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PubMed2005

An FDK-like cone-beam SPECT reconstruction algorithm for non-uniform attenuated projections acquired using a circular trajectory.

In this paper, Novikov's inversion formula of the attenuated two-dimensional (2D) Radon transform is applied to the reconstruction of attenuated fan-beam projections acquired with equal detector spacing and of attenuated cone-beam projections acquired with a flat planar detector and circular trajectory. The derivation of the fan-beam algorithm is obtained by transformation from parallel-beam coordinates to fan-beam coordinates. The cone-beam reconstruction algorithm is an extension of the fan-beam reconstruction algorithm using Feldkamp-Davis-Kress's (FDK) method. Computer simulations indicate that the algorithm is efficient and is accurate in reconstructing slices close to the central slice of the cone-beam orbit plane. When the attenuation map is set to zero the implementation is equivalent to the FDK method. Reconstructed images are also shown for noise corrupted projections.

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PubMed2005

A pencil beam algorithm for intensity modulated proton therapy derived from Monte Carlo simulations.

A pencil beam algorithm as a component of an optimization algorithm for intensity modulated proton therapy (IMPT) is presented. The pencil beam algorithm is tuned to the special accuracy requirements of IMPT, where in heterogeneous geometries both the position and distortion of the Bragg peak and the lateral scatter pose problems which are amplified by the spot weight optimization. Heterogeneity corrections are implemented by a multiple raytracing approach using fluence-weighted sub-spots. In order to derive nuclear interaction corrections, Monte Carlo simulations were performed. The contribution of long ranged products of nuclear interactions is taken into account by a fit to the Monte Carlo results. Energy-dependent stopping power ratios are also implemented. Scatter in optional beam line accessories such as range shifters or ripple filters is taken into account. The collimator can also be included, but without additional scattering. Finally, dose distributions are benchmarked against Monte Carlo simulations, showing 3%/1 mm agreement for simple heterogeneous phantoms. In the case of more complicated phantoms, principal shortcomings of pencil beam algorithms are evident. The influence of these effects on IMPT dose distributions is shown in clinical examples.

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PubMed2005

Weighted expectation maximization reconstruction algorithms with application to gated megavoltage tomography.

We propose and investigate weighted expectation maximization (EM) algorithms for image reconstruction in x-ray tomography. The development of the algorithms is motivated by the respiratory-gated megavoltage tomography problem, in which the acquired asymmetric cone-beam projections are limited in number and unevenly sampled over view angle. In these cases, images reconstructed by use of the conventional EM algorithm can contain ring- and streak-like artefacts that are attributable to a combination of data inconsistencies and truncation of the projection data. By use of computer-simulated and clinical gated fan-beam megavoltage projection data, we demonstrate that the proposed weighted EM algorithms effectively mitigate such image artefacts.

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PubMed2005

The influence of beam model differences in the comparison of dose calculation algorithms for lung cancer treatment planning.

In this study, we show that beam model differences play an important role in the comparison of does calculated with various algorithms for lung cancer treatment planning. These differences may impact the accurate correlation of dose with clinical outcome. To accomplish this, we modified the beam model penumbral parameters in an equivalent path length (EPL) algorithm and subsequently compared the EPL doses with those generated with Monte Carlo (MC). A single AP beam was used for beam fitting. Two different beam models were generated for EPL calculations: (1) initial beam model (init_fit) and (2) optimized beam model (best_fit) , with parameters optimized to produce the best agreement with MC calculated profiles at several depths in a water phantom. For the 6 MV, AP beam, EPL(init_fit) calculations were on average within 2%/2 mm (1.4 mm max.) agreement with MC; the agreement for EPL(best_fit) was 2%/1.0 mm (1.3 mm max.) for EPL(best_fit). Treatment planning was performed using a realistic lung phantom using 6 and 15 MV photons. In all homogeneous phantom plans, EPL(best_fit) calculations were in better agreement with MC. In the heterogeneous 6 MV plan, differences between EPL(best_fit and init_fit) and MC were significant for the tumour. The EPL(init_fit), unlike the EPL(best_fit) calculation, showed large differences in the lung relative to MC. For the 15 MV heterogeneous plan, clinically important differences were found between EPL(best_fit or init_fit) and MC for tumour and lung, suggesting that the algorithmic difference in inhomogeneous cases, differences between EPL(best_fit) and MC for lung tissues were smaller compared to those between EPL(init_fit) and MC. Although the extent to which beam model differences impact the dose comparisons will be dependent upon beam parameters (orientation, field size and energy), and the size and location of the tumour, this study shows that failing to correctly account for beam model differences will lead to biased comparisons between dose algorithms. This may ultimately hinder our ability to accurately correlate dose with clinical outcome.

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PubMed2005

Minimum data image reconstruction algorithms with shift-invariant filtering for helical, cone-beam CT.

We derive accurate and efficient reconstruction algorithms for helical, cone-beam CT that employ shift-invariant filtering. Specifically, a new backprojection-filtration algorithm is developed, and a minimum data filtered-backprojection algorithm is derived. These reconstruction algorithms with shift-invariant filtering can accept data with transverse truncation, and hence allow for minimum data image reconstruction.

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PubMed2006

Accuracy of device-specific 2D and 3D image distortion correction algorithms for magnetic resonance imaging of the head provided by a manufacturer.

For the application of magnetic resonance imaging (MRI) in precision radiotherapy, image distortions must be reduced to a minimum to maintain geometrical accuracy. Recently, two-dimensional (2D) and three-dimensional (3D) algorithms for MRI-device-specific distortion corrections were developed by the manufacturers of MRI devices. A previously developed phantom (Karger C P et al 2003 Phys. Med. Biol. 48 211-21) was used to quantify and assess the size of geometrical image distortions before and after application of the 2D and 3D correction algorithm in the head region. Four different types of MRI devices with different gradient systems were measured. For comparison, measurements were also performed with two computed tomography (CT) devices. Mean distortions of up to 4.6+/-1.4 mm (maximum: 5.8 mm) were found prior to the correction. After the correction, the mean distortions were well below 2.0 mm in most cases. Distortions in the CT images were below or equal to 1.0 mm on average. Generally, the 3D algorithm produced comparable or better results than the 2D algorithm. The remaining distortions after the correction appear to be acceptable for fractionated radiotherapy.

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PubMed2006

A combination-weighted Feldkamp-based reconstruction algorithm for cone-beam CT.

The combination-weighted Feldkamp algorithm (CW-FDK) was developed and tested in a phantom in order to reduce cone-beam artefacts and enhance cranio-caudal reconstruction coverage in an attempt to improve image quality when utilizing cone-beam computed tomography (CBCT). Using a 256-slice cone-beam CT (256CBCT), image quality (CT-number uniformity and geometrical accuracy) was quantitatively evaluated in phantom and clinical studies, and the results were compared to those obtained with the original Feldkamp algorithm. A clinical study was done in lung cancer patients under breath holding and free breathing. Image quality for the original Feldkamp algorithm is degraded at the edge of the scan region due to the missing volume, commensurate with the cranio-caudal distance between the reconstruction and central planes. The CW-FDK extended the reconstruction coverage to equal the scan coverage and improved reconstruction accuracy, unaffected by the cranio-caudal distance. The extended reconstruction coverage with good image quality provided by the CW-FDK will be clinically investigated for improving diagnostic and radiotherapy applications. In addition, this algorithm can also be adapted for use in relatively wide cone-angle CBCT such as with a flat-panel detector CBCT.

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PubMed2006

An enhanced block matching algorithm for fast elastic registration in adaptive radiotherapy.

Image registration has many medical applications in diagnosis, therapy planning and therapy. Especially for time-adaptive radiotherapy, an efficient and accurate elastic registration of images acquired for treatment planning, and at the time of the actual treatment, is highly desirable. Therefore, we developed a fully automatic and fast block matching algorithm which identifies a set of anatomical landmarks in a 3D CT dataset and relocates them in another CT dataset by maximization of local correlation coefficients in the frequency domain. To transform the complete dataset, a smooth interpolation between the landmarks is calculated by modified thin-plate splines with local impact. The concept of the algorithm allows separate processing of image discontinuities like temporally changing air cavities in the intestinal track or rectum. The result is a fully transformed 3D planning dataset (planning CT as well as delineations of tumour and organs at risk) to a verification CT, allowing evaluation and, if necessary, changes of the treatment plan based on the current patient anatomy without time-consuming manual re-contouring. Typically the total calculation time is less than 5 min, which allows the use of the registration tool between acquiring the verification images and delivering the dose fraction for online corrections. We present verifications of the algorithm for five different patient datasets with different tumour locations (prostate, paraspinal and head-and-neck) by comparing the results with manually selected landmarks, visual assessment and consistency testing. It turns out that the mean error of the registration is better than the voxel resolution (2 x 2 x 3 mm(3)). In conclusion, we present an algorithm for fully automatic elastic image registration that is precise and fast enough for online corrections in an adaptive fractionated radiation treatment course.

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PubMed2006

An analytical algorithm for skew-slit collimator SPECT with uniform attenuation correction.

To replace the conventional pinhole (normal cone-beam) collimator, a novel skew-slit collimator was previously proposed and a Novikov-type algorithm developed to reconstruct images using the skew-slit geometry. The goal of this paper is to develop a reconstruction algorithm that has better noise control than the Novikov-type algorithm. The new algorithm is able to compensate for uniform attenuation, and computer simulation results show that reconstructed images are less noisy.

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PubMed2006

Dosimetric validation of the anisotropic analytical algorithm for photon dose calculation: fundamental characterization in water.

In July 2005 a new algorithm was released by Varian Medical Systems for the Eclipse planning system and installed in our institute. It is the anisotropic analytical algorithm (AAA) for photon dose calculations, a convolution/superposition model for the first time implemented in a Varian planning system. It was therefore necessary to perform validation studies at different levels with a wide investigation approach. To validate the basic performances of the AAA, a detailed analysis of data computed by the AAA configuration algorithm was carried out and data were compared against measurements. To better appraise the performance of AAA and the capability of its configuration to tailor machine-specific characteristics, data obtained from the pencil beam convolution (PBC) algorithm implemented in Eclipse were also added in the comparison. Since the purpose of the paper is to address the basic performances of the AAA and of its configuration procedures, only data relative to measurements in water will be reported. Validation was carried out for three beams: 6 MV and 15 MV from a Clinac 2100C/D and 6 MV from a Clinac 6EX. Generally AAA calculations reproduced very well measured data, and small deviations were observed, on average, for all the quantities investigated for open and wedged fields. In particular, percentage depth-dose curves showed on average differences between calculation and measurement smaller than 1% or 1 mm, and computed profiles in the flattened region matched measurements with deviations smaller than 1% for all beams, field sizes, depths and wedges. Percentage differences in output factors were observed as small as 1% on average (with a range smaller than +/-2%) for all conditions. Additional tests were carried out for enhanced dynamic wedges with results comparable to previous results. The basic dosimetric validation of the AAA was therefore considered satisfactory.

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PubMed2006

A virtual-accelerator-based verification of a Monte Carlo dose calculation algorithm for electron beam treatment planning in homogeneous phantoms.

By introducing Monte Carlo (MC) techniques to the verification procedure of dose calculation algorithms in treatment planning systems (TPSs), problems associated with conventional measurements can be avoided and properties that are considered unmeasurable can be studied. The aim of the study is to implement a virtual accelerator, based on MC simulations, to evaluate the performance of a dose calculation algorithm for electron beams in a commercial TPS. The TPS algorithm is MC based and the virtual accelerator is used to study the accuracy of the algorithm in water phantoms. The basic test of the implementation of the virtual accelerator is successful for 6 and 12 MeV (gamma < 1.0, 0.02 Gy/2 mm). For 18 MeV, there are problems in the profile data for some of the applicators, where the TPS underestimates the dose. For fields equipped with patient-specific inserts, the agreement is generally good. The exception is 6 MeV where there are slightly larger deviations. The concept of the virtual accelerator is shown to be feasible and has the potential to be a powerful tool for vendors and users.

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PubMed2004

The spatial resolution improvement of EIT images by GVSPM-FOCUSS algorithm.

The focal underdetermined system solver (FOCUSS) algorithm is a recursive algorithm to find the localized energy solution. It is an initialization-dependent algorithm. The generalized vector sample pattern matching (GVSPM) method has been applied to solve the inverse problem of electrical impedance tomography (EIT) and obtain smooth reconstructed images. By combining the GVSPM solution as the initial estimation of the FOCUSS algorithm, an idea termed the GVSPM-FOCUSS method is presented in this paper to improve the spatial resolution and precision of localization for EIT images. The comparisons are carried out between the EIT images reconstructed with the GVSPM-FOCUSS method and the GVSPM method alone. The effectiveness is verified by simulated and tank data for a model of a two-dimensional homogeneous circular disk.

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PubMed2005

Spatial resolution improvement of 3D EIT images by the shrinking sLORETA-FOCUSS algorithm.

This paper describes the use of the shrinking sLORETA-FOCUSS algorithm to improve the spatial resolution of three-dimensional (3D) EIT images. Conventional EIT yields inaccurate, low spatial resolution images, due to noise, the low sensitivity of boundary voltages to inner conductivity perturbations and a limited number of boundary voltage measurements. The focal underdetermined system solver (FOCUSS) algorithm produces a localized energy solution based on the weighted minimum-norm least-squares (MNLS) solution. It was successfully applied for the spatial resolution improvement of EIT images of simulated and tank data for a 2D homogeneous circular disc. However, due to the fact that a 3D mesh system contains many more elements, much more memory is required to store the weighting matrix. In order to extend the work to 3D, the shrinking-FOCUSS method is utilized to shrink the solution space as well as the weighting matrix in each iteration step. The solution of the standardized low resolution electromagnetic tomography algorithm (sLORETA) is adopted as the initial estimate of the shrinking-FOCUSS. The effectiveness is verified by implementing the new algorithm on tank data for a three-dimensional homogeneous sphere.

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PubMed2005

A template matching algorithm for sperm tracking and classification.

The conventional assessment of human semen, especially sperm movement characteristics, is a highly subjective assessment, with considerable intra- and inter-technician variability. Computer-assisted sperm analysis (CASA) systems provide a rapid and automated assessment of the parameters of sperm motion, together with improved standardization and quality control. However, it should be noted that the measurement of the sperm head motion by CASA is sensitive to the technique of experimentation. While conventional CASA systems use digital microscopes with phase-contrast accessories that make the sperm's head appear brighter and sharper than the other parts, in this research, a regular light microscope was used with a digital camera directly attached to its eyepiece. One of the drawbacks of this method is that the images lack proper contrast and sharpness. To remedy this, we have proposed an algorithm for sperm tracking that is insensitive to image acquisition conditions. This tracking algorithm was used after the background and extra particles were successfully removed through a two-step enhancement algorithm. Additionally, in this research, a template matching method was used for finding the sperm's path. Upon examination, it was proven that our tracking algorithm worked well with different image acquisition conditions. This paper explains how this method reduces error probability in finding and tracking sperm in various frames.

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PubMedDate not supplied

A greedy algorithm for aligning DNA sequences.

For aligning DNA sequences that differ only by sequencing errors, or by equivalent errors from other sources, a greedy algorithm can be much faster than traditional dynamic programming approaches and yet produce an alignment that is guaranteed to be theoretically optimal. We introduce a new greedy alignment algorithm with particularly good performance and show that it computes the same alignment as does a certain dynamic programming algorithm, while executing over 10 times faster on appropriate data. An implementation of this algorithm is currently used in a program that assembles the UniGene database at the National Center for Biotechnology Information.

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PubMed2001

An algorithm for approximate tandem repeats.

A perfect single tandem repeat is defined as a nonempty string that can be divided into two identical substrings, e.g., abcabc. An approximate single tandem repeat is one in which the substrings are similar, but not identical, e.g., abcdaacd. In this paper we consider two criterions of similarity: the Hamming distance (k mismatches) and the edit distance (k differences). For a string S of length n and an integer k our algorithm reports all locally optimal approximate repeats, r = umacro û, for which the Hamming distance of umacro and û is at most k, in O(nk log (n/k)) time, or all those for which the edit distance of umacro and û is at most k, in O(nk log k log (n/k)) time. This paper concentrates on a more general type of repeat called multiple tandem repeats. A multiple tandem repeat in a sequence S is a (periodic) substring r of S of the form r = u(a)u', where u is a prefix of r and u' is a prefix of u. An approximate multiple tandem repeat is a multiple repeat with errors; the repeated subsequences are similar but not identical. We precisely define approximate multiple repeats, and present an algorithm that finds all repeats that concur with our definition. The time complexity of the algorithm, when searching for repeats with up to k errors in a string S of length n, is O(nka log (n/k)) where a is the maximum number of periods in any reported repeat. We present some experimental results concerning the performance and sensitivity of our algorithm. The problem of finding repeats within a string is a computational problem with important applications in the field of molecular biology. Both exact and inexact repeats occur frequently in the genome, and certain repeats occurring in the genome are known to be related to diseases in the human.

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PubMed2002

Fast and accurate phylogeny reconstruction algorithms based on the minimum-evolution principle.

The Minimum Evolution (ME) approach to phylogeny estimation has been shown to be statistically consistent when it is used in conjunction with ordinary least-squares (OLS) fitting of a metric to a tree structure. The traditional approach to using ME has been to start with the Neighbor Joining (NJ) topology for a given matrix and then do a topological search from that starting point. The first stage requires O(n(3)) time, where n is the number of taxa, while the current implementations of the second are in O(p n(3)) or more, where p is the number of swaps performed by the program. In this paper, we examine a greedy approach to minimum evolution which produces a starting topology in O(n(2)) time. Moreover, we provide an algorithm that searches for the best topology using nearest neighbor interchanges (NNIs), where the cost of doing p NNIs is O(n(2) + p n), i.e., O(n(2)) in practice because p is always much smaller than n. The Greedy Minimum Evolution (GME) algorithm, when used in combination with NNIs, produces trees which are fairly close to NJ trees in terms of topological accuracy. We also examine ME under a balanced weighting scheme, where sibling subtrees have equal weight, as opposed to the standard "unweighted" OLS, where all taxa have the same weight so that the weight of a subtree is equal to the number of its taxa. The balanced minimum evolution scheme (BME) runs slower than the OLS version, requiring O(n(2) x diam(T)) operations to build the starting tree and O(p n x diam(T)) to perform the NNIs, where diam(T) is the topological diameter of the output tree. In the usual Yule-Harding distribution on phylogenetic trees, the diameter expectation is in log(n), so our algorithms are in practice faster that NJ. Moreover, this BME scheme yields a very significant improvement over NJ and other distance-based algorithms, especially with large trees, in terms of topological accuracy.

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PubMed2003

Recognition of translation initiation sites of eukaryotic genes based on an EM algorithm.

With the rapid increase of DNA databases of human and other eukaryotic model organisms, a large great number of genes need to be distinguished from the DNA databases. Exact recognition of translation initiation sites (TISs) of eukaryotic genes is very important to understand the translation initiation process, predict the detailed structure of eukaryotic genes, and annotate uncharacterized sequences. The problem has not been solved satisfactorily, especially for recognizing TISs of the eukaryotic genes with shorter first exons. It is an important task for extracting new features and finding new powerful algorithms for recognizing TISs of eukaryotic genes. In this paper, the important characteristics of shorter flanking fragments around TISs are extracted and an expectation-maximization (EM) algorithm based on incomplete data is used to recognize TISs of eukaryotic genes. The accuracy is up to 87.8% over a six-fold cross-validation test. The result shows that the identification variables are effectively extracted and the EM algorithm is a powerful tool to predict the TISs of eukaryotic genes. The algorithm also can be applied to other classification or clustering tasks in bioinformatics.

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