Optimized radiotherapy treatment planning using the complication probability factor (CPF).
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Computers↗
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Results for “Probability Theory”
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By way of introduction: modelling living systems, their diversity and their complexity: some methodological and theoretical problems.
Some principles for a current methodology for biological systems' modelling are presented. It seems possible to promote a model-centred approach of these complex systems. Among present questions, the role of mechanisms producing random or quasi-random issues is underlined, because they are implied in biological diversification and in resulting complexity of living systems. Now, biodiversity is one of our societies' and scientific research's main concerns. Basically, it can be interpreted as a manner, for Life, to resist environmental hazards. Thus, one may assume that biodiversity producing mechanisms could be selected during evolution to face to corresponding risks of disappearance: necessity of chance? Therefore, analysing and modelling these 'biological and ecological roulettes' would be important, and not only their outputs like nowadays by using the theory of probabilities. It is then suggested that chaotic behaviours generated by deterministic dynamical systems could mimic random processes, and that 'biological and ecological roulettes' would be represented by such models. Practical consequences can be envisaged in terms of biodiversity management, and more generally in terms of these 'roulettes' control to generate selected biological and ecological events' distribution.
Biodiversity↗
Voxel-based homogeneity probability maps of gray matter in groups: assessing the reliability of functional effects.
A subject of increasing importance in magnetic resonance imaging (MRI) is the analysis of intersubject structural differences, particularly when comparing groups of subjects with different conditions or diagnoses. On the other hand, determining structural homogeneity across subjects using voxel-based morphological (VBM) methods has become even more important to investigators who test for group brain activation using functional magnetic resonance images (fMRI) or positron emission tomography (PET). In the absence of methods that evaluate structural differences, one does not know how much reliability to assign to the functional differences. Here, we describe a voxel-based method for quantitatively assessing the homogeneity of tissues from structural magnetic resonance images of groups. Specifically, this method determines the homogeneity of gray matter for a group of subjects. Homogeneity probability maps (HPMs) of a given tissue type (e.g., gray matter) are generated by using a confidence interval based on binomial distribution. These maps indicate for each voxel the probability that the tissue type is gray for the population being studied. Therefore, HPMs can accompany functional analyses to indicate the confidence one can assign to functional difference at any given voxel. In this paper, examples of HPMs generated for a group of control subjects are shown and discussed. The application of this method to functional analysis is demonstrated.
Adult↗
Cortical thickness analysis examined through power analysis and a population simulation.
We have previously developed a procedure for measuring the thickness of cerebral cortex over the whole brain using 3-D MRI data and a fully automated surface-extraction (ASP) algorithm. This paper examines the precision of this algorithm, its optimal performance parameters, and the sensitivity of the method to subtle, focal changes in cortical thickness. The precision of cortical thickness measurements was studied using a simulated population study and single subject reproducibility metrics. Cortical thickness was shown to be a reliable method, reaching a sensitivity (probability of a true-positive) of 0.93. Six different cortical thickness metrics were compared. The simplest and most precise method measures the distance between corresponding vertices from the white matter to the gray matter surface. Given two groups of 25 subjects, a 0.6-mm (15%) change in thickness can be recovered after blurring with a 3-D Gaussian kernel (full-width half max = 30 mm). Smoothing across the 2-D surface manifold also improves precision; in this experiment, the optimal kernel size was 30 mm.
Algorithms↗
ROC-based assessments of 3D cortical surface-matching algorithms.
Algorithms for the semi-automated analysis of brain surfaces have recently received considerable attention, and yet, they rarely receive a rigorous assessment of their performance. We present a method for the quantitative assessment of performance across differing surface analysis algorithms and across various modifications of a single algorithm. The sensitivity and specificity of an algorithm for detecting known deformations added synthetically to the brains being studied are assessed using curves for Receiver Operating Characteristics (ROC). We also present a method for the isolation of sources of variance in MRI data sets that can contribute to degradation in performance of surface-matching algorithms. Isolation of these sources of variance allows determination of whether degradation in performance of surface-matching algorithms derives primarily from errors in registration of brains to a common coordinate space, from errors in placement of the known deformation, or from interindividual or between-group variability in morphology of the cortical surface. We apply these methods to the study of surface-matching algorithms that are based on fluid flow (FF) deformation, geodesic (GD) interpolation, or nearest neighbor (NN) proximity. We show that the performances of surface-matching algorithms depend on the presence of interindividual and between-group variability in the surfaces surrounding the cortical deformation. We also show that, in general, the FF algorithm performs as well as or better than the GD and NN algorithms. The large variance in identifying point correspondences across brain surfaces using the GD and the NN algorithms suggests strongly that these point correspondences are less valid than those determined by the FF algorithm. The GD and NN algorithms, moreover, are both vulnerable to detecting false-positive activations at points of high curvature, particularly along large fissures, cisterns, and cortical sulci.
Algorithms↗
MR-based automatic delineation of volumes of interest in human brain PET images using probability maps.
The purpose of this study was to develop and validate an observer-independent approach for automatic generation of volume-of-interest (VOI) brain templates to be used in emission tomography studies of the brain. The method utilizes a VOI probability map created on the basis of a database of several subjects' MR-images, where VOI sets have been defined manually. High-resolution structural MR-images and 5-HT(2A) receptor binding PET-images (in terms of (18)F-altanserin binding) from 10 healthy volunteers and 10 patients with mild cognitive impairment were included for the analysis. A template including 35 VOIs was manually delineated on the subjects' MR images. Through a warping algorithm template VOI sets defined from each individual were transferred to the other subjects MR-images and the voxel overlap was compared to the VOI set specifically drawn for that particular individual. Comparisons were also made for the VOI templates 5-HT(2A) receptor binding values. It was shown that when the generated VOI set is based on more than one template VOI set, delineation of VOIs is better reproduced and shows less variation as compared both to transfer of a single set of template VOIs as well as manual delineation of the VOI set. The approach was also shown to work equally well in individuals with pronounced cerebral atrophy. Probability-map-based automatic delineation of VOIs is a fast, objective, reproducible, and safe way to assess regional brain values from PET or SPECT scans. In addition, the method applies well in elderly subjects, even in the presence of pronounced cerebral atrophy.
Aged↗
Unified segmentation.
A probabilistic framework is presented that enables image registration, tissue classification, and bias correction to be combined within the same generative model. A derivation of a log-likelihood objective function for the unified model is provided. The model is based on a mixture of Gaussians and is extended to incorporate a smooth intensity variation and nonlinear registration with tissue probability maps. A strategy for optimising the model parameters is described, along with the requisite partial derivatives of the objective function.
Algorithms↗
Classifying brain states and determining the discriminating activation patterns: Support Vector Machine on functional MRI data.
In the present study, we applied the Support Vector Machine (SVM) algorithm to perform multivariate classification of brain states from whole functional magnetic resonance imaging (fMRI) volumes without prior selection of spatial features. In addition, we did a comparative analysis between the SVM and the Fisher Linear Discriminant (FLD) classifier. We applied the methods to two multisubject attention experiments: a face matching and a location matching task. We demonstrate that SVM outperforms FLD in classification performance as well as in robustness of the spatial maps obtained (i.e. discriminating volumes). In addition, the SVM discrimination maps had greater overlap with the general linear model (GLM) analysis compared to the FLD. The analysis presents two phases: during the training, the classifier algorithm finds the set of regions by which the two brain states can be best distinguished from each other. In the next phase, the test phase, given an fMRI volume from a new subject, the classifier predicts the subject's instantaneous brain state.
Aged↗
Probabilistic models of cognition: conceptual foundations.
Remarkable progress in the mathematics and computer science of probability has led to a revolution in the scope of probabilistic models. In particular, 'sophisticated' probabilistic methods apply to structured relational systems such as graphs and grammars, of immediate relevance to the cognitive sciences. This Special Issue outlines progress in this rapidly developing field, which provides a potentially unifying perspective across a wide range of domains and levels of explanation. Here, we introduce the historical and conceptual foundations of the approach, explore how the approach relates to studies of explicit probabilistic reasoning, and give a brief overview of the field as it stands today.
Algorithms↗
Probabilistic models of cognition: where next?
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Algorithms↗
The use of information theory in evaluating the contribution of radiological and laboratory investigations to diagnosis and management.
Using information theory, the value of radiological and laboratory investigations has been assessed in the diagnosis and management of 67 patients suspected of having inflammatory polyarthritis. There were only three changes in diagnosis made as a result of the investigations. Both the radiological and laboratory tests supplied a small but significant amount of information in improving the physician's confidence in diagnosis. Changes in management occurred more frequently but the final management decision differed from the pre-investigation decision in only 17 of the 67 patients (25%). Radiological examination failed to decrease uncertainty using a simple 'change in uncertainty' measure. Both types of investigation supplied a limited bu significant amount of information towards the final management decision, although the contribution from radiology was only significant when view before the receipt of the results of the laboratory tests. In view of the limited value of the investigations - particularly radiology - in this study, it is important to fully asses present and future diagnostic procedures especially in relation to patient management.
Arthritis↗
Responding to uncertainty in nursing practice.
Uncertainty is a fact of life for practising clinicians and cannot be avoided. This paper outlines the model of uncertainty presented by Katz (1988, Cambridge University Press, Cambridge, UK. pp. 544-565) and examines the descriptive and normative power of three broad theoretical and strategic approaches to dealing with uncertainty: rationality, bounded rationality and intuition. It concludes that nursing research and development (R&D) must acknowledge uncertainty more fully in its R&D agenda and that good-quality evaluation studies which directly compare intuitive with rational-analytical approaches for given clinical problems should be a dominant feature of future R&D.
Adaptation, Psychological↗
Division rules for polygonal cells.
A number of fascinating mathematical problems concerning the division of two-dimensional space are formulated from questions about the planes of cell division in embryonic epithelia. Their solution aids in the quantitative description of cellular arrangement in epithelia. Cells, considered as polygons, site their division line according to stochastic rules, eventually forming a tessellation of the plane. The equilibrium distributions for the resulting mix of polygonal types are explored for a range of stochastic rules. We find surprising links with some classical distributions from the theory of probability.
Cell Division↗
The lod score method.
The lod score method originated in a seminal article by Newton Morton in 1955. The method is broadly concerned with issues of power and the posterior probability of linkage, ensuring that a reported linkage has a high probability of being a true linkage. In addition, the method is sequential, so that pedigrees or lod curves may be combined from published reports to pool data for analysis. This approach has been remarkably successful for 50 years in identifying disease genes for Mendelian disorders. After discussing these issues, we consider the situation for complex disorders, where the maximum lod score (MLS) statistic shares some of the advantages of the traditional lod score approach but is limited by unknown power and the lack of sharing of the primary data needed to optimally combine analytic results. We may still learn from the lod score method as we explore new methods in molecular biology and genetic analysis to utilize the complete human DNA sequence and the cataloging of all human genes.
Genetic Linkage↗
The possible meaning of the upper and lower alpha frequency ranges for cognitive and creative tasks.
This study is aimed at verifying the functional independence of two frequency bands within the alpha range. It is based on experiments that examined the role of these two hands with regard to the amount of local electrogenesis (amplitude) and the cooperation of brain areas (coherence) in mental tasks concerning: (1) visual perception and imagery; (2) listening to and composing music; (3) verbal and visual creativity; and (4) aspects of mood. In all experiments EEG were recorded for at least 1 min during each task, separated one from another by at rest periods of at least equal lengths. EEG electrodes were pasted according to the 10/20 system (averaged ear lobes as reference). After FFT power was calculated for all 19 electrodes, coherence was estimated for all possible electrode pairs (i.e. 171). This was done for six frequency ranges between 1.5 and 31.5 Hz, the alpha range having been divided into two (7.5-9 Hz and 9.5-12.5 Hz). The spectral parameters obtained during each task were compared with those of the merged EEG at rest, significant changes (P < or = 0.01-P < or = 0.05) were entered into schematic maps of the brain. Generally, fewer differences were found for amplitude than for coherence. In all four tasks concerning visual perception the clearest differences were found in single person studies. But also in group studies more or less distinct differences were found between alpha 1 and 2. Also in the series with music the two alpha bands did not behave uniformly, nor were uniform features found in the two series of musically trained and untrained subjects. Distinct discrepancies were also found in a verbal and visual imagery task. With respect to mood, only elevated mood was correlated with a decrease of coherence in alpha 2 and an increase of amplitude in alpha 1. This study though hinting at a different functional significance of these two alpha bands, however, does not allow to draw any conclusions as to their distinct functional meanings. Generally, the long-term coherence changes observed under these different mental tasks support the idea that part of information processing in the brain is reflected by the EEG. Structural peculiarities and microelectrode recordings of the cortex support this conclusion.
Adult↗
Perception as probability.
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History, 20th Century↗
Analysis of Tikhonov regularization for function approximation by neural networks.
This paper is devoted to the convergence and stability analysis of Tikhonov regularization for function approximation by a class of feed-forward neural networks with one hidden layer and linear output layer. We investigate two frequently used approaches, namely regularization by output smoothing and regularization by weight decay, as well as a combination of both methods to combine their advantages. We show that in all cases stable approximations are obtained converging to the approximated function in a desired Sobolev space as the noise in the data tends to zero (in the weaker L(2)-norm) if the regularization parameter and the number of units in the network are chosen appropriately. Under additional smoothness assumptions we are able to show convergence rates results in terms of the noise level and the number of units in the network. In addition, we show how the theoretical results can be applied to the important classes of perceptrons with one hidden layer and to translation networks. Finally, the performance of the different approaches is compared in some numerical examples.
Algorithms↗
Integrating model-based decision support in a multi-modal reasoning system for managing type 1 diabetic patients.
We present a multi-modal reasoning (MMR) methodology that integrates case-based reasoning (CBR), rule-based reasoning (RBR) and model-based reasoning (MBR), meant to provide physicians with a reliable decision support tool in the context of type 1 diabetes mellitus management. In particular, we have implemented a decision support system that is able to jointly exploit a probabilistic model of the glucose-insulin system at the steady state, a RBR system for suggestion generation and a CBR system for patient's profiling. The integration of the CBR, RBR and MBR paradigms allows for an optimized exploitation of all the available information, and for the definition of a therapy properly tailored to the patient's needs, overcoming the single approaches limitations. The system has been tested both on simulated and on real patients' data.
Artificial Intelligence↗