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The influence of tomograph sensitivity on kinetic parameter estimation in positron emission tomography imaging studies of the rat brain
Nuclear Medicine & Biology, Vol. 27, pp. 617– 625, 2000 Copyright © 2000 Elsevier Science Inc. All rights reserved.
ISSN 0969-8051/00/$–see front matter PII S0969-8051(00)00105-0
The Influence of Tomograph Sensitivity on Kinetic Parameter Estimation in Positron Emission Tomography Imaging Studies of the Rat Brain Steven R. Meikle, Stefan Eberl, Roger R. Fulton, Michael Kassiou and Michael J. Fulham DEPARTMENT OF PET AND NUCLEAR MEDICINE, ROYAL PRINCE ALFRED HOSPITAL, SYDNEY, AUSTRALIA
ABSTRACT. We investigated the influence of tomograph sensitivity on reliability of parameter estimation in positron emission tomography studies of the rat brain. The kinetics of two tracers in rat striatum and cerebellum were simulated. A typical injected dose of 10 MBq and a reduced dose of 1 MBq were assumed. Kinetic parameters were estimated using a region of interest (ROI) analysis and two pixel-by-pixel analyses. Striatal binding potential was estimated as a function of effective tomograph sensitivity (Seff) using a simplified reference tissue model. A Seff value of >1% was required to ensure reliable parameter estimation for ROI analysis and a Seff of 3– 6% was required for pixel-by-pixel analysis. We conclude that effective tomograph sensitivity of 3% may be an appropriate design goal for rat brain imaging. NUCL MED BIOL 27;6: 617– 625, 2000. © 2000 Elsevier Science Inc. All rights reserved. KEY WORDS. Small animal imaging, PET, Rat brain, Tracer kinetics, Parameter estimation INTRODUCTION
tomographs are in routine use and clearly demonstrate the value of dedicated instrumentation for performing small animal imaging studies. They also provide benchmarks against which other designs can be compared. However, the question of how much sensitivity is required for such studies has not been addressed, which makes it difficult to set appropriate design goals. The problem of relating reliability of parameter estimation to tomograph sensitivity is complicated by the wide range of tracer kinetics and activity concentrations that are observed in vivo. For example, Hume et al. (14) pointed out that when using receptor radioligands, the injected dose may in some cases be limited by the allowable mass of ligand before tracer kinetics are violated. Thus, the maximal tissue tracer concentration may vary by an order of magnitude and tomograph sensitivity may become the limiting factor in determining the viability of such studies. The purpose of this study was to gain insight into the influence of tomograph sensitivity on parameter estimation under study conditions that are typical of those encountered in small animal imaging studies. We chose the rat dopaminergic system as the focus of our study because it is an active area for tracer development and basic research and is prone to the mass effects referred to above. A number of generic reconstruction and analysis algorithms were employed, with the hope that the findings of this study will assist other researchers in setting design goals for future small animal tomographs. We also report on the results of applying our methodology to a particular tomograph design that is currently under development within our institution.
A number of tomograph designs and detector technologies have recently been proposed for imaging single photon emission computed tomography (SPECT) and positron emission tomography (PET) radiotracers in small animals (3, 6, 9, 18, 19, 21, 24). With dedicated instrumentation for animal imaging studies, the design can be optimized to suit particular applications. Our main interests are in the evaluation of new SPECT and PET radiotracers in the preclinical setting and new forms of therapy in cancer and neurologic disease. Therefore, our aim is to develop dedicated instrumentation that will enable a wide variety of tracers to be assessed in suitable animal models. In addition to providing high spatial resolution, such instrumentation should ideally be capable of providing sufficient sensitivity to determine pharmacokinetic parameters at both the region of interest (ROI) and image pixel level. Design goals for small animal tomographs are often based on the perceived need for high spatial resolution, which makes it easier to identify anatomical landmarks and minimizes partial volume errors. However, for kinetic studies such as those demanded by our application, tomograph sensitivity may be at least as important, if not more important, than spatial resolution. Of the several tomograph designs that have been proposed, relatively few have been fully evaluated in terms of their performance. Two notable exceptions are RATPET (3), developed at the MRC Cyclotron Unit (Hammersmith Hospital, London, England) and MicroPET (5, 6), developed at the Crump Institute for Biological Imaging (UCLA School of Medicine, Los Angeles, CA USA). These scanners have quite different performance characteristics. MicroPET has better and more uniform spatial resolution and RATPET has higher sensitivity (approximately 4% versus approximately 1%). Both
Simulated Tracers
Address correspondence to: Steven Meikle, Ph.D., Department of PET and Nuclear Medicine, Royal Prince Alfred Hospital, Missenden Road, Camperdown NSW2050, Australia; e-mail: [email protected]. Received 11 December 1999. Accepted 21 March 2000.
We simulated the kinetic behavior of two tracers that are used to image the dopaminergic systems of rats and humans. Tracer A closely approximates [11C]raclopride, a D2 receptor radioligand, and tracer B approximates [11C]RTI-121, a radioligand for the dopamine transporter. These tracers were chosen because their kinetics are
METHODS
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sented the kinetics of the tracer in a region devoid of specific binding sites was generated using a typical arterial input function normalized to an injected dose of 10 MBq and a single tissue compartment model. The values for K1 and k2 were the same as those used for striatum and cortex in Table 1. The striatal and cortical curves were then generated using the following equation and the parameter values in Table 1:
冉
C T共t兲 ⫽ R 1C R共t兲 ⫹ k 2 ⫺
冊
R 1k 2 C 共t兲 䊟 e ⫺关k2/共1⫹BP兲兴t 1 ⫹ BP R
(1)
where CR and CT are the tracer concentrations in the reference and target tissues, respectively, R1 is the ratio of K1 in the target tissue to K1 in the reference tissue (R1 ⫽ 1 in our simulations), and BP is the binding potential. Although 10 MBq is a typical dose for rat studies, in some instances the injected dose may be as low as 1 MBq due to limitations on the allowable injected mass of ligand for tracer kinetics to hold (14). Therefore, a second set of time-activity curves was generated for each tracer using an input function normalized to an injected dose of 1 MBq. Peak striatal uptake ranged from 100 kBq/mL for 10 MBq of tracer A down to 5 kBq/mL for 1 MBq of tracer B. All time-activity data were binned into frame intervals of 6 ⫻ 20 sec, 8 ⫻ 60 sec, and 16 ⫻ 300 sec for a scan duration of 90 min.
Rat Brain Phantom
FIG. 1. Simulated time-activity curves for (A) tracer A, which approximates the D2 radioligand [11C]raclopride, and (B) tracer B, which approximates the dopamine transporter radioligand [11C]-RTI-121. quite different and cover a wide range of peak striatal uptake and clearance (Fig. 1). The kinetics in striatum and cerebral cortex were based on the simplified reference tissue model described by Lammertsma and Hume (16). First, a reference tissue time-activity curve that repre-
A numerical rat brain phantom was created by segmenting a coronal section of the UCLA rat brain atlas (23). The image was resampled into a 128 ⫻ 128 matrix with pixel dimensions of 0.25 ⫻ 0.25 mm, resulting in a field of view of 3.2 cm. The image was then manually segmented into striatum and cerebral cortex. Dynamic image sequences were generated by assigning tracer concentration values to the pixels of each brain region based on the kinetics of the simulated receptor radioligands described above. Each dynamic image sequence was then forward projected to produce a dynamic sequence of sinograms with dimensions of 128 ⫻ 128. For simplicity, projection data were binned into two-dimensional (2D) sinograms representing a single imaging slice. This allowed Poisson noise to be added to the projection data reflecting the counting statistics expected for a volume imaging device while using a 2D algorithm to reconstruct the image data. This is based on the premises (7, 8) that (i) the noise behavior of 2D- and threedimensional (3D)-filtered backprojection are similar because both the ramp filter and Colsher filter are proportional to the modulus of the spatial frequency, and (ii) image variance depends on the count statistics in the projections but is independent of sampling in projection space. Note that our approach will result in image variance that is appropriate for a central slice but not one near the edge of the tomograph, because signal-to-noise is maximal at the axial center of a volume imaging tomograph and falls off toward the
TABLE 1. Simulated Tracer Kinetic Parameters Tracer A Parameter K1 k2 BP BP, binding potential.
Striatum ⫺1
0.15 min 0.3 min⫺1 1.0
Tracer B Cortex ⫺1
0.15 min 0.3 min⫺1 0.1
Striatum ⫺1
0.043 min 0.04 min⫺1 1.0
Cortex 0.043 min⫺1 0.04 min⫺1 0.1
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edges. The sinograms were attenuated using an attenuation matrix that assumed uniform density in the head (average ⫽ 0.1 cm⫺1) and a skull thickness of 1 mm. Sinogram counts were scaled according to the desired tomograph sensitivity (see below) and Poisson noise was added before correcting the sinograms for attenuation.
Kinetic Parameter Estimation Three methods of estimating kinetic parameters were employed. In the first method, dynamic images were reconstructed using 2Dfiltered backprojection with a Hann window cut off at the Nyquist frequency (fnyq ⫽ 20 cycles/cm) forming 64 ⫻ 64 matrices with pixel dimensions of 0.5 mm3. An irregular ROI was defined that contained 16 voxels (total volume 2 mL) and enclosed approximately one half the cross-sectional area of the striata (left and right). The time-activity curve derived from this ROI was fitted with the simplified reference tissue model using the basis function method of Gunn et al. (11), which directly estimates the value of R1, BP, and k2. In the second method, images were reconstructed using filtered backprojection as above, however, BP was estimated for each pixel in the image space, enabling a parametric image of BP to be formed. The ROI defined above was used to determine the mean value of BP in the striata. These first two methods represent reasonably straightforward and commonly employed approaches to kinetic parameter estimation. In the third method, kinetic parameter estimation was incorporated into the image reconstruction process using the expectation maximization parametric image reconstruction algorithm (EMPIRA) (4). This algorithm is based on the steady-state EM algorithm (17, 22) but is extended by (i) allowing the tracer distribution (N in projection space, in image space) to change over time and (ii) fitting a tracer kinetic model during each iterative update of the image sequence. N itn ⫽
冘
b ijt jtn
(2)
j⑀Ji
n⫹
jt
1 2
⫽
冘 冘 jtn
b ijt
b ijt
i⑀Ij
y it N itn
(3)
i⑀IJ
冉
n⫹
1
jtn⫹1 ⫽ arg min Q jt 2,
冊
variance, taking only the counting efficiency of the tomograph into account; that is, count rate-dependent effects such as deadtime and randoms were neglected. Noisy projection data were simulated for tomograph sensitivities ranging from 0.5 to 10%. Estimates of BP were obtained using each of the methods described above. In each case, bias was calculated as a function of tomograph sensitivity by comparing the mean BP value in the ROI with the expected value of 1.0. The reconstructions were repeated for 12 independent realizations at each noise level. In the case of the ROI-based estimation (method 1), the coefficient of variation (CV) was taken to be the standard deviation of BP values over 12 different realizations divided by the mean. In the remaining cases, where BP was estimated at the pixel level, CV was calculated as the standard deviation of BP estimates over all pixels within the ROI and this value was averaged over the 12 independent realizations. EXTENDED TOMOGRAPH MODEL. Subsequently, we investigated the bias and variance in parameter estimates that can be expected using a more realistic tomograph model that includes count ratedependent effects. The extended model was used to assess the suitability of a dual head design for performing kinetic studies. The proposed tomograph comprises two detector heads arranged in opposing fans, with a field of view of 10 cm ⫻ 5 cm (transaxial ⫻ axial) and the ability to vary the distance between the heads. In the design we tested, each head comprises 18 detector blocks (6 transaxial and 3 axial) and each block is formed by an 8 ⫻ 8 array of detector elements individually coupled to each channel of a multi-channel photomultiplier tube. The simulated detector elements comprised 1 cm deep YSO crystals abutted to 1 cm deep LSO crystals (each 2 mm ⫻ 2 mm in cross-section), providing stopping power of 0.805 for 511 keV photons. For the purpose of the simulation we assumed 10-cm separation between the heads. The absolute sensitivity of the tomograph was determined by Monte Carlo simulation using the SimSET code (12), assuming a uniform cylindrical source distribution of positron emitter approximating the rat head (2 cm diameter). Energy thresholds of 380 keV and 650 keV were used and energy resolution of 20% FWHM was assumed. Sensitivity was expressed as the number of coincidence events detected within the photopeak window as a fraction of the annihilations occurring within the phantom. The count rate performance of the proposed scanner was pre-
(4)
Equations 2 and 3 are the familiar forward- and backprojection steps, respectively, in the conventional EM algorithm, except that they are performed on each frame in the dynamic sequence. For generality, the probability matrix b is allowed to vary with time so that bijt describes the probability of a photon emitted from pixel j being detected in projection bin i during the time interval t. In this article, we made the b matrix constant with respect to time. Equation 4 is the model-fitting step (with Q as the cost function and as the parameter vector), which completes the iterative cycle. In this study, model fitting was performed using the basis function approach discussed above (11). We also employed the one-step late approach (10) to regularize the reconstruction and ordered subsets to accelerate it (13).
Experimental Initially, we studied the effect of tomograph sensitivity on parameter bias and BIAS/VARIANCE VERSUS TOMOGRAPH SENSITIVITY.
FIG. 2. Predicted count rate performance and effective sensitivity of a dual-head small animal tomograph design. NEC, noise equivalent count rate.
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FIG. 3. Reliability of parameter estimation using region of interest analysis of filtered backprojection images as a function of tomograph sensitivity. The graphs indicate (a) bias and (b) coefficient of variation (CV) for an injected dose of 10 MBq and (c) bias and (d) CV for an injected dose of 1 MBq. dicted using a component-based PET count rate model (20). The above geometry was modeled, including 1 “bucket” per head, which combines positioning, energy, and timing data from each of the 18 blocks. We assumed a typical block integration time of 80 ns, a coincidence time window of 12 ns, and a coincidence processor with bandwidth of 2.6 MHz. Given the absolute sensitivity and count rate performance of the scanner, we calculated the effective sensitivity as a function of activity in the field of view. Effective sensitivity is defined as (1): S eff共 x兲 ⫽ S abs ⫻
NEC共 x兲 T ideal共 x兲
(5)
where Sabs is the absolute sensitivity, NEC is the noise equivalent count rate, and Tideal is the ideal true coincidence rate for a given radioactivity concentration x. The effective sensitivity of the proposed tomograph varies from nearly 2% at low concentrations to ⬍1% at 1,000 kBq/mL (Fig. 2). However, the maximum expected concentration in animal imaging studies is ⬍200 kBq/mL and in the current study the maximum simulated brain concentration was 100 kBq/mL.
The sinograms obtained previously by forward projection of the rat brain phantom were scaled by the effective sensitivity at each time point during the dynamic “scans” and Poisson noise was added accordingly. Sinograms were corrected for attenuation and parametric images of R1 and BP were reconstructed into 128 ⫻ 128 matrices using 4 iterations and 16 subsets of EM-PIRA. The reconstructions were repeated for 12 independent realizations at the same noise level and the mean and standard deviations of parameter values in the striatal ROI defined above were evaluated. RESULTS
Bias/Variance versus Tomograph Sensitivity Bias and variance (expressed as CV) of BP estimates obtained by ROI analysis are plotted as a function of tomograph sensitivity in Figure 3 for each of the tracers and each of the injected doses. Similar plots are shown for pixel-by-pixel analysis of filtered backprojection images in Figure 4 and for EM-PIRA in Figure 5. For the ROI analysis, BP was accurately estimated (bias ⬍ 5%) for both tracers over the range of tomograph sensitivities investi-
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FIG. 4. Reliability of parameter estimation using pixel-by-pixel analysis of filtered backprojection images as a function of tomograph sensitivity. The graphs indicate (a) bias and (b) coefficient of variation (CV) for an injected dose of 10 MBq and (c) bias and (d) CV for an injected dose of 1 MBq. gated. As expected, the CV was considerably greater when the injectate was only 1 MBq compared with an injectate of 10 MBq and it was greater for tracer B than for tracer A. This trend was observed for all the parameter estimation methods studied. In the case of ROI analysis, the CV fell below 20% for 1 MBq of tracer B when the tomograph sensitivity was ⱕ1% (Fig. 3d). For pixel-by-pixel analysis of filtered backprojection images (Fig. 4), tomograph sensitivity of ⬎6% was required to reduce both the bias and CV to acceptable levels (bias ⬍ 5%, CV ⬍ 20%) when the injectate was only 1 MBq. However, for a 10 MBq dose, sensitivity of 1% was sufficient to achieve these goals. When EM-PIRA was used to obtain pixel-by-pixel estimates of BP (Fig. 5), tomograph sensitivity of 3– 4% was sufficient to ensure reliable parameter estimation in all situations.
When the injectate was 10 MBq, acceptable images of relative tracer delivery (R1) and BP were obtained for both tracer A and tracer B. When the injectate was reduced to 1 MBq, the parametric images were noticeably more noisy, particularly for tracer B. The bias and CV of parameter estimates corresponding to these images are given in Table 2. The bias in R1 and BP for both tracers was ⬍10% when the injectate was 10 MBq and the CV was acceptable. When the injectate was 1 MBq, the bias remained ⬍10% for tracer A but the CV was 40% when estimating R1 and 21% when estimating BP. Given that BP is the main parameter of interest in receptor-ligand binding studies, these parameter estimates may be considered acceptable. However, for tracer B the bias in estimating BP was ⫹25% for tracer B at 1 MBq and the CV was unacceptably high at 46%.
Extended Tomograph Model
DISCUSSION
Figure 6 shows parametric and nonparametric images predicted by the extended model when imaging tracer A and tracer B with the proposed tomograph at typical (Fig. 6a) and reduced doses (Fig. 6b).
In this study, we investigated the influence of tomograph sensitivity, parameter estimation methodology, and tracer specific effects on the reliability of kinetic parameter estimates obtained from rat
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FIG. 5. Reliability of parameter estimation using pixel-by-pixel analysis of expectation maximization parametric image reconstruction algorithm (EM-PIRA) images as a function of tomograph sensitivity. The graphs indicate (a) bias and (b) coefficient of variation (CV) for an injected dose of 10 MBq and (c) bias and (d) CV for an injected dose of 1 MBq. brain imaging studies. We found that, for the range of tracers and injectates investigated, a tomograph sensitivity of 1% is sufficient for accurate and reliable parameter estimation when using conventional image reconstruction and ROI analysis. For pixel-by-pixel fitting, the demands on signal-to-noise are greater and tomograph sensitivity of ⱖ3% is required when using an iterative reconstruction/parameter estimation approach such as EM-PIRA (4). The demands are still greater when filtered backprojection is employed along with pixel-by-pixel analysis. Therefore, higher tomograph sensitivity is required for parameter estimation at the pixel level, but this can be offset by careful choice of image reconstruction and kinetic analysis methods. The benefit of the EM-PIRA approach over filtered backprojection comes not only from the favorable signal-to-noise properties of the EM algorithm (25) but also from the use of a tracer kinetic model as a form of regularization (15). It should be noted, however, that EM-PIRA may not be the best choice in all situations. In particular, we found that filtered backprojection performed better than EM-PIRA at the pixel level in the high-activity case (compare
Figs. 4a and 4b with Figs. 5a and 5b), whereas the converse was true in the low-activity case (compare Figs. 4c and 4d with Figs. 5c and 5d). This is consistent with the known noise properties of the two reconstruction algorithms (25). In particular, EM is known to produce better local signal-to-noise ratio in reconstructed images when count statistics are relatively poor (as in the low-activity case), whereas filtered backprojection outperforms EM when count statistics are relatively high (as in the high-activity case). This is due to the fact that the variance in EM images depends mainly on the local mean pixel value, whereas the variance in filtered backprojection images depends more on the global count level (i.e., noise is more highly correlated across pixels) (2, 26). This makes it difficult to recommend a particular algorithm for all situations. However, we believe that EM, when combined with regularization by use of a tracer kinetic model, offers a more robust alternative to filtered backprojection. Similarly, the basis function implementation of the simplified reference tissue model seems to derive some of its robustness from the use of constraints on the possible range of parameter values (11); however, this has not been fully explored.
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FIG. 6. Parametric images predicted by our extended model of a dual-head animal scanner for (a) an injected dose of 10 MBq and (b) an injected dose of 1 MBq. Images were scaled to a common maximum as indicated. The first column is the accumulated tracer distribution over the 90 min following injection. The second and third columns are parametric images of R1, which represents relative tracer delivery, and binding potential (BP), respectively.
We also found that some tracers are more susceptible to parameter estimation errors when the administered dose must be reduced to avoid pharmacologic effects. For example, in our study the reliability of parameter estimates with tracer B, which approximates the dopamine transporter radioligand [11C]RTI-121, was severely affected by reducing the injected dose from 10 MBq to 1 MBq. In comparison, parameter estimates with tracer A, which approximates the D2 radioligand [11C]raclopride, were relatively unaffected by reducing the injected dose. However, in practice, [11C]RTI-121 is less likely to be dose-limited than is [11C]raclopride because the population of dopamine reuptake sites in the brain is approximately one order of magnitude greater than the population of D2 receptors. Thus, given the same specific activity of the injectate and similar affinity for their respective binding sites, [11C]RTI-121 has much lower receptor occupancy than does [11C]raclopride. Nevertheless, our results suggest that tomograph sensitivity may become the limiting factor if the tomograph is to be used for imaging tracers where factors such as specific activity, affinity, and receptor availability conspire to place a constraint on the allowable injected dose.
There are some limitations of the rat brain simulations performed in this study. For example, we did not model activity contained in extra-brain compartments such as musculature and other soft tissues. However, we do not believe that more detailed modeling of these additional compartments would significantly affect the results for the following reasons. In general, there are two ways in which extra-brain activity may affect the local signal-to-noise ratio in striatal brain regions. One is by increasing the total photon flux (singles and coincidences), including randoms and scatter, recorded by the tomograph, which in turn reduces the NEC and the effective sensitivity. However, because the first part of our work (see Bias/Variance versus Tomograph Sensitivity) did not include countrate effects or scatter, and in the second part, effective sensitivity was relatively constant over the wide range of activities considered (Fig. 2), this effect would have little or no influence on the reconstructed signal-to-noise ratio. The other effect is because of correlation of noise across image pixels. This effect is greater when using filtered backprojection than iterative reconstruction, due to the greater extent of the correlation function (which derives from
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TABLE 2. Parameter Bias and Variance for the Proposed Scanner BP
R1 Tracer 10 MBq tracer A 10 MBq tracer B 1 MBq tracer A 1 MBq tracer B
Bias
CV
Bias
CV
⫹1 ⫾ 2% ⫺2 ⫾ 1% ⫺5 ⫾ 7% ⫺12 ⫾ 8%
11 ⫾ 2% 8 ⫾ 1% 40 ⫾ 8% 35 ⫾ 14%
⫺1 ⫾ 1% ⫹9 ⫾ 5% ⫺1 ⫾ 3% ⫹25 ⫾ 6%
10 ⫾ 1% 22 ⫾ 4% 21 ⫾ 3% 46 ⫾ 7%
BP, binding potential; CV, coefficient of variation.
the smearing of the backprojection process). However, in our study, ROIs were drawn over the striata, which were fairly central in the image, and this would have further reduced the impact of noise correlation on local SNR in the striata due to extra-brain activity. To test these assumptions, we performed some additional simulations in which extra-brain activity was modeled by adding a rim to the rat brain phantom, which increased the diameter of the brain by 55% and the volume by 145%. The rim contained 50% of the maximum activity concentration, resulting in a greater than twofold increase in sinogram counts. We then reconstructed the sinograms with and without extra-brain activity after adding Poisson noise (see Methods) and calculated the CV in a striatal ROI. We found that there was only a 10% increase in CV when we used filtered backprojection (0.069 ⫾ 0.009 versus 0.063 ⫾ 0.007) and no significant increase when we used iterative reconstruction (0.109 ⫾ 0.02 versus 0.110 ⫾ 0.009). Thus, we do not believe that ignoring extra-brain activity would have influenced our main findings. A further limitation was that our simulations did not include the effects of activity beyond the axial field of view of the scanner and intra-detector scatter. These factors would further reduce the achievable effective sensitivity of the proposed tomograph in practice. However, the predicted scatter fraction was ⬍5% for the proposed tomograph and is still ⬍10% when activity beyond the axial field of view is taken into account. Furthermore, it is worth emphasizing that the particular scanner design discussed in this article is less important than is the general concept of considering the impact of tomograph sensitivity on parameter estimation when designing small animal PET instrumentation. We used this scanner design as an example to illustrate how the tomograph sensitivity can be predicted and its potential impact on parameter estimation evaluated. Thus, several factors should be taken into account when setting design goals for dedicated instrumentation for small animal imaging. These include the physiologic systems to be studied, the tracers to be employed, and the image reconstruction algorithms and data analysis methods to be adopted. We investigated a number of approaches to image reconstruction/analysis and designed the simulations to cover a reasonably diverse set of typical tracer kinetics, including dose effects. We believe, therefore, that these results can be extrapolated to a wide range of situations in imaging the rat brain and should provide useful guidelines for the design of future small animal tomographs. Although this work focussed on the capability of small animal tomographs designed for PET, in future work we will adapt our methodology to predict the dynamic capability of dedicated SPECT animal scanners. To extend the methodology to SPECT will require modeling single photon attenuation, scattering, and collimator efficiency during the forward projection step and incorporating a count rate model appropriate for SPECT. Until such a study is performed, it is difficult to predict what magnitude of tomograph
sensitivity will be required for successful small animal imaging with SPECT. However, we expect the greatly reduced counting efficiency of SPECT compared with PET (1–2 orders of magnitude) to be largely offset by the higher specific activities encountered with SPECT radiopharmaceuticals. Nevertheless, careful design of SPECT camera geometry and, in particular, collimation will be important considerations. CONCLUSIONS The tomograph sensitivity required for small animal imaging is dependent on several factors, including the tracers of interest and the method of parameter estimation employed. However, to ensure reliable parameter estimation at the ROI and pixel level, effective tomograph sensitivity of 3% may be considered an appropriate design goal for imaging the rat brain. We would like to acknowledge the helpful advice of Sue Hume from the MRC Cyclotron Unit, Hammersmith Hospital, and Simon Cherry from the Crump Institute for Biological Imaging, UCLA School of Medicine. This work was presented at the 1998 IEEE Medical Imaging Conference in Toronto.
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18. Lecomte R., Cadorette J., Rodrique S., Lapointe D., Rouleau D., Bentourkia M., Yao R. and Msaki P. (1996) Initial results from the Sherbrooke avalanche photodiode positron tomograph. IEEE Trans. Nucl. Sci. 43, 1952–1957. 19. Liu X., Rajeswaran S., Smolik W., Tavernier S., Zhang S. and Bruyndonckx P. (1996) Design and physical characteristics of a small animal PET using BaF2 crystals and a photosensitive wire chamber. Nucl. Inst. Meth. A382, 589 – 600. 20. Moisan C., Rogers J. G. and Douglas J. L. (1997) A count rate model for PET and its application to an LSO HR plus scanner. IEEE Trans. Nucl. Sci. 44, 1219 –1224. 21. Pichler B., Boning C., Lorenz E., Mirzoyan R., Pimpl W., Schwaiger M. and Ziegler S. I. (1998) Studies with a prototype high resolution PET scanner based on LSO-APD modules. IEEE Trans. Nucl. Sci. 45, 1298 –1302. 22. Shepp L. A. and Vardi Y. (1982) Maximum likelihood reconstruction for emission tomography. IEEE Trans. Med. Imag. MI-1, 113–122. 23. Toga A. W., Santori E. M., Hazani R. and Ambach K. (1995) A 3D digital map of rat brain. Brain Res. Bull. 38, 77– 85. 24. Watanabe M., Uchida H., Okada H., Shimizu K., Satoh N., Yoshikawa E., Ohmura T., Yamashita T. and Tanaka E. (1992) A high resolution PET for animal studies. IEEE Trans. Med. Imag. 11, 577–580. 25. Wilson D. W. and Tsui B. M. W. (1993) Noise properties of filteredbackprojection and ML-EM reconstructed emission tomographic images. IEEE Trans. Nucl. Sci. 40, 1198 –1203. 26. Wilson D. W., Tsui B. M. W. and Barrett H. H. (1994) Noise properties of the EM algorithm: II. Monte Carlo simulations. Phys. Med. Biol. 39, 847– 871.
ISSN 0969-8051/00/$–see front matter PII S0969-8051(00)00105-0
The Influence of Tomograph Sensitivity on Kinetic Parameter Estimation in Positron Emission Tomography Imaging Studies of the Rat Brain Steven R. Meikle, Stefan Eberl, Roger R. Fulton, Michael Kassiou and Michael J. Fulham DEPARTMENT OF PET AND NUCLEAR MEDICINE, ROYAL PRINCE ALFRED HOSPITAL, SYDNEY, AUSTRALIA
ABSTRACT. We investigated the influence of tomograph sensitivity on reliability of parameter estimation in positron emission tomography studies of the rat brain. The kinetics of two tracers in rat striatum and cerebellum were simulated. A typical injected dose of 10 MBq and a reduced dose of 1 MBq were assumed. Kinetic parameters were estimated using a region of interest (ROI) analysis and two pixel-by-pixel analyses. Striatal binding potential was estimated as a function of effective tomograph sensitivity (Seff) using a simplified reference tissue model. A Seff value of >1% was required to ensure reliable parameter estimation for ROI analysis and a Seff of 3– 6% was required for pixel-by-pixel analysis. We conclude that effective tomograph sensitivity of 3% may be an appropriate design goal for rat brain imaging. NUCL MED BIOL 27;6: 617– 625, 2000. © 2000 Elsevier Science Inc. All rights reserved. KEY WORDS. Small animal imaging, PET, Rat brain, Tracer kinetics, Parameter estimation INTRODUCTION
tomographs are in routine use and clearly demonstrate the value of dedicated instrumentation for performing small animal imaging studies. They also provide benchmarks against which other designs can be compared. However, the question of how much sensitivity is required for such studies has not been addressed, which makes it difficult to set appropriate design goals. The problem of relating reliability of parameter estimation to tomograph sensitivity is complicated by the wide range of tracer kinetics and activity concentrations that are observed in vivo. For example, Hume et al. (14) pointed out that when using receptor radioligands, the injected dose may in some cases be limited by the allowable mass of ligand before tracer kinetics are violated. Thus, the maximal tissue tracer concentration may vary by an order of magnitude and tomograph sensitivity may become the limiting factor in determining the viability of such studies. The purpose of this study was to gain insight into the influence of tomograph sensitivity on parameter estimation under study conditions that are typical of those encountered in small animal imaging studies. We chose the rat dopaminergic system as the focus of our study because it is an active area for tracer development and basic research and is prone to the mass effects referred to above. A number of generic reconstruction and analysis algorithms were employed, with the hope that the findings of this study will assist other researchers in setting design goals for future small animal tomographs. We also report on the results of applying our methodology to a particular tomograph design that is currently under development within our institution.
A number of tomograph designs and detector technologies have recently been proposed for imaging single photon emission computed tomography (SPECT) and positron emission tomography (PET) radiotracers in small animals (3, 6, 9, 18, 19, 21, 24). With dedicated instrumentation for animal imaging studies, the design can be optimized to suit particular applications. Our main interests are in the evaluation of new SPECT and PET radiotracers in the preclinical setting and new forms of therapy in cancer and neurologic disease. Therefore, our aim is to develop dedicated instrumentation that will enable a wide variety of tracers to be assessed in suitable animal models. In addition to providing high spatial resolution, such instrumentation should ideally be capable of providing sufficient sensitivity to determine pharmacokinetic parameters at both the region of interest (ROI) and image pixel level. Design goals for small animal tomographs are often based on the perceived need for high spatial resolution, which makes it easier to identify anatomical landmarks and minimizes partial volume errors. However, for kinetic studies such as those demanded by our application, tomograph sensitivity may be at least as important, if not more important, than spatial resolution. Of the several tomograph designs that have been proposed, relatively few have been fully evaluated in terms of their performance. Two notable exceptions are RATPET (3), developed at the MRC Cyclotron Unit (Hammersmith Hospital, London, England) and MicroPET (5, 6), developed at the Crump Institute for Biological Imaging (UCLA School of Medicine, Los Angeles, CA USA). These scanners have quite different performance characteristics. MicroPET has better and more uniform spatial resolution and RATPET has higher sensitivity (approximately 4% versus approximately 1%). Both
Simulated Tracers
Address correspondence to: Steven Meikle, Ph.D., Department of PET and Nuclear Medicine, Royal Prince Alfred Hospital, Missenden Road, Camperdown NSW2050, Australia; e-mail: [email protected]. Received 11 December 1999. Accepted 21 March 2000.
We simulated the kinetic behavior of two tracers that are used to image the dopaminergic systems of rats and humans. Tracer A closely approximates [11C]raclopride, a D2 receptor radioligand, and tracer B approximates [11C]RTI-121, a radioligand for the dopamine transporter. These tracers were chosen because their kinetics are
METHODS
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sented the kinetics of the tracer in a region devoid of specific binding sites was generated using a typical arterial input function normalized to an injected dose of 10 MBq and a single tissue compartment model. The values for K1 and k2 were the same as those used for striatum and cortex in Table 1. The striatal and cortical curves were then generated using the following equation and the parameter values in Table 1:
冉
C T共t兲 ⫽ R 1C R共t兲 ⫹ k 2 ⫺
冊
R 1k 2 C 共t兲 䊟 e ⫺关k2/共1⫹BP兲兴t 1 ⫹ BP R
(1)
where CR and CT are the tracer concentrations in the reference and target tissues, respectively, R1 is the ratio of K1 in the target tissue to K1 in the reference tissue (R1 ⫽ 1 in our simulations), and BP is the binding potential. Although 10 MBq is a typical dose for rat studies, in some instances the injected dose may be as low as 1 MBq due to limitations on the allowable injected mass of ligand for tracer kinetics to hold (14). Therefore, a second set of time-activity curves was generated for each tracer using an input function normalized to an injected dose of 1 MBq. Peak striatal uptake ranged from 100 kBq/mL for 10 MBq of tracer A down to 5 kBq/mL for 1 MBq of tracer B. All time-activity data were binned into frame intervals of 6 ⫻ 20 sec, 8 ⫻ 60 sec, and 16 ⫻ 300 sec for a scan duration of 90 min.
Rat Brain Phantom
FIG. 1. Simulated time-activity curves for (A) tracer A, which approximates the D2 radioligand [11C]raclopride, and (B) tracer B, which approximates the dopamine transporter radioligand [11C]-RTI-121. quite different and cover a wide range of peak striatal uptake and clearance (Fig. 1). The kinetics in striatum and cerebral cortex were based on the simplified reference tissue model described by Lammertsma and Hume (16). First, a reference tissue time-activity curve that repre-
A numerical rat brain phantom was created by segmenting a coronal section of the UCLA rat brain atlas (23). The image was resampled into a 128 ⫻ 128 matrix with pixel dimensions of 0.25 ⫻ 0.25 mm, resulting in a field of view of 3.2 cm. The image was then manually segmented into striatum and cerebral cortex. Dynamic image sequences were generated by assigning tracer concentration values to the pixels of each brain region based on the kinetics of the simulated receptor radioligands described above. Each dynamic image sequence was then forward projected to produce a dynamic sequence of sinograms with dimensions of 128 ⫻ 128. For simplicity, projection data were binned into two-dimensional (2D) sinograms representing a single imaging slice. This allowed Poisson noise to be added to the projection data reflecting the counting statistics expected for a volume imaging device while using a 2D algorithm to reconstruct the image data. This is based on the premises (7, 8) that (i) the noise behavior of 2D- and threedimensional (3D)-filtered backprojection are similar because both the ramp filter and Colsher filter are proportional to the modulus of the spatial frequency, and (ii) image variance depends on the count statistics in the projections but is independent of sampling in projection space. Note that our approach will result in image variance that is appropriate for a central slice but not one near the edge of the tomograph, because signal-to-noise is maximal at the axial center of a volume imaging tomograph and falls off toward the
TABLE 1. Simulated Tracer Kinetic Parameters Tracer A Parameter K1 k2 BP BP, binding potential.
Striatum ⫺1
0.15 min 0.3 min⫺1 1.0
Tracer B Cortex ⫺1
0.15 min 0.3 min⫺1 0.1
Striatum ⫺1
0.043 min 0.04 min⫺1 1.0
Cortex 0.043 min⫺1 0.04 min⫺1 0.1
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edges. The sinograms were attenuated using an attenuation matrix that assumed uniform density in the head (average ⫽ 0.1 cm⫺1) and a skull thickness of 1 mm. Sinogram counts were scaled according to the desired tomograph sensitivity (see below) and Poisson noise was added before correcting the sinograms for attenuation.
Kinetic Parameter Estimation Three methods of estimating kinetic parameters were employed. In the first method, dynamic images were reconstructed using 2Dfiltered backprojection with a Hann window cut off at the Nyquist frequency (fnyq ⫽ 20 cycles/cm) forming 64 ⫻ 64 matrices with pixel dimensions of 0.5 mm3. An irregular ROI was defined that contained 16 voxels (total volume 2 mL) and enclosed approximately one half the cross-sectional area of the striata (left and right). The time-activity curve derived from this ROI was fitted with the simplified reference tissue model using the basis function method of Gunn et al. (11), which directly estimates the value of R1, BP, and k2. In the second method, images were reconstructed using filtered backprojection as above, however, BP was estimated for each pixel in the image space, enabling a parametric image of BP to be formed. The ROI defined above was used to determine the mean value of BP in the striata. These first two methods represent reasonably straightforward and commonly employed approaches to kinetic parameter estimation. In the third method, kinetic parameter estimation was incorporated into the image reconstruction process using the expectation maximization parametric image reconstruction algorithm (EMPIRA) (4). This algorithm is based on the steady-state EM algorithm (17, 22) but is extended by (i) allowing the tracer distribution (N in projection space, in image space) to change over time and (ii) fitting a tracer kinetic model during each iterative update of the image sequence. N itn ⫽
冘
b ijt jtn
(2)
j⑀Ji
n⫹
jt
1 2
⫽
冘 冘 jtn
b ijt
b ijt
i⑀Ij
y it N itn
(3)
i⑀IJ
冉
n⫹
1
jtn⫹1 ⫽ arg min Q jt 2,
冊
variance, taking only the counting efficiency of the tomograph into account; that is, count rate-dependent effects such as deadtime and randoms were neglected. Noisy projection data were simulated for tomograph sensitivities ranging from 0.5 to 10%. Estimates of BP were obtained using each of the methods described above. In each case, bias was calculated as a function of tomograph sensitivity by comparing the mean BP value in the ROI with the expected value of 1.0. The reconstructions were repeated for 12 independent realizations at each noise level. In the case of the ROI-based estimation (method 1), the coefficient of variation (CV) was taken to be the standard deviation of BP values over 12 different realizations divided by the mean. In the remaining cases, where BP was estimated at the pixel level, CV was calculated as the standard deviation of BP estimates over all pixels within the ROI and this value was averaged over the 12 independent realizations. EXTENDED TOMOGRAPH MODEL. Subsequently, we investigated the bias and variance in parameter estimates that can be expected using a more realistic tomograph model that includes count ratedependent effects. The extended model was used to assess the suitability of a dual head design for performing kinetic studies. The proposed tomograph comprises two detector heads arranged in opposing fans, with a field of view of 10 cm ⫻ 5 cm (transaxial ⫻ axial) and the ability to vary the distance between the heads. In the design we tested, each head comprises 18 detector blocks (6 transaxial and 3 axial) and each block is formed by an 8 ⫻ 8 array of detector elements individually coupled to each channel of a multi-channel photomultiplier tube. The simulated detector elements comprised 1 cm deep YSO crystals abutted to 1 cm deep LSO crystals (each 2 mm ⫻ 2 mm in cross-section), providing stopping power of 0.805 for 511 keV photons. For the purpose of the simulation we assumed 10-cm separation between the heads. The absolute sensitivity of the tomograph was determined by Monte Carlo simulation using the SimSET code (12), assuming a uniform cylindrical source distribution of positron emitter approximating the rat head (2 cm diameter). Energy thresholds of 380 keV and 650 keV were used and energy resolution of 20% FWHM was assumed. Sensitivity was expressed as the number of coincidence events detected within the photopeak window as a fraction of the annihilations occurring within the phantom. The count rate performance of the proposed scanner was pre-
(4)
Equations 2 and 3 are the familiar forward- and backprojection steps, respectively, in the conventional EM algorithm, except that they are performed on each frame in the dynamic sequence. For generality, the probability matrix b is allowed to vary with time so that bijt describes the probability of a photon emitted from pixel j being detected in projection bin i during the time interval t. In this article, we made the b matrix constant with respect to time. Equation 4 is the model-fitting step (with Q as the cost function and as the parameter vector), which completes the iterative cycle. In this study, model fitting was performed using the basis function approach discussed above (11). We also employed the one-step late approach (10) to regularize the reconstruction and ordered subsets to accelerate it (13).
Experimental Initially, we studied the effect of tomograph sensitivity on parameter bias and BIAS/VARIANCE VERSUS TOMOGRAPH SENSITIVITY.
FIG. 2. Predicted count rate performance and effective sensitivity of a dual-head small animal tomograph design. NEC, noise equivalent count rate.
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FIG. 3. Reliability of parameter estimation using region of interest analysis of filtered backprojection images as a function of tomograph sensitivity. The graphs indicate (a) bias and (b) coefficient of variation (CV) for an injected dose of 10 MBq and (c) bias and (d) CV for an injected dose of 1 MBq. dicted using a component-based PET count rate model (20). The above geometry was modeled, including 1 “bucket” per head, which combines positioning, energy, and timing data from each of the 18 blocks. We assumed a typical block integration time of 80 ns, a coincidence time window of 12 ns, and a coincidence processor with bandwidth of 2.6 MHz. Given the absolute sensitivity and count rate performance of the scanner, we calculated the effective sensitivity as a function of activity in the field of view. Effective sensitivity is defined as (1): S eff共 x兲 ⫽ S abs ⫻
NEC共 x兲 T ideal共 x兲
(5)
where Sabs is the absolute sensitivity, NEC is the noise equivalent count rate, and Tideal is the ideal true coincidence rate for a given radioactivity concentration x. The effective sensitivity of the proposed tomograph varies from nearly 2% at low concentrations to ⬍1% at 1,000 kBq/mL (Fig. 2). However, the maximum expected concentration in animal imaging studies is ⬍200 kBq/mL and in the current study the maximum simulated brain concentration was 100 kBq/mL.
The sinograms obtained previously by forward projection of the rat brain phantom were scaled by the effective sensitivity at each time point during the dynamic “scans” and Poisson noise was added accordingly. Sinograms were corrected for attenuation and parametric images of R1 and BP were reconstructed into 128 ⫻ 128 matrices using 4 iterations and 16 subsets of EM-PIRA. The reconstructions were repeated for 12 independent realizations at the same noise level and the mean and standard deviations of parameter values in the striatal ROI defined above were evaluated. RESULTS
Bias/Variance versus Tomograph Sensitivity Bias and variance (expressed as CV) of BP estimates obtained by ROI analysis are plotted as a function of tomograph sensitivity in Figure 3 for each of the tracers and each of the injected doses. Similar plots are shown for pixel-by-pixel analysis of filtered backprojection images in Figure 4 and for EM-PIRA in Figure 5. For the ROI analysis, BP was accurately estimated (bias ⬍ 5%) for both tracers over the range of tomograph sensitivities investi-
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FIG. 4. Reliability of parameter estimation using pixel-by-pixel analysis of filtered backprojection images as a function of tomograph sensitivity. The graphs indicate (a) bias and (b) coefficient of variation (CV) for an injected dose of 10 MBq and (c) bias and (d) CV for an injected dose of 1 MBq. gated. As expected, the CV was considerably greater when the injectate was only 1 MBq compared with an injectate of 10 MBq and it was greater for tracer B than for tracer A. This trend was observed for all the parameter estimation methods studied. In the case of ROI analysis, the CV fell below 20% for 1 MBq of tracer B when the tomograph sensitivity was ⱕ1% (Fig. 3d). For pixel-by-pixel analysis of filtered backprojection images (Fig. 4), tomograph sensitivity of ⬎6% was required to reduce both the bias and CV to acceptable levels (bias ⬍ 5%, CV ⬍ 20%) when the injectate was only 1 MBq. However, for a 10 MBq dose, sensitivity of 1% was sufficient to achieve these goals. When EM-PIRA was used to obtain pixel-by-pixel estimates of BP (Fig. 5), tomograph sensitivity of 3– 4% was sufficient to ensure reliable parameter estimation in all situations.
When the injectate was 10 MBq, acceptable images of relative tracer delivery (R1) and BP were obtained for both tracer A and tracer B. When the injectate was reduced to 1 MBq, the parametric images were noticeably more noisy, particularly for tracer B. The bias and CV of parameter estimates corresponding to these images are given in Table 2. The bias in R1 and BP for both tracers was ⬍10% when the injectate was 10 MBq and the CV was acceptable. When the injectate was 1 MBq, the bias remained ⬍10% for tracer A but the CV was 40% when estimating R1 and 21% when estimating BP. Given that BP is the main parameter of interest in receptor-ligand binding studies, these parameter estimates may be considered acceptable. However, for tracer B the bias in estimating BP was ⫹25% for tracer B at 1 MBq and the CV was unacceptably high at 46%.
Extended Tomograph Model
DISCUSSION
Figure 6 shows parametric and nonparametric images predicted by the extended model when imaging tracer A and tracer B with the proposed tomograph at typical (Fig. 6a) and reduced doses (Fig. 6b).
In this study, we investigated the influence of tomograph sensitivity, parameter estimation methodology, and tracer specific effects on the reliability of kinetic parameter estimates obtained from rat
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FIG. 5. Reliability of parameter estimation using pixel-by-pixel analysis of expectation maximization parametric image reconstruction algorithm (EM-PIRA) images as a function of tomograph sensitivity. The graphs indicate (a) bias and (b) coefficient of variation (CV) for an injected dose of 10 MBq and (c) bias and (d) CV for an injected dose of 1 MBq. brain imaging studies. We found that, for the range of tracers and injectates investigated, a tomograph sensitivity of 1% is sufficient for accurate and reliable parameter estimation when using conventional image reconstruction and ROI analysis. For pixel-by-pixel fitting, the demands on signal-to-noise are greater and tomograph sensitivity of ⱖ3% is required when using an iterative reconstruction/parameter estimation approach such as EM-PIRA (4). The demands are still greater when filtered backprojection is employed along with pixel-by-pixel analysis. Therefore, higher tomograph sensitivity is required for parameter estimation at the pixel level, but this can be offset by careful choice of image reconstruction and kinetic analysis methods. The benefit of the EM-PIRA approach over filtered backprojection comes not only from the favorable signal-to-noise properties of the EM algorithm (25) but also from the use of a tracer kinetic model as a form of regularization (15). It should be noted, however, that EM-PIRA may not be the best choice in all situations. In particular, we found that filtered backprojection performed better than EM-PIRA at the pixel level in the high-activity case (compare
Figs. 4a and 4b with Figs. 5a and 5b), whereas the converse was true in the low-activity case (compare Figs. 4c and 4d with Figs. 5c and 5d). This is consistent with the known noise properties of the two reconstruction algorithms (25). In particular, EM is known to produce better local signal-to-noise ratio in reconstructed images when count statistics are relatively poor (as in the low-activity case), whereas filtered backprojection outperforms EM when count statistics are relatively high (as in the high-activity case). This is due to the fact that the variance in EM images depends mainly on the local mean pixel value, whereas the variance in filtered backprojection images depends more on the global count level (i.e., noise is more highly correlated across pixels) (2, 26). This makes it difficult to recommend a particular algorithm for all situations. However, we believe that EM, when combined with regularization by use of a tracer kinetic model, offers a more robust alternative to filtered backprojection. Similarly, the basis function implementation of the simplified reference tissue model seems to derive some of its robustness from the use of constraints on the possible range of parameter values (11); however, this has not been fully explored.
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FIG. 6. Parametric images predicted by our extended model of a dual-head animal scanner for (a) an injected dose of 10 MBq and (b) an injected dose of 1 MBq. Images were scaled to a common maximum as indicated. The first column is the accumulated tracer distribution over the 90 min following injection. The second and third columns are parametric images of R1, which represents relative tracer delivery, and binding potential (BP), respectively.
We also found that some tracers are more susceptible to parameter estimation errors when the administered dose must be reduced to avoid pharmacologic effects. For example, in our study the reliability of parameter estimates with tracer B, which approximates the dopamine transporter radioligand [11C]RTI-121, was severely affected by reducing the injected dose from 10 MBq to 1 MBq. In comparison, parameter estimates with tracer A, which approximates the D2 radioligand [11C]raclopride, were relatively unaffected by reducing the injected dose. However, in practice, [11C]RTI-121 is less likely to be dose-limited than is [11C]raclopride because the population of dopamine reuptake sites in the brain is approximately one order of magnitude greater than the population of D2 receptors. Thus, given the same specific activity of the injectate and similar affinity for their respective binding sites, [11C]RTI-121 has much lower receptor occupancy than does [11C]raclopride. Nevertheless, our results suggest that tomograph sensitivity may become the limiting factor if the tomograph is to be used for imaging tracers where factors such as specific activity, affinity, and receptor availability conspire to place a constraint on the allowable injected dose.
There are some limitations of the rat brain simulations performed in this study. For example, we did not model activity contained in extra-brain compartments such as musculature and other soft tissues. However, we do not believe that more detailed modeling of these additional compartments would significantly affect the results for the following reasons. In general, there are two ways in which extra-brain activity may affect the local signal-to-noise ratio in striatal brain regions. One is by increasing the total photon flux (singles and coincidences), including randoms and scatter, recorded by the tomograph, which in turn reduces the NEC and the effective sensitivity. However, because the first part of our work (see Bias/Variance versus Tomograph Sensitivity) did not include countrate effects or scatter, and in the second part, effective sensitivity was relatively constant over the wide range of activities considered (Fig. 2), this effect would have little or no influence on the reconstructed signal-to-noise ratio. The other effect is because of correlation of noise across image pixels. This effect is greater when using filtered backprojection than iterative reconstruction, due to the greater extent of the correlation function (which derives from
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TABLE 2. Parameter Bias and Variance for the Proposed Scanner BP
R1 Tracer 10 MBq tracer A 10 MBq tracer B 1 MBq tracer A 1 MBq tracer B
Bias
CV
Bias
CV
⫹1 ⫾ 2% ⫺2 ⫾ 1% ⫺5 ⫾ 7% ⫺12 ⫾ 8%
11 ⫾ 2% 8 ⫾ 1% 40 ⫾ 8% 35 ⫾ 14%
⫺1 ⫾ 1% ⫹9 ⫾ 5% ⫺1 ⫾ 3% ⫹25 ⫾ 6%
10 ⫾ 1% 22 ⫾ 4% 21 ⫾ 3% 46 ⫾ 7%
BP, binding potential; CV, coefficient of variation.
the smearing of the backprojection process). However, in our study, ROIs were drawn over the striata, which were fairly central in the image, and this would have further reduced the impact of noise correlation on local SNR in the striata due to extra-brain activity. To test these assumptions, we performed some additional simulations in which extra-brain activity was modeled by adding a rim to the rat brain phantom, which increased the diameter of the brain by 55% and the volume by 145%. The rim contained 50% of the maximum activity concentration, resulting in a greater than twofold increase in sinogram counts. We then reconstructed the sinograms with and without extra-brain activity after adding Poisson noise (see Methods) and calculated the CV in a striatal ROI. We found that there was only a 10% increase in CV when we used filtered backprojection (0.069 ⫾ 0.009 versus 0.063 ⫾ 0.007) and no significant increase when we used iterative reconstruction (0.109 ⫾ 0.02 versus 0.110 ⫾ 0.009). Thus, we do not believe that ignoring extra-brain activity would have influenced our main findings. A further limitation was that our simulations did not include the effects of activity beyond the axial field of view of the scanner and intra-detector scatter. These factors would further reduce the achievable effective sensitivity of the proposed tomograph in practice. However, the predicted scatter fraction was ⬍5% for the proposed tomograph and is still ⬍10% when activity beyond the axial field of view is taken into account. Furthermore, it is worth emphasizing that the particular scanner design discussed in this article is less important than is the general concept of considering the impact of tomograph sensitivity on parameter estimation when designing small animal PET instrumentation. We used this scanner design as an example to illustrate how the tomograph sensitivity can be predicted and its potential impact on parameter estimation evaluated. Thus, several factors should be taken into account when setting design goals for dedicated instrumentation for small animal imaging. These include the physiologic systems to be studied, the tracers to be employed, and the image reconstruction algorithms and data analysis methods to be adopted. We investigated a number of approaches to image reconstruction/analysis and designed the simulations to cover a reasonably diverse set of typical tracer kinetics, including dose effects. We believe, therefore, that these results can be extrapolated to a wide range of situations in imaging the rat brain and should provide useful guidelines for the design of future small animal tomographs. Although this work focussed on the capability of small animal tomographs designed for PET, in future work we will adapt our methodology to predict the dynamic capability of dedicated SPECT animal scanners. To extend the methodology to SPECT will require modeling single photon attenuation, scattering, and collimator efficiency during the forward projection step and incorporating a count rate model appropriate for SPECT. Until such a study is performed, it is difficult to predict what magnitude of tomograph
sensitivity will be required for successful small animal imaging with SPECT. However, we expect the greatly reduced counting efficiency of SPECT compared with PET (1–2 orders of magnitude) to be largely offset by the higher specific activities encountered with SPECT radiopharmaceuticals. Nevertheless, careful design of SPECT camera geometry and, in particular, collimation will be important considerations. CONCLUSIONS The tomograph sensitivity required for small animal imaging is dependent on several factors, including the tracers of interest and the method of parameter estimation employed. However, to ensure reliable parameter estimation at the ROI and pixel level, effective tomograph sensitivity of 3% may be considered an appropriate design goal for imaging the rat brain. We would like to acknowledge the helpful advice of Sue Hume from the MRC Cyclotron Unit, Hammersmith Hospital, and Simon Cherry from the Crump Institute for Biological Imaging, UCLA School of Medicine. This work was presented at the 1998 IEEE Medical Imaging Conference in Toronto.
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