Cover Page. The handle holds various files of this Leiden University dissertation

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1 Cover Pge The hndle holds vrious files of this Leiden University disserttion Author: Olofsen, E. Title: Phrmcokinetic nd phrmcodynmic nlysis in nesthesi : modeling odyssey Issue Dte:

2 Chpter 4 Stochstic Phrmcokinetic-Phrmcodynmic Anlysis of the Effect of Trnsderml Buprenorphine on Electroencephlogrm nd Anlgesi* Opioids re used widely in the tretment of moderte-to-severe cncer nd noncncer pin. 91 There re currently 2 monumentl chllenges in the tretment of chronic pin: the objective ssessment of opioid effect in setting in which buse nd ccidentl overdose is highly prevlent nd the need for proper dosing strtegies. The efficcy of opioids nd other centrlly cting nlgesics often is determined rther subjectively by the use of quntittive sensory testing, questionnires, nd so on. 59 To determine suitble objective biomrker s mesure of opioid drug effect is chllenging. One possibility is the electroencephlogrphy (EEG), which is widely vilble nd noninvsive tool for recording brinwve ctivity simultneously from multiple brin regions. Severl drug clsses tht ct on the centrl nervous system generte reproducible effect on the EEG obtined t rest. 46,5 For exmple, Liley et l. 48 showed tht the effect of remifentnil on frontlly recorded resting EEG could be dissocited from the EEG effects of propofol, n nesthetic cting t different receptor trget in the centrl nervous system. The EEG is therefore of gret interest in evluting the effect of drugs used in nesthesi nd pin tretment. Becuse opioid effects re delyed reltive to their plsm concentrtion profile, becuse of the time needed to rech nd interct with the opioid receptors, phrmcokinetic-phrmcodynmic (PK-PD) nlysis my be used. 49,52 PK-PD nlysis links dose to effect nd mkes it possible to tke inter- nd intrindividul vribility into considertion when designing pproprite dosing strtegies. 52 Indeed, drug-induced EEG effect cn produce dynmic outcome pplicble in PK-PD modeling, which my be * A E Olesen, E Olofsen, T Andresen, C Grversen, A M Drewes, A Dhn, Anesth Anlg 215; 121:

3 46 Chpter 4 used to determine popultion-predicted vlues for dose nd effect, leding to more rtionl pproch for effective dosing regimens. In the current study, we ssessed the effect of trnsderml buprenorphine on the resting EEG nd experimentl pin in helthy volunteers to elucidte the PK-PD profile of trnsderml buprenorphine. Trnsderml buprenorphine is n ppeling tretment for chronic pin, becuse it is n gonist for nlgesi but prtil gonist for respirtory depression over its clinicl dose rnge. 26,25 Modeling the effect of n opioid given by trnsderml ptch should consider the possibility tht the bsorption rte my not be constnt. For exmple, chnges in skin temperture my led to chnges in drug bsorption from the ptch. 56 Hence, the PK-PD model tht we pply should tke into ccount vrible uptke of drug from ptch or derml reservoir. Here, we pplied stochstic PK-PD technique tht ccounts for vrying drug bsorption s first described by Tornøe et l. 89 We previously pplied stochstic PK-PD (SPKPD) model to ssess the effect of ketmine on crdic output nd chronic pin relief. 64,24 We mesured 2 opioid effects: pin relief nd chnges in EEG. Rther thn using conventionl indices derived from the EEG, such s spectrl edge, medin frequency, pek frequency, or power spectrum, we used the rtio of slow-to-fst EEG frequencies s biomrker for opioid effect. Dichotomizing the frequency spectrum into low- nd high-frequency components hs the dvntge in tht it compenstes for interindividul vribility in the frequency distributions nd minimizes the number of EEG fetures trditionlly obtined from the vrious frequency bnds. 88 We hypothesize (1) tht the resting EEG is relible nd objective surrogte for buprenorphine s effect nd (2) tht SPKPD nlysis llows the computtion of the timedependent vribility in drug bsorption from ptch to blood. Our pproch will led to better understnding of the behvior of the ptch. 4.1 Methods This double-blind, rndomized, plcebo-controlled, crossover study ws pproved by the North Denmrk Region Committee on Helth Reserch Ethics nd the Dnish Helth nd Medicines Authority nd registered t CliniclTrils.gov under number NCT The study ws performed ccording to the principles of Good Clinicl Prctice of the Europen Union from June 28 until August 29 in the reserch lbortories of Mech-Sense, Alborg University Hospitl, Denmrk, nd ll subjects gve written informed consent. Descriptions nd nlyses of portion of the dt were reported previously. 6,5,7,33,81,82 These reports include dt on the effect of buprenorphine nd fentnyl on evoked potentils, nlgesi, nd ntihyperlgesi using set of nociceptive tests (including pressure pin, ultrviolet B light burn injury, intrderml cpsicininduced hyperlgesi, nd conditioned pin modultion) Study Design Twenty-two helthy, opioid-nive mle volunteers (men ge 23.1 ± 3.8 yers) were recruited to prticipte in the study. Subjects received trnsderml ptch (Norspn TM 144-h; Norphrm, Vedbæk, Denmrk) or plcebo ptch (Norphrm) identicl in ppernce for 144 hours, followed, fter removl of the ptch, by 3-dy follow-up period.

4 Chpter 4 47 A wshout period of 1 dys ws observed between tretments. The subjects were hospitlized during the tretment phse, with regulr ssessments of blood pressure, hert rte, respirtory rte, nd oxygen sturtion. An independent phrmcist performed the rndomiztion using n electronic rndomiztion list downloded from rndomiztion.com. Smple size clcultion ws bsed on previous studies on the influence of opioids on experimentl het pin nd ws used to set the number of subjects to detect n effect in these previous descriptive studies. 81,82 To show n increse in pin tolernce threshold of 2 C (with power of 9%, SD = 1.7 nd α =.5), 16 subjects re required in ech group. Tken into ccount the vribility nd possible loss of dt, the number in ech group ws incresed to 22. Blood Smpling nd Buprenorphine Assy Nine microliters of venous blood smples were collected in EDTA blood collection tubes t bseline nd 6, 9, 12, 24, 36, 48, 6, 72, 78, 84, 96, 12, 144, 168, 192, nd 216 hours fter ppliction of the ptches. The blood smples were immeditely centrifuged t 4 C t 3 rpm for 15 minutes. Next, plsm ws seprted into two 2-mL polypropylene tubes (the second smple served s duplicte). Both tubes were stored t -8 C until nlysis. The buprenorphine nlysis hs been published before. 6 Therml Cutneous Stimultion The response to noxious therml stimulus ws obtined t bseline nd 24, 48, 72, nd 144 hours fter ppliction of the ptches. Pin ws pplied using thermode (TSA II NeuroSensory Anlyser; Medoc Ltd, Rmt Yishi, Isrel) pplied to the right volr forerm. The temperture incresed from bseline of 32 C to mximum of 52 C with rte of 1 C/s. The subject pressed button on reching the het pin tolernce threshold. Three consecutive stimultions were performed, nd the verge ws computed. All subjects were fmilirized with the procedure before the study. The Electroencephlogrm The resting EEG ws recorded t bseline nd 4, 24, 48, 72, nd 144 hours fter ppliction of the ptches. An EEG mplifier (NuAmp; Neuroscn, El Pso, TX) ws used to record the electricl ctivity on the sclp. Two electrodes were plced t Cz nd CPz loctions ccording to the interntionl 1-2 system. In ddition, one electrode ws mounted t the right erlobe serving s reference, wheres one electrode ws plced 2 cm frontl to the Cz electrode serving s ground electrode. The electrodes were mounted using electrode gel to reduce the impednce to < 5 kω, nd the positions of the electrodes were mintined during the experiment by using n elstic fixtion cp (Crefix Hed, Ikst, Denmrk). The EEG dt were recorded with smpling rte of 1 khz. The dt were recorded with n online notch filter t 5 Hz nd bnd pss filter with cutoff frequencies of.5 nd 3 Hz. Resting EEG recordings were obtined fter pin tests nd blood smpling by reserch nurse in quiet room with dimmed light s prticipnts ly in supine position with eyes open. The EEG signls were processed off-line. The processing included the following steps: (1) Artifct rejection by visul inspection, leving t lest 1 minute of vlid recording for further nlysis (Neuroscn version 4.3.1; Compumedics, El Pso, TX); nd (2) high-pss

5 48 Chpter 4 filtering to remove DC offset nd liner detrending by first-order Butterworth filter with cutoff frequency.5 Hz performed in MATLAB (The MthWorks Inc., Ntick, MA) Dt Anlysis EEG Anlysis: Time-Frequency Anlysis Time-frequency nlysis cn be pplied in severl wys; recent studies showed tht continuous wvelet trnsform (CWT) is dvntgeous over more trditionl methods such s the Fourier trnsform. 3 The CWT is bsed on mother wvelet function, which ws complex Morlet wvelet for the current study. 7,84,35,27 The time-frequency coefficients of the Cz EEG chnnel were rectified nd integrted over time to obtin the mrginl distribution in the frequency bnds: δ ( Hz), θ ( Hz), α 1 ( Hz), α 2 ( Hz), β 1 ( Hz), β 2 ( Hz), nd β 3 ( Hz). The frequency bnds were normlized into percentge of the totl power (.5-32 Hz). An EEG rtio ws used to evlute the results. The EEG rtio ws defined s the percentge sum of the slow conducting frequency bnds (δ + θ + α 1 ) divided by the percentge sum of the fst conducting frequency bnds (α 2 + β 1 + β 2 + β 3 ). Stochstic Model for Buprenorphine Absorption We ssume tht the bsorption rte of buprenorphine from ptch into the disposition comprtment vried over time; see Figure 4.1. The noise in the bsorption (i.e., process noise) ws modeled using the following stochstic differentil equtions: 89,64,24,9,61,53,42 da (t)/dt = k (t) A (t) (4.1) da d (t)/dt = k (t) A (t) k e (t) A d (t) (4.2) k (t) = exp(z(t)) (4.3) dz(t) = σ w dw(t), (4.4) where A (t) is mount of drug in the bsorption comprtment t time t (A () = 2 mg), A d (t) is the mount of drug in the disposition comprtment, k (t) is the bsorption rte (set to zero when the ptch is removed), k e (t) is the elimintion rte constnt, Z is link vrible, w(t) is the Wiener process, nd σ w is the stndrd devition of chnges in Z(t) per the squre root of time (i.e., σ w is the vribility in the bsorption rte constnt in the log domin). A Wiener process is model of Brownin rndom motion resulting from sum of mny smll normlly distributed fluctutions. 32 This prmeteriztion constrins k (t) to be positive; k (t = ) is vrible to be estimted. The buprenorphine concentrtion is given by the rtio of A d nd the volume of distribution, V d. Phrmcodynmic (PD) Anlysis The PD prt of the models ssumes n effect comprtment in which the drug ppers with dely: dc e (t)/dt = k e (C d (t) C e (t)) (4.5)

6 Chpter 4 49 ν C bup Effect Ptch k V d Effect Site k el k e ν e Figure 4.1: Schemtic representtion of the stochstic phrmcokineticphrmcodynmic model, in which the phrmcokinetic prt consists of the trnsfer of drug from ptch to disposition comprtment V d with rte constnt k. Fluctutions in k re modeled by noise process ν. V d is linked to the effect-site comprtment. k e is the blood effect-site equilibrtion constnt; possible fluctutions re modeled by noise process ν e. where C d (t) is the drug concentrtion in the disposition comprtment t time t, C e (t) is the effect-site concentrtion t time t, nd k e is the blood effect-site equilibrtion rte constnt. The PD effect (EF) ws ssumed to be relted to C e (t): EF(t) = BLN (1 + (C e (t)/c 1 ) γ ) (4.6) where BLN is the bseline vlue, C 1 is the effect-site concentrtion cusing 1% increse in surrogte effect mesure, nd γ is shpe prmeter. Finlly, n dditionl stochstic differentil eqution for k e ws tested. Sttisticl Anlysis The popultion phrmcokinetic-phrmcokinetic (PK-PD) nlyses were performed by implementing the models in the sttisticl softwre pckge NONMEM (version VII, level 2; Icon Development Solutions, Hnover, MD). For the SPKPD nlysis, n extended Klmn filter ws incorported. 9,61,53,42 NONMEM s subroutine ADVAN13 ws used to integrte drug mounts in bsorption, disposition, nd effect comprtments nd dditionl Klmn filter stte vribles. PK nd PD dt were nlyzed simultneously. The 2 PD dt sets were nlyzed seprtely (PK/resting EEG, PK/skin pin tolernce). Residul error ws ssumed to hve both n dditive nd reltive error for concentrtions nd only n dditive error term for the PD end points. Goodness-of-fit plots were creted for the PK nd PD dt to check for model dequcy nd possible outliers. P vlues <.1 were considered significnt. 4.2 Results EEG Spectrum nd Pin Response EEG dt were not vilble from 3 subjects becuse of technicl problems with the EEG equipment. These subjects did provide pin dt. The men ge of the subjects (± SD, n = 22) ws 22.5 ± 1.8 yers, men height ± 5.8 cm, nd men weight 73.3 ± 7.4 kg.

7 5 Chpter 4 Figure 4.2 displys the impct of buprenorphine nd plcebo on the spectrl distribution of the EEG t bseline nd fter 72 hours of ptch ppliction. Figure 4.2E shows greter shift from fst to slow ctivity of the EEG spectrum in the buprenorphine group fter 72 hours (dotted nd solid red lines) thn in the bseline group (dotted nd solid blue lines). The bsolute nd reltive individul nd verge EEG rtio nd pin tolernce dt re given in Figures 4.3 nd 4.4. Compred with plcebo, buprenorphine incresed EEG rtio by.2 to.3 points (pired t test: P =.6 t t = 48 hours; P =.6 t 72 hours; P =.1 t 144 hours) nd het pin tolernce threshold by 1 to 2 C (pired t test: P =.8 t 48 hours; P =.5 t 72 hours; P =.3 t 144 hours) PK-PD Anlysis The individul nd verge plsm buprenorphine concentrtions re given in Figure 4.3E nd Figure 4.3F. A seprte PK-PD nlysis ws performed on the PK/resting EEG rtio dt nd the PK/skin pin tolernce dt. In none of the nlyses, prmeter γ ws significntly different from 1, indicting tht the PD effect ws linerly relted to the buprenorphine effect-site concentrtion. PK Anlysis The PK prmeters re given in Tble 4.1. The initil vlue for the bsorption rte constnt (k ) ws.5 h -1, elimintion rte constnt.4 h -1, nd volume of distribution 11 L. Similrly, the stndrd devition of the noise of the bsorption process nd stndrd devitions nd residul errors were of similr mgnitude between nlyses (σ w.11 1/ h, σ 1.1 ng/ml, nd σ 2.14). The vribility in the bsorption rte is quntified by σ w, indicting tht k vries by.11 per hour nd, for exmple, will rnge between pproximtely.3 h -1 nd.8 h -1 fter 1 hours of the ptch ppliction if no informtion vi PK or PD smples is obtined. PK goodness-of-fit plots re given in Figure 4.5, nd exmples of PK dt fits re given in Figure Figure 4.6, (pnels G, H, nd I). Both show tht the SPKPD model dequtely described the PK dt. For none of the PK prmeters ws interindividul error estimble, which indictes tht the vribility in the prmeter estimtes ws minly cused by within-subject, rther thn between-subject, vribility. In none of the subjects did drug bsorption remin constnt during the 144-hour buprenorphine tretment, s observed by the fluctutions in k over time (Figure 4.6, pnels J, K, nd L). PD Anlysis Exmples of PD dt fits re given in Figure 4.6 (pnels A-C nd D-F). For EEG rtio, the best, medin, nd worst fits re given s bsed on the coefficient of determintion (R2). Note tht negtive vlue for R2 ws observed for the worst fit, indicting tht the fit is worse thn just using the men of the dt. PD prmeter estimtes re given in Tble 4.1. For ll dt fits, the 95% confidence intervls were clculted (broken lines in Figure 4.6). These intervls re bsed on both the mesurement nd the prediction errors nd my therefore vry in time, depending on the informtion obtined from the mesurements (PK or PD), which is fed bck to the stochstic differentil equtions of

8 Chpter 4 51 Figure 4.2: A-E: Exmples from one subject of the spectrl distribution of the resting electroencephlogrphy mesurement t bseline (A nd B) nd fter 72 hours of plcebo (C) nd buprenorphine (D). A shift is visible fter 72 h of buprenorphine tretment from fst towrd slow oscilltions. E: Frequency versus bsolute ctivity for buprenorphine nd plcebo tretment t bseline nd 72 h. Absolute ctivity ws clculted by continuous wvelet trnsform using complex Morlet function with bndwidth prmeter of 128 Hz nd wvelet center frequency of.5 Hz.

9 52 Chpter 4 EEG rtio A B buprenorphine plcebo EEG rtio Het pin tolernce ( C) C D buprenorphine plcebo Het pin tolernce ( C).5 E F.5 Cbup (ng/ml) Cbup (ng/ml) Figure 4.3: Individul dt (A) nd verges (B) of the effect of 144 h (6 dy) dministrtion of buprenorphine by trnsderml ptch on the electroencephlogrphy (EEG) rtio. In pnel B, the plcebo verges re given. Over time buprenorphine incresed the EEG rtio significntly compred with plcebo. Individul dt (C) nd verges (D) of the effect of the 144 h buprenorphine ptch on skin het pin tolernce (units C). In pnel D, the plcebo verges re included. Over time buprenorphine incresed skin het pin tolernce significntly compred with plcebo. Individul (E) nd verge (F) buprenorphine plsm concentrtions during nd 2.5 dys fter the buprenorphine ptch ppliction. In pnels A, C, nd E, ech line represents one subject; in pnels B, D, nd F, the dt re men ± SEM.

10 Chpter 4 53 A B.5 EEG rtio C D Het pin tolernce ( C) Figure 4.4: A-D: Individul nd verge electroencephlogrphy rtio nd pin tolernce reltive to bseline vlues. A. Popultion B. Individul Mesured/predicted Figure 4.5: Phrmcokinetic goodness-of-fit plots. A: Mesured versus popultionpredicted plsm buprenorphine concentrtions. B: Mesured versus individul predicted plsm buprenorphine concentrtions.

11 54 Chpter 4 ID = 9 ID = 4 ID = A (R 2 = -2.5) B (R 2 =.66) C (R 2 =.96) EEG rtio Het pin tolernce ( C) D (R 2 = -.42) G E (R 2 =.83) H F (R 2 = -.8) I Cbup (ng/ml) J K L k (h -1 ) Figure 4.6: Best (A), medin (B), nd (C) worst dt fits of the electroencephlogrphy (EEG) rtio nd corresponding dt fits of skin het pin tolernce (D, E, nd F), nd plsm buprenorphine concentrtion (G, H, nd I). Goodness of fit ws bsed on the coefficient of determintion (R 2 ). The bottom grphs (J, K, nd L) depict the chnging bsorption rte constnt (k ) over time. The blck dots re the mesured dt; the continuous lines re the dt fit; nd the broken lines re the 95% confidence intervls; in pnels G-I, the dotted lines re the buprenorphine effect-site concentrtions (derived from EEG dt). Note tht t t = 144 h the ptch ws removed (k set to ).

12 Chpter 4 55 Tble 4.1: Prmeter Estimtes of the SPKPD Anlysis Resting EEG rtio Het pin tolernce Prmeter Estimte ± SEE ω 2 ± SEE Estimte ± SEE ω 2 ± SEE k (h -1 ).5 ±.1.5 ±.1 k e (h -1 ).4 ±.2.4 ±.2 V d (L) b 11.6 ± ±.9 σ w (1/ h).11 ±.1.11 ±.1 σ 1 (ng/ml).1 ±.3.1 ±.3 σ 2.14 ±.3.14 ±.3 BLN c 1.18 ±.6.3 ± ±.6.2 ±.6 t ½,ke (h) 24.8 ± 8.7 ±.4 C 1 (ng/ml).9 ± ± 2.5 σ 3.11 ± ±.2 SPKPD = stochstic phrmcodynmic-phrmcodynmics; EEG = electroencephlogrphy; SEE = stndrd error of estimte; ω 2 = between-subject vribility (in the log-domin); k = initil bsorption rte constnt, i.e., t t = ; k e = elimintion rte constnt; V d = volume of distribution; σ w = stndrd devition of the noise process (Z in Equtions (4.3) nd (4.4)); σ 1 nd σ 2 = stndrd devitions of dditive nd reltive error; respectively, for the concentrtion estimtes; BLN = bseline vlue; t ½,ke = blood effect-site equilibrtion hlf-life; C 1 = effect-site concentrtion cusing 1% increse (i.e., doubling) in effect; σ 3 = dditive error for the effect estimtes with unit for pin tolernce C; Not estimble; b V d vlues re reltive to the buprenorphine biovilbility (it is ssumed tht 1% of the buprenorphine bsorbed from the ptch becomes systemiclly vilble); c Unit for BLN pin tolernce is C.

13 56 Chpter A. EEG rtio B. Het pin tolernce ( C) 55 Mesured Mesured Pop. predicted Pop. predicted 2.5 C. EEG rtio D. Het pin tolernce ( C) 55 Mesured Mesured Ind. predicted Ind. predicted Figure 4.7: Phrmcodynmic goodness-of-fit plots. A nd C, Mesured electroencephlogrphy (EEG) rtio versus individul-predicted nd popultion-predicted EEG rtio. B nd D, Mesured skin het pin tolernce (units C) versus individulpredicted nd popultion-predicted skin het pin tolernce. the model. 9 The updted sttes of the differentil equtions cn be seen s sudden updtes of the estimted bsorption rtes, concentrtions, nd PD end points. Goodness-of-fit plots re given in Figures 4.7 to 4.9. Figure 4.7 shows the mesured versus popultion-predicted (Fig. 4.7A, EEG rtio; nd Fig. 4.7B, het pin tolernce) nd mesured versus individul-predicted (Fig. 4.7C, EEG rtio; nd Fig. 4.7D, het pin tolernce) dt. Figure 4.8 shows the spghetti plots for EEG rtio error (Fig. 4.8A) nd het pin tolernce error (Fig. 4.8B). Figure 4.9 gives the log-likelihood profiles of the (PK nd PD) model prmeters. The objective function is most sensitive to chnges in prmeter BLN (EEG rtio, Fig. 4.9E; nd het pin tolernce, Fig. 4.9F) nd lest sensitive to chnges in t ½,ke (hlf-life from k e ) (EEG rtio, Fig. 4.9C). A bootstrp nlysis (1 simultions drwing rndom smples from the subject pool) ws performed to ssess the sensitivity of the model output to exclude subjects from the dt set (dt not shown). The results show tht excluding subjects did not result in systemtic chnges in prmeter vlues. Overll, the inspection of the dt fits nd dignostic plots indictes tht the SPKPD dequtely described the dt.

14 Chpter 4 57 EEG rtio error A B Het pin tolernce error ( C) Figure 4.8: Spghetti plots for electroencephlogrphy rtio (A) nd pin tolernce (B) showing residul error versus time. Hysteresis In Figure 4.1, exmples of buprenorphine plsm concentrtion versus effect re plotted nd show tht no significnt hysteresis ws detected for pin tolernce. In contrst, significnt hysteresis ws observed for EEG rtio, with vlue for prmeter t ½,ke of 24 ± 8 hours. The log-likelihood profile of prmeter t ½,ke shows rther flt surfce profile with vlues tht rnge from -5% to +1% of the optiml estimte within its 95% confidence intervl (Fig. 4.9C). Removl of prmeter t ½,ke from the model resulted in n increse of Objective Function Vlue > 2 points. A stochstic differentil eqution to ccount for fluctutions of k e did not improve the dt fits. Hence, this pproch ws discrded. EEG Rtio versus Het Pin Tolernce The EEG rtio ws more sensitive to buprenorphine thn skin pin tolernce, with 1 ± 3 (men ± SE) times greter potency: resting EEG rtio C 1 =.9 ±.1 ng/ml versus EEG rtio C 1 = 9.1 ± 1.9 ng/ml. To get n indiction of whether the EEG is good predictor of het pin tolernce, the 2 PD models were coupled vi their corresponding plsm concentrtions (obtined from tking the mesurement vribility σ, into ccount). Figure 4.11 shows tht the EEG predicts het pin tolernce with cceptble uncertinty compred with the skin test when coupling the PD models to their corresponding plsm concentrtions. 4.3 Discussion Our min findings re tht the EEG rtio cn be used s surrogte mesure of buprenorphine effect nd tht the SPKPD nlysis, which includes trcking nd updte fetures, llowed the computtion of the time-dependent vribility in drug bsorption from ptch to blood. Both results confirm our study hypotheses. We demonstrted tht buprenorphine s bsorption vried over time, rnging from -4% to +6% of bseline

15 58 Chpter 4 OFV chnge A. k OFV chnge B. k e C. t 1 2,k e OFV chnge D. V d E. BLN F. BLN OFV chnge G. σ w H. C 1 EEG rtio I. C 1 Het pin Prmeter chnge Prmeter chnge Prmeter chnge Figure 4.9: Likelihood profiles showing the chnge in objective function versus reltive chnge in the denoted prmeter (A-I) while estimting the remining prmeters. The dshed line denotes chnge of 3.84 points in objective function (OFV), indicting the P =.5 level. The crossings of the likelihood profiles with the dshed lines give prmeter rnge corresponding to 95% confidence intervl. (A) k is the buprenorphine bsorption rte; (B) k e is the buprenorphine elimintion rte constnt; (C) t ½,ke is the blood effect-site equilibrtion constnt; (D) V d is the volume of distribution; (E) Bseline (BLN) is the electroencephlogrphy (EEG) rtio bseline estimte; (F) BLN is the het pin tolernce bseline estimte; (G) σ w is the vribility in the bsorption rte constnt in the log domin; (H) C 1 is the effect-site concentrtion cusing 1% increse in EEG rtio; (I) C 1 is the effect-site concentrtion cusing 1% increse in het pin tolernce.

16 Chpter A B C EEG rtio Het pin tolernce ( C) D E F C bup (ng/ml) C bup (ng/ml) C bup (ng/ml) Figure 4.1: Rndom exmples of effect versus plsm concentrtion for electroencephlogrphy rtio (A-C) nd pin tolernce (D-F). Ech pnel represents the dt of one subject. Het pin tolernce ( C) EEG rtio Figure 4.11: Reltionship between the electroencephlogrphy rtio nd het pin tolernce s derived from the 2 stochstic phrmcokinetic-phrmcodynmic (SPKPD) nlyses. Shown is the medin ± 1 SD.

17 6 Chpter 4 bsorption, nd tht buprenorphine s effect on the EEG rtio is 1 times more sensitive thn buprenorphine s effect on dulling noxious skin stimuli Vritions in Absorption Rte The het pin tolernce dt were previously nlyzed by Andresen et l. 6 The input to their PD model consisted of cubic splines fitted to the mesured concentrtions becuse no PK model could be found to dequtely describe trnsderml drug delivery. Although splines give smooth curves, they cnnot correct for mesurement error, which my result in possibly mplified errors of the interpolted vlues. Although the structurl PK model tht we pplied my be simple, it provides the PD model with interpolted concentrtion vlues bsed on best estimtes of drug bsorption nd disposition t the smpling times of the effect prmeters. Tornøe et l. 89 were the first to model subcutneous drug bsorption with vrying bsorption rte. In the current study, we nlyzed trnsderml drug bsorption using n pproch similr to theirs. Assuming tht the relese of drug from the ptch is constnt over time, vritions in drug bsorption from the skin my be relted to diurnl chnges in locl skin blood flow becuse of fluctutions in skin temperture, crdic output, nd mbient temperture. For exmple, the drug lbel for buprenorphine wrns ptients to void exposing the ptch to externl het. For the fentnyl trnsderml ptch, het-relted toxicity hs been described nd ws relted to significnt (25%- 3%) increse in plsm fentnyl concentrtion becuse of n incresed drug relese from the ptch. 56 In our study, it is unknown whether the k fluctutions ffected our PD outcome significntly. Theoreticlly, quntifying the fluctutions in k by modeling, the process noise could increse the precision of the estimte of the onset nd offset of effect. However, the design of our study prohibited the precise estimtion of t ½,ke. For het pin tolernce, no hysteresis between plsm concentrtion nd effect ws detected, nd for EEG rtio, the log-likelihood profile of t ½,ke exhibits rther lrge 95% confidence intervl (12-48 hours), indicting tht the support for hysteresis is limited. Still, excluding this prmeter from the model hd significnt negtive effect on the objective function vlue, which suggests tht the slow distribution of buprenorphine from plsm to brin is detectble in the EEG dt. It is of interest to note tht Andresen et l. 6 found direct nd liner effect of buprenorphine on het pin tolernce similr to our observtions EEG Rtio s Biomrker of Opioid Effect The response to skin het pin test is quite subjective, wheres the resting EEG is more objective mesure of drug effect. 59 This is the first study to ssess the effect of the long-term dministrtion of n opioid on the EEG nd prticulrly on the EEG rtio. Most studies on the effect of opioids on resting EEG use Fst Fourier Trnsform to convert the rw EEG signl into quntifible mesures, such s spectrl edge nd medin frequency. 49 Severl of these studies show tht slowing of the frequency of the EEG reflects nrcotic or sedtive drug effect. 46,49,73,66 In the current study, CWT ws used to extrct informtion from the rw EEG signl, followed by the evlution of multiple frequency bnds combined in single EEG rtio. The design of the wvelet

18 Chpter 4 61 nlysis ws chosen to be comprble with previous studies on nlgesic effect nd resting EEG. 35,34 The rtionle for using n EEG rtio is tht opioids produce high-voltge corticl bursts ssocited with increses in EEG spectrl power in predominntly the lowfrequency rnge (-1 Hz). 99 However, the frequency-specific ltertions in corticl EEG oscilltions depend on the receptor type tht is ctivted. 99 Becuse buprenorphine is mixed gonist-ntgonist opioid receptor modultor (i.e., cting t multiple opioid receptors), it seems more rtionl to ssess the entire frequency rnge rther thn the individul frequency bnds independently. In ddition, becuse the EEG power between subjects vries considerbly, opioids my cuse lrger effects in some subjects (e.g., subjects with n initil higher power). Using the rtio of the normlized EEG spectrl distribution prtly cncels out such bis, s the EEG rtio ssesses the reltive distribution between low- nd high-frequency oscilltions nd quntifies how this blnce is ltered by buprenorphine dministrtion in comprison with plcebo tretment. An interesting observtion in our study is tht the resting EEG effects were more sensitive to buprenorphine thn the pin responses, with just one-tenth of the concentrtion t the effect-site required for doubling of effect (C 1 ). This mkes the EEG rtio n ttrctive biomrker of opioid effect compred with pin intensity testing when mesuring the PD of opioid nlgesics, especilly when long-term dministrtions re tested. The findings on the effect of buprenorphine on the resting EEG rtio were obtined in helthy mle volunteers without codministrtion of sedtive hypnotic gents. For clinicl use, it would be interesting to investigte in future studies whether the rtio would still be detectble in the presence of potent IV or inhled nesthetic gent. Although the mechnisms behind codministrtion re not yet understood, severl recent studies hve been focused on this topic. Liley et l. 48 used fixed-order utoregressive moving verge model to nlyze EEG signls from 2 frontl electrodes nd found tht during the simultneous dministrtion of remifentnil nd propofol, incresing remifentnil concentrtions cused significnt chnges in the corticl EEG. In line with this, Kortelinen et l. 47 used the frequency spectrum from the Fz chnnel to seprte the effects of propofol nd remifentnil nd found the entire frequency rnge from 2 to 2 Hz to contribute to the remifentnil effect, lthough the low frequencies from 1 to 5 Hz showed the most discrimintive oscilltions. 4.4 Conclusions In this study, the effect of trnsderml buprenorphine on the corticl EEG (EEG rtio) nd on het pin tolernce ws investigted; the EEG rtio ws defined s (% slow frequency bnds, -1.5 Hz)/(% fst frequency bnds, Hz). We showed tht the EEG rtio is relible surrogte mesure of buprenorphine effect, with 1-fold greter sensitivity thn het pin tolernce. In ddition, we successfully nlyzed the dt with SPKPD model tht llowed us to compute the time-dependent vribility in drug bsorption from ptch to skin. The nlysis showed high vribility in bsorption, possibly relted to diurnl vritions in skin blood flow.

19 62 Chpter 4