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

Mathematical Models for FDG Kinetics in Cancer: A Review

Compartmental analysis is the mathematical framework for the modelling of tracer kinetics in dynamical Positron Emission Tomography. This paper provides a review of how compartmental models are constructed and numerically optimized. Specific focus is given on the identifiability and sensitivity issues and on the impact of complex physiological conditions on the mathematical properties of the models.

Parametric Mapping for TSPO PET Imaging with Spectral Analysis Impulsive Response Function

PURPOSE

The aim of this study was to investigate the use of spectral analysis (SA) for voxel-wise analysis of TSPO PET imaging studies. TSPO PET quantification is methodologically complicated by the heterogeneity of TSPO expression and its cell-dependent modulation during neuroinflammatory response. Compartmental models to account for this complexity exist, but they are unreliable at the high noise typical of voxel data. On the contrary, SA is noise-robust for parametric mapping and provides useful information about tracer kinetics with a free compartmental structure.

PROCEDURES

SA impulse response function (IRF) calculated at 90 min after tracer injection was used as main parameter of interest in 3 independent PET imaging studies to investigate its sensitivity to (1) a TSPO genetic polymorphism (rs6971) known to affect tracer binding in a cross-sectional analysis of healthy controls scanned with [11C]PBR28 PET; (2) TSPO density with [11C]PBR28 in a competitive blocking study with a TSPO blocker, XBD173; and (3) the higher affinity of a second radiotracer for TSPO, by using data from a head-to-head comparison between [11C]PBR28 and [11C]ER176 scans.

RESULTS

SA-IRF produced parametric maps of visually good quality. These were sensitive to TSPO genotype (mean relative difference between high- and mixed-affinity binders = 25 %) and TSPO availability (mean signal displacement after 90 mg oral administration of XBD173 = 39 %). Regional averages of voxel-wise IRF estimates were strongly associated with regional total distribution volume (V_T) estimated with a 2-tissue compartmental model with vascular compartment (Pearson's r = 0.86 ± 0.11) but less strongly with standard 2TCM-V_T (Pearson's r = 0.76 ± 0.32). Finally, SA-IRF estimates for [11C]ER176 were significantly higher than [11C]PBR28 ones, consistent with the higher amount of specific binding of the former tracer.

CONCLUSIONS

SA-IRF can be used for voxel-wise quantification of TSPO PET data because it generates high-quality parametric maps, it is sensitive to TSPO availability and genotype, and it accounts for the complexity of TSPO tracer kinetics with no additional assumptions.

The role of endoplasmic reticulum in in vivo cancer FDG kinetics

A recent result obtained by means of an in vitro experiment with cancer cultured cells has configured the endoplasmic reticulum as the preferential site for the accumulation of 2-deoxy-2-[¹⁸F]fluoro-D-glucose (FDG). Such a result is coherent with cell biochemistry and is made more significant by the fact that the reticular accumulation rate of FDG is dependent upon extracellular glucose availability. The objective of the present paper is to confirm in vivo the result obtained in vitro concerning the crucial role played by the endoplasmic reticulum in FDG cancer metabolism. This study utilizes data acquired by means of a Positron Emission Tomography scanner for small animals in the case of CT26 models of cancer tissues. The recorded concentration images are interpreted within the framework of a three-compartment model for FDG kinetics, which explicitly assumes that the endoplasmic reticulum is the dephosphorylation site for FDG in cancer cells. The numerical reduction of the compartmental model is performed by means of a regularized Gauss-Newton algorithm for numerical optimization. This analysis shows that the proposed three-compartment model equals the performance of a standard Sokoloff’s two-compartment system in fitting the data. However, it provides estimates of some of the parameters, such as the phosphorylation rate of FDG, more consistent with prior biochemical information. These results are made more solid from a computational viewpoint by proving the identifiability and by performing a sensitivity analysis of the proposed compartment model.

Test-retest reproducibility of quantitative binding measures of [11C]Ro15-4513, a PET ligand for GABAA receptors containing alpha5 subunits

INTRODUCTION

Alteration of γ-aminobutyric acid "A" (GABAA) receptor-mediated neurotransmission has been associated with various neurological and psychiatric disorders. [11C]Ro15-4513 is a PET ligand with high affinity for α5-subunit-containing GABAA receptors, which are highly expressed in limbic regions of the human brain (Sur et al., 1998). We quantified the test-retest reproducibility of measures of [11C]Ro15-4513 binding derived from six different quantification methods (12 variants).

METHODS

Five healthy males (median age 40 years, range 38-49 years) had a 90-min PET scan on two occasions (median interval 12 days, range 11-30 days), after injection of a median dose of 441 MegaBequerels of [11C]Ro15-4513. Metabolite-corrected arterial plasma input functions (parent plasma input functions, ppIFs) were generated for all scans. We quantified regional binding using six methods (12 variants), some of which were region-based (applied to the average time-activity curve within a region) and others were voxel-based: 1) Models requiring arterial ppIFs - regional reversible compartmental models with one and two tissue compartments (2kbv and 4kbv); 2) Regional and voxelwise Logan's graphical analyses (Logan et al., 1990), which required arterial ppIFs; 3) Model-free regional and voxelwise (exponential) spectral analyses (SA; (Cunningham and Jones, 1993)), which also required arterial ppIFs; 4) methods not requiring arterial ppIFs - voxelwise standardised uptake values (Kenney et al., 1941), and regional and voxelwise simplified reference tissue models (SRTM/SRTM2) using brainstem or alternatively cerebellum as pseudo-reference regions (Lammertsma and Hume, 1996; Gunn et al., 1997). To compare the variants, we sampled the mean values of the outcome parameters within six bilateral, non-reference grey matter regions-of-interest. Reliability was quantified in terms of median absolute percentage test-retest differences (MA-TDs; preferentially low) and between-subject coefficient of variation (BS-CV, preferentially high), both compounded by the intraclass correlation coefficient (ICC). These measures were compared between variants, with particular interest in the hippocampus.

RESULTS

Two of the six methods (5/12 variants) yielded reproducible data (i.e. MA-TD <10%): regional SRTMs and voxelwise SRTM2s, both using either the brainstem or the cerebellum; and voxelwise SA. However, the SRTMs using the brainstem yielded a lower median BS-CV (7% for regional, 7% voxelwise) than the other variants (8-11%), resulting in lower ICCs. The median ICCs across six regions were 0.89 (interquartile range 0.75-0.90) for voxelwise SA, 0.71 (0.64-0.84) for regional SRTM-cerebellum and 0.83 (0.70-0.86) for voxelwise SRTM-cerebellum. The ICCs for the hippocampus were 0.89 for voxelwise SA, 0.95 for regional SRTM-cerebellum and 0.93 for voxelwise SRTM-cerebellum.

CONCLUSION

Quantification of [11C]Ro15-4513 binding shows very good to excellent reproducibility with SRTM and with voxelwise SA which, however, requires an arterial ppIF. Quantification in the α5 subunit-rich hippocampus is particularly reliable. The very low expression of the α5 in the cerebellum (Fritschy and Mohler, 1995; Veronese et al., 2016) and the substantial α1 subunit density in this region may hamper the application of reference tissue methods.

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.

Model-free quantification of dynamic PET data using nonparametric deconvolution

Dynamic positron emission tomography (PET) data are usually quantified using compartment models (CMs) or derived graphical approaches. Often, however, CMs either do not properly describe the tracer kinetics, or are not identifiable, leading to nonphysiologic estimates of the tracer binding. The PET data are modeled as the convolution of the metabolite-corrected input function and the tracer impulse response function (IRF) in the tissue. Using nonparametric deconvolution methods, it is possible to obtain model-free estimates of the IRF, from which functionals related to tracer volume of distribution and binding may be computed, but this approach has rarely been applied in PET. Here, we apply nonparametric deconvolution using singular value decomposition to simulated and test-retest clinical PET data with four reversible tracers well characterized by CMs ([(11)C]CUMI-101, [(11)C]DASB, [(11)C]PE2I, and [(11)C]WAY-100635), and systematically compare reproducibility, reliability, and identifiability of various IRF-derived functionals with that of traditional CMs outcomes. Results show that nonparametric deconvolution, completely free of any model assumptions, allows for estimates of tracer volume of distribution and binding that are very close to the estimates obtained with CMs and, in some cases, show better test-retest performance than CMs outcomes.

Test-retest reproducibility of cannabinoid-receptor type 1 availability quantified with the PET ligand [¹¹C]MePPEP

Background

Endocannabinoids are involved in normal cognition, and dysfunction in cannabinoid-receptor-mediated neurotransmission has been suggested in a variety of neurological and psychiatric pathologies. The type 1 cannabinoid receptor (CB₁) is widely expressed in the human central nervous system. The objective of this study was to quantify the test–retest reproducibility of measures of the PET ligand [¹¹C]MePPEP in order to assess the stability of CB₁-receptor quantification in humans in vivo.

Methods

Fifteen healthy subjects (eight females; median age 32 years, range 25 to 65 years) had a 90-minute PET scan on two occasions after injection of a median dose of [¹¹C]MePPEP of 364 MBq. Metabolite-corrected arterial plasma input functions were obtained for all scans. Eight ROIs, reflecting different levels of receptor densities/concentrations, were defined automatically: hippocampus, anterior cingulate gyrus, inferior frontal gyrus, caudate nucleus, globus pallidus, nucleus accumbens, thalamus, and pons. We used seven quantification methods: reversible compartmental models with one and two tissue classes, two and four rate constants, and a variable blood volume term (2kbv; 4kbv); model-free (spectral) analyses with and without regularisation, including one with voxel-wise quantification; the simplified reference tissue model (SRTM) with pons as a pseudo-reference region; and modified standard uptake values (mSUVs) calculated for the period of ~ 30–60 min after injection. Percentage test–retest change and between-subject variability were both assessed, and test–retest reliability was quantified by the intraclass correlation coefficient (ICC). The ratio of binding estimates pallidum:pons served as an indicator of a method's ability to reflect binding heterogeneity.

Results

Neither the SRTM nor the 4kbv model produced reliable measures, with ICCs around zero. Very good (> 0.75) or excellent (> 0.80) ICCs were obtained with the other methods. The most reliable were spectral analysis parametric maps (average across regions ± standard deviation 0.83 ± 0.03), rank shaping regularised spectral analysis (0.82 ± 0.05), and the 2kbv model (0.82 ± 0.09), but mSUVs were also reliable for most regions (0.79 ± 0.13). Mean test–retest changes among the five well-performing methods ranged from 12 ± 10% for mSUVs to 16% for 2kbv. Intersubject variability was high, with mean between-subject coefficients of variation ranging from 32 ± 13% for mSUVs to 45% for 2kbv. The highest pallidum:pons ratios of binding estimates were achieved by mSUV (4.2), spectral analysis-derived parametric maps (3.6), and 2kbv (3.6).

Conclusion

Quantification of CB₁ receptor availability using [¹¹C]MePPEP shows good to excellent reproducibility with several kinetic models and model-free analyses, whether applied on a region-of-interest or voxelwise basis. Simple mSUV measures were also reliable for most regions, but do not allow fully quantitative interpretation. [¹¹C]MePPEP PET is well placed as a tool to investigate CB₁-receptor mediated neurotransmission in health and disease.

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[11C]MePPEP is a PET tracer for cannabinoid receptors (CB1R).

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Extensive evaluation of [11C]MePPEP data quantification strategies in large sample

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We highlight successful methods to quantify CB1R in regions of interest.

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Highly reliable parametric maps (ICC 0.83 ± 0.03) allow whole-brain surveys.

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Modified standard uptake values also reliable, without arterial input functions

Spatio-temporal pharmacokinetic model based registration of 4D PET neuroimaging data

In dynamic positron emission tomography (PET) neuroimaging studies, where scan durations often exceed 1h, registration of motion-corrupted dynamic PET images is necessary in order to maintain the integrity of the physiological, pharmacological, or biochemical information derived from the tracer kinetic analysis of the scan. In this work, we incorporate a pharmacokinetic model, which is traditionally used to analyse PET data following any registration, into the registration process itself in order to allow for a groupwise registration of the temporal time frames. The new method is shown to achieve smaller registration errors and improved kinetic parameter estimates on validation data sets when compared with image similarity based registration approaches. When applied to measured clinical data from 10 healthy subjects scanned with [(11)C]-(+)-PHNO (a dopamine D3/D2 receptor tracer), it reduces the intra-class variability on the receptor binding outcome measure, further supporting the improvements in registration accuracy. Our method incorporates a generic tracer kinetic model which makes it applicable to different PET radiotracers to remove motion artefacts and increase the integrity of dynamic PET studies.

Estimate of FDG excretion by means of compartmental analysis and ant colony optimization of nuclear medicine data

[¹⁸F]fluoro-2-deoxy-D-glucose (FDG) is one of the most utilized tracers for positron emission tomography (PET) applications in oncology. FDG-PET relies on higher glycolytic activity in tumors compared to normal structures as the basis of image contrast. As a glucose analog, FDG is transported into malignant cells which typically exhibit an increased radioactivity. However, different from glucose, FDG is not reabsorbed by the renal system and is excreted to the bladder. The present paper describes a novel computational method for the quantitative assessment of this excretion process. The method is based on a compartmental analysis of FDG-PET data in which the excretion process is explicitly accounted for by the bladder compartment and on the application of an ant colony optimization (ACO) algorithm for the determination of the tracer coefficients describing the FDG transport effectiveness. The validation of this approach is performed by means of both synthetic data and real measurements acquired by a PET device for small animals (micro-PET). Possible oncological applications of the results are discussed in the final section.

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.

Voxelwise quantification of [(11)C](R)-rolipram PET data: a comparison between model-based and data-driven methods

This study compared model-based and data-driven methods to assess the best methodology for generating precise and accurate parametric maps of the parameters of interest in [(11)C](R)-rolipram brain positron-emission tomography studies. Parametric images were generated using (1) a two-tissue compartmental model (2TCM) solved with the hierarchical basis function method (H-BFM) linear estimator; (2) data-driven spectral-based methods: standard spectral analysis (std SA) and rank-shaping SA (RS); and (3) the Logan graphical plot. Nonphysiologic VT estimates were eliminated and the remaining ones were compared with the reference values, i.e., those obtained with a voxelwise 2TCM solved with a nonlinear estimator. With regard to voxelwise VT estimates, H-BFM showed the best agreement with weighted nonlinear least square (WNLLS) values and the lowest percentage of mean relative difference (1±1%). All methods showed comparable variability in the relative differences. H-BFM provided the best correlation with WNLLS (y=1.034x-0.013; R(2)=0.973). Despite a slight bias, the other three methods also showed good agreement and high correlation (R(2)>0.96). H-BFM yielded the most reliable voxelwise quantification of [(11)C](R)-rolipram as well as the complete description of the tracer kinetic. The Logan plot represents a valid alternative if only VT estimation is required. Its marginally higher bias was outweighed by a low computational time, ease of implementation, and robustness.

Use of spectral analysis with iterative filter for voxelwise determination of regional rates of cerebral protein synthesis with L-[1-11C]leucine PET

A spectral analysis approach was used to estimate kinetic parameters of the L-[1-(11)C]leucine positron emission tomography (PET) method and regional rates of cerebral protein synthesis (rCPS) on a voxel-by-voxel basis. Spectral analysis applies to both heterogeneous and homogeneous tissues; it does not require prior assumptions concerning number of tissue compartments. Parameters estimated with spectral analysis can be strongly affected by noise, but numerical filters improve estimation performance. Spectral analysis with iterative filter (SAIF) was originally developed to improve estimation of leucine kinetic parameters and rCPS in region-of-interest (ROI) data analyses. In the present study, we optimized SAIF for application at the voxel level. In measured L-[1-(11)C]leucine PET data, voxel-level SAIF parameter estimates averaged over all voxels within a ROI (mean voxel-SAIF) generally agreed well with corresponding estimates derived by applying the originally developed SAIF to ROI time-activity curves (ROI-SAIF). Region-of-interest-SAIF and mean voxel-SAIF estimates of rCPS were highly correlated. Simulations showed that mean voxel-SAIF rCPS estimates were less biased and less variable than ROI-SAIF estimates in the whole brain and cortex; biases were similar in white matter. We conclude that estimation of rCPS with SAIF is improved when the method is applied at voxel level than in ROI analysis.

Cumulative input function method for linear compartmental models and spectral analysis in PET

Compartmental modeling and spectral analysis are often used for tracer kinetic modeling in positron emission tomography (PET). The concentrations in kinetic equations are usually considered to be instantaneous, whereas PET data are inherently integrated over time, which leads to uncertainties in the results. A new formalism for kinetic analysis that uses cumulative tracer concentrations and avoids approximating the image-derived input function and PET measurements with midframe instantanous values was developed. We assessed the improvements of the new formalism over the midframe approximation methods for three commonly used radiopharmaceuticals: [(11)C]raclopride, 2'-deoxy-2'-[(18)F]fluoro-D-glucose (FDG), and 3'-deoxy-3'-[(18)F]fluoro-thymidine (FLT). We found that improvements are case dependent and often not negligible. Improvements for determination of binding potential for [(11)C]raclopride ranged from 5% to 25%. Improvements in estimation accuracy of FDG and FLT microparameters ranged up to 25%. On the other hand, estimation of macroparameter K(i)=K(1)k(3)/(k(2)+k(3)) for FDG or FLT did not show significant benefit with the new method; only modest improvement up to 2% was observed. Assessment of the benefits of using new method is far from being exhaustive, but possibly significant improvement was demonstrated. Therefore, we consider the proposed algorithm a necessary component of any kinetic analysis software.

A spectral analysis approach for determination of regional rates of cerebral protein synthesis with the L-[1-(11)C]leucine PET method

A spectral analysis approach was used to estimate kinetic model parameters of the L-[1-(11)C]leucine positron emission tomography (PET) method and regional rates of cerebral protein synthesis (rCPS) in predefined regions of interest (ROIs). Unlike analyses based on the assumption that tissue ROIs are kinetically homogeneous, spectral analysis allows for heterogeneity within a region. To improve estimation performance, a new approach was developed-spectral analysis with iterative filter (SAIF). In simulation SAIF produced low bias, low variance estimates of the influx rate constant for leucine (K(1)), blood volume fraction (V(b)), fraction of unlabeled leucine in the tissue precursor pool for protein synthesis derived from arterial plasma (lambda), and rCPS. Simulation of normal count rate studies showed that SAIF applied to ROI time-activity curves (TACs) performed comparably to the basis function method (BFM) applied to voxel TACs when voxelwise estimates were averaged over all voxels in the ROI. At low count rates, however, SAIF performed better. In measured L-[1-(11)C]leucine PET data, there was good agreement between ROI-based SAIF estimates and average voxelwise BFM estimates of K(1), V(b), lambda, and rCPS. We conclude that SAIF sufficiently addresses the problem of tissue heterogeneity in ROI data and provides a valid tool for estimation of rCPS, even in low count rate studies.

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.

Molecular kinetics modeling in hemodialysis: on-line molecular monitoring and spectral analysis

The knowledge of the underlying molecular kinetics is a key point for the development of a dialysis treatment as well as for patient monitoring. In this work, we propose a kinetic inference method that is general enough to be used on different molecular types measured in the spent dialysate. It estimates the number and significance of the compartments involved in the overall process of dialysis by means of a spectral deconvolution technique, characterizing therefore the kinetic behavior of the patient. The method was applied to 52 patients to reveal the underlying kinetics from dialysate time-concentration profiles of urea, which has a well-known molecular kinetic. Three types of behaviors were found: one-compartmental (exponential decay Tau = 180 +/- 61.64 minutes), bicompartmental (Tau1 = 24.96 +/- 19.33 minutes, Tau2 = 222.32 +/- 76.59 minutes), and tricompartmental (Tau1 = 23.03 +/- 14.21 minutes; Tau2 = 85.75 +/- 27.48 minutes; and Tau3 = 337 +/- 85.52 minutes). In patients with bicompartmental kinetics, the Tau2 was related to the level of dialysis dose. The study concluded that spectral deconvolution technique can be considered a powerful tool for molecular kinetics inference that could be integrated in on-line molecular analysis devices. Furthermore, the method could be used in the analysis of poorly understood molecules as well as in new hemodialysis target biomarkers.

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.

Positron emission tomography compartmental models: a basis pursuit strategy for kinetic modeling

A kinetic modeling approach for the quantification of in vivo tracer studies with dynamic positron emission tomography (PET) is presented. The approach is based on a general compartmental description of the tracer's fate in vivo and determines a parsimonious model consistent with the measured data. The technique involves the determination of a sparse selection of kinetic basis functions from an overcomplete dictionary using the method of basis pursuit denoising. This enables the characterization of the systems impulse response function from which values of the systems macro parameters can be estimated. These parameter estimates can be obtained from a region of interest analysis or as parametric images from a voxel-based analysis. In addition, model order estimates are returned that correspond to the number of compartments in the estimated compartmental model. Validation studies evaluate the methods performance against two preexisting data led techniques, namely, graphical analysis and spectral analysis. Application of this technique to measured PET data is demonstrated using [11C]diprenorphine (opiate receptor) and [11C]WAY-100635 (5-HT1A receptor). Although the method is presented in the context of PET neuroreceptor binding studies, it has general applicability to the quantification of PET/SPECT radiotracer studies in neurology, oncology, and cardiology.

Positron emission tomography compartmental models

The current article presents theory for compartmental models used in positron emission tomography (PET). Both plasma input models and reference tissue input models are considered. General theory is derived and the systems are characterized in terms of their impulse response functions. The theory shows that the macro parameters of the system may be determined simply from the coefficients of the impulse response functions. These results are discussed in the context of radioligand binding studies. It is shown that binding potential is simply related to the integral of the impulse response functions for all plasma and reference tissue input models currently used in PET. This article also introduces a general compartmental description for the behavior of the tracer in blood, which then allows for the blood volume-induced bias in reference tissue input models to be assessed.