka GmbH ype GTB, Heusens amm, Ge many) , wi h an ou low opening diame e o 25±0.01 mm ollowing he ule DIN 53916 and i was made only o clozapine. 2.2.2.2. Pa icle size analysis The pa icle size analysis o he d ug and excipien s was ca ied ou using lase di ac ion in a Mas e size X 2.18 e sion (Mal e n Ins umen s L d., UK) equipped wi h MSX d y powde eede . The esul s a e exp essed as pe cen iles 10, 50 and 90 % o he olume diame e . Each sample was pe o med in duplica e and he esul s a e exp essed as he mean ± s anda d de ia ion. 2.2.2.3. Di e en ial Scanning Calo ime y 7 Di e en ial Scanning Calo ime y was pe o med in a Se a am 131, F ance DSC in o de o in es iga e po en ial solid s a e in e ac ions be ween d ug and excipien s. S anda d aluminium sample pans (40 μl) we e used and a hea ing a e o 10ºC/min was employed in he ange o 25 – 400 ºC. 2.2.2.4. Op ical Mic oscopy Olympus SZ binocula s wi h a magni ica ion o 10X in e aced ia a digi al came a Mo icam 2300 o a compu e wi h he so wa e Mo ic Image .2.0 and Leica S8APO binocula s wi h a magni ica ion o 10X in e aced ia a digi al came a Leica DC 300 .2.0 o a compu e wi h he so wa e Leica IM50 .1.20 we e used o pe o m he image analysis o he d ug, excipien s, and pelle s. 2.2.2.5. Pelle s size Pelle s p oduced we e subjec ed o sie e analysis using a nes o s anda d sie es (Re sch, Ge many). The ac ion o pelle s co esponding o he ange 0.710 o 1mm o he di e en ba ches was used o u he cha ac e isa ion. Mean pa icle diame e was de e mined using an image analyze p og am (Image-P o Plus .6). 2.2.2.6. Sphe ici y index The sphe ici y index (SI) o he ac ion o pelle s wi h size comp ised be ween 0.710 and 1mm was de e mined by image analysis employing he p og am Image-P o plus .6. This index was calcula ed as indica ed in equa ion (5): (5)         = max min D D SI min D and max D a e he smalles and la ges diame e o a pelle (Galland e al., 2005). 2.2.2.7. Scanning elec on mic oscopy The mo phology o he d ug and excipien s as well as he d ug dis ibu ion wi hin he pelle s was s udied by means o a scanning elec on mic oscope (Philips XL-30, Eindho en, Holland), a e coa ing he samples wi h a hin laye o gold on a spu e coa e (Edwa ds Pi ani 501 Scan-Coa Six, C awley, Wes Sussex, UK). Mic opho og aphs we e ob ained a a magni ica ion app op ia e o pa icle size. 2.2.2.8. Pa icle densi y The pa icle densi y was de e mined o bo h, d ug and excipien s, using a helium pycnome e (Mic ome i ics SA ype Mul i olume pycnome e 1305), employing a known mass o powde be ween 7.5 and 10.5 g. The sample olume is de e mined using equa ion 6: 8 (6) )1/( 21 − −= PP V VV cs Whe e Vs is he sample olume, Vc is he cell olume, V is he e e ence olume, P 1 is he ini ial p essu e and P 2 is he inal p essu e. The densi y o he powde mass, ρ , is gi en by equa ion 7: (7) ρ = m/ Vs The es was epea ed wo imes o each p oduc . 2.2.2.9. S udy o he d ug elease Ha d gela ine capsules we e illed wi h pelle s o he di e en ba ches con aining 25 mg o clozapine. The dissolu ion s udies o ba ches 1 o 9 we e pe o med using he baske me hod (Eu opean pha macopoeia, 2007) in a dissolu ion es e (Pha ma es DT70, Ge many). 900 ml o pH 4 ace a e bu e dissolu ion media (USP, 2009) was used o he assay. The empe a u e was ixed a 37 ± 0.5ºC and he s i ing speed was 50 pm. Samples we e analysed using a con inuous low- h ough sys em a ached o an 8 cell UV/VIS (Speco d 250, Ge many) spec opho ome e . The wa eleng h was se o 260 nm. Readings o abso bance we e aken e e y 10 minu es un il 100% o he d ug was eleased. Fo ba ches A o D, he dissolu ion s udies we e ca ied ou using he baske me hod (Eu opean pha macopoeia, 2007) in a So ax AT7 sma (Allschwil, Swi ze land). 900 ml o pH 4 ace a e bu e dissolu ion media (USP, 2009) was used o he assay. The empe a u e was ixed a 37 ± 0.5ºC and he s i ing speed was 50 pm. 5 ml samples we e wi hd awn a each ime pe iod du ing 7 hou s and measu ed in a UV/VIS Agilen 8453 (Cali o nia, USA) a 260 nm. The clozapine con en was calcula ed using a p e iously de e mined calib a ion cu e. All he elease da a a e exp essed as he mean ± s anda d de ia ion (S.D.) o six samples. 2.2.2.10. Dissolu ion da a analysis D ug elease da a (M /M∞ ≤ 0.9) we e analyzed acco ding o Higuchi (1963) (8), Ko smeye e al. (1983) (9), Ze o o de (10), Fi s o de (11) and Peppas and Sahlin (1989) (12) equa ions: 15 he clus e s connec ed wi h he pelle ’s su ace. Fa abo e he d ug pe cola ion h eshold, he e ec o he d ug pa icle size is clea ly less e iden . Acknowledgemen s This wo k has been suppo ed by an F.P.U. g an om he Spanish Go e nmen . Lis o symbols and abb e ia ions MCC Mic oc ys alline cellulose HPMC Hyd oxyp opylme hyl cellulose cp Cen ipoise ρ bulk Bulk densi y V bulk Bulk olume ρ apped Tapped densi y V apped Tapped olume CI Comp esibili y index V 0 Ini ial olume o he pou ed powde V Final olume o he apped pwde HR Haussne a io SI Sphe ici y index min D The smalles diame e o a pelle max D The la ges diame e o a pelle V s Sample olume V c Cell olume V Re e ence olume P 1 Ini ial p essu e P 2 Final p essu e ρ T ue densi y M D ug amoun eleased a ime M ∞ D ug amoun eleased a in ini e ime b Higuchi’s elease a e cons an k k Ko smeye ’s kine ic cons an 16 k 0 Ze o o de elease a e cons an k 1 Fi s o de elease a e cons an n Ko smeye ’s ime exponen k d Di usional a e cons an k Relaxa ional a e cons an m Pu ely Fickian di usion exponen Re e ences Ba aille, B., Liga ski, K., Jacob, M., Thomas, C., Du u, C., 1993. 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Ri ge , P.L., Peppas, N.A., 1987. A simple equa ion o desc ip ion o solu e elease I. Fickian and non- ickian elease om non-swellable de ices in he o m o slabs, sphe es, cylinde s o discs. J Con olled Release. 5, 23-36. S au e , D., Aha ony, A., 1992. In oduc ion o pe cola ion heo y, Taylo &F ancis, London. USP 32, 2009. Clozapine o icial monog aph, pp 2005-2007. Rock ille. Ve ae , C., Bae , L., Remon, J.P., 1995. Ex usion-sphe onisa ion. A li e a u e e iew. In J Pha m. 116, 131-146. Vila Ja o, J.L., 1997. Tecnología Fa macéu ica 1: Aspec os undamen ales de los sis emas a macéu icos y ope aciones básicas, Sín esis, Mad id. 20 Figu e cap ions Figu e 1. DSC he mog ams o ( om op o bo om): a) pu e clozapine, b) 1:1 blend o clozapine wi h HPMC 4000 cp, c) 1:1 blend clozapine-HPMC 100000 cp, d) 1:1 blend clozapine- MCC and e) 1:1 blend clozapine-Mg s ea a e. Figu e 2. Mic opho og aph co esponding o clozapine pa icles. Figu e 3. Mic opho og aph co esponding o an uncu pelle om ba ch 2 (20% o clozapine (pa icle size smalle han 125 μm) /40% HPMC 100000 cp/40% MCC). Figu e 4. Mic opho og aph co esponding o an uncu pelle om ba ch A (20% o clozapine (pa icle size smalle han 125 μm) /2% HPMC 4000 cp/78% MCC). Figu e 5. Mic opho og aph co esponding o he c oss sec ion o a cu pelle om ba ch A (20% o clozapine (pa icle size smalle han 125 μm)/2% HPMC 4000 cp/78% MCC). Figu e 6. Mic opho og aph co esponding o he c oss sec ion o a cu pelle om ba ch D (30% o clozapine (pa icle size bigge han 250 μm) /2% HPMC 4000 cp/68% MCC). Figu e 7. Pe cen age o clozapine eleased e sus ime o ba ches 1 o 9. Figu e 8. Pe cen age o clozapine eleased e sus ime o ba ches A o D, ha ing ba ches A and B 20% o d ug and ba ches C an D 30% o clozapine. Ba ches B and D con ain he coa ses pa icles o clozapine. TABLE 1. Composi ion and sphe onisa ion condi ions o he di e en ba ches manu ac u ed 1 2 3 4 5 6 7 8 9 A B C D Clozapine Mix u e Size ac ion: x < 125µm 125 < x < 250 µm x > 250 µm 20% 20% 20% 20% 30% 30% 30% 40% 20% 20% 20% 30% 30% HPMC 4000 cp 10% 2% 2% 2% 2% HPMC 100000 cp 40% 40% 40% 40% 40% 40% 40% 40% MCC 70% 40% 40% 40% 30% 30% 30% 20% 38.5% 78% 78% 68% 68% Mg s ea a e 1.5% G anula ion liquid (ml): E hanol/Wa e : (90%/10%) (85%/15%) (80%/20%) Dis illed wa e : 140 240 236 238 240 240 248 233 240 85 88 65 60 Sphe onisa ion Time (min) Speed ( pm) 3 1040 2 +1 a 1040 (1600) 2+1 a 1040 (1600) 2 1040 2+ 1.5 a 1040 (1600) 2+1 a 1040 (1600) 2+ 0.5 a 1040 (1600) 2+ 1 a 1040 (1460) 2 + 0.5 a 1040 (1460) 2 1040 2 1040 2 1040 2 1040 a Addi ional sphe onisa ion ime a he speed indica ed in pa en hesis TABLE 2 Densi ies o d ug and excipien s, Comp essibili y Index, Hausne Ra io, Res angle and Flowabili y Sample Bulk densi y a Tapped densi y a Comp essibili y Index a Hausne Ra io a Res angle a Flowabili y a (g/cm 3 ) (g/cm 3 ) ( 0 ) (g/s) MCC 0.335±0.003 0.477±0.002 29.65±0.99 1.42±0.02 0 HPMC 4000 cp 0.332±0.002 0.502±0.004 33.82±0.74 1.51±0.02 0 HPMC 100000 cp 0.310±0.003 0.493±0.006 37.28±0.12 1.59±0.00 0 Clozapine 36.67±2.67 79.04±2.11 a Mean alue ± s anda de ia ion ( h ee eplica es) TABLE 3 Mal e n ® pa icle size analysis da a o Clozapine, MCC, HPMC 4000 cp and HPMC 100000 cp powde s Ma e ial D ( ,0.1) a D ( ,0.5) b D ( ,0.9) c Clozapine 6.26±0.30 58.28±3.12 205.13±3.75 MCC 18.96±0.25 59.3±0.37 135.7±1.05 HPMC 4000 cp 22.36±0.14 72.53±0.25 181.6±1.20 HPMC 100000 cp 23.89±0.16 75.85±0.20 179.76±1.45 a Mean ± s anda d de ia ion (n = 2) o he pe cen ile 10 o he olume diame e o pa icles b Mean ± s anda d de ia ion (n = 2) o he pe cen ile 50 o he olume diame e o pa icles c Mean ± s anda d de ia ion (n = 2) o he pe cen ile 90 o he olume diame e o pa icles TABLE 4. Pelle s Mean Diame e (mm) and sphe ici y index Ba ch 1 Ba ch 2 Ba ch 3 Ba ch 4 Ba ch 5 Ba ch 6 Ba ch 7 Ba ch 8 Ba ch 9 Ba ch A Ba ch B Ba ch C Ba ch D Pelle mean diame e (mm) Mean 1.159 0.966 1.003 0.898 0.911 0.941 0.943 0.989 1.009 0.979 0.991 1.042 0.992 S.D. 0.200 0.144 0.173 0.123 0.121 0.104 0.147 0.139 0.123 0.122 0.118 0.093 0.107 Pelle sphe ici y index a Mean 0.698 0.668 0.651 0.699 0.673 0.717 0.656 0.628 0.613 0.771 0.792 0.812 0.801 S.D. 0.133 0.108 0.134 0.118 0.115 0.102 0.129 0.119 0.116 0.096 0.097 0.078 0.081 a Calcula ed as he mean a io be ween he smalles and he la ges diame e o 75 pelle s TABLE 5. Ma hema ical modelling and d ug elease kine ics om pelle s o he di e en ba ches a Higuchi elease a e cons an , b Ko smeye ’s kine ic cons an , c Ko smeye ’s ime exponen , d Ze o o de kine ic cons an , e Fi s o de kine ic cons an ; Peppas di usion kine ic cons an ; g Peppas elaxa ion kine ic cons an ; h De e mina ion coe icien . Ba ch Higuchi Ko smeye Ze o o de Fi s O de Peppas and Sahlin b a (min - 0. 5 ) 2 h k k b (min - n ) n c 2 h k 0 d (min - 1 ) 2 h k 1 e (min - 1 ) 2 h k d (min - 0.425 ) k g (min - 0.850 ) 2 h 1 0.135 0.948 0.089 0.614 0.806 0.021 0.905 0.028 0.772 0.098 0.017 0.953 2 0.075 0.873 0.127 0.422 0.847 0.005 0.682 0.006 0.573 0.190 -0.009 0.933 3 0.044 0.919 0.145 0.328 0.922 0.002 0.754 0.003 0.665 0.128 -0.004 0.985 4 0.062 0.855 0.176 0.333 0.838 0.004 0.652 0.004 0.574 0.184 -0.009 0.950 5 0.076 0.926 0.002 1.294 0.655 0.005 0.809 0.014 0.357 0.125 0.000 0.926 6 0.100 0.925 0.001 1.468 0.720 0.009 0.918 0.026 0.482 0.038 0.013 0.942 7 0.090 0.977 0.105 0.479 0.947 0.008 0.838 0.010 0.756 0.145 -0.002 0.986 8 0.099 0.981 0.035 0.730 0.984 0.009 0.954 0.018 0.838 0.058 0.012 0.991 9 0.106 0.941 0.011 1.019 0.904 0.009 0.901 0.021 0.665 0.069 0.011 0.945 A 0.141 0.958 0.050 0.790 0.893 0.022 0.949 0.035 0.808 0.058 0.027 0.975 B 0.102 0.985 0.069 0.597 0.969 0.010 0.874 0.015 0.771 0.115 0.004 0.982 C 0.127 0.970 0.057 0.712 0.920 0.017 0.934 0.027 0.814 0.080 0.017 0.977 D 0.116 0.988 0.083 0.588 0.963 0.014 0.906 0.019 0.837 0.115 0.008 0.987