Optimization-derived blood input function using a kernel method and its evaluation with total-body PET for brain parametric imaging

Dynamic PET allows quantification of physiological parameters through tracer kinetic modeling. For dynamic imaging of brain or head and neck cancer on conventional PET scanners with a short axial field of view, the image-derived input function (ID-IF) from intracranial blood vessels such as the carotid artery (CA) suffers from severe partial volume effects. Alternatively, optimization-derived input function (OD-IF) by the simultaneous estimation (SIME) method does not rely on an ID-IF but derives the input function directly from the data. However, the optimization problem is often highly ill-posed. We proposed a new method that combines the ideas of OD-IF and ID-IF together through a kernel framework. While evaluation of such a method is challenging in human subjects, we used the uEXPLORER total-body PET system that covers major blood pools to provide a reference for validation.

METHODS

The conventional SIME approach estimates an input function using a joint estimation together with kinetic parameters by fitting time activity curves from multiple regions of interests (ROIs). The input function is commonly parameterized with a highly nonlinear model which is difficult to estimate. The proposed kernel SIME method exploits the CA ID-IF as a priori information via a kernel representation to stabilize the SIME approach. The unknown parameters are linear and thus easier to estimate. The proposed method was evaluated using 18F-fluorodeoxyglucose studies with both computer simulations and 20 human-subject scans acquired on the uEXPLORER scanner. The effect of the number of ROIs on kernel SIME was also explored.

RESULTS

The estimated OD-IF by kernel SIME showed a good match with the reference input function and provided more accurate estimation of kinetic parameters for both simulation and human-subject data. The kernel SIME led to the highest correlation coefficient (R = 0.97) and the lowest mean absolute error (MAE = 10.5 %) compared to using the CA ID-IF (R = 0.86, MAE = 108.2 %) and conventional SIME (R = 0.57, MAE = 78.7 %) in the human-subject evaluation. Adding more ROIs improved the overall performance of the kernel SIME method.

CONCLUSION

The proposed kernel SIME method shows promise to provide an accurate estimation of the blood input function and kinetic parameters for brain PET parametric imaging.

Kinetic Modeling of Brain [18-F]FDG Positron Emission Tomography Time Activity Curves with Input Function Recovery (IR) Method

Accurate positron emission tomography (PET) data quantification relies on high-quality input plasma curves, but venous blood sampling may yield poor-quality data, jeopardizing modeling outcomes. In this study, we aimed to recover sub-optimal input functions by using information from the tail (5th-100th min) of curves obtained through the frequent sampling protocol and an input recovery (IR) model trained with reference curves of optimal shape. Initially, we included 170 plasma input curves from eight published studies with clamp [18F]-fluorodeoxyglucose PET exams. Model validation involved 78 brain PET studies for which compartmental model (CM) analysis was feasible (reference (ref) + training sets). Recovered curves were compared with original curves using area under curve (AUC), max peak standardized uptake value (maxSUV). CM parameters (ref + training sets) and fractional uptake rate (FUR) (all sets) were computed. Original and recovered curves from the ref set had comparable AUC (d = 0.02, not significant (NS)), maxSUV (d = 0.05, NS) and comparable brain CM results (NS). Recovered curves from the training set were different from the original according to maxSUV (d = 3) and biologically plausible according to the max theoretical K1 (53//56). Brain CM results were different in the training set (p < 0.05 for all CM parameters and brain regions) but not in the ref set. FUR showed reductions similarly in the recovered curves of the training and test sets compared to the original curves (p < 0.05 for all regions for both sets). The IR method successfully recovered the plasma inputs of poor quality, rescuing cases otherwise excluded from the kinetic modeling results. The validation approach proved useful and can be applied to different tracers and metabolic conditions.

Simultaneous estimation of a model-derived input function for quantifying cerebral glucose metabolism with [18F]FDG PET

BACKGROUND

Quantification of the cerebral metabolic rate of glucose (CMRGlu) by dynamic [18F]FDG PET requires invasive arterial sampling. Alternatives to using an arterial input function (AIF) include the simultaneous estimation (SIME) approach, which models the image-derived input function (IDIF) by a series of exponentials with coefficients obtained by fitting time activity curves (TACs) from multiple volumes-of-interest. A limitation of SIME is the assumption that the input function can be modelled accurately by a series of exponentials. Alternatively, we propose a SIME approach based on the two-tissue compartment model to extract a high signal-to-noise ratio (SNR) model-derived input function (MDIF) from the whole-brain TAC. The purpose of this study is to present the MDIF approach and its implementation in the analysis of animal and human data.

METHODS

Simulations were performed to assess the accuracy of the MDIF approach. Animal experiments were conducted to compare derived MDIFs to measured AIFs (n = 5). Using dynamic [18F]FDG PET data from neurologically healthy volunteers (n = 18), the MDIF method was compared to the original SIME-IDIF. Lastly, the feasibility of extracting parametric images was investigated by implementing a variational Bayesian parameter estimation approach.

RESULTS

Simulations demonstrated that the MDIF can be accurately extracted from a whole-brain TAC. Good agreement between MDIFs and measured AIFs was found in the animal experiments. Similarly, the MDIF-to-IDIF area-under-the-curve ratio from the human data was 1.02 ± 0.08, resulting in good agreement in grey matter CMRGlu: 24.5 ± 3.6 and 23.9 ± 3.2 mL/100 g/min for MDIF and IDIF, respectively. The MDIF method proved superior in characterizing the first pass of [18F]FDG. Groupwise parametric images obtained with the MDIF showed the expected spatial patterns.

CONCLUSIONS

A model-driven SIME method was proposed to derive high SNR input functions. Its potential was demonstrated by the good agreement between MDIFs and AIFs in animal experiments. In addition, CMRGlu estimates obtained in the human study agreed to literature values. The MDIF approach requires fewer fitting parameters than the original SIME method and has the advantage that it can model the shape of any input function. In turn, the high SNR of the MDIFs has the potential to facilitate the extraction of voxelwise parameters when combined with robust parameter estimation methods such as the variational Bayesian approach.

Parametric and non-parametric Poisson regression for modelling of the arterial input function in positron emission tomography

Full quantification of Positron Emission Tomography (PET) requires an arterial input function (AIF) for measurement of certain targets, or using particular radiotracers, or for the quantification of specific outcome measures. The AIF represents the measurement of radiotracer concentrations in the arterial blood plasma over the course of the PET examination. Measurement of the AIF is prone to error as it is a composite measure created from the combination of multiple measurements of different samples with different equipment, each of which can be sources of measurement error. Moreover, its measurement requires a high degree of temporal granularity for early time points, which necessitates a compromise between quality and quantity of recorded samples. For these reasons, it is often desirable to fit models to this data in order to improve its quality before using it for quantification of radiotracer binding in the tissue. The raw observations of radioactivity in arterial blood and plasma samples are derived from radioactive decay, which is measured as a number of recorded counts. Count data have several specific properties, including the fact that they cannot be negative as well as a particular mean-variance relationship. Poisson regression is the most principled modelling strategy for working with count data, as it both incorporates and exploits these properties. However, no previous studies to our knowledge have taken this approach, despite the advantages of greater efficiency and accuracy which result from using the appropriate distributional assumptions. Here, we implement a Poisson regression modelling approach for the AIF as proof-of-concept of its application. We applied both parametric and non-parametric models for the input function curve. We show that a negative binomial distribution is a more appropriate error distribution for handling overdispersion. Furthermore, we extend this approach to a hierarchical non-parametric model which is shown to be highly resilient to missing data. We thus demonstrate that Poisson regression is both feasible and effective when applied to AIF data, and propose that this is a promising strategy for modelling blood count data for PET in future.

An update on the use of image-derived input functions for human PET studies: new hopes or old illusions?

BACKGROUND

The need for arterial blood data in quantitative PET research limits the wider usability of this imaging method in clinical research settings. Image-derived input function (IDIF) approaches have been proposed as a cost-effective and non-invasive alternative to gold-standard arterial sampling. However, this approach comes with its own limitations-partial volume effects and radiometabolite correction among the most important-and varying rates of success, and the use of IDIF for brain PET has been particularly troublesome.

MAIN BODY

This paper summarizes the limitations of IDIF methods for quantitative PET imaging and discusses some of the advances that may make IDIF extraction more reliable. The introduction of automated pipelines (both commercial and open-source) for clinical PET scanners is discussed as a way to improve the reliability of IDIF approaches and their utility for quantitative purposes. Survey data gathered from the PET community are then presented to understand whether the field's opinion of the usefulness and validity of IDIF is improving. Finally, as the introduction of next-generation PET scanners with long axial fields of view, ultra-high sensitivity, and improved spatial and temporal resolution, has also brought IDIF methods back into the spotlight, a discussion of the possibilities offered by these state-of-the-art scanners-inclusion of large vessels, less partial volume in small vessels, better description of the full IDIF kinetics, whole-body modeling of radiometabolite production-is included, providing a pathway for future use of IDIF.

CONCLUSION

Improvements in PET scanner technology and software for automated IDIF extraction may allow to solve some of the major limitations associated with IDIF, such as partial volume effects and poor temporal sampling, with the exciting potential for accurate estimation of single kinetic rates. Nevertheless, until individualized radiometabolite correction can be performed effectively, IDIF approaches remain confined at best to a few tracers.

Quantitation of dynamic total-body PET imaging: recent developments and future perspectives

BACKGROUND

Positron emission tomography (PET) scanning is an important diagnostic imaging technique used in disease diagnosis, therapy planning, treatment monitoring, and medical research. The standardized uptake value (SUV) obtained at a single time frame has been widely employed in clinical practice. Well beyond this simple static measure, more detailed metabolic information can be recovered from dynamic PET scans, followed by the recovery of arterial input function and application of appropriate tracer kinetic models. Many efforts have been devoted to the development of quantitative techniques over the last couple of decades.

CHALLENGES

The advent of new-generation total-body PET scanners characterized by ultra-high sensitivity and long axial field of view, i.e., uEXPLORER (United Imaging Healthcare), PennPET Explorer (University of Pennsylvania), and Biograph Vision Quadra (Siemens Healthineers), further stimulates valuable inspiration to derive kinetics for multiple organs simultaneously. But some emerging issues also need to be addressed, e.g., the large-scale data size and organ-specific physiology. The direct implementation of classical methods for total-body PET imaging without proper validation may lead to less accurate results.

CONCLUSIONS

In this contribution, the published dynamic total-body PET datasets are outlined, and several challenges/opportunities for quantitation of such types of studies are presented. An overview of the basic equation, calculation of input function (based on blood sampling, image, population or mathematical model), and kinetic analysis encompassing parametric (compartmental model, graphical plot and spectral analysis) and non-parametric (B-spline and piece-wise basis elements) approaches is provided. The discussion mainly focuses on the feasibilities, recent developments, and future perspectives of these methodologies for a diverse-tissue environment.

Simulation of a novel, non-invasive radiation detector to measure the arterial input function for dynamic positron emission tomography

BACKGROUND

Dynamic positron emission tomography (dPET) is a nuclear medicine imaging technique providing functional images for organs of interest with applications in oncology, cardiology, and drug discovery. This technique requires the acquisition of the time-course arterial plasma activity concentration, called the arterial input function (AIF), which is conventionally acquired via arterial blood sampling.

PURPOSE

The aim of this study was to (A) optimize the geometry for a novel and cost efficient non-invasive detector called NID designed to measure the AIF for dPET scans through Monte Carlo simulations and (B) develop a clinical data analysis chain to successfully separate the arterial component of a simulated AIF signal from the venous component.

METHODS

The NID was optimized by using an in-house Geant4-based software package. The sensitive volume of the NID consists of a band of 10 cm long and 1 mm in diameter scintillating fibers placed over a wrist phantom. The phantom was simulated as a cylinder, 10 cm long and 6.413 cm in diameter comprised of polyethylene with two holes placed through it to simulate the patient's radial artery and vein. This phantom design was chosen to match the wrist phantom used in our previous proof of concept work. Two geometries were simulated with different arrangements of scintillating fibers. The first design used a single layer of 64 fibers. The second used two layers, an inner layer with 29 fibers and an outer layer with 30 fibers. Four positron emitting radioisotopes were simulated: ¹⁸ F, ¹¹ C, ¹⁵ O, and ⁶⁸ Ga with 100 million simulated decay events per run. The total and intrinsic efficiencies of both designs were calculated as well as the full width half maximum (FWHM) of the signal. In addition, contribution by the annihilation photons versus positrons to the signal was investigated. The results obtained from the two simulated detector models were compared. A clinical data analysis chain using an expectation maximization maximum likelihood algorithm was tested. This analysis chain will be used to separate arterial counts from the total signal.

RESULTS

The second NID design with two layers of scintillating fibers had a higher efficiency for all simulations with a maximum increase of 17% total efficiency for ¹¹ C simulation. All simulations had a significant annihilation photon contribution. The signal for ¹⁸ F and ¹¹ C was almost entirely due to photons. The clinical data analysis chain was within 1% of the true value for 434 out of 440 trials. Further experimental studies to validate these simulations will be required.

CONCLUSIONS

The design of the NID was optimized and its efficiency increased through Monte Carlo simulations. A clinical data analysis chain was successfully developed to separate the arterial component of an AIF signal from the venous component. The simulations show that the NID can be used to accurately measure the AIF non-invasively for dPET scans.

Total-Body PET Kinetic Modeling and Potential Opportunities Using Deep Learning

The uEXPLORER total-body PET/CT system provides a very high level of detection sensitivity and simultaneous coverage of the entire body for dynamic imaging for quantification of tracer kinetics. This article describes the fundamentals and potential benefits of total-body kinetic modeling and parametric imaging focusing on the noninvasive derivation of blood input function, multiparametric imaging, and high-temporal resolution kinetic modeling. Along with its attractive properties, total-body kinetic modeling also brings significant challenges, such as the large scale of total-body dynamic PET data, the need for organ and tissue appropriate input functions and kinetic models, and total-body motion correction. These challenges, and the opportunities using deep learning, are discussed.

PET Parametric Imaging: Past, Present, and Future

Positron emission tomography (PET) is actively used in a diverse range of applications in oncology, cardiology, and neurology. The use of PET in the clinical setting focuses on static (single time frame) imaging at a specific time-point post radiotracer injection and is typically considered as semi-quantitative; e.g. standardized uptake value (SUV) measures. In contrast, dynamic PET imaging requires increased acquisition times but has the advantage that it measures the full spatiotemporal distribution of a radiotracer and, in combination with tracer kinetic modeling, enables the generation of multiparametric images that more directly quantify underlying biological parameters of interest, such as blood flow, glucose metabolism, and receptor binding. Parametric images have the potential for improved detection and for more accurate and earlier therapeutic response assessment. Parametric imaging with dynamic PET has witnessed extensive research in the past four decades. In this paper, we provide an overview of past and present activities and discuss emerging opportunities in the field of parametric imaging for the future.