A mathematical model for the infectivity-dilution curve of tobacco mosaic virus: experimental tests.
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Computers↗
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Results for “Mathematical Computing”
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Features of carotid artery flow velocity in healthy subjects and consequences for evaluating stenosis in the internal carotid artery.
C-W-Doppler analysis of flow velocity in the carotid arteries was performed in 98 healthy volunteers, age 16-74 years, 49 of each sex, and in 23 subjects with carotid disease. Maximum frequency shift (MFS) and total band-width in the healthy proximal internal carotid artery were negatively correlated to age in both sexes (p less than 0.001). MFS was lower in the normal proximal internal carotid artery than in the common carotid artery in both sexes. Minimum frequency shifts were more often, and more negative in the proximal than in the distal part of the internal carotid artery (p less than 0.001 in men and less than 0.01 in women) and still more so in the proximal part of the pathological internal carotids as compared with the normal ones (p less than 0.001). The computer-fitted regression between MFS and the degree of angiographic stenosis in the subjects with carotid artery disease was nearly identical with the mathematically calculated relationship for an ellipsoid stenosis. There is reason to believe that the degree of area stenosis calculated from frequency shift and predicted normal values gives a more true interpretation of functional stenosis than angiography, while the latter might be superior for evaluating vascular patho-anatomy, giving information also about intrathoracic and intracranial vessels, which also is important for evaluating patients with TIA and related symptoms.
Adolescent↗
Drug calculation errors of baccalaureate nursing students.
Most researchers who study the dosage calculation skills of nursing students have looked at the mathematical or computational ability of the students. The authors report findings from a study that analyzed the dosage calculation errors of nursing students from conceptual, mathematical, and measurement perspectives.
Adult↗
Computational biology: toward deciphering gene regulatory information in mammalian genomes.
Computational biology is a rapidly evolving area where methodologies from computer science, mathematics, and statistics are applied to address fundamental problems in biology. The study of gene regulatory information is a central problem in current computational biology. This article reviews recent development of statistical methods related to this field. Starting from microarray gene selection, we examine methods for finding transcription factor binding motifs and cis-regulatory modules in coregulated genes, and methods for utilizing information from cross-species comparisons and ChIP-chip experiments. The ultimate understanding of cis-regulatory logic in mammalian genomes may require the integration of information collected from all these steps.
Animals↗
Coupled map lattices as computational systems.
The coupled map lattice (CML) as a mathematical model for a computer is considered. Using the theory of synchronous concurrent algorithms, it is shown that the CML is a valid new model for a parallel deterministic analog machine, but that, in principle, such a CML computer does not generate computations that cannot be reproduced by the standard mathematical models for computing on real numbers. The analysis is based on new general mathematical definitions of CMLs, and an axiomatic approach to determining which models of computation can be used to simulate CMLs.
Journal Article↗
Differences and similarities in insular and temporal pole MRI gray matter volume abnormalities in first-episode schizophrenia and affective psychosis.
CONTEXT: Whether psychoses associated with schizophrenia and affective disorder represent manifestations of different disorders or the same disorder is an important but unresolved question in psychiatry. Results of previous volumetric magnetic resonance imaging investigations indicate that gray matter volume reductions in neocortical regions may be specific to schizophrenia. OBJECTIVE: To simultaneously evaluate multiple olfactocentric paralimbic regions, which play crucial roles in human emotion and motivation, in first-episode patients with schizophrenia and affective psychosis. DESIGN: A cross-sectional study using high-spatial resolution magnetic resonance imaging in patients with schizophrenia and affective psychosis at their first hospitalization. SETTING: Inpatient units at a private psychiatric hospital. PARTICIPANTS: Fifty-three first-episode patients, 27 with schizophrenia and 26 with affective (mainly manic) psychosis, and 29 control subjects. MAIN OUTCOME MEASURES: Using high-spatial resolution magnetic resonance imaging, the gray matter volumes of 2 olfactocentric paralimbic regions of interest, the insular cortex and the temporal pole, were evaluated. RESULTS: A bilateral volume reduction in insular cortex gray matter was specific to first-episode patients with schizophrenia. In contrast, both first-episode psychosis groups showed a volume reduction in left temporal pole gray matter and an absence of normal left-greater-than-right asymmetry. Region of interest correlations showed that only patients with schizophrenia lacked a positive correlation between left temporal pole and left anterior amygdala-hippocampal complex gray matter volumes, whereas both psychosis groups were similar in lacking normal positive correlations between left temporal pole and left anterior superior temporal gyrus gray matter volumes. CONCLUSIONS: These partially different and partially similar patterns of structural abnormalities in olfactocentric paralimbic regions and their associated abnormalities in other temporolimbic regions may be important factors in the differential and common manifestations of the 2 psychoses.
Acute Disease↗
Midline corpus callosum is a neuroanatomical focus of fetal alcohol damage.
Prenatal exposure to high levels of alcohol often induces birth defects that combine morphological stigmata with neurological or neuropsychological deficits. But it has proved problematic to diagnose these syndromes in adolescents and adults, in whom the morphological signs are absent or attenuated, the behavioral deficits nonspecific, and the exposure history often difficult to reconstruct. Localizing the associated brain abnormalities might circumvent most of these difficulties. To this end, three-dimensional (3D) locations were recorded for 67 homologous points on or near the corpus callosum in magnetic resonance (MR) brain images from 60 adolescents and adults who were normal, 60 diagnosed with fetal alcohol syndrome, and 60 diagnosed with fetal alcohol effects. We combined the standard statistical approach to this type of geometric data, Procrustes analysis, with a multivariate strategy focusing on differences in variability. In this data set, the shape of the corpus callosum and its vicinity proves systematically much more variable in the alcohol-affected brains than in those of the normal subjects. From this excess variability follows a promising classification rule, having both high sensitivity (100 out of 117) and high specificity (49 out of 60) in this sample. The discrimination uses four landmark points and two summary scores of callosal outline shape. The information from the corpus callosum and vicinity, as viewed in MR brain images of full-grown subjects, may serve as a permanent record of the prenatal effects of alcohol, even in patients who are first suspected of these syndromes relatively late in life or who lack the facial signs of prenatal alcohol damage. The statistical pattern underlying the callosal diagnosis also leads to speculations on mechanisms of the prenatal damage.
Adolescent↗
Mathematical model to predict inspired oxygen concentration: description and validation.
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Computers↗
Magnetic resonance artifact induced by the electrode Activa 3389: an in vitro and in vivo study.
BACKGROUND: The electrode Activa 3389 is widely implanted for deep brain stimulation (DBS) and MRI is often used to control the position of the electrode. However, induced distorsion artifacts may result in imprecise localization and may lead to misinterpretations of the clinical effects and mechanisms of DBS. METHODS: In vitro 3D MR study: the proximal and distal contacts of one electrode were spotted by two localizers. The maximal artifact height (MAH) and width (MAW: measured on distal contact), and the distances between the artifact and the localizers (proximal, distal and lateral) were measured on 2 transverse and sagittal MR sequences with 90 degrees rotation of frequency-encoded gradient and phase direction. In vivo 3D MR study: coronal and sagittal reconstructions along the main axis of the electrode were performed on 10 postoperative MR (20 electrodes) to measure MAH and MAW. A Student t test was used to compare in vitro and in vivo measurements. FINDINGS: In vitro study: A MAH of 10.35 mm (+/-0.23) and MAW of 3.6 mm (+/-0.2) were found. We measured symmetrical extensions of the artifact over the distal contact. In vivo study: A MAH of 10.36 mm (+/-0.44) and MAW of 3.56 mm (+/-0.30) were obtained. No significant different artifact dimensions were measured between in vitro and in vivo studies (p<0.0001). INTERPRETATION: Precise 3D localization of the electrode in implanted patients is provided by MR identification of the limits of the distal contact artifact. The position of the other contacts is deduced given the size of the contacts and the intercontact distance.
Artifacts↗
Flow study on a newly developed impeller for a left ventricular assist device.
Nowadays, left ventricular assist devices are usually designed as high-speed, electric, rotary blood pumps. The pump drains blood from the left ventricular apex via an inlet cannula and ejects into the aortic root via an outlet conduit. To develop a high-performance pump, the present study utilizes partial differential equations to generate a surface representation of the impeller of the blood pump. Flow analysis around the impeller is performed by using the finite volume method to solve the fully incompressible three-dimensional Navier-Stokes equations along with the k-epsilon turbulence model. The numerical results highlight flow features in the end-wall region of the pump, namely the clearance leakage cross-flow, and the vortex associated with this leakage. These secondary flows induce major energy losses in the pumping device. On the test study, a test loop was proposed to measure the performance characteristics. It was shown that the design would provide a flow rate of 4.4 l/min with a pressure head of 122 mmHg. The DC motor power under these conditions was about 6 W and the rotational speed was 4500 rpm. Both the flow rate and head can satisfy the demand for the left artificial heart to work normally.
Computational Biology↗
On computing pericardial potentials and current densities in inverse electrocardiography.
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Action Potentials↗
BASIC computer program to summarize data using nonparametric and parametric statistics including Anderson-Darling test for normality.
Tools for calculating Gaussian parametric statistics are widely available in hand-held calculators and program packages for desktop as well as mainframe computers. The standard deviation calculated from non-Gaussian data may, however, be meaningless or even absurd. Furthermore, the standard error of the mean is frequently used as a descriptive statistic even if it really does not describe the variation in the observations themselves. However, comprehensive tools for calculating nonparametric descriptive statistics and judging whether observations have a Gaussian distribution are hard to come by. The present paper attempts to provide the essential statistical reasoning behind the calculation of descriptive statistics and introduces a computer program written in Microsoft BASIC that applies the methods described in the text.
Mathematical Computing↗
A personal computer-based system for parallel line analysis of bioassay data.
A program is described for symmetric parallel line analysis of bioassay data with a logistic dose-response relationship. Dose-response relationship is transformed to semilog or log-log. A regression line can be calculated for the dose-response curve for standard and test samples, and produces potency estimate of test sample preparation relative to the standard preparation based on parallel-line bioassay statistical methods [3,4], together with detailed analysis of variance, estimates of slope, intercept and chi 2 test which permits a very sensitive test for linearity and parallelism of standard and test sample and facilitates detection of 'outliers', i.e. samples exhibiting non-parallelism. The general comparison of dose-response relationships produced by the program are a feature of particular interest.
Analysis of Variance↗
Early life stress and morphometry of the adult anterior cingulate cortex and caudate nuclei.
BACKGROUND: Early life stress (ELS) is linked to adult psychopathology and may contribute to long-term brain alterations, as suggested by studies of women who suffered childhood sexual abuse. We examine whether reported adverse ELS defined as stressful and/or traumatic adverse childhood events (ACEs) is associated with smaller limbic and basal ganglia volumes. METHOD: 265 healthy Australian men and women without psychopathology or brain disorders were studied. ACEs were assessed by the ELSQ and current emotional state by the DASS. Anterior cingulate cortex (ACC), hippocampus, amygdala, and caudate nucleus volumes were measured from T1-weighted MRI. Analyses examined ROI volumetric associations with reported ACEs and DASS scores. RESULTS: Participants with greater than two ACEs had smaller ACC and caudate nuclei than those without ACEs. A significant association between total ACEs and ROI volumes for these structures was observed. Regression analysis also revealed that ELS was more strongly associated than current emotional state (DASS) with these ROI volumes. CONCLUSIONS: Reported ELS is associated with smaller ACC and caudate volumes, but not the hippocampal or amygdala volumes. The reasons for these brain effects are not entirely clear, but may reflect the influence of early stress and traumatic events on the developing brain.
Adolescent↗
Bayesian model averaging in EEG/MEG imaging.
In this paper, the Bayesian Theory is used to formulate the Inverse Problem (IP) of the EEG/MEG. This formulation offers a comparison framework for the wide range of inverse methods available and allows us to address the problem of model uncertainty that arises when dealing with different solutions for a single data. In this case, each model is defined by the set of assumptions of the inverse method used, as well as by the functional dependence between the data and the Primary Current Density (PCD) inside the brain. The key point is that the Bayesian Theory not only provides for posterior estimates of the parameters of interest (the PCD) for a given model, but also gives the possibility of finding posterior expected utilities unconditional on the models assumed. In the present work, this is achieved by considering a third level of inference that has been systematically omitted by previous Bayesian formulations of the IP. This level is known as Bayesian model averaging (BMA). The new approach is illustrated in the case of considering different anatomical constraints for solving the IP of the EEG in the frequency domain. This methodology allows us to address two of the main problems that affect linear inverse solutions (LIS): (a) the existence of ghost sources and (b) the tendency to underestimate deep activity. Both simulated and real experimental data are used to demonstrate the capabilities of the BMA approach, and some of the results are compared with the solutions obtained using the popular low-resolution electromagnetic tomography (LORETA) and its anatomically constraint version (cLORETA).
Artifacts↗
Mapping hippocampal and ventricular change in Alzheimer disease.
We developed an anatomical mapping technique to detect hippocampal and ventricular changes in Alzheimer disease (AD). The resulting maps are sensitive to longitudinal changes in brain structure as the disease progresses. An anatomical surface modeling approach was combined with surface-based statistics to visualize the region and rate of atrophy in serial MRI scans and isolate where these changes link with cognitive decline. Sixty-two [corrected] high-resolution MRI scans were acquired from 12 AD patients (mean [corrected] age +/- SE at first scan: 68.7 +/- 1.7 [corrected] years) and 14 matched controls (age: 71.4 +/- 0.9 years) [corrected] each scanned twice (1.9 +/- 0.2 [corrected] years apart, when all subjects are pooled [corrected] 3D parametric mesh models of the hippocampus and temporal horns were created in sequential scans and averaged across subjects to identify systematic patterns of atrophy. As an index of radial atrophy, 3D distance fields were generated relating each anatomical surface point to a medial curve threading down the medial axis of each structure. Hippocampal atrophic rates and ventricular expansion were assessed statistically using surface-based permutation testing and were faster in AD than in controls. Using color-coded maps and video sequences, these changes were visualized as they progressed anatomically over time. Additional maps localized regions where atrophic changes linked with cognitive decline. Temporal horn expansion maps were more sensitive to AD progression than maps of hippocampal atrophy, but both maps correlated with clinical deterioration. These quantitative, dynamic visualizations of hippocampal atrophy and ventricular expansion rates in aging and AD may provide a promising measure to track AD progression in drug trials.
Aged↗
A method for the analysis of the geometrical relationship between white matter pathology and the vascular architecture of the brain.
A novel method for the visual and quantitative analysis of the geometrical relationship between the vascular architecture of the brain and white matter pathology is presented. The cerebro vascular system is implicated in the pathogenesis of many diseases of the cerebral white matter, for example, stroke, microcerebrovascular disease, and multiple sclerosis (MS). In our work, white matter lesions and vessels are depicted using magnetic resonance imaging (MRI) and extracted using image analysis techniques. We focus on measuring distance relationships between white matter lesions and vessels, and distribution of lesions with respect to vessel caliber. Vascular distance maps are generated by computing for each voxel the Euclidean distance to the closest vessel. Analogously, radius maps assign the radius of the closest vessel to each voxel in the image volume. The distance and radius maps are used to analyze the distribution of lesions with respect to the vessels' locations and their calibers. The method was applied to three MS patients to demonstrate its functionality and feasibility. Preliminary findings indicate that larger MS lesions tend to be farther from detected vessels and that the caliber of the vessels nearest to larger lesions tends to be smaller, suggesting a possible role of relative hypoperfusion or hypoxia in lesion formation.
Brain↗
Structural brain variation and general intelligence.
Total brain volume accounts for about 16% of the variance in general intelligence scores (IQ), but how volumes of specific regions-of-interest (ROIs) relate to IQ is not known. We used voxel-based morphometry (VBM) in two independent samples to identify substantial gray matter (GM) correlates of IQ. Based on statistical conjunction of both samples (N = 47; P < 0.05 corrected for multiple comparisons), more gray matter is associated with higher IQ in discrete Brodmann areas (BA) including frontal (BA 10, 46, 9), temporal (BA 21, 37, 22, 42), parietal (BA 43 and 3), and occipital (BA 19) lobes and near BA 39 for white matter (WM). These results underscore the distributed neural basis of intelligence and suggest a developmental course for volume--IQ relationships in adulthood.
Adult↗