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PubMed2005

The validation of a pesticide exposure algorithm using biological monitoring results.

A pesticide exposure algorithm was developed to calculate pesticide exposure intensity scores based on responses to questions about pesticide handling procedures and application methods in a self-administered questionnaire. The validity of the algorithm was evaluated through comparison of the algorithm scores with biological monitoring data from a study of 126 pesticide applicators who applied the herbicides MCPA or 2,4-D. The variability in the algorithm scores calculated for these applicators was due primarily to differences in their use of personal protective equipment (PPE). Rubber gloves were worn by 75% of applicators when mixing and 22% when applying pesticides, rubber boots were worn by 33% when mixing and 23% when applying, and goggles were worn by 33% and 17% of applicators when mixing and when applying, respectively. Only 2% of applicators wore all three types of PPE when both mixing and applying, and 15% wore none of these three types of PPE when either mixing or applying. Substantial variability was also observed in the concentrations of pesticides detected in the post application urine samples. The concentration of MCPA detected in urine samples collected on the second day after the application ranged from less than < 1.0 to 610 microg/L among 84 of the applicators who applied MCPA. The concentrations of 2,4-D detected in the urine samples ranged from less than < 1.0 to 514 microg/L among 41 of the applicators who applied 2,4-D. When categorized into three groups based on the algorithm scores, the geometric mean in the highest exposure group was 20 microg/L compared with 5 microg/L in the lowest exposure group for the MCPA applicators, and 29 microg/L in highest exposure group compared with 2 microg/L in the low exposure group for the 2,4-D applicators. A regression analysis detected statistically significant trends in the geometric mean of the urine concentrations across the exposure categories for both the 2,4-D and the MCPA applicators. The algorithm scores, based primarily on the use of PPE, appear to provide a reasonably valid measure of exposure intensity for these applicators, however, further studies are needed to generalize these results to other types of pesticides and application methods.

2,4-Dichlorophenoxyacetic Acid↗

PubMed1989

A three-dimensional electron pencil-beam algorithm.

We describe the implementation of a three-dimensional electron-dose algorithm based on a Gaussian pencil-beam model. The algorithm calculates dose to an arbitrarily distributed set of points in a heterogeneous volume. Multiple non-coplanar beams can be positioned relative to the volume. The algorithm consists of three basic components: (i) the transport of a pencil-beam through a heterogeneous volume, (ii) the evaluation of the pencil-beam fluence at a given depth in the volume in the presence of irregular fields, and (iii) the matching of points in the volume receiving a significant fluence contribution from a pencil-beam at a given depth in the volume and the calculation of dose to those points. An efficient point-matching algorithm reduces the computation time to the level of conventional two-dimensional implementations. The algorithm uses an optimised subdivision for irregular fields, and accurately predicts output factors for irregular fields placed between the final collimators and the patient. We show comparisons between the new algorithm and conventional two-dimensional calculations using measurements and calculations for finite heterogeneities, irregular fields and output factors.

Algorithms↗

PubMed1994

A performance study of 3D reconstruction algorithms for positron emission tomography.

This paper investigates the statistical and systematic accuracy of five three-dimensional reconstruction algorithms for multi-ring PET scanners operated without septa: the reprojection method, the direct Fourier reconstruction, the FAVOR algorithm, and the single-slice and multi-slice rebinning algorithms. Simulated data of a uniform cylinder, of Gaussian sources, and of spherical sources are used to compare respectively the noise properties, the modulation transfer function, and the recovery coefficients of the algorithms. Brain scans reconstructed with the different algorithms are compared by calculating the linear regression of the mean values within regions of interest. The most significant observations are a slight loss of transaxial resolution with the reprojection algorithm in the external slices of the scanner, and increased noise in the images reconstructed using multi-slice rebinning.

Algorithms↗

PubMed1994

Implementation of an accelerated iterative algorithm for cone-beam SPECT.

In this paper we describe the implementation of an accelerated iterative reconstruction algorithm (AIRA) for cone-beam (CB) projections using a single circular orbit in single-photon-emission computed tomography (SPECT). This algorithm is a modified maximum-likelihood-expectation-maximization (ML-EM) algorithm and several approaches have been used to accelerate the reconstruction process. These approaches include: (i) the use of ordered subsets; (ii) the use of active areas and volumes; and (iii) the storing in memory of the transition vector for a given ray (during the forward projection step). This algorithm, which compensates for collimator geometric sensitivity variation as a function of position and makes uniform attenuation corrections has been evaluated using experimentally acquired phantom data. The results demonstrate a two-orders-of-magnitude decrease of the computational time of this algorithm over the conventional ML-EM algorithm with similar convergence properties.

Algorithms↗

PubMed1995

A filtered backprojection algorithm for axial head motion correction in fan-beam SPECT.

In this study we present an approximate, but practical, three-dimensional filtered backprojection (FBP) reconstruction algorithm in fan-beam SPECT to correct for axial motion (both translation and rotation). A one-dimensional filter kernel was applied to the projections. It is assumed that the object is rigid and that its axial motion can be characterized by three components: one-dimensional translation and yaw and pitch rotations. It is further assumed that the motions that have occurred during the SPECT acquisition have been determined separately. The determined angular-view-dependent translation/rotation parameters were incorporated into the proposed FBP algorithm to correct for multiple axial head motions. The proposed axial head motion correction algorithm was evaluated using simulated three-dimensional Hoffman brain phantom data. Projections both with axial translation and with axial rotation, and with their combinations were generated. Images of a Hoffman brain phantom reconstructed using the proposed FBP algorithm and the conventional FBP algorithm were compared. Artefacts were observed in images without motion correction, but the artefacts were greatly reduced using the proposed reconstruction algorithm.

Algorithms↗

PubMed1995

A filtered-backprojection algorithm for fan-beam SPECT which corrects for patient motion.

In this study we have derived a filtered-backprojection (FBP) reconstruction algorithm for fan-beam SPECT that eliminates artifacts associated with patient motion during brain imaging. It is assumed that the patient motion is known or can be measured separately, and that the head is rigid. The in-plane translation and rotation were studied and were incorporated into the proposed FBP reconstruction algorithm. Angular-dependent translation/rotation parameters were used to correct for multiple motions that could occur during a scan. The proposed FBP reconstruction algorithm was evaluated using Monte Carlo simulated phantom data, including a two-point-source phantom and the Hoffman brain phantom. Projections with translation, rotation and their combinations were generated, and images reconstructed using the proposed algorithm and the standard FBP algorithm were compared. Artifacts were observed in images without the motion correction, but the artifacts were eliminated or greatly reduced using the proposed reconstruction algorithm.

Algorithms↗

PubMed1997

Noise analysis of MAP-EM algorithms for emission tomography.

The ability to theoretically model the propagation of photon noise through PET and SPECT tomographic reconstruction algorithms is crucial in evaluating the reconstructed image quality as a function of parameters of the algorithm. In a previous approach for the important case of the iterative ML-EM (maximum-likelihood-expectation-maximization) algorithm, judicious linearizations were used to model theoretically the propagation of a mean image and a covariance matrix from one iteration to the next. Our analysis extends this approach to the case of MAP (maximum a posteriori)-EM algorithms, where the EM approach incorporates prior terms. We analyse in detail two cases: a MAP-EM algorithm incorporating an independent gamma prior, and a one-step-late (OSL) version of a MAP-EM algorithm incorporating a multivariate Gaussian prior, for which familiar smoothing priors are special cases. To validate our theoretical analyses, we use a Monte Carlo methodology to compare, at each iteration, theoretical estimates of mean and covariance with sample estimates, and show that the theory works well in practical situations where the noise and bias in the reconstructed images do not assume extreme values.

Algorithms↗

PubMed1998

Execution times of five reconstruction algorithms in 3D positron emission tomography.

Various analytical, iterative and rebinning algorithms have been proposed for 3D reconstruction in positron emission tomography. This paper examines execution times of five analytical and rebinning algorithms. Meaningful comparisons are obtained by using similar software modules in all implementations. Reconstruction times are shown to differ by vast amounts: the Favor algorithm of Defrise et al is more than twice as fast as the widely used reprojection algorithm of Kinahan and Rogers; the Fourier rebinning algorithm (Fore) recently developed by Defrise is more than 15 times faster than the reprojection algorithm.

Algorithms↗

PubMed2001

Comparative behaviour of the dynamically penalized likelihood algorithm in inverse radiation therapy planning.

This paper presents a description of tests carried out to compare the behaviour of five algorithms in inverse radiation therapy planning: (1) The Dynamically Penalized Likelihood (DPL), an algorithm based on statistical estimation theory; (2) an accelerated version of the same algorithm: (3) a new fast adaptive simulated annealing (ASA) algorithm; (4) a conjugate gradient method; and (5) a Newton gradient method. A three-dimensional mathematical phantom and two clinical cases have been studied in detail. The phantom consisted of a U-shaped tumour with a partially enclosed 'spinal cord'. The clinical examples were a cavernous sinus meningioma and a prostate case. The algorithms have been tested in carefully selected and controlled conditions so as to ensure fairness in the assessment of results. It has been found that all five methods can yield relatively similar optimizations, except when a very demanding optimization is carried out. For the easier cases. the differences are principally in robustness, ease of use and optimization speed. In the more demanding case, there are significant differences in the resulting dose distributions. The accelerated DPL emerges as possibly the algorithm of choice for clinical practice. An appendix describes the differences in behaviour between the new ASA method and the one based on a patent by the Nomos Corporation.

Algorithms↗

PubMed2001

Rebinning-based algorithms for helical cone-beam CT.

Several image reconstruction algorithms based on rebinning have been proposed recently for helical cone-beam CT. These algorithms separate the 3D reconstruction into a set of independent 2D reconstructions for a set of surfaces: planar or non-planar surfaces are defined and then reconstructed using 2D filtered backprojection from a 2D fan-beam or parallel-beam set of data estimated from the cone-beam (CB) measurements. The first part of this paper presents a unified derivation of rebinning algorithms for planar and non-planar surfaces. An integral equation is derived for the surface allowing the best rebinning and an iterative algorithm converging to the solution of that equation is given. The second part presents an efficient method to correct the residual reconstruction artefacts observed with rebinning algorithms when the cone-angle is too large for the required accuracy. This correction algorithm involves a CB backprojection and the reconstruction time is slightly longer than for the zero-boundary (ZB) method.

Algorithms↗

PubMed2002

Multiobjective anatomy-based dose optimization for HDR-brachytherapy with constraint free deterministic algorithms.

In high dose rate (HDR) brachytherapy, conventional dose optimization algorithms consider multiple objectives in the form of an aggregate function that transforms the multiobjective problem into a single-objective problem. As a result, there is a loss of information on the available alternative possible solutions. This method assumes that the treatment planner exactly understands the correlation between competing objectives and knows the physical constraints. This knowledge is provided by the Pareto trade-off set obtained by single-objective optimization algorithms with a repeated optimization with different importance vectors. A mapping technique avoids non-feasible solutions with negative dwell weights and allows the use of constraint free gradient-based deterministic algorithms. We compare various such algorithms and methods which could improve their performance. This finally allows us to generate a large number of solutions in a few minutes. We use objectives expressed in terms of dose variances obtained from a few hundred sampling points in the planning target volume (PTV) and in organs at risk (OAR). We compare two- to four-dimensional Pareto fronts obtained with the deterministic algorithms and with a fast-simulated annealing algorithm. For PTV-based objectives, due to the convex objective functions, the obtained solutions are global optimal. If OARs are included, then the solutions found are also global optimal, although local minima may be present as suggested.

Algorithms↗

PubMed2003

Global convergence analysis of fast multiobjective gradient-based dose optimization algorithms for high-dose-rate brachytherapy.

We consider the problem of the global convergence of gradient-based optimization algorithms for interstitial high-dose-rate (HDR) brachytherapy dose optimization using variance-based objectives. Possible local minima could lead to only sub-optimal solutions. We perform a configuration space analysis using a representative set of the entire non-dominated solution space. A set of three prostate implants is used in this study. We compare the results obtained by conjugate gradient algorithms, two variable metric algorithms and fast-simulated annealing. For the variable metric algorithm BFGS from numerical recipes, large fluctuations are observed. The limited memory L-BFGS algorithm and the conjugate gradient algorithm FRPR are globally convergent. Local minima or degenerate states are not observed. We study the possibility of obtaining a representative set of non-dominated solutions using optimal solution rearrangement and a warm start mechanism. For the surface and volume dose variance and their derivatives, a method is proposed which significantly reduces the number of required operations. The optimization time, ignoring a preprocessing step, is independent of the number of sampling points in the planning target volume. Multiobjective dose optimization in HDR brachytherapy using L-BFGS and a new modified computation method for the objectives and derivatives has been accelerated, depending on the number of sampling points, by a factor in the range 10-100.

Algorithms↗

PubMed2004

Weighted FBP--a simple approximate 3D FBP algorithm for multislice spiral CT with good dose usage for arbitrary pitch.

A new 3D reconstruction scheme, weighted filtered backprojection (WFBP) for multirow spiral CT based on an extension of the two-dimensional SMPR algorithm is described and results are presented. In contrast to other 3D algorithms available, the algorithm makes use of all available data for all pitch values. The algorithm is a FBP algorithm: linear convolution of the parallel data along the row direction followed by a 3D backprojection. Data usage for arbitrary pitch values is maintained through a weighting scheme which takes into account redundant data. If proper row weighting is applied, the image quality is superior to the image quality of the SMPR algorithm.

Algorithms↗

PubMed2004

A unified analysis of FBP-based algorithms in helical cone-beam and circular cone- and fan-beam scans.

A circular scanning trajectory is and will likely remain a popular choice of trajectory in computed tomography (CT) imaging because it is easy to implement and control. Filtered-backprojection (FBP)-based algorithms have been developed previously for approximate and exact reconstruction of the entire image or a region of interest within the image in circular cone-beam and fan-beam cases. Recently, we have developed a 3D FBP-based algorithm for image reconstruction on PI-line segments in a helical cone-beam scan. In this work, we demonstrated that the 3D FBP-based algorithm indeed provided a rather general formulation for image reconstruction from divergent projections (such as cone-beam and fan-beam projections). On the basis of this formulation we derived new approximate or exact algorithms for image reconstruction in circular cone-beam or fan-beam scans, which can be interpreted as special cases of the helical scan. Existing algorithms corresponding to the derived algorithms were identified. We also performed a preliminary numerical study to verify our theoretical results in each of the cases. The results in the work can readily be generalized to other non-circular trajectories.

Algorithms↗

PubMed2005

A particle swarm optimization algorithm for beam angle selection in intensity-modulated radiotherapy planning.

Automatic beam angle selection is an important but challenging problem for intensity-modulated radiation therapy (IMRT) planning. Though many efforts have been made, it is still not very satisfactory in clinical IMRT practice because of overextensive computation of the inverse problem. In this paper, a new technique named BASPSO (Beam Angle Selection with a Particle Swarm Optimization algorithm) is presented to improve the efficiency of the beam angle optimization problem. Originally developed as a tool for simulating social behaviour, the particle swarm optimization (PSO) algorithm is a relatively new population-based evolutionary optimization technique first introduced by Kennedy and Eberhart in 1995. In the proposed BASPSO, the beam angles are optimized using PSO by treating each beam configuration as a particle (individual), and the beam intensity maps for each beam configuration are optimized using the conjugate gradient (CG) algorithm. These two optimization processes are implemented iteratively. The performance of each individual is evaluated by a fitness value calculated with a physical objective function. A population of these individuals is evolved by cooperation and competition among the individuals themselves through generations. The optimization results of a simulated case with known optimal beam angles and two clinical cases (a prostate case and a head-and-neck case) show that PSO is valid and efficient and can speed up the beam angle optimization process. Furthermore, the performance comparisons based on the preliminary results indicate that, as a whole, the PSO-based algorithm seems to outperform, or at least compete with, the GA-based algorithm in computation time and robustness. In conclusion, the reported work suggested that the introduced PSO algorithm could act as a new promising solution to the beam angle optimization problem and potentially other optimization problems in IMRT, though further studies need to be investigated.

Algorithms↗

PubMed2005

Reassessing the clinical efficacy of two MR quantitative DSC PWI CBF algorithms following cross-calibration with PET images.

Clinical cerebral blood flow (CBF) maps generated through dynamic- susceptibility contrast (DSC) magnetic resonance (MR) perfusion imaging are currently cross-calibrated with PET studies. The cross-calibration is achieved by rescaling the MR CBF values so that normal white matter CBF corresponds to 22 ml/100 g/min. Examples are provided in this paper to show how this rescaling procedure changes both the clinical interpretation of CBF maps and the manner by which the performance of a given deconvolution algorithm should be assessed. (i) Singular-value decomposition-based (SVD) algorithms produce absolute CBF estimates that are inherently under-estimated for all tissue mean transit times (MTT) but, after rescaling, will generate CBF maps that are over-estimated for MTT >4.8 s. (ii) In principle, frequency-domain modelling techniques are expected to be inherently less sensitive to contrast recirculation biases than the time-domain SVD algorithms. However, it is shown that both CBF algorithms become greatly less sensitive to distortions from recirculation after clinical cross-calibration through rescaling has been performed. It is concluded that, when rescaling procedures are employed, it is relatively more important to develop deconvolution algorithms that produce CBF estimates with accuracies that vary little with MTT than to produce algorithms that provide inherently more accurate CBF estimates, but whose relative accuracy varies significantly with MTT.

Algorithms↗

PubMed2006

A shift-invariant filtered backprojection (FBP) cone-beam reconstruction algorithm for the source trajectory of two concentric circles using an equal weighting scheme.

In this paper, a shift-invariant filtered backprojection cone-beam image reconstruction algorithm is derived, based upon Katsevich's general inversion scheme, and validated for the source trajectory of two concentric circles. The source trajectory is complete according to Tuy's data sufficiency condition and is used as the basis for an exact image reconstruction algorithm. The algorithm proceeds according to the following steps. First, differentiate the cone-beam projection data with respect to the detector coordinates and with respect to the source trajectory parameter. The data are then separately filtered along three different orientations in the detector plane with a shift-invariant Hilbert kernel. Eight different filtration groups are obtained via linear combinations of weighted filtered data. Voxel-based backprojection is then carried out from eight sets of view angles, where separate filtered data are backprojected from each set according to the backprojection sets' associated filtration group. The algorithm is first derived for a scanning configuration consisting of two concentric and orthogonal circles. By performing an affine transformation on the image object, the developed image reconstruction algorithm has been generalized to the case where the two concentric circles are not orthogonal. Numerical simulations are presented to validate the reconstruction algorithm and demonstrate the dose advantage of the equal weighting scheme.

Algorithms↗

PubMed2005

Convergence study of an accelerated ML-EM algorithm using bigger step size.

In SPECT/PET, the maximum-likelihood expectation-maximization (ML-EM) algorithm is getting more attention as the speed of computers increases. This is because it can incorporate various physical aspects into the reconstruction process leading to a more accurate reconstruction than other analytical methods such as filtered-backprojection algorithms. However, the convergence rate of the ML-EM algorithm is very slow. Several methods have been developed to speed it up, such as the ordered-subset expectation-maximization (OS-EM) algorithm. Even though OS-type algorithms can bring about significant acceleration in the iterative reconstruction, it is generally believed that ML-EM produces better images, in terms of statistical noise in the reconstruction. In this paper, we present an accelerated ML-EM algorithm with bigger step size and show its convergence characteristics in terms of variance noise and log-likelihood values. We also show some advantages of our method over other accelerating methods using additive forms.

Algorithms↗