Quantification of [18F]diprenorphine kinetics in the human brain with compartmental and non-compartmental modeling approaches

www.elsevier.com/locate/ynimg NeuroImage 22 (2004) 1523 – 1533

Quantification of [18F]diprenorphine kinetics in the human brain with compartmental and non-compartmental modeling approaches Mary E. Spilker, a,* Till Sprenger, b Michael Valet, b Gjermund Henriksen, a Klaus Wagner, c Hans-J. Wester, a Thomas R. Toelle, b and Henning Boecker a a

Nuklearmedizinische Klinik und Poliklinik, Klinikum rechts der Isar, Technische Universita¨t Mu¨nchen, Mu¨nchen, Germany Neurologische Klinik und Poliklinik, Klinikum rechts der Isar, Technische Universita¨t Mu¨nchen, Mu¨nchen, Germany c Klinik fu¨r Ana¨sthesiologie, Klinikum rechts der Isar, Technische Universita¨t Mu¨nchen, Mu¨nchen, Germany b

Received 31 October 2003; revised 31 March 2004; accepted 6 April 2004

6-O-(2-[18F]fluoroethyl)-6-O-desmethyldiprenorphine ([18F]FDPN) is a nonselective opiate ligand that binds to postsynaptic M, K and D opiate receptors. Due to the longer half-life of F-18, compared to C-11, labeling DPN with F-18 allows for alternative experimental protocols and potentially the evaluation of endogenous opioid release. The applicability of this compound to assorted experimental protocols motivated the evaluation of [18F]FDPN kinetics with compartmental and non-compartmental models. The results indicate that a two-tissue compartmental model best characterizes the data obtained following a bolus injection of [18F]FDPN (120-min scanning protocol). Estimates of distribution volume (DV) were robust, being highly correlated for the one-tissue compartmental model as well as the invasive Logan model and the basis function method. Furthermore, the DV estimates were also stable under a shortened protocol of 60 min, showing a significant correlation with the full protocol. The binding potential (BP) values showed more variability between methods and in some cases were more sensitive to protocol length. In conclusion, this evaluation of [18F]FDPN kinetics illustrates that DV values can be estimated robustly using compartmental modeling, the basis function method or the invasive Logan modeling approach on a volume of interest level. BP values were also found to correlate with DV values; however, these results should be interpreted with the understanding that specific binding in the reference region (occipital region) may exist. D 2004 Elsevier Inc. All rights reserved. Keywords: [18F]diprenorphine; Kinetic models; Ligand; Opiate receptors; PET

Abbreviations: DV, distribution volume; BP, binding potential; 2T, twotissue compartmental model; 1T, one-tissue compartmental model; Inv_Logan, invasive Logan model; BFN, basis function method; NonInv_Logan, noninvasive Logan model; SRTM, simplified reference tissue model; TRM, tissue ratio method. * Corresponding author. Nuklearmedizinische Klinik und Poliklinik der Technischen Universita¨t Mu¨nchen, Klinikum rechts der Isar, Ismaninger Strasse 22, 81675 Mu¨nchen, Germany. Fax: +49-89-4140-4938. E-mail address: [email protected] (M.E. Spilker). Available online on ScienceDirect (www.sciencedirect.com.) 1053-8119/$ - see front matter D 2004 Elsevier Inc. All rights reserved. doi:10.1016/j.neuroimage.2004.04.009

Introduction The radioligand, [11C]diprenorphine ([11C]DPN), is commonly used to assess the opiate receptor system in physiologic and pathophysiologic conditions (Duncan, 1999; Jones et al., 1991; Mayberg et al., 1991; Sadzot et al., 1990; Weeks et al., 1997). However, applicability of this radioligand to long acquisition protocols can be limited due to the short half-life of 11C (t1/2, C-11 = 20 min). Thus, efforts were made to synthesize 6-O-(2-[18F]fluoroethyl)-6-O-desmethyldiprenorphine ([18F]FDPN) (Wester et al., 2000), which has similar pharmacologic properties to [11C]DPN, but a longer half-life (t1/2, F-18 = 109.7 min). [18F]FDPN is now applicable to alternative experimental designs, including single bolus protocols investigating endogenous ligand release (Alpert et al., 2003; Pappata et al., 2002; Sprenger et al., 2003), which may serve as alternatives to the two scan or bolus plus constant infusion approaches. Furthermore, this compound can be used at centers without an on-site cyclotron, thereby increasing its usage in the assessment of the opiate receptor system as well as its use in routine clinical evaluations. Due to the longer half-life, this compound also shows improved signal intensity compared that of [11C]DPN, which results in an improved signal to noise ratio (SNR) (Wester et al., 2000). The potential application of [18F]FDPN within the scientific and medical community motivated the characterization of this compound’s time-varying dynamics in a population of normal healthy subjects. Therefore, we have undertaken a kinetic study to compare the performance of various modeling approaches with the [18F]FDPN tracer. The invasive models assessed here include the standard one-tissue and two-tissue compartmental models, the Logan model and the basis function method. Additionally, three reference tissue models were examined, including the noninvasive Logan model, the simplified reference tissue model and the tissue ratio method. The performance of each model is evaluated and estimates of distribution volume (DV) and binding potential (BP) are compared. Lastly, the stability of the DV and BP parameters are also examined for a shortened protocol.

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Materials and methods Data acquisition Six healthy volunteers (mean age 42 years, range 30 – 59 years; two females, four males) underwent a [18F]FDPN PET-study as part of an existing protocol. All subjects gave informed written consent and the study protocol was approved by the ethics committee at the Technische Universita¨t Mu¨nchen and the radiation protection authorities. Images were acquired over 120 min with the following frame durations: 6
30 s; 7
1 min; 4
2.5 min; 2
5 min; 3
10 min; 5
2 min; 4
2.5 min; 2
5 min; 3
10 min for a total of 36 frames. The subjects studied here served as controls in a protocol involving a challenge at 60 min p.i.; while they did not receive any challenge, the frame lengths reflect such a paradigm. PET scans were acquired using a Siemens/CTI ECAT EXACT HR+ scanner (Knoxville, TN, USA) in 3D mode with septa retracted. A neck-shield (NeuroShield, Scanwell Systems, Lavigne St., Montreal, Canada) was used to reduce random count rates. Attenuation was corrected using transmission scanning before the [18F]FDPN studies. The acquired data were reconstructed using filtered backprojection with a ramp filter (cut-off 0.3 cycles per projection element) into 63 image planes with a 128 by 128 pixel image matrix and a final spatial resolution of 2.0594
2.0594
2.425 mm. In addition to the dynamic PET images, high-resolution T1-weighted anatomical MR images were also acquired for each subject using an MPRage sequence. The radioactive tracer was injected as an intravenous bolus with a mean injected radioactive dose of 3 mCi (specific activity: 1000 – 1500 mCi/Amol). Arterial blood samples were acquired throughout the scanning period as fast as possible for the first 2 min followed by samples at increasingly spaced intervals ranging from 20 s to 5 min. The metabolites were measured at time points of 5, 15, 30, 60 and 90 min p.i. to allow for the generation of a metabolite corrected arterial input function. This is performed by fitting a biexponential function [A exp(a  t) + B exp(b  t)] to the fraction of intact tracer. The total plasma curve is then multiplied by this function to arrive at the metabolite corrected input function. Following acquisition, all images were transferred to a standard PC and then realigned and resliced using SPM99 (Wellcome Dept. of Cognitive Neurology, London, UK). The MR images were coregistered to the 4D (x, y, z, time) dynamic PET data sets using the Mutual Information subroutine in SPM99. The MR images were then used to select individualized volumes of interest (VOIs) corresponding to the following locations: occipital cortex, cingulate cortex, frontal cortex, putamen/caudate, thalamus and cerebellum. The cingulate cortex, putamen/caudate, thalamus and cerebellum were selected using free-form VOIs, while 10-mm spherical VOIs were used for the occipital and frontal regions. These regions were selected based on a priori knowledge that they contain a range of opiate receptor densities, from minimal opiate receptors in the occipital region to high receptor density in the thalamus and basal ganglia.

mertsma and Hume, 1996), the basis function method (Gunn et al., 2001, 2002) and the tissue ratio method (Endres et al., 2003; Frost et al., 1989). The models are described below and their parameters, along with their relationship to DV and BP are summarized in Table 1. There are also several detailed reviews of these models available in the literature (Laruelle et al., 2002; Meyer and Ichise, 2001). Note that the occipital region was specified as the reference region for all models and calculations where necessary. Unless otherwise stated, all modeling was performed using the Kinetic tool in the PMOD Medical Imaging Program, version 2.4 (PMOD Group, Zurich, Switzerland). The PMOD program uses the Levenburg – Marquardt routine when performing nonlinear least-squares fitting and otherwise solves the analytical model equation(s) when appropriate. The error model for the nonlinear fitting was assumed to be Gaussian with mean zero and standard deviation proportional to the square root of the total counts within each frame divided by the frame’s duration. Invasive kinetic models A two-tissue compartmental model (2T) with a plasma input function was applied to the data and adjusted appropriately to evaluate both reversible and irreversible specific binding. The differential equations corresponding to the 2T model with reversible kinetics are given below. dCF þ NS ðtÞ ¼ K1 Cp ðtÞ  ðk2 þ k3 ÞCF þ NS ðtÞ þ k4 CS ðtÞ dt

ð1Þ

dCS ðtÞ ¼ k3 CF þ NS ðtÞ  k4 CS ðtÞ dt

ð2Þ

CVOI ðtÞ ¼ CF þ NS ðtÞ þ CS ðtÞ þ Vp CWP ðtÞ

ð3Þ

where Cp is the metabolite corrected arterial plasma tracer concentration (kBq ml1); CF + NS is the concentration in the free and nonspecifically bound tracer in the tissue (kBq ml1); CS is the Table 1 Model parameter summary Invasive methods 2T Parameters K1, k2, k3, k4,Vp
 k1 k3 DV 1þ k2 k4 k3 k4 BP

1T

Inv_Logan

K1, k2, Vp

slope, intercept /i,hi

k1 k2 DVVOI 1 DVref

slope

BFN

DV ¼

n P /i i ¼1

DVVOI 1 DVref

hi

DVVOI 1 DVref

Noninvasive methods SRTM

NonInv_Logan TRM

Kinetic model descriptions and implementation

Parameters R1, k2, BP DV – BP BP

The kinetic behavior of [18F]FDPN was quantified using compartmental models (one- and two-tissue models) (Slifstein and Laruelle, 2000), the Logan model (invasive and noninvasive) (Logan, 2000), the simplified reference tissue model (Lam-

2T, two-tissue compartment model; 1T, one-tissue compartment model; Inv_Logan, invasive Logan model; BFN, basis function method; SRTM, simplified reference tissue model; NonInv_Logan, noninvasive Logan model; TRM, tissue ratio method; DVR, distribution volume ratio.

DVR, intercept BPratio DVR – DVR  1 BPratio

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concentration of specifically bound tracer in the tissue (kBq ml1); CWP is the concentration of tracer in whole plasma without correction for metabolites. K1 (ml ml1 min1) is the tracer’s rate of exchange from the vasculature to the tissue, while k2 describes the efflux of tracer from tissue to plasma. The rate constants, k3 and k4, quantify the rate of specific binding and release of the ligand. The rate constants, k2, k3 and k4, are first-order rate constants with units of min1, while Vp (ml/ml) is the fractional plasma volume within the VOI. Although a three-tissue compartmental model (free, nonspecific and specific compartments) was evaluated, the kinetic parameters of this model could not be identified with adequate precision and the model was simplified. If it is assumed that the free and nonspecific binding compartments exchange at a faster rate than the free and specific binding compartments, then the former can be lumped together, reducing the model to the two-tissue compartmental model described here. A one-tissue compartmental model (1T) was also applied to the data for each VOI according to Eqs. (4) and (5). CT ðtÞ ¼ K1 ek2 t  Cp ðtÞ

ð4Þ

CVOI ðtÞ ¼ CT ðtÞ þ Vp CWP ðtÞ

ð5Þ

Here, the estimated parameters include K1, k2 and Vp and the symbol, , represents the convolution function. This model is most appropriate when the specific binding compartment cannot be resolved due to rapid binding and release of the ligand. The basis function (BFN) method is a data-driven modeling approach where no a priori structure is assumed to characterize the data. Instead, an impulse response function is generated from a sum of exponentials that describes the data given the input function. The DV is then determined from the integral of the impulse response function. The BFN method evaluated here uses basis pursuit denoising as implemented in the DEPICT software (Gunn et al., 2001, 2002) according to Eq. (6) and the DV is calculated as defined in Eq. (7). This method eliminates the positive constraint on the coefficients (/i) that was necessary under the spectral analysis method by including a regularization term so that the underdetermined system of equations can be solved.

CT ðtÞ ¼ Vp CWP ðtÞ þ ð1  Vp Þ

n X

/i eh;t  Cp ðtÞ

ð6Þ

i¼1

DV ¼

n X /i i¼1

ð7Þ

hi

The final invasive model applied to the data was the invasive Logan model (Inv_ Logan), which transforms the data so that a linear relationship exists between two variables and the slope of this relationship equals the DV. Z

Z

t

CVOI ðuÞdu

0

CVOI ðtÞ

¼ DV

t

Cp ðuÞdu

0

CVOI ðtÞ

þ int

ð8Þ

1525

To ensure linearity in the transformed data, frames 60 – 120 min p.i. were included in the invasive Logan analysis. For the shortened protocol, a linear fit was performed with the transformed data corresponding to original frames between 25 and 60 min p.i. Noninvasive (reference region) models The noninvasive Logan model (NonInv_ Logan) replaces Cp(t) in Eq. (8) with CREF(t) and an additional term, CREF(t) / kref 2 , is added to the equation. Z

Z

t

CVOI ðuÞdu

0

CVOI ðtÞ

¼ DVR

0

t

CREF ðuÞdu þ CREF ðtÞ=k2ref CVOI ðtÞ

þ Int

ð9Þ

In this model’s analysis, the linear fit was performed between the same frames as described for the invasive Logan model. This model was implemented using a gradient-expansion algorithm for nonlinear least-squares fitting in IDL 5.6 (Research Systems Inc, Boulder, CO, USA). The simplified reference tissue model (SRTM) assumes that the VOI data can be characterized using a one-tissue compartment model and that the distribution volume in the tissue of interest and the reference region are approximately equal, such that K1,VOI / k2,VOI = K1,REF / k2,REF. With these assumptions, the parameter, R1, is defined as K1,VOI / K1,REF, and the operational equation can be defined for a VOI as follows. CVOI ðtÞ ¼ R1 CREF ðtÞ þ ½k2 þ R1 k2 =ð1 þ BPÞ CREF ðtÞ  exp½k2 t=ð1 þ BPÞ

ð10Þ

In the above equation, the three parameters that are estimated include R1, k2 and BP. The full four-parameter reference tissue model was also examined; however, it performed approximately as well as the SRTM; therefore, only results from the SRTM are presented here. Tissue ratio method The tissue ratio method (TRM) calculates a binding potential ratio: BPratio = (TACVOI  TACREF)/TACREF, where TACVOI and TACREF are the time activity curves for the receptor rich and reference regions, respectively (Endres et al., 2003; Frost et al., 1989). For this data set, the BPratio was calculated as the average of the ratio values from time points of 80 – 120 min p.i. using standard data processing software. The choice to start at 80 min was made since a plateau in the BPratio began between 70 and 80 min p.i. Model assessment Several criteria were used to compare the performance of each compartmental model. Goodness of fit was assessed both visually and statistically using the Runs Test of the residuals, which is a statistical test for the randomness of the residuals. Model parsimony was evaluated using the Akaike Information Criteria (AIC), where the lowest AIC value is an indication of the better model fit to the data (Akaike, 1974). Finally, parameter coefficients of

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variation (CV = standard deviation / mean) were examined to quantify parameter precision. The performance of the various models was also compared in terms of the DV and BP values. For consistency, all measures of bias in DV and BP between the various methods were compared to the 2T model with reversible specific binding and reported as percentages according to the following equation.

%Bias ¼

ðhˆ  h2T Þ 100% h2T

ð11Þ

where, hˆ is the model’s estimate of DV or BP and h2T is the estimate of DV or BP as determined from the 2T model. All correlation measures are reported as Pearson R2 values. Correlations and statistical tests were performed in GraphPad Prism version 4.00 for Windows (GraphPad Software, San Diego, CA, www.graphpad.com). Results Compartmental model performance Representative time activity curves from a single subject are shown in Fig. 1. Fig. 2 presents the model fits from the 2T and 1T analyses to data from the occipital and thalamus VOIs of this subject. In general, the 1T model tended to underestimate the kinetic behavior at early and late time points while overestimating the concentration in the middle portion of the curve. This was especially evident in the occipital and cerebellum VOIs, which were both fit optimally with a 2T model. The performance criteria for each compartmental model are summarized in Table 2. The results of this work found that the 2T model with reversible specific binding best characterized the majority of the VOIs across all regions and subjects as determined from the AIC values (67%) and random scatter of the residuals (89%). While a 2T model with irreversible specific binding (k4 = 0) performed better than the 1T model with regards to AIC values and

random scatter of the residuals, it did not perform as well as the 2T model with reversible specific binding (k4 p 0) when considering all of the model performance criteria. This is appropriate since [18F]FDPN is an antagonist and not expected to be internalized after binding. In general, the parameter CVs were higher for the 2T model compared to the 1T model, which is expected given the increased model complexity resulting from the presence of the specific binding compartment. In 14% of the 2T model fits, at least one parameter had a CV greater than 100%. Usually, the k3 and k4 parameters showed the highest CVs, with the maximal CV of 158% observed across all subjects and regions. However, even with larger CVs on the parameters, the model fits to the data were clearly improved for the 2T model vs. the 1T model. While the 2T model produced an optimal fit to the majority of the VOIs, the k3/k4 ratio did not reflect BP values consistent with those found in the literature for [11C]DPN (determined from a pulse-chase experiment) (Jones et al., 1994) and [18F]FDPN (determined from spectral analysis and reference tissue models) (Lochmann et al., 2003). Note that Jones et al. (1994) also found it difficult to attain reliable k3/k4 values from a tracer study for [11C]DPN. In the current study, BP was determined for the 2T model in the same manner as with the other methods, namely, (BP = DVVOI/DVREF)  1, where a 2T model was applied to both the VOI and reference region. Distribution volume The DV values from the compartmental, Inv_Logan and BFN methods are reported in Table 3. The regional DV values are consistent with the expected outcome of high receptor density in the thalamus, decreasing to the lowest in the occipital region. The BFN method resulted in the highest DV values for all regions except the occipital region, where the 2T model resulted in higher DV values. The large standard deviations associated with each regional mean DV value illustrate the degree of interindividual variability within this population of normal, healthy subjects.

Fig. 1. Time activity curves for a single subject. Occipital (x); cerebellum (5); frontal cortex (n); putamen/caudate (+); thalamus (E).

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Fig. 2. Representative 2T and 1T model fits. Occipital (x); thalamus (E); 2T model fit (solid line); 1T model fit (dashed line).

The range of the DV values from minimum to maximum across all subjects and regions was also examined and found to be smaller for the Inv_ Logan model (37.01), but quite similar between the compartmental models (40.84 2T model; 40.39 1T model). The largest range was observed with the BFN method (43.93). DV values determined from the 2T model correlate well with those from the 1T model, Inv_ Logan model and BFN method (Fig. 3). The BFN method exhibited the most variability in DV values compared to the 2T model and thus resulted in the lower R2 value of 0.917 compared to the other methods, which had R2 values greater than 0.934; however, all correlations were significant (P < 0.0001). The mean bias between the 2T model and other invasive modeling approaches was less than 15% (Table 4) when excluding the occipital region, which showed an increased difference between modeling methods. The DV for the occipital region was consistently underestimated by the 1T and Inv_ Logan approaches. The Inv_ Logan model also consistently underestimated the DV values, with the exception of the frontal region, suggesting a unidirectional bias in the results of this modeling approach. This is not always the case when considering the 1T and BFN models, as can be observed from the large standard deviations compared with the mean values.

Binding potential In this study, an estimate of the BP independent of the reference region was not possible; therefore, any biases introduced by the reference region could not be evaluated. Instead, a comparison of the BP values between the different models is presented. The mean BP values across all regions are reported in Table 5. These values are lower than those observed for [11C]DPN (Jones et al., 1994) and with the exception of the cerebellum are consistent with those reported for [18F]FDPN (Lochmann et al., 2003). Discrepancies between the 2T and other methods are likely influenced by the occipital DV values, which were consistently higher with the 2T model compared with the other invasive models. Furthermore, while the R2 values of the BP regressions with the 2T model derived BP values were reduced (Table 5) compared to the regressions with DV values (Fig. 3), all methods still resulted in significant correlations ( P < 0.0001). Additionally, the normalized mean BP values (Table 6) illustrate a larger range of values across regions for the invasive methods compared to the noninvasive methods. A regression analysis was performed between the BP values determined from all models and the DV values estimated from the Table 3 DV values across regions

Table 2 Model performance summary a

Lowest AIC value Randomly scattered residualsb CVs < 100%b

2T (k4 p 0) (%)

2T (k4 = 0) (%)

67 89

25 83

8 39

86

86

100

1T (%)

A total of 36 VOIs were evaluated. 2T( k4 p 0) corresponds to a 2T model with reversible specific binding; 2T (k4 = 0) corresponds to an 2T model with irreversible specific binding. a Percentage of VOIs meeting the criterion between all three models. b Percentage of VOIs meeting criterion for each model.

Refer to Table 1 for label descriptions. Values are reported as mean F SD. Colored lines report results from the full 120-min protocol, while white lines report results from the 60-min protocol.

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Fig. 3. Distribution volume. Lines represent regression with the 2T model. 1T model (5; dotted line); Inv_ Logan model (E; dashed line); BP (x; solid line).

2T model. When all subjects were examined together, the BP values exhibited more variability and lower R2 values (0.291 – 0.717) but all correlations were still significant (P V 0.0025). In examining the plots, it was observed that the BP values of two subjects were significantly higher than the values determined for the other subjects. This in turn was adding variability to the correlation plot and thereby reducing the correlation’s R2 value. When the BP and DV values were compared on a per subject basis, the minimum R2 value observed was 0.716 for the comparison of the BP determined with the basis function method vs. the DV value estimated from the 2T model. These results illustrate the consistency between DV and BP estimates. Shortened protocol A shorter protocol with a length of 60 min rather than the full 120 min p.i. was performed to examine the stability of the DV and BP estimates. The DV values from the short and full protocol are reported in Table 3. It can be seen that the short protocol resulted in lower DV values than those determined from the 120min protocol. In some cases, it was more difficult to resolve the extra compartment with the shorter protocol and it can be observed that the 2T and 1T model results are becoming increasingly similar.

Table 4 Percentage of differences in DV values (120-min protocol) Region 1T Inv_ Logan Thalamus Putamen/caudate Cingulate Frontal Cerebellum Occipital

7.92 5.29 3.04 2.59 4.04 21.61

F F F F F F

13.42 10.67 7.90 10.59 6.05 8.90 5.25 3.26 8.84 3.59 16.93 18.45

F F F F F F

8.51 7.44 2.99 3.48 3.28 13.52

The DV values from the shorter protocol were found to correlate with the DV values estimated from the 2T model applied to the entire 120-min data set (R2 values: 2T model, 0.854; 1T model, 0.865; Inv_ Logan, 0.847; BFN, 0.606). The basis function method showed the most variability in DV values and therefore resulted in the lower R2 values observed here. Additionally, all correlations of DV values between the long and short protocols were found to be significant (P < 0.0001). The BP values were used to evaluate the performance of the noninvasive methods under the 60-min protocol and are reported in Table 5. It can be observed that the SRTM showed minimal changes in BP values between the long and short protocols. The majority of regions assessed with the noninvasive methods showed a decrease in BP under the short protocol when compared to the long protocol, while the invasive methods showed the opposite effect. Also, excluding the 1T model, the noninvasive methods were less variable than the invasive methods when each was compared separately for differences between long and short protocols (R2 values: noninvasive methods, 0.936 – 0.972; invasive methods, 0.339 – 0.857; 1T, 0.937). These within method regressions were significant at P < 0.0001, with the exception of the BFN method (P = 0.0017). Lastly, it can be observed that the basis function method resulted in smaller estimates of BP for the cerebellum. This is propagated into the large differences in the normalized BP values observed with the basis function method presented in Table 6.

BFN

14.38 4.89 1.53 12.67 10.30 10.29

F F F F F F

21.27 19.86 17.20 11.41 21.68 18.67

Values were compared with the 2T model using Eq. (11) and are reported as mean F SD. 1T, one-tissue compartmental model; Inv_ Logan, invasive Logan model; BFN, basis function method.

Discussion In ligand binding studies, it is desired to determine the receptor density and the binding/release of a ligand under different physiologic conditions. Thus, in the analysis of PET radioligand experiments, kinetic models have been formulated that provide surrogate measures of ligand binding kinetics (e.g. Bmax/Kd) (Mintun et al., 1984). In this regard, the macro-parameters of DV and BP have been established as standard outcome measures

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Table 5 Binding potential values

Refer to Table 1 for label descriptions. Values are reported as mean F SD. Colored lines report results from the full 120-min protocol, while white lines report results from the 60-min protocol. a BP was calculated as (DVVOI/DVREF)  1 rather than k3/k4. b Regressions with BP determined from the 2T model for the long protocol (120 min). All were significant at p < 0.0001. c Mean BP values taken from literature. [18F]FDPN, BP values determined from spectral analysis (Lochmann et al., 2003); [11C]DPN, BP values determined from a pulse-chase experiment (Jones et al., 1994).

for ligand binding studies. These parameters are combinations of the directly estimated model parameters and are often more stable than the micro-parameters that generate them. To provide some insight into the appropriate models and outcome measures for [18F]FDPN, we evaluated this tracer’s kinetics using seven standard models, including both invasive and noninvasive models under a bolus injection protocol. The macro-parameters, DV and BP, were then compared between the various modeling approaches. In this study, invasive compartmental models were applied to determine the maximal number of identifiable compartments given the current protocol, noise level and kinetic behavior of the data. It was observed that a two-tissue compartmental model could successfully characterize the majority of the VOIs evaluated. The parameter precisions degraded somewhat with increasing model complexity; however, the DV estimates were comparable for both the 2T and 1T models. Table 6 Normalized BP values

Refer to Table 1 for label descriptions. All values are normalized to the cerebellum. Colored lines present results from the full 120-min protocol, while white lines present results from the 60-min protocol.

Under the shortened protocol, a 2T model could still be applied; however, the 2T and 1T model fits were increasingly similar and the DV estimates from these two model structures appear to be converging. This suggests that under the shortened protocol, it is increasingly difficult to quantify k3 and k4 appropriately and that a simplification to the 1T model may be necessary, which may in turn lead to an underestimation of absolute DV values. The other outcome measure of interest, BP, can be defined as the k3/k4 ratio estimated from the 2T model; however, we were unable to attain reasonable estimates for this ratio. Jones et al. (1994) also found it difficult to attain reliable k3/k4 values from a tracer study for [11C]DPN, yet noted that the DV estimates from the tracer studies correlated well to the BP values obtained from pulsechase studies. Additionally, the significant correlations between BP and DV values observed here suggest that DV and BP values are providing similar relative information about [18F]FDPN binding kinetics. While compartmental models provide the most physiologically detailed description of the data (where compartments and rate constants often have direct physiologic interpretations), it is unlikely that the SNR of the data at a voxel level is sufficient to allow for the application of a compartmental model to the formation of parametric images. There is, however, increasing interest and utility in generating parametric images. Therefore, two additional invasive models (Inv_ Logan and BFN) that have previously been used in parametric image analysis were also evaluated. The BFN method is a data-driven method that does not make any assumptions on the connectivity of the compartments as does the compartmental modeling approach and its counterpart, spectral analysis, has been

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previously applied in the analysis of [11C]DPN data (Piccini et al., 1997; Weeks et al., 1997; Willoch et al., 1999, 2004) and [18F]FDPN (Lochmann et al., 2003). For the data analyzed here, we observed that the BFN method performed well and the resulting DV values were significantly correlated with those from the 2T model (R2: 0.917; P < 0.0001). This method resulted in DV values that were more variable across subjects and the values were slightly higher, yet consistent with the other methods. While differences in the absolute mean DV values were observed (Table 3), the mean regional DV distributions when normalized to the occipital region were more similar between the long and short protocols for the BFN method than the other methods. This may reflect the method’s ability to characterize the data without imposing a particular compartmental structure upon the data. This aspect of the method supports its use in future studies. The Logan model is a graphical-based method which can be easily applied on a voxel-by-voxel basis since it is performing a linear fit to the transformed data. However, this approach can lead to biased estimates for DV and additionally requires that the data be evaluated for times when a linear relationship exists between the transformed variables (Logan, 2000; Slifstein and Laruelle, 2000, 2001). Thus, the invasive Logan model was evaluated against the compartmental approaches to determine any potential biases in the model’s DV estimates for [18F]FDPN. A greater mean bias from the 2T model was observed with the Inv_ Logan model compared with that observed for the 1T model. The Inv_ Logan model also consistently underestimated DV across all regions with greater biases observed in regions with higher DV values. This is consistent with the findings in the literature (Logan, 2000; Slifstein and Laruelle, 2000). Note that the results presented here are based on a VOI analysis and the performance of the Logan model may be more variable in a parametric analysis due to the increased amount of noise on each voxel. Noninvasive modeling methods, which are also commonly referred to as reference region methods, could potentially circumvent the need for arterial sampling thereby reducing the risk and discomfort to the patient and simplifying the experimental and analysis protocols. While these methods are clearly attractive, the performance of reference region methods should be carefully evaluated before routine application. We thus included three such methods (the noninvasive Logan model, SRTM and tissue ratio method), which are all applicable to the generation of parametric images. The occipital region was chosen as the reference region for the noninvasive models. With regards to the models implemented here, the SRTM and NonInv_ Logan models resulted in similar BP values, which were consistent with those estimated from the 2T model. When comparing the full and shortened protocols, the NonInv_ Logan showed a greater difference under the shortened protocol than did the SRTM, which may reflect the fact that the NonInv_ Logan is affected by the noise in the transformed variables and possibly the fact that fewer data points were contributing to the analysis, since the model was applied to data between 25 and 60 min p.i., whereas the SRTM made use of the entire data set up to 60 min. The TRM’s BPratio values were found to correlate with estimates of BP determined by the 2T model, although they were higher across all regions under the full protocol. Since the current analysis follows a bolus injection protocol, we have most likely reached a transient equilibrium. Here, a constant BP value can be achieved since a constant ratio exists between the VOI and reference region, which is due to an equivalent rate of radioactive

clearance between the two regions. However, we must emphasize that the resulting BP values may not be equivalent to the actual BP that is achieved at true equilibrium or through kinetic modeling. Carson et al. (1993) has illustrated that large errors in DV can result from the application of this method to bolus injection protocols. These errors are somewhat reduced with ratios of tissues (BPratio values), as we have calculated here, yet can still be significant. Additionally, Carson highlights the fact that this method is sensitive to differences in plasma clearance between subjects and patient populations. Therefore, while this method is simpler to implement than kinetic modeling methods, it should only be applied when a state of true equilibrium can be achieved, such as with bolus plus constant infusion protocols. Distribution volume and binding potential The regional distributions of DV and BP values were consistent with opioid receptor distributions known from post-mortem and [11C]DPN studies (Jones et al., 1994; Pfeiffer et al., 1982). The thalamus and basal ganglia contain high opioid receptor density, followed by the frontal regions with decreasing receptor densities in the cerebellum and minimal opioid receptors in the occipital cortex. While it is assumed that [18F]FDPN and [11C]DPN have similar kinetic and metabolite behaviors, there are subtle differences between the fate of the two compounds that manifest themselves in differences in the outcome parameters (DV and BP). For example, the IRF60 distribution of [18F]DPN has also been previously shown to correspond to that of [11C]DPN, although higher nonspecific binding with [18F]FDPN is expected due to its higher lipophilicity (Wester et al., 2000). The increased nonspecific binding may also impact the binding potential values which were found to be lower than those determined from pulsechase experiments for [11C]DPN (Table 5) (Jones et al., 1994). DV was consistent between the models evaluated here with fairly low mean bias (<15% in applicable models and all regions except the occipital) and strong correlations between the models (R2 > 0.917; P < 0.0001). The occipital region was optimally fit by a 2T model, while the 1T model and Inv_ Logan model appear to underestimate the true value of the occipital region, leading to increased bias in these regions when compared with the 2T model. A broad range of DV values is important to adequately resolve subtle differences in regional DV values. The observed range of DV values was slightly reduced in the Inv_ Logan model compared with that observed for the compartmental models. While the BFN method exhibited a somewhat greater range in values compared with the compartmental models, it was also found to contain the most variability. The consistency of DV values determined by the various modeling approaches supports its use as an outcome measure reflective of receptor density for [18F]FDPN studies. However, it should be mentioned that the DV values calculated here will contain a contribution from the nonspecific binding compartment. Therefore, variability in the nonspecific compartment will be reflected in the DV values and may be contributing to some of the interindividual variability observed in this study. While the compartmental modeling approach is supported for VOI data with good SNR, alternative methods such as the Logan model and basis function methods may be better suited for voxelby-voxel analyses. Data-driven methods, such as the basis function and spectral analysis methods, have already been established as valid approaches for [11C]DPN and the work herein supports such

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an approach with [18F]FDPN as well. These methods may be better choices than the Logan model since they avoid transforming the data that propagates errors into the analysis. With regards to BP, our results indicated that the 2T compartmental and reference region modeling methods were strongly correlated (R2 values > 0.763; P < 0.0001). The BFN method was not found to correlate as well with the other methods, which may be reflective of the increased variability observed in the BFN’s DV values and thus propagated to the BP values. The higher BP values observed with the BFN method are most likely influenced by the method’s lower DV estimates for the occipital region and higher DV values across other regions. Regardless of the differences in BP values (Table 5), the normalized values (Table 6) illustrate that all methods were able to generate similar distribution ratios between the various regions under the full 120-min protocol. It is encouraging that a strong correlation was observed between BP estimates and the DV estimates on an individual subject basis, which indicate that the values we are calculating are reflective of the underlying binding potential, although their actual magnitude may be biased due to the use of the occipital reference region. The interindividual variability and the improved correlations of BP and DV values on an individual basis also suggest that when evaluating a study with statistical parametric mapping, it may be more appropriate to use proportional scaling in the evaluation.

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researcher. Therefore, we performed a stability analysis of DV and BP estimates for a protocol length of 60 min. In general, the shortened protocol resulted in DV values that were reduced in absolute value yet significantly correlated with the full protocol’s results (P < 0.0001). As mentioned earlier, the BFN method resulted in a consistent distribution of DV values under the long and short protocol, suggesting its use in a protocol of a shorter duration. Of the noninvasive methods, the SRTM resulted in very consistent BP values between the long and short protocols. This stability analysis showed promising results and we would encourage a future study for optimization of protocol length and other experimental factors in the quantification of [18F]FDPN. A secondary motivation for examining the 60-min data is focused on developing an appropriate protocol for potential displacement studies, where a challenge is delivered at some point during a single scan. The first requirement of such an analysis is to accurately quantify the prechallenge binding of the tracer. Our data suggest that accurate quantification of prechallenge binding is feasible; however, since this was not the main motivation for this manuscript, we would again suggest further studies to determine an efficient and accurate experimental design for displacement studies, including exploring alternative dosing protocols (e.g. twoinjection protocols or bolus plus constant infusion), scan length and placement of the challenge. Study improvements

Reference region There is recent evidence from a naloxone blocking study with 95% occupancy of available opiate receptors that the occipital region cannot serve as an ideal receptor free reference region for [11C]DPN (Asselin et al., 2003). Nonetheless, previous studies have employed the use of a reference region when evaluating DPN data (Lochmann et al., 2003; Piccini et al., 1997; Willoch et al., 2004). The occipital region is commonly used as such a reference region for DPN studies and although it may contain a small amount of opiate receptors, specific binding in this region is expected to be minimal. Thus, we also used the occipital region as the reference region for the noninvasive modeling methods. While we were unable to evaluate the bias introduced by using the occipital cortex as a reference region, we presented a comparison between the modeling methods and evaluated BP against DV estimates. The consistency of the normalized BP values between methods suggests that in a longitudinal study where subjects are evaluated more than once, the noninvasive methods and the use of BP may be a viable analysis approach. However, due to the presence of minimal yet nonnegligible specific binding in the occipital region, any potential change in specific binding within the occipital region between conditions should be investigated. If DV values within the reference region are changing significantly between conditions, this will influence BP estimates. In such a setting, it would be more reasonable to use an invasive approach and DV values rather than BP, assuming that the nonspecific binding remains relatively constant across regions and subjects. Shortened protocol A shortened protocol that accurately quantifies [18F]FDPN binding kinetics would be beneficial to both the subject and

This study has provided an initial examination of [18F]FDPN binding kinetics in humans and has also revealed some areas for potential methodological improvements. For example, the estimation of K1 and Vp may be improved by shortening the initial imaging frames. Additionally, for practical reasons, the last metabolite sample was acquired at 90 min. It has been pointed out elsewhere that errors in the metabolite estimation and hence the metabolite corrected input function will have a direct effect on the estimate of binding parameters (Lammertsma, 2002). Therefore, an additional sample at 120 min may improve the accuracy of the final results, although we have found large errors associated with metabolite samples at late time points. As shown in Eqs. (3) and (5), we have been estimating plasma volume, rather than blood volume. Ideally, the whole blood measurement should be acquired and used in the modeling process (Lammertsma, 2002). However, in this study, whole blood measurements were not acquired; therefore, the whole plasma curve (without metabolite correction) was used to estimate a plasma volume term. Thus, to improve the full interpretation of future study results, we would also suggest acquiring whole blood values for the estimation of blood volume. Summary This work shows that DV values estimated from compartmental, basis function and invasive Logan modeling approaches are robustly determined by each of these methods for [18F]FDPN. The fact that the invasive Logan and basis function methods are providing similar results to those of the compartmental analyses is encouraging for their application to parametric image generation, although the level of noise in the data should be considered when applying the invasive Logan model parametrically. The binding potential values correlated well with one another although more variability was observed in these values compared with the

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DV values. The BP values were also significantly correlated with the DV values estimated from the 2T model, illustrating consistency between DV and BP measures of [18F]FDPN binding. The noninvasive methods resulted in BP values consistent with those of the invasive methods, and additionally showed less interindividual variability. The results also suggest that a shorter protocol may be feasible to assess [18F]FDPN kinetics following a bolus injection, although the appropriate analysis method should be considered. In conclusion, all models evaluated in this study were able to quantify [18F]FDPN kinetics. The distribution volume appears to be a more consistent parameter for the quantification of receptor density for [18F]DPN and is not influenced by the choice of reference region. However, the noninvasive methods and binding potential values may be of value in clinical research when large numbers of patients are examined and a manageable study protocol (without arterial sampling) is necessary.

Acknowledgments We would like to acknowledge the work of our colleagues Brigitte Dzewas and Choletta Kruschke for their excellent technical assistance in data acquisition. This work was supported by grants from the KKF (8764153), the Deutsche Forschungsgesellschaft (SFB 391, TP C9), the German Network for Neuropathic Pain by BMBF and the Norwegian Research Council Project number 151445/432.

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