Effect of tissue heterogeneity on quantification in positron emission tomography

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 a novel hypoxia PET tracer [18F]HX4 in patients with non-small cell lung cancer

Background

[¹⁸F]HX4 is a promising new PET tracer developed to identify hypoxic areas in tumor tissue. This study analyzes [¹⁸F]HX4 kinetics and assesses the performance of simplified methods for quantification of [¹⁸F]HX4 uptake.

To this end, eight patients with non-small cell lung cancer received dynamic PET scans at three different time points (0, 120, and 240 min) after injection of 426 ± 72 MBq [¹⁸F]HX4, each lasting 30 min. Several compartment models were fitted to time activity curves (TAC) derived from various areas within tumor tissue using image-derived input functions.

Results

Best fits were obtained using the reversible two-tissue compartment model with blood volume parameter (2T4k+V_B). Simplified measures correlated well with V_T estimates (tumor-to-blood ratio (TBr) R² = 0.96, tumor-to-muscle ratio R² = 0.94, standardized uptake value R² = 0.89).

Conclusions

[¹⁸F]HX4 shows reversible kinetics in tumor tissue: 2T4k+V_B. TBr based on static imaging at 2 or 4 h can be used for quantification of [¹⁸F]HX4 uptake.

Electronic supplementary material

The online version of this article (doi:10.1186/s40658-016-0167-y) contains supplementary material, which is available to authorized users.

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.

A method for comparing intra-tumoural radioactivity uptake heterogeneity in preclinical positron emission tomography studies

Background

Non-uniformity influences the interpretation of nuclear medicine based images and consequently their use in treatment planning and monitoring. However, no standardised method for evaluating and ranking heterogeneity exists. Here, we have developed a general algorithm that provides a ranking and a visualisation of the heterogeneity in small animal positron emission tomography (PET) images.

Methods

The code of the algorithm was written using the Matrix Laboratory software (MATLAB). Parameters known to influence the heterogeneity (distances between deviating peaks, gradients and size compensations) were incorporated into the algorithm. All data matrices were mathematically constructed in the same format with the aim of maintaining overview and control. Histograms visualising the spread and frequency of contributions to the heterogeneity were also generated. The construction of the algorithm was tested using mathematically generated matrices and by varying post-processing parameters. It was subsequently applied in comparisons of radiotracer uptake in preclinical images in human head and neck carcinoma and endothelial and ovarian carcinoma xenografts.

Results

Using the developed algorithm, entire tissue volumes could be assessed and gradients could be handled in an indirect manner. Similar-sized volumes could be compared without modifying the algorithm. Analyses of the distribution of different tracers gave results that were generally in accordance with single plane preclinical images, indicating that it could appropriately handle comparisons of targeting vs. non-targeting tracers and also for different target levels. Altering the reconstruction algorithm, pixel size, tumour ROI volumes and lower cut-off limits affected the calculated heterogeneity factors in expected directions but did not reverse conclusions about which tumour was more or less heterogeneous.

Conclusions

The algorithm constructed is an objective and potentially user-friendly tool for one-to-one comparisons of heterogeneity in whole similar-sized tumour volumes in PET imaging.

Brain perfusion CT compared with ¹⁵O-H₂O PET in patients with primary brain tumours

Purpose

Perfusion CT (PCT) measurements of regional cerebral blood flow (rCBF) have been proposed as a fast and easy method for identifying angiogenically active tumours. In this study, quantitative PCT rCBF measurements in patients with brain tumours were compared to the gold standard PET rCBF with ¹⁵O-labelled water (¹⁵O-H₂O).

Methods

On the same day within a few hours, rCBF was measured in ten adult patients with treatment-naïve primary brain tumours, twice using ¹⁵O-H₂O PET and once with PCT performed over the central part of the tumour. Matching rCBF values in tumour and contralateral healthy regions of interest were compared.

Results

PCT overestimated intratumoural blood flow in all patients with volume-weighted mean rCBF values of 28.2 ± 18.8 ml min⁻¹ 100 ml⁻¹ for PET and 78.9 ± 41.8 ml min⁻¹ 100 ml⁻¹ for PCT. There was a significant method by tumour grade interaction with a significant tumour grade rCBF difference for PCT of 32.9 ± 15.8 ml min⁻¹ 100 ml⁻¹ for low-grade (WHO I + II) and 81.5 ± 15.4 ml min⁻¹ 100 ml⁻¹ for high-grade (WHO III + IV) tumours, but not for PET. The rCBF PCT and PET correlation was only significant within tumours in two patients.

Conclusion

Although intratumoural blood flow measured by PCT may add valuable information on tumour grade, the method cannot substitute quantitative measurements of blood flow by PET and ¹⁵O-H₂O PET in brain tumours.

Reproducibility of tumor perfusion measurements using 15O-labeled water and PET

PET and 15O-labeled water (H215O) can be used to noninvasively monitor tumor perfusion. This allows evaluation of the direct target of antiangiogenic drugs, that is, tumor vasculature. Because these drugs often result in consolidation rather than regression of the tumor mass, a change in perfusion might be a more sensitive way to evaluate response than are indirect size measures on a CT scan. However, to use the technique for serial imaging of individual patients, good reproducibility is essential. The purpose of the present study was to evaluate the reproducibility of quantitative H215O measurements.

METHODS

Nine patients with non-small-cell lung cancer (NSCLC) were scanned twice within 7 d and before any therapy. All H215O scans were followed by an 18F-fluorothymidine scan to allow for adequate volume-of-interest (VOI) definition. VOIs were defined using a 3-dimensional threshold technique. Tumor perfusion and the volume of distribution (VT) were obtained using a 1-tissue-compartment model including an arterial blood volume component and an image-derived input function. The level of agreement between test and retest values was assessed using the intraclass correlation coefficient (ICC) and Bland-Altman analyses. Possible dependency on absolute values and lesion size was assessed by linear regression.

RESULTS

All primary tumors and more than 90% of clinically suspected locoregional metastases could be delineated. In total, 14 lesions in 9 patients were analyzed. Tumor perfusion showed excellent reproducibility, with an ICC of 0.95 and SD of 9%. The VT was only moderately reproducible, with an ICC of 0.52 and SD of 16%. No dependency was found on absolute values of perfusion (P = 0.14) and VT (P = 0.15). In addition, tumor volume did not influence the reproducibility of perfusion (P = 0.46) and VT (P = 0.25).

CONCLUSION

Quantitative measurements of tumor perfusion using H215O and PET are reproducible in NSCLC. When patients are repeatedly being scanned during therapy, changes of more than 18% in tumor perfusion and 32% in VT (>1.96 x SD) are likely to represent treatment effects.

Stochastic dynamic model for estimation of rate constants and their variances from noisy and heterogeneous PET measurements

Tissue heterogeneity, radioactive decay and measurement noise are the main error sources in compartmental modeling used to estimate the physiologic rate constants of various radiopharmaceuticals from a dynamic PET study. We introduce a new approach to this problem by modeling the tissue heterogeneity with random rate constants in compartment models. In addition, the Poisson nature of the radioactive decay is included as a Poisson random variable in the measurement equations. The estimation problem will be carried out using the maximum likelihood estimation. With this approach, we do not only get accurate mean estimates for the rate constants, but also estimates for tissue heterogeneity within the region of interest and other possibly unknown model parameters, e.g. instrument noise variance, as well. We also avoid the problem of the optimal weighting of the data related to the conventionally used weighted least-squares method. The new approach was tested with simulated time-activity curves from the conventional three compartment - three rate constants model with normally distributed rate constants and with a noise mixture of Poisson and normally distributed random variables. Our simulation results showed that this new model gave accurate estimates for the mean of the rate constants, the measurement noise parameter and also for the tissue heterogeneity, i.e. for the variance of the rate constants within the region of interest.

Non-invasive assessment of distribution volume ratios and binding potential: tissue heterogeneity and interindividually averaged time-activity curves

Due to the stochastic nature of radioactive decay, any measurement of radioactivity concentration requires spatial averaging. In pharmacokinetic analysis of time-activity curves (TAC), such averaging over heterogeneous tissues may introduce a systematic error (heterogeneity error) but may also improve the accuracy and precision of parameter estimation. In addition to spatial averaging (inevitable due to limited scanner resolution and intended in ROI analysis), interindividual averaging may theoretically be beneficial, too. The aim of this study was to investigate the effect of such averaging on the binding potential ( BP) calculated with Logan's non-invasive graphical analysis and the "simplified reference tissue method" (SRTM) proposed by Lammertsma and Hume, on the basis of simulated and measured positron emission tomography data [[(11)C] d- threo-methylphenidate (dMP) and [(11)C]raclopride (RAC) PET]. dMP was not quantified with SRTM since the low k(2) (washout rate constant from the first tissue compartment) introduced a high noise sensitivity. Even for considerably different shapes of TAC (dMP PET in parkinsonian patients and healthy controls, [(11)C]raclopride in patients with and without haloperidol medication) and a high variance in the rate constants (e.g. simulated standard deviation of K(1)=25%), the BP obtained from average TAC was close to the mean BP (error <5%). However, unfavourably distributed parameters, especially a correlated large variance in two or more parameters, may lead to larger errors. In Monte Carlo simulations, interindividual averaging before quantification reduced the variance from the SRTM (beyond a critical signal to noise ratio) and the bias in Logan's method. Interindividual averaging may further increase accuracy when there is an error term in the reference tissue assumption E= DV(2)- DV' ( DV(2) = distribution volume of the first tissue compartment, DV' = distribution volume of the reference tissue). This can be explained by the fact that the distribution volume ratio ( DVR= DV/DV') obtained from averaged TAC is an approximation for Sigma DV/Sigma DV' rather than for Sigma DVR/ n. We conclude that Logan's non-invasive method and SRTM are suitable for heterogeneous tissues and that discussion of group differences in PET studies generally should include qualitative and quantitative assessment of interindividually averaged TAC.

Positron emission tomographic imaging of angiogenesis and vascular function

Surrogate markers of clinical outcome are important in anticancer drug research, since clinical criteria of response develop only slowly and may be confounded by other processes than drug effect. The need for surrogate outcome markers is especially great with newer agents that may act by tumour stabilization as opposed to shrinkage. Neoplastic angiogenesis is associated with a number of detectable changes at molecular and microcirculatory levels. Therefore, direct study of angiogenic molecular biology and tumour circulation before during and after treatment may offer useful surrogate markers for vascular-targeted therapies. The main advantage of radiotracer imaging with positron emission tomography (PET) is its functional specificity. This article will review two main areas: (a) the methodology behind PET imaging of tumour blood supply with 15O-oxygen labelled compounds; and (b) newer tracers in development as markers of angiogenetic biology.

Quantitative cerebral blood flow measurements in the rat using a beta-probe and H2 15O

Beta-probes are a relatively new tool for tracer kinetic studies in animals. They are highly suited to evaluate new positron emission tomography tracers or measure physiologic parameters at rest and after some kind of stimulation or intervention. In many of these experiments, the knowledge of CBF is highly important. Thus, the purpose of this study was to evaluate the method of CBF measurements using a beta-probe and H2 15O. CBF was measured in the barrel cortex of eight rats at baseline and after acetazolamide challenge. Trigeminal nerve stimulation was additionally performed in five animals. In each category, three injections of 250 to 300 MBq H2 15O were performed at 10-minute intervals. Data were analyzed using a standard one-tissue compartment model (K1 = CBF, k2 = CBF/p, where p is the partition coefficient). Values for K1 were 0.35 +/- 0.09, 0.58 +/- 0.16, and 0.49 +/- 0.03 mL x min(-1) x mL(-1) at rest, after acetazolamide challenge, and during trigeminal nerve stimulation, respectively. The corresponding values for k2 were 0.55 +/- 0.12, 0.94 +/- 0.16, and 0.85 +/- 0.12 min(-7), and for p were 0.64 +/- 0.05, 0.61 +/- 0.07, and 0.59 +/- 0.06. The standard deviation of the difference between two successive experiments, a measure for the reproducibility of the method, was 10.1%, 13.0%, and 5.7% for K1, k2, and p, respectively. In summary, beta-probes in conjunction with H2 15O allow the reproducible quantitative measurement of CBF, although some systematic underestimation seems to occur, probably because of partial volume effects.

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.

Quantitation of regional cerebral blood flow corrected for partial volume effect using O-15 water and PET: I. Theory, error analysis, and stereologic comparison

Limited spatial resolution of positron emission tomography (PET) can cause significant underestimation in the observed regional radioactivity concentration (so-called partial volume effect or PVE) resulting in systematic errors in estimating quantitative physiologic parameters. The authors have formulated four mathematical models that describe the dynamic behavior of a freely diffusible tracer (H215O) in a region of interest (ROI) incorporating estimates of regional tissue flow that are independent of PVE. The current study was intended to evaluate the feasibility of these models and to establish a methodology to accurately quantify regional cerebral blood flow (CBF) corrected for PVE in cortical gray matter regions. Five monkeys were studied with PET after IV H2(15)O two times (n = 3) or three times (n = 2) in a row. Two ROIs were drawn on structural magnetic resonance imaging (MRI) scans and projected onto the PET images in which regional CBF values and the water perfusable tissue fraction for the cortical gray matter tissue (hence the volume of gray matter) were estimated. After the PET study, the animals were killed and stereologic analysis was performed to assess the gray matter mass in the corresponding ROIs. Reproducibility of the estimated parameters and sensitivity to various error sources were also evaluated. All models tested in the current study yielded PVE-corrected regional CBF values (approximately 0.8 mL x min(-1) x g(-1) for models with a term for gray matter tissue and 0.5 mL x min(-1) x g(-1) for models with a term for a mixture of gray matter and white matter tissues). These values were greater than those obtained from ROIs tracing the gray matter cortex using conventional H2(15)O autoradiography (approximately 0.40 mL x min(-1) x g(-1)). Among the four models, configurations that included two parallel tissue compartments demonstrated better results with regards to the agreement of tissue time-activity curve and the Akaike's Information Criteria. Error sensitivity analysis suggested the model that fits three parameters of the gray matter CBF, the gray matter fraction, and the white matter fraction with fixed white matter CBF as the most reliable and suitable for estimating the gray matter CBF. Reproducibility with this model was 11% for estimating the gray matter CBF. The volume of gray matter tissue can also be estimated using this model and was significantly correlated with the results from the stereologic analysis. However, values were significantly smaller compared with those measured by stereologic analysis by 40%, which can not be explained by the methodologic errors. In conclusion, the partial volume correction was essential in quantitation of regional CBF. The method presented in this article provided the PVE-corrected regional CBF in the cortical gray matter tissue. This study also suggests that further studies are required before using MRI derived anatomic information for PVE correction in PET.

The effect of hyperglycaemia on regional cerebral glucose oxidation in humans studied with [1-11C]-D-glucose

The effect of hyperglycaemia on regional cerebral glucose utilization was studied in five healthy males fasted over-night using positron emission tomography. Selectively labelled glucose, [1-11C]-D-glucose, was used as a tracer. After correction for the small loss of [11C]CO2 from the tissue, this tracer measures the rate of glucose oxidation rather than the total rate of glucose metabolism. Each subject was investigated twice: during normoglycaemia (plasma glucose 5.3 +/- 0.3 mumol mL-1) and at the end of a 2-h period of hyperglycaemia (plasma glucose 13.8 +/- 0.7 mumol mL-1). Assuming unchanged rate constant for loss of labelled CO2 at normo- and hyperglycaemia the oxidative metabolic rate of glucose was found to be slightly larger at combined hyperglycaemia and hypersulinemia (0.30 +/- 0.01 mmol mL-1 min-1) than at normal glucose and insulin levels (0.25 +/- 0.01 mmol mL-1 min-1). This suggests that the process of glucose phosphorylation might not be fully saturated in the human brain or, alternatively, that the glycogen deposition increases during short-term hyperglycaemia. The relative increase of oxidative metabolic rate was considerably larger (approximately 50%) in white matter than in the brain as a whole (20%). The brain glucose content was found to increase non-linearly with increasing plasma glucose. Together with data from previous studies these results suggest that the free glucose in the human brain is close to zero when the plasma glucose is below 2 mumol mL-1.