- Email: [email protected]
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the availability of commercial small animal PET cameras, should facilitate the application of small animal PET both in preclinical investigations of new drugs and in experimental studies of the relationship of receptor occupancy to animal behavior. Acknowledgments This work was carried out at Brookhaven National Laboratory under Contract DEAC02-98CH10886 with the U.S. Department of Energy and supported by its Office of Biological and Environmental Research and the National Institutes of Health (EB002630).
[13] Quantitative Analysis of Dopamine D2 Receptor Kinetics with Small Animal Positron Emission Tomography By Susanne Nikolaus, Markus Beu, Henning Vosberg, Hans-Wilhelm Mu¨ller, and Rolf Larisch Introduction
During the last decade, small animal positron emission tomography (PET) has been employed increasingly for the investigation of dopamine D2 receptor binding in animal models of reinforcement,1–3 senescence,4–6 and neurodegenerative disorders, including Parkinson’s and Huntington’s disease.7–12 1
H. Tsukada, J. Kreuter, C. E. Maggos, E. M. Unterwald, T. Kakiuchi, S. Nishiyama, M. Futatsubashi, and M. J. Kreek, J. Neurosci. 16, 7670 (1996). 2 E. M. Unterwald, H. Tsukada, T. Kakiuchi, T. Kosugi, S. Nishiyama, and M. J. Kreek, Brain Res. 775, 183 (1997). 3 C. E. Maggos, H. Tsukada, T. Kakiuchi, S. Nishiyama, J. H. Myers, J. Kreuter, S. D. Schlussman, E. M. Unterwald, A. Ho, and M. J. Kreek, Neuropsychopharmacology 19, 146 (1998). 4 O. Ogawa, H. Umegaki, K. Ishiwata, Y. Asai, H. Ikari, K. Oda, H. Toyama, D. K. Ingram, G. S. Roth, A. Iguchi, and M. Senda, Neuroreport 11, 743 (2000). 5 M. Suzuki, K. Hatano, Y. Sakiyama, J. Kawasumi, T. Kato, and K. Ito, Synapse 41, 285 (2001). 6 H. Umegaki, K. Ishiwata, O. Ogawa, D. K. Ingram, G. S. Roth, J. Yoshimura, K. Oda, H. Matsui-Hirai, H. Ikari, A. Iguchi, and M. Senda, Synapse 43, 195 (2002). 7 J. Opacka-Juffry, S. Ashworth, R. G. Ahier, and S. P. Hume, J. Neural Transm. 105, 349 (1998). 8 E. M. Torres, R. A. Fricker, S. P. Hume, R. Myers, J. Opacka-Juffry, S. Ashworth, D. J. Brooks, and S. B. Dunnett, Neuroreport 6, 2017 (1995).
METHODS IN ENZYMOLOGY, VOL. 385
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A prerequisite for the accurate derivation of receptor-binding parameters with in vivo imaging methods is the measurement of the arterial free ligand concentration. Arterial input functions, however, are difficult to obtain in investigations performed on rat or mouse models, as sufficient amounts of blood may not be drawn repeatedly from animals of this small size. In the studies performed until now, the need for an arterial input function was avoided either by confinement to a semiquantitative approach expressing radioactive values as a percentage of the injected dose per tissue volume4 or by applying dynamic,1–3 noninvasive graphic,5,11 and simplified reference tissue models.6–10,12 For a thorough overview of the main concepts underlying model-based invasive as well as noninvasive quantification methods, the reader is referred to the excellent review article by Slifstein and Laruelle.13 As none of the described methods allow the separate assessment of Bmax and KD, we validated a method that applies saturation-binding analysis to in vivo imaging of small laboratory animals and thus allows the determination of KD and Bmax in analogy to in vitro experiments with nonlinear or linear (Scatchard) regression analysis.14 Model-based in vivo methods generally proceed from the notion of ‘‘compartment,’’ which is a physiological or biochemical space characterized by homogeneous tracer concentrations, C(t). Thereby, the arterial vessel constitutes the first compartment, C1, from which the radioligand enters the free tissue compartment, C2. The free ligand in C2 eventually binds to specific sites and, by this, enters the third compartment, C3. Most radioligands also exhibit nonspecific binding. As equilibration between C2 and the nonspecific compartment, C20 , is assumed to be rapid compared to the kinetics of specific binding, C2 and C20 are often pooled into one compartment, yielding a three-compartment configuration. In this model, the exchange of radioligand between compartments is governed by four rate constants, K1 to k4. When C2 and C20 are considered as separate compartments, a four-compartment configuration is obtained with six rate 9
S. P. Hume, A. A. Lammertsma, R. Myers, S. Rajeswaran, P. M. Bloomfield, S. Ashworth, R. A. Fricker, E. M. Torres, I. Watson, and T. Jones, J. Neurosci. Methods 67, 103 (1996). 10 R. A. Fricker, E. M. Torres, S. P. Hume, R. Myers, J. Opacka-Juffry, S. Ashworth, D. J. Brooks, and S. B. Dunnett, Neuroscience 79, 711 (1997). 11 T. V. Nguyen, A. L. Brownell, Y. C. I. Chen, E. Livni, J. T. Coyle, B. R. Rosen, F. Cavagna, and B. G. Jenkins, Synapse 36, 57 (2000). 12 D. M. Araujo, S. R. Cherry, K. J. Tatsukawa, T. Toyokuni, and H. I. Kornblum, Exp. Neurol. 166, 287 (2000). 13 M. Slifstein and M. Laruelle, Nucl. Med. Biol. 28, 595 (2001). 14 S. Nikolaus, R. Larisch, M. Beu, F. Forutan, H. Vosberg, and H. W. Mu¨ller-Ga¨rtner, Eur. J. Nucl. Med. 30, 390 (2003).
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Fig. 1. Two ( , )-, three (h)-, and four-compartment configurations (h plus ), (1) In vitro two-compartment system consisting of the ligand-containing buffer solution and the receptor-containing tissue samples. (2) Three-compartment configuration consisting of arterial blood (C1), free compartment (C2), and receptor compartment (C3). (3) Twocompartment configuration consisting of C1 and the nonspecific compartment (C20 ). In the three-compartment model, C20 and C2 are pooled, whereas in the four-compartment model, C20 and C2 are assumed to exchange. Bmax, concentration of receptors (mol/g); C1, plasma activity of unmetabolized radioligand (Bq/ml); C2, tissue radioligand activity in the free compartment (Bq/ml); C20 , tissue radioligand activity in the nonspecifically bound compartment /Bq/ml); C3, tissue radioligand activity in the specifically bound compartment (Bq/ ml); f1, free fraction of unmetabolized radioligand in plasma; f2, free fraction of radioligand in C2; KD, equilibrium dissociation constant with KD ¼ koff/kon, kon, koff, association [(g/ml min)1] and dissociation (min1) rate constants, respectively; K1, transfer constant from plasma to free compartment (min1); K1, transfer constant from plasma to nonspecific compartment (min1); k2, transfer constants from free compartment to plasma (min1); k2, transfer constant from nonspecific compartment to plasma (min1); k3, k4, transfer constants between free and specifically bound compartment (min1); k5, k6, transfer constants between free and nonspecifically bound compartment in the four-compartment configuration (min1); [L], concentration of unbound radioligand (Bq/ml); [LR], concentration of bound radioligand (Bq/ml); [R], concentration of unbound receptors (mol/g); REF, reference region; and ROI, region of interest.
constants, K1 to k6 (Fig. 1). In vitro radioligand-binding assays can be conceived as two-compartment systems with both compartments localized in the same test tube and representing the ligand-containing buffer solution and the receptor-containing tissue samples, respectively (Fig. 1). In transferring the principle of autoradiographic evaluation to in vivo imaging methods, the free ligand concentration, [L], can be assigned to the pooled compartments C2 þ C20 , whereas the concentrations of unbound receptors, [R], and receptor–radioligand complexes, [LR], adhere to C3. Specific
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binding is determined by subtracting the nonspecific and free radioactivity concentrations, [L], as measured in the reference region, REF, from total radioactivity concentrations, [LR], in the region of interest, ROI. The interaction of receptor and radioligand can be described by ½L þ ½R $ ½LR
(1)
As this reaction is governed by the association and dissociation constants kon and koff, at equilibrium kon ½L½R ¼ koff ½LR
(2)
according to the laws of mass reaction. Because the equilibrium dissociation constant, KD, is defined as koff/kon and the receptor density, Bmax, is [R] þ [LR], substitution in Eq. (2) and rearrangement yields ½L½R ¼
Bmax ½L KD þ ½L
(3)
At tracer dose, with [L] KD, the ratio of bound to free radioligand is obtained by rearrangement of Eq. (3) with ½LR Bmax ¼ ½L KD
(4)
This last expression is referred to as the binding potential, BP. When [LR] is plotted against [L], Bmax and KD as in in vitro saturation-binding analysis may be derived from the resulting hyperbolic curve by nonlinear regression analysis. The saturation-binding approach per definition requires the saturation of receptor binding and, thus, the application of increasing radioligand concentrations. As a consequence, varying and low specific activities, which may confound the performance of PET investigations according to the tracer principle, may become advantageous when the method of saturation-binding analysis can be applied. This approach is described for the investigation of striatal D2 receptor binding in the rat with the D2 receptor antagonist N-[18F]-methlybenperidol (FMB) and a dedicated small animal tomograph. Material and Methods
Instrumentation The small animal tomograph was developed at the Central Laboratory for Electronics, Research Center Ju¨ lich, Ju¨ lich, Germany (‘‘TierPET’’15). The camera consists of two orthogonal pairs of detectors mounted on an
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aluminium wheel. Each detector block contains a matrix of 400 yttrium aluminium perovskite scintillator crystals (2 2 15 mm3; Preciosa Crytur Ltd., Turnov, Czech Republic), which are coupled to a position-sensitive photomultiplier (R2487; Hamamatsu Photonics, Herrsching, Germany). Axial and transaxial fields of view (FOV) have a diameter of 40 mm. The sensitivity is 3.24 cps/kBq for a center-detector distance of 80 mm. The spatial resolution is 2.1 mm [full width at half-maximum (FWHM)]. One cps/mm3, as registered with the PET camera, corresponds to 444 Bq/mm2.16 Radiochemistry FMB is synthesized as described previously.17 Radiochemical purity is assessed with high-performance liquid chromatography and, routinely, exceeds 98%. For the performance of saturation-binding analyses, the specific activity of the radioligand should cover one order of magnitude. In our validation study, specific activity ranged from >11 to >100 TBq/mmol. Protocol Anesthesia. For short-time inhalation anesthesia, the rat is placed into a lockable acrylic box containing a pad moistened with 1-chloro-2,2,2-trifluoroethyldifluoromethylether (Forene; Abbott GmbH, Wiesbaden, Germany). The anesthetized animal is administered a mixture of ketaminehydrochloride (Ketavet; Pharmacia GmbH, Erlangen, Germany; concentration, 100 mg/ml; dose, 0.9 ml/kg) and xylazinehydrochloride (Rompun; Bayer Vital GmbH, Leverkusen, Germany; concentration, 0.02 mg/ml; dose, 0.4 ml/kg) into the gluteal muscle. Radioligand Application. Upon shaving and skin disinfection, the thorax of the rat is opened on the right side at the level of the third rib. FMB is diluted in 0.9% saline containing 10% ethanol and is injected into the right jugular vein. Thereby, application is facilitated if the needle (Microlance 25G5/8; Becton Dickinson, Drogheda, Ireland) is fixed in the pectoral muscle. Injection into the tail vein is also feasible. In this case, we recommend usage of a winged needle infusion set (Butterfly-23 with 15
S. Weber, A. Terstegge, H. Herzog, R. Reinartz, P. Reinhart, F. Rongen, H. W. MullerGartner, and H. Halling, IEEE Trans. Med. Imaging 16, 684 (1997). 16 S. Nikolaus, R. Larisch, M. Beu, H. Vosberg, and H. W. Mu¨ ller-Ga¨ rtner, J. Nucl. Med. 42, 1691 (2001). 17 S. M. Moerlein, J. S. Perlmutter, J. Markham, and M. J. Welch, J. Cereb. Blood Flow Metab. 17, 833 (1997).
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an outer needle diameter of 0.6 mm; Venisystems, Abbott, Sligo, Ireland). The injected amount of radioactivity should be adjusted to the performance characteristics of the employed small animal tomograph. With the employed small animal scanner, a rat has to be administered at least 74 MBq in order to achieve a sufficient count rate. In our study, the injected radioactivity dose amounted to 158 24 MBq/kg (mean SD). Data Acquisition. After surgical dressing, the rat is positioned on the object tablet with an associated acrylic head holder comprising ear and tooth bars. The head holder (Institute of Medicine, Research Center Ju¨ lich, Ju¨ lich, Germany) allows both the fixation and the accurate and reproducible positioning of the rat head. The motor-controlled object tablet is moved along the x, y, and z axes such that the striata are localized centrally within the FOV. During scanning of the brain, the body of the animal is kept within a lead tube (wall thickness, 20 mm) in order to reduce perturbations due to scattered photons. The tube is perfused consistently by warm water to main tain a body temperature of 37 . Images are acquired for 36 min (six time frames of 6 min each) with angular steps of 7.5 (30 s per angular step). Evaluation Images are analyzed with the multipurpose imaging tool (version 2.57; Advanced Tomo Vision, Erfstadt, Germany). After summation of the six time frames, striata are localized individually for each animal on coronal sections. Two standard circular ROIs with diameters of 2.5 mm are drawn around the centers of both striata. The positions of the ROIs are adjusted individually for each animal. The obtained radioactivity values are corrected for radioactive decay. As time–activity curves have shown that the equilibrium between radioactivity concentrations of specifically bound and both nonspecifically bound and free FMB is reached at 20 min postinjection, left and right radioactivity concentrations in time frames four to six are averaged.18 The investigation of small targets is biased by the partial-volume effect. This nonlinear artifact leads to an underestimation of the radioactivity concentration in objects smaller than twice the resolution of the employed scanning device. On the coronal sections, where the ROIs have been delineated, the mesiolateral striatal diameters amount to 2.5 mm, which is in the range of the spatial resolution of the system. Phantom studies with
18
H. Ito, J. Hietala, G. Blomqvist, C. Halldin, and L. Farde, J. Cereb. Blood Flow Metab. 18, 941 (1998).
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water-filled cylinders of various radii have shown that in a target with a diameter of 2.5 mm, radioactivity is underestimated by approximately 60%. On the basis of these measurements, the mean radioactivity values of time frames four to six are fixed to 60% of the true striatal radioactivity, and the respective 100% values are calculated (see discussion later). Radioligand accumulation in the retroorbital Harderian glands may lead to an overestimation of radioactivity concentrations in adjacent tissues due to spillover effects. To estimate the various amounts of spillover affecting striatal and cortical radioactivity concentrations, Gaussian model functions (Fig. 2; y ¼ AHG expð0:5½ðx mHG Þ=sHG 2 þ ASTR expð0:5 ½ðx mSTR Þ=sSTR 2 þ ACOR expð0:5½ðx mCOR Þ=sCOR 2 are fitted to lineactivity profiles through the Harderian gland, striatum, and adjacent occipital cortex with AHG, ASTR, and ACOR as normalization factors; mHG, mSTR, and mCOR as the x coordinates of the peaks; and sHG, sSTR, and sCOR as the FWHM values of glandular, striatal, and cortical curves. After decomposition of the sum function into a glandular, striatal, and cortical portion, the amount of spillover is determined by relating the integrals of the overlaps to the integrals of the curves. The percentual contributions of one curve to another are subtracted for each side from the mean striatal radioactivity concentrations.19 Cortical radioactivity as obtained from Gaussian fitting provides an estimate of the free and nonspecifically bound radioligand in brain tissue (see discussion later). From striatal and cortical radioactivity concentrations (MBq/mm3) and the known specific activity at the beginning of the fourth time frame, both striatal and cortical molar radioligand concentrations (fmol/mg) are calculated. For each animal, cortical molar concentrations are subtracted from left and right striatal radioligand concentrations in order to obtain specific binding. Specific binding obtained for left and right striatum is averaged. For nonlinear regression analysis (Fig. 3; GraphPad Prism, GraphPad Software, San Diego, CA), saturation-binding curves are generated by fitBmax x ting the hyperbolic function y ¼ K to the data set with x and y D þx corresponding to the concentrations of free, [L], and bound radioligand, [LR], respectively. For linear regression analysis, the straight line function y0 ¼ K1D x0 þ BKmax is fitted to Scatchard transformed data with x0 and y0 D corresponding to [LR] and [LR]/[L], respectively. Thereby, the x intercept of the Scatchard line represents Bmax, whereas the slope equals 1/KD.
19
M. Beu, S. Nikolaus, R. Larisch, S. Weber, H. Vosberg, and H. W. Mu¨ ller-Ga¨ rtner, Nuklearmedizin 39, 162 (2000).
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Fig. 2. Characteristic transversal slice of a Sprague–Dawley rat head obtained with a PET camera (left). In order to estimate the influence of the retroorbital radioactivity on the determination of striatal radioactivity concentrations, Gaussian model functions (r) are fitted to the line activity profiles (s; ) of both striata (1) and Harderian glands (2) of each side (right). After decomposition of the sum function into the three components, ‘‘striatal’’ Ðt 0 Ðt Ð t (&), and ‘‘background’’ radioactivity’’ (m), the overlap ( 0 STR = Ð( t ), ‘‘retroorbital’’ 0 HG and 0 HG= 0 STR) between striatal and orbital curves is taken as a measure for spillover. Cortical radioactivity (3) is used to estimate free and nonspecific binding. For each animal, mean cortical values are subtracted from striatal radioactivity concentrations as averaged over time frames four to six.
Results and Discussion
In our validation study, KD and Bmax values of FMB as determined with nonlinear regression analysis amount to 6.2 nM and 16 fmol/mg, respectively (Fig. 3). With linear regression analysis, KD and Bmax values of 5 nM and 15.3 fmol/mg, respectively, are obtained (Fig. 3, inset). In vitro assessment of KD and Bmax with storage phosphor autoradiography has yielded values within the same order of magnitude (KD: 4.4 nM, Bmax: 84 fmol/mg20). For the sake of comparability, the in vivo estimation of specific binding has also been applied to autoradiographic data. Thereby, the determination of specific binding in the striatum by subtraction of cortical binding instead of striatal binding in the presence of a competitor has led to similar results (KD ¼ 7.9 nM, Bmax ¼ 70 fmol/mg20). The agreement of
20
S. Nikolaus, R. Larisch, M. Beu, K. Hamacher, F. Forutan, H. Vosberg, and H. W. Mu¨ ller, J. Nucl. Med. 44, 618 (2003).
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Fig. 3. Nonlinear regression analysis of FMB binding to striatal dopamine D2 receptors. Binding data were acquired from eight Sprague–Dawley rats with an animal PET device. The free radioligand concentration in the occipital cortex was used as the concentration parameter. (Inset) Scatchard analysis of binding data contingent on linear transformation.
values shows that KD and Bmax can be measured in the living brain in analogy to in vitro saturation-binding studies. For small animal scanners with the characteristics of the TierPET as to sensitivity and spatial resolution, we propose using cortical rather than cerebellar radioactivity concentrations as an estimate of free and nonspecific radioligand binding. Due to the low D2 receptor concentration and the lack of anatomical landmarks it is difficult to delineate cerebellar ROIs in a reproducible manner. Cortical radioactivity concentrations are negligible as well21 and have the advantage that they may be determined on the same slices used for striatal ROI definition (Fig. 2). Thereby, we recommend usage of the occipitocortical region, as previous investigations have shown that occipital D2 receptor concentrations fall short of frontal ones by approximately one-third.22 Because occipital D2 receptor density is that low, radioactivity concentrations in this region can be assumed to provide a reasonable estimate of free and nonspecific radioligand concentrations in brain tissue. 21
R. M. Kessler, N. S. Mason, J. R. Votaw, T. De Paulis, J. A. Clanton, M. S. Ansari, D. E. Schmidt, R. G. Manning, and R. L. Bell, Eur. J. Pharmacol. 223, 105 (1992). 22 M. S. Lidow, P. S. Goldman-Rakic, P. Rakic, and R. B. Innis, Proc. Natl. Acad. Sci. USA 86, 6412 (1989).
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In our in vivo saturation-binding analysis, KD values correspond to in vitro results, whereas Bmax values are lower compared to in vitro results, although still lying within the same order of magnitude. In comparing in vivo and in vitro measurements, various issues should be taken into account. First, the exact determination of the anterioposterior stereotaxic coordinates of the PET slices is hampered when no concurrent morphological imaging may be performed. Noncorresponding sectional planes between PET and autoradiography thus offer one explanation for the difference between receptor densities obtained in vivo and in vitro. Second, the applied partial-volume correction factor is estimated on the basis of phantom studies and enters as a constant factor into the quantification of radioactivity values irrespective of the actual striatal diameters on the slices selected for ROI definition. Thus, if striatal diameters fall short of 2.5 mm, the used correction factor leads to underestimations of radioactivity concentrations compared to autoradiography. Third, the accuracy of our method depends on the correctness of the assumption that C2 and C20 may be pooled into one compartment. Actually, we derive [L], i.e., both the free and the nonspecifically bound radioligand concentration, from the cortical reference region. Thus, in our approach, 0 BP is given by ½LR ½L 1. As [L] corresponds to C2 þ C2 , the nonspecifically bound radioligand enters into the denominator in addition to the free radioligand concentration. Thus, the correctness of parameter estimation suffers from the fact that the free fraction of radioligand in C2, f2, may not be determined accurately. Actually, with our method, we derive B0 max (¼f2Bmax) and thus underestimate Bmax consistently. Because a reference region is used for the estimation of C2 þ C20 in the simplified reference tissue model,23 the portion of nonspecifically bound radioligand in this approach may also lead to an underestimation of BP. Actually, instead of Bmax/KD, f2Bmax/KD is obtained as an outcome measure. With the dynamic approach,24–26 the receptor parameter 3 ðtÞ k3 ¼ kon ðBmax CSA f 2 is estimated with SA denoting the specific activity of the radioligand. If SA is high and the radioligand is administered in 3 ðtÞ tracer amounts, then CSA Bmax and an estimate of k3 is provided by the product of kon, Bmax, and f2. Thereby, f2 usually is inferred from in vitro
23
A. A. Lammertsma and S. P. Hume, Neuroimage 4, 153 (1996). M. A. Mintun, M. E. Raichle, M. R. Kilbourn, G. F. Wooten, and M. J. Welch, Ann. Neurol. 15, 217 (1984). 25 J. S. Perlmutter, K. B. Larson, M. E. Raichle, J. Markham, M. A. Mintun, M. R. Kilbourn, and M. J. Welch, J. Cereb. Blood Flow Metab. 6, 154 (1986). 26 D. F. Wong, A. Gjedde, H. N. Wagner, Jr., R. F. Dannals, K. H. Douglass, J. M. Links, and M. J. Kuhar, J. Cereb. Blood Flow Metab. 6, 147 (1986). 24
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studies or is estimated from the kinetics in tissue regions lacking specific binding. If the latter is the case, the product of Bmax and kon provides an estimate of BP, the goodness of which, as is the case for in vivo saturation binding and the simplified reference tissue approach, depends on the accuracy, with which f2 may be determined. A similar problem occurs with the noninvasive graphic model,27 which yields the distribution volume ratio, DVR, as an outcome measure. The DVR is the ratio of the equilibrium distribution volume in the ROI to that in the REF. Thereby, DVR ¼ BP þ 1 if the distribution volumes of REF and C2 are assumed to be equal.13 Thus, also in this approach, existing nonspecific radioligand binding leads to inaccurate BP estimates. As the tissue-to-plasma efflux constant, k2, is required for this kind of analysis, the goodness of BP estimates furthermore may depend on the feasibility of inferring k2 from an independent sample. In discussing possible errors of parameter estimation, their degree, however, should be viewed in relation to other error sources inherent to the method of in vivo PET imaging, such as spillover and partial-volume effect. For the nonspecific binding moreover holds that it is characterized by both tissue and radioligand properties, which are not assumed to vary over time or between subjects. Thus, f2Bmax and KD, f2Bmax/KD, f2konBmax, and DVR as obtained with in vivo saturation-binding analysis, the simplified reference tissue model, the dynamic approach, and the noninvasive graphic model, respectively, can be considered to provide reasonable estimates of the receptor parameters in question. Thereby, the advantage of in vivo saturation-binding analysis is the provision of Bmax(0 ) and KD as separate values and direct measures of receptor density and affinity. In vivo saturation-binding analysis represents an equilibrium method, which for the first time was described by Phelps and collaborators.28 So far, in vivo saturation-binding analysis with small animal tomographs has been applied in two studies: Nikolaus and collaborators14 investigated time-dependent changes of Bmax in the rat 6-hydroxydopamine model, whereas Tsukada and collaborators1 utilized the saturation-binding approach as a complement to PET in order to analyze whether the observed effect on D2 receptor binding was due to alterations in KD or Bmax. These investigations are examples for scientific questions requiring methods for the separate determination of KD and Bmax in small laboratory animals. 27
J. Logan, J. S. Fowler, N. D. Volkow, G. J. Wang, Y. S. Ding, and D. L. Alexoff, J. Cereb. Blood Flow Metab. 16, 834 (1996). 28 M. E. Phelps, J. C. Mazziotta, and H. R. Schelbert, ‘‘Positron Emission Tomography and Autoradiography: Principles and Applications for the Brain and Heart.’’ Raven Press, New York, 1986.
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With the in vivo saturation-binding approach, the benefits of two concepts are brought together. By applying the in vitro method to in vivo imaging, KD and Bmax may be determined in analogy to in vitro experiments preserving all advantages of the in vivo method, such as the possibility to reuse an animal for several investigations and to assess receptor kinetics in the living subject instead of utilizing cryosections or membrane homogenates as mere models of cerebral tissue and receptor surface. Finally, an enormous disadvantage of in vivo methods, the struggle with varying and low specific activities, is changed to the opposite, as with the method of saturation binding, increasing concentrations of radioligand have to be applied in order to reach the state of receptor saturation. It is important to note, however, that there is one fundamental difference between in vivo saturation-binding analysis yielding Bmax and KD and other approaches quantifying BP or related outcome measures: with the saturation-binding method, various radioligand concentrations must be applied to several animals. In contrast, in the other approaches, outcome measures may be obtained for one animal with one radioligand concentration. Thus, basically, with in vivo saturation-binding analysis, more animals are required, leading to a greater influence of interindividual variance. Theoretically, application of more than one concentration to a single animal is also feasible; in this case, individual values of both Bmax and KD may be determined for each animal. PET investigations, however, should lie a sufficient time apart to account for radioactive decay and to permit recovery from aftereffects of anesthesia and surgery. Acknowledgments This work was supported by a grant from the ‘‘Forschungskommission’’ of the Faculty of Medicine, Heinrich-Heine-University, Du¨ sseldorf, Germany. The authors acknowledge Dr. Simone Weber from the Central Laboratory for Electronics and Dr. Karl Hamacher from the Institute of Nuclear Chemistry (Forschungszentrum Ju¨ lich GmbH, Ju¨ lich, Germany) for their contributions to the experiments.
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the availability of commercial small animal PET cameras, should facilitate the application of small animal PET both in preclinical investigations of new drugs and in experimental studies of the relationship of receptor occupancy to animal behavior. Acknowledgments This work was carried out at Brookhaven National Laboratory under Contract DEAC02-98CH10886 with the U.S. Department of Energy and supported by its Office of Biological and Environmental Research and the National Institutes of Health (EB002630).
[13] Quantitative Analysis of Dopamine D2 Receptor Kinetics with Small Animal Positron Emission Tomography By Susanne Nikolaus, Markus Beu, Henning Vosberg, Hans-Wilhelm Mu¨ller, and Rolf Larisch Introduction
During the last decade, small animal positron emission tomography (PET) has been employed increasingly for the investigation of dopamine D2 receptor binding in animal models of reinforcement,1–3 senescence,4–6 and neurodegenerative disorders, including Parkinson’s and Huntington’s disease.7–12 1
H. Tsukada, J. Kreuter, C. E. Maggos, E. M. Unterwald, T. Kakiuchi, S. Nishiyama, M. Futatsubashi, and M. J. Kreek, J. Neurosci. 16, 7670 (1996). 2 E. M. Unterwald, H. Tsukada, T. Kakiuchi, T. Kosugi, S. Nishiyama, and M. J. Kreek, Brain Res. 775, 183 (1997). 3 C. E. Maggos, H. Tsukada, T. Kakiuchi, S. Nishiyama, J. H. Myers, J. Kreuter, S. D. Schlussman, E. M. Unterwald, A. Ho, and M. J. Kreek, Neuropsychopharmacology 19, 146 (1998). 4 O. Ogawa, H. Umegaki, K. Ishiwata, Y. Asai, H. Ikari, K. Oda, H. Toyama, D. K. Ingram, G. S. Roth, A. Iguchi, and M. Senda, Neuroreport 11, 743 (2000). 5 M. Suzuki, K. Hatano, Y. Sakiyama, J. Kawasumi, T. Kato, and K. Ito, Synapse 41, 285 (2001). 6 H. Umegaki, K. Ishiwata, O. Ogawa, D. K. Ingram, G. S. Roth, J. Yoshimura, K. Oda, H. Matsui-Hirai, H. Ikari, A. Iguchi, and M. Senda, Synapse 43, 195 (2002). 7 J. Opacka-Juffry, S. Ashworth, R. G. Ahier, and S. P. Hume, J. Neural Transm. 105, 349 (1998). 8 E. M. Torres, R. A. Fricker, S. P. Hume, R. Myers, J. Opacka-Juffry, S. Ashworth, D. J. Brooks, and S. B. Dunnett, Neuroreport 6, 2017 (1995).
METHODS IN ENZYMOLOGY, VOL. 385
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A prerequisite for the accurate derivation of receptor-binding parameters with in vivo imaging methods is the measurement of the arterial free ligand concentration. Arterial input functions, however, are difficult to obtain in investigations performed on rat or mouse models, as sufficient amounts of blood may not be drawn repeatedly from animals of this small size. In the studies performed until now, the need for an arterial input function was avoided either by confinement to a semiquantitative approach expressing radioactive values as a percentage of the injected dose per tissue volume4 or by applying dynamic,1–3 noninvasive graphic,5,11 and simplified reference tissue models.6–10,12 For a thorough overview of the main concepts underlying model-based invasive as well as noninvasive quantification methods, the reader is referred to the excellent review article by Slifstein and Laruelle.13 As none of the described methods allow the separate assessment of Bmax and KD, we validated a method that applies saturation-binding analysis to in vivo imaging of small laboratory animals and thus allows the determination of KD and Bmax in analogy to in vitro experiments with nonlinear or linear (Scatchard) regression analysis.14 Model-based in vivo methods generally proceed from the notion of ‘‘compartment,’’ which is a physiological or biochemical space characterized by homogeneous tracer concentrations, C(t). Thereby, the arterial vessel constitutes the first compartment, C1, from which the radioligand enters the free tissue compartment, C2. The free ligand in C2 eventually binds to specific sites and, by this, enters the third compartment, C3. Most radioligands also exhibit nonspecific binding. As equilibration between C2 and the nonspecific compartment, C20 , is assumed to be rapid compared to the kinetics of specific binding, C2 and C20 are often pooled into one compartment, yielding a three-compartment configuration. In this model, the exchange of radioligand between compartments is governed by four rate constants, K1 to k4. When C2 and C20 are considered as separate compartments, a four-compartment configuration is obtained with six rate 9
S. P. Hume, A. A. Lammertsma, R. Myers, S. Rajeswaran, P. M. Bloomfield, S. Ashworth, R. A. Fricker, E. M. Torres, I. Watson, and T. Jones, J. Neurosci. Methods 67, 103 (1996). 10 R. A. Fricker, E. M. Torres, S. P. Hume, R. Myers, J. Opacka-Juffry, S. Ashworth, D. J. Brooks, and S. B. Dunnett, Neuroscience 79, 711 (1997). 11 T. V. Nguyen, A. L. Brownell, Y. C. I. Chen, E. Livni, J. T. Coyle, B. R. Rosen, F. Cavagna, and B. G. Jenkins, Synapse 36, 57 (2000). 12 D. M. Araujo, S. R. Cherry, K. J. Tatsukawa, T. Toyokuni, and H. I. Kornblum, Exp. Neurol. 166, 287 (2000). 13 M. Slifstein and M. Laruelle, Nucl. Med. Biol. 28, 595 (2001). 14 S. Nikolaus, R. Larisch, M. Beu, F. Forutan, H. Vosberg, and H. W. Mu¨ller-Ga¨rtner, Eur. J. Nucl. Med. 30, 390 (2003).
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Fig. 1. Two ( , )-, three (h)-, and four-compartment configurations (h plus ), (1) In vitro two-compartment system consisting of the ligand-containing buffer solution and the receptor-containing tissue samples. (2) Three-compartment configuration consisting of arterial blood (C1), free compartment (C2), and receptor compartment (C3). (3) Twocompartment configuration consisting of C1 and the nonspecific compartment (C20 ). In the three-compartment model, C20 and C2 are pooled, whereas in the four-compartment model, C20 and C2 are assumed to exchange. Bmax, concentration of receptors (mol/g); C1, plasma activity of unmetabolized radioligand (Bq/ml); C2, tissue radioligand activity in the free compartment (Bq/ml); C20 , tissue radioligand activity in the nonspecifically bound compartment /Bq/ml); C3, tissue radioligand activity in the specifically bound compartment (Bq/ ml); f1, free fraction of unmetabolized radioligand in plasma; f2, free fraction of radioligand in C2; KD, equilibrium dissociation constant with KD ¼ koff/kon, kon, koff, association [(g/ml min)1] and dissociation (min1) rate constants, respectively; K1, transfer constant from plasma to free compartment (min1); K1, transfer constant from plasma to nonspecific compartment (min1); k2, transfer constants from free compartment to plasma (min1); k2, transfer constant from nonspecific compartment to plasma (min1); k3, k4, transfer constants between free and specifically bound compartment (min1); k5, k6, transfer constants between free and nonspecifically bound compartment in the four-compartment configuration (min1); [L], concentration of unbound radioligand (Bq/ml); [LR], concentration of bound radioligand (Bq/ml); [R], concentration of unbound receptors (mol/g); REF, reference region; and ROI, region of interest.
constants, K1 to k6 (Fig. 1). In vitro radioligand-binding assays can be conceived as two-compartment systems with both compartments localized in the same test tube and representing the ligand-containing buffer solution and the receptor-containing tissue samples, respectively (Fig. 1). In transferring the principle of autoradiographic evaluation to in vivo imaging methods, the free ligand concentration, [L], can be assigned to the pooled compartments C2 þ C20 , whereas the concentrations of unbound receptors, [R], and receptor–radioligand complexes, [LR], adhere to C3. Specific
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binding is determined by subtracting the nonspecific and free radioactivity concentrations, [L], as measured in the reference region, REF, from total radioactivity concentrations, [LR], in the region of interest, ROI. The interaction of receptor and radioligand can be described by ½L þ ½R $ ½LR
(1)
As this reaction is governed by the association and dissociation constants kon and koff, at equilibrium kon ½L½R ¼ koff ½LR
(2)
according to the laws of mass reaction. Because the equilibrium dissociation constant, KD, is defined as koff/kon and the receptor density, Bmax, is [R] þ [LR], substitution in Eq. (2) and rearrangement yields ½L½R ¼
Bmax ½L KD þ ½L
(3)
At tracer dose, with [L] KD, the ratio of bound to free radioligand is obtained by rearrangement of Eq. (3) with ½LR Bmax ¼ ½L KD
(4)
This last expression is referred to as the binding potential, BP. When [LR] is plotted against [L], Bmax and KD as in in vitro saturation-binding analysis may be derived from the resulting hyperbolic curve by nonlinear regression analysis. The saturation-binding approach per definition requires the saturation of receptor binding and, thus, the application of increasing radioligand concentrations. As a consequence, varying and low specific activities, which may confound the performance of PET investigations according to the tracer principle, may become advantageous when the method of saturation-binding analysis can be applied. This approach is described for the investigation of striatal D2 receptor binding in the rat with the D2 receptor antagonist N-[18F]-methlybenperidol (FMB) and a dedicated small animal tomograph. Material and Methods
Instrumentation The small animal tomograph was developed at the Central Laboratory for Electronics, Research Center Ju¨ lich, Ju¨ lich, Germany (‘‘TierPET’’15). The camera consists of two orthogonal pairs of detectors mounted on an
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aluminium wheel. Each detector block contains a matrix of 400 yttrium aluminium perovskite scintillator crystals (2 2 15 mm3; Preciosa Crytur Ltd., Turnov, Czech Republic), which are coupled to a position-sensitive photomultiplier (R2487; Hamamatsu Photonics, Herrsching, Germany). Axial and transaxial fields of view (FOV) have a diameter of 40 mm. The sensitivity is 3.24 cps/kBq for a center-detector distance of 80 mm. The spatial resolution is 2.1 mm [full width at half-maximum (FWHM)]. One cps/mm3, as registered with the PET camera, corresponds to 444 Bq/mm2.16 Radiochemistry FMB is synthesized as described previously.17 Radiochemical purity is assessed with high-performance liquid chromatography and, routinely, exceeds 98%. For the performance of saturation-binding analyses, the specific activity of the radioligand should cover one order of magnitude. In our validation study, specific activity ranged from >11 to >100 TBq/mmol. Protocol Anesthesia. For short-time inhalation anesthesia, the rat is placed into a lockable acrylic box containing a pad moistened with 1-chloro-2,2,2-trifluoroethyldifluoromethylether (Forene; Abbott GmbH, Wiesbaden, Germany). The anesthetized animal is administered a mixture of ketaminehydrochloride (Ketavet; Pharmacia GmbH, Erlangen, Germany; concentration, 100 mg/ml; dose, 0.9 ml/kg) and xylazinehydrochloride (Rompun; Bayer Vital GmbH, Leverkusen, Germany; concentration, 0.02 mg/ml; dose, 0.4 ml/kg) into the gluteal muscle. Radioligand Application. Upon shaving and skin disinfection, the thorax of the rat is opened on the right side at the level of the third rib. FMB is diluted in 0.9% saline containing 10% ethanol and is injected into the right jugular vein. Thereby, application is facilitated if the needle (Microlance 25G5/8; Becton Dickinson, Drogheda, Ireland) is fixed in the pectoral muscle. Injection into the tail vein is also feasible. In this case, we recommend usage of a winged needle infusion set (Butterfly-23 with 15
S. Weber, A. Terstegge, H. Herzog, R. Reinartz, P. Reinhart, F. Rongen, H. W. MullerGartner, and H. Halling, IEEE Trans. Med. Imaging 16, 684 (1997). 16 S. Nikolaus, R. Larisch, M. Beu, H. Vosberg, and H. W. Mu¨ ller-Ga¨ rtner, J. Nucl. Med. 42, 1691 (2001). 17 S. M. Moerlein, J. S. Perlmutter, J. Markham, and M. J. Welch, J. Cereb. Blood Flow Metab. 17, 833 (1997).
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an outer needle diameter of 0.6 mm; Venisystems, Abbott, Sligo, Ireland). The injected amount of radioactivity should be adjusted to the performance characteristics of the employed small animal tomograph. With the employed small animal scanner, a rat has to be administered at least 74 MBq in order to achieve a sufficient count rate. In our study, the injected radioactivity dose amounted to 158 24 MBq/kg (mean SD). Data Acquisition. After surgical dressing, the rat is positioned on the object tablet with an associated acrylic head holder comprising ear and tooth bars. The head holder (Institute of Medicine, Research Center Ju¨ lich, Ju¨ lich, Germany) allows both the fixation and the accurate and reproducible positioning of the rat head. The motor-controlled object tablet is moved along the x, y, and z axes such that the striata are localized centrally within the FOV. During scanning of the brain, the body of the animal is kept within a lead tube (wall thickness, 20 mm) in order to reduce perturbations due to scattered photons. The tube is perfused consistently by warm water to main tain a body temperature of 37 . Images are acquired for 36 min (six time frames of 6 min each) with angular steps of 7.5 (30 s per angular step). Evaluation Images are analyzed with the multipurpose imaging tool (version 2.57; Advanced Tomo Vision, Erfstadt, Germany). After summation of the six time frames, striata are localized individually for each animal on coronal sections. Two standard circular ROIs with diameters of 2.5 mm are drawn around the centers of both striata. The positions of the ROIs are adjusted individually for each animal. The obtained radioactivity values are corrected for radioactive decay. As time–activity curves have shown that the equilibrium between radioactivity concentrations of specifically bound and both nonspecifically bound and free FMB is reached at 20 min postinjection, left and right radioactivity concentrations in time frames four to six are averaged.18 The investigation of small targets is biased by the partial-volume effect. This nonlinear artifact leads to an underestimation of the radioactivity concentration in objects smaller than twice the resolution of the employed scanning device. On the coronal sections, where the ROIs have been delineated, the mesiolateral striatal diameters amount to 2.5 mm, which is in the range of the spatial resolution of the system. Phantom studies with
18
H. Ito, J. Hietala, G. Blomqvist, C. Halldin, and L. Farde, J. Cereb. Blood Flow Metab. 18, 941 (1998).
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water-filled cylinders of various radii have shown that in a target with a diameter of 2.5 mm, radioactivity is underestimated by approximately 60%. On the basis of these measurements, the mean radioactivity values of time frames four to six are fixed to 60% of the true striatal radioactivity, and the respective 100% values are calculated (see discussion later). Radioligand accumulation in the retroorbital Harderian glands may lead to an overestimation of radioactivity concentrations in adjacent tissues due to spillover effects. To estimate the various amounts of spillover affecting striatal and cortical radioactivity concentrations, Gaussian model functions (Fig. 2; y ¼ AHG expð0:5½ðx mHG Þ=sHG 2 þ ASTR expð0:5 ½ðx mSTR Þ=sSTR 2 þ ACOR expð0:5½ðx mCOR Þ=sCOR 2 are fitted to lineactivity profiles through the Harderian gland, striatum, and adjacent occipital cortex with AHG, ASTR, and ACOR as normalization factors; mHG, mSTR, and mCOR as the x coordinates of the peaks; and sHG, sSTR, and sCOR as the FWHM values of glandular, striatal, and cortical curves. After decomposition of the sum function into a glandular, striatal, and cortical portion, the amount of spillover is determined by relating the integrals of the overlaps to the integrals of the curves. The percentual contributions of one curve to another are subtracted for each side from the mean striatal radioactivity concentrations.19 Cortical radioactivity as obtained from Gaussian fitting provides an estimate of the free and nonspecifically bound radioligand in brain tissue (see discussion later). From striatal and cortical radioactivity concentrations (MBq/mm3) and the known specific activity at the beginning of the fourth time frame, both striatal and cortical molar radioligand concentrations (fmol/mg) are calculated. For each animal, cortical molar concentrations are subtracted from left and right striatal radioligand concentrations in order to obtain specific binding. Specific binding obtained for left and right striatum is averaged. For nonlinear regression analysis (Fig. 3; GraphPad Prism, GraphPad Software, San Diego, CA), saturation-binding curves are generated by fitBmax x ting the hyperbolic function y ¼ K to the data set with x and y D þx corresponding to the concentrations of free, [L], and bound radioligand, [LR], respectively. For linear regression analysis, the straight line function y0 ¼ K1D x0 þ BKmax is fitted to Scatchard transformed data with x0 and y0 D corresponding to [LR] and [LR]/[L], respectively. Thereby, the x intercept of the Scatchard line represents Bmax, whereas the slope equals 1/KD.
19
M. Beu, S. Nikolaus, R. Larisch, S. Weber, H. Vosberg, and H. W. Mu¨ ller-Ga¨ rtner, Nuklearmedizin 39, 162 (2000).
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Fig. 2. Characteristic transversal slice of a Sprague–Dawley rat head obtained with a PET camera (left). In order to estimate the influence of the retroorbital radioactivity on the determination of striatal radioactivity concentrations, Gaussian model functions (r) are fitted to the line activity profiles (s; ) of both striata (1) and Harderian glands (2) of each side (right). After decomposition of the sum function into the three components, ‘‘striatal’’ Ðt 0 Ðt Ð t (&), and ‘‘background’’ radioactivity’’ (m), the overlap ( 0 STR = Ð( t ), ‘‘retroorbital’’ 0 HG and 0 HG= 0 STR) between striatal and orbital curves is taken as a measure for spillover. Cortical radioactivity (3) is used to estimate free and nonspecific binding. For each animal, mean cortical values are subtracted from striatal radioactivity concentrations as averaged over time frames four to six.
Results and Discussion
In our validation study, KD and Bmax values of FMB as determined with nonlinear regression analysis amount to 6.2 nM and 16 fmol/mg, respectively (Fig. 3). With linear regression analysis, KD and Bmax values of 5 nM and 15.3 fmol/mg, respectively, are obtained (Fig. 3, inset). In vitro assessment of KD and Bmax with storage phosphor autoradiography has yielded values within the same order of magnitude (KD: 4.4 nM, Bmax: 84 fmol/mg20). For the sake of comparability, the in vivo estimation of specific binding has also been applied to autoradiographic data. Thereby, the determination of specific binding in the striatum by subtraction of cortical binding instead of striatal binding in the presence of a competitor has led to similar results (KD ¼ 7.9 nM, Bmax ¼ 70 fmol/mg20). The agreement of
20
S. Nikolaus, R. Larisch, M. Beu, K. Hamacher, F. Forutan, H. Vosberg, and H. W. Mu¨ ller, J. Nucl. Med. 44, 618 (2003).
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Fig. 3. Nonlinear regression analysis of FMB binding to striatal dopamine D2 receptors. Binding data were acquired from eight Sprague–Dawley rats with an animal PET device. The free radioligand concentration in the occipital cortex was used as the concentration parameter. (Inset) Scatchard analysis of binding data contingent on linear transformation.
values shows that KD and Bmax can be measured in the living brain in analogy to in vitro saturation-binding studies. For small animal scanners with the characteristics of the TierPET as to sensitivity and spatial resolution, we propose using cortical rather than cerebellar radioactivity concentrations as an estimate of free and nonspecific radioligand binding. Due to the low D2 receptor concentration and the lack of anatomical landmarks it is difficult to delineate cerebellar ROIs in a reproducible manner. Cortical radioactivity concentrations are negligible as well21 and have the advantage that they may be determined on the same slices used for striatal ROI definition (Fig. 2). Thereby, we recommend usage of the occipitocortical region, as previous investigations have shown that occipital D2 receptor concentrations fall short of frontal ones by approximately one-third.22 Because occipital D2 receptor density is that low, radioactivity concentrations in this region can be assumed to provide a reasonable estimate of free and nonspecific radioligand concentrations in brain tissue. 21
R. M. Kessler, N. S. Mason, J. R. Votaw, T. De Paulis, J. A. Clanton, M. S. Ansari, D. E. Schmidt, R. G. Manning, and R. L. Bell, Eur. J. Pharmacol. 223, 105 (1992). 22 M. S. Lidow, P. S. Goldman-Rakic, P. Rakic, and R. B. Innis, Proc. Natl. Acad. Sci. USA 86, 6412 (1989).
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In our in vivo saturation-binding analysis, KD values correspond to in vitro results, whereas Bmax values are lower compared to in vitro results, although still lying within the same order of magnitude. In comparing in vivo and in vitro measurements, various issues should be taken into account. First, the exact determination of the anterioposterior stereotaxic coordinates of the PET slices is hampered when no concurrent morphological imaging may be performed. Noncorresponding sectional planes between PET and autoradiography thus offer one explanation for the difference between receptor densities obtained in vivo and in vitro. Second, the applied partial-volume correction factor is estimated on the basis of phantom studies and enters as a constant factor into the quantification of radioactivity values irrespective of the actual striatal diameters on the slices selected for ROI definition. Thus, if striatal diameters fall short of 2.5 mm, the used correction factor leads to underestimations of radioactivity concentrations compared to autoradiography. Third, the accuracy of our method depends on the correctness of the assumption that C2 and C20 may be pooled into one compartment. Actually, we derive [L], i.e., both the free and the nonspecifically bound radioligand concentration, from the cortical reference region. Thus, in our approach, 0 BP is given by ½LR ½L 1. As [L] corresponds to C2 þ C2 , the nonspecifically bound radioligand enters into the denominator in addition to the free radioligand concentration. Thus, the correctness of parameter estimation suffers from the fact that the free fraction of radioligand in C2, f2, may not be determined accurately. Actually, with our method, we derive B0 max (¼f2Bmax) and thus underestimate Bmax consistently. Because a reference region is used for the estimation of C2 þ C20 in the simplified reference tissue model,23 the portion of nonspecifically bound radioligand in this approach may also lead to an underestimation of BP. Actually, instead of Bmax/KD, f2Bmax/KD is obtained as an outcome measure. With the dynamic approach,24–26 the receptor parameter 3 ðtÞ k3 ¼ kon ðBmax CSA f 2 is estimated with SA denoting the specific activity of the radioligand. If SA is high and the radioligand is administered in 3 ðtÞ tracer amounts, then CSA Bmax and an estimate of k3 is provided by the product of kon, Bmax, and f2. Thereby, f2 usually is inferred from in vitro
23
A. A. Lammertsma and S. P. Hume, Neuroimage 4, 153 (1996). M. A. Mintun, M. E. Raichle, M. R. Kilbourn, G. F. Wooten, and M. J. Welch, Ann. Neurol. 15, 217 (1984). 25 J. S. Perlmutter, K. B. Larson, M. E. Raichle, J. Markham, M. A. Mintun, M. R. Kilbourn, and M. J. Welch, J. Cereb. Blood Flow Metab. 6, 154 (1986). 26 D. F. Wong, A. Gjedde, H. N. Wagner, Jr., R. F. Dannals, K. H. Douglass, J. M. Links, and M. J. Kuhar, J. Cereb. Blood Flow Metab. 6, 147 (1986). 24
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studies or is estimated from the kinetics in tissue regions lacking specific binding. If the latter is the case, the product of Bmax and kon provides an estimate of BP, the goodness of which, as is the case for in vivo saturation binding and the simplified reference tissue approach, depends on the accuracy, with which f2 may be determined. A similar problem occurs with the noninvasive graphic model,27 which yields the distribution volume ratio, DVR, as an outcome measure. The DVR is the ratio of the equilibrium distribution volume in the ROI to that in the REF. Thereby, DVR ¼ BP þ 1 if the distribution volumes of REF and C2 are assumed to be equal.13 Thus, also in this approach, existing nonspecific radioligand binding leads to inaccurate BP estimates. As the tissue-to-plasma efflux constant, k2, is required for this kind of analysis, the goodness of BP estimates furthermore may depend on the feasibility of inferring k2 from an independent sample. In discussing possible errors of parameter estimation, their degree, however, should be viewed in relation to other error sources inherent to the method of in vivo PET imaging, such as spillover and partial-volume effect. For the nonspecific binding moreover holds that it is characterized by both tissue and radioligand properties, which are not assumed to vary over time or between subjects. Thus, f2Bmax and KD, f2Bmax/KD, f2konBmax, and DVR as obtained with in vivo saturation-binding analysis, the simplified reference tissue model, the dynamic approach, and the noninvasive graphic model, respectively, can be considered to provide reasonable estimates of the receptor parameters in question. Thereby, the advantage of in vivo saturation-binding analysis is the provision of Bmax(0 ) and KD as separate values and direct measures of receptor density and affinity. In vivo saturation-binding analysis represents an equilibrium method, which for the first time was described by Phelps and collaborators.28 So far, in vivo saturation-binding analysis with small animal tomographs has been applied in two studies: Nikolaus and collaborators14 investigated time-dependent changes of Bmax in the rat 6-hydroxydopamine model, whereas Tsukada and collaborators1 utilized the saturation-binding approach as a complement to PET in order to analyze whether the observed effect on D2 receptor binding was due to alterations in KD or Bmax. These investigations are examples for scientific questions requiring methods for the separate determination of KD and Bmax in small laboratory animals. 27
J. Logan, J. S. Fowler, N. D. Volkow, G. J. Wang, Y. S. Ding, and D. L. Alexoff, J. Cereb. Blood Flow Metab. 16, 834 (1996). 28 M. E. Phelps, J. C. Mazziotta, and H. R. Schelbert, ‘‘Positron Emission Tomography and Autoradiography: Principles and Applications for the Brain and Heart.’’ Raven Press, New York, 1986.
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With the in vivo saturation-binding approach, the benefits of two concepts are brought together. By applying the in vitro method to in vivo imaging, KD and Bmax may be determined in analogy to in vitro experiments preserving all advantages of the in vivo method, such as the possibility to reuse an animal for several investigations and to assess receptor kinetics in the living subject instead of utilizing cryosections or membrane homogenates as mere models of cerebral tissue and receptor surface. Finally, an enormous disadvantage of in vivo methods, the struggle with varying and low specific activities, is changed to the opposite, as with the method of saturation binding, increasing concentrations of radioligand have to be applied in order to reach the state of receptor saturation. It is important to note, however, that there is one fundamental difference between in vivo saturation-binding analysis yielding Bmax and KD and other approaches quantifying BP or related outcome measures: with the saturation-binding method, various radioligand concentrations must be applied to several animals. In contrast, in the other approaches, outcome measures may be obtained for one animal with one radioligand concentration. Thus, basically, with in vivo saturation-binding analysis, more animals are required, leading to a greater influence of interindividual variance. Theoretically, application of more than one concentration to a single animal is also feasible; in this case, individual values of both Bmax and KD may be determined for each animal. PET investigations, however, should lie a sufficient time apart to account for radioactive decay and to permit recovery from aftereffects of anesthesia and surgery. Acknowledgments This work was supported by a grant from the ‘‘Forschungskommission’’ of the Faculty of Medicine, Heinrich-Heine-University, Du¨ sseldorf, Germany. The authors acknowledge Dr. Simone Weber from the Central Laboratory for Electronics and Dr. Karl Hamacher from the Institute of Nuclear Chemistry (Forschungszentrum Ju¨ lich GmbH, Ju¨ lich, Germany) for their contributions to the experiments.