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PubMed2004

Experiments with the nonlinear and chaotic behaviour of the multiplicative algebraic reconstruction technique (MART) algorithm for computed tomography.

Among the iterative reconstruction algorithms for tomography, the multiplicative algebraic reconstruction technique (MART) has two advantages that make it stand out from other algorithms: it confines the image (and therefore the projection data) to the convex hull of the patient, and it maximizes entropy. In this paper, we have undertaken a series of experiments to determine the importance of MART nonlinearity to image quality. Variants of MART were implemented aiming to exploit and exaggerate the nonlinear properties of the algorithm. We introduce the Power MART, Boxcar Averaging MART and Bouncing MART algorithms. Power MART is linked to the relaxation concept. Its behaviour is similar to that of the chaos of a logistic equation. There appears to be an antagonism between increasing nonlinearity and noise in the projection data. The experiments confirm our general observation that regularization as a means of solving simultaneous linear equations that are underdetermined is suboptimal: it does not necessarily select the correct image from the hyperplane of solutions, and so does not maximize the image quality:x-ray dose ratio. Our investigations prove that there is scope to optimize CT algorithms and thereby achieve greater dose reduction.

Algorithms↗

PubMed2005

Statistical image reconstruction for transmission tomography using relaxed ordered subset algorithms.

Statistical reconstruction methods offer possibilities for improving image quality as compared to analytical methods, but current reconstruction times prohibit routine clinical applications in x-ray computed tomography (CT). To reduce reconstruction times, we have applied (under) relaxation to ordered subset algorithms. This enables us to use subsets consisting of only single projection angle, effectively increasing the number of image updates within an entire iteration. A second advantage of applying relaxation is that it can help improve convergence by removing the limit cycle behaviour of ordered subset algorithms, which normally do not converge to an optimal solution but rather a suboptimal limit cycle consisting of as many points as there are subsets. Relaxation suppresses the limit cycle behaviour by decreasing the stepsize for approaching the solution. A simulation study for a 2D mathematical phantom and three different ordered subset algorithms shows that all three algorithms benefit from relaxation: equal noise-to-resolution trade-off can be achieved using fewer iterations than the conventional algorithms, while a lower minimal normalized mean square error (NMSE) clearly indicates a better convergence. Two different schemes for setting the relaxation parameter are studied, and both schemes yield approximately the same minimal NMSE.

Algorithms↗

PubMed2005

Exact fan-beam image reconstruction algorithm for truncated projection data acquired from an asymmetric half-size detector.

In this paper, we present a new algorithm designed for a specific data truncation problem in fan-beam CT. We consider a scanning configuration in which the fan-beam projection data are acquired from an asymmetrically positioned half-sized detector. Namely, the asymmetric detector only covers one half of the scanning field of view. Thus, the acquired fan-beam projection data are truncated at every view angle. If an explicit data rebinning process is not invoked, this data acquisition configuration will reek havoc on many known fan-beam image reconstruction schemes including the standard filtered backprojection (FBP) algorithm and the super-short-scan FBP reconstruction algorithms. However, we demonstrate that a recently developed fan-beam image reconstruction algorithm which reconstructs an image via filtering a backprojection image of differentiated projection data (FBPD) survives the above fan-beam data truncation problem. Namely, we may exactly reconstruct the whole image object using the truncated data acquired in a full scan mode (2pi angular range). We may also exactly reconstruct a small region of interest (ROI) using the truncated projection data acquired in a short-scan mode (less than 2pi angular range). The most important characteristic of the proposed reconstruction scheme is that an explicit data rebinning process is not introduced. Numerical simulations were conducted to validate the new reconstruction algorithm.

Algorithms↗

PubMed2006

Strategy of extraction methods and reconstruction algorithms in computed tomography of diffraction enhanced imaging.

Computed tomography of diffraction enhanced imaging (DEI-CT) is a novel x-ray phase-contrast computed tomography which is applied to inspect weakly absorbing low-Z samples. Refraction-angle images which are extracted from a series of raw DEI images measured in different positions of the rocking curve of the analyser can be regarded as projections of DEI-CT. Based on them, the distribution of refractive index decrement in the sample can be reconstructed according to the principles of CT. How to combine extraction methods and reconstruction algorithms to obtain the most accurate reconstructed results is investigated in detail in this paper. Two kinds of comparison, the comparison of different extraction methods and the comparison between "two-step" algorithms and the Hilbert filtered backprojection (HFBP) algorithm, draw the conclusion that the HFBP algorithm based on the maximum refraction-angle (MRA) method may be the best combination at present. Though all current extraction methods including the MRA method are approximate methods and cannot calculate very large refraction-angle values, the HFBP algorithm based on the MRA method is able to provide quite acceptable estimations of the distribution of refractive index decrement of the sample. The conclusion is proved by the experimental results at the Beijing Synchrotron Radiation Facility.

Algorithms↗

PubMed2001

Validation of a 3D reconstruction algorithm for EIT of human brain function in a realistic head-shaped tank.

Previous work has demonstrated that electrical impedance tomography can be used to image human brain activity during evoked responses, but two-thirds of the reconstructed images fail to localize an impedance change to the expected stimulated cortical area. The localization failure may be caused by modelling the head as a homogenous sphere in the reconstruction algorithm. This assumption may lead to errors when used to reconstruct data obtained from the human head. In this study a 3D reconstruction algorithm, based on a model of the head as a homogenous sphere, was characterized by simulating the algorithm model, the head shape and the presence of the skull in saline-filled tanks. EIT images of a sponge, 14 cm3 volume with a resistivity contrast of 12%, were acquired in three different positions in tanks filled with 0.2% saline. In a hemispherical tank, 19 cm in diameter, the sponge was localized to within 3.4-10.7% of the tank diameter. In a head-shaped tank, the errors were between 3.1 and 13.3% without a skull and between 10.3 and 18.7% when a real human skull was present. A significant increase in localization error therefore occurs if an algorithm based on a homogeneous sphere is used on data acquired from a head-shaped tank. The increased error is due to the presence of the skull, as no significant increase in error occurred if a head-shaped tank was used without the skull present, compared to the localization error within the hemispherical tank. The error due to the skull significantly shifted the impedance change within the skull towards the centre of the image. Although the increased localization error due to the skull is not sufficient to explain the localization errors of up to 50% of the image diameter present in the images of some human subjects, the future use of a realistic head model in the reconstruction algorithm is likely to reduce the localization error in the human images due to the presence of the skull.

Algorithms↗

PubMedDate not supplied

Algorithms for optical mapping.

Optical mapping is a novel technique for determining the restriction sites on a DNA molecule by directly observing a number of partially digested copies of the molecule under a light microscope. The problem is complicated by uncertainty as to the orientation of the molecules and by erroneous detection of cuts. In this paper we study the problem of constructing a restriction map based on optical mapping data. We give several variants of a polynomial reconstruction algorithm, as well as an algorithm that is exponential in the number of cut sites, and hence is appropriate only for small number of cut sites. We give a simple probabilistic model for data generation and for the errors and prove probabilistic upper and lower bounds on the number of molecules needed by each algorithm in order to obtain a correct map, expressed as a function of the number of cut sites and the error parameters. To the best of our knowledge, this is the first probabilistic analysis of algorithms for the problem. We also provide experimental results confirming that our algorithms are highly effective on simulated data.

Algorithms↗

PubMed2000

Algorithms for extracting structured motifs using a suffix tree with an application to promoter and regulatory site consensus identification.

This paper introduces two exact algorithms for extracting conserved structured motifs from a set of DNA sequences. Structured motifs may be described as an ordered collection of p > or = 1 "boxes" (each box corresponding to one part of the structured motif), p substitution rates (one for each box) and p - 1 intervals of distance (one for each pair of successive boxes in the collection). The contents of the boxes--that is, the motifs themselves--are unknown at the start of the algorithm. This is precisely what the algorithms are meant to find. A suffix tree is used for finding such motifs. The algorithms are efficient enough to be able to infer site consensi, such as, for instance, promoter sequences or regulatory sites, from a set of unaligned sequences corresponding to the noncoding regions upstream from all genes of a genome. In particular, both algorithms time complexity scales linearly with N2n where n is the average length of the sequences and N their number. An application to the identification of promoter and regulatory consensus sequences in bacterial genomes is shown.

Algorithms↗

PubMed2000

The practical use of the A* algorithm for exact multiple sequence alignment.

Multiple alignment is an important problem in computational biology. It is well known that it can be solved exactly by a dynamic programming algorithm which in turn can be interpreted as a shortest path computation in a directed acyclic graph. The A* algorithm (or goal-directed unidirectional search) is a technique that speeds up the computation of a shortest path by transforming the edge lengths without losing the optimality of the shortest path. We implemented the A* algorithm in a computer program similar to MSA (Gupta et al., 1995) and FMA (Shibuya and Imai, 1997). We incorporated in this program new bounding strategies for both lower and upper bounds and show that the A* algorithm, together with our improvements, can speed up computations considerably. Additionally, we show that the A* algorithm together with a standard bounding technique is superior to the well-known Carrillo-Lipman bounding since it excludes more nodes from consideration.

Algorithms↗

PubMed2001

Tsukuba BB: a branch and bound algorithm for local multiple alignment of DNA and protein sequences.

In this paper we present a branch and bound algorithm for local gapless multiple sequence alignment (motif alignment) and its implementation. The algorithm uses both score-based bounding and a novel bounding technique based on the "consistency" of the alignment. A sequence order independent search tree is used in conjunction with a technique for avoiding redundant calculations inherent in the structure of the tree. This is the first program to exploit the fact that the motif alignment problem is easier for short motifs. Indeed, for a short fixed motif width, the running time of the algorithm is asymptotically linear in the size of the input. We tested the performance of the program on a dataset of 300 E. coli promoter sequences and a dataset of 85 lipocalin protein sequences. For a motif width of 4, the optimal alignment of the entire set of sequences can be found. For the more natural motif width of 6, the program can align 21 sequences of length 100, more than twice the number of sequences which can be aligned by the best previous exact algorithm. The algorithm can relax the constraint of requiring each sequence to be aligned, and align 105 of the 300 promoter sequences with a motif width of 6. For the lipocalin dataset, we introduce a technique for reducing the effective alphabet size with a minimal loss of useful information. With this technique, we show that the program can find meaningful motifs in a reasonable amount of time by optimizing the score over three motif positions.

Algorithms↗

PubMed2002

Predicting CNS permeability of drug molecules: comparison of neural network and support vector machine algorithms.

Two different machine-learning algorithms have been used to predict the blood-brain barrier permeability of different classes of molecules, to develop a method to predict the ability of drug compounds to penetrate the CNS. The first algorithm is based on a multilayer perceptron neural network and the second algorithm uses a support vector machine. Both algorithms are trained on an identical data set consisting of 179 CNS active molecules and 145 CNS inactive molecules. The training parameters include molecular weight, lipophilicity, hydrogen bonding, and other variables that govern the ability of a molecule to diffuse through a membrane. The results show that the support vector machine outperforms the neural network. Based on over 30 different validation sets, the SVM can predict up to 96% of the molecules correctly, averaging 81.5% over 30 test sets, which comprised of equal numbers of CNS positive and negative molecules. This is quite favorable when compared with the neural network's average performance of 75.7% with the same 30 test sets. The results of the SVM algorithm are very encouraging and suggest that a classification tool like this one will prove to be a valuable prediction approach.

Algorithms↗

PubMed2003

Analysis of continuous glucose monitoring data from non-diabetic and diabetic children: a tale of two algorithms.

Use of the Medtronic MiniMed Continuous Glucose Monitoring System (CGMS) in non-diabetic children has revealed many low and high sensor glucose (SG) values, suggesting that the original analytical algorithm (Solutions 2.0) might be overreading glycemic excursions. A revised algorithm (Solutions 3.0) was introduced in 2001. Our aim was to compare analyses of the same sensor profiles using both programs. Twenty-five lean, non-diabetic subjects (mean age 14 +/- 4 years) underwent continuous glucose monitoring with CGMS for up to 72 h. Sensor tracings were analyzed with both algorithms and compared. Separate analyses were performed for nocturnal readings (12-6 a.m.). Mean SG values were similar (103 +/- 24 mg/dL for version 2.0 vs. 100 +/- 14 for version 3.0), but the distribution was significantly different: 13.8% of total SG were <70 mg/dL by version 2.0 versus 8.2% by version 3.0 (p < 0.001), and 7.7% of total SG were >150 mg/dL by version 2.0 versus 4.7% by version 3.0 (p = 0.02). Of nocturnal SG values, 25.8% were <70 mg/dL by version 2.0 compared with 17.9% by version 3.0, and 9.4% were >150 mg/dL by version 2.0 compared with 4.0% by version 3.0. In lean non-diabetic children, Solutions 2.0 identified significantly more hypoglycemia and hyperglycemia than Solutions 3.0. Similar analyses in 40 children with type 1 diabetes revealed no significant differences. Solutions 3.0 may be a more useful algorithm for preventing over-reading of low and high SG readings in non-diabetic children, whereas both algorithms give similar results in children with diabetes.

Adolescent↗

PubMed1996

Prediction of HIV peptide epitopes by a novel algorithm.

Identification of promiscuous or multideterminant T cell epitopes is essential for HIV vaccine development, however, current methods for T cell epitope identification are both cost intensive and labor intensive. We have developed a computer-driven algorithm, named EpiMer, which searches protein amino acid sequences for putative MHC class I- and/or class II-restricted T cell epitopes. This algorithm identifies peptides that contain multiple MHC-binding motifs from protein sequences. To evaluate the predictive power of EpiMer, the amino acid sequences of the HIV-1 proteins nef, gp160, gag p55, and tat were searched for regions of MHC-binding motif clustering. We assessed the algorithm's predictive power by comparing the EpiMer-predicted peptide epitopes to T cell epitopes that have been published in the literature. The EpiMer method of T cell epitope identification was compared to the standard method of synthesizing short, overlapping peptides and testing them for immunogenicity (overlapping peptide method), and to an alternate algorithm that has been used to identify putative T cell epitopes from primary structure (AMPHI). For the four HIV-1 proteins analyzed, the in vitro testing of EpiMer peptides for immunogenicity would have required the synthesis of fewer total peptides than either AMPHI or the overlapping peptide method. The EpiMer algorithm proved to be more efficient and more sensitive per amino acid than both the overlapping peptide method and AMPHI. The EpiMer predictions for these four HIV proteins are described. Since EpiMer-predicted peptides have the potential to bind to multiple MHC alleles, they are strong candidates for inclusion in a synthetic HIV vaccine.

Algorithms↗

PubMed2005

A direct comparison of drug susceptibility to HIV type 1 from antiretroviral experienced subjects as assessed by the antivirogram and PhenoSense assays and by seven resistance algorithms.

HIV-1 drug resistance methodologies are being increasingly utilized to guide treatment decisions; however, information comparing the various assays is limited. Duplicate plasma samples from 70 ART-experienced subjects were analyzed by both the Antivirogram and PhenoSense phenotypic assays and the results compared. HIV genotypes were also obtained and analyzed using seven different resistance algorithms. These results were also compared with the phenotypic assay results. Concordances between the phenotypic tests and between each algorithm, and between the two phenotypic assays were calculated and kappa coefficients (KC) determined. Overall agreement between the two phenotypic assays was good (86.9% concordance; KC 0.621). The highest concordance by drug class was seen for protease inhibitors (93.4%; KC 0.679) and the lowest (79.8%; KC 0.549) for nucleoside reverse transcriptase inhibitors. Concordance between the two phenotypic assays, when evaluating individual drugs, was good for all drugs tested except for abacavir, zalcitabine, and indinavir. Agreement between the seven algorithms and each phenotypic assay was variable, though most had good or excellent agreement. The highest overall level of agreement for an individual drug was observed when comparing lamivudine susceptibility to either assay. Concordance for abacavir, didanosine, zalcitabine, and saquinavir was generally problematic when comparing one or more phenotypic assays to the drug resistance predictive algorithms. In conclusion, results comparing these two phenotypic tests were mostly similar, but comparisons of the predictive resistance algorithms for specific drugs, as well as to specific phenotypic assays, were more inconsistent.

Adult↗

PubMed1996

An algorithm for finding maximal common subtopologies in a set of protein structures.

For the comparison and analysis of protein structures, it is of interest to find maximal common substructures in a given set of proteins. This question is also relevant for motif definition and structure classification. In this paper we describe first a new suitable representation of the secondary structure topology of a protein by an undirected labeled graph. Based on this representation we developed a new fast algorithm that finds all common subtopologies in a set of protein structures. Our method is based on the algorithm by Bron and Kerbosch (1973), which enumerates all maximal cliques in a graph. The main improvement of our algorithm is to restrict the search process to cliques that represent connected substructures. This restriction reduces the number of cliques to be considered during the search process and the size of the search tree drastically. Thus we are able to handle large proteins. Experiments show the efficiency and superiority of our algorithm in comparison with other existing algorithms basing on graph-theoretical methods.

Algorithms↗

PubMed2005

Exact algorithms for planted motif problems.

The problem of identifying meaningful patterns (i.e., motifs) from biological data has been studied extensively due to its paramount importance. Three versions of this problem have been identified in the literature. One of these three problems is the planted (l, d)-motif problem. Several instances of this problem have been posed as a challenge. Numerous algorithms have been proposed in the literature that address this challenge. Many of these algorithms fall under the category of heuristic algorithms. In this paper we present algorithms for the planted (l, d)-motif problem that always find the correct answer(s). Our algorithms are very simple and are based on some ideas that are fundamentally different from the ones employed in the literature. We believe that the techniques we introduce in this paper will find independent applications.

Algorithms↗

PubMed2005

Algorithms for selecting informative marker panels for population assignment.

Given a set of potential source populations, genotypes of an individual of unknown origin at a collection of markers can be used to predict the correct source population of the individual. For improved efficiency, informative markers can be chosen from a larger set of markers to maximize the accuracy of this prediction. However, selecting the loci that are individually most informative does not necessarily produce the optimal panel. Here, using genotypes from eight species--carp, cat, chicken, dog, fly, grayling, human, and maize--this univariate accumulation procedure is compared to new multivariate "greedy" and "maximin" algorithms for choosing marker panels. The procedures generally suggest similar panels, although the greedy method often recommends inclusion of loci that are not chosen by the other algorithms. In seven of the eight species, when applied to five or more markers, all methods achieve at least 94% assignment accuracy on simulated individuals, with one species--dog--producing this level of accuracy with only three markers, and the eighth species--human--requiring approximately 13-16 markers. The new algorithms produce substantial improvements over use of randomly selected markers; where differences among the methods are noticeable, the greedy algorithm leads to slightly higher probabilities of correct assignment. Although none of the approaches necessarily chooses the panel with optimal performance, the algorithms all likely select panels with performance near enough to the maximum that they all are suitable for practical use.

Algorithms↗

PubMedDate not supplied

A novel ensemble-based scoring and search algorithm for protein redesign and its application to modify the substrate specificity of the gramicidin synthetase a phenylalanine adenylation enzyme.

Realization of novel molecular function requires the ability to alter molecular complex formation. Enzymatic function can be altered by changing enzyme-substrate interactions via modification of an enzyme's active site. A redesigned enzyme may either perform a novel reaction on its native substrates or its native reaction on novel substrates. A number of computational approaches have been developed to address the combinatorial nature of the protein redesign problem. These approaches typically search for the global minimum energy conformation among an exponential number of protein conformations. We present a novel algorithm for protein redesign, which combines a statistical mechanics-derived ensemble-based approach to computing the binding constant with the speed and completeness of a branch-and-bound pruning algorithm. In addition, we developed an efficient deterministic approximation algorithm, capable of approximating our scoring function to arbitrary precision. In practice, the approximation algorithm decreases the execution time of the mutation search by a factor of ten. To test our method, we examined the Phe-specific adenylation domain of the nonribosomal peptide synthetase gramicidin synthetase A (GrsA-PheA). Ensemble scoring, using a rotameric approximation to the partition functions of the bound and unbound states for GrsA-PheA, is first used to predict binding of the wildtype protein and a previously described mutant (selective for leucine), and second, to switch the enzyme specificity toward leucine, using two novel active site sequences computationally predicted by searching through the space of possible active site mutations. The top scoring in silico mutants were created in the wetlab and dissociation/binding constants were determined by fluorescence quenching. These tested mutations exhibit the desired change in specificity from Phe to Leu. Our ensemble-based algorithm, which flexibly models both protein and ligand using rotamer-based partition functions, has application in enzyme redesign, the prediction of protein-ligand binding, and computer-aided drug design.

Adenosine Triphosphate↗

PubMed2005

An efficient algorithm to compute the landscape of locally optimal RNA secondary structures with respect to the Nussinov-Jacobson energy model.

We make a novel contribution to the theory of biopolymer folding, by developing an efficient algorithm to compute the number of locally optimal secondary structures of an RNA molecule, with respect to the Nussinov-Jacobson energy model. Additionally, we apply our algorithm to analyze the folding landscape of selenocysteine insertion sequence (SECIS) elements from A. Bock (personal communication), hammerhead ribozymes from Rfam (Griffiths-Jones et al., 2003), and tRNAs from Sprinzl's database (Sprinzl et al., 1998). It had previously been reported that tRNA has lower minimum free energy than random RNA of the same compositional frequency (Clote et al., 2003; Rivas and Eddy, 2000), although the situation is less clear for mRNA (Seffens and Digby, 1999; Workman and Krogh, 1999; Cohen and Skienna, 2002),(1) which plays no structural role. Applications of our algorithm extend knowledge of the energy landscape differences between naturally occurring and random RNA. Given an RNA molecule a(1), ... , a(n) and an integer k > or = 0, a k-locally optimal secondary structure S is a secondary structure on a(1), ... , a(n) which has k fewer base pairs than the maximum possible number, yet for which no basepairs can be added without violation of the definition of secondary structure (e.g., introducing a pseudoknot). Despite the fact that the number numStr(k) of k-locally optimal structures for a given RNA molecule in general is exponential in n, we present an algorithm running in time O(n (4)) and space O(n (3)), which computes numStr(k) for each k. Structurally important RNA, such as SECIS elements, hammerhead ribozymes, and tRNA, all have a markedly smaller number of k-locally optimal structures than that of random RNA of the same dinucleotide frequency, for small and moderate values of k. This suggests a potential future role of our algorithm as a tool to detect noncoding RNA genes.

Algorithms↗