Generalized linear least squares method for fast generation of myocardial blood flow parametric images with N-13 ammonia PET

Assessment of Lesion Detectability in Dynamic Whole-Body PET Imaging Using Compartmental and Patlak Parametric Mapping

PURPOSE

Hybrid dynamic imaging allows not only the estimation of whole-body (WB) macroparametric maps but also the estimation of microparameters in the initial bed position targeting the blood pool region containing the pathology owing to the limited axial field of view of PET scanners. In this work, we assessed the capability of multipass WB F-FDG PET parametric imaging in terms of lesion detectability through qualitative and quantitative evaluation of simulation and clinical studies.

METHODS

Simulation studies were conducted by generating data incorporating 3 liver and 3 lung lesions produced by 3 noise levels and 20 noise realizations for each noise level to estimate bias and lesion detection features. The total scan time for the clinical studies of 8 patients addressed for lung and liver lesions staging, including dynamic and static WB imaging, lasted 80 minutes. An in-house-developed MATLAB code was utilized to derive the microparametric and macroparametric maps. We compared lesion detectability and different image-derived PET metrics including the SUVs, Patlak-derived influx rate constant (Ki) and distribution volume (V) and K1, k2, k3, blood volume (bv) microparameters, and Ki estimated using the generalized linear least square approach.

RESULTS

In total, 104 lesions were detected, among which 47 were located in the targeted blood pool bed position where all quantitative parameters were calculated, thus enabling comparative analysis across all parameters. The evaluation encompassed visual interpretation performed by an expert nuclear medicine specialist and quantitative analysis. High correlation coefficients were observed between SUVmax and Kimax derived from the generalized linear least square approach, as well as Ki generated by Patlak graphical analysis. Moreover, 3 contrast-enhanced CT-proven malignant lesions located in the liver and a biopsy-proven malignant liver lesion not visible on static SUV images and Patlak maps were clearly pinpointed on K1 and k2 maps.

CONCLUSIONS

Our results demonstrate that full compartmental modeling for the region containing the pathology has the potential of providing complementary information and, in some cases, more accurate diagnosis than conventional static SUV imaging, favorably comparing to Patlak graphical analysis.

Multimodality quantitative assessments of myocardial perfusion using dynamic contrast enhanced magnetic resonance and 15O-labelled water positron emission tomography imaging

Kinetic modelling of myocardial perfusion imaging data allows the absolute quantification of myocardial blood flow (MBF) and can improve the diagnosis and clinical assessment of coronary artery disease (CAD). Positron emission tomography (PET) imaging is considered the reference standard technique for absolute quantification, whilst oxygen-15 (¹⁵O)-water has been extensively implemented for MBF quantification. Dynamic contrast enhanced magnetic resonance imaging (DCE-MRI) has also been used for MBF quantification and showed comparable diagnostic performance against (¹⁵O)-water PET studies. We investigated for the first time the diagnostic performance of two different PET MBF analysis softwares PMOD and Carimas, for obstructive CAD detection against invasive clinical standard methods in 20 patients with known or suspected CAD. Fermi and distributed parameter modelling-derived MBF quantification from DCE-MRI was also compared against (¹⁵O)-water PET, in a subgroup of 6 patients. The sensitivity and specificity for PMOD was significantly superior for obstructive CAD detection in both per vessel (0.83, 0.90) and per patient (0.86, 0.75) analysis, against Carimas (0.75, 0.65), (0.81, 0.70), respectively. We showed strong, significant correlations between MR and PET MBF quantifications (r=0.83-0.92). However, DP and PMOD analysis demonstrated comparable and higher haemodynamic differences between obstructive versus (no, minor or non)-obstructive CAD, against Fermi and Carimas analysis. Our MR method assessments against the optimum PET reference standard technique for perfusion analysis showed promising results in per segment level and can support further multi-modality assessments in larger patient cohorts. Further MR against PET assessments may help to determine their comparative diagnostic performance for obstructive CAD detection.

Comparative evaluation of the algorithms for parametric mapping of the novel myocardial PET imaging agent 18F-FPTP

Objective

(¹⁸F-fluoropentyl)triphenylphosphonium salt (¹⁸F-FPTP) is a new promising myocardial PET imaging tracer. It shows high accumulation in cardiomyocytes and rapid clearance from liver. We performed compartmental analysis of ¹⁸F-FPTP PET images in rat and evaluated two linear analyses: linear least-squares (LLS) and a basis function method (BFM) for generating parametric images. The minimum dynamic scan duration for kinetic analysis was also investigated and computer simulation undertaken.

Methods

¹⁸F-FPTP dynamic PET (18 min) and CT images were acquired from rats with myocardial infarction (MI) (n = 12). Regions of interest (ROIs) were on the left ventricle, normal myocardium, and MI region. Two-compartment (K₁ and k₂; 2C2P) and three-compartment (K₁–k₃; 3C3P) models with irreversible uptake were compared for goodness-of-fit. Partial volume and spillover correction terms (V_a and α = 1 − V_a) were also incorporated. LLS and BFM were applied to ROI- and voxel-based kinetic parameter estimations. Results were compared with the standard ROI-based nonlinear least-squares (NLS) results of the corresponding compartment model. A simulation explored statistical properties of the estimation methods.

Results

The 2C2P model was most suitable for describing ¹⁸F-FPTP kinetics. Average K₁, k₂, and V_a values were, respectively, 6.8 (ml/min/g), 1.1 (min⁻¹), and 0.44 in normal myocardium and 1.4 (ml/min/g), 1.1 (min⁻¹), and 0.32, in MI tissue. Ten minutes of data was sufficient for the estimation. LLS and BFM estimations correlated well with NLS values for the ROI level (K₁: y = 1.06x + 0.13, r² = 0.96 and y = 1.13x + 0.08, r² = 0.97) and voxel level (K₁: y = 1.22x − 0.30, r² = 0.90 and y = 1.26x + 0.00, r² = 0.92). Regional distribution of kinetic parametric images (αK₁, K₁, k₂, V_a) was physiologically relevant. LLS and BFM showed more robust characteristics than NLS in the simulation.

Conclusions

Fast kinetics and highly specific uptake of ¹⁸F-FPTP by myocardium enabled quantitative analysis with the 2C2P model using only the initial 10 min of data. LLS and BFM were feasible for estimating voxel-wise parameters. These two methods will be useful for quantitative evaluation of ¹⁸F-FPTP distribution in myocardium and in further studies with different conditions, disease models, and species.

Electronic supplementary material

The online version of this article (doi:10.1007/s12149-017-1171-6) contains supplementary material, which is available to authorized users.

Postreconstruction filtering of 3D PET images by using weighted higher-order singular value decomposition

Background

Positron emission tomography (PET) always suffers from high levels of noise due to the constraints of the injected dose and acquisition time, especially in the studies of dynamic PET imaging. To improve the quality of PET image, several approaches have been introduced to suppress noise. However, traditional filters often blur the image edges, or erase small detail, or rely on multiple parameters. In order to solve such problems, nonlocal denoising methods have been adapted to denoise PET images.

Methods

In this paper, we propose to use the weighted higher-order singular value decomposition for PET image denoising. We first modeled the noise in the PET image as Poisson distribution. Then, we transformed the noise to an additive Gaussian noise by use of the anscombe root transformation. Finally, we denoised the transformed image using the proposed higher-order singular value decomposition (HOSVD)-based algorithms. The denoised results were compared with results from some general filters by performing physical phantom and mice studies.

Results

Compared to other commonly used filters, HOSVD-based denoising algorithms can preserve boundaries and quantitative accuracy better. The spatial resolution and the low activity features in PET image also can be preserved by use of HOSVD-based methods. Comparing with the standard HOSVD-based algorithm, the proposed weighted HOSVD algorithm can suppress the stair-step artifact, and the time-consumption is about half of that needed by the Wiener-augmented HOSVD algorithm.

Conclusions

The proposed weighted HOSVD denoising algorithm can suppress noise while better preserving of boundary and quantity in PET images.

Electronic supplementary material

The online version of this article (doi:10.1186/s12938-016-0221-y) contains supplementary material, which is available to authorized users.

Federated optimisation of kinetic analysis problems

Positron Emission Tomography (PET) data is intrinsically dynamic, and kinetic analysis of dynamic PET data can substantially augment the information provided by static PET reconstructions. Yet despite the insights into disease that kinetic analysis offers, it is not used clinically and seldom used in research beyond the preclinical stage. The utility of PET kinetic analysis is hampered by several factors including spatial inconsistency within regions of homogeneous tissue and relative computational expense when fitting complex models to individual voxels. Even with sophisticated algorithms inconsistencies can arise because local optima frequently have narrow basins of convergence, are surrounded by relatively flat (uninformative) regions, have relatively low-gradient valley floors, or combinations thereof. Based on the observation that cost functions for individual voxels frequently bear some resemblance to each-other, this paper proposes the federated optimisation of the individual kinetic analysis problems within a given image. This approach shares parameters proposed during optimisation with other, similar voxels. Federated optimisation exploits the redundancy typical of large medical images to improve the optimisation residuals, computational efficiency and, to a limited extent, image consistency. This is achieved without restricting the formulation of the kinetic model, resorting to an explicit regularisation parameter, or limiting the resolution at which parameters are computed.

Fitting the two-compartment model in DCE-MRI by linear inversion

PURPOSE

Model fitting of dynamic contrast-enhanced-magnetic resonance imaging-MRI data with nonlinear least squares (NLLS) methods is slow and may be biased by the choice of initial values. The aim of this study was to develop and evaluate a linear least squares (LLS) method to fit the two-compartment exchange and -filtration models.

METHODS

A second-order linear differential equation for the measured concentrations was derived where model parameters act as coefficients. Simulations of normal and pathological data were performed to determine calculation time, accuracy and precision under different noise levels and temporal resolutions. Performance of the LLS was evaluated by comparison against the NLLS.

RESULTS

The LLS method is about 200 times faster, which reduces the calculation times for a 256 × 256 MR slice from 9 min to 3 s. For ideal data with low noise and high temporal resolution the LLS and NLLS were equally accurate and precise. The LLS was more accurate and precise than the NLLS at low temporal resolution, but less accurate at high noise levels.

CONCLUSION

The data show that the LLS leads to a significant reduction in calculation times, and more reliable results at low noise levels. At higher noise levels the LLS becomes exceedingly inaccurate compared to the NLLS, but this may be improved using a suitable weighting strategy. Magn Reson Med 76:998-1006, 2016. © 2015 Wiley Periodicals, Inc.

Quality and precision of parametric images created from PET sinogram data by direct reconstruction: proof of concept

We have previously implemented the direct reconstruction of dense kinetic model parameter images ("parametric images") from sinogram data, and compared it to conventional image domain kinetic parameter estimation methods . Although it has been shown that the direct reconstruction algorithm estimates the kinetic model parameters with lower root mean squared error than the conventional image domain techniques, some theoretical obstacles remain. These obstacles include the difficulty of evaluating the accuracy and precision of the estimated parameters. In image domain techniques, the reconstructed time activity curve (TAC) and the model predicted TAC are compared, and the goodness-of-fit is evaluated as a measure of the accuracy and precision of the estimated parameters. This approach cannot be applied to the direct reconstruction technique as there are no reconstructed TACs. In this paper, we propose ways of evaluating the precision and goodness-of-fit of the kinetic model parameters estimated by the direct reconstruction algorithm. Specifically, precision of the estimates requires the calculation of variance images for each parameter, and goodness-of-fit is addressed by reconstructing the difference between the measured and the fitted sinograms. We demonstrate that backprojecting the difference from sinogram space to image space creates error images that can be examined for goodness-of-fit and model selection purposes. The presence of nonrandom structures in the error images may indicate an inadequacy of the kinetic model that has been incorporated into the direct reconstruction algorithm. We introduce three types of goodness-of-fit images. We propose and demonstrate a number-of-runs image as a means of quantifying the adequacy or deficiency of the model. We further propose and demonstrate images of the F statistic and the change in the Akaike Information Criterion as devices for identifying the statistical advantage of one model over another at each voxel. As direct reconstruction to parametric images proliferates, it will be essential for imagers to adopt methods such as those proposed herein to assess the accuracy and precision of their parametric images.

Fourier domain closed-form formulas for estimation of kinetic parameters in reversible multi-compartment models

Background

Compared with static imaging, dynamic emission computed tomographic imaging with compartment modeling can quantify in vivo physiologic processes, providing useful information about molecular disease processes. Dynamic imaging involves estimation of kinetic rate parameters. For multi-compartment models, kinetic parameter estimation can be computationally demanding and problematic with local minima.

Methods

This paper offers a new perspective to the compartment model fitting problem where Fourier linear system theory is applied to derive closed-form formulas for estimating kinetic parameters for the two-compartment model. The proposed Fourier domain estimation method provides a unique solution, and offers very different noise response as compared to traditional non-linear chi-squared minimization techniques.

Results

The unique feature of the proposed Fourier domain method is that only low frequency components are used for kinetic parameter estimation, where the DC (i.e., the zero frequency) component in the data is treated as the most important information, and high frequency components that tend to be corrupted by statistical noise are discarded. Computer simulations show that the proposed method is robust without having to specify the initial condition. The resultant solution can be fine tuned using the traditional iterative method.

Conclusions

The proposed Fourier-domain estimation method has closed-form formulas. The proposed Fourier-domain curve-fitting method does not require an initial condition, it minimizes a quadratic objective function and a closed-form solution can be obtained. The noise is easier to control, simply by discarding the high frequency components, and emphasizing the DC component.

Kinetic parameter estimation using a closed-form expression via integration by parts

Dynamic emission computed tomographic imaging with compartment modeling can quantify in vivo physiologic processes, eliciting more information regarding underlying molecular disease processes than is obtained from static imaging. However, estimation of kinetic rate parameters for multi-compartment models can be computationally demanding and problematic due to local minima. A number of techniques for kinetic parameter estimation have been studied and are in use today, generally offering a tradeoff between computation time, robustness of fit and flexibility with differing sets of assumptions. This paper presents a means to eliminate all differential operations by using the integration-by-parts method to provide closed-form formulas, so that the mathematical model is less sensitive to data sampling and noise. A family of closed-form formulas are obtained. Computer simulations show that the proposed method is robust without having to specify the initial condition.

Computation of variance in compartment model parameter estimates from dynamic PET data

PURPOSE

This paper investigates the validity of the analytical framework for variance ("analytical variance") in kinetic parameter and macroparameter estimations. Analytical variance is compared against the variance obtained from Monte Carlo simulations ("MC variance") for two different compartment models at different noise levels.

METHODS

Kinetic parameters for one-tissue (1T) and two-tissue (2T) compartment models are used to generate time-activity curves (TAC). Gaussian noise is added to the noiseless TAC to generate noise realizations for each noise level. The kinetic parameters are then estimated by minimizing the weighted squared error between the noisy TAC and the model output. Standard deviation is computed statistically from the estimated parameters and computed analytically using the framework at each noise level. The ratio of standard deviation to true parameter value obtained from Monte Carlo simulations and analytical computations is compared.

RESULTS

Difference between the analytical and MC variance increases with the level of noise and complexity of the compartment model. The standard deviation of the analytical variance also increases with the noise-level and model complexity. The difference between the analytical and MC variance is less than 3% for 1T compartment model and less than 10% for 2T compartment model at all noise levels. In addition, the standard deviation in the analytical variance is less than 15% for 1T and 2T compartment models at all noise levels.

CONCLUSIONS

These results indicate that the proposed framework for the variance in the kinetic parameter estimations can be used for 1T and 2T compartment models even in the existence of high noise.

FDG-PET parametric imaging by total variation minimization

Parametric imaging of the cerebral metabolic rate for glucose (CMRGlc) using [(18)F]-fluoro deoxyglucose positron emission tomography is considered. Traditional imaging is hindered due to low signal-to-noise ratios at individual voxels. We propose to minimize the total variation of the tracer uptake rates while requiring good fit of traditional Patlak equations. This minimization guarantees spatial homogeneity within brain regions and good distinction between brain regions. Brain phantom simulations demonstrate significant improvement in quality of images by the proposed method as compared to Patlak images with post-filtering using Gaussian or median filters.

Constructing reliable parametric images using enhanced GLLS for dynamic SPECT

The generalized linear least square (GLLS) method can successfully construct unbiased parametric images from dynamic positron emission tomography data. Quantitative dynamic single photon emission computed tomography (SPECT) also has the potential to generate physiological parametric images. However, the high level of noise, intrinsic in SPECT, can give rise to unsuccessful voxelwise fitting using GLLS, resulting in physiologically meaningless estimates. In this paper, we systematically investigated the applicability of our recently proposed approaches to improve the reliability of GLLS to parametric image generation from noisy dynamic SPECT data. The proposed approaches include use of a prior estimate of distribution volume (V(d)), a bootstrap Monte Carlo (BMC) resampling technique, as well as a combination of both techniques. Full Monte Carlo simulations were performed to generate dynamic projection data, which were then reconstructed with and without resolution recovery, before generating parametric images with the proposed methods. Four experimental clinical datasets were also included in the analysis. The GLLS methods incorporating BMC resampling could successfully and reliably generate parametric images. For high signal-to-noise ratio (SNR) imaging data, the BMC-aided GLLS provided the best estimates of K(1) , while the BMC-V(d)-aided GLLS proved superior for estimating V(d). The improvement in reliability gained with BMC-aided GLLS in low SNR image data came at the expense of some overestimation of V(d) and increased computation time.

Fast and reliable estimation of multiple parametric images using an integrated method for dynamic SPECT

Dynamic single photon emission computed tomography (SPECT) has demonstrated the potential to quantitatively estimate physiological parameters in the brain and the heart. The generalized linear least square (GLLS) method is a well-established method for solving linear compartment models with fast computational speed. However, the high level of noise intrinsic in the SPECT data leads to reliability and instability problems of GLLS for generating parametric images. An integrated method is proposed to restrict the noise in both the temporal and spatial domains to estimate multiple parametric images for dynamic SPECT. This method comprises three steps which are optimum image sampling schedule in the projection space, cluster analysis applied postreconstruction and parametric image generation with GLLS. The simulation and experimental studies for the neuronal nicotine acetylcholine receptor tracer of 5-[123I]-iodo-A-85380 were employed to evaluate the performance of the proposed method. The results of influx rate of K1 and volume of distribution of Vd demonstrated that the integrated method was successful in generating low noise parametric images for high noise SPECT data without enhancing the partial volume effect. Furthermore, the integrated method is computationally efficient for potential clinical applications.

Parametric image of myocardial blood flow generated from dynamic H2(15)O PET using factor analysis and cluster analysis

Algorithm-based parametric imaging of myocardial blood flow (MBF), as measured by H2(15)O PET, has been the goal of many research efforts. A method for generating parametric images of regional MBF by factor and cluster analysis on H2(15)O dynamic myocardial PET was validated by its comparison with gold-standard MBF values determined invasively using radiolabelled microspheres. Right and left ventricular blood pool activities and their factor images were obtained by the application of factor analysis to dynamic frames. By subtraction of the factor images multiplied by their corresponding values on the factors from the original dynamic images for each frame, pure tissue dynamic images were obtained, from which arterial blood activities were excluded. Cluster analysis that averaged pixels having time-activity curves with the same shape was applied to pure tissue images to generate parametric MBF images. The usefulness of this method for quantifying regional MBF was evaluated using canine experiment data. H2(15)O PET scans and microsphere studies were performed on seven dogs at rest and after pharmacological stress. The image qualities and the contrast of parametric images obtained using the proposed method were significantly improved over either the tissue factor images or the parametric images obtained using a conventional method. Regional MBFs obtained using the proposed method correlated well with those obtained by the region of interest method (r = 0.94) and by the microsphere technique (r = 0.90). A non-invasive method is presented for generating parametric images of MBF from H2(15)O PET, using factor and cluster analysis.

Enhanced parameter estimation with GLLS and the Bootstrap Monte Carlo method for dynamic SPECT

The generalized linear least squares (GLLS) method has been shown to successfully construct unbiased parametric images from dynamic positron emission tomography (PET). However, the high level of noise intrinsic in single photon emission computed tomography (SPECT) can give rise to unsuccessful voxel-wise fitting using GLLS, resulting in physiologically meaningless estimates, such as negative kinetic parameters for compartment models. In this study, three approaches were investigated to improve the reliability of GLLS applied to dynamic SPECT data. The simulation and experimental results showed that GLLS with the aid of Bootstrap Monte Carlo method proved successful in generating parametric images and preserving all of the major advantages of all the originally GLLS method, although at the expense of increased computation time.

Fast parametric imaging algorithm for dual-input biomedical system parameter estimation

Medical parametric imaging with dynamic positron emission tomography (PET) plays an increasingly potential role in modern biomedical research and clinical diagnosis. The key issue in parametric imaging is to estimate parameters based on sampled data at the pixel-by-pixel level from certain dynamic processes described by valid mathematical models. Classic nonlinear least squares (NLS) algorithm requires a "good" initial guess and the computational time-complexity is high, which is impractical for image-wide parameter estimation. Although a variety of fast parametric imaging techniques have been developed, most of them focus on single input systems, which do not provide an optimal solution for dual-input biomedical system parameter estimation, which is the case of liver metabolism. In this study, a dual-input-generalized linear least squares (D-I-GLLS) algorithm was proposed to identify the model parameters including the parameter in the dual-input function. Monte Carlo simulation was conducted to examine this novel fast algorithm. The results of the quantitative analysis suggested that the proposed technique could provide comparable reliability of the parameter estimation with NLS fitting and accurately identify the parameter in the dual-input function. This method may be potentially applicable to other dual-input biomedical system parameter estimation as well.

Evaluation of Basis Function and Linear Least Squares Methods for Generating Parametric Blood Flow Images Using 15O-Water and Positron Emission Tomography

PURPOSE

Parametric analysis of (15)O-water positron emission tomography (PET) studies allows determination of blood flow (BF), perfusable tissue fraction (PTF), and volume of distribution (V (d)) with high spatial resolution. In this paper the performance of basis function and linear least squares methods for generating parametric flow data were evaluated.

PROCEDURES

Monte Carlo simulations were performed using typical perfusion values for brain, tumor, and heart. Clinical evaluation was performed using seven cerebral and 10 myocardial (15)O-water PET studies. Basis function (BFM), linear least squares (LLS), and generalized linear least squares (GLLS) methods were used to calculate BF, PTF, or V(d).

RESULTS

Monte Carlo simulations and human studies showed that, for low BF values (<1 ml/min(-1)ml(-1), BF, PTF, and V(d) were calculated with accuracies better than 5% for all methods tested. For high BF (>2 ml/min(-1)ml(-1)), use of BFM provided more accurate V(d) compared with (G)LLS.

CONCLUSIONS

In general, BFM provided the most accurate estimates of BF, PTF, and V(d).

Direct reconstruction of kinetic parameter images from dynamic PET data

Our goal in this paper is the estimation of kinetic model parameters for each voxel corresponding to a dense three-dimensional (3-D) positron emission tomography (PET) image. Typically, the activity images are first reconstructed from PET sinogram frames at each measurement time, and then the kinetic parameters are estimated by fitting a model to the reconstructed time-activity response of each voxel. However, this "indirect" approach to kinetic parameter estimation tends to reduce signal-to-noise ratio (SNR) because of the requirement that the sinogram data be divided into individual time frames. In 1985, Carson and Lange proposed, but did not implement, a method based on the expectation-maximization (EM) algorithm for direct parametric reconstruction. The approach is "direct" because it estimates the optimal kinetic parameters directly from the sinogram data, without an intermediate reconstruction step. However, direct voxel-wise parametric reconstruction remained a challenge due to the unsolved complexities of inversion and spatial regularization. In this paper, we demonstrate and evaluate a new and efficient method for direct voxel-wise reconstruction of kinetic parameter images using all frames of the PET data. The direct parametric image reconstruction is formulated in a Bayesian framework, and uses the parametric iterative coordinate descent (PICD) algorithm to solve the resulting optimization problem. The PICD algorithm is computationally efficient and is implemented with spatial regularization in the domain of the physiologically relevant parameters. Our experimental simulations of a rat head imaged in a working small animal scanner indicate that direct parametric reconstruction can substantially reduce root-mean-squared error (RMSE) in the estimation of kinetic parameters, as compared to indirect methods, without appreciably increasing computation.

Statistical assessment of regional time-density measurement of myocardial perfusion

RATIONALE AND OBJECTIVES

The measurement of time-density relationships of the myocardium in studies of magnetic resonance perfusion images is a clinical technique used in assessing myocardial perfusion. This article presents a new technique, allowing regional time-density measurement and display of myocardial perfusion with improved accuracy compared with traditional manual trace techniques. Moreover, a method using statistical methods to discriminate relative decreased perfusion regions that differ significantly from the normally perfused myocardial tissue is introduced.

MATERIALS AND METHODS

Human datasets were obtained using a 1.5 T Signa Echospeed system (GE Medical Systems, Milwaukee, WI). The perfusion sequence was a 2D cardiac-gated fast gradient echo sequence with echo train readout, generating an in-plane pixel size of 1.46 mm2. Seven 10-mm-thick contiguous short axis tomographic slice images were obtained during a prolonged single breathhold. Data was collected at 30 time phases per slice image level during passage of 20 cc gadolinium contrast injected at a rate of 4-5 cc/sec into an antecubital vein.

RESULTS

Dilution properties can be determined and displayed as color-encoded regions superimposed on the myocardial slice according to the area of interest. Time-density curves throughout the perfusion study can be generated. Moreover, displays of normal and decreased perfusion areas can be used as statistically enhanced diagnosis guides.

CONCLUSION

This measurement, display, and diagnosis technique adds diagnostically important information to previous measurement and visualization techniques, providing enhanced detection and quantitative evaluation of regional deficits in myocardial contractility and perfusion, providing improved reliability and reproducibility of clinical diagnoses from MR-perfusion data.

Linear regression with spatial constraint to generate parametric images of ligand-receptor dynamic PET studies with a simplified reference tissue model

For the quantitative analysis of ligand-receptor dynamic positron emission tomography (PET) studies, it is often desirable to apply reference tissue methods that eliminate the need for arterial blood sampling. A common technique is to apply a simplified reference tissue model (SRTM). Applications of this method are generally based on an analytical solution of the SRTM equation with parameters estimated by nonlinear regression. In this study, we derive, based on the same assumptions used to derive the SRTM, a new set of operational equations of integral form with parameters directly estimated by conventional weighted linear regression (WLR). In addition, a linear regression with spatial constraint (LRSC) algorithm is developed for parametric imaging to reduce the effects of high noise levels in pixel time activity curves that are typical of PET dynamic data. For comparison, conventional weighted nonlinear regression with the Marquardt algorithm (WNLRM) and nonlinear ridge regression with spatial constraint (NLRRSC) were also implemented using the nonlinear analytical solution of the SRTM equation. In contrast to the other three methods, LRSC reduces the percent root mean square error of the estimated parameters, especially at higher noise levels. For estimation of binding potential (BP), WLR and LRSC show similar variance even at high noise levels, but LRSC yields a smaller bias. Results from human studies demonstrate that LRSC produces high-quality parametric images. The variance of R(1) and k(2) images generated by WLR, WNLRM, and NLRRSC can be decreased 30%-60% by using LRSC. The quality of the BP images generated by WLR and LRSC is visually comparable, and the variance of BP images generated by WNLRM can be reduced 10%-40% by WLR or LRSC. The BP estimates obtained using WLR are 3%-5% lower than those estimated by LRSC. We conclude that the new linear equations yield a reliable, computationally efficient, and robust LRSC algorithm to generate parametric images of ligand-receptor dynamic PET studies.

Generalized linear least squares algorithms for modeling glucose metabolism in the human brain with corrections for vascular effects

The generalized linear least squares (GLLS) algorithm has been found useful in image-wide parameter estimation for the generation of parametric images with positron emission tomography (PET) as it is computationally efficient and statistically reliable. However, the original algorithm was designed for parameter estimation with non-uniformly sampled instantaneous measurements. When dynamic PET data are sampled with the optimal image sampling schedule (OISS) to reduce memory and storage space, only a few temporal image frames are recorded. As a result, the direct application of GLLS is no longer appropriate. In this paper, we extend the GLLS algorithm to a five parameter model for the study of human brain metabolism, which accounts for the effect of cerebral blood volume (CBV), using OISS sampled data, with as few as five temporal samples. The formulation for this new GLLS algorithm is developed, and its computational efficiency and statistical reliability are investigated and validated using computer simulations and clinical PET [18F]-2-fluoro-2-deoxy-D-glucose (FDG) data.

Improved parametric image generation using spatial-temporal analysis of dynamic PET studies

The value of parametric images that represent both spatial distribution and quantification of the physiological parameters of tracer kinetics has long been recognized. However, the inherent high noise level of pixel kinetics of dynamic PET makes it unsuitable to generate parametric images of the microparameters of tracer kinetic model by conventional weighted nonlinear least squares (WNLS) fitting. Based on the concept that both spatial and temporal information should be integrated to improve parametric image quality, a nonlinear ridge regression with spatial constraint (NLRRSC) parametric imaging algorithm was proposed in this study. For NLRRSC, a term that penalizes local spatial variation of parameters was added to the cost function of WNLS fitting. The initial estimates and spatial constraint were estimated by component representation model (CRM) with cluster analysis. A hierarchical cluster with average linkage method was used to extract components. The ridge parameter was determined by linear ridge regression theory at each iteration, and a modified Gauss-Newton algorithm was used for minimizing the cost function. Results from a computer simulation showed that the percent mean square error of estimates obtained by NLRRSC can be decreased by 60-80% compared to that of WNLS. The parametric images estimated by NLRRSC are significantly better than the ones generated by WNLS. A highly correlated linear relationship was found between the ROI values calculated from the microparametric images generated by NLRRSC and estimates from ROI kinetic fitting. NLRRSC provided a reliable estimate of glucose metabolite uptake rate with a comparable image quality compared to Patlak analysis. In conclusion, NLRRSC is a reliable and robust parametric imaging algorithm for dynamic PET studies.

Fast formation of statistically reliable FDG parametric images based on clustering and principal components

Formation of parametric images requires voxel-by-voxel estimation of rate constants, a process sensitive to noise and computationally demanding. A model-based clustering method for a two-parameter model (CAKS) was extended to the FDG three-parameter model. The concept was to average voxels with similar kinetic signatures to reduce noise. Voxel kinetics were categorized by the first two principal components of the tissue time-activity curves for all voxels. k2 and k3 were estimated cluster-by-cluster, and K1 was estimated voxel-by-voxel within clusters. When CAKS was applied to simulated images with noise levels similar to brain FDG scans, estimation bias was well suppressed, and estimation errors were substantially smaller--1.3 times for Ki and 1.5 times for k3-than those of conventional voxel-based estimation. The statistical reliability of voxel-level estimation by CAKS was comparable with ROI analysis including 100 voxels. CAKS was applied to clinical cases with Alzheimer's disease (ALZ) and cortico basal degeneration (CBD). In ALZ, the affected regions had low Ki (K1k3/(k2 +k3)) and k3. In CBD, Ki was low, but k3 was preserved. These results were consistent with ROI-based kinetic analysis. Because CAKS decreased the number of invoked estimations, the calculation time was reduced substantially. In conclusion, CAKS has been extended to allow parametric imaging of a three-compartment model. The method is computationally efficient. with low bias and excellent noise properties.

Information technology applications in biomedical functional imaging

In parallel with rapid advances in computer technology, biomedical functional imaging is having an ever-increasing impact on healthcare. Functional imaging allows us to see dynamic processes quantitatively in the living human body. However, as we need to deal with four-dimensional time-varying images, space requirements and computational complexity are extremely high. This makes information management, processing, and communication difficult. Using the minimum amount of data to represent the required information, developing fast algorithms to process the data, organizing the data in such a way as to facilitate information management, and extracting the maximum amount of useful information from the recorded data have become important research tasks in biomedical information technology. For the last ten years, the Biomedical and Multimedia Information Technology (BMIT) Group and, recently, the Center for Multimedia Signal Processing have conducted systematic studies on these topics. Some of the results relating to functional imaging data acquisition, compression, storage, management, processing, modeling, and simulation are briefly reported in this paper.

Linear least squares compartmental-model-independent parameter identification in PET

A simplified approach involving linear-regression straight-line parameter fitting of dynamic scan data is developed for both specific and nonspecific models. Where compartmental-model topologies apply, the measured activity may be expressed in terms of: its integrals, plasma activity and plasma integrals--all in a linear expression with macroparameters as coefficients. Multiple linear regression, as in spreadsheet software, determines parameters for best data fits. Positron emission tomography (PET)-acquired gray-matter images in a dynamic scan are analyzed: both by this method and by traditional iterative nonlinear least squares. Both patient and simulated data were used. Regression and traditional methods are in expected agreement. Monte-Carlo simulations evaluate parameter standard deviations, due to data noise, and much smaller noise-induced biases. Unique straight-line graphical displays permit visualizing data influences on various macroparameters as changes in slopes. Advantages of regression fitting are: simplicity, speed, ease of implementation in spreadsheet software, avoiding risks of convergence failures or false solutions in iterative least squares, and providing various visualizations of the uptake process by straight line graphical displays. Multiparameter model-independent analyses on lesser understood systems is also made possible.