Improved parametric image generation using spatial-temporal analysis of dynamic PET studies

Noninvasive quantification of nonhuman primate dynamic 18F-FDG PET imaging

¹⁸F-FDG uptake rate constant K_i is the main physiology parameter measured in dynamic PET studies. A model-independent graphical analysis using Patlak plot with plasma input function (PIF) is a standard approach used to estimate K_i . The PIF is the ¹⁸F-FDG time activity curve (TAC) in plasma that is obtained by serial arterial blood sampling. The purpose of the study is to evaluate a Patlak plot-based optimization approach with reduced blood samples for noninvasive quantification of dynamic ¹⁸F-FDG PET imaging. Eight 60 min rhesus monkey brain dynamic ¹⁸F-FDG PET scans with arterial blood samples were collected. The measured PIF (mPIF) was determined by arterial blood samples. TACs of seven cerebral regions of interest were generated from each study. With a given number of blood samples, the population-based PIF (pPIF) was determined by either interpolation or extrapolation method using scale calibrated population mean of normalized PIF. The optimal sampling scheme with given blood sample size was determined by maximizing the correlations between the K_i estimated from pPIF and those obtained by mPIF. A leave-two-out cross-validation method was used for evaluation. The linear correlations between the K_i estimates from pPIF with optimal sampling schemes and those from mPIF were: K_i (pPIF 1 sample at 40 min) = 1.015 K_i (mPIF) - 0.000, R ² = 0.974; K_i (pPIF 2 samples at 35 and 50 min) = 1.052 K_i (mPIF) - 0.001, R ² = 0.976; K_i (pPIF 3 samples at 12, 40, and 50 min) = 1.030 K_i (mPIF) - 0.000, R ² = 0.985; and K_i (pPIF 4 samples at 10, 20, 40, and 50 min) = 1.016 K_i (mPIF)- 0.000, R ² = 0.993. As the sample size became greater or equal to 4, the K_i estimates from pPIF with the optimal protocol were almost identical to those from mPIF. The Patlak plot-based optimization approach is a reliable method to estimate PIF for noninvasive quantification of non-human primate dynamic ¹⁸F-FDG PET imaging and is potentially extendable to further translational human studies.

Robust nonlinear parameter estimation in tracer kinetic analysis using infinity norm regularization and particle swarm optimization

In positron emission tomography (PET) studies, the voxel-wise calculation of individual rate constants describing the tracer kinetics is quite challenging because of the nonlinear relationship between the rate constants and PET data and the high noise level in voxel data. Based on preliminary simulations using a standard two-tissue compartment model, we can hypothesize that it is possible to reduce errors in the rate constant estimates when constraining the overestimation of the larger of two exponents in the model equation. We thus propose a novel approach based on infinity-norm regularization for limiting this exponent. Owing to the non-smooth cost function of this regularization scheme, which prevents the use of conventional Jacobian-based optimization methods, we examined a proximal gradient algorithm and the particle swarm optimization (PSO) through a simulation study. Because it exploits multiple initial values, the PSO method shows much better convergence than the proximal gradient algorithm, which is susceptible to the initial values. In the implementation of PSO, the use of a Gamma distribution to govern random movements was shown to improve the convergence rate and stability compared to a uniform distribution. Consequently, Gamma-based PSO with regularization was shown to outperform all other methods tested, including the conventional basis function method and Levenberg-Marquardt algorithm, in terms of its statistical properties.

Association of PET-measured myocardial flow reserve with echocardiography-estimated pulmonary artery systolic pressure in patients with hypertrophic cardiomyopathy

BACKGROUND

Pulmonary hypertension (PH) is a known complication of HCM and is a strong predictor of mortality. We aim to investigate the relationship between microvascular dysfunction measured by quantitative PET and PH in HCM patients.

METHODS

Eighty-nine symptomatic HCM patients were included in the study. Each patient underwent two 20-min 13N-NH3 dynamic PET scans for rest and stress conditions, respectively. A 2-tissue irreversible compartmental model was used to fit the segments time activity curves for estimating segmental and global myocardial blood flow (MBF) and myocardial flow reserve (MFR). Echocardiographic derived PASP was utilized to estimate PH.

RESULTS

Patients were categorized into two groups across PASP: PH (PASP > 36 mmHg) and no-PH (PASP ≤ 36 mmHg). patients with PH had larger left atrium, ratio of higher inflow early diastole (E) and atrial contraction (A) waves, E/A, and ratio of inflow and peak early diastolic waves, E/e', significantly reduced global stress MBF (1.85 ± 0.52 vs. 2.13 ± 0.56 ml/min/g; p = 0.024) and MFR (2.21 ± 0.57 vs. 2.62 ± 0.75; p = 0.005), while the MBFs at rest between the two groups were similar. There were significant negative correlations between global stress MBF/MFR and PASP (stress MBF: r = -0.23, p = 0.03; MFR: r = -0.32, p = 0.002); for regional MBF and MFR measurements, the highest linear correlation coefficients were observed in the septal wall (stress MBF: r = -0.27, p = 0.01; MFR: r = -0.31, p = 0.003). Global MFR was identified to be independent predictor for PH in multivariate regression analysis.

CONCLUSION

Echocardiography-derived PASP is negatively correlated with global MFR measured by 13N-NH3 dynamic PET. Global MFR is suggested to be an index of PH in HCM patients.

Dynamic whole-body PET imaging: principles, potentials and applications

PURPOSE

In this article, we discuss dynamic whole-body (DWB) positron emission tomography (PET) as an imaging tool with significant clinical potential, in relation to conventional standard uptake value (SUV) imaging.

BACKGROUND

DWB PET involves dynamic data acquisition over an extended axial range, capturing tracer kinetic information that is not available with conventional static acquisition protocols. The method can be performed within reasonable clinical imaging times, and enables generation of multiple types of PET images with complementary information in a single imaging session. Importantly, DWB PET can be used to produce multi-parametric images of (i) Patlak slope (influx rate) and (ii) intercept (referred to sometimes as "distribution volume"), while also providing (iii) a conventional 'SUV-equivalent' image for certain protocols.

RESULTS

We provide an overview of ongoing efforts (primarily focused on FDG PET) and discuss potential clinically relevant applications.

CONCLUSION

Overall, the framework of DWB imaging [applicable to both PET/CT(computed tomography) and PET/MRI (magnetic resonance imaging)] generates quantitative measures that may add significant value to conventional SUV image-derived measures, with limited pitfalls as we also discuss in this work.

Spectral Analysis of Dynamic PET Studies: A Review of 20 Years of Method Developments and Applications

In Positron Emission Tomography (PET), spectral analysis (SA) allows the quantification of dynamic data by relating the radioactivity measured by the scanner in time to the underlying physiological processes of the system under investigation. Among the different approaches for the quantification of PET data, SA is based on the linear solution of the Laplace transform inversion whereas the measured arterial and tissue time-activity curves of a radiotracer are used to calculate the input response function of the tissue. In the recent years SA has been used with a large number of PET tracers in brain and nonbrain applications, demonstrating that it is a very flexible and robust method for PET data analysis. Differently from the most common PET quantification approaches that adopt standard nonlinear estimation of compartmental models or some linear simplifications, SA can be applied without defining any specific model configuration and has demonstrated very good sensitivity to the underlying kinetics. This characteristic makes it useful as an investigative tool especially for the analysis of novel PET tracers. The purpose of this work is to offer an overview of SA, to discuss advantages and limitations of the methodology, and to inform about its applications in the PET field.

Federated optimisation of kinetic analysis problems

Positron Emission Tomography (PET) data is intrinsically dynamic, and kinetic analysis of dynamic PET data can substantially augment the information provided by static PET reconstructions. Yet despite the insights into disease that kinetic analysis offers, it is not used clinically and seldom used in research beyond the preclinical stage. The utility of PET kinetic analysis is hampered by several factors including spatial inconsistency within regions of homogeneous tissue and relative computational expense when fitting complex models to individual voxels. Even with sophisticated algorithms inconsistencies can arise because local optima frequently have narrow basins of convergence, are surrounded by relatively flat (uninformative) regions, have relatively low-gradient valley floors, or combinations thereof. Based on the observation that cost functions for individual voxels frequently bear some resemblance to each-other, this paper proposes the federated optimisation of the individual kinetic analysis problems within a given image. This approach shares parameters proposed during optimisation with other, similar voxels. Federated optimisation exploits the redundancy typical of large medical images to improve the optimisation residuals, computational efficiency and, to a limited extent, image consistency. This is achieved without restricting the formulation of the kinetic model, resorting to an explicit regularisation parameter, or limiting the resolution at which parameters are computed.

Specific binding of [(18)F]fluoroethyl-harmol to monoamine oxidase A in rat brain cryostat sections, and compartmental analysis of binding in living brain

We investigated [(18)F]fluoroethyl-harmol ([(18)F]FEH) as a reversible and selective ligand for positron emission tomography (PET) studies of monoamine oxidase A (MAO-A). Binding of [(18)F]FEH in rat brain cryostat sections indicated high affinity (KD = 3 nM), and density (Bmax; 600 pmol/g). The plasma free fraction was 45%, and untransformed parent constituted only 13% of plasma radioactivity at 10 min after injection. Compartmental analysis of PET recordings in pargyline-treated rats showed high permeability to brain (K1; 0.32 mL/g/min) and slow washout (k2; 0.024/min), resulting in a uniformly high equilibrium distribution volume (VD; 20 mL/g). Using this VD to estimate unbound ligand in brain of untreated rats, the binding potential ranged from 4.2 in cerebellum to 7.2 in thalamus. We also calculated maps of rats receiving [(18)F]FEH at a range of specific activities, and then estimated saturation binding parameters in the living brain. In thalamus, striatum and frontal cortex KD was globally close to 300 nM and Bmax was close to 1600 pmol/g; the 100-fold discrepancy in affinity suggests a very low free fraction for [(18)F]FEH in the living brain. Based on a synthesis of findings, we calculate the endogenous dopamine concentration to be 0.4 μM in the striatal compartment containing MAO-A, thus unlikely to exert competition against [(18)F]FEH binding in vivo. In summary, [(18)F]FEH has good properties for the detection of MAO-A in the rat brain by PET, and may present logistic advantages for clinical research at centers lacking a medical cyclotron. We made a compartmental analysis of [(18)F]fluoroethylharmol ([(18)F]FEH) binding to monoamine oxidase A (MAO-A) in living rat brain and estimated the saturation binding parameters from the binding potential (BPND). The Bmax was of comparable magnitude to that in vitro, but with apparent affinity (300 nM), it was 100-fold lower in vivo. PET imaging with [(18) F]FEH is well suited for quantitation of MAO-A in living brain.

Quantitative myocardial perfusion PET parametric imaging at the voxel-level

Quantitative myocardial perfusion (MP) PET has the potential to enhance detection of early stages of atherosclerosis or microvascular dysfunction, characterization of flow-limiting effects of coronary artery disease (CAD), and identification of balanced reduction of flow due to multivessel stenosis. We aim to enable quantitative MP-PET at the individual voxel level, which has the potential to allow enhanced visualization and quantification of myocardial blood flow (MBF) and flow reserve (MFR) as computed from uptake parametric images. This framework is especially challenging for the (82)Rb radiotracer. The short half-life enables fast serial imaging and high patient throughput; yet, the acquired dynamic PET images suffer from high noise-levels introducing large variability in uptake parametric images and, therefore, in the estimates of MBF and MFR. Robust estimation requires substantial post-smoothing of noisy data, degrading valuable functional information of physiological and pathological importance. We present a feasible and robust approach to generate parametric images at the voxel-level that substantially reduces noise without significant loss of spatial resolution. The proposed methodology, denoted physiological clustering, makes use of the functional similarity of voxels to penalize deviation of voxel kinetics from physiological partners. The results were validated using extensive simulations (with transmural and non-transmural perfusion defects) and clinical studies. Compared to post-smoothing, physiological clustering depicted enhanced quantitative noise versus bias performance as well as superior recovery of perfusion defects (as quantified by CNR) with minimal increase in bias. Overall, parametric images obtained from the proposed methodology were robust in the presence of high-noise levels as manifested in the voxel time-activity-curves.

Recent advances in parametric neuroreceptor mapping with dynamic PET: basic concepts and graphical analyses

Tracer kinetic modeling in dynamic positron emission tomography (PET) has been widely used to investigate the characteristic distribution patterns or dysfunctions of neuroreceptors in brain diseases. Its practical goal has progressed from regional data quantification to parametric mapping that produces images of kinetic-model parameters by fully exploiting the spatiotemporal information in dynamic PET data. Graphical analysis (GA) is a major parametric mapping technique that is independent on any compartmental model configuration, robust to noise, and computationally efficient. In this paper, we provide an overview of recent advances in the parametric mapping of neuroreceptor binding based on GA methods. The associated basic concepts in tracer kinetic modeling are presented, including commonly-used compartment models and major parameters of interest. Technical details of GA approaches for reversible and irreversible radioligands are described, considering both plasma input and reference tissue input models. Their statistical properties are discussed in view of parametric imaging.

[11C]NS8880, a promising PET radiotracer targeting the norepinephrine transporter

INTRODUCTION

Positron emission tomography (PET) imaging of the norepinephrine transporter (NET) is still hindered by the availability of useful PET imaging probes. The present study describes the radiosynthesis and pre-clinical evaluation of a new compound, exo-3-(6-methoxypyridin-2-yloxy)-8-H-8-azabicyclo[3.2.1]octane (NS8880), targeting NET. NS8880 has an in vitro binding profile comparable to desipramine and is structurally not related to reboxetine.

METHODS

Labeling of NS8880 with [(11)C] was achieved by a non-conventional technique: substitution of pyridinyl fluorine with [(11)C]methanolate in a Boc-protected precursor. The isolated [(11)C]NS8880 was evaluated pre-clinically both in a pig model (PET scanning) and in a rat model (μPET scanning) and compared to (S,S)-[(11)C]-O-methylreboxetine ([(11)C]MeNER).

RESULTS

The radiolabeling technique yielded [(11)C]NS8880 in low (<10%) but still useful yields with high purity. The PET in vivo evaluation in pig and rat revealed a rapid brain uptake of [(11)C]NS8880 and fast obtaining of equilibrium. Highest binding was observed in thalamic and hypothalamic regions. Pretreatment with desipramine efficiently reduced binding of [(11)C]NS8880.

CONCLUSION

Based on the pre-clinical results obtained so far [(11)C]NS8880 displays promising properties for PET imaging of NET.

VOXEL-LEVEL MAPPING OF TRACER KINETICS IN PET STUDIES: A STATISTICAL APPROACH EMPHASIZING TISSUE LIFE TABLES

Most radiotracers used in dynamic positron emission tomography (PET) scanning act in a linear time-invariant fashion so that the measured time-course data are a convolution between the time course of the tracer in the arterial supply and the local tissue impulse response, known as the tissue residue function. In statistical terms the residue is a life table for the transit time of injected radiotracer atoms. The residue provides a description of the tracer kinetic information measurable by a dynamic PET scan. Decomposition of the residue function allows separation of rapid vascular kinetics from slower blood-tissue exchanges and tissue retention. For voxel-level analysis, we propose that residues be modeled by mixtures of nonparametrically derived basis residues obtained by segmentation of the full data volume. Spatial and temporal aspects of diagnostics associated with voxel-level model fitting are emphasized. Illustrative examples, some involving cancer imaging studies, are presented. Data from cerebral PET scanning with 18F fluoro-deoxyglucose (FDG) and 15O water (H2O) in normal subjects is used to evaluate the approach. Cross-validation is used to make regional comparisons between residues estimated using adaptive mixture models with more conventional compartmental modeling techniques. Simulations studies are used to theoretically examine mean square error performance and to explore the benefit of voxel-level analysis when the primary interest is a statistical summary of regional kinetics. The work highlights the contribution that multivariate analysis tools and life-table concepts can make in the recovery of local metabolic information from dynamic PET studies, particularly ones in which the assumptions of compartmental-like models, with residues that are sums of exponentials, might not be certain.

3.5D dynamic PET image reconstruction incorporating kinetics-based clusters

Standard 3D dynamic positron emission tomographic (PET) imaging consists of independent image reconstructions of individual frames followed by application of appropriate kinetic model to the time activity curves at the voxel or region-of-interest (ROI). The emerging field of 4D PET reconstruction, by contrast, seeks to move beyond this scheme and incorporate information from multiple frames within the image reconstruction task. Here we propose a novel reconstruction framework aiming to enhance quantitative accuracy of parametric images via introduction of priors based on voxel kinetics, as generated via clustering of preliminary reconstructed dynamic images to define clustered neighborhoods of voxels with similar kinetics. This is then followed by straightforward maximum a posteriori (MAP) 3D PET reconstruction as applied to individual frames; and as such the method is labeled '3.5D' image reconstruction. The use of cluster-based priors has the advantage of further enhancing quantitative performance in dynamic PET imaging, because: (a) there are typically more voxels in clusters than in conventional local neighborhoods, and (b) neighboring voxels with distinct kinetics are less likely to be clustered together. Using realistic simulated (11)C-raclopride dynamic PET data, the quantitative performance of the proposed method was investigated. Parametric distribution-volume (DV) and DV ratio (DVR) images were estimated from dynamic image reconstructions using (a) maximum-likelihood expectation maximization (MLEM), and MAP reconstructions using (b) the quadratic prior (QP-MAP), (c) the Green prior (GP-MAP) and (d, e) two proposed cluster-based priors (CP-U-MAP and CP-W-MAP), followed by graphical modeling, and were qualitatively and quantitatively compared for 11 ROIs. Overall, the proposed dynamic PET reconstruction methodology resulted in substantial visual as well as quantitative accuracy improvements (in terms of noise versus bias performance) for parametric DV and DVR images. The method was also tested on a 90 min (11)C-raclopride patient study performed on the high-resolution research tomography. The proposed method was shown to outperform the conventional method in visual as well as quantitative accuracy improvements (in terms of noise versus regional DVR value performance).

Fourier domain closed-form formulas for estimation of kinetic parameters in reversible multi-compartment models

Background

Compared with static imaging, dynamic emission computed tomographic imaging with compartment modeling can quantify in vivo physiologic processes, providing useful information about molecular disease processes. Dynamic imaging involves estimation of kinetic rate parameters. For multi-compartment models, kinetic parameter estimation can be computationally demanding and problematic with local minima.

Methods

This paper offers a new perspective to the compartment model fitting problem where Fourier linear system theory is applied to derive closed-form formulas for estimating kinetic parameters for the two-compartment model. The proposed Fourier domain estimation method provides a unique solution, and offers very different noise response as compared to traditional non-linear chi-squared minimization techniques.

Results

The unique feature of the proposed Fourier domain method is that only low frequency components are used for kinetic parameter estimation, where the DC (i.e., the zero frequency) component in the data is treated as the most important information, and high frequency components that tend to be corrupted by statistical noise are discarded. Computer simulations show that the proposed method is robust without having to specify the initial condition. The resultant solution can be fine tuned using the traditional iterative method.

Conclusions

The proposed Fourier-domain estimation method has closed-form formulas. The proposed Fourier-domain curve-fitting method does not require an initial condition, it minimizes a quadratic objective function and a closed-form solution can be obtained. The noise is easier to control, simply by discarding the high frequency components, and emphasizing the DC component.

Kinetic parameter estimation using a closed-form expression via integration by parts

Dynamic emission computed tomographic imaging with compartment modeling can quantify in vivo physiologic processes, eliciting more information regarding underlying molecular disease processes than is obtained from static imaging. However, estimation of kinetic rate parameters for multi-compartment models can be computationally demanding and problematic due to local minima. A number of techniques for kinetic parameter estimation have been studied and are in use today, generally offering a tradeoff between computation time, robustness of fit and flexibility with differing sets of assumptions. This paper presents a means to eliminate all differential operations by using the integration-by-parts method to provide closed-form formulas, so that the mathematical model is less sensitive to data sampling and noise. A family of closed-form formulas are obtained. Computer simulations show that the proposed method is robust without having to specify the initial condition.

Parametric imaging with Bayesian priors: a validation study with (11)C-Altropane PET

It has been suggested that Bayesian estimation methods may be used to improve the signal-to-noise ratio of parametric images. However, there is little experience with the method and some of the underlying assumptions and performance properties of Bayesian estimation remain to be investigated. We used a sample population of 54 subjects, studied previously with (11)C-Altropane, to empirically evaluate the assumptions, performance and some practical issues in forming parametric images. By using normality tests, we showed that the underpinning normality assumptions of data and parametric distribution apply to more than 80% of voxels. The standard deviation of the binding potential can be reduced 30-50% using Bayesian estimation, without introducing substantial bias. The sample size required to form the a priori information was found to be modest; as little as ten subjects may be sufficient and the choice of specific subjects has little effect on Bayesian estimation. A realistic simulation study showed that detection of localized differences in parametric images, e.g. by statistical parametric mapping (SPM), could be made more reliable and/or conducted with smaller sample size using Bayesian estimation. In conclusion, Bayesian estimation can improve the SNR of parametric images and better detect localized changes in cohorts of subjects.

Clustering-based linear least square fitting method for generation of parametric images in dynamic FDG PET studies

Parametric images generated from dynamic positron emission tomography (PET) studies are useful for presenting functional/biological information in the 3-dimensional space, but usually suffer from their high sensitivity to image noise. To improve the quality of these images, we proposed in this study a modified linear least square (LLS) fitting method named cLLS that incorporates a clustering-based spatial constraint for generation of parametric images from dynamic PET data of high noise levels. In this method, the combination of K-means and hierarchical cluster analysis was used to classify dynamic PET data. Compared with conventional LLS, cLLS can achieve high statistical reliability in the generated parametric images without incurring a high computational burden. The effectiveness of the method was demonstrated both with computer simulation and with a human brain dynamic FDG PET study. The cLLS method is expected to be useful for generation of parametric images from dynamic FDG PET study.

Parametric mapping of [18F]fluoromisonidazole positron emission tomography using basis functions

In this study, we show a basis function method (BAFPIC) for voxelwise calculation of kinetic parameters (K(1), k(2), k(3), K(i)) and blood volume using an irreversible two-tissue compartment model. BAFPIC was applied to rat ischaemic stroke micro-positron emission tomography data acquired with the hypoxia tracer [(18)F]fluoromisonidazole because irreversible two-tissue compartmental modelling provided good fits to data from both hypoxic and normoxic tissues. Simulated data show that BAFPIC produces kinetic parameters with significantly lower variability and bias than nonlinear least squares (NLLS) modelling in hypoxic tissue. The advantage of BAFPIC over NLLS is less pronounced in normoxic tissue. K(i) determined from BAFPIC has lower variability than that from the Patlak-Gjedde graphical analysis (PGA) by up to 40% and lower bias, except for normoxic tissue at mid-high noise levels. Consistent with the simulation results, BAFPIC parametric maps of real data suffer less noise-induced variability than do NLLS and PGA. Delineation of hypoxia on BAFPIC k(3) maps is aided by low variability in normoxic tissue, which matches that in K(i) maps. BAFPIC produces K(i) values that correlate well with those from PGA (r(2)=0.93 to 0.97; slope 0.99 to 1.05, absolute intercept <0.00002 mL/g per min). BAFPIC is a computationally efficient method of determining parametric maps with low bias and variance.

Global-two-stage filtering of clinical PET parametric maps: application to [(11)C]-(R)-PK11195

INTRODUCTION

In Positron Emission Tomography (PET) quantification of physiological parameters at the voxel level may result in unreliable estimates due to the high noise of voxel time activity curves. Global-Two-Stage (GTS), an estimation technique belonging to the group of "population approaches", can be used to tackle this problem. GTS was previously tested on simulated PET data and yielded substantial improvements when compared to standard estimation approaches such as Weighted NonLinear Least Squares (WNLLS) and Basis Function Method (BFM). In this work GTS performance is assessed in a clinical context using the neuroinflammation marker [(11)C]-(R)-PK11195 applied to a cohort of Huntington's disease (HD) patients with and without symptoms.

MATERIALS AND METHODS

Parametric maps of binding potential (BP(ND)) of 12 normal controls (NC), 9 symptomatic and 9 presymptomatic HD patients were generated by applying a modified reference tissue model that accounts for tracer vascular activity in both reference and target tissues (SRTMV). GTS was then applied to SRTMV maps and its performance compared with that of SRTMV. Three smoothed versions of SRTMV, obtained by filtering the original SRTMV maps with Gaussian filters of 3 mm, 5 mm and 7 mm Full Width Half Maximum (FWHM), were also included in the comparison. Since striatal degeneration is the hallmark of HD, sensitivity was assessed for all methods by computing the mean of z-scores in caudate, putamen and globus pallidus in the voxel-by-voxel statistical comparison of BP(ND) between HD and NC.

RESULTS

Application of GTS to parametric maps brought a substantial qualitative improvement to SRTMV maps to the extent that anatomical structures often became visible. In addition, most parameter estimates that were outside the physiological range with SRTMV were corrected by GTS. GTS yielded a 2.3-fold increase in sensitivity with respect to SRTMV for the symptomatic cohort (mean of striatal z-scores of 0.76 for SRTMV and 1.79 for GTS) and an even more substantial increase for the presymptomatic cohort (mean of striatal z-scores of 0.34 for SRTMV and 0.96 for GTS). The sensitivity of GTS was similar to the one obtained with a filter of 7 mm FWHM applied to the initial SRTMV maps but GTS images were not characterized by the notable loss of resolution typical of smoothed maps. GTS, additionally, does not require to change/define settings according to the tracer and level of noise, whereas the choice of the FWHM value of the Gaussian filter normally employed in the smoothing procedure is typically arbitrary.

CONCLUSIONS

GTS is a powerful and robust tool for improving the quality of parametric maps in PET. The method is particularly appealing in that it can be applied to any tracer and estimation method, provided that initial estimates of the parameter vector and of its covariance are available. Although the benefits of GTS are far from being exhaustively assessed, the significant improvements obtained both on real and simulated data suggest that it could become an important tool for dynamic PET in the future.

Evaluation of a bolus/infusion protocol for 11C-ABP688, a PET tracer for mGluR5

(11)C-ABP-688 is a selective tracer for the mGluR5 receptor. Its kinetics is fast and thus favourable for an equilibrium approach to determine receptor-related parameters. The purpose of this study was to test the hypothesis that the pattern of the (11)C-ABP688 uptake using a bolus-plus-infusion (B/I) protocol at early time points corresponds to the perfusion and at a later time point to the total distribution volume.

METHODS

A bolus and a B/I study (1 h each) was performed in five healthy male volunteers. With the B/I protocol, early and late scans were normalized to gray matter, cerebellum and white matter. The same normalization was done on the maps of the total distribution volume (Vt) and K(1) which were calculated in the study with bolus only injection and the Logan method (Vt) and a two-tissue compartment model (K(1)).

RESULTS

There was an excellent correlation close to the identity line between the pattern of the late uptake in the B/I study and Vt of the bolus-only study for all three normalizations. The pattern of the early uptake in the B/I study correlated well with the K(1) maps, but only when normalized to gray matter and cerebellum, not to white matter.

CONCLUSION

It is demonstrated that with a B/I protocol the (11)C-ABP688 distribution in late scans reflects the pattern of the total distribution volume and is therefore a measure for the density pattern of mGluR5. The early scans following injection are related to blood flow, although not in a fully quantitative manner. The advantage of the B/I protocol is that no arterial blood sampling is required, which is advantageous in clinical studies.

Dynamic PET denoising with HYPR processing

HighlY constrained backPRojection (HYPR) is a promising image-processing strategy with widespread application in time-resolved MRI that is also well suited for PET applications requiring time series data. The HYPR technique involves the creation of a composite image from the entire time series. The individual time frames then provide the basis for weighting matrices of the composite. The signal-to-noise ratio (SNR) of the individual time frames can be dramatically improved using the high SNR of the composite image. In this study, we introduced the modified HYPR algorithm (the HYPR method constraining the backprojections to local regions of interest [HYPR-LR]) for the processing of dynamic PET studies. We demonstrated the performance of HYPR-LR in phantom, small-animal, and human studies using qualitative, semiquantitative, and quantitative comparisons. The results demonstrate that significant improvements in SNR can be realized in the PET time series, particularly for voxel-based analysis, without sacrificing spatial resolution. HYPR-LR processing holds great potential in nuclear medicine imaging for all applications with low SNR in dynamic scans, including for the generation of voxel-based parametric images and visualization of rapid radiotracer uptake and distribution.

Multi-graphical analysis of dynamic PET

In quantitative dynamic PET studies, graphical analysis methods including the Gjedde-Patlak plot, the Logan plot, and the relative equilibrium-based graphical plot (RE plot) (Zhou Y., Ye W., Brasić J.R., Crabb A.H., Hilton J., Wong D.F. 2009b. A consistent and efficient graphical analysis method to improve the quantification of reversible tracer binding in radioligand receptor dynamic PET studies. Neuroimage 44(3):661-670) are based on the theory of a compartmental model with assumptions on tissue tracer kinetics. If those assumptions are violated, then the resulting estimates may be biased. In this study, a multi-graphical analysis method was developed to characterize the non-relative equilibrium effects on the estimates of total distribution volume (DV(T)) from the RE plot. A novel bi-graphical analysis method using the RE plot with the Gjedde-Patlak plot (RE-GP plots) was proposed to estimate DV(T) for the quantification of reversible tracer kinetics that may not be at relative equilibrium states during PET study period. The RE-GP plots and the Logan plot were evaluated by 19 [(11)C]WIN35,428 and 10 [(11)C]MDL100,907 normal human dynamic PET studies with brain tissue tracer kinetics measured at both region of interest (ROI) and pixel levels. A 2-tissue compartment model (2TCM) was used to fit ROI time activity curves (TACs). By applying multi-graphical plots to the 2TCM fitted ROI TACs which were considered as the noise-free tracer kinetics, the estimates of DV(T) from the RE-GP plots, the Logan plot, and the 2TCM fitting were equal to each other. For the measured ROI TACs, there was no significant difference between the estimates of the DV(T) from the RE-GP plots and those from 2TCM fitting (p=0.77), but the estimates of the DV(T) from the Logan plot were significantly (p<0.001) lower, 2.3% on average, than those from 2TCM fitting. There was a highly linear correlation between the ROI DV(T) from the parametric images (Y) and those from the ROI kinetics (X) by using the RE-GP plots (Y=1.01X+0.23, R(2)=0.99). For the Logan plot, the ROI estimates from the parametric images were 13% to 83% lower than those from ROI kinetics. The computational time for generating parametric images was reduced by 69% on average by the RE-GP plots in contrast to the Logan plot. In conclusion, the bi-graphical analysis method using the RE-GP plots was a reliable, robust and computationally efficient kinetic modeling approach to improve the quantification of dynamic PET.

Wavelet denoising in voxel-based parametric estimation of small animal PET images: a systematic evaluation of spatial constraints and noise reduction algorithms

Voxel-based estimation of PET images, generally referred to as parametric imaging, can provide invaluable information about the heterogeneity of an imaging agent in a given tissue. Due to high level of noise in dynamic images, however, the estimated parametric image is often noisy and unreliable. Several approaches have been developed to address this challenge, including spatial noise reduction techniques, cluster analysis and spatial constrained weighted nonlinear least-square (SCWNLS) methods. In this study, we develop and test several noise reduction techniques combined with SCWNLS using simulated dynamic PET images. Both spatial smoothing filters and wavelet-based noise reduction techniques are investigated. In addition, 12 different parametric imaging methods are compared using simulated data. With the combination of noise reduction techniques and SCWNLS methods, more accurate parameter estimation can be achieved than with either of the two techniques alone. A less than 10% relative root-mean-square error is achieved with the combined approach in the simulation study. The wavelet denoising based approach is less sensitive to noise and provides more accurate parameter estimation at higher noise levels. Further evaluation of the proposed methods is performed using actual small animal PET datasets. We expect that the proposed method would be useful for cardiac, neurological and oncologic applications.

Mechanisms of dopaminergic and serotonergic neurotransmission in Tourette syndrome: clues from an in vivo neurochemistry study with PET

Tourette syndrome (TS) is a neuropsychiatric disorder with childhood onset characterized by motor and phonic tics. Obsessive-compulsive disorder (OCD) is often concomitant with TS. Dysfunctional tonic and phasic dopamine (DA) and serotonin (5-HT) metabolism may play a role in the pathophysiology of TS. We simultaneously measured the density, affinity, and brain distribution of dopamine D2 receptors (D2-R's), dopamine transporter binding potential (BP), and amphetamine-induced dopamine release (DA(rel)) in 14 adults with TS and 10 normal adult controls. We also measured the brain distribution and BP of serotonin 5-HT2A receptors (5-HT2AR), and serotonin transporter (SERT) BP, in 11 subjects with TS and 10 normal control subjects. As compared with controls, DA rel was significantly increased in the ventral striatum among subjects with TS. Adults with TS+OCD exhibited a significant D(2)-R increase in left ventral striatum. SERT BP in midbrain and caudate/putamen was significantly increased in adults with TS (TS+OCD and TS-OCD). In three subjects with TS+OCD, in whom D2-R, 5-HT2AR, and SERT were measured within a 12-month period, there was a weakly significant elevation of DA rel and 5-HT2A BP, when compared with TS-OCD subjects and normal controls. The current study confirms, with a larger sample size and higher resolution PET scanning, our earlier report that elevated DA rel is a primary defect in TS. The finding of decreased SERT BP, and the possible elevation in 5-HT2AR in individuals with TS who had increased DA rel, suggest a condition of increased phasic DA rel modulated by low 5-HT in concomitant OCD.

Estimating neurotransmitter kinetics with ntPET: a simulation study of temporal precision and effects of biased data

We recently introduced neurotransmitter PET (ntPET), an analysis technique that estimates the kinetics of stimulus-induced neurotransmitter (NT) release. Here, we evaluate two formulations of ntPET. The arterial (ART) approach measures the tracer input function (TIF) directly. The reference (REF) approach derives the TIF from reference region data. Arterial sampling is considered the gold standard in PET modeling but reference region approaches are preferred for reduced cost and complexity. If simulated PET data with unbiased TIFs were analyzed using ART or REF, temporal precision was better than 3 min provided NT concentration peaked less than 30 min into the scanning session. The consequences of biased TIFs or stimulus-induced changes in tracer delivery were also evaluated. ART TIFs were biased by the presence of uncorrected radiometabolites in the plasma whereas REF TIFs were biased by specific binding in the reference region. Simulated changes in tracer delivery emulated ethanol-induced blood flow alterations observed previously with PET. ART performance deteriorated significantly if metabolites amounted to 50% of plasma radioactivity by 60 min. The accuracy and precision of REF were preserved even if the reference region contained 40% of the receptor density of the target region. Both methods were insensitive to blood flow alterations (proportional changes in K(1) and k(2)). Our results suggest that PET data contain information--heretofore not extracted--about the timing of NT release. The REF formulation of ntPET proved to be robust to many plausible model violations and under most circumstances is an appropriate alternative to ART.

Using a reference tissue model with spatial constraint to quantify [11C]Pittsburgh compound B PET for early diagnosis of Alzheimer's disease

INTRODUCTION

Reference tissue model (RTM) is a compartmental modeling approach that uses reference tissue time activity curve (TAC) as input for quantification of ligand-receptor dynamic PET without blood sampling. There are limitations in applying the RTM for kinetic analysis of PET studies using [11C]Pittsburgh compound B ([11C]PIB). For region of interest (ROI) based kinetic modeling, the low specific binding of [11C]PIB in a target ROI can result in a high linear relationship between the output and input. This condition may result in amplification of errors in estimates using RTM. For pixel-wise quantification, due to the high noise level of pixel kinetics, the parametric images generated by RTM with conventional linear or nonlinear regression may be too noisy for use in clinical studies.

METHODS

We applied RTM with parameter coupling and a simultaneous fitting method as a spatial constraint for ROI kinetic analysis. Three RTMs with parameter coupling were derived from a classical compartment model with plasma input: an RTM of 4 parameters (R(1), k'(2R), k(4), BP) (RTM4P); an RTM of 5 parameters (R(1), k(2R), NS, k(6), BP) (RTM5P); and a simplified RTM (SRTM) of 3 parameters (R(1), k'(2R), BP) (RTM3P). The parameter sets [k'(2R), k(4)], [k(2R), NS, k(6)], and k'(2R) are coupled among ROIs for RTM4P, RTM5P, and RTM3P, respectively. A linear regression with spatial constraint (LRSC) algorithm was applied to the SRTM for parametric imaging. Logan plots were used to estimate the distribution volume ratio (DVR) (=1+BP (binding potential)) in ROI and pixel levels. Ninety-minute [11C]PIB dynamic PET was performed in 28 controls and 6 individuals with mild cognitive impairment (MCI) on a GE Advance scanner. ROIs of cerebellum (reference tissue) and 15 other regions were defined on coregistered MRIs.

RESULTS

The coefficients of variation of DVR estimates from RTM3P obtained by the simultaneous fitting method were lower by 77-89% (in striatum, frontal, occipital, parietal, and cingulate cortex) as compared to that by conventional single ROI TAC fitting method. There were no significant differences in both TAC fitting and DVR estimates between the RTM3P and the RTM4P or RTM5P. The DVR in striatum, lateral temporal, frontal and cingulate cortex for MCI group was 25% to 38% higher compared to the control group (p < or = 0.05), even in this group of individuals with generally low PIB retention. The DVR images generated by the SRTM with LRSC algorithm had high linear correlations with those from the Logan plot (R2 = 0.99).

CONCLUSION

In conclusion, the RTM3P with simultaneous fitting method is shown to be a robust compartmental modeling approach that may be useful in [11C]PIB PET studies to detect early markers of Alzheimer's disease where specific ROIs have been hypothesized. In addition, the SRTM with LRSC algorithm may be useful in generating R(1) and DVR images for pixel-wise quantification of [11C]PIB dynamic PET.

Assessing the limitations of the Banister model in monitoring training

The aim of this study was to carry out a statistical analysis of the Banister model to verify how useful it is in monitoring the training programmes of elite swimmers. The accuracy, the ill-conditioning and the stability of this model were thus investigated. The training loads of nine elite swimmers, measured over one season, were related to performances with the Banister model. First, to assess accuracy, the 95% bootstrap confidence interval (95% CI) of parameter estimates and modelled performances were calculated. Second, to study ill-conditioning, the correlation matrix of parameter estimates was computed. Finally, to analyse stability, iterative computation was performed with the same data but minus one performance, chosen at random. Performances were related to training loads for all participants (R(2) = 0.79 +/- 0.13, P < 0.05) and the estimation procedure seemed to be stable. Nevertheless, the range of 95% CI values of the most useful parameters for monitoring training was wide: t(a) = 38 (17, 59), t(f) = 19 (6, 32), t(n) = 19 (7, 35), t(g) = 43 (25, 61). Furthermore, some parameters were highly correlated, making their interpretation worthless. We suggest possible ways to deal with these problems and review alternative methods to model the training-performance relationships.

Evaluation of objective functions for estimation of kinetic parameters

There is growing interest in quantitatively analyzing in vivo image data, as this facilitates objective comparisons and measurement of effect. In this regard, people increasingly turn to pharmacokinetic models and estimation of parameters of such models. In this work several parameter estimation methodologies were compared within the context of the most common pharmacokinetic model used in positron emission tomography imaging to describe glucose metabolism and receptor-ligand interactions at tracer concentrations. Simulated data were generated with 1000 realizations at each of 5 different noise levels. Estimates of the kinetic parameters were made for each realization using seven iterative, nonlinear estimation methodologies: ordinary least squares (OLS), weighted least squares (WLS), penalized weighted least squares (PWLS), iteratively reweighted least squares (IRLS), and variations of extended least squares (ELS0, ELS1, ELS3). Additionally, generalized linear least squares (GLLS) was also used. With relatively noise-free data, the iterative nonlinear estimation methods generally produced low-bias, high-precision parameter estimates, whereas with GLLS the bias was more prominent. Greater distinction between the estimation methods was seen at the higher, more realistic noise levels, with ELS and IRLS methods generally achieving better precision than the other methods. At the high noise levels WLS, GLLS, and PWLS yielded parameter estimates with large bias (>200%) for some kinetic parameters. In general, there are more favorable estimator methodologies than the frequently employed WLS. Methods that determine values of weights based on model output--IRLS, ELS0, ELS1 and ELS3--generally perform better than methods that determine values of weights based directly on the experimental data.

Direct reconstruction of kinetic parameter images from dynamic PET data

Our goal in this paper is the estimation of kinetic model parameters for each voxel corresponding to a dense three-dimensional (3-D) positron emission tomography (PET) image. Typically, the activity images are first reconstructed from PET sinogram frames at each measurement time, and then the kinetic parameters are estimated by fitting a model to the reconstructed time-activity response of each voxel. However, this "indirect" approach to kinetic parameter estimation tends to reduce signal-to-noise ratio (SNR) because of the requirement that the sinogram data be divided into individual time frames. In 1985, Carson and Lange proposed, but did not implement, a method based on the expectation-maximization (EM) algorithm for direct parametric reconstruction. The approach is "direct" because it estimates the optimal kinetic parameters directly from the sinogram data, without an intermediate reconstruction step. However, direct voxel-wise parametric reconstruction remained a challenge due to the unsolved complexities of inversion and spatial regularization. In this paper, we demonstrate and evaluate a new and efficient method for direct voxel-wise reconstruction of kinetic parameter images using all frames of the PET data. The direct parametric image reconstruction is formulated in a Bayesian framework, and uses the parametric iterative coordinate descent (PICD) algorithm to solve the resulting optimization problem. The PICD algorithm is computationally efficient and is implemented with spatial regularization in the domain of the physiologically relevant parameters. Our experimental simulations of a rat head imaged in a working small animal scanner indicate that direct parametric reconstruction can substantially reduce root-mean-squared error (RMSE) in the estimation of kinetic parameters, as compared to indirect methods, without appreciably increasing computation.

Linear regression with spatial constraint to generate parametric images of ligand-receptor dynamic PET studies with a simplified reference tissue model

For the quantitative analysis of ligand-receptor dynamic positron emission tomography (PET) studies, it is often desirable to apply reference tissue methods that eliminate the need for arterial blood sampling. A common technique is to apply a simplified reference tissue model (SRTM). Applications of this method are generally based on an analytical solution of the SRTM equation with parameters estimated by nonlinear regression. In this study, we derive, based on the same assumptions used to derive the SRTM, a new set of operational equations of integral form with parameters directly estimated by conventional weighted linear regression (WLR). In addition, a linear regression with spatial constraint (LRSC) algorithm is developed for parametric imaging to reduce the effects of high noise levels in pixel time activity curves that are typical of PET dynamic data. For comparison, conventional weighted nonlinear regression with the Marquardt algorithm (WNLRM) and nonlinear ridge regression with spatial constraint (NLRRSC) were also implemented using the nonlinear analytical solution of the SRTM equation. In contrast to the other three methods, LRSC reduces the percent root mean square error of the estimated parameters, especially at higher noise levels. For estimation of binding potential (BP), WLR and LRSC show similar variance even at high noise levels, but LRSC yields a smaller bias. Results from human studies demonstrate that LRSC produces high-quality parametric images. The variance of R(1) and k(2) images generated by WLR, WNLRM, and NLRRSC can be decreased 30%-60% by using LRSC. The quality of the BP images generated by WLR and LRSC is visually comparable, and the variance of BP images generated by WNLRM can be reduced 10%-40% by WLR or LRSC. The BP estimates obtained using WLR are 3%-5% lower than those estimated by LRSC. We conclude that the new linear equations yield a reliable, computationally efficient, and robust LRSC algorithm to generate parametric images of ligand-receptor dynamic PET studies.