Estimation of component and parameter distributions in spectral analysis

Analysis of hypoxia in human glioblastoma tumors with dynamic 18F-FMISO PET imaging

Gliomas are the most common type of primary brain tumors and are classified as grade IV. Necrosis and hypoxia are essential diagnostic features which result in poor prognosis of gliomas. The aim of this study was to report quantitative temporal analyses aiming at determining the hypoxic regions in glioblastoma multiforme and to suggest an optimal time for the clinical single scan of hypoxia. Nine subjects were imaged with PET and 18F-FMISO in dynamic mode for 15 min followed with static scans at 2, 3 and 4 h post-injection. Spectral analysis, tumor-to-blood ratio (TBR) and tumor-to-normal tissue ratio (TNR) were used to delimit perfused and hypoxic tumor regions. TBR and TNR images were further scaled by thresholding at 1.2, 1.4, 2 and 2.5 levels. The images showed a varying tumor volume with time. TBR produced broader images of the tumor than TNR considering the same thresholds on intensity. Spectral analysis reliably determined hypoxia with different degrees of perfusion. By comparing TBR and TNR with spectral analysis images, weak to moderate correlation coefficients were found for most thresholding values and imaging times (range: 0 to 0.69). Hypoxic volume (HV) estimated from the net uptake rate (K_i) were changing among imaging times. The minimum HV changes were found between 3 h and 4 h, confirming that after 3 h, there was a very low exchange of 81F-FMISO between blood and tumor. On the other hand, hypoxia started to dominate the perfused tissue at 90 min, suggesting this time is suitable for a single scan acquisition irrespective of tumor status being highly hypoxic or perfused. At this time, TBR and TNR were respectively found in the nine subjects as 1.72 ± 0.22 and 1.74 ± 0.19.

Impact of tissue kinetic heterogeneity on PET quantification: case study with the L-[1-11C]leucine PET method for cerebral protein synthesis rates

Functional quantification with PET is generally based on modeling that assumes tissue regions are kinetically homogeneous. Even in regions sufficiently small to approach homogeneity, spillover due to resolution limitations of PET scanners may introduce heterogeneous kinetics into measured data. Herein we consider effects of kinetic heterogeneity at the smallest volume accessible, the single image voxel. We used L-[1-¹¹C]leucine PET and compared rates of cerebral protein synthesis (rCPS) estimated voxelwise with methods that do (Spectral Analysis Iterative Filter, SAIF) and do not (Basis Function Method, BFM) allow for kinetic heterogeneity. In high resolution PET data with good counting statistics BFM produced estimates of rCPS comparable to SAIF, but at lower computational cost; thus the simpler, less costly method can be applied. With poorer counting statistics (lower injected radiotracer doses), BFM estimates were more biased. In data smoothed to simulate lower resolution PET, BFM produced estimates of rCPS 9-14% higher than SAIF, overestimation consistent with applying a homogeneous tissue model to kinetically heterogeneous data. Hence with lower resolution data it is necessary to account for kinetic heterogeneity in the analysis. Kinetic heterogeneity may impact analyses of other tracers and scanning protocols differently; assessments should be made on a case by case basis.

Pharmacokinetic modeling of [11C]flumazenil kinetics in the rat brain

Background

Preferred models for the pharmacokinetic analysis of [¹¹C]flumazenil human studies have been previously established. However, direct translation of these models and settings to animal studies might be sub-optimal. Therefore, this study evaluates pharmacokinetic models for the quantification of [¹¹C]flumazenil binding in the rat brain.

Dynamic (60 min) [¹¹C]flumazenil brain PET scans were performed in two groups of male Wistar rats (tracer dose (TD), n = 10 and pre-saturated (PS), n = 2). Time-activity curves from five regions were analyzed, including the pons (pseudo-reference region). Distribution volume (V_T) was calculated using one- and two-tissue compartment models (1TCM and 2TCM) and spectral analysis (SA). Binding potential (BP_ND) was determined from full and simplified reference tissue models with one or two compartments for the reference tissue (FRTM, SRTM, and SRTM-2C). Model preference was determined by Akaike information criterion (AIC), while parameter agreement was assessed by linear regression, repeated measurements ANOVA and Bland-Altman plots.

Results

1TCM and 2TCM fits of regions with high specific binding showed similar AIC, a preference for the 1TCM, and good V_T agreement (0.1% difference). In contrast, the 2TCM was markedly preferred and necessary for fitting low specific-binding regions, where a worse V_T agreement (17.6% difference) and significant V_T differences between the models (p < 0.005) were seen. The PS group displayed results similar to those of low specific-binding regions. All reference models (FRTM, SRTM, and SRTM-2C) resulted in at least 13% underestimation of BP_ND.

Conclusions

Although the 1TCM was sufficient for the quantification of high specific-binding regions, the 2TCM was found to be the most adequate for the quantification of [¹¹C]flumazenil in the rat brain based on (1) higher fit quality, (2) lower AIC values, and (3) ability to provide reliable fits for all regions. Reference models resulted in negatively biased BP_ND and were affected by specific binding in the pons of the rat.

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.

SAKE: a new quantification tool for positron emission tomography studies

In dynamic positron emission tomography (PET) studies, spectral analysis (SA) refers to a data-driven quantification method, based on a single-input single-output model for which the transfer function is described by a sum of exponential terms. SA allows to quantify numerosities, amplitudes and eigenvalues of the transfer function allowing, in this way, to separate kinetic components of the tissue tracer activity with minimal model assumptions. The SA model can be solved with a linear estimator alone or with numerical filters, resulting in different types of SA approaches. Once estimated the number, amplitudes and eigenvalues of the transfer function, one can distinguish the presence in the system of irreversible and/or reversible components as well as derive parameters of physiological significance. These characteristics make it an appealing alternative method to compartmental models which are widely used for the quantitative analysis of dynamic studies acquired with PET. However, despite its applicability to a large number of PET tracers, its implementation is not straightforward and its utilization in the nuclear medicine community has been limited especially by the lack of an user-friendly software application. In this paper we proposed SAKE, a computer program for the quantitative analysis of PET data through the main SA methods. SAKE offers a unified pipeline of analysis usable also by people with limited computer knowledge but with high interest in SA.

RECONSTRUCTION OF DYNAMIC PET IMAGES USING ACCURATE SYSTEM POINT SPREAD FUNCTION MODELING: EFFECTS ON PARAMETRIC IMAGES

Quantitative analysis of positron emission tomography (PET) dynamic images allows to estimate physiological parameters such as glucose metabolic rate (GMR), perfusion, and cardiac output (CO). However, several physical effects such as photon attenuation, scatter and partial volume can reduce the accuracy of parameter estimation. The main goal of this work was to improve small animal PET image quality by introducing system point spread function (PSF) in the reconstruction scheme and to evaluate the effect of partial volume correction (PVC) on physiological parameter estimation. Images reconstructed respectively using constant and spatially variant (SV) PSFs and no PSF modeling was compared. The proposed algorithms were tested on simulated and real phantoms and mice images. Results show that the SV-PSF-based reconstruction method provides a significant contrast improvement of small animals PET cardiac images and, thus, the effects of PVC on physiological parameters were evaluated using such algorithm. Simulations show that the proposed PVC method reduces errors with respect to the true values for parametric images of GMR and perfusion. A reduction of CO percentage error with respect to the original value was also obtained using the SF-PSF approach. In conclusion, SV-PSF reconstruction method provides a more accurate estimation of several physiological parameters obtained from a dynamic PET scan.

Measurement error analysis for the determination of dopamine D(2) receptor occupancy using the agonist radioligand [(11)C]MNPA

The purpose of this study is to investigate errors in quantitative analysis for estimating dopamine D(2) receptor occupancy of antipsychotics with agonist radioligand [(11)C]MNPA by numerical simulation, with particular attention to the validity of a quantitative approach based on the use of a reference region. Synthetic data were validated using clinical data combined with a bootstrap approach. Time-activity curves (TACs) of [(11)C]MNPA were simulated, and the reliability of binding potential (BP(ND)) and occupancy estimated by nonlinear least square (NLS) fitting and a simplified reference tissue model (SRTM) were investigated for various noise levels and scan durations. In the human positron emission tomography (PET) study with and without antipsychotic, risperidone, the uncertainty of BP(ND) and occupancy estimated by SRTM was investigated using resampled TACs based on bootstrap approach with weighted residual errors of fitting. For both NLS and SRTM, it was possible to have <3% of bias in occupancy estimates of [(11)C]MNPA by 60 mins. However, shortened scan duration degrades the quantification of very small binding potentials, especially in case of SRTM. Observations were replicated on the clinical data. Results showed that dopamine D(2) receptor occupancy by antipsychotics can be estimated precisely in region of interest analysis by SRTM with a longer than 60-min [(11)C]MNPA PET scan duration.

A new model for prediction of drug distribution in tumor and normal tissues: pharmacokinetics of temozolomide in glioma patients

Difficulties in direct measurement of drug concentrations in human tissues have hampered the understanding of drug accumulation in tumors and normal tissues. We propose a new system analysis modeling approach to characterize drug distribution in tissues based on human positron emission tomography (PET) data. The PET system analysis method was applied to temozolomide, an important alkylating agent used in the treatment of brain tumors, as part of standard temozolomide treatment regimens in patients. The system analysis technique, embodied in the convolution integral, generated an impulse response function that, when convolved with temozolomide plasma concentration input functions, yielded predicted normal brain and brain tumor temozolomide concentration profiles for different temozolomide dosing regimens (75-200 mg/m(2)/d). Predicted peak concentrations of temozolomide ranged from 2.9 to 6.7 microg/mL in human glioma tumors and from 1.8 to 3.7 microg/mL in normal brain, with the total drug exposure, as indicated by the tissue/plasma area under the curve ratio, being about 1.3 in tumor compared with 0.9 in normal brain. The higher temozolomide exposures in brain tumor relative to normal brain were attributed to breakdown of the blood-brain barrier and possibly secondary to increased intratumoral angiogenesis. Overall, the method is considered a robust tool to analyze and predict tissue drug concentrations to help select the most rational dosing schedules.

Dynamic positron emission tomography data-driven analysis using sparse Bayesian learning

A method is presented for the analysis of dynamic positron emission tomography (PET) data using sparse Bayesian learning. Parameters are estimated in a compartmental framework using an over-complete exponential basis set and sparse Bayesian learning. The technique is applicable to analyses requiring either a plasma or reference tissue input function and produces estimates of the system's macro-parameters and model order. In addition, the Bayesian approach returns the posterior distribution which allows for some characterisation of the error component. The method is applied to the estimation of parametric images of neuroreceptor radioligand studies.

Error analysis for PET measurement of dopamine D2 receptor occupancy by antipsychotics with [11C]raclopride and [11C]FLB 457

Dopamine D(2) receptor occupancy by antipsychotic drugs has been measured with positron emission tomography (PET) by comparing the binding potential (BP) values before and after drug administration. This occupancy has been found to be related to clinical effects and side effects. In this study, we evaluated the uncertainty of the quantitative analysis for estimating the dopamine D(2) receptor occupancy by antipsychotics in simulation and human studies of [(11)C]raclopride and for the high affinity ligand [(11)C]FLB 457. Time-activity curves of [(11)C]raclopride and [(11)C]FLB 457 were simulated, and the reliability of BP estimated by a simplified reference tissue model and the calculated occupancy were investigated for various noise levels, BP values, and scan durations. Then, in the human PET study with and without antipsychotics, the uncertainty of BP and occupancy estimates and the scan duration required for a reliable estimation were investigated by a bootstrap approach. Reliable and unbiased estimates of [(11)C]raclopride BP(ND) could be obtained with recording as short as 32 min, with the relative standard deviation (SD) of the striatal occupancy remaining less than 10%. Conversely, in [(11)C]FLB 457 studies, the mean value increased and SD of the temporal cortex and thalamus exceeded 10% when the scan duration was shorter than 60 min. These results demonstrated that dopamine D(2) receptor occupancy by antipsychotics can be estimated precisely with an optimal scan duration with [(11)C]raclopride and [(11)C]FLB 457.

Opioid Imaging

Many breakthrough scientific discoveries have been made using opioid imaging. Developments include the application of ever higher resolution whole-brain positron emission tomography (PET) scanners, the availability of several radioligands, the combination of PET with advanced structural imaging, advances in modeling macroparameters of PET ligand binding, and large-scale statistical analysis of imaging datasets. Suitable single-photon emission computed tomography (SPECT) tracers are lacking, but with the increase in the number of available PET (or PET/CT) cameras and cyclotrons thanks to the clinical successes of PET in oncology, PET may become widespread enough to overcome this. In the coming decade, there should be a more widespread application of the available techniques to patients and an impact in clinical medicine.

Opioid Imaging

Many breakthrough scientific discoveries have been made using opioid imaging, particularly in the fields of pain, addiction and epilepsy research. Recent developments include the application of ever higher resolution whole-brain positron emission tomography (PET) scanners, the availability of several radioligands, the combination of PET with advanced structural imaging, advances in modeling macroparameters of PET ligand binding, and large-scale statistical analysis of imaging datasets. Suitable single-photon emission computed tomography (SPECT) tracers are lacking, but with the increase in the number of available PET (or PET/CT) cameras and cyclotrons thanks to the clinical successes of PET in oncology, PET may become widespread enough to overcome this limitation. In the coming decade, we hope to see a more widespread application of the techniques developed in healthy volunteers to patients and more clinical impact of opioid imaging.

Bootstrapped DEPICT for error estimation in PET functional imaging

Basis pursuit denoising is a new approach for data-driven estimation of parametric images from dynamic positron emission tomography (PET) data. At present, this kinetic modeling technique does not allow for the estimation of the errors on the parameters. These estimates are useful when performing subsequent statistical analysis, such as, inference across a group of subjects or when applying partial volume correction algorithms. The difficulty with calculating the error estimates is a consequence of using an overcomplete dictionary of kinetic basis functions. In this paper, a bootstrap approach for the estimation of parameter errors from dynamic PET data is presented. This paper shows that the bootstrap can be used successfully to compute parameter errors on a region of interest or parametric image basis. Validation studies evaluate the methods performance on simulated and measured PET data ([(11)C]Diprenorphine-opiate receptor and [(11)C]Raclopride-dopamine D(2) receptor). The method is presented in the context of PET neuroreceptor binding studies, however, it has general applicability to a wide range of PET/SPET radiotracers in neurology, oncology and cardiology.

Rank-shaping regularization of exponential spectral analysis for application to functional parametric mapping

Compartmental models are widely used for the mathematical modelling of dynamic studies acquired with positron emission tomography (PET). The numerical problem involves the estimation of a sum of decaying real exponentials convolved with an input function. In exponential spectral analysis (SA), the nonlinear estimation of the exponential functions is replaced by the linear estimation of the coefficients of a predefined set of exponential basis functions. This set-up guarantees fast estimation and attainment of the global optimum. SA, however, is hampered by high sensitivity to noise and, because of the positivity constraints implemented in the algorithm, cannot be extended to reference region modelling. In this paper, SA limitations are addressed by a new rank-shaping (RS) estimator that defines an appropriate regularization over an unconstrained least-squares solution obtained through singular value decomposition of the exponential base. Shrinkage parameters are conditioned on the expected signal-to-noise ratio. Through application to simulated and real datasets, it is shown that RS ameliorates and extends SA properties in the case of the production of functional parametric maps from PET studies.

On the undecidability among kinetic models: from model selection to model averaging

This article deals with the problem of model selection for the mathematical description of tracer kinetics in nuclear medicine. It stems from the consideration of some specific data sets where different models have similar performances. In these situations, it is shown that considerate averaging of a parameter's estimates over the entire model set is better than obtaining the estimates from one model only. Furthermore, it is also shown that the procedure of averaging over a small number of "good" models reduces the "generalization error," the error introduced when the model selected over a particular data set is applied to different conditions, such as subject populations with altered physiologic parameters, modified acquisition protocols, and different signal-to-noise ratios. The method of averaging over the entire model set uses Akaike coefficients as measures of an individual model's likelihood. To facilitate the understanding of these statistical tools, the authors provide an introduction to model selection criteria and a short technical treatment of Akaike's information-theoretic approach. The new method is illustrated and epitomized by a case example on the modeling of [11C]flumazenil kinetics in the brain, containing both real and simulated data.

Present and future capabilities of molecular imaging techniques to understand brain function

This article focuses on the use of positron emitting tracers and positron emission tomography (PET) as the most specific and sensitive means for imaging molecular interactions and pathways within the human brain. The concept of the imaging science of PET is developed whereby the key components that contribute to the overall accuracy of the image of molecular activity need to be separately optimized. These include radiolabelling of tracer molecules and ligands with radioisotopes of short radioactive half-life, the search for specific radioligands and tracers, and hence the need to mine molecular databases for molecules suitable for in-vivo imaging. The sensitivity and accuracy of PET scanners need to be advanced along with improvements in the signal-to-noise ratio of the tomographic reconstruction algorithms. Finally, the models used for the analysis of serial time frames of kinetic data need to be developed, the operation of which have to be effected with the minimum of noise propagation. The future use of PET for drug discovery and development is discussed whereby it offers proof principle for assays of in-vivo expression of therapeutic molecular targets as accessed from the blood stream; tissue pharmacokinetics of novel compounds; degree of occupancy of molecular targets; and pharmacodynamic measures of drug action. The future application of PET rests heavily on drug discoverers contributing to discovering specific PET radioligands and tracers in order to provide these assays through in-vivo molecular imaging.

Which linear compartmental systems can be analyzed by spectral analysis of PET output data summed over all compartments?

General linear time-invariant compartmental systems were examined to determine which systems meet the conditions necessary for application of the spectral analysis technique to the sum of the concentrations in all compartments. Spectral analysis can be used to characterize the reversible and irreversible components of the system and to estimate the minimum number of compartments, but it applies only to systems in which the measured data can be expressed as a positively weighted sum of convolution integrals of the input function with an exponential function that has real-valued nonpositive decay constants. The conditions are met by compartmental systems that are strongly connected, have exchange of material with the environment confined to a single compartment, and do not contain cycles, i.e., there is no possibility for material to pass from one compartment through two or more compartments back to the initial compartment. Certain noncyclic systems with traps, systems with cycles that obey a specified loop condition, and noninterconnected collections of such systems also meet the conditions. Dynamic positron emission tomographic data obtained after injection of a radiotracer, the kinetics of which can be described by any model in the class of models identified here, can be appropriately analyzed with the spectral analysis technique.