Variational Approach to the Modulational Instability

We study the modulational stability of the nonlinear Schr\"odinger equation (NLS) using a time-dependent variational approach. Within this framework, we derive ordinary differential equations (ODEs) for the time evolution of the amplitude and phase of modulational perturbations. Analyzing the ensuing ODEs, we re-derive the classical modulational instability criterion. The case (relevant to applications in optics and Bose-Einstein condensation) where the coefficients of the equation are time-dependent, is also examined

On non-local variational problems with lack of compactness related to non-linear optics

We give a simple proof of existence of solutions of the dispersion manage- ment and diffraction management equations for zero average dispersion, respectively diffraction. These solutions are found as maximizers of non-linear and non-local vari- ational problems which are invariant under a large non-compact group. Our proof of existence of maximizer is rather direct and avoids the use of Lions' concentration compactness argument or Ekeland's variational principle.Comment: 30 page

Prognosis of the individual course of disease - steps in developing a decision support tool for Multiple Sclerosis

<p>Abstract</p> <p>Background</p> <p>Multiple sclerosis is a chronic disease of uncertain aetiology. Variations in its disease course make it difficult to impossible to accurately determine the prognosis of individual patients. The Sylvia Lawry Centre for Multiple Sclerosis Research (SLCMSR) developed an "online analytical processing (OLAP)" tool that takes advantage of extant clinical trials data and allows one to model the near term future course of this chronic disease for an individual patient.</p> <p>Results</p> <p>For a given patient the most similar patients of the SLCMSR database are intelligently selected by a model-based matching algorithm integrated into an OLAP-tool to enable real time, web-based statistical analyses. The underlying database (last update April 2005) contains 1,059 patients derived from 30 placebo arms of controlled clinical trials. Demographic information on the entire database and the portion selected for comparison are displayed. The result of the statistical comparison is provided as a display of the course of Expanded Disability Status Scale (EDSS) for individuals in the database with regions of probable progression over time, along with their mean relapse rate. Kaplan-Meier curves for time to sustained progression in the EDSS and time to requirement of constant assistance to walk (EDSS 6) are also displayed. The software-application OLAP anticipates the input MS patient's course on the basis of baseline values and the known course of disease for similar patients who have been followed in clinical trials.</p> <p>Conclusion</p> <p>This simulation could be useful for physicians, researchers and other professionals who counsel patients on therapeutic options. The application can be modified for studying the natural history of other chronic diseases, if and when similar datasets on which the OLAP operates exist.</p

Protocol for the saMS trial (supportive adjustment for multiple sclerosis): a randomized controlled trial comparing cognitive behavioral therapy to supportive listening for adjustment to multiple sclerosis

BackgroundMultiple Sclerosis (MS) is an incurable, chronic, potentially progressive and unpredictable disease of the central nervous system. The disease produces a range of unpleasant and debilitating symptoms, which can have a profound impact including disrupting activities of daily living, employment, income, relationships, social and leisure activities, and life goals. Adjusting to the illness is therefore particularly challenging. This trial tests the effectiveness of a cognitive behavioural intervention compared to supportive listening to assist adjustment in the early stages of MS.MethodsThis is a two arm randomized multi-centre parallel group controlled trial. 122 consenting participants who meet eligibility criteria will be randomly allocated to receive either Cognitive Behavioral Therapy or Supportive Listening. Eight one hour sessions of therapy (delivered over a period of 10 weeks) will be delivered by general nurses trained in both treatments. Self-report questionnaire data will be collected at baseline (0 weeks), mid-therapy (week 5 of therapy), post-therapy (15 weeks) and at six months (26 weeks) and twelve months (52 weeks) follow-up. Primary outcomes are distress and MS-related social and role impairment at twelve month follow-up. Analysis will also consider predictors and mechanisms of change during therapy. In-depth interviews to examine participants’ experiences of the interventions will be conducted with a purposively sampled sub-set of the trial participants. An economic analysis will also take place. DiscussionThis trial is distinctive in its aims in that it aids adjustment to MS in a broad sense. It is not a treatment specifically for depression. Use of nurses as therapists makes the interventions potentially viable in terms of being rolled out in the NHS. The trial benefits from incorporating patient input in the development and evaluation stages. The trial will provide important information about the efficacy, cost-effectiveness and acceptability of the interventions as well as mechanisms of psychosocial adjustment.Trial registrationCurrent Controlled Trials ISRCTN91377356<br/

Influence of FK 506 (tacrolimus) on circulating CD4 ⁺ t cells expressing cd25 and cd45ra antigens in 19 patients with chronic progressive multiple sclerosis participating in an open label drug safety trial

We have taken the opportunity of a clinical trial of the potential efficacy and safety of FK 506 (tacrolimus) in chronic progressive multiple sclerosis (MS) to examine the influence of this potent new immunosuppressant on circulating T-lymphocytes in an otherwise healthy non-transplant population. Peripheral blood levels of subsets of CD4+ T lymphocytes expressing the activation molecule interleukin-2 receptor (p55 α chain; CD25) or the CD45RA isoform were determined sequentially in 19 patients that were treated continuously with oral FK 506 (starting dose 0.15 mg/kg/day) for 12 months. No significant change in the proportion of circulating CD25 + CD4+ cells was observed over the study period in which the mean trough plasma FK 506 level rose from 0.3 ±0.2 to 0.5 ±0.4 ng/ml. There was also no significant effect of FK 506 on the percentage of CD45RA + CD4 + cells in the peripheral blood at 12 months compared with pretreatment values. Analysis of a subgroup of 7 patients, who showed a sustained reduction in CD25 + CD4+ cells and a reciprocal increase in CD45RA* CD4 * cells for at least 6 months after start of treatment, did not reveal any difference in disability at one year compared with the treatment group as a whole. The side effects of FK 506 were mild and the overall degree of disability estimated by the mean Kurtzke expanded disability status scale (EDSS) score or the ambulation index did not deteriorate significantly in the 19 patients studied over the 12 months of FK 506 administration. © 1994 Informa UK Ltd All rights reserved: reproduction in whole or part not permitted

MRI characteristics are predictive for CDMS in monofocal, but not in multifocal patients with a clinically isolated syndrome

BACKGROUND: To diagnose multiple sclerosis (MS), evidence for dissemination in space and time is required. There is no clear definition on how symptoms and signs of a patient indicate clinical dissemination in space. To provide a uniform approach on this subject, a clinical classification system was described recently differentiating patients with mono- and multifocal clinical presentation. Here we assess the predictive value of clinically defined dissemination in space at first presentation for time to clinically definite MS (CDMS). METHODS: Four hundred and sixty-eight patients with a first episode suggestive of MS were classified as clinically mono- or multifocal by two neurologists blinded to magnetic resonance imaging (MRI) results. These patients were part of the BENEFIT study in which 292 patients were randomized to interferon beta-1b (IFNB-1b) and 176 to placebo. By using Kaplan-Meier statistics the risk for CDMS was studied in mono- and multifocal patients of the placebo group, both with and without taking into account MRI measures of potential prognostic relevance. RESULTS: Time to CDMS was similar in monofocal and multifocal patients. In monofocal patients, the risk for CDMS over 2 years was significantly higher when <or= 9 T2 lesions or at least one Gd-enhancing lesion were present at the first event or 3 or 6 months after the first event. In patients with multifocal presentation, these MRI measures had no significant added value in predicting time to CDMS. CONCLUSION: These data indicate that a carefully performed neurological assessment of symptoms and signs, combined with lesions on MRI, is important for defining the risk of conversion to CDMS. TRIAL REGISTRATION: The Benefit trial has been registered under NCT00185211 http://www.clinicaltrials.gov

Evidence for the different physiological significance of the 6- and 2-minute walk tests in multiple sclerosis

<p>Abstract</p> <p>Background</p> <p>Researchers have recently advocated for the 2-minute walk (2MW) as an alternative for the 6-minute walk (6MW) to assess long distance ambulation in persons with multiple sclerosis (MS). This recommendation has not been based on physiological considerations such as the rate of oxygen consumption (V·O₂) over the 6MW range.</p> <p>Objective</p> <p>This study examined the pattern of change in V·O₂over the range of the 6MW in a large sample of persons with MS who varied as a function of disability status.</p> <p>Method</p> <p>Ninety-five persons with clinically-definite MS underwent a neurological examination for generating an Expanded Disability Status Scale (EDSS) score, and then completion of the 6MW protocol while wearing a portable metabolic unit and an accelerometer.</p> <p>Results</p> <p>There was a time main effect on V·O₂during the 6MW (<it>p </it>= .0001) such that V·O₂increased significantly every 30 seconds over the first 3 minutes of the 6MW, and then remained stable over the second 3 minutes of the 6MW. This occurred despite no change in cadence across the 6MW (<it>p </it>= .84).</p> <p>Conclusions</p> <p>The pattern of change in V·O₂indicates that there are different metabolic systems providing energy for ambulation during the 6MW in MS subjects and steady state aerobic metabolism is reached during the last 3 minutes of the 6MW. By extension, the first 3 minutes would represent a test of mixed aerobic and anaerobic work, whereas the second 3 minutes would represent a test of aerobic work during walking.</p

Reproducibility over a 1-month period of 1H-MR spectroscopic imaging NAA/Cr ratios in clinically stable multiple sclerosis patients

N-acetylaspartate/creatine (NAA/Cr) ratios, assessed with proton magnetic resonance spectroscopy, are increasingly used as a surrogate marker for axonal dysfunction and degeneration in multiple sclerosis (MS). The purpose of this study was to test short-time reproducibility of NAA/Cr ratios in patients with clinically stable MS. In 35 MS patients we analysed NAA/Cr ratios obtained with 1H-MR spectroscopic imaging at the centrum semiovale either with lateral ventricles partially included (group 1; n=15) or more cranially with no ventricles included (group 2; n=20). To test short-term reproducibility of the NAA/Cr measurements, patients were scanned twice 4 weeks apart. We determined mean NAA/Cr and Cho/Cr ratios of 12 grey matter and 24 white matter voxels. Mean NAA/Cr ratios of both the white and grey matter did not change after 4 weeks. Overall 4-week reproducibility of the NAA/Cr ratio, expressed as coefficient of variation, was 4.8% for grey matter and 3.5% for white matter. Reproducibility of cranial scanning of the ventricles was slightly better than with cerebrospinal fluid included. Our study shows good short-term reproducibility of NAA/Cr ratio measurements in the centrum semiovale, which supports the reliability of this technique for longitudinal studies

Efficacy of repeated intrathecal triamcinolone acetonide application in progressive multiple sclerosis patients with spinal symptoms

BACKGROUND: There are controversial results on the efficacy of the abandoned, intrathecal predominant methylprednisolone application in multiple sclerosis (MS) in contrast to the proven effectiveness in intractable postherpetic neuralgia. METHODS: We performed an analysis of the efficacy of the application of 40 mg of the sustained release steroid triamcinolone acetonide (TCA). We intrathecally injected in sterile saline dissolved TCA six times within three weeks on a regular basis every third day in 161 hospitalized primary and predominant secondary progressive MS patients with spinal symptoms. The MS patients did not experience an acute onset of exacerbation or recent distinct increased progression of symptoms. We simultaneously scored the MS patients with the EDSS and the Barthel index, estimated the walking distance and measured somatosensory evoked potentials. Additionally the MS patients received a standardized rehabilitation treatment. RESULTS: EDSS score and Barthel index improved, walking distance increased, latencies of somatosensory evoked potentials of the median and tibial nerves shortened in all MS patients with serial evaluation (p < 0.0001 for all variables). Side effects were rare, five patients stopped TCA application due to onset of a post lumbar puncture syndrome. CONCLUSIONS: Repeated intrathecal TCA application improves spinal symptoms, walking distance and SSEP latencies in progressive MS patients in this uncontrolled study. Future trials should evaluate the long-term benefit of this invasive treatment

Patient-orientated longitudinal study of multiple sclerosis in south west England (The South West Impact of Multiple Sclerosis Project, SWIMS) 1: protocol and baseline characteristics of cohort

<p>Abstract</p> <p>Background</p> <p>There is a need for greater understanding of the impact of multiple sclerosis (MS) from the perspective of individuals with the condition. The South West Impact of MS Project (SWIMS) has been designed to improve understanding of disease impact using a patient-centred approach. The purpose is to (1) develop improved measurement instruments for clinical trials, (2) evaluate longitudinal performance of a variety of patient-reported outcome measures, (3) develop prognostic predictors for use in individualising drug treatment for patients, particularly early on in the disease course.</p> <p>Methods</p> <p>This is a patient-centred, prospective, longitudinal study of multiple sclerosis and clinically isolated syndrome (CIS) in south west England. The study area comprises two counties with a population of approximately 1.7 million and an estimated 1,800 cases of MS. Self-completion questionnaires are administered to participants every six months (for people with MS) or 12 months (CIS). Here we present descriptive statistics of the baseline data provided by 967 participants with MS.</p> <p>Results</p> <p>Seventy-five percent of those approached consented to participate. The male:female ratio was 1.00:3.01 (n = 967). Average (standard deviation) age at time of entry to SWIMS was 51.6 (11.5) years (n = 961) and median (interquartile range) time since first symptom was 13.3 (6.8 to 24.5) years (n = 934). Fatigue was the most commonly reported symptom, with 80% of participants experiencing fatigue at baseline. Although medication use for symptom control was common, there was little evidence of effectiveness, particularly for fatigue. Nineteen percent of participants were unable to classify their subtype of MS. When patient-reported subtype was compared to neurologist assessment for a sample of participants (n = 396), agreement in disease sub-type was achieved in 63% of cases. There were 836 relapses, reported by 931 participants, in the twelve months prior to baseline. Twenty-three percent of the relapsing-remitting group and 12% of the total sample were receiving disease-modifying therapy at baseline.</p> <p>Conclusions</p> <p>Demographics of this sample were similar to published data for the UK. Overall, the results broadly reflect clinical experience in confirming high symptom prevalence, with relatively little complete symptom relief. Participants often had difficulty in defining MS relapses and their own MS type.</p