Metabolic images from dynamic positron emission tomography studies

The contribution of physics to Nuclear Medicine: physicians' perspective on future directions

Background

Advances in Nuclear Medicine physics enabled the specialty of Nuclear Medicine and directed research in other aspects of radiotracer imaging, ultimately leading to Nuclear Medicine’s emergence as an important component of current medical practice.

Discussion

Nuclear Medicine’s unique ability to characterize in vivo biology without perturbing it will assure its ongoing role in a practice of medicine increasingly driven by molecular biology. However, in the future, it is likely that advances in molecular biology and radiopharmaceutical chemistry will increasingly direct future developments in Nuclear Medicine physics, rather than relying on physics as the primary driver of advances in Nuclear Medicine.

Summary

Working hand-in-hand with clinicians, chemists, and biologists, Nuclear Medicine physicists can greatly enhance the specialty by creating more sensitive and robust imaging devices, by enabling more facile and sophisticated image analysis to yield quantitative measures of regional in vivo biology, and by combining the strengths of radiotracer imaging with other imaging modalities in hybrid devices, with the overall goal to enhance Nuclear Medicine’s ability to characterize regional in vivo biology.

Quantitative assessment of dynamic PET imaging data in cancer imaging

Clinical imaging in positron emission tomography (PET) is often performed using single-time-point estimates of tracer uptake or static imaging that provides a spatial map of regional tracer concentration. However, dynamic tracer imaging can provide considerably more information about in vivo biology by delineating both the temporal and spatial pattern of tracer uptake. In addition, several potential sources of error that occur in static imaging can be mitigated. This review focuses on the application of dynamic PET imaging to measuring regional cancer biologic features and especially in using dynamic PET imaging for quantitative therapeutic response monitoring for cancer clinical trials. Dynamic PET imaging output parameters, particularly transport (flow) and overall metabolic rate, have provided imaging end points for clinical trials at single-center institutions for years. However, dynamic imaging poses many challenges for multicenter clinical trial implementations from cross-center calibration to the inadequacy of a common informatics infrastructure. Underlying principles and methodology of PET dynamic imaging are first reviewed, followed by an examination of current approaches to dynamic PET image analysis with a specific case example of dynamic fluorothymidine imaging to illustrate the approach.

NCI-sponsored trial for the evaluation of safety and preliminary efficacy of 3'-deoxy-3'-[18F]fluorothymidine (FLT) as a marker of proliferation in patients with recurrent gliomas: preliminary efficacy studies

PURPOSE

3'-Deoxy-3'-[18F]fluorothymidine ([18F]FLT) is being developed for imaging cellular proliferation. The goals were to explore the capacity of FLT-positron emission tomography (PET) to distinguish between recurrence and radionecrosis in gliomas and compare the results to those obtained with 2-fluoro-2-deoxy-D: -glucose (FDG).

PROCEDURES

Fifteen patients with tumor recurrence and four with radionecrosis, determined by clinical course and magnetic resonance imaging results, were studied by dynamic [18F]FLT-PET with arterial blood sampling. A two-tissue compartment four-rate constant model was used to determine metabolic flux (K (FLT)), blood to tissue transport (K (1)), and phosphorylation (k (3)). FDG-PET scans were obtained 75-90 min postinjection.

RESULTS

K (FLT) and k (3), but not K (1) or k (3)/k (2) + k (3), reached significance for separating the recurrence from radionecrosis groups. Standardized uptake value and visual analyses of FLT or FDG images did not reach significance.

CONCLUSIONS

K (FLT) (flux) appears to distinguish recurrence from radionecrosis better than other parameters, FLT and FDG semiquantitative approaches, or visual analysis of images of either tracer.

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.

A Factor-Image Framework to Quantification of Brain Receptor Dynamic PET Studies

The positron emission tomography (PET) imaging technique enables the measurement of receptor distribution or neurotransmitter release in the living brain and the changes of the distribution with time and thus allows quantification of binding sites as well as the affinity of a radioligand. However, quantification of receptor binding studies obtained with PET is complicated by tissue heterogeneity in the sampling image elements (i.e., voxels, pixels). This effect is caused by a limited spatial resolution of the PET scanner. Spatial heterogeneity is often essential in understanding the underlying receptor binding process. Tracer kinetic modeling also often requires an intrusive collection of arterial blood samples. In this paper, we propose a likelihood-based framework in the voxel domain for quantitative imaging with or without the blood sampling of the input function. Radioligand kinetic parameters are estimated together with the input function. The parameters are initialized by a subspace-based algorithm and further refined by an iterative likelihood-based estimation procedure. The performance of the proposed scheme is examined by simulations. The results show that the proposed scheme provides reliable estimation of factor time-activity curves (TACs) and the underlying parametric images. A good match is noted between the result of the proposed approach and that of the Logan plot. Real brain PET data are also examined, and good performance is observed in determining the TACs and the underlying factor images.

MAP-based kinetic analysis for voxel-by-voxel compartment model estimation: Detailed imaging of the cerebral glucose metabolism using FDG

We propose a novel algorithm for voxel-by-voxel compartment model analysis based on a maximum a posteriori (MAP) algorithm. Voxel-by-voxel compartment model analysis can derive functional images of living tissues, but it suffers from high noise statistics in voxel-based PET data and extended calculation times. We initially set up a feature space of the target radiopharmaceutical composed of a measured plasma time activity curve and a set of compartment model parameters, and measured the noise distribution of the PET data. The dynamic PET data were projected onto the feature space, and then clustered using the Mahalanobis distance. Our method was validated using simulation studies, and compared with ROI-based ordinary kinetic analysis for FDG. The parametric images exhibited an acceptable linear relation with the simulations and the ROI-based results, and the calculation time took about 10 min. We therefore concluded that our proposed MAP-based algorithm is practical.

Locally constrained mixture representation of dynamic imaging data from PET and MR studies

Dynamic positron emission tomography (PET) studies provide measurements of the kinetics of radiotracers in living tissue. This is a powerful technology which can play a major role in the study of biological processes, potentially leading to better understanding and treatment of disease. Dynamic PET data relate to complex spatiotemporal processes and its analysis poses significant challenges. In previous work, mixture models that expressed voxel-level PET time course data as a convex linear combination of a finite number of dominant time course characteristics (called sub-TACs) were introduced. This paper extends that mixture model formulation to allow for a weighted combination of scaled sub-TACs and also considers the imposition of local constraints in the number of sub-TACs that can be active at any one voxel. An adaptive 3D scaled segmentation algorithm is developed for model initialization. Increases in the weighted residual sums of squares is used to guide the choice of the number of segments and the number of sub-TACs in the final mixture model. The methodology is applied to five data sets from representative PET imaging studies. The methods are also applicable to other contexts in which dynamic image data are acquired. To illustrate this, data from an echo-planar magnetic resonance (MR) study of cerebral hemodynamics are considered. Our analysis shows little indication of departure from a locally constrained mixture model representation with at most two active components at any voxel. Thus, the primary sources of spatiotemporal variation in representative dynamic PET and MR imaging studies would appear to be accessible to a substantially simplified representation in terms of the generalized locally constrained mixture model introduced.

True tracers: comparing FDG with glucose and FLT with thymidine

As PET metabolic imaging becomes routine in clinical practice, there is a tendency to make imaging and data analysis fast and simple, but interpretation of these pictures by visual inspection does not do justice to the power of PET technology. Tissue data and blood data can be analyzed mathematically to provide parametric images of the PET tracer's biochemistry in terms of a transport parameter and a metabolic flux. The methods for parametric imaging with (11)C tracers of glucose and thymidine have been validated, but the short half-life of this radionuclide and the rapid metabolism of these labeled substrates to [(11)C]CO(2) have led investigators to develop (18)F analogs. While (18)F substitution at critical positions in the natural substrate can block metabolism, it has other effects on the transport and metabolism of the analog tracer. The fidelity with which analog tracers mimic tracers of the authentic substrate is critically evaluated for [(18)F]-2-fluoro-2-deoxyglucose and [(18)F]-3'-fluoro-3'-deoxythymidine.

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.

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

The value of parametric images that represent both spatial distribution and quantification of the physiological parameters of tracer kinetics has long been recognized. However, the inherent high noise level of pixel kinetics of dynamic PET makes it unsuitable to generate parametric images of the microparameters of tracer kinetic model by conventional weighted nonlinear least squares (WNLS) fitting. Based on the concept that both spatial and temporal information should be integrated to improve parametric image quality, a nonlinear ridge regression with spatial constraint (NLRRSC) parametric imaging algorithm was proposed in this study. For NLRRSC, a term that penalizes local spatial variation of parameters was added to the cost function of WNLS fitting. The initial estimates and spatial constraint were estimated by component representation model (CRM) with cluster analysis. A hierarchical cluster with average linkage method was used to extract components. The ridge parameter was determined by linear ridge regression theory at each iteration, and a modified Gauss-Newton algorithm was used for minimizing the cost function. Results from a computer simulation showed that the percent mean square error of estimates obtained by NLRRSC can be decreased by 60-80% compared to that of WNLS. The parametric images estimated by NLRRSC are significantly better than the ones generated by WNLS. A highly correlated linear relationship was found between the ROI values calculated from the microparametric images generated by NLRRSC and estimates from ROI kinetic fitting. NLRRSC provided a reliable estimate of glucose metabolite uptake rate with a comparable image quality compared to Patlak analysis. In conclusion, NLRRSC is a reliable and robust parametric imaging algorithm for dynamic PET studies.

Use of ridge regression for improved estimation of kinetic constants from PET data

The estimation of parameters in radio-tracer models from positron emission tomography (PET) data by nonlinear least squares (NLS) often leads to results with unacceptable mean square error (ME) characteristics. The introduction of constraints on parameters has the potential to address this problem. We examine a ridge-regression technique that augments the standard NLS criterion by the addition of a term which penalizes estimates which deviate from physiologically reasonable values. A variation on a plug-in methodology of Hoerl et al. [7] is examined for data-dependent selection of the degree of reliance to place on the penalizing term. A simulation study is carried out to evaluate the performance of this approach in the context of estimation of kinetic constants in the three-compartment model used to analyze data from PET studies with fluoro-deoxyglucose (FDG). Results show that over a range of realistic noise levels, the ridge-regression procedure can be expected to reduce the root ME of parameter estimates by 60%. This result is not found to be substantially dependent on the precise formulation of the penalty function used. Thus, the use of ridge regression for estimation of kinetic parameters in PET studies is considered to be a promising tool.