Evaluation of Tracer Kinetic Models for Analysis of [¹⁸F]FDDNP Studies

Abstract

Purpose

Different pharmacokinetic methods for [¹⁸F]FDDNP studies were evaluated using both simulations and clinical data.

Procedures

Methods included two-tissue reversible plasma (2T4k), simplified reference tissue input (SRTM), and a modified 2T4k models. The latter included an additional compartment for metabolites (2T1M). For plasma input models, binding potential, BP_ND, was obtained both directly (=k₃/k₄) and indirectly (using volume of distribution ratios).

Results

For clinical data, 2T1M was preferred over 2T4k according to Akaike criterion. Indirect BP_ND using 2T1M correlated better with SRTM then direct BP_ND. Fairly constant volume of distribution of metabolites was found across brain and across subjects, which was strongly related to bias in BP_ND obtained from SRTM as seen in simulations. Furthermore, in simulations, SRTM showed constant bias with best precision if metabolites entered brain.

Conclusions

SRTM is the method of choice for quantitative analysis of [¹⁸F]FDDNP even if it is unclear whether labeled metabolites enter the brain.

Introduction

[¹⁸F] FDDNP has recently been introduced [1] as a positron emission tomography (PET) ligand for in vivo imaging of amyloid plaques and neurofibrillary tangles in the human brain. Plaques and tangles are thought to be the hallmark of Alzheimer’s disease (AD) [2], and early in vivo detection of these neuropathological lesions could be an important step in evaluating future treatment strategies for AD.

So far, only a few methods for quantification of [¹⁸F]FDDNP have been evaluated, such as residence time within a cerebral region relative to that in pons [3], standardized uptake value (SUV) [4], distribution volume ratio (DVR) [4] obtained with Logan analysis [5] using cerebellum as reference region, and several simplified reference tissue-based methods [6] also using cerebellum as reference region. Using Logan analysis, Kepe et al. [7] recently reported increased levels of [¹⁸F]FDDNP binding in neocortical regions compared with that in cerebellum in AD patients, whereas no difference in uptake between cerebellum and other regions was found in healthy controls (HC). In addition, Small et al. [8] found that global DVR values in HC were lower than in patients with mild cognitive impairment (MCI), which in turn were lower than in AD subjects. However, arterial sampling was not used in any of these studies. Arterial sampling is considered to be the gold standard, especially if pathological changes may also affect reference regions.

The purpose of the present study was to investigate which pharmacokinetic model could best be used for quantitative analysis of [¹⁸F]FDDNP studies. To this end, both simulated and clinical [¹⁸F]FDDNP data were used. Data were analyzed using various compartmental models based on plasma [9] and reference tissue [10–12] input data. In addition, a plasma input model was evaluated, which accounted for uptake of labeled metabolites in the brain. Finally, standard uptake value ratios with cerebellum (SUV_r) were investigated.

Methods

Scanning Protocol

Clinical data were derived from ongoing patient studies consisting of 12 subjects (six HC, three MCI [13], and three AD) with ages ranging from 58 to 72 years. Mean age (±SD) was 66 ± 5, 68 ± 4, and 63 ± 6 for HC, MCI, and AD, respectively. AD patients were diagnosed with probable AD meeting NINCDS-ADRDA criteria [14]. The study was approved by the Medical Ethics Committee of the VU University Medical Centre, and each subject gave written informed consent prior to inclusion in the study. Clinical results are beyond the scope of the present study and will be reported elsewhere.

As part of the study protocol, each subject first underwent a T1-weighted magnetic resonance imaging (MRI) scan using a 1.5-T SONATA scanner (Siemens Medical Solutions, Erlangen, Germany). This MRI scan was performed to exclude anatomical abnormalities and for co-registration and segmentation purposes.

PET studies were performed using an ECAT EXACT HR+ scanner (CTI/Siemens, Knoxville, USA). The characteristics of this scanner have been described previously [15]. First, a 10-min transmission scan in 2D acquisition mode was performed. This scan was used to correct the subsequent emission scan for tissue attenuation. Next, a dynamic emission scan in 3D acquisition mode was performed following bolus injection of 168 ± 8 MBq [¹⁸F]FDDNP [16]. This dynamic emission scan consisted of 23 frames (1 × 15, 3 × 5, 3 × 10, 2 × 30, 3 × 60, 2 × 150, 2 × 300, 7 × 600 s) with a total scan duration of 90 min. All frames were reconstructed using FORE+ 2D filtered back projection [17] and a Hanning filter with a cutoff of 0.5 times the Nyquist frequency. Reconstructions included all standard corrections, such as normalization, and decay, dead time, attenuation, randoms, and scatter [18] corrections.

The protocol also included continuous arterial sampling, starting 2 min prior to injection and continuing up to 60 min, using a dedicated online detection system [19]. In addition, at set times (5, 10, 20, 40, and 60 min post-injection), arterial sampling was interrupted briefly for the withdrawal of discrete arterial samples. After each sample, the arterial line was flushed with heparinized saline in order to avoid clotting within the line. Finally, two manual samples were withdrawn at 75 and 90 min post-injection.

Arterial blood samples were used to determine plasma and whole blood radioactivity concentrations using a well counter cross calibrated against the PET scanner [20]. In addition, plasma parent tracer and metabolite concentrations were determined using solid phase extraction combined with high-performance liquid chromatography technology and equipped with off-line radioactivity detection [21]. An arterial whole blood curve was obtained by correcting the online sampler curve for decay, removing the flushing periods, and calibrating against the discrete (whole blood) sample data. Finally, a metabolite-corrected plasma curve was derived from this whole blood curve using both plasma to whole blood ratios and metabolite fractions obtained from the manual blood samples. To this end, the total fraction of labeled metabolites as function of time was fitted to a Hill-type function [22]. This function provided more accurate fits than other functions such as multi-exponentials. Arterial blood sampling was not available for six subjects (three HC and three MCI). Data from these subjects were only used for investigating reference tissue models.

Image Analysis

De-skulled T1-weighted MRI scans [23] were co-registered [24, 25] with a summed PET image (frames 3–12, 25 s–5 min post-injection). This summed PET image resembles a flow image, thereby maximizing cortical information. Time–activity curves were then generated using MR-based automatic delineation of regions of interest (ROI), as described by Svarer et al. [26]. For the purpose of the present study, only TACs from 17 regions (cerebellum, orbital frontal cortex, medial inferior frontal cortex, anterior cingulate cortex, thalamus, insula, caudate, putamen, superior temporal cortex, parietal cortex, medial inferior temporal cortex, superior frontal cortex, occipital cortex, sensory motor cortex, posterior cingulate cortex, enthorinal cortex, hippocampus), all averaged over left and right hemispheres, were analyzed. These anatomical regions were small and defined in gray matter only, thereby minimizing signal dilution due to partial volume effects as much as possible.

Kinetic Analyses of Clinical Data

Clinical data were analyzed using conventional plasma input and reference tissue-based algorithms [9]. As there is some concern that labeled [¹⁸F]FDDNP metabolites might cross the blood–brain barrier [27, 28], additional analyses were performed using a plasma input model accounting for metabolites entering the brain. In addition, average regional activity concentration ratios with the reference region (SUV_r) were derived over the time intervals of 40–60, 60–90, and 80–90 min after injection. For all reference tissue models and SUV_r cerebellar gray matter was used as reference region based on its relatively low levels of amyloid and neurofibrillary tangles [2].

Five different conventional compartmental models were evaluated: single-tissue (1T2k), two-tissue irreversible (2T3k) and two-tissue reversible (2T4k) plasma input models, and simplified (SRTM) [12] and full (FRTM) [10, 11] reference tissue models. Plasma input models contained one additional fit parameter for blood volume. The SRTM was used to estimate binding potential directly . The 2T4k plasma input model was used to estimate binding potential both directly and indirectly using volume of distribution ratios [11]. The latter approach will be indicated by 2T4kⁱ.

Based on the possibility of metabolites entering the brain [27, 28], also a modified 2T4k model was used. This model included an additional (parallel) single-tissue compartment for labeled metabolites (2T1M, Fig. 1). The metabolite input curve was based only on polar metabolites and ignores the minor fraction of other metabolites. The direct binding potential for this model was defined as k₃/k₄ (Fig. 1), and the volumes of distributions, V_T and V_Tm, were defined as and K_1m/k_2m, respectively. Similar to 2T4kⁱ, the binding potential was also estimated indirectly using the volume of distribution ratios with the cerebellum as reference region . All 2T1M fits were repeated after fixing V_Tm to the cerebellum value (=2T1M_fvtm). This model was also used to estimate binding potential both directly and indirectly using DVR − 1 . The indirect methods for estimating BP_ND using 2T1M and 2T1M_fvtm will be indicated by 2T1Mⁱ and , respectively.

Fig. 1.

Schematic diagram of the model that includes a tissue metabolite compartment. BBB represents the blood–brain barrier; P^Parent and P^Met are tracer plasma radioactivity concentrations (Bq ml⁻¹) of parent and labeled metabolites, respectively; T is the radioactivity concentration in tissue, F+NS^Parent that of free and non-specifically bound parent in tissue, S^Parent that of bound parent in tissue; and F+NS^Met that of labeled metabolites in tissue (Bq ml⁻¹); K₁ (ml·cm⁻³·min⁻¹) and k₂ (min⁻¹) are rate constants, describing exchange of parent between plasma and tissue; k₃ and k₄ are rate constants (min⁻¹), describing exchange of parent between free and bound compartments; K_1m (ml·cm⁻³·min⁻¹) and k_2m (min⁻¹) are rate constants, describing exchange of labeled metabolites between plasma and tissue.

Clinical Studies

Clinical results were evaluated in several ways. First, for all compartmental models (SRTM, FRTM, 1T2k, 2T3k, 2T4k, 2T1M, and 2T1M_fvtm), fitted TACs were evaluated using the Akaike criterion. Next, where possible, BP_ND values were estimated both directly and indirectly using V_T ratios with cerebellum (i.e., 2T4kⁱ, 2T1Mⁱ and ). In addition, estimates of BP_ND were compared with . Finally, SUV_r − 1 values were estimated and compared with , given that at true equilibrium, SUV_r corresponds with DVR.

Simulation Studies

Conventional Simulations

Simulated time–activity curves (TACs) for target and reference regions were generated using a typical [¹⁸F]FDDNP plasma input function in combination with the two-tissue reversible plasma input model (2T4k). In the simulations, variations in binding, delivery, and fractional blood volume were investigated.

Kinetic parameters were based on typical 2T4k parameters obtained from clinical data. Default parameters for simulated reference and target tissue TACs are given by R1 and T1, respectively, as listed in Table 1. Target tissue parameters were varied with respect to binding potential ( and : T2–T5), fractional blood volume (V_b: T6, T7), and delivery (K₁: T8–T15). One hundred TACs were generated for each run and noise was added to simulate an average noise level of 7.5% coefficient of variation (COV). Noise simulation was based on clinically derived typical values of total scanner true counts, frame lengths, and decay correction factors. A detailed description of the noise simulation used is given in [29].

Table 1.

Kinetic parameters used to generate reference (R) and target (T) tissue time activity curves (TAC)

TAC	K1 (ml·cm−3·min−1)		Vb	VT
R 1	0.35	1.63	0.050	8.7	–
T 1	0.35	2.3	0.050	11	0.25
T 2	0.35	1.7	0.050	8.9	0.03
T 3	0.35	2.0	0.050	9.9	0.14
T 4	0.35	2.6	0.050	12	0.37
T 5	0.35	2.9	0.050	13	0.48
T 6	0.35	2.3	0.025	11	0.25
T 7	0.35	2.3	0.075	11	0.25
T 8	0.21	2.3	0.050	11	0.25
T 9	0.25	2.3	0.050	11	0.25
T 10	0.28	2.3	0.050	11	0.25
T 11	0.32	2.3	0.050	11	0.25
T 12	0.39	2.3	0.050	11	0.25
T 13	0.43	2.3	0.050	11	0.25
T 14	0.46	2.3	0.050	11	0.25
T 15	0.50	2.3	0.050	11	0.25

K₁, k₂, and k₃ are rate constants, V_b is fractional blood volume, V_T is volume of distribution, and and are binding potentials estimated directly (2T4k) and indirectly (2T4kⁱ) using the reversible two-tissue model, respectively. The indirect calculation of BP_ND was performed using target to reference volumes of distribution ratios. During all simulations, k₄ (0.032 min⁻¹) and K₁/k₂ (3.3) were fixed

Simulated data were analyzed using conventional models as described above (1T2k, 2T3k, 2T4k, SRTM, FRTM, and 2T4kⁱ) and SUV_r methods over the time intervals 40–60, 60–90, and 80–90 min. Fits were evaluated by comparing goodness of fit according to the Akaike criterion. Next, models were evaluated by comparing bias and COV of estimated binding potential (where appropriate, also the indirect estimation through volumes of distribution). Bias was estimated in relative terms using , where represents BP_ND estimated using the method of analysis under investigation and simulated BP_ND, which was set to either or for direct and indirect methods, respectively.

Metabolite Model

To simulate the effects of cerebral uptake of labeled metabolites, simulated TACs were generated using a typical [¹⁸F]FDDNP plasma input function in combination with the 2T1M model. Kinetic parameters were based on typical 2T1M parameters obtained from clinical data. Default parameters for simulated reference and target tissue TACs are given by R1 and T1, respectively, as listed in Table 2. Target tissue parameters were varied, including binding potential ( and : T2–T9), delivery of metabolites (K_1m: T10–T13), and volume of distribution of metabolites (V_Tm: T14–T21). One hundred TACs were generated for each run and noise was added to simulate an average noise level of 7.5% COV, as described above.

Table 2.

Kinetic parameters used to generate reference (R) and target (T) TAC

TAC	K1 (ml·cm−3·min−1)		Vb	VT		K1m (ml·cm−3·min−1)	VTm
R 1	0.34	0.65	0.05	4	–	–	–
T 1	0.34	1.3	0.05	5.59	0.39	0.50	0.59
T 2	0.34	0.8	0.05	4.37	0.09	0.50	0.6
T 3	0.34	1.0	0.05	4.86	0.21	0.50	0.6
T 4	0.34	1.2	0.05	5.34	0.33	0.50	0.6
T 5	0.34	1.4	0.05	5.83	0.45	0.50	0.6
T 6	0.34	1.6	0.05	6.31	0.58	0.50	0.6
T 7	0.34	1.8	0.05	6.80	0.70	0.50	0.6
T 8	0.34	2.1	0.05	7.53	0.88	0.50	0.6
T 9	0.34	2.3	0.05	8.01	1.00	0.50	0.6
T 10	0.34	1.3	0.05	5.59	0.39	0.00	0.6
T 11	0.34	1.3	0.05	5.59	0.39	0.01	0.6
T 12	0.34	1.3	0.05	5.59	0.39	0.03	0.6
T 13	0.34	1.3	0.05	5.59	0.39	0.05	0.6
T 14	0.34	1.3	0.05	5.59	0.39	0.50	0.1
T 15	0.34	1.3	0.05	5.59	0.39	0.50	0.2
T 16	0.34	1.3	0.05	5.59	0.39	0.50	0.3
T 17	0.34	1.3	0.05	5.59	0.39	0.50	0.4
T 18	0.34	1.3	0.05	5.59	0.39	0.50	0.5
T 19	0.34	1.3	0.05	5.59	0.39	0.50	0.7
T 20	0.34	1.3	0.05	5.59	0.39	0.50	0.8
T 21	0.34	1.3	0.05	5.59	0.39	0.50	0.9

A two-tissue reversible compartmental model with an additional single-tissue compartment for metabolites was used. K₁, k₂, and k₃ are rate constants, V_b is fractional blood volume, and V_T is volume of distribution for [¹⁸F]FDDNP. and and are binding potentials estimated directly and indirectly using the metabolite model, respectively. The indirect calculation of BP_ND was performed using target to reference volumes of distribution ratios. K_1m is a rate constant and V_Tm the volume of distribution for the metabolites. During all simulations, k₄ (0.099 min⁻¹) and K₁/k₂ (2.4) were fixed, and same, the K_1m and k_2m were used in reference and target tissues

Simulated data were analyzed using 2T4k, 2T4kⁱ, 2T1M_fvtm (i.e., 2T1M with V_Tm fixed to the simulated value), (i.e., indirect estimation through volumes of distribution), and SRTM. Bias and COV of binding potential obtained were compared between the various models. Bias for direct and indirect 2T1M models was defined in a similar way as for the standard models, i.e., using , where represents BP_ND estimated using the method of analysis under investigation and simulated BP_ND, set to either or for direct and indirect models, respectively.

In addition to BP_ND, in metabolite simulations, also V_T values were estimated using 2T4k and the 2T1M_fvtm models. Bias in estimated V_T for the 2T4k model was defined as , where is . Bias in estimated V_T for the 2T1M_fvtm model was defined as , where is (K₁/k₂) × (1 + BP_ND).

Results

Time–Activity Curves

Typical parent [¹⁸F]FDDNP and polar metabolite plasma curves are shown in Fig. 2a and typical time–activity curves for cerebellum and frontal cortex in Fig. 2b. The average (N = 5) fractions of [¹⁸F]-labeled metabolites in plasma as function of time are shown in Fig. 3, fitted using a Hill type function. Very rapid metabolism of [¹⁸F]FDDNP can be seen, with metabolite-related [¹⁸F] activity primarily due to polar metabolites (Fig. 3). The polar metabolites are composed of N-dealkylated fragments with similar chromatogram retention times as primarily fluoroethanal and with a smaller fractions of fluoroacetic acids [28].

Fig. 2.

Typical [¹⁸F]FDDNP decay corrected time activity curves from an AD subject for a metabolite-corrected parent compound and polar metabolites in plasma and b cerebellum and frontal cortex (ctx) gray matter.

Fig. 3.

Fraction of [¹⁸F]-labeled polar metabolites (dark dashed line) and parent compound (dark line) in plasma as function of time, averaged over seven subjects, together with standard deviations (dashed light gray lines at one SD from average).

Clinical Studies

Fig. 4 show typical fits using various compartmental models. In general, poor fits were seen for the 1T2k model (Fig. 4a). Metabolite models showed slightly better fits (Fig. 4b) than all conventional models (Fig. 4a). Good fits were seen for the reference tissue models (Fig. 4c). Similarly, the Akaike criterion gave preference to 2T1M models above other plasma input models (2T1M_fvtm 37.3%, 2T1M 31.7%, 2T4k 26.2%, 2T3k 4.8%, and 1T2k 0% preference, respectively). With respect to reference tissue models, the Akaike criterion had strong preference for SRTM (88%).

Fig. 4.

Decay corrected frontal cortex gray matter time–activity curve from an AD subject (=data) with fits using a conventional plasma input, b metabolite, and c reference tissue models.

Average values of the various parameters, together with observed range, for 2T4k, 2T1M, and SRTM models are given in Tables 3, 4, and 5 for typical AD regions, i.e., for regions previously shown to be involved in AD [8]. These regions were used in order to accurately estimate typical kinetic parameters for AD subjects, as the latter parameter estimates were used in the simulations.

Table 3.

Average (±SD) values of the kinetic parameters together with their range given between brackets for the reversible two-tissue compartment model

Data	K1	k2	k3		VT		Vb
HC ctx	0.25 ± 0.03 (0.2–0.3)	0.06 ± 0.01 (0.04–0.08)	0.02 ± 0.01 (0.01–0.05)	2.14 ± 0.71 (1–4)	14 ± 6 (7–25)	0.22 ± 0.18 (−0.04–0.7)	0.03 ± 0.01 (0.01–0.05)
AD ctx	0.36 ± 0.08 (0.3–0.5)	0.06 ± 0.01 (0.04–0.08)	0.02 ± 0.01 (0.01–0.04)	1.76 ± 0.71 (1–3)	17 ± 5 (9–26)	0.23 ± 0.20 (−0.03–0.6)	0.05 ± 0.03 (0.02–0.11)
AD + HC cer	0.35 ± 0.09 (0.3–0.5)	0.07 ± 0.01 (0.06–0.09)	0.02 ± 0.02 (0.01–0.06)	1.67 ± 0.56 (1–3)	13 ± 5 (6–20)	–	0.03 ± 0.02 (0.01–0.07)

These consisted of several typical AD cortical (ctx, i.e., orbital frontal cortex, medial inferior frontal cortex, anterior cingulate cortex, superior temporal cortex, parietal cortex, medial inferior temporal cortex, superior frontal cortex, enthorinal cortex, hippocampus) and cerebellar (cer) gray matter regions from healthy controls (HC) and AD subjects. K₁ and K_1m are given in ml·cm⁻³·min⁻¹, k₂ and k₃ in min⁻¹. and are binding potentials estimated directly and indirectly, respectively, using the reversible two-tissue plasma input model. and are binding potentials estimated directly and indirectly, respectively, using the metabolite model. is the binding potential estimated using the simplified reference tissue model

Table 4.

Average (±SD) values of the kinetic parameters together with their range given between brackets for the 2T1M metabolite model

Data	K1	k2	k3		VT		Vb	K1m	VTm
HC ctx	0.28 ± 0.05 (0.2–0.4)	0.33 ± 0.30 (0.09–0.68)	1.06 ± 0.75 (0.01–2.43)	3.07 ± 2.89 (0.4–11)	3.70 ± 0.62 (3–5)	0.03 ± 0.14 (−0.18–0.44)	0.03 ± 0.01 (0.01–0.05)	0.08 ± 0.10 (0.01–0.5)	0.66 ± 0.07 (0.49–0.76)
AD ctx	0.41 ± 0.10 (0.3–0.6)	0.24 ± 0.15 (0.09–0.73)	0.54 ± 0.50 (0.05–1.84)	2.06 ± 1.65 (0.6–8)	5.19 ± 0.86 (4–7)	0.06 ± 0.11 (−0.2–0.3)	0.04 ± 0.02 (0.01–0.09)	0.16 ± 0.27 (0.03–0.93)	0.65 ± 0.06 (0.55–0.78)
AD + HC cer	0.39 ± 0.13 (0.3–0.6)	0.28 ± 0.16 (0.10–0.53)	0.49 ± 0.47 (0.04–1.30)	1.89 ± 1.42 (0.5–4)	4.24 ± 1.07 (3–6)	–	0.02 ± 0.02 (0.01–0.05)	0.34 ± 0.46 (0.02–1.00)	0.60 ± 0.04 (0.53–0.67)

These consisted of several typical AD cortical (ctx, i.e., orbital frontal cortex, medial inferior frontal cortex, anterior cingulate cortex, superior temporal cortex, parietal cortex, medial inferior temporal cortex, superior frontal cortex, enthorinal cortex, hippocampus) and cerebellar (cer) gray matter regions from healthy controls (HC) and AD subjects. K₁ and K_1m are given in ml·cm⁻³·min⁻¹, k₂ and k₃ in min⁻¹. and are binding potentials estimated directly and indirectly, respectively, using the reversible two-tissue plasma input model. and are binding potentials estimated directly and indirectly, respectively, using the metabolite model. is the binding potential estimated using the simplified reference tissue model

Table 5.

Average (±SD) values of the kinetic parameters together with their range given between brackets for the simplified reference tissue model, derived from clinical data

Data	R1	k2
HC ctx	0.89 ± 0.06 (0.7–1.0)	0.08 ± 0.02 (0.03–0.11)	0.06 ± 0.04 (−0.07–0.12)
AD ctx	0.87 ± 0.08 (0.7–1.0)	0.06 ± 0.02 (0.03–0.11)	0.07 ± 0.04 (0.00–0.14)

Fig. 5 shows high correlation (R² = 0.95) between K_1m and k_2m values from the 2T1M model over all regions and subjects, indicating an almost constant V_T for metabolites. Table 6 shows correlation coefficients obtained from linear regression analyses of various outcome measures with . As expected, high correlation was found between BP_ND estimates of SRTM and FRTM (R² = 0.99). In addition, good correlation was obtained for SUV_r over 40–60 min (R² = 0.93). Note that the 2T1Mⁱ models, i.e., including a compartment for metabolites entering the brain, correlated better with SRTM than the conventional 2T4kⁱ model (Table 6 and Fig. 6).

Fig. 5.

Correlation between metabolite influx (K_1m) and efflux (k_2m) rate constants for clinical [¹⁸F]FDDNP data from several regions of interests and subjects. These rate constants were obtained using a modified two-tissue reversible model, including an additional single-tissue compartment for metabolites.

Table 6.

Outcome parameters (slope, intercept, and Pearson product moment correlation coefficient R²) for linear regression of different models versus

Model	Slope	Intercept	R2
FRTM	0.97	0.01	0.99
2T4k	−4.11	2.21	0.15
2T4ki	NAa	NA	NA
2T1M	NA	NA	NA
2T1Mi	2.66	−0.11	0.68
2T1Mfvtm	NA	NA	NA
	2.59	−0.09	0.58
SUVr40–60	1.14	0.03	0.93
SUVr60–90	0.64	0.06	0.69
SUVr80–90	0.46	0.06	0.43

In the case of SUV_r methods, SUV_r − 1 was taken as an estimate of BP_ND

^aNA indicates poor correlation, i.e., R² < 0.10

Fig. 6.

Correlation of BP_ND from 2T1Mⁱ_fvtm and 2T4kⁱ, respectively, with for clinical [¹⁸F]FDDNP data obtained from several regions of interest and subjects. 2T4kⁱ represents the reversible two-tissue plasma input model and 2T1Mⁱ_fvtm the modified reversible two-tissue model, which includes an additional parallel single-tissue compartment for metabolites. For both models, BP_ND was estimated indirectly through calculation of distribution volume ratios.

Simulation Studies

Conventional Simulations

In general, SRTM produced better fits than FRTM according to the Akaike criterion (∼85% preference). According to the same criterion, 2T4k showed better fits than both 1T2k and 2T3k in all simulations (∼96% preference). At lower K₁ values, however, preference for 2T4k reduced in favor of 2T3k (max. 33% preference for 2T3k). Visual inspection showed poor fits for the 1T2k model, similar to what was seen in clinical fits, and therefore, it was excluded from further evaluation.

When simulating different levels of binding the 2T4k model (direct estimation of BP_ND) showed good overall accuracy (5% bias BP_ND), but mediocre precision (24% COV BP_ND). Results for reference tissue-based models, including SUV_r, are summarized in Table 7. In general, all reference tissue-based methods showed increased bias at lower levels of binding, but results were more stable at higher levels. Therefore, bias estimates were averaged only over the stable part, i.e., for . In contrast, absolute differences with simulated values were more stable and are shown over the full range of simulated values (Table 7). Average bias (Table 7) over the stable range of was lowest for indirect 2T4k (2T4kⁱ). 2T4kⁱ and SRTM both showed relatively constant bias and high precision for higher simulated BP_ND levels. Finally, best accuracy and precision for SUV_r was obtained with SUV_r40–60.

Table 7.

Average bias and absolute difference (diff.) with simulated BP_ND over a range of simulated for various reference tissue models

Model	Bias (%)	SD in bias (%)	Diff.	SD in diff.
2T4ki	1	17	0.041	0.033
SRTM	−12	16	0.053	0.062
FRTM	−13	23	0.094	0.175
SUVr40–60	−1	14	0.034	0.026
SUVr60–90	16	15	0.054	0.037
SUVr80–90	22	33	0.095	0.072

In addition, corresponding SD are given. In the case of SUV_r methods, SUV_r − 1 was taken as an estimate of BP_ND. For bias, the range was set from 0.25 to 0.48 due to the large relative biases at lower specific binding. For absolute difference, the range was set from 0.03 to 0.48

All models were less sensitive to changes in V_b. At a fixed level of binding (BP_ND = 2.3, ), variations in derived BP_ND due to changes in simulated V_b were smaller than 5% for all compartmental models. For SUV_r methods, bias (±COV) in approximated BP_ND (i.e., SUV_r − 1) depended on the actual time interval used and changed from 21 ± 16% to 10 ± 18%, from 30 ± 22% to 28 ± 21%, and from 31 ± 41% to 34 ± 45% for SUV_r40–60, SUV_r60–90, and SUV_r80–90, respectively, when varying V_b of the target region from 0.025 to 0.075.

Delivery differences affected all compartmental methods, including plasma input models. For the direct 2T4k model, bias in BP_ND varied from 10% to −2% when varying K₁ of the target region from 0.212 to 0.496. Results for indirect 2T4k and SRTM are shown in Fig. 7. Results from FRTM are not included, as BP_ND bias was as high as 250%. Bias in BP_ND (±COV), based on SUV_r − 1, ranged from −27 ± 18% to 3 ± 17%, from 25 ± 20% to −3 ± 18%, and from 48 ± 36% to −7 ± 39% for SUV_r40–60, SUV_r60–90, and SUV_r80–90, respectively, when varying K₁ of the target region from 0.212 to 0.496.

Fig. 7.

Bias of BP_ND for different compartment models for simulated [¹⁸F]FDDNP data (obtained using 2T4k) as function of variable target influx rates (K₁ target). Error bars represent SD in bias. K₁ in reference region was fixed to 0.35, and K₁/k₂ was fixed to 3.3 for both target and reference regions. 2T4kⁱ and SRTM represent indirect (using volumes of distribution) two-tissue reversible and simplified reference tissue models, respectively.

Metabolite Simulations

Metabolite simulations were limited to 2T4k, 2T1M_fvtm, and SRTM. SRTM provided the most precise estimation of BP_ND over the range of simulated K_1m with a COV of 4.0 ± 0.4%. Although there was a strong negative bias (−42 ± 7%) for SRTM, it was very constant (Fig. 8a). provided a more accurate estimate of BP_ND (5 ± 7% bias), but precision (COV of 37 ± 20%) was much poorer than for SRTM (Fig. 8a). 2T1M_fvtm, 2T4k, and 2T4kⁱ provided lower precision and higher bias in estimated BP_ND over the range of simulated K_1m (Fig. 8a, b). However, V_T estimates with the 2T1M_fvtm model were much more accurate and had higher precision (Fig. 8c).

Fig. 8.

Bias of a indirect and reference tissue model BP_ND, b direct BP_ND, and cV_T estimates from different compartment models. Error bars represent SD in bias. Simulated [¹⁸F]FDDNP data were generated using the metabolite plasma input model (2T1M) with variable metabolite influx rates (K_1m).

Simulations over a range of different binding levels showed strong negative bias (−46 ± 4% with COV of 7 ± 6%) for SRTM, but again, resulting BP_ND estimates were the most stable amongst all models tested (Fig. 9a). Similarly, most accurate results were obtained with indirect 2T1M_fvtm (Fig. 9a). Precision of both SRTM and improved with increasing BP_ND. BP_ND estimates obtained with 2T1M_fvtm, 2T4k, and 2T4kⁱ were not precise and strongly biased (Fig. 9). Finally, Fig. 10a shows nearly linearly increasing (negative) bias in BP_ND obtained with SRTM for increasing V_Tm. In contrast, Fig. 10b illustrates that this bias was independent of K_1m for K_1m > 0.1.

Fig. 9.

Bias of a indirect (and reference tissue) and b direct BP_ND estimates from different compartment models for simulated [¹⁸F]FDDNP data generated using the metabolite plasma input model (2T1M) with various target tissue binding potentials. Error bars represent SD in bias.

Fig. 10.

Bias of BP_ND estimated with the simplified reference tissue model (SRTM) for simulated [¹⁸F]FDDNP data generated using the metabolite plasma input model (2T1M) as function of a various V_Tm values and b various metabolite influx rates (K_1m). Error bars represent SD in bias.

Discussion

Clinical Studies

Due to rapid plasma clearance and metabolism [¹⁸F]FDDNP scans, it proved to be difficult to obtain reliable measurements of metabolite fractions at later time points. As a result, only incomplete plasma data were available for six of the subjects, and data from these subjects were only used for evaluation of reference tissue models. Although only six subjects with complete plasma input data remained, this seems to be sufficient for this initial evaluation of quantitative (plasma input) models. Clearly, however, the difficulties in obtaining reliable plasma metabolite data should be taken into account when selecting a method for routine clinical studies.

Clinical [¹⁸F]FDDNP data were analyzed using conventional models, models correcting for possible metabolites entering the brain, and activity ratios. Clearly, due to the very nature of clinical data, absolute statements about accuracy and precision cannot be given. Therefore, the various methods were compared using the Akaike criterion. In addition, resulting BP_ND values were compared with SRTM, as this model showed stable results during simulations.

On the basis of the Akaike criterion, plasma input models with a compartment for metabolites were preferred over conventional plasma input models, and SRTM was preferred over FRTM. Good correlations with SRTM were obtained only for FRTM, SUV_r40–60, and plasma input models that included a compartment for metabolites entering the brain, such as 2T1Mⁱ and 2T1Mⁱ_fvtm (Fig. 6). For most other methods, correlations with SRTM were poor (R² < 0.1).

Specifically, in the case of the metabolite models, somewhat large values were seen for the micro parameters K_1m and k_2m (Fig. 5). However, the majority of observed K_1m values are below 0.5 (many overlapping data at lower K_1m), and K_1m and k_2m are well correlated. The higher K_1m and k_2m values are possibly the result of noise, as the higher values for K_1m and k_2m were generally seen for the smallest ROIs used. Moreover, the relative slow in-grow of metabolites, i.e., the metabolite input function shows a slow increase rather than a sharp peak, makes estimation of individual micro-parameters less precise. Note, however, that the macro-parameter V_Tm is reasonably stable across anatomical regions and subjects.

Observed improvements in fits and correlations for models that incorporate a labeled metabolite compartment, together with the reasonably constant V_Tm, suggest that metabolites enter the brain. This is in line with a previous assessment using multi-input spectral analysis [27] and initial animal studies where labeled metabolites of [¹⁸F]FDDNP were injected [28]. Additional studies are, however, needed to confirm whether this is indeed the case.

Simulation Studies

The standard 2T4k plasma input model was not a good model for estimating the level of specific [¹⁸F]FDDNP binding directly (i.e., as defined by k₃/k₄). Firstly, although BP_ND bias calculated relative to total binding potential showed good accuracy, it only had mediocre precision. Secondly, at lower regional delivery (=K₁) levels, its bias was sensitive to the actual value of K₁. This increased sensitivity to K₁ is related to the kinetics of [¹⁸F]FDDNP, which, for a normal level of binding in regions with low delivery, are relatively slow. Under those conditions, within the time frame of a scan, tracer kinetics are best described by an irreversible compartment model, which is illustrated by the increased preference for the 2T3k model according to the Akaike criterion.

The 2T1M_fvtm model did not provide accurate estimates of (direct) BP_ND in the metabolite simulations (Figs. 8b and 9b). Although data were simulated using the same model, BP_ND was very sensitive to noise as a result of the large number of fit parameters. However, V_T estimates obtained with the 2T1M_fvtm model were less sensitive to noise and provided highly accurate and precise V_T values (Fig. 8c).

For plasma input models, more accurate and precise results were obtained with indirect estimates of BP_ND (2T4kⁱ and ) than with their direct counterparts (2T4k and 2T1M_fvtm), especially in the case of metabolite simulations. In most cases, these indirect methods showed lower bias than . This higher accuracy of 2T4kⁱ (in conventional simulations) and (in metabolite simulations) was, however, accompanied with lower precision compared with .

SRTM was better than FRTM, both in terms of bias and COV. In addition, in the majority of the simulations, it was preferred by the Akaike criterion. SRTM results were comparable in conventional and metabolite simulations. If no metabolites entered the brain, SRTM-derived BP_ND showed a constant negative bias, although it was affected by changes in delivery. On the other hand, when polar metabolites entered the brain, SRTM showed increasing negative bias with increasing V_Tm. However, clinical data showed an overall constant V_Tm (Fig. 5). This indicates that variable bias in SRTM-derived BP_ND due to variability in V_Tm will be limited. Simulations showed that for V_Tm fixed to the clinical estimated value (V_Tm = 0.6), this bias also was not sensitive to metabolite influx (Fig. 10b, K_1m > 0.01, BP_ND bias ∼−46%). Furthermore, the bias found in these simulations could be related to the slope between versus (slope = 2.59, Table 6; 100% × (1/2.59) = 39%) for the clinical studies, indicating a relatively constant metabolite contribution in practice. Thus, SRTM seems to be a useful method, irrespective whether labeled metabolites enter the brain, provided that V_Tm is relatively constant across the brain and between subjects, as actually suggested by the clinical results.

Among SUV_r methods, over the range of simulated binding levels, only SUV_r40–60 showed acceptable results, with much better accuracy (−1%) than SRTM (−12%). However, apart from a strong dependency on variations in delivery, SUV_r results were also highly dependent on differences in blood volume fractions with only an acceptable accuracy for a specific time interval (SUV_r60–90). In general, SUV_r results varied widely between different time intervals which, together with the large uncertainties, indicate that this might not be the ideal method for clinical studies.

In general, SRTM showed best overall performance, although it showed some sensitivity to regional flow/delivery differences. As expected, SRTM, like all other reference tissue-based models, showed larger biases at lower regional binding levels. Important advantages of SRTM were its overall high precision and a relatively constant bias in BP_ND even in the presence of labeled metabolites. Although this bias was dependent on the actual value of V_Tm, clinical data indicated that this was constant across the brain and among subjects.

General Considerations

Amyloid plaques (and neurofibrillary tangles) do not behave like neuroreceptors. They have complex structures with multiple affinity sites for [¹⁸F]FDDNP. In addition, it is likely that access to amyloid sites will become more difficult with increasing plaque size [30]. Consequently, use of receptor-ligand models to assess amyloid load might provide an increasing underestimation with increasing load. In addition, quantification might be compromised by the possibility of labeled metabolites entering the brain, especially since the fraction of labeled (polar) metabolites in blood is high due to rapid metabolism of [¹⁸F]FDDNP.

Nevertheless, [¹⁸F]FDDNP may still be of value if a difference between MCI and healthy controls can be demonstrated, and it might be used to study pathological effects as a function of disease severity/progression [8]. In addition, at early stages, a stable receptor-ligand model is likely to provide a reasonable quantitative estimate of the pathological changes associated with AD and could therefore be an important tool in evaluating effects of therapy. Clearly, given its relatively small specific signal, the value of [¹⁸F]FDDNP can only be determined by large comparative clinical studies, such as the one by Small et al. [8]. From the present study, it follows that such a comparison should preferably be performed using SRTM as method of analysis, as it showed high precision and constant bias across the brain and among subjects even when metabolites enter the brain.

Conclusion

SRTM outperformed other models, providing BP_ND estimates with high precision. As clinical data indicated that the volume of distribution of labeled metabolites V_Tm was constant across the brain and among subjects, bias in SRTM-derived BP_ND will be constant and predictable. The main potential drawback is its sensitivity to variations in regional K₁, although this did not appear to be a problem in the clinical studies.