Pharmacoresistance in epilepsy : modelling and prediction of disease progression

progression

Liefaard, C.

Citation

Liefaard, C. (2008, September 17). Pharmacoresistance in epilepsy : modelling and prediction of disease progression. Retrieved from https://hdl.handle.net/1887/13102

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Population pharmacokinetic analysis for simultaneous determination of B

and K

in vivo by positron emission tomography

Lia C. Liefaard^a, Bart A. Ploeger^ab, Carla F.M. Molthoff^c, Ronald Boellaard^c, Adriaan A. Lammertsma^c, Meindert Danhof^a, Rob A. Voskuyl^ad

aDivision of Pharmacology, LACDR, Leiden University, Leiden, The Netherlands

bLAP&P Consultants BV, Leiden, The Netherlands

cDepartment of Nuclear Medicine & PET Research, VU University Medical Center, Amsterdam, The Netherlands

dSEIN – Epilepsy Institutes of The Netherlands Foundation, Heemstede, The Netherlands

Mol Imaging Biol, 7(6):411–421, 2005 Summary

Purpose Changes in GABA_Areceptor density and affinity play an important role in many forms of epilepsy. A novel approach, using PET and [¹¹C]flumazenil, was developed for simultaneous estimation of GABA_Areceptor properties, characterised by B_maxand K_D.

Methods Following an injection of [¹¹C]flumazenil (dose range: 1–2000 μg) to 21 rats, concentration-time curves of flumazenil in brain (using PET) and blood (using HPLC-UV) were analysed simultaneously using a population pharmacokinetic (PK) model, containing expressions to describe the time-course of the plasma concentration (including distribution to the body), the brain distribution, and the specific binding within the brain.

Results Application of this method in control rats resulted in estimates of Bmax and KD

(14.5± 3.7 ng/ml and 4.68 ± 1.5 ng/ml respectively).

Conclusions The proposed population PK model allowed for simultaneous estimation of Bmax

and KDfor a group of animals using single injection PET experiments per animal.

5.1 Introduction

It has been well established that impairment of GABA

receptor mediated inhibition

plays a role in many forms of epilepsy.

Numerous pre– and postsynaptic alterations

can underlie a decrease in GABAergic transmission. Postsynaptic cell loss, decrease in

receptor density or alteration in structural or biophysical properties of the receptors

may contribute to generation of seizures.

These alterations may cause loss of efficacy

of anticonvulsant drugs in pharmacoresistant types of epilepsy. For example, there is

evidence for such a reduction in efficacy of benzodiazepines in different animal models

of epilepsy.

It is important to understand how changes in GABA

receptor properties are related to the natural course of epilepsy and how they contribute to the development of pharmacoresistance. That could enable the development of diagnostic tools for predicting the development of pharmacoresistance. In addition, it is essential for the design of effective therapies. Positron emission tomography (PET) is a powerful non-invasive technique to obtain receptor information in vivo. GABA

receptor properties can be studied using [

C]labelled flumazenil, which binds to the benzodiazepine binding site on the GABA

receptor complex. Moreover, high-resolution PET-scanners are now available which can be used for studies in small laboratory animals. This facilitates integration of information from mechanistic studies in experimental animal models with clinical studies in humans.

Different PET methods for in vivo quantification of benzodiazepine receptor properties using [

C]flumazenil have been reported. The method reported by Koeppe et al

provides a quantitative measure of the “ligand distribution volume”, which is related to the ratio of B

and K

. In order to obtain estimates of B

and K

separately, at least two different levels of receptor occupancy need to be investigated. Several studies have been published based on multiple scans with different amounts of unlabelled ligand in the same subject.

Delforge et al have described a complex multi-injection protocol to estimate the binding parameters in a single experimental session.

The partial saturation method, described by Delforge et al

is based on Scatchard analysis under nonequilibrium conditions. After administration of a dose, resulting in partial saturation of the receptor, a PET scan is acquired from which the range of bound ligand concentrations needed for Scatchard analysis is calculated. However, a recognised drawback of Scatchard analysis is the error sensitivity to the linear transformation used.

The method developed by Lassen et al

uses tracer kinetics under “steady state”

conditions and is based on comparison of two levels of receptor-occupancy, to estimate B

and K

. This requires 2 injections with a tracer amount of ligand on separate occasions. The first is given at 0% receptor occupancy and the second under a steady state condition of approximately 50% receptor occupancy, achieved by infusion of unlabelled flumazenil.

To determine the fraction of non-receptor bound radioligand, a reference tissue approach can be used.

This region should be devoid of receptors and have similar levels of free and non-specifically bound ligand as the target region. Nevertheless, the validity of this approach is questionable, because no region in the brain is entirely free of GABA

receptors.

The purpose of the present study was to develop a PET-approach that could be used for longitudinal studies on the development of epilepsy and related processes in rats.

As longitudinal studies require by nature repeated experiments and as rats need to be

immobilised by anaesthesia during scanning, the challenge was to minimise the number

of injections needed to estimate B

and K

separately. This can be achieved by taking

advantage of the short biological half-life of flumazenil in the rat, which is 8.3 minutes,

This means that flumazenil is very rapidly cleared from the body and that during a scan of 30 minutes nearly the whole range of receptor occupancies between 100 and 0% is covered.

In this study, a set of animals was investigated in which each animal received a single administration of [

C]flumazenil, but where across animals this dose varied over the entire range from tracer to saturating dose. After injection, the concentration- time courses of flumazenil in blood and brain were measured. Subsequently, the data of the entire study population were analysed simultaneously on the basis of a novel pharmacokinetic model with a specific expression to characterise specific binding in the brain, using non-linear mixed effects modelling. Non-linear mixed effects modelling, or population modelling, allow analysis of all data of all animals simultaneously, whilst still taking inter-individual variability into account. Thus, using this approach, individual estimates of different parameters can be obtained. A further advantage of population modelling is that also individuals with an incomplete dataset can be included in the analysis.

5.2 Methods

5.2.1 Production of [¹¹]flumazenil

[¹¹C]Flumazenil was produced according to the method as described by Maziere et al,²¹yielding a solution of 8–12 GBq of [¹¹C]flumazenil in a mixture of 1 ml of ethanol and 14 ml of 7.1 mM NaH2PO4 solution in saline with a specific activity of 33–850 GBq/μmol. Both chemical and radiochemical purity proved to be>99.8%.

5.2.2 Animals

Adult male Wistar rats (Harlan, Horst, The Netherlands), weighing 250–400 g were used. The animals were housed individually, at a constant temperature of 21^○C and a 12 hour light/dark cycle, in which the lights were switched on at 8 AM. Food (standard rat/mouse chow: SRM-A, Hope Farms, Woerden, The Netherlands) and water were available ad libitum.

Animal procedures were performed in accordance with Dutch laws on animal experimen- tation. All experiments were approved by the Ethics Committee for Animal Experiments of the

“Vrije Universiteit” in Amsterdam.

5.2.3 Specific uptake of [¹¹C]flumazenil in rats

In order to determine the feasibility of characterising specific [¹¹C]flumazenil binding, in a pilot experiment two rats were scanned under two different conditions. The first rat received an injection with a tracer amount of [¹¹C]flumazenil (37 MBq, 160 ng) via a canula implanted in the jugular vein. Subsequently, the rat was positioned in the PET camera with the head in the centre of the field of view (FOV) and scanned for 30 minutes.

The second rat received 100 μg unlabelled flumazenil (Anexate; Roche Nederland BV, The Netherlands) via a canula implanted in the jugular vein. After 10 minutes this rat was also injected with a tracer amount of [¹¹C]flumazenil (37 MBq, 700 ng). The rat was then positioned in the PET camera with the head in the centre of the FOV and was scanned for 30 minutes. The data were histogrammed on-line into a single frame of 1800 s and subsequently reconstructed as described below.

5.2.4 Scanning protocol

After anaesthetising the animals with ketamine base (Ketalar, Parke-Davis, Hoofddorp, The Netherlands, 1 μg/g body weight, subcutaneously (sc)) and medetomidine hydrochloride (Domitor, Pfizer, Capelle a/d IJssel, 0.1 μg/g body weight, intramuscular (im)), canulas were implanted in the jugular vein for administration of [¹¹C]flumazenil and the femoral artery for arterial blood sampling.

Two days after surgery, animals were scanned according to the following protocol. At first, rats were anaesthetised with ketamine base and medetomidine hydrochloride and positioned in the PET camera with their heads in the centre of the FOV. These anaesthetic drugs were chosen because they do not directly interfere with the GABA_A receptor complex.^{22, 23} Two rats were scanned together and placed side by side on a temperature pad, which kept the animals at 37^○C.

Subsequently, an intravenous (iv) bolus injection of [¹¹C]flumazenil, consisting of a mixture of [¹¹C]flumazenil (approximately 37 MBq) and unlabelled flumazenil, was given. The unlabelled flumazenil (Sigma Chemical Co., USA) was dissolved in 200 μl N,N-dimethylacetamide (Sigma Chemical Co., USA). After administration the exact total dosage of flumazenil was calculated, based on injected volume and injected amount of radioactivity, specific activity and activity concentration. These exact doses were used for data analysis. The following dosages of flumazenil were used (mean± SD): 1753 ± 3 μg (n = 2), 919 μg (n = 1), 477 ± 15 μg (n = 7), 89 ± 2 μg (n = 3), 47± 2 μg (n = 3), 26 ± 2 μg (n = 2), and 0.8 ± 0.1 μg (n = 6). In the results section the dosages will be indicated using the approximate values of 2000, 1000, 500, 100, 50, 25, and 1 μg.

Three animals were scanned twice at an interval of 2 days after administration of the following dose combinations (in order of administration): 474 and 1.06 μg, 462 and 919 μg, and 1750 and 0.63 μg. Thus in total 21 animals were used, resulting in 24 studies. This range was chosen based on results from Mandema et al, who showed that the effect of midazolam (a benzodiazepine) was completely inhibited by administration of 1.25 mg flumazenil, suggesting that 1.25 mg flumazenil could fully saturate the GABA_Areceptor complex.²⁴

All PET scans were obtained using a prototype single crystal layer 3D high-resolution research tomograph (HRRT) (CTI, Knoxville, TN), which was designed for small animal and human brain studies. The transaxial and axial resolutions were 2.7± 0.2 mm and 3.2 ± 0.2 mm full width at half maximum (FWHM) at the centre of the FOV. Scan duration was 30 min, based on the metabolic half-life of flumazenil (t_1/2= 8.3 min¹⁹). The performance characteristics of the scanner have been described elsewhere.²⁵

All emission data were acquired in 3D mode and rebinned into a 32-bit list mode file.

Subsequently, files were histogrammed off-line into 16 frames, with frame duration increasing from 15 up to 300 s.

A transmission scan was acquired using a 740 MBq ¹³⁷Cs point source for attenuation correction. For image reconstruction the transmission scan was first reconstructed and the resulting μ-image was scaled to correct for the difference in photon energy between emission (511 keV) and transmission (662 keV) scans. The scaled μ-image was then forward projected to obtain a 3D attenuation correction file, i.e., attenuation correction factors for all lines of response (LORs) of the 3D emission sinogram. Subsequently, the emission scan was multiplied with the attenuation correction file and normalised to correct for variation of sensitivity amongst all LORs. Dead time losses were less than 5%. Scatter correction was performed by a single scatter simulation algorithm.^{25, 26}Because the eight flat detector heads are arranged in an octagon, there were gaps of approximately 2 cm between each of the detector heads.^{25, 27} Consequently, data in sinograms exhibited gaps that needed to be filled prior to reconstruction. These gaps were

corrected for by angular and transaxial interpolation.^{25, 27}Fully corrected 3d emission scans were Fourier rebinned²⁸into 207 image planes of 1.21 mm, which were subsequently reconstructed by 2D filtered back projection (FBP).

During the experiment 11 blood samples (100 μl) were taken at t = 1, 2, 3, 5, 7, 10, 12, 15, 20, 25, and 30 min after injection, and immediately diluted with 0.5 ml 0.42% NaF in water at 0^○C to inhibit esterase activity and thus prevent flumazenil metabolism. Immediately after the experiment, samples were stored at -80^○C until the time of analysis.

5.2.5 Image analysis

In order to determine the activity-time curve of flumazenil in brain tissue, a region of interest (ROI) was placed over the cortex using the CAPP software package (version 7.2.1, CTI/Siemens, Knoxville, TN). The position of this ROI was defined visually on frame 5 (i.e., 60–75 s post injection, at the peak of the concentration-time curve). This ROI was projected onto all dynamic frames, which, after decay correction, resulted in an activity-time curve of [¹¹C]flumazenil. Using the injected amount of radioactivity and the exact total dosage of flumazenil, the specific activity of the injected total dose of flumazenil was calculated. From this specific activity, the concentration- time curve of total flumazenil in brain was obtained.

5.2.6 Drug analysis in blood

The blood concentrations of flumazenil were determined by HPLC using UV detection as described previously,¹⁹with the following modifications. The chromatographic system consisted of a Shimadzu LC-10AD solvent pump (Shimadzu, ’s Hertogenbosch, The Netherlands), a WISP 717plus automatic sample injector (Waters Associates, Milford, MA, USA), an Alltima C18 column (5 micron, 150 mm, 4.6 mm, of Alltima, Breda, The Netherlands), and a Spectroflow 757 spectrophotometer (Kratos, UV, Spark Holland B.V., Emmen, The Netherlands) set at 254 nm. The mobile phase consisted of a mixture of 25 mM phosphatebuffer (pH 7.5) and acetonitrile at a ratio of 45:55 with a flow rate of 1 ml/min. Retention times were 4.2 min for flumazenil and 10 min for nitrazepam (internal standard). Peak height was measured using a Shimadzu C-R3A integrator (Shimadzu, ’s Hertogenbosch, The Netherlands). The detection limit of the HPLC-UV analysis was 10 ng/ml. As the concentrations following injection of the lowest dosage were below the detection limit, these concentrations could not be measured.

5.2.7 Data analysis

The data were analysed by means of non-linear mixed effect (population) modelling. A population pharmacokinetic (PK) model consists of a structural PK model and a stochastic model. The structural PK model describes the relationship between the applied dose and the concentrations in blood and/or tissue in terms of structural PK parameters, e.g. clearance and volume of distribution. The stochastic model can be divided into 2 levels. The first level describes inter- individual variability (IIV) by assuming random variability of structural model parameters within the study population. The second level of random-effects describes the variability of the difference between observed and predicted responses. This residual error includes model misspecification, but also random intra-individual variability and measurement error. In the mixed-effects modelling approach, structural and stochastic parameters are simultaneously estimated by fitting the model to the data. The parameters (and their standard error, SE) that are estimated are the structural PK parameters, variance and covariance of all inter-individual variabilities and variance of each residual error. The precision of parameter estimation is assessed

Figure 5.1: The structural 4-compartment PK model. CB, CT, CBrF, CBrBare concentrations of flumazenil in blood, tissue, brain free and brain bound compartments, respectively. Ri n fis the zero-order administration rate. VC, VT, VBr are pharmacokinetic volumes of distribution of blood, tissue and brain compartments, respectively; k12, k21, k13, k31 describe exchange between compartments; kon, ko f f, Bmax describe specific binding; k10describes total elimination from the body.

by calculating the coefficient of variation in % (SE as percentage of the parameter estimate). As a result of fitting population-type models to the data, individual post hoc estimates of parameters associated with inter-individual variability can be obtained.

The user-written structural PK model consisted of a 4-compartment model as depicted in figure 5.1. The concentration-time profile of flumazenil in blood can be described by a two- compartment model,¹⁹ indicated here as “Blood” (equation 5.1) and “Tissue” (equation 5.2), in which the concentration in the blood compartment describes the measured concentration in the blood samples. After administration, flumazenil is transported across the blood-brain barrier into the brain (“Brain Free”, equation 5.3), where it can bind to the GABAAreceptor complex (“Brain Bound”, equation 5.4). Because the binding is reversible, flumazenil can also dissociate from the GABAAreceptor complex. All these terms are incorporated in equation 5.4, taking into account both maximum binding capacity of this receptor for flumazenil and binding by flumazenil itself.

The corresponding free flumazenil concentration in brain is derived from equation 5.3.

Blood dAB

dt = Ri n f − k12⋅ AB+ k21⋅ AT− k10⋅ AB− k13⋅ AB+ k31⋅ (CBrF⋅ VBr) (5.1) C_B= A_B

VC

Tissue dAT

dt = k12⋅ AB− k21⋅ AT (5.2)

C_T = A_T VT

Brain Free dCBrF

dt = k13⋅ AB

VBr

− k31⋅ CBrF− kon⋅ (Bmax− CBrB) ⋅ CBrF+ ko f f ⋅ CBrB (5.3) Brain Bound

dC_BrB

dt = kon⋅ (Bmax− CBrB) ⋅ CBrF− ko f f⋅ CBrB (5.4) In the differential equations, ABand AT are the amounts (ng) in blood and tissue, and CB, CT, CBrF, and CBrBare the concentrations of flumazenil (ng/ml) in blood, tissue, brain free and brain bound compartments, respectively. VC, VT, and VBrare pharmacological volumes of distribution, which are used to scale amount to concentration. Ri n f is the zero-order administration rate (ng/min), calculated using the amount of injected flumazenil and the time needed for injection.

k12, k21, k13 and k31 are inter-compartmental rate constants (min⁻¹) between blood and tissue or brain respectively, and k10 is the elimination rate constant from the body. konis the receptor association rate constant (ml/min/ng), ko f fis the receptor dissociation rate constant (min⁻¹), and B_max(ng/ml) is the total concentration of receptors.

The total flumazenil concentration in the brain as calculated from the activity-time curve, measured by PET, reflects the sum of the concentrations in the Brain Free and the Brain Bound compartment:

PET-data

CPET= CBrF+ CBrB (5.5)

The dissociation constant KD(ng/ml) is related to ko f f and kon: K_D= k_{o f f}

kon

(5.6) Two different models were tested. In model A, the following structural PK parameters were defined: V_C, V_T, CL, Q, V_Br, Q_Br, B_max and K_D. CL (elimination clearance, ml/min), Q and Q_Br(inter-compartmental clearances between blood and tissue or brain respectively, ml/min) are calculated from the different rate constants and volumes of distribution according to the principles of pharmacokinetics²⁹(CL= k10⋅ VC, Q= k12⋅ VC= k21⋅ VT, QBr = k13⋅ VC= k31⋅ VBr).

To increase statistical power the model was simplified to model B, in which a correlation was assumed between VBrand QBr:

VBr = C ⋅ QBr (5.7)

First, only the structural model parameters were optimised. Subsequently, it was tested whether inter-individual variabilities in different parameters, assuming lognormal distribution, were significantly greater than 0, improving the fits. The residual error was assumed to be proportional to the concentration in blood and brain (σ_{b l}²(proportional) and σ_br² respectively). In addition, an additive residual error (σ_{b l}²(additive)) was used to take into consideration the greater uncertainty in blood concentrations that are close to the detection limit. The additive residual variance was fixed to the square of half of the detection limit.

The model was implemented in the NONMEM ADVAN9 subroutine and the analysis was performed using the first order method. All fitting procedures were performed on a IBM- compatible personal computer (AMD Athlon processor) running under Windows 2000 with the

use of the Compaq Visual FORTRAN standard edition 6.6.a (Compaq Computer Cooperation, Euston, Texas, USA) with NONMEM version V (NONMEM project group, University of California, San Francisco, USA).³⁰

To evaluate goodness of fit, different diagnostic plots were inspected. Firstly, the data of individual observations versus individual or population predictions should be randomly distributed around the line of identity. Secondly, the weighted residuals versus time or population predictions should be randomly distributed around zero.

5.3 Results

Injection of a tracer dose of [

C]flumazenil in a rat showed clear uptake in the brain, and eliminating organs (liver and kidneys), as can be seen in figure 5.2. Prior administration of an excess amount of unlabelled flumazenil effectively blocked the uptake of a subsequently injected tracer amount of [

C]flumazenil in the brain (figure 5.2, panel B), indicating that the binding of flumazenil in the brain was predominantly specific.

In figure 5.3 measured concentration-time profiles of flumazenil in blood and brain are shown for two typical rats. In panel A the blood concentration versus time profile after administration of an intermediate (50 μg) or a high (2000 μg) dose of flumazenil are shown and in panel B the brain concentration versus time profile after administration of a low (1 μg), an intermediate (50 μg) or a high (2000 μg) dose of flumazenil are shown.

Following the administration of a dose of 1 μg blood concentrations of flumazenil could not be analysed as the values were below the detection limit of the HPLC-UV analysis.

From this figure it is clear that the pharmacokinetics (PK) in blood and brain changes with dose. The initial decline in the blood concentration of flumazenil is more rapid at

Figure 5.2: Coronal slice of uptake (panel A) and inhibition of uptake (panel B) of a tracer amount of [¹¹]flumazenil in the rat. After injection of a tracer amount of [¹¹C]flumazenil a rat was scanned for 30 minutes.

in panel B, the specific binding of [¹¹C]flumazenil is blocked by an excess amount of unlabelled flumazenil prior to injection of a tracer amount of [¹¹C]flumazenil.

Figure 5.3: Representative examples of concentration-time profiles of flumazenil in blood and brain. After injection of a dose of 1 μg (open circles, panel B), 50 μg (open triangles) or 2000 μg (open squares) flumazenil the concentration-time curves of flumazenil in blood (panel B) and brain (panel B) were measured. Note that no bloodsamples were analysed after administration of 1 μg because of the detection limit of the HPLC-UV system (10 ng/ml).

lower doses, whereas in the brain the peak is sharper at higher dose levels. This suggests a dose-dependent distribution, rather than a dose-dependent metabolism, because in the latter case the last part of the curve would change with dose, which is not observed in the data. Furthermore, when the blood data were analysed separately (data not shown) individual estimates for CL were obtained, which showed no correlation with dose.

Analysis of the data with the proposed population PK-model resulted in estimates as summarised in table 5.1. All parameters, except K

, were accurately estimated (table 5.1, model A). The uncertainty in the estimated K

value indicates that not all parameters can be optimised simultaneously, which could be due to high statistical correlation among model parameters. Therefore, it was evaluated whether assuming a 1:1 correlation between structural model parameters would result in an adequate model. It appeared that fitting V

as fraction of Q

(model B; equation 5.7) resulted in more precise parameter estimates compared to model A, while still estimating both B

and K

simultaneously.

In addition, inclusion of a random effect for the inter-individual variability in C further increased the goodness of fit, without altering the values of the parameter estimates significantly (table 5.1, model B).

In figure 5.4, the model-predicted concentration-time profiles are presented. This

figure clearly shows that the population PK-model describes the observed dose-

dependent concentration-time profiles of flumazenil in the brain, with sharper peaks at

higher dose levels. The model also describes the observed differences in concentration-

time profiles in the blood at different dosages. Because non-linear mixed effects modelling

was applied, all data from all rats and all dosages measured in both blood and brain were

analysed simultaneously.

Table 5.1: Parameter estimates in the population PK-model.

Parameter Value Value 95% confidence

model A^a model B^b interval^c Structural parameters

VC(l) 0.0389 (23.3) 0.0353 (29.2) 0.0151–0.0555

VT(l) 0.179 (15.3) 0.176 (16.1) 0.121–0.231

CL (l/min) 0.0189 (4.0) 0.0185 (4.7) 0.0168–0.0202 Q (l/min) 0.0203 (15.7) 0.0189 (18.6) 0.0120–0.0258

VBr(l) 0.0254 (16.9) NA NA

C NA 0.989 (28.1) 0.444–1.534

QBr(l/min) 0.0263 (21.7) 0.0281 (22.8) 0.0156–0.0406 Bmax(ng/ml) 14.1 (39.1) 14.5 (25.5) 7.25–21.8 KD(ng/ml) 4.55 (50.8) 4.68 (32.1) 1.74–7.62

Inter-individual variability

ω²(C) NA 0.0631 (49.9) 0.00136–0.125

Residual errors

σ_{b l}²(proportional) 0.158 (17.3) 0.152 (18.4) 0.0973–0.207

σ_{b l}²(additive)^d 25 (NA) 25 (NA) NA

σ_{PE T}² 0.232 (14.0) 0.210 (15.3) 0.147–0.273

aParameter estimates of model with all parameters. Between brackets coefficient of variation in %.

bParameter estimate of model with VBr= C ⋅ QBr. Between brackets coefficient of variation in %.

c95% confidence interval of parameter estimates of model B.

dDetection limit of HPLC-UV system is 10 ng/ml; σ_{b l}²(additive) is fixed at ((det.lim.)/2)².

The brain-data of the 1 μg dose were also included in the analysis, even though no blood concentrations were available for this dosage. When the model is used to predict the flumazenil blood concentrations after 1 μg, this resulted in flumazenil concentrations below the detection limit (figure 5.5).

The diagnostic plots of the model fit with model B (figure 5.6) show that the

model described the concentrations of flumzenil in blood adequately, as the data of the

individual observed flumzenil blood concentrations versus the individual predictions

(panel A) or the population predictions (panel B) are randomly distributed around the

line of identity. In addition, in panels C and D the weighted residuals versus time and

population predictions respectively are also randomly scattered around zero. Some bias

is observed at the higher concentration ranges of flumazenil in the brain (panels E-

H), as the model underestimates the maximum concentration after the highest doses

levels (1000 μg and 2000 μg, figure 5.4). In order to assess whether the observed bias

Figure 5.4: Concentration time profiles for flumazenil in blood (panel A) and brain (panel B). All concentration-time profiles after administration of the different intravenous doses (1–2000 μg) are shown.

Symbols represent observed flumazenil concentrations and lines individual predictions by the proposed model. Agreement between data of individual rats and corresponding fits can be found in figure 5.6.

Figure 5.5: Simulated concentration time profile in blood at a dose of 1 μg. The proposed model and the parameter estimates were used to simulate the concentration time profile in blood after administration of a dose of 1 μg, resulting in concentrations below the detection limit.

influenced the binding parameters (B

and K

) of flumazenil-binding to the GABA

receptor complex, the described population PK-model was fitted to the data, without the data corresponding to the doses of 1000 μg and 2000 μg. In this case, there were no significant differences between the estimations of the binding parameters with or without the data from the experiments with high flumazenil dosages (B

= 14.5 ± 3.7 ng/ml vs 16.0 ± 8.3 ng/ml; K

= 4.68 ± 1.5 ng/ml vs 4.52 ± 2.8 ng/ml).

5.4 Discussion

In this study a novel full saturation approach is presented to quantify the properties of the GABA

receptor complex in the rat brain in vivo with [

C]flumzenil and PET. The two main advantages of the overall approach developed in this study are that 1) each animal has to be scanned only once, and 2) blood concentration time profiles can be obtained by measuring non-radioactive flumazenil concentrations. The latter is a direct result of giving a saturating dose of flumazenil, thereby reaching blood concentrations that are high enough for HPLC-UV detection. The first advantage is based on the rapid metabolism of flumazenil in the rat (t

= 8.3 min

). Therefore, a single injection of [

C]flumazenil in each animal was sufficient to cover the entire range of in vivo receptor occupancies for the determination of both B

and K

.

A population model was developed, which was able to predict both B

and K

. This method has several advantages. Using mixed effects modelling it was possible to model all data from all rats and all dosages simultaneously, resulting in better statistical power for estimation of the binding parameters. A further advantage of the used population approach is that also individuals with an incomplete dataset can be included in the analysis. Thus, for the rats receiving a dose of 1 μg, for which no flumazenil concentrations in blood could be determined, the PET data could still be used. Finally, based on variability in the population, individual post hoc estimates of parameters can in principle be obtained using a population model. Depending on the biological variation within the study population, it is possible to estimate inter-individual variability of different structural parameters. Because in the current study a very homogenous population was used (control experimental animals), the biological (random) variability between the animals was rather limited. Therefore, most of the variability could be described by one parameter for the inter-individual variability in the structural parameter C. As a result, only for this parameter, individual-specific estimates could be obtained using the present dataset. However, it is expected that within a population of animals from a disease model, or within a clinical population, more biological variation will be present enabling the identification of inter-individual variability in more structural model parameters.

Future studies are needed to confirm the identifiability of individual estimates for these parameters.

As shown in table 5.1 (model B), using the present method, all structural parameters, including B

and K

, could be estimated simultaneously with adequate precision.

Including a random effect for the inter-individual variability in C resulted in increased

Figure 5.6: Diagnostic plots for flumazenil concentrations in blood (A–D) and brain (E–H). In panel A (blood) and E (brain) observed versus individual predicted concentrations are shown, in panel B (blood) and F (brain) observed versus population predicted concentrations, in panel C (blood) and G (brain) weighted residuals versus time and in panel D (blood) and H (brain) weighted residuals versus population predicted concentrations are shown. Al dots represent individual datapoints and the lines in panels A, B, E and F are identity lines.

statistical power for identification of B

and K

(table 5.1, model B). Adding inter- individual variability also to other parameters did not improve the model fit further.

Using the present population model, it is possible to characterise both transport from blood to brain (Q

= 0.0281 l/min) and binding of flumazenil to the GABA

receptor complex (K

= 4.68 ng/ml; B

= 14.5 ng/ml) simultaneously, as the correlation between all parameters was less then 0.95.

The estimated in vivo K

(4.68 ng/ml) closely resembles reported in vitro K

values at 37

C of 2.2 ng/ml in living rat cortex slices,

3.2 ng/ml in rat cortex homogenates,

and 7.1 ng/ml in rat brain homogenates.

Comparison of presently estimated B

with reported in vitro B

values is more difficult, because the latter values are usually expressed as mol per mg protein. To overcome this, Murata et al assumed that 1 ml of brain tissue contains 100 mg protein.

Using this assumption, the presently estimated in vivo B

(14.5 ng/ml) is in the same order of magnitude as in vitro B

values of 4.4 ng/ml in living rat cortex slices,

3.3 ng/ml in rat cortex homogenates,

and 54.5 ng/ml in rat brain homogenates.

Mandema et al

reported values for CL and V

(total, or sum of volumes of distribution) of 30 ml/min and 299 ml, which are similar to the presently estimated values (18.5 ml/min and 239 ml, table 5.1).

In the present method, several important experimental issues should be taken into account: the immobilisation of the animals and instability of flumazenil in rat blood.

Firstly, care has to be taken that anaesthesia does not interfere with the receptor being studied. Therefore, a combination of ketamine and medetomidine was used.

These anaesthetic drugs are commonly used, and do not directly interfere with the GABA

receptor complex.

Other anaesthetic drugs, such as pentobarbital, propofol, etomidate, and the inhalation anaesthetics halothane and isoflurane all interfere with the GABA

receptor complex.

Flumazenil is very unstable in rat blood, as reported by Mandema et al,

who reported a disappearance half-life (mean ± SE, n = 5) of 8.3 ± 1 min and 31 ± 4 min at 38

C and 23

C respectively. In the presented investigations, the flumazenil concentration in blood was measured using HPLC-UV analysis, in which flumazenil was stabilised by adding NaF to the blood samples and cooling to 0

C. Although the detection limit of the HPLC-UV method prevents measurement of very low flumazenil concentrations, the present method using population PK-modelling allows for analysis of PET data without accompanying blood data.

Using the present model, the observed dose-dependency in the concentration-time

curves in blood and brain was described adequately (figure 5.4). This was expected,

because dose-dependency was only observed in the first part of the curves, indicating

a dose-dependent distribution, rather than metabolism. In the model a dose-dependent

distribution was described by specific binding to the GABA

receptor complex. From

literature, it is known that the affinity of flumazenil for periferal GABA

receptors is

very small.

Therefore, it was assumed that specific binding takes place in the brain

only. This assumption is confirmed by the results presented in figure 5.2, as the uptake of [

C]flumazenil in the brain is blocked by an excess amount of unlabelled flumazenil.

Another issue is potential heterogeneity of binding in the ROI used, caused either by non-uniform receptor density or by populations of receptor subtypes with different binding characteristics for flumazenil. As the image resolution is about 3 mm and therefore includes a relatively large area, placement of the ROI by visual inspection might introduce variability in the sampling. If so, the estimates of the binding parameters might be biased. On the other hand, studies of subunit distributions in the neocortex do not show prominent non-uniformity in density

and flumazenil does not exhibit pronounced selectivity for the majority of receptor subtypes.

Furthermore, if the same method is used to compare control groups and treated or disease groups the possible bias will be the same for both groups, and thus it will be possible to reliably detect differences in both B

and K

between these groups.

Visual inspection of the diagnostic plots of the model fit (figure 5.6) showed that in general the fits were good, except for some bias at the higher concentration ranges of flumazenil in the brain. This reflects the observation that the peak concentrations at the highest doses were underestimated (figure 5.4). Different factors may contribute to the underestimation of the maximum brain concentration after high doses flumazenil (1000 and 2000 μg).

The first reason is that intravascular flumazenil in the brain might explain the observed high peak concentration. An attempt to include the fractional cerebral blood volume in the model failed, because the additional parameter could not be estimated. In addition, fixing this parameter to reported values did not improve the model fit either. Presumably, adequate characterisation of the peak concentration in brain requires adequate data on the peak concentration in blood. These data are currently missing, as the first blood sample was taken 1 minute after injection of flumazenil, whereas the PET-data were sampled every 15 seconds for the first 1.5 minutes. Continuously measuring the peak of the concentration-time curve of flumazenil in blood using radioactivity detection could overcome this problem. Unfortunately, this method can not be used, because flumazenil is unstable in blood.

Secondly, although the transport of flumazenil into the brain could be identified

accurately using the present method, this description could be improved further by

having more information about the concentration-time profile of unbound flumazenil

in the brain. For this purpose, intracerebral microdialysis is a useful technique.

However, there are several limitations related to this technique. The concentrations in the

microdialysate samples are very low, typically in the pico– to nanomolar range, implying

that the detection limit of the assay method for analysing the compound is an important

issue to consider.

Furthermore, the half life of the compound in the body is an important

issue to consider, as microdialysate data represent “average” concentrations obtained in

the sampling interval, which usually is in the range of 5 to 20 minutes.

This precludes

the use of microdialysis for compounds with a very short biological half life, such as that for flumazenil (t

= 8.3 min

).

Thirdly, non-specific binding could play a role. Because non-specific binding is non- saturable, the amount of non-specific binding increases at higher concentration of ligand, resulting in a more important role for non-specific binding at higher dose levels. However, including non-specific binding into the model resulted in imprecise estimates of non- specific binding and in addition, it did not improve the model fit (data not shown).

Therefore non-specific binding was not incorporated in the current model. If the dataset would be expanded, it should be possible to estimate more parameters, including non- specific binding. Increasing the number of animals in the dataset would increase the statistical power to identify the parameters for non-specific binding adequately.

A fourth explanation might be that mainly after high doses (1000–2000 μg) a second binding place, with a lower affinity, plays a role. Also in this case enlarging the dataset by adding data from additional animals will be useful to estimate parameters for a second binding place.

However, when all parameters were estimated using the dataset without the concentrations measured in the brain after administration of a dose of 1000 or 2000 μg there was no difference between the estimates of the binding parameters with or without the PET data of the doses of 1000 and 2000 μg. This indicates that the observed bias at the very high concentration ranges in the brains has no influence on the estimation of the binding parameters.

In the present study, an attempt was made to perform experiments according to the method described by Lassen et al,

in order to compare the results of the present method with a more conventional method. With the latter method a tracer amount of [

C]flumazenil is injected under two steady state conditions: 0% and 50% receptor occupancy. However, injection of a tracer amount of [

C]flumazenil resulted in blood flumazenil concentrations that were below the detection limit of the HPLC-UV system.

As discussed above, measuring radioactivity of blood samples is difficult because of the instability of flumazenil in rat blood. This implies that the use of a tracer method in rats will remain difficult. Nevertheless, further studies are required to provide a direct comparison between the methods.

In theory, the proposed method could also be used for human studies. It should be

noted, however, that the use of a full saturating dose dictates that the administered ligand

has no adverse pharmacological effect. As this condition is fulfilled for flumazenil, the

present method could indeed be used in humans. However, as the biological clearance

of flumazenil in humans is slower than in rats, human studies will require longer PET-

scan duration. Further studies are needed to assess what would be optimal in the human

situation.

5.5 Conclusion

In conclusion, a novel full saturation method is presented, which allows for the measurement of both B

and K

from a single PET study, using only a single bolus injection. Using animal models of epilepsy, this approach could be used to monitor progressive changes in density and properties of the GABA

receptor complex during the time course of epileptogenesis. Furthermore, because flumazenil has no intrinsic activity, the present approach could also be applicable to human studies. This facilitates extrapolation of results from animal to clinical studies.

Acknowledgements

The authors wish to thank Dr. W. Hunkeler and Dr. P. Weber of Novartis for the generous gift of flumazenil and desmethyl-flumazenil (RO 15-5528), the BV Cyclotron VU for the production of¹¹C-CO₂, Dr. A.D. Windhorst, M.P.J. Mooijer and P.J. Klein for synthesising [¹¹C]flumazenil, F.L. Buijs and Dr. H.W.A.M. de Jong for operating the PET scanner and reconstructing the scans, S.M. Bos-van Maastricht and K.B. Postel-Westra for help with the surgeries, and M.C.M. Blom- Roosemalen for help with the HPLC-analysis of the blood samples.

This project was sponsored by the “Christelijke Vereniging voor de Verpleging van Lijders aan Epilepsie” and the National Epilepsy Fund – “The Power of the Small”, project number 02-06.

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