Principal component analysis of dynamic positron emission tomography images

A Review of Machine Learning Approaches for Brain Positron Emission Tomography Data Analysis

Positron emission tomography (PET) imaging has moved forward the development of medical diagnostics and research across various domains, including cardiology, neurology, infection detection, and oncology. The integration of machine learning (ML) algorithms into PET data analysis has further enhanced their capabilities of including disease diagnosis and classification, image segmentation, and quantitative analysis. ML algorithms empower researchers and clinicians to extract valuable insights from complex big PET datasets, which enabling automated pattern recognition, predictive health outcome modeling, and more efficient data analysis. This review explains the basic knowledge of PET imaging, statistical methods for PET image analysis, and challenges of PET data analysis. We also discussed the improvement of analysis capabilities by combining PET data with machine learning algorithms and the application of this combination in various aspects of PET image research. This review also highlights current trends and future directions in PET imaging, emphasizing the driving and critical role of machine learning and big PET image data analytics in improving diagnostic accuracy and personalized medical approaches. Integration between PET imaging will shape the future of medical diagnosis and research.

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.

Parametric Imaging With Dynamic PET for Oncological Applications: Protocols, Interpretation, Current Applications and Limitations for Clinical Use

Nuclear medicine imaging modalities, and in particular positron emission tomography (PET), provide functional images that demonstrate the mean radioactivity distribution at a defined point in time. With the help of mathematical model's, it is possible to depict isolated parameters of the radiotracers' pharmacokinetics and to visualize them. These so called parametric images add a new dimension to the existing conventional PET images and provide more detailed information about the tracer distribution over time and space. Prerequisite for the calculation of parametric images, which reflect specific pharmacokinetic parameters, is the dynamic PET (dPET) data acquisition. Hitherto, PET parametric imaging has mainly found use for research purposes. However, it has not been yet implemented into clinical routine, since it is more time-consuming, it requires a complicated analysis and still lacks a clear benefit over conventional PET imaging. However, the recent introduction of new PET-CT scanners with an ultralong field of view, which allow a faster data acquisition and are associated with higher sensitivity, as well as the development of more sophisticated evaluation software packages will probably lead to a renaissance of dPET and parametric maps even of the whole body. The implementation of dPET imaging in daily routine with appropriate acquisition protocols, as well as the calculation, interpretation and potential clinical applications of parametric images will be discussed in this review article.

Voxelwise Principal Component Analysis of Dynamic [S-Methyl-11C]Methionine PET Data in Glioma Patients

Recent works have demonstrated the added value of dynamic amino acid positron emission tomography (PET) for glioma grading and genotyping, biopsy targeting, and recurrence diagnosis. However, most of these studies are based on hand-crafted qualitative or semi-quantitative features extracted from the mean time activity curve within predefined volumes. Voxelwise dynamic PET data analysis could instead provide a better insight into intra-tumor heterogeneity of gliomas. In this work, we investigate the ability of principal component analysis (PCA) to extract relevant quantitative features from a large number of motion-corrected [S-methyl-¹¹C]methionine ([¹¹C]MET) PET frames. We first demonstrate the robustness of our methodology to noise by means of numerical simulations. We then build a PCA model from dynamic [¹¹C]MET acquisitions of 20 glioma patients. In a distinct cohort of 13 glioma patients, we compare the parametric maps derived from our PCA model to these provided by the classical one-compartment pharmacokinetic model (1TCM). We show that our PCA model outperforms the 1TCM to distinguish characteristic dynamic uptake behaviors within the tumor while being less computationally expensive and not requiring arterial sampling. Such methodology could be valuable to assess the tumor aggressiveness locally with applications for treatment planning and response evaluation. This work further supports the added value of dynamic over static [¹¹C]MET PET in gliomas.

Kinetic modeling and parametric imaging with dynamic PET for oncological applications: general considerations, current clinical applications, and future perspectives

Dynamic PET (dPET) studies have been used until now primarily within research purposes. Although it is generally accepted that the information provided by dPET is superior to that of conventional static PET acquisitions acquired usually 60 min post injection of the radiotracer, the duration of dynamic protocols, the limited axial field of view (FOV) of current generation clinical PET systems covering a relatively small axial extent of the human body for a dynamic measurement, and the complexity of data evaluation have hampered its implementation into clinical routine. However, the development of new-generation PET/CT scanners with an extended FOV as well as of more sophisticated evaluation software packages that offer better segmentation algorithms, automatic retrieval of the arterial input function, and automatic calculation of parametric imaging, in combination with dedicated shorter dynamic protocols, will facilitate the wider use of dPET. This is expected to aid in oncological diagnostics and therapy assessment. The aim of this review is to present some general considerations about dPET analysis in oncology by means of kinetic modeling, based on compartmental and noncompartmental approaches, and parametric imaging. Moreover, the current clinical applications and future perspectives of the modality are outlined.

Principal Component Analysis Based Dynamic Cone Beam X-Ray Luminescence Computed Tomography: A Feasibility Study

Cone beam X-ray luminescence computed tomography (CB-XLCT) is a promising imaging technique in studying the physiological and pathological processes in small animals. However, the dynamic bio-distributions of probes in small animal, especially in adjacent targets are still hard to be captured directly from dynamic CB-XLCT. In this paper, a 4D temporal-spatial reconstruction method based on principal component analysis (PCA) in the projection space is proposed for dynamic CB-XLCT. First, projections of angles in each 3D frame are compressed to reduce the noises initially. Then a temporal PCA is performed on the projection data to decorrelate the 4D problem into separate 3D problems in the PCA domain. In the PCA domain, the difference between dynamic behaviors of multiple targets can be reflected by the first several principal components which can be further used for fast and improved reconstruction by a restarted Tikhonov regularization method. At last, by discarding the principal components mainly reflecting noise, the concentration series of targets are recovered from the first few reconstruction results with a mask as the constraint. The numerical simulation and phantom experiment demonstrate that the proposed method can resolve multiple targets and recover the dynamic distributions with high computation efficiency. The proposed method provides new feasibility for imaging dynamic bio-distributions of probes in vivo.

Dynamic whole-body PET imaging: principles, potentials and applications

PURPOSE

In this article, we discuss dynamic whole-body (DWB) positron emission tomography (PET) as an imaging tool with significant clinical potential, in relation to conventional standard uptake value (SUV) imaging.

BACKGROUND

DWB PET involves dynamic data acquisition over an extended axial range, capturing tracer kinetic information that is not available with conventional static acquisition protocols. The method can be performed within reasonable clinical imaging times, and enables generation of multiple types of PET images with complementary information in a single imaging session. Importantly, DWB PET can be used to produce multi-parametric images of (i) Patlak slope (influx rate) and (ii) intercept (referred to sometimes as "distribution volume"), while also providing (iii) a conventional 'SUV-equivalent' image for certain protocols.

RESULTS

We provide an overview of ongoing efforts (primarily focused on FDG PET) and discuss potential clinically relevant applications.

CONCLUSION

Overall, the framework of DWB imaging [applicable to both PET/CT(computed tomography) and PET/MRI (magnetic resonance imaging)] generates quantitative measures that may add significant value to conventional SUV image-derived measures, with limited pitfalls as we also discuss in this work.

Methods for detecting host genetic modifiers of tumor vascular function using dynamic near-infrared fluorescence imaging

Vascular supply is a critical component of the tumor microenvironment (TME) and is essential for tumor growth and metastasis, yet the endogenous genetic modifiers that impact vascular function in the TME are largely unknown. To identify the host TME modifiers of tumor vascular function, we combined a novel genetic mapping strategy [Consomic Xenograft Model] with near-infrared (NIR) fluorescence imaging and multiparametric analysis of pharmacokinetic modeling. To detect vascular flow, an intensified cooled camera based dynamic NIR imaging system with 785 nm laser diode based excitation was used to image the whole-body fluorescence emission of intravenously injected indocyanine green dye. Principal component analysis was used to extract the spatial segmentation information for the lungs, liver, and tumor regions-of-interest. Vascular function was then quantified by pK modeling of the imaging data, which revealed significantly altered tissue perfusion and vascular permeability that were caused by host genetic modifiers in the TME. Collectively, these data demonstrate that NIR fluorescent imaging can be used as a non-invasive means for characterizing host TME modifiers of vascular function that have been linked with tumor risk, progression, and response to therapy.

Noise-Corrected Principal Component Analysis of fluorescence lifetime imaging data

Fluorescence Lifetime Imaging (FLIM) is an attractive microscopy method in the life sciences, yielding information on the sample otherwise unavailable through intensity-based techniques. A novel Noise-Corrected Principal Component Analysis (NC-PCA) method for time-domain FLIM data is presented here. The presence and distribution of distinct microenvironments are identified at lower photon counts than previously reported, without requiring prior knowledge of their number or of the dye's decay kinetics. A noise correction based on the Poisson statistics inherent to Time-Correlated Single Photon Counting is incorporated. The approach is validated using simulated data, and further applied to experimental FLIM data of HeLa cells stained with membrane dye di-4-ANEPPDHQ. Two distinct lipid phases were resolved in the cell membranes, and the modification of the order parameters of the plasma membrane during cholesterol depletion was also detected. Noise-corrected Principal Component Analysis of FLIM data resolves distinct microenvironments in cell membranes of live HeLa cells.

Sparsity Constrained Mixture Modeling for the Estimation of Kinetic Parameters in Dynamic PET

The estimation and analysis of kinetic parameters in dynamic positron emission tomography (PET) is frequently confounded by tissue heterogeneity and partial volume effects. We propose a new constrained model of dynamic PET to address these limitations. The proposed formulation incorporates an explicit mixture model in which each image voxel is represented as a mixture of different pure tissue types with distinct temporal dynamics. We use Cramér-Rao lower bounds to demonstrate that the use of prior information is important to stabilize parameter estimation with this model. As a result, we propose a constrained formulation of the estimation problem that we solve using a two-stage algorithm. In the first stage, a sparse signal processing method is applied to estimate the rate parameters for the different tissue compartments from the noisy PET time series. In the second stage, tissue fractions and the linear parameters of different time activity curves are estimated using a combination of spatial-regularity and fractional mixture constraints. A block coordinate descent algorithm is combined with a manifold search to robustly estimate these parameters. The method is evaluated with both simulated and experimental dynamic PET data.

Objective models of compressed breast shapes undergoing mammography

PURPOSE

To develop models of compressed breasts undergoing mammography based on objective analysis, that are capable of accurately representing breast shapes in acquired clinical images and generating new, clinically realistic shapes.

METHODS

An automated edge detection algorithm was used to catalogue the breast shapes of clinically acquired cranio-caudal (CC) and medio-lateral oblique (MLO) view mammograms from a large database of digital mammography images. Principal component analysis (PCA) was performed on these shapes to reduce the information contained within the shapes to a small number of linearly independent variables. The breast shape models, one of each view, were developed from the identified principal components, and their ability to reproduce the shape of breasts from an independent set of mammograms not used in the PCA, was assessed both visually and quantitatively by calculating the average distance error (ADE).

RESULTS

The PCA breast shape models of the CC and MLO mammographic views based on six principal components, in which 99.2% and 98.0%, respectively, of the total variance of the dataset is contained, were found to be able to reproduce breast shapes with strong fidelity (CC view mean ADE = 0.90 mm, MLO view mean ADE = 1.43 mm) and to generate new clinically realistic shapes. The PCA models based on fewer principal components were also successful, but to a lesser degree, as the two-component model exhibited a mean ADE = 2.99 mm for the CC view, and a mean ADE = 4.63 mm for the MLO view. The four-component models exhibited a mean ADE = 1.47 mm for the CC view and a mean ADE = 2.14 mm for the MLO view. Paired t-tests of the ADE values of each image between models showed that these differences were statistically significant (max p-value = 0.0247). Visual examination of modeled breast shapes confirmed these results. Histograms of the PCA parameters associated with the six principal components were fitted with Gaussian distributions. The six-component model was also used to generate CC and MLO view mammogram breast shapes, using the mean PCA parameter values of these distributions and randomly generated values based on the fitted Gaussian distributions, which resemble clinically encountered breasts. A spreadsheet with the data necessary to apply this model is provided as the supplementary material.

CONCLUSIONS

Our PCA models of breast shapes in both mammographic views successfully reproduce analyzed breast shapes and generate new clinically relevant shapes. This work can aid in research applications which incorporate breast shape modeling, such as x-ray scatter correction, dosimetry, and image registration.

jClustering, an open framework for the development of 4D clustering algorithms

We present jClustering, an open framework for the design of clustering algorithms in dynamic medical imaging. We developed this tool because of the difficulty involved in manually segmenting dynamic PET images and the lack of availability of source code for published segmentation algorithms. Providing an easily extensible open tool encourages publication of source code to facilitate the process of comparing algorithms and provide interested third parties with the opportunity to review code. The internal structure of the framework allows an external developer to implement new algorithms easily and quickly, focusing only on the particulars of the method being implemented and not on image data handling and preprocessing. This tool has been coded in Java and is presented as an ImageJ plugin in order to take advantage of all the functionalities offered by this imaging analysis platform. Both binary packages and source code have been published, the latter under a free software license (GNU General Public License) to allow modification if necessary.

The 2D Hotelling filter - a quantitative noise-reducing principal-component filter for dynamic PET data, with applications in patient dose reduction

Background

In this paper we apply the principal-component analysis filter (Hotelling filter) to reduce noise from dynamic positron-emission tomography (PET) patient data, for a number of different radio-tracer molecules. We furthermore show how preprocessing images with this filter improves parametric images created from such dynamic sequence.

We use zero-mean unit variance normalization, prior to performing a Hotelling filter on the slices of a dynamic time-series. The Scree-plot technique was used to determine which principal components to be rejected in the filter process. This filter was applied to [¹¹C]-acetate on heart and head-neck tumors, [¹⁸F]-FDG on liver tumors and brain, and [¹¹C]-Raclopride on brain. Simulations of blood and tissue regions with noise properties matched to real PET data, was used to analyze how quantitation and resolution is affected by the Hotelling filter. Summing varying parts of a 90-frame [¹⁸F]-FDG brain scan, we created 9-frame dynamic scans with image statistics comparable to 20 MBq, 60 MBq and 200 MBq injected activity. Hotelling filter performed on slices (2D) and on volumes (3D) were compared.

Results

The 2D Hotelling filter reduces noise in the tissue uptake drastically, so that it becomes simple to manually pick out regions-of-interest from noisy data. 2D Hotelling filter introduces less bias than 3D Hotelling filter in focal Raclopride uptake. Simulations show that the Hotelling filter is sensitive to typical blood peak in PET prior to tissue uptake have commenced, introducing a negative bias in early tissue uptake. Quantitation on real dynamic data is reliable. Two examples clearly show that pre-filtering the dynamic sequence with the Hotelling filter prior to Patlak-slope calculations gives clearly improved parametric image quality. We also show that a dramatic dose reduction can be achieved for Patlak slope images without changing image quality or quantitation.

Conclusions

The 2D Hotelling-filtering of dynamic PET data is a computer-efficient method that gives visually improved differentiation of different tissues, which we have observed improve manual or automated region-of-interest delineation of dynamic data. Parametric Patlak images on Hotelling-filtered data display improved clarity, compared to non-filtered Patlak slope images without measurable loss of quantitation, and allow a dramatic decrease in patient injected dose.

Spontaneous oscillations in intrinsic signals reveal the structure of cerebral vasculature

Functional imaging of intrinsic signals allows minimally invasive spatiotemporal mapping of stimulus representations in the cortex, but representations are often corrupted by stimulus-independent spatial artifacts, especially those originating from the blood vessels. In this paper, we present novel algorithms for unsupervised identification of cerebral vascularization, allowing blind separation of stimulus representations from noise. These algorithms commonly take advantage of the temporal fluctuations in global reflectance to extract anatomic information. More specifically, the phase of low-frequency oscillations relative to global fluctuations reveals local vascular identity. Arterioles can be reconstructed using their characteristically high power in those frequencies corresponding to respiration, heartbeat, and vasomotion signals. By treating the vasculature as a dynamic flow network, we finally demonstrate that direction of blood perfusion can be quantitatively visualized. Application of these methods for removal of stimulus-independent changes in reflectance permits isolation of stimulus-evoked representations even if the representation spatially overlaps with blood vessels. The algorithms can be expanded further to extract temporal information on blood flow, monitor revascularization following a focal stroke, and distinguish arterioles from venules and parenchyma.

Principal component analysis of dynamic fluorescence diffuse optical tomography images

Challenges remain in resolving drug distributions within small animals utilizing fluorescence diffuse optical tomography (FDOT). In this paper, we present a new method for detecting and visualizing organs with different kinetics utilizing principal component analysis (PCA). Indocynaine green (ICG) metabolic processes are simulated and imaged using FDOT. When applied to the time series of generated FDOT images, PCA provides a set of the principal components (PCs) which can represent spatial patterns associated with different kinetic behavior. Simulation and experiment studies are both performed to validate the performance of the proposed algorithm. The results suggest that we are able to extract and illustrate changes in ICG kinetic behavior between the heart and the lungs.

Performance of principal component analysis and independent component analysis with respect to signal extraction from noisy positron emission tomography data - a study on computer simulated images

Multivariate image analysis tools are used for analyzing dynamic or multidimensional Positron Emission Tomography, PET data with the aim of noise reduction, dimension reduction and signal separation. Principal Component Analysis is one of the most commonly used multivariate image analysis tools, applied on dynamic PET data. Independent Component Analysis is another multivariate image analysis tool used to extract and separate signals. Because of the presence of high and variable noise levels and correlation in the different PET images which may confound the multivariate analysis, it is essential to explore and investigate different types of pre-normalization (transformation) methods that need to be applied, prior to application of these tools. In this study, we explored the performance of Principal Component Analysis (PCA) and Independent Component Analysis (ICA) to extract signals and reduce noise, thereby increasing the Signal to Noise Ratio (SNR) in a dynamic sequence of PET images, where the features of the noise are different compared with some other medical imaging techniques. Applications on computer simulated PET images were explored and compared. Application of PCA generated relatively similar results, with some minor differences, on the images with different noise characteristics. However, clear differences were seen with respect to the type of pre-normalization. ICA on images normalized using two types of normalization methods also seemed to perform relatively well but did not reach the improvement in SNR as PCA. Furthermore ICA seems to have a tendency under some conditions to shift over information from IC1 to other independent components and to be more sensitive to the level of noise. PCA is a more stable technique than ICA and creates better results both qualitatively and quantitatively in the simulated PET images. PCA can extract the signals from the noise rather well and is not sensitive to type of noise, magnitude and correlation, when the input data are correctly handled by a proper pre-normalization. It is important to note that PCA as inherently a method to separate signal information into different components could still generate PC1 images with improved SNR as compared to mean images.

Lesion detection in dynamic FDG-PET using matched subspace detection

We describe a matched subspace detection algorithm to assist in the detection of small tumors in dynamic positron emission tomography (PET) images. The algorithm is designed to differentiate tumors from background using the time activity curves (TACs) that characterize the uptake of PET tracers. TACs are modeled using linear subspaces with additive Gaussian noise. Using TACs from a primary tumor region of interest (ROI) and one or more background ROIs, each identified by a human observer, two linear subspaces are identified. Applying a matched subspace detector to these identified subspaces on a voxel-by-voxel basis throughout the dynamic image produces a test statistic at each voxel which on thresholding indicates potential locations of secondary or metastatic tumors. The detector is derived for three cases: using a single TAC with white noise of unknown variance, using a single TAC with known noise covariance, and detection using multiple TACs within a small ROI with known noise covariance. The noise covariance is estimated for the reconstructed image from the observed sinogram data. To evaluate the proposed method, a simulation-based receiver operating characteristic (ROC) study for dynamic PET tumor detection is designed. The detector uses a dynamic sequence of frame-by-frame 2-D reconstructions as input. We compare the performance of the subspace detectors with that of a Hotelling observer applied to a single frame image and of the Patlak method applied to the dynamic data. We also show examples of the application of each detection approach to clinical PET data from a breast cancer patient with metastatic disease.

Improving PET receptor binding estimates from Logan plots using principal component analysis

This work reports a principal component analysis (PCA)-based approach for reducing bias in distribution volume ratio (DVR) estimates from Logan plots in positron emission tomography (PET). Comparison has been made of all existing bias-removal methods with the proposed PCA method, for both single-estimate PET studies and intervention studies where pre- and post-intervention estimates are made. Bias in Logan-based DVR estimates is because of the noise in the PET time-activity curves (TACs) that propagates as correlated errors in dependent and independent variables of the Logan equation. Intervention studies show this same bias but also higher variance in DVR estimates. In this work, noise in the TACs was reduced by fitting the curves to a low-dimension PCA-based linear model, leading to reduced bias and variance in DVR. For validating the approach, TACs with realistic noise were simulated for a 11C-labeled tracer with carfentanil (CFN)-like kinetics for both single-measurement and intervention studies. Principal component analysis and existing methods were applied to the simulated data and their performance was compared by statistical analysis. The results indicated that existing methods either removed only part of the bias or reduced bias at the expense of precision. The proposed method removed approximately 90% of the bias while also improving precision in both single- and dual-measurement simulations. After validation of the proposed method in simulations, PCA, along with the existing methods, was applied to human [11C]CFN data acquired for both single estimation of DVR and dual-estimation intervention studies. Similar results were observed in human scans as were seen in the simulation studies.

Detecting functional nodes in large-scale cortical networks with functional magnetic resonance imaging: a principal component analysis of the human visual system

This study aimed to demonstrate how a regional variant of principal component analysis (PCA) can be used to delineate the known functional subdivisions of the human visual system. Unlike conventional eigenimage analysis, PCA was carried out as a second-level analysis subsequent to model-based General Linear Model (GLM)-type functional activation mapping. Functional homogeneity of the functional magnetic resonance imaging (fMRI) time series within and between clusters was examined on several levels of the visual network, starting from the level of individual clusters up to the network level comprising two or more distinct visual regions. On each level, the number of significant components was identified and compared with the number of clusters in the data set. Eigenimages were used to examine the regional distribution of the extracted components. It was shown that voxels within individual clusters and voxels located in bilateral homologue visual regions can be represented by a single component, constituting the characteristic functional specialization of the cluster(s). If, however, PCA was applied to time series of voxels located in functionally distinct visual regions, more than one component was observed with each component being dominated by voxels in one of the investigated regions. The model of functional connections derived by PCA was in accordance with the well-known functional anatomy and anatomical connectivity of the visual system. PCA in combination with conventional activation mapping might therefore be used to identify the number of functionally distinct nodes in an fMRI data set in order to generate a model of functional connectivity within a neuroanatomical network.

Analysis and interpretation of dynamic FDG PET oncological studies using data reduction techniques

Background

Dynamic positron emission tomography studies produce a large amount of image data, from which clinically useful parametric information can be extracted using tracer kinetic methods. Data reduction methods can facilitate the initial interpretation and visual analysis of these large image sequences and at the same time can preserve important information and allow for basic feature characterization.

Methods

We have applied principal component analysis to provide high-contrast parametric image sets of lower dimensions than the original data set separating structures based on their kinetic characteristics. Our method has the potential to constitute an alternative quantification method, independent of any kinetic model, and is particularly useful when the retrieval of the arterial input function is complicated. In independent component analysis images, structures that have different kinetic characteristics are assigned opposite values, and are readily discriminated. Furthermore, novel similarity mapping techniques are proposed, which can summarize in a single image the temporal properties of the entire image sequence according to a reference region.

Results

Using our new cubed sum coefficient similarity measure, we have shown that structures with similar time activity curves can be identified, thus facilitating the detection of lesions that are not easily discriminated using the conventional method employing standardized uptake values.

Multiscale representation for automatic identification of structures in medical images

The identification of structures is a key step in several applications of medical imaging. In this work we propose a method for the identification of structures using a multiscale approach with inclusion of a priori information about the searched objects. After describing the image structures in the multiscale representation, a matching step determines which structure most likely corresponds to the target. Patterns are generated by previous application of the method to a set of images. We present a prototype for identifying structures in 2D images. A set of experiments was carried out to evaluate the prototype leading to encouraging results.

A new application of pre-normalized principal component analysis for improvement of image quality and clinical diagnosis in human brain PET studies—Clinical brain studies using [11C]-GR205171, [11C]-l-deuterium-deprenyl, [11C]-5-Hydroxy-l-Tryptophan, [11C]-l-DOPA and Pittsburgh Compound-B

Principal component analysis (PCA) is one of the most applied multivariate image analysis tool on dynamic Positron Emission Tomography (PET). Independent of used reconstruction methodologies, PET images contain correlation in-between pixels, correlations in-between frame and errors caused by the reconstruction algorithm including different corrections, which can affect the performance of the PCA. In this study, we have investigated a new approach of application of PCA on pre-normalized, dynamic human PET images. A range of different tracers have been used for this purpose to explore the performance of the new method as a way to improve detection and visualization of significant changes in tracer kinetics and to enhance the discrimination between pathological and healthy regions in the brain. We compare the new results with the results obtained using other methods. Images generated using the new approach contain more detailed anatomical information with higher quality, precision and visualization, compared with images generated using other methods.

Non-isotropic noise correlation in PET data reconstructed by FBP but not by OSEM demonstrated using auto-correlation function

Background

Positron emission tomography (PET) is a powerful imaging technique with the potential of obtaining functional or biochemical information by measuring distribution and kinetics of radiolabelled molecules in a biological system, both in vitro and in vivo. PET images can be used directly or after kinetic modelling to extract quantitative values of a desired physiological, biochemical or pharmacological entity. Because such images are generally noisy, it is essential to understand how noise affects the derived quantitative values. A pre-requisite for this understanding is that the properties of noise such as variance (magnitude) and texture (correlation) are known.

Methods

In this paper we explored the pattern of noise correlation in experimentally generated PET images, with emphasis on the angular dependence of correlation, using the autocorrelation function (ACF). Experimental PET data were acquired in 2D and 3D acquisition mode and reconstructed by analytical filtered back projection (FBP) and iterative ordered subsets expectation maximisation (OSEM) methods. The 3D data was rebinned to a 2D dataset using FOurier REbinning (FORE) followed by 2D reconstruction using either FBP or OSEM. In synthetic images we compared the ACF results with those from covariance matrix. The results were illustrated as 1D profiles and also visualized as 2D ACF images.

Results

We found that the autocorrelation images from PET data obtained after FBP were not fully rotationally symmetric or isotropic if the object deviated from a uniform cylindrical radioactivity distribution. In contrast, similar autocorrelation images obtained after OSEM reconstruction were isotropic even when the phantom was not circular. Simulations indicated that the noise autocorrelation is non-isotropic in images created by FBP when the level of noise in projections is angularly variable. Comparison between 1D cross profiles on autocorrelation images obtained by FBP reconstruction and covariance matrices produced almost identical results in a simulation study.

Conclusion

With asymmetric radioactivity distribution in PET, reconstruction using FBP, in contrast to OSEM, generates images in which the noise correlation is non-isotropic when the noise magnitude is angular dependent, such as in objects with asymmetric radioactivity distribution. In this respect, iterative reconstruction is superior since it creates isotropic noise correlations in the images.

"Population" approach improves parameter estimation of kinetic models from dynamic PET data

Kinetic modeling is used to indirectly measure physiological parameters from dynamic positron emission tomography (PET) data. Usually, the unknown parameters of the model are estimated, in any given region of interest (ROI), by least squares (LS). However, when the signal-to-noise ratio (SNR) of PET data is too low, LS does not allow reliable parameter estimation. To overcome this problem, we study in this paper the applicability of approaches originally developed in the pharmacokinetic/pharmacodynamic literature and referred to as "population approaches." In particular, we consider the iterative two stage (ITS) method, which, given a set of M ROIs drawn on PET images of a given individual, estimates the unknown model parameters of each ROI by exploiting the information contained in all the M ROIs. After having revised the theory behind ITS, we assess its performance versus LS by using Monte Carlo simulations which allow us to evaluate the bias of the two methods in a variety of situations. Then, we compare the performance of LS and ITS in two case studies on [18F]FDG kinetics in human skeletal muscle. Both simulated and real case studies results show that a population approach is of potential in modeling PET images since it allows to reliably estimate model parameters also in those ROIs where either a bad SNR or a poor sampling (e.g., infrequent scanning and/or short experiment duration) make the use of LS unsuccessful.

Performance evaluation of principal component analysis in dynamic FDG-PET studies of recurrent colorectal cancer

Performance evaluation of principal component analysis (PCA) of dynamic F-18-FDG-PET studies of patients with recurrent colorectal cancer. Principal component images (PCI) of 17 iteratively reconstructed data sets were visually and quantitatively evaluated. The F-18-FDG compartment model parameters were estimated using polynomial regression. All structures were present in PCI1. PCI2 was correlated with the vascular component and PCI3 with the tumor. The vessel density in the tumor was estimated with a correlation coefficient equal to 0.834. PCA supports the visual interpretation of dynamic F-18-FDG-PET studies, facilitates the application of compartment modeling and is a promising quantification technique.

Determination of arterial input function using fuzzy clustering for quantification of cerebral blood flow with dynamic susceptibility contrast-enhanced MR imaging

An accurate determination of the arterial input function (AIF) is necessary for quantification of cerebral blood flow (CBF) using dynamic susceptibility contrast-enhanced magnetic resonance imaging. In this study, we developed a method for obtaining the AIF automatically using fuzzy c-means (FCM) clustering. The validity of this approach was investigated with computer simulations. We found that this method can automatically extract the AIF, even under very noisy conditions, e.g., when the signal-to-noise ratio is 2. The simulation results also indicated that when using a manual drawing of a region of interest (ROI) (manual ROI method), the contamination of surrounding pixels (background) into ROI caused considerable overestimation of CBF. We applied this method to six subjects and compared it with the manual ROI method. The CBF values, calculated using the AIF obtained using the manual ROI method [CBF(manual)], were significantly higher than those obtained with FCM clustering [CBF(fuzzy)]. This may have been due to the contamination of non-arterial pixels into the manually drawn ROI, as suggested by simulation results. The ratio of CBF(manual) to CBF(fuzzy) ranged from 0.99-1.83 [1.31 +/- 0.26 (mean +/- SD)]. In conclusion, our FCM clustering method appears promising for determination of AIF because it allows automatic, rapid and accurate extraction of arterial pixels. J. Magn. Reson. Imaging 2001;13:797-806.

Factor analysis with a priori knowledge--application in dynamic cardiac SPECT

Two factor analysis of dynamic structures (FADS) methods for the extraction of time-activity curves (TACs) from cardiac dynamic SPECT data sequences were investigated. One method was based on a least squares (LS) approach which was subject to positivity constraints. The other method was the well known apex-seeking (AS) method. A post-processing step utilizing a priori information was employed to correct for the non-uniqueness of the FADS solution. These methods were used to extract 99mTc-teboroxime TACs from computer simulations and from experimental canine and patient studies. In computer simulations, the LS and AS methods, which are completely different algorithms, yielded very similar and accurate results after application of the correction for non-uniqueness. FADS-obtained blood curves correlated well with curves derived from region of interest (ROI) measurements in the experimental studies. The results indicate that the factor analysis techniques can be used for semi-automatic estimation of activity curves derived from cardiac dynamic SPECT images, and that they can be used for separation of physiologically different regions in dynamic cardiac SPECT studies.

Experimental comparison of data transformation procedures for analysis of principal components

Results of principal component analysis depend on data scaling. Recently, based on theoretical considerations, several data transformation procedures have been suggested in order to improve the performance of principal component analysis of image data with respect to the optimum separation of signal and noise. The aim of this study was to test some of those suggestions, and to compare several procedures for data transformation in analysis of principal components experimentally. The experiment was performed with simulated data and the performance of individual procedures was compared using the non-parametric Friedman's test. The optimum scaling found was that which unifies the variance of noise in the observed images. In data with a Poisson distribution, the optimum scaling was the norm used in correspondence analysis. Scaling mainly affected the definition of the signal space. Once the dimension of the signal space was known, the differences in error of data and signal reproduction were small. The choice of data transformation depends on the amount of available prior knowledge (level of noise in individual images, number of components, etc), on the type of noise distribution (Gaussian, uniform, Poisson, other), and on the purpose of analysis (data compression, filtration, feature extraction).

Head and neck cancer: detection of recurrence with three-dimensional principal components analysis at dynamic FDG PET

Fully automated principal components analysis (PCA) was applied to dynamic 2-[fluorine-18]fluoro-2-deoxy-D-glucose (FDG) positron emission tomographic (PET) images obtained in 15 patients with previously treated head and neck cancer. PCA with time-activity curves incorporated kinetic information about FDG uptake, which improved tissue characterization on FDG PET images. The combination of standardized uptake value and PCA image sets likely will improve the reliability of tumor detection in head and neck cancers.

Principal component analysis of the dynamic response measured by fMRI: a generalized linear systems framework

Principal component analysis (PCA) is one of several structure-seeking multivariate statistical techniques, exploratory as well as inferential, that have been proposed recently for the characterization and detection of activation in both PET and fMRI time series data. In particular, PCA is data driven and does not assume that the neural or hemodynamic response reaches some steady state, nor does it involve correlation with any pre-defined or exogenous experimental design template. In this paper, we present a generalized linear systems framework for PCA based on the singular value decomposition (SVD) model for representation of spatio-temporal fMRI data sets. Statistical inference procedures for PCA, including point and interval estimation will be introduced without the constraint of explicit hypotheses about specific task-dependent effects. The principal eigenvectors capture both the spatial and temporal aspects of fMRI data in a progressive fashion; they are inherently matched to unique and uncorrelated features and are ranked in order of the amount of variance explained. PCA also acts as a variation reduction technique, relegating most of the random noise to the trailing components while collecting systematic structure into the leading ones. Features summarizing variability may not directly be those that are the most useful. Further analysis is facilitated through linear subspace methods involving PC rotation and strategies of projection pursuit utilizing a reduced, lower-dimensional natural basis representation that retains most of the information. These properties will be illustrated in the setting of dynamic time-series response data from fMRI experiments involving pharmacological stimulation of the dopaminergic nigro-striatal system in primates.

Multivariate cluster analysis of dynamic iodine-123 iodobenzamide SPET dopamine D2 receptor images in schizophrenia

This paper describes the application of a multivariate statistical technique to investigate striatal dopamine D2 receptor concentrations measured by iodine-123 iodobenzamide (123I-IBZM) single-photon emission tomography (SPET). This technique enables the automatic segmentation of dynamic nuclear medicine images based on the underlying time-activity curves present in the data. Once the time-activity curves have been extracted, each pixel can be mapped back on to the underlying distribution, considerably reducing image noise. Cluster analysis has been verified using computer simulations and phantom studies. The technique has been applied to SPET images of dopamine D2 receptors in a total of 20 healthy and 20 schizophrenic volunteers (22 male, 18 female), using the ligand 123I-IBZM. Following automatic image segmentation, the concentration of striatal dopamine D2 receptors shows a significant left-sided asymmetry in male schizophrenics compared with male controls. The mean left-minus-right laterality index for controls is -1.52 (95% CI -3.72-0.66) and for patients 4.04 (95% CI 1.07-7.01). Analysis of variance shows a case-by-sex-by-side interaction, with F=10.01, P=0. 005. We can now demonstrate that the previously observed male sex-specific D2 receptor asymmetry in schizophrenia, which had failed to attain statistical significance, is valid. Cluster analysis of dynamic nuclear medicine studies provides a powerful tool for automatic segmentation and noise reduction of the images, removing much of the subjectivity inherent in region-of-interest analysis. The observed striatal D2 asymmetry could reflect long hypothesized disruptions in dopamine-rich cortico-striatal-limbic circuits in schizophrenic males.

Linear dimension reduction of sequences of medical images: III. Factor analysis in signal space

A method is presented for improving the precision of factor analysis by utilizing physiological information. The first step is an optimal linear dimension reduction, whereby the data are projected onto a low-dimensional signal space. Then principal component analysis is performed in the signal space rather than in the entire data space. This improves the precision of the principal components. Unlike ordinary principal component analysis, the present method is not degraded when the time intervals are subdivided, provided that the signal space is correct. Alternatively, but with identical results, the covariance matrix can be calculated from the whole data space. The covariance matrix is then transformed and principal component analysis is performed in either a low-rank matrix or a low-dimensional submatrix instead of in the whole covariance matrix. Factor analysis using the intersection method with a theory space may be improved by employing the present method. In simulations based on a [11C]flumazenil study with 27 frames, the proposed method required only 58 per cent of the radioactivity to produce the same precision as the intersection method and only 27 per cent when compared to ordinary principal component analysis.

Nuclear medicine and mathematics

The purpose of this review is not to present a comprehensive description of all the mathematical tools used in nuclear medicine, but to emphasize the importance of the mathematical method in nuclear medicine and to elucidate some of the mathematical concepts currently used. We can distinguish three different areas in which mathematical support has been offered to nuclear medicine: physiology, methodology and data processing. Nevertheless, the boundaries between these areas can be indistinct. It is impossible in a single article to give even an idea of the extent and complexity of the procedures currently used in nuclear medicine, such as image processing, reconstruction from projections and artificial intelligence. These disciplines do not belong to nuclear medicine: they are already branches of engineering, and my interest will reside simply in revealing a little of the elegance and the fantastic potential of these new "allies" of nuclear medicine. In this review the mathematics of physiological interpretation and methodology are considered together in the same section. General aspects of data-processing methods, including image processing and artificial intelligence, are briefly analysed. The mathematical tools that are most often used to assist the interpretation of biological phenomena in nuclear medicine are considered; these include convolution and deconvolution methods, Fourier analysis, factorial analysis and neural networking.