Kinetic parameter estimation from renal measurements with a three-headed SPECT system: a simulation study

Fast direct estimation of the blood input function and myocardial time activity curve from dynamic SPECT projections via reduction in spatial and temporal dimensions

PURPOSE

Reconstruction of parametric images from dynamic single photon emission computed tomography (SPECT) data acquired with slow rotating cameras is a challenge because the estimation of the time-activity curves (TACs) may involve fitting data to an inconsistent underdetermined system of equations. This work presents a novel algorithm for the estimation of the blood input function and myocardial TAC with high accuracy and high efficiency directly from these projections.

METHODS

In the proposed dynamic reconstruction method, the information from the segmentation of functional regions from the static reconstructed image was used as a prior to construct a sparse matrix, through which the spatial distribution of the radioactive tracer was represented. Then the temporal distribution of the radioactive tracer was modeled by nonuniform B-spline basis functions which were determined according to a new selection rule. With reduction in both the spatial and temporal dimensions of the reconstructed image, the blood input function and myocardial TAC were estimated using the 4D maximum likelihood expectation maximization algorithm. The method was validated using data from both digital phantom simulations and an experimental rat study.

RESULTS

Compared with the conventional dynamic SPECT reconstruction method without the reduction in spatial dimensions, the proposed method provides more accurate TACs with less computation time in both phantom simulation studies and a rat experimental study.

CONCLUSIONS

The proposed method is promising in both providing more accurate time-activity curves and reducing the computation time, which makes it practical for small animal studies using clinical systems with slow rotating cameras.

Direct estimation of kinetic parametric images for dynamic PET

Dynamic positron emission tomography (PET) can monitor spatiotemporal distribution of radiotracer in vivo. The spatiotemporal information can be used to estimate parametric images of radiotracer kinetics that are of physiological and biochemical interests. Direct estimation of parametric images from raw projection data allows accurate noise modeling and has been shown to offer better image quality than conventional indirect methods, which reconstruct a sequence of PET images first and then perform tracer kinetic modeling pixel-by-pixel. Direct reconstruction of parametric images has gained increasing interests with the advances in computing hardware. Many direct reconstruction algorithms have been developed for different kinetic models. In this paper we review the recent progress in the development of direct reconstruction algorithms for parametric image estimation. Algorithms for linear and nonlinear kinetic models are described and their properties are discussed.

An optimization transfer algorithm for nonlinear parametric image reconstruction from dynamic PET data

Direct reconstruction of kinetic parameters from raw projection data is a challenging task in molecular imaging using dynamic positron emission tomography (PET). This paper presents a new optimization transfer algorithm for penalized likelihood direct reconstruction of nonlinear parametric images that is easy to use and has a fast convergence rate. Each iteration of the proposed algorithm can be implemented in three simple steps: a frame-by-frame maximum likelihood expectation-maximization (EM)-like image update, a frame-by-frame image smoothing, and a pixel-by-pixel time activity curve fitting. Computer simulation shows that the direct algorithm can achieve a better bias-variance performance than the indirect reconstruction algorithm. The convergence rate of the new algorithm is substantially faster than our previous algorithm that is based on a separable paraboloidal surrogate function. The proposed algorithm has been applied to real 4-D PET data.

Dynamic single photon emission computed tomography--basic principles and cardiac applications

The very nature of nuclear medicine, the visual representation of injected radiopharmaceuticals, implies imaging of dynamic processes such as the uptake and wash-out of radiotracers from body organs. For years, nuclear medicine has been touted as the modality of choice for evaluating function in health and disease. This evaluation is greatly enhanced using single photon emission computed tomography (SPECT), which permits three-dimensional (3D) visualization of tracer distributions in the body. However, to fully realize the potential of the technique requires the imaging of in vivo dynamic processes of flow and metabolism. Tissue motion and deformation must also be addressed. Absolute quantification of these dynamic processes in the body has the potential to improve diagnosis. This paper presents a review of advancements toward the realization of the potential of dynamic SPECT imaging and a brief history of the development of the instrumentation. A major portion of the paper is devoted to the review of special data processing methods that have been developed for extracting kinetics from dynamic cardiac SPECT data acquired using rotating detector heads that move as radiopharmaceuticals exchange between biological compartments. Recent developments in multi-resolution spatiotemporal methods enable one to estimate kinetic parameters of compartment models of dynamic processes using data acquired from a single camera head with slow gantry rotation. The estimation of kinetic parameters directly from projection measurements improves bias and variance over the conventional method of first reconstructing 3D dynamic images, generating time-activity curves from selected regions of interest and then estimating the kinetic parameters from the generated time-activity curves. Although the potential applications of SPECT for imaging dynamic processes have not been fully realized in the clinic, it is hoped that this review illuminates the potential of SPECT for dynamic imaging, especially in light of new developments that enable measurement of dynamic processes directly from projection measurements.

Acceleration of the direct reconstruction of linear parametric images using nested algorithms

Parametric imaging using dynamic positron emission tomography (PET) provides important information for biological research and clinical diagnosis. Indirect and direct methods have been developed for reconstructing linear parametric images from dynamic PET data. Indirect methods are relatively simple and easy to implement because the image reconstruction and kinetic modeling are performed in two separate steps. Direct methods estimate parametric images directly from raw PET data and are statistically more efficient. However, the convergence rate of direct algorithms can be slow due to the coupling between the reconstruction and kinetic modeling. Here we present two fast gradient-type algorithms for direct reconstruction of linear parametric images. The new algorithms decouple the reconstruction and linear parametric modeling at each iteration by employing the principle of optimization transfer. Convergence speed is accelerated by running more sub-iterations of linear parametric estimation because the computation cost of the linear parametric modeling is much less than that of the image reconstruction. Computer simulation studies demonstrated that the new algorithms converge much faster than the traditional expectation maximization (EM) and the preconditioned conjugate gradient algorithms for dynamic PET.

Generalized algorithms for direct reconstruction of parametric images from dynamic PET data

Indirect and direct methods have been developed for reconstructing parametric images from dynamic positron emission tomography (PET) data. Indirect methods are simple and easy to implement because reconstruction and kinetic modeling are performed in two separate steps. Direct methods estimate parametric images directly from dynamic PET sinograms and, in theory, can be statistically more efficient, but the algorithms are often difficult to implement and are very specific to the kinetic model being used. This paper presents a class of generalized algorithms for direct reconstruction of parametric images that are relatively easy to implement and can be adapted to different kinetic models. The proposed algorithms use optimization transfer principle to convert the maximization of a penalized likelihood into a pixel-wise weighted least squares (WLS) kinetic fitting problem at each iteration. Thus, it can employ existing WLS algorithms developed for kinetic models. The proposed algorithms resemble the empirical iterative implementation of the indirect approach, but converge to a solution of the direct formulation. Computer simulations showed that the proposed direct reconstruction algorithms are flexible and achieve a better bias-variance tradeoff than indirect reconstruction methods.

Global Compartmental Pharmacokinetic Models for Spatiotemporal SPECT and PET Imaging

A new mathematical framework is introduced for combining the linear compartmental models used in pharmacokinetics with the spatiotemporal distributions of activity that are measured in single photon emission computed tomography (SPECT) and PET imaging. This approach is global in the sense that the compartmental differential equations involve only the overall spatially integrated activity in each compartment. The kinetics for the local compartmental activities are not specified by the model and would be determined from data. It is shown that an increase in information about the spatial distribution of the local compartmental activities leads to an increase in the number of identifiable quantities associated with the compartmental matrix. These identifiable quantities, which are important kinetic parameters in applications, are determined by computing the invariants of a symmetry group. This group generates the space of compartmental matrices that are compatible with a given activity distribution, input function, and set of support constraints. An example is provided where all of the compartmental spatial supports have been separated, except that of the vascular compartment. The question of estimating the identifiable parameters from SPECT and PET data is also discussed.

A direct ROI quantification method for inherent PVE correction: accuracy assessment in striatal SPECT measurements

PURPOSE

The clinical potential of striatal imaging with dopamine transporter (DAT) SPECT tracers is hampered by the limited capability to recover activity concentration ratios due to partial volume effects (PVE). We evaluated the accuracy of a least squares method that allows retrieval of activity in regions of interest directly from projections (LS-ROI).

METHODS

An Alderson striatal phantom was filled with striatal to background ratios of 6:1, 9:1 and 28:1; the striatal and background ROIs were drawn on a coregistered X-ray CT of the phantom. The activity ratios of these ROIs were derived both with the LS-ROI method and with conventional SPECT EM reconstruction (EM-SPECT). Moreover, the two methods were compared in seven patients with motor symptoms who were examined with N-3-fluoropropyl-2-beta-carboxymethoxy-3-beta-(4-iodophenyl) (FP-CIT) SPECT, calculating the binding potential (BP).

RESULTS

In the phantom study, the activity ratios obtained with EM-SPECT were 3.5, 5.3 and 17.0, respectively, whereas the LS-ROI method resulted in ratios of 6.2, 9.0 and 27.3, respectively. With the LS-ROI method, the BP in the seven patients was approximately 60% higher than with EM-SPECT; a linear correlation between the LS-ROI and the EM estimates was found (r=0.98, p=0.03).

CONCLUSION

The LS-ROI PVE correction capability is mainly due to the fact that the ill-conditioning of the LS-ROI approach is lower than that of the EM-SPECT one. The LS-ROI seems to be feasible and accurate in the examination of the dopaminergic system. This approach can be fruitful in monitoring of disease progression and in clinical trials of dopaminergic drugs.

Evaluation of (123)I-orthoiodohippurate single kidney clearance rate by renal sequential scintigraphy in a large cohort of likely normal subjects aged between 0 and 18 years

PURPOSE

Age-related values of (123)I-orthoiodohippurate (OIH) single kidney clearance rate (Cl) were estimated in a large cohort of likely normal children aged between 0 and 18 years.

METHODS

Among 4,111 children examined in the past 10 years, 917 were selected with the following inclusion criteria: (a) mild ultrasonographic hydronephrosis with right differential renal function (DRF) <53% and >47% (498 pts), (b) known or suspected urinary tract infection with normal ultrasound, serum creatinine and DMSA and DRF <53% and >47% (419 pts). (123)I-OIH-Cl was assessed using a validated gamma camera method. Children were divided into 21 age classes: from 0 to 2 years, eight 3-month classes; from 2 to 14 years, twelve 1-year classes; from 14 to 18 years, one 4-year class.

RESULTS

Cl, plotted against age, was fitted using an increasing function (y=a-be-cx). Mean (123)I-OIH-Cl of 1,834 kidneys was 306+/-22 ml/min/1.73 m(2) BSA. Mean (123)I-OIH-Cl of the right and left kidneys was 307+/-23 and 305+/-22 ml/min/1.73 m(2) BSA, respectively (p<0.002). The best-fitting (123)I-OIH-Cl growing function was: Cl=311-230e-0.69xAge (months). (123)I-OIH-Cl improved progressively starting from birth, reaching 96% and 98% of the mature value at 1 and 1.5 years, respectively. (123)I-OIH-Cl at birth (age=0) was 81 ml/min/1.73 m(2) BSA. After 18.6 days of life, the renal function had doubled its starting value, and it reached a plateau of 311 ml/min/1.73 m(2) BSA at 2 years.

CONCLUSION

This work represents a systematic evaluation of ERPF by a gamma camera method in a large cohort of selected likely normal paediatric subjects.

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.