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1.
Pilot Feasibility Stud ; 10(1): 53, 2024 Mar 26.
Article in English | MEDLINE | ID: mdl-38532490

ABSTRACT

BACKGROUND: A serious game called SPARX (Smart, Positive, Active, Realistic, X-factor thoughts), originally developed in New Zealand and incorporating cognitive behavioural therapy (CBT) principles, has been shown to help reduce symptoms of depression and anxiety in adolescents with mild to moderate depression in studies undertaken in Australasia. However, SPARX has never been trialled in the United Kingdom (UK), and there have been issues relating to low engagement when it has been used in a real-world context. AIMS: To conduct the first pilot and feasibility randomised controlled trial (RCT) in England to explore the use of SPARX in different settings. The trial will explore whether SPARX supported by an e-coach (assistant psychologists) improves adherence and engagement compared with self-directed (i.e. self-help) use. The trial results will be used to inform the optimal mode of delivery (SPARX supported vs. SPARX self-directed), to calculate an appropriate sample size for a full RCT, and to decide which setting is most suitable. METHODS: Following consultation with young people to ensure study suitability/appropriateness, a total of 120 adolescents (11-19 years) will be recruited for this three-arm study. Adolescents recruited for the study across England will be randomised to receive either SPARX with human support (from an e-coach), self-directed SPARX, or a waitlist control group. Assessments will be conducted online at baseline, week 4, and 8-10-week post-randomisation. The assessments will include measures which capture demographic, depression (Patient Health Questionnaire modified for adolescents [PHQ-A]) and anxiety (Revised Child Anxiety and Depression Scale [RCADS]) symptomatology, and health-related quality-of-life data (EQ-5D-Y and proxy version). Analyses will be primarily descriptive. Qualitative interviews will be undertaken with a proportion of the participants and clinical staff as part of a process evaluation, and the qualitative data gathered will be thematically analysed. Finally, feasibility data will be collected on recruitment details, overall study uptake and engagement with SPARX, participant retention, and youth-reported acceptability of the intervention. DISCUSSION: The findings will inform the design of a future definitive RCT of SPARX in the UK. If the subsequent definitive RCT demonstrates that SPARX is effective, then an online serious game utilising CBT principles ultimately has the potential to improve the provision of care within the UK's health services if delivered en masse. TRIAL REGISTRATION: ISRCTN: ISRCTN15124804. Registered on 16 January 2023, https://www.isrctn.com/ISRCTN15124804 .

2.
J Neurosci Methods ; 372: 109556, 2022 04 15.
Article in English | MEDLINE | ID: mdl-35271873

ABSTRACT

BACKGROUND: Functional MRI and voxel-based morphometry are important in neuroscience. They are technically challenging with no globally optimal analysis method, and the multiple approaches have been shown to produce different results. It is useful to be able to meta-analyse results from such studies that tested a similar hypothesis potentially using different analysis methods. The aim is to identify replicable results and infer hypothesis specific effects. Coordinate based meta-analysis (CBMA) offers this, but the multiple algorithms can produce different results, making interpretation conditional on the algorithm. NEW METHOD: Here a new model based CBMA algorithm, Analysis of Brain Coordinates (ABC), is presented. ABC aims to be simple to understand by avoiding empirical elements where possible and by using a simple to interpret statistical threshold, which relates to the primary aim of detecting replicable effects. RESULTS: ABC is compared to both the most used and the most recently developed CBMA algorithms, by reproducing a published meta-analysis of localised grey matter changes in schizophrenia. There are some differences in results and the type of data that can be analysed, which are related to the algorithm specifics. COMPARISON TO OTHER METHODS: Compared to other algorithms ABC eliminates empirical elements where possible and uses a simple to interpret statistical threshold. CONCLUSIONS: There may be no optimal way to meta-analyse neuroimaging studies using CBMA. However, by eliminating some empirical elements and relating the statistical threshold directly to the aim of finding replicable effects, ABC makes the impact of the algorithm on any conclusion easier to understand.


Subject(s)
Brain , Neuroimaging , Algorithms , Brain/diagnostic imaging , Gray Matter/diagnostic imaging , Magnetic Resonance Imaging
3.
Eur J Neurol ; 27(1): 105-112, 2020 01.
Article in English | MEDLINE | ID: mdl-31309645

ABSTRACT

BACKGROUND AND PURPOSE: We aimed to determine the burden of comorbidities at the time of diagnosis of multiple sclerosis (MS), the risk of developing new comorbidities after diagnosis and the effect of comorbidities on mortality in patients with MS. METHODS: This study used data from 2526 patients with incident MS and 9980 age-, sex- and physician-matched controls without MS identified from the UK Clinical Practice Research Datalink. RESULTS: Before the MS diagnosis, the adjusted odds ratio for the association between MS and a Charlson comorbidity index score of 1-2, 3-4 or ≥5 was 131 [95% confidence interval (CI), 1.17-1.47], 1.65 (95% CI, 1.20-2.26) or 3.26 (95% CI, 1.58-6.70), respectively. MS was associated with increased risks of cardiovascular and neurological/mental diseases. After diagnosis, the adjusted hazard ratio for the association between MS and an increased risk of developing comorbidities was 1.13 (95% CI, 1.00-1.29). The risk of developing any comorbidity in terms of neoplasms, musculoskeletal/connective tissue diseases or neurological/mental diseases was higher in MS. Patients with MS had a higher mortality risk compared with controls, with a hazard ratio of 2.29 (95% CI, 1.81-2.73) after adjusting for comorbidities. There was a dose effect of pre-existing comorbidities on mortality. CONCLUSIONS: Patients with MS have an increased risk of developing multiple comorbidities both before and after diagnosis and pre-existing comorbidities have an impact on survival.


Subject(s)
Multiple Sclerosis/complications , Multiple Sclerosis/mortality , Adult , Age of Onset , Cause of Death , Comorbidity , Female , Humans , Incidence , Male , Middle Aged , Risk Assessment , Survival Analysis , United Kingdom/epidemiology
4.
Neuroimage ; 205: 116259, 2020 01 15.
Article in English | MEDLINE | ID: mdl-31626896

ABSTRACT

Meta-analysis of summary results from published neuroimaging studies independently testing a common hypothesis is performed using coordinate based meta-analysis (CBMA), which tests for consistent activation (in the case of functional MRI studies) of the same anatomical regions. Using just the reported coordinates it is also possible to meta-analyse coactivated regions to reveal a network-like structure of coordinate clusters (network nodes) distributed at the coactivated locations and a measure of the coactivation strength (network edges), which is determined by the presence/absence of reported activation. Here a new coordinate-based method to estimate a network of coactivations is detailed, which utilises the Z score accompanying each reported. Coordinate based meta-analysis of networks (CBMAN) assumes that if the activation pattern reported by independent studies is truly consistent, then the relative magnitude of these Z scores might also be consistent. It is hypothesised that this is detectable as Z score covariance between coactivated regions provided the within study variances are small. Advantages of using the Z scores instead of coordinates to measure coactivation strength are that censoring by the significance thresholds can be considered, and that using a continuous measure rather than a dichotomous one can increase statistical power. CBMAN uses maximum likelihood estimation to fit multivariate normal distributions to the standardised Z scores, and the covariances are considered as edges of a network of coactivated clusters (nodes). Here it is validated by numerical simulation and demonstrated on real data used previously to demonstrate CBMA. Software to perform CBMAN is freely available.


Subject(s)
Brain Mapping , Brain/diagnostic imaging , Brain/physiology , Network Meta-Analysis , Adult , Brain Mapping/methods , Brain Mapping/statistics & numerical data , Humans
6.
Eur J Neurol ; 26(2): 342-e23, 2019 02.
Article in English | MEDLINE | ID: mdl-30312502

ABSTRACT

BACKGROUND AND PURPOSE: We aimed to determine the prevalence of epilepsy in patients with multiple sclerosis (MS) at diagnosis, the risk of developing epilepsy after the diagnosis of MS and the relative risk of mortality associated with epilepsy. METHODS: We used the UK Clinical Practice Research Data-link to identify 2526 patients with incident MS and 9980 age-, sex- and index year-matched non-MS controls from 1997 to 2006. Logistic regression was used to estimate odds ratios [95% confidence interval (CI)] for epilepsy and Cox regression was used to estimate hazard ratios (HRs) (95% CI) for epilepsy and mortality. RESULTS: Patients with incident MS were on average 45 years old and 70.9% were female. At diagnosis, the prevalence of epilepsy in patients with MS was 1.30% compared with 0.57% in non-MS controls. At diagnosis, MS was associated with an adjusted odds ratio (95% CI) of 2.11 (1.36-3.27) for pre-existing epilepsy. Among epilepsy-free patients, the cumulative probabilities of developing epilepsy, first recorded within 10 years of the index date, were 2.77% for patients with MS and 0.90% for controls. MS was associated with an adjusted HR (95% CI) of 6.01 (2.94-12.29) for epilepsy. Among patients with MS, epilepsy was associated with an HR (95% CI) of 2.23 (1.02-4.84) for all-cause mortality. CONCLUSIONS: This population-based study found an increased prevalence of epilepsy in patients with MS at diagnosis when compared with non-MS controls and the risk of developing epilepsy was also higher following the MS diagnosis. Patients with MS with epilepsy had a higher risk of mortality compared with those without.


Subject(s)
Epilepsy/epidemiology , Multiple Sclerosis/epidemiology , Adult , Databases, Factual , Epilepsy/mortality , Female , Humans , Male , Middle Aged , Multiple Sclerosis/mortality , Prevalence , Survival Rate , Young Adult
7.
Neuroimage ; 153: 293-306, 2017 06.
Article in English | MEDLINE | ID: mdl-28389386

ABSTRACT

Low power in neuroimaging studies can make them difficult to interpret, and Coordinate based meta-analysis (CBMA) may go some way to mitigating this issue. CBMA has been used in many analyses to detect where published functional MRI or voxel-based morphometry studies testing similar hypotheses report significant summary results (coordinates) consistently. Only the reported coordinates and possibly t statistics are analysed, and statistical significance of clusters is determined by coordinate density. Here a method of performing coordinate based random effect size meta-analysis and meta-regression is introduced. The algorithm (ClusterZ) analyses both coordinates and reported t statistic or Z score, standardised by the number of subjects. Statistical significance is determined not by coordinate density, but by a random effects meta-analyses of reported effects performed cluster-wise using standard statistical methods and taking account of censoring inherent in the published summary results. Type 1 error control is achieved using the false cluster discovery rate (FCDR), which is based on the false discovery rate. This controls both the family wise error rate under the null hypothesis that coordinates are randomly drawn from a standard stereotaxic space, and the proportion of significant clusters that are expected under the null. Such control is necessary to avoid propagating and even amplifying the very issues motivating the meta-analysis in the first place. ClusterZ is demonstrated on both numerically simulated data and on real data from reports of grey matter loss in multiple sclerosis (MS) and syndromes suggestive of MS, and of painful stimulus in healthy controls. The software implementation is available to download and use freely.


Subject(s)
Meta-Analysis as Topic , Neuroimaging , Reproducibility of Results , Algorithms , Brain/physiopathology , Brain Mapping , Cluster Analysis , Computer Simulation , Humans , Multiple Sclerosis/physiopathology , Pain/physiopathology , Regression Analysis
8.
J Neurol Sci ; 287(1-2): 212-5, 2009 Dec 15.
Article in English | MEDLINE | ID: mdl-19695579

ABSTRACT

BACKGROUND: Multiple sclerosis (MS) is a chronic inflammatory disease of the CNS. Therapies that affect the endocannabinoid (EC) system may have immunomodulatory, symptomatic and neuroprotective effects. AIM: The aim of this study was to determine how levels of EC and related compounds are altered in MS. METHODS: Plasma and whole blood were collected from 24 MS patients (10 relapsing-remitting (RR); 8 secondary-progressive (SP); 6 primary-progressive (PP); 19 females; 25-66 years) and 17 controls (10 females; 22-62 years). Plasma EC and related compounds were quantified by liquid chromatography-tandem mass spectrometry. Fatty acid amide hydrolase (FAAH), cannabinoid receptors CB(1) and CB(2) mRNA were measured by quantitative reverse transcriptase-polymerase chain reaction. RESULTS: Anandamide (AEA) and palmitoylethanolamide (PEA) were higher in RRMS compared to controls (p=0.001 and p=0.027). AEA, PEA and oleoylethanolamide were also increased in SPMS plasma (p=0.001, p=0.004, and p=0.005). PPMS patients had higher AEA plasma levels compared to controls (p=0.009). FAAH mRNA was decreased in SPMS (p=0.04) but not in RRMS or PPMS blood. CB(1) (p=0.012) and CB(2) mRNA (p=0.003) were increased in the PPMS. CONCLUSION: The EC system is altered in MS. It may be dynamically modulated depending on the subtype of the disease, but further studies with larger subgroups are needed to confirm this.


Subject(s)
Brain/metabolism , Cannabinoid Receptor Modulators/blood , Endocannabinoids , Multiple Sclerosis/blood , Adult , Aged , Amides , Amidohydrolases/genetics , Arachidonic Acids/analysis , Arachidonic Acids/blood , Brain/physiopathology , Brain Chemistry/genetics , Cannabinoid Receptor Modulators/analysis , Cannabinoids/pharmacology , Cannabinoids/therapeutic use , Chromatography, Liquid , Cytoprotection/drug effects , Cytoprotection/physiology , Disability Evaluation , Ethanolamines , Female , Humans , Male , Mass Spectrometry , Middle Aged , Multiple Sclerosis/drug therapy , Multiple Sclerosis/physiopathology , Oleic Acids/analysis , Oleic Acids/blood , Palmitic Acids/analysis , Palmitic Acids/blood , Polyunsaturated Alkamides/analysis , Polyunsaturated Alkamides/blood , RNA, Messenger/analysis , RNA, Messenger/metabolism , Receptors, Cannabinoid/genetics
9.
J Neurol Neurosurg Psychiatry ; 79(4): 437-41, 2008 Apr.
Article in English | MEDLINE | ID: mdl-17673493

ABSTRACT

BACKGROUND: Cognitive impairment is one of the frequent and early findings in multiple sclerosis (MS). OBJECTIVE: To determine the relation between cognitive abnormalities and the extent of macroscopic and microscopic tissue damage in the corpus callosum (CC), revealed by conventional magnetic resonance imaging (MRI), magnetisation transfer imaging (MTI) and diffusion tensor imaging (DTI). METHODS: Conventional dual-echo, DTI and MTI of the brain were obtained from 36 patients with relapsing remitting (RR) MS, and 13 age and gender matched normal controls. Voxels from CC were identified using a tractography based algorithm. Mean apparent diffusion coefficient (ADC(av)) and MT ratio were measured for the CC as defined by tractography. Corpus callosum area (CCA) was measured using edge detection on the mid-sagittal slice on high resolution MRI images. The Expanded Disability Status Scale (EDSS) and Paced Auditory Serial Addition Test (PASAT) were scored. RESULTS: Nine patients (25%) were found to be cognitively impaired. The CCA was not significantly different in the whole cohort of patients from controls (608.2 (428.6-713.0) mm(2) vs 674.2 (585.8-754.4) mm(2), p = 0.1), but was smaller in cognitively impaired than unimpaired group (417 (290-634) mm(2) vs 652 (511-718) mm(2), p = 0.04). The mean MT ratio of CC in patients was lower than in controls (0.41 (0.39-0.042) vs 0.43 (0.42-0.43), p<0.001). The ADC(av) in the CC in patients was higher than in controls (0.94 (0.89-0.99) vs 0.87 (0.85-0.89), p<0.001). PASAT was correlated with mean MT ratio (r = 0.47, p = 0.0046), ADC(av) (r = -0.53, p = 0.0012), CCA (r = 0.42, p = 0.01) and total T(2) lesion load (r = -0.4, p = 0.017), but not with T(2) lesion load within the CC (r = -0.24, p = 0.16), disease duration (r = -0.2, p = 0.24) or EDSS (r = -0.27, p = 0.12). CONCLUSIONS: ADC(av), MTR and atrophy measures in the CC may offer a sensitive method detecting subtle macroscopic and microscopic changes associated with cognitive impairment in MS.


Subject(s)
Cognition Disorders/diagnosis , Corpus Callosum/pathology , Diffusion Magnetic Resonance Imaging/methods , Image Processing, Computer-Assisted/methods , Magnetic Resonance Imaging/methods , Multiple Sclerosis, Relapsing-Remitting/diagnosis , Adult , Cognition Disorders/pathology , Disability Evaluation , Female , Humans , Male , Middle Aged , Multiple Sclerosis, Relapsing-Remitting/pathology , Neuropsychological Tests , Problem Solving/physiology , Software , Statistics as Topic
10.
Expert Rev Neurother ; 7(9): 1203-11, 2007 Sep.
Article in English | MEDLINE | ID: mdl-17868018

ABSTRACT

The spinal cord is commonly affected by acute demyelinating lesions, chronic tissue loss and atrophy in multiple sclerosis, and is a clinically eloquent site. Historically, however, more attention has been focussed on the analysis and contribution of brain lesions. In this review, we discuss some of the key findings from MRI analysis and histopathological examination of the spinal cord, and how they relate to the clinical characteristics of this common and disabling disease.


Subject(s)
Multiple Sclerosis/pathology , Neural Pathways/pathology , Spinal Cord/pathology , Humans
11.
J Neurol Neurosurg Psychiatry ; 74(8): 1090-4, 2003 Aug.
Article in English | MEDLINE | ID: mdl-12876240

ABSTRACT

BACKGROUND: Pathology in the cervical spinal cord is considered an important cause of disability in multiple sclerosis. However, the majority of serial studies have failed to find a correlation between spinal cord atrophy and disability. OBJECTIVES: To use a highly reproducible and accurate method to quantify spinal cord area change on three dimensional magnetic resonance imaging and relate this to disability change in patients with multiple sclerosis. METHODS: 38 patients with multiple sclerosis (20 with the relapsing-remitting (RRMS) form and 18 with the secondary progressive (SPMS) form) were imaged at baseline and at months 6, 12, 18, and 48 during two treatment trials of the high dose subcutaneous thrice weekly interferon beta-1a (IFNbeta, Rebif). Thirty one healthy subjects were also imaged at baseline. Upper cervical cord area (UCCA) was measured using Sobel edge detection. RESULTS: The intraobserver coefficient of variation of the method was 0.42%. A significant reduction in UCCA was detected at month 6 in the placebo group (p = 0.04) and at month 12 for INFbeta (p = 0.03). The mean reduction of UCCA at month 48 was 5.7% for patients initially on placebo who received treatment at 24 months (RRMS) or at 36 months (SPMS), and 4.5% for those on IFNbeta throughout the study (p = 0.35). The change in UCCA was significantly correlated with change in the expanded disability status scale at month 12 (r = 0.4, p = 0.016), month 18 (r = 0.32, p = 0.05), and month 48 (r = 0.4, p = 0.016) in the total cohort. CONCLUSIONS: Despite the small number of patients studied and the possible confounding effects of interferon treatment, this study showed that edge detection is reproducible and sensitive to changes in spinal cord area, and that this change is related to changes in clinical disability. This suggests a role for measurement of spinal cord atrophy in monitoring disease progression and possible treatment effects in clinical trails.


Subject(s)
Disability Evaluation , Image Enhancement/methods , Image Processing, Computer-Assisted/methods , Imaging, Three-Dimensional , Magnetic Resonance Imaging/methods , Multiple Sclerosis, Chronic Progressive/diagnosis , Multiple Sclerosis, Relapsing-Remitting/diagnosis , Spinal Cord/pathology , Adult , Atrophy , Cohort Studies , Disease Progression , Dose-Response Relationship, Drug , Female , Follow-Up Studies , Humans , Injections, Subcutaneous , Interferon beta-1a , Interferon-beta/administration & dosage , Male , Middle Aged , Multiple Sclerosis, Chronic Progressive/drug therapy , Multiple Sclerosis, Relapsing-Remitting/drug therapy , Observer Variation
12.
J Neurol Neurosurg Psychiatry ; 74(2): 203-7, 2003 Feb.
Article in English | MEDLINE | ID: mdl-12531950

ABSTRACT

BACKGROUND: Current magnetic resonance imaging (MRI) outcome measures such as T2 lesion load correlate poorly with disability in multiple sclerosis. Diffusion tensor imaging (DTI) of the brain can provide unique information regarding the orientation and integrity of white matter tracts in vivo. OBJECTIVE: To use this information to map the pyramidal tracts of patients with multiple sclerosis, investigate the relation between burden of disease in the tracts and disability, and compare this with more global magnetic resonance estimates of disease burden. METHODS: 25 patients with relapsing-remitting multiple sclerosis and 17 healthy volunteers were studied with DTI. An algorithm was used that automatically produced anatomically plausible maps of white matter tracts. The integrity of the pyramidal tracts was assessed using relative anisotropy and a novel measure (L(t)) derived from the compounded relative anisotropy along the tracts. The methods were compared with both traditional and more recent techniques for measuring disease burden in multiple sclerosis (T2 lesion load and "whole brain" diffusion histograms). RESULTS: Relative anisotropy and L(t) were significantly lower in patients than controls (p < 0.05). Pyramidal tract L(t) in the patients correlated significantly with both expanded disability status scale (r = -0.48, p < 0.05), and to a greater degree, the pyramidal Kurtzke functional system score (KFS-p) (r = -0.75, p < 0.0001). T2 lesion load and diffusion histogram parameters did not correlate with disability. CONCLUSIONS: Tract mapping using DTI is feasible and may increase the specificity of MRI in multiple sclerosis by matching appropriate tracts with specific clinical scoring systems. These techniques may be applicable to a wide range of neurological conditions.


Subject(s)
Brain Mapping , Diffusion Magnetic Resonance Imaging , Disability Evaluation , Image Processing, Computer-Assisted , Multiple Sclerosis, Relapsing-Remitting/diagnosis , Pyramidal Tracts/pathology , Adult , Anisotropy , Artifacts , Brain/pathology , Cost of Illness , Echo-Planar Imaging , Female , Humans , Male , Middle Aged , Reference Values , Reproducibility of Results , Software
13.
Magn Reson Med ; 48(4): 677-83, 2002 Oct.
Article in English | MEDLINE | ID: mdl-12353285

ABSTRACT

Diffusion tensor imaging (DTI) promises a robust means of visualizing in vivo white matter fibers in individual subjects, and of inferring direct connectivity between distant points in the brain. By following the primary eigenvector of the diffusion tensor, trajectories may be defined that trace the path of the underlying fiber tract. However, fiber tracking is prone to cumulative error from acquisition noise and partial volume, which limits the repeatability of such techniques. An image-processing method based on stochastic labeling, by which the noisy primary eigenvectors may be reconfigured according to anatomically reasonable assumptions, is described. The method's potential to improve fiber tracking is first demonstrated on numerical test data. It is then applied to real data acquired from healthy volunteers. Trajectories defined within the corpus callosum and the pyramidal tracts are rendered using 3D graphic imaging software, and the results are compared before and after processing. Fiber tracking was shown to produce anatomically plausible results, and typical errors were largely resolved by the method. Further, the sensitivity of trajectories to their start point was greatly reduced after processing. The use of stochastic labeling may therefore improve the reliability of experiments using white matter fiber tracking.


Subject(s)
Corpus Callosum/anatomy & histology , Magnetic Resonance Imaging/methods , Nerve Fibers , Pyramidal Tracts/anatomy & histology , Diffusion Magnetic Resonance Imaging , Echo-Planar Imaging , Humans , Image Processing, Computer-Assisted/methods , Imaging, Three-Dimensional , Stochastic Processes
14.
Magn Reson Med ; 47(5): 967-72, 2002 May.
Article in English | MEDLINE | ID: mdl-11979576

ABSTRACT

Diffusion tensor MRI is used to define trajectories that reflect the long-range order of in vivo white matter (WM) fiber tracts. Fiber tracking is particularly prone to cumulative error from noise and partial volume along the length of the trajectory paths, but the overall shape of each path is anatomically meaningful. By considering only the long-range similarity of path shapes, a method of constructing 3D maps of specific WM structures has been developed. A trajectory is first computed from an operator-selected seed voxel, located within the anatomical structure of interest (SOI). Voxels from the same structure are then automatically identified based on the similarity of trajectory path shapes, assessed using Pearson's correlation coefficient. The corpus callosum and pyramidal tracts in 14 patients with multiple sclerosis, and in 10 healthy controls were mapped by this method, and the apparent diffusion coefficient (ADC) was measured. The ADC was significantly higher in patients than in controls, and higher in the corpus callosum than in the pyramidal tracts for both groups. Using this method the different functional structures in the WM may be identified and mapped. Within these maps, MRI parameters can be measured for subsequent comparison with relevant clinical data.


Subject(s)
Brain Mapping/methods , Magnetic Resonance Imaging/methods , Algorithms , Corpus Callosum/anatomy & histology , Humans , Multiple Sclerosis/diagnosis , Pyramidal Tracts/anatomy & histology
15.
Phys Rev E Stat Nonlin Soft Matter Phys ; 64(4 Pt 2): 047701, 2001 Oct.
Article in English | MEDLINE | ID: mdl-11690185

ABSTRACT

We present a fourth-order finite difference (FD) method for solving two-dimensional partial differential equations. The FD operator uses a compact nine-point stencil on a regular square grid. Despite the regular grid, Dirichlet boundary conditions can be applied on an arbitrarily shaped boundary without resorting to the usual stepped approximation. We demonstrate the superior convergence of the method over second-order techniques by solving the Schrödinger equation for an electron in a semiconductor quantum dot with a smoothly varying potential which generates classically chaotic dynamics.

16.
Phys Rev Lett ; 87(4): 046803, 2001 Jul 23.
Article in English | MEDLINE | ID: mdl-11461635

ABSTRACT

We investigate chaotic electron transport in the lowest miniband of a semiconductor superlattice with a tilted magnetic field. This experimentally accessible non-Kolmogorov-Arnol'd-Moser system involves only stationary electric and magnetic fields, but is dynamically equivalent to a time-dependent kicked harmonic oscillator. The onset of chaos strongly delocalizes the electron orbits, thus raising the electrical conductivity. When the cyclotron and Bloch frequencies are commensurate, the phase space is threaded by a stochastic web, which produces a further resonant increase in the conductivity.

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