Model-free quantification of dynamic PET data using nonparametric deconvolution

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.

Determination of hepatic extraction fraction with gadoxetate low‐temporal resolution DCE‐MRI ‐based deconvolution analysis: validation with ALBI score and Child‐Pugh class

INTRODUCTION

In this study, we aimed to investigate the feasibility of gadoxetate low-temporal resolution (LTR) DCE-MRI for voxel-based hepatic extraction fraction (HEF) quantification for liver sparing radiotherapy using a deconvolution analysis (DA) method.

METHODS

The accuracy and consistency of the deconvolution implementation in estimating liver function was first assessed using simulation data. Then, the method was applied to DCE-MRI data collected retrospectively from 64 patients (25 normal liver function and 39 cirrhotic patients) to generate HEF maps. The normal liver function patient data were used to measure the variability of liver function quantification. Next, a correlation between HEF and ALBI score (a new model for assessing the severity of liver dysfunction) was assessed using Pearson's correlation. Differences in HEF between Child-Pugh score classifications were assessed for significance using the Kruskal-Wallis test for all patient groups and Mann-Whitney U-test for inter-groups. A statistical significance was considered at a P-value <0.05 in all tests.

RESULTS

The results showed that the implemented method accurately reproduced simulated liver function; root-mean-square error between estimated and simulated liver response functions was 0.003, and the coefficient-of-variance of HEF was <20%. HEF correlation with ALBI score was r = -0.517, P < 0.0001, and HEF was significantly decreased in the cirrhotic patients compared to normal patients (P < 0.0001). Also, HEF in Child-Pugh B/C was significantly lower than in Child-Pugh A (P = 0.024).

CONCLUSION

The study demonstrated the feasibility of gadoxetate LTR-DCE MRI for voxel-based liver function quantification using DA. HEF could distinguish between different grades of liver function impairment and could potentially be used for functional guidance in radiotherapy.

Inference in functional mixed regression models with applications to Positron Emission Tomography imaging data

In a function-on-scalar regression framework, we present some modeling strategies for functional mixed models and also some approaches for making inference about various aspects of the fixed effects. This is presented in the context of modeling positron emission tomography (PET) data in order to explore the density of various proteins of interest throughout the human brain. For this application, information about the density of the target protein in a given brain region is encapsulated in the impulse response function (IRF) of the region. Previous work on nonparametric estimation of the IRF is limited in that it is only able to model a single brain region at a time. We propose an extension, based on principles of functional data analysis, that will allow modeling of multiple brain regions simultaneously. Applicable more broadly to functional mixed regression modeling, we discuss two general approaches for permutation testing and describe valid strategies for identifying exchangeable units within the model and building corresponding permutation tests. We illustrate our methods with an application to PET data and explore the effects of depression and sex on the IRF.

Brain serotonin transporter binding, plasma arachidonic acid and depression severity: A positron emission tomography study of major depression

BACKGROUND

Serotonin transporter (5-HTT) binding and polyunsaturated fatty acids (PUFAs) are implicated in major depressive disorder (MDD). Links between the two systems in animal models have not been investigated in humans.

METHODS

Using positron emission tomography (PET) and [¹¹C]DASB, we studied relationships between 5-HTT binding potential and plasma levels of PUFAs docosahexaenoic acid (DHA), eicosapentaenoic acid (EPA), and arachidonic acid (AA) in medication-free MDD patients (n = 21). PUFAs were quantified using transesterification and gas chromatography. Binding potential BP_P, and alternative outcome measures BP_F and BP_ND, were determined for [¹¹C]DASB in six a priori brain regions of interest (ROIs) using likelihood estimation in graphical analysis (LEGA) to calculate radioligand total distribution volume (V_T), and a validated hybrid deconvolution approach (HYDECA) that estimates radioligand non-displaceable distribution volume (V_ND) without a reference region. Linear mixed models used PUFA levels as predictors and binding potential measures as outcomes across the specified ROIs; age and sex as fixed effects; and subject as random effect to account for across-region binding correlations. As nonlinear relationships were observed, a quadratic term was added to final models.

RESULTS

AA predicted both 5-HTT BP_P and depression severity nonlinearly, described by an inverted U-shaped curve. 5-HTT binding potential mediated the relationship between AA and depression severity.

LIMITATIONS

Given the small sample and multiple comparisons, results require replication.

CONCLUSIONS

Our findings suggest that AA status may impact depression pathophysiology through effects on serotonin transport. Future studies should examine whether these relationships explain therapeutic effects of PUFAs in the treatment of MDD.

Functional Data Analysis of Dynamic PET Data

One application of positron emission tomography (PET), a nuclear imaging technique, in neuroscience involves in vivo estimation of the density of various proteins (often, neuroreceptors) in the brain. PET scanning begins with the injection of a radiolabeled tracer that binds preferentially to the target protein; tracer molecules are then continuously delivered to the brain via the bloodstream. By detecting the radioactive decay of the tracer over time, dynamic PET data are constructed to reflect the concentration of the target protein in the brain at each time. The fundamental problem in the analysis of dynamic PET data involves estimating the impulse response function (IRF), which is necessary for describing the binding behavior of the injected radiotracer. Virtually all existing methods have three common aspects: summarizing the entire IRF with a single scalar measure; modeling each subject separately; and the imposition of parametric restrictions on the IRF. In contrast, we propose a functional data analytic approach that regards each subject's IRF as the basic analysis unit, models multiple subjects simultaneously, and estimates the IRF nonparametrically. We pose our model as a linear mixed effect model in which population level fixed effects and subject-specific random effects are expanded using a B-spline basis. Shrinkage and roughness penalties are incorporated in the model to enforce identifiability and smoothness of the estimated curves, respectively, while monotonicity and non-negativity constraints impose biological information on estimates. We illustrate this approach by applying it to clinical PET data with subjects belonging to three diagnosic groups. We explore differences among groups by means of pointwise confidence intervals of the estimated mean curves based on bootstrap samples.

Nonlinear Mixed-Effects Models for PET Data

OBJECTIVE

The current state-of-the-art for compartment modeling of dynamic PET data can be described as a two-stage approach. In Stage 1, individual estimates of kinetic parameters are obtained by fitting models using standard techniques, such as nonlinear least squares, to each individual's data one subject at a time. Population-level effects, such as the difference between diagnostic groups, are analyzed in Stage 2 using standard statistical methods by treating the individual estimates as if they were observed data. While this approach is generally valid, it is possible to increase efficiency and precision of the analysis, allow more complex models to be fitted, and also to permit parameter-specific investigation by fitting data across subjects simultaneously. We explore the application of nonlinear mixed-effects (NLME) models for estimation and inference in this setting.

METHODS

In the NLME framework, subjects are modeled simultaneously through the inclusion of random effects of subjects for each kinetic parameter; meanwhile, population parameters are estimated directly in a joint model.

RESULTS

Simulation results indicate that NLME outperforms the two-stage approach in estimating group-level effects and also has improved power to detect differences across groups. We applied our NLME approach to clinical PET data and found effects not detected by the two-stage approach.

CONCLUSION

The proposed NLME approach is more accurate and correspondingly more powerful than the two-stage approach in compartment modeling of PET data.

SIGNIFICANCE

The NLME method can broaden the methodological scope of PET modeling because of its efficiency and stability.

A Functional Approach to Deconvolve Dynamic Neuroimaging Data

Positron emission tomography (PET) is an imaging technique which can be used to investigate chemical changes in human biological processes such as cancer development or neurochemical reactions. Most dynamic PET scans are currently analyzed based on the assumption that linear first-order kinetics can be used to adequately describe the system under observation. However, there has recently been strong evidence that this is not the case. To provide an analysis of PET data which is free from this compartmental assumption, we propose a nonparametric deconvolution and analysis model for dynamic PET data based on functional principal component analysis. This yields flexibility in the possible deconvolved functions while still performing well when a linear compartmental model setup is the true data generating mechanism. As the deconvolution needs to be performed on only a relative small number of basis functions rather than voxel by voxel in the entire three-dimensional volume, the methodology is both robust to typical brain imaging noise levels while also being computationally efficient. The new methodology is investigated through simulations in both one-dimensional functions and 2D images and also applied to a neuroimaging study whose goal is the quantification of opioid receptor concentration in the brain.