Modeling Mortality Based on Pollution and Temperature Using a New Birnbaum-Saunders Autoregressive Moving Average Structure with Regressors and Related-Sensors Data.

Environmental agencies are interested in relating mortality to pollutants and possible environmental contributors such as temperature. The Gaussianity assumption is often violated when modeling this relationship due to asymmetry and then other regression models should be considered. The class of Birnbaum-Saunders models, especially their regression formulations, has received considerable attention in the statistical literature. These models have been applied successfully in different areas with an emphasis on engineering, environment, and medicine. A common simplification of these models is that statistical dependence is often not considered. In this paper, we propose and derive a time-dependent model based on a reparameterized Birnbaum-Saunders (RBS) asymmetric distribution that allows us to analyze data in terms of a time-varying conditional mean. In particular, it is a dynamic class of autoregressive moving average (ARMA) models with regressors and a conditional RBS distribution (RBSARMAX). By means of a Monte Carlo simulation study, the statistical performance of the new methodology is assessed, showing good results. The asymmetric RBSARMAX structure is applied to the modeling of mortality as a function of pollution and temperature over time with sensor-related data. This modeling provides strong evidence that the new ARMA formulation is a good alternative for dealing with temporal data, particularly related to mortality with regressors of environmental temperature and pollution.

Improved identification of abdominal aortic aneurysm using the Kernelized Expectation Maximization algorithm.

Abdominal aortic aneurysm (AAA) monitoring and risk of rupture is currently assumed to be correlated with the aneurysm diameter. Aneurysm growth, however, has been demonstrated to be unpredictable. Using PET to measure uptake of [18F]-NaF in calcified lesions of the abdominal aorta has been shown to be useful for identifying AAA and to predict its growth. The PET low spatial resolution, however, can affect the accuracy of the diagnosis. Advanced edge-preserving reconstruction algorithms can overcome this issue. The kernel method has been demonstrated to provide noise suppression while retaining emission and edge information. Nevertheless, these findings were obtained using simulations, phantoms and a limited amount of patient data. In this study, the authors aim to investigate the usefulness of the anatomically guided kernelized expectation maximization (KEM) and the hybrid KEM (HKEM) methods and to judge the statistical significance of the related improvements. Sixty-one datasets of patients with AAA and 11 from control patients were reconstructed with ordered subsets expectation maximization (OSEM), HKEM and KEM and the analysis was carried out using the target-to-blood-pool ratio, and a series of statistical tests. The results show that all algorithms have similar diagnostic power, but HKEM and KEM can significantly recover uptake of lesions and improve the accuracy of the diagnosis by up to 22% compared to OSEM. The same improvements are likely to be obtained in clinical applications based on the quantification of small lesions, like for example cancer. This article is part of the theme issue 'Synergistic tomographic image reconstruction: part 1'.

Iterative reconstruction incorporating background correction improves quantification of [18F]-NaF PET/CT images of patients with abdominal aortic aneurysm.

BACKGROUND: A confounding issue in [18F]-NaF PET/CT imaging of abdominal aortic aneurysms (AAA) is the spill in contamination from the bone into the aneurysm. This study investigates and corrects for this spill in contamination using the background correction (BC) technique without the need to manually exclude the part of the AAA region close to the bone. METHODS: Seventy-two (72) datasets of patients with AAA were reconstructed with the standard ordered subset expectation maximization (OSEM) algorithm incorporating point spread function (PSF) modelling. The spill in effect in the aneurysm was investigated using two target regions of interest (ROIs): one covering the entire aneurysm (AAA), and the other covering the aneurysm but excluding the part close to the bone (AAAexc). ROI analysis was performed by comparing the maximum SUV in the target ROI (SUVmax(T)), the corrected cSUVmax (SUVmax(T) - SUVmean(B)) and the target-to-blood ratio (TBR = SUVmax(T)/SUVmean(B)) with respect to the mean SUV in the right atrium region. RESULTS: There is a statistically significant higher [18F]-NaF uptake in the aneurysm than normal aorta and this is not correlated with the aneurysm size. There is also a significant difference in aneurysm uptake for OSEM and OSEM + PSF (but not OSEM + PSF + BC) when quantifying with AAA and AAAexc due to the spill in from the bone. This spill in effect depends on proximity of the aneurysms to the bone as close aneurysms suffer more from spill in than farther ones. CONCLUSION: The background correction (OSEM + PSF + BC) technique provided more robust AAA quantitative assessments regardless of the AAA ROI delineation method, and thus it can be considered as an effective spill in correction method for [18F]-NaF AAA studies.

Comparison of Correction Techniques for the Spill in Effect in Emission Tomography.

In positron emission tomography (PET) imaging, accurate clinical assessment is often affected by the partial volume effect (PVE) leading to overestimation (spill-in) or underestimation (spill-out) of activity in various small regions. The spill-in correction, in particular, can be very challenging when the target region is close to a hot background region. Therefore, this study evaluates and compares the performance of various recently developed spill-in correction techniques, namely: background correction (BC), local projection (LP), and hybrid kernelized (HKEM) methods. We used a simulated digital phantom and [18F]-NaF PET data of three patients with abdominal aortic aneurysms (AAA) acquired with Siemens Biograph mMR™ and mCT™ scanners respectively. Region of Interest (ROI) analysis was performed and the extracted SUV mean , SUV max and target-to-background ratio (TBR) scores were compared. Results showed substantial spill-in effects from hot regions to targeted regions, which are more prominent in small structures. The phantom experiment demonstrated the feasibility of spill-in correction with all methods. For the patient data, large differences in SUV mean , SUV max and TBR max scores were observed between the ROIs drawn over the entire aneurysm and ROIs excluding some regions close to the bone. Overall, BC yielded the best performance in spill-in correction in both phantom and patient studies.

Hybrid PET/MR Kernelised Expectation Maximisation Reconstruction for Improved Image-Derived Estimation of the Input Function from the Aorta of Rabbits.

Positron emission tomography (PET) provides simple noninvasive imaging biomarkers for multiple human diseases which can be used to produce quantitative information from single static images or to monitor dynamic processes. Such kinetic studies often require the tracer input function (IF) to be measured but, in contrast to direct blood sampling, the image-derived input function (IDIF) provides a noninvasive alternative technique to estimate the IF. Accurate estimation can, in general, be challenging due to the partial volume effect (PVE), which is particularly important in preclinical work on small animals. The recently proposed hybrid kernelised ordered subsets expectation maximisation (HKEM) method has been shown to improve accuracy and contrast across a range of different datasets and count levels and can be used on PET/MR or PET/CT data. In this work, we apply the method with the purpose of providing accurate estimates of the aorta IDIF for rabbit PET studies. In addition, we proposed a method for the extraction of the aorta region of interest (ROI) using the MR and the HKEM image, to minimise the PVE within the rabbit aortic region-a method which can be directly transferred to the clinical setting. A realistic simulation study was performed with ten independent noise realisations while two, real data, rabbit datasets, acquired with the Biograph Siemens mMR PET/MR scanner, were also considered. For reference and comparison, the data were reconstructed using OSEM, OSEM with Gaussian postfilter and KEM, as well as HKEM. The results across the simulated datasets and different time frames show reduced PVE and accurate IDIF values for the proposed method, with 5% average bias (0.8% minimum and 16% maximum bias). Consistent results were obtained with the real datasets. The results of this study demonstrate that HKEM can be used to accurately estimate the IDIF in preclinical PET/MR studies, such as rabbit mMR data, as well as in clinical human studies. The proposed algorithm is made available as part of an open software library, and it can be used equally successfully on human or animal data acquired from a variety of PET/MR or PET/CT scanners.

Effect of PET-MR Inconsistency in the Kernel Image Reconstruction Method.

Anatomically-driven image reconstruction algorithms have become very popular in positron emission tomography (PET) where they have demonstrated improved image resolution and quantification. This work, consider the effect of spatial inconsistency between MR and PET images in hot and cold regions of the PET image. We investigate these effects on the kernel method from machine learning, in particular, the hybrid kernelized expectation maximization (HKEM). These were applied to Jaszczak phantom and patient data acquired with the Biograph Siemens mMR. The results show that even a small shift can cause a significant change in activity concentration. In general, the PET-MR inconsistencies can induce the partial volume effect, more specifically the 'spill-in' of the affected cold regions and the 'spill-out' from the hot regions. The maximum change was about 100% for the cold region and 10% for the hot lesion using KEM, against the 37% and 8% obtained with HKEM. The findings of this work suggest that including PET information in the kernel enhances the flexibility of the reconstruction in case of spatial inconsistency. Nevertheless, accurate registration and choice of the appropriate MR image for the creation of the kernel is essential to avoid artifacts, blurring, and bias.

Generalized Student's t-distribution mixtures for autoradiographic image spread modelling.

In this paper, a new class of models for autoradiographic hot-line data is proposed. The models, for which there is theoretical justification, are a linear combination of generalized Student's t-distributions and have as special cases all currently accepted line-spread models. The new models are used to analyse experimental hot-line data and compared with the fit of current models. The data are from a line source labelled with iodine-125 in a resin section of 0.6 µm in thickness. It will be shown that a significant improvement in goodness of fit, over that of previous models, can be achieved by choosing from this new class of models. A single model from this class will be proposed that has a simple form made up of only two components, but which fits experimental data significantly better than previous models. A short sensitivity analysis indicates that estimation is reliable. The modelling approach, although motivated by and applied to autoradiography, is appropriate for any mixture modelling situation.

Markov chain Monte Carlo techniques and spatial-temporal modelling for medical EIT.

Many imaging problems such as imaging with electrical impedance tomography (EIT) can be shown to be inverse problems: that is either there is no unique solution or the solution does not depend continuously on the data. As a consequence solution of inverse problems based on measured data alone is unstable, particularly if the mapping between the solution distribution and the measurements is also nonlinear as in EIT. To deliver a practical stable solution, it is necessary to make considerable use of prior information or regularization techniques. The role of a Bayesian approach is therefore of fundamental importance, especially when coupled with Markov chain Monte Carlo (MCMC) sampling to provide information about solution behaviour. Spatial smoothing is a commonly used approach to regularization. In the human thorax EIT example considered here nonlinearity increases the difficulty of imaging, using only boundary data, leading to reconstructions which are often rather too smooth. In particular, in medical imaging the resistivity distribution usually contains substantial jumps at the boundaries of different anatomical regions. With spatial smoothing these boundaries can be masked by blurring. This paper focuses on the medical application of EIT to monitor lung and cardiac function and uses explicit geometric information regarding anatomical structure and incorporates temporal correlation. Some simple properties are assumed known, or at least reliably estimated from separate studies, whereas others are estimated from the voltage measurements. This structural formulation will also allow direct estimation of clinically important quantities, such as ejection fraction and residual capacity, along with assessment of precision.