Precision computerised cognitive behavioural therapy (cCBT) for adolescents with depression: a pilot and feasibility randomised controlled trial protocol for SPARX-UK

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 .

Age at onset predicts outcome in aquaporin-4-IgG positive neuromyelitis optica spectrum disorder from a United Kingdom population

BACKGROUND

There are few studies exploring the prognostic factors in patients with aquaporin-4 (AQP4)-IgG positive neuromyelitis optica spectrum disorder (NMOSD).

OBJECTIVE

To assess the predictors of outcome in patients with AQP4-antibody positive NMOSD from a United Kingdom (UK) population.

METHODS

A retrospective study of 52 patients from 2 neuroscience centres in the UK Midlands.

RESULTS

The most common initial presentations were acute myelitis and optic neuritis, with 22/52 cases (42.3%) each. Relapsing course was seen in 32 patients (61.5%) with mean annualised relapse rate of 0.43 (standard deviation 0.45) and a mean interval time to first relapse of 31 months (range 2-108). The median Expanded Disability Status Scale (EDSS) score at the last follow up was 4 (range 1-9). Age at onset was an independent predictor of disability in the whole cohort of patients with NMOSD. For every 10-year increase in age at disease onset, the risk of developing an EDSS score of ≥4 increased by 34%. Patients who presented initially with a longitudinally extensive transverse myelitis (LETM) showed a higher risk to develop disability, compared to other clinical presentations (median time of 4 years versus 13 years). Late onset (LO-NMOSD) patients were likely to reach an EDSS score of 4 more quickly, compared to early onset (EO-NMOSD) (median time of 7 years versus 13 years). Higher median EDSS score at last follow up was observed in LO-NMOSD compared to EO-NMOSD (6 versus 2).

CONCLUSION

Increasing age at onset and LETM predict disability in AQP-4-IgG positive NMOSD patients.

Single Test to ARrive at Multiple Sclerosis (STAR-MS) diagnosis: A prospective pilot study assessing the accuracy of the central vein sign in predicting multiple sclerosis in cases of diagnostic uncertainty

Background:

Misdiagnosis is common in multiple sclerosis (MS) as a proportion of patients present with atypical clinical/magnetic resonance imaging (MRI) findings. The central vein sign has the potential to be a non-invasive, MS-specific biomarker.

Objective:

To test the accuracy of the central vein sign in predicting a diagnosis of MS in patients with diagnostic uncertainty at disease presentation using T2*-weighted, 3 T MRI.

Methods:

In this prospective pilot study, we recruited individuals with symptoms unusual for MS but with brain MRI consistent with the disease, and those with a typical clinical presentation of MS whose MRI did not suggest MS. We calculated the proportion of lesions with central veins for each patient and compared the results to the eventual clinical diagnoses. The optimal central vein threshold for diagnosis was established.

Results:

Thirty-eight patients were scanned, 35 of whom have received a clinical diagnosis. Median percentage of lesions with central veins was 51% in MS and 28% in non-MS. A threshold of 40.7% lesions with central veins resulted in 100% sensitivity and 73.9% specificity.

Conclusion:

The central vein sign assessed with a clinically available T2* scan can successfully diagnose MS in cases of diagnostic uncertainty. The central vein sign should be considered as a diagnostic biomarker in MS.

Coordinate based meta-analysis of networks in neuroimaging studies

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.

Epilepsy and associated mortality in patients with multiple sclerosis

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.

Coordinate based random effect size meta-analysis of neuroimaging studies

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.

Plasma endocannabinoid levels in multiple sclerosis

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.

Use of combined conventional and quantitative MRI to quantify pathology related to cognitive impairment in multiple sclerosis

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.

Multiple sclerosis findings in the spinal cord

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.

Spinal cord atrophy and disability in multiple sclerosis over four years: application of a reproducible automated technique in monitoring disease progression in a cohort of the interferon beta-1a (Rebif) treatment trial

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.

Magnetic resonance imaging of the cervical spinal cord in multiple sclerosis--a quantitative T1 relaxation time mapping approach

BACKGROUND

The spinal cord is a common site of involvement in multiple sclerosis (MS) where pathology contributes substantially to locomotor disability. Previous studies have demonstrated significant correlations between clinical disability and cervical cord atrophy, but not with cord T(2) lesion load. We evaluate cervical cord pathology using, for the first time, quantitative T(1) relaxation time (T(1)), which shows histopathological specificity for tissue damage in the cerebral white matter.

METHOD

Cervical cord T(1) was compared in 15 MS patients [8 relapsing-remitting (RR), 7 secondary progressive (SP)] and 6 healthy controls, and related to normalised upper cervical cord area (UCCa), cerebral white matter T(1), T(2) lesion load and disability measures including the Expanded Disability Status Scale (EDSS), Ambulation index (AI) and timed 25-foot walk. T1 maps of the brain and cervical cord were acquired using a high-resolution, 3-dimensional fast low-angle shot sequence. Dual-echo sequences were also obtained.

RESULTS

Median cervical cord T(1) [mean (standard deviation)] was significantly greater in RR [854 [28] ms] (p = 0.0006) and SP patients [927 [67] ms] (p < 0.0001) compared with controls [888 [61] ms], and in SP vs. RR patients (p = 0.002). In the overall patient cohort, it correlated significantly with median cerebral white matter T1 (r = 0.7, p = 0.0046), UCCa (r = -0.87, p < 0.0001), but not T2 lesion loads. Both median cervical cord T1 and UCCa (respectively) correlated significantly with the EDSS (r = 0.55, p = 0.03; r = -0.54, p = 0.04), AI (r = 0.77, p = 0.001; r = -0.60, p = 0.02) and timed 25-foot walk (r = 0.56, p = 0.03; r = -0.55, p = 0.04).

CONCLUSION

Cervical cord T(1) distinguishes between MS subgroups and could also prove a useful surrogate outcome measure in MS. The relation of cervical cord T(1) to cerebral white matter T(1) suggests that cord pathology may be influenced by tissue damage upstream.

Pyramidal tract mapping by diffusion tensor magnetic resonance imaging in multiple sclerosis: improving correlations with disability

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.

Improved white matter fiber tracking using stochastic labeling

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.

T 1 relaxation time mapping of white matter tracts in multiple sclerosis defined by diffusion tensor imaging

T(1) relaxation time (T(1)) is a quantitative magnetic resonance measure that enables a global evaluation of white matter disease in multiple sclerosis (MS). We aimed to investigate whether mapping of T(1) values in critical white matter tracts, defined by diffusion tensor (DT) imaging, could provide a stronger surrogate marker of disability. 25 patients with relapsing-remitting MS and 14 healthy controls were imaged with a dual-echo T(2)-weighted sequence. Whole brain T(1) maps were acquired using a multi-slice inversion recovery sequence and DT images generated from a spin-echo, echo-planar diffusion weighted sequence. Trajectories were defined to follow the course of white matter fibre tracts in the pyramidal pathways and corpus callosum. T(1) values were sampled along these trajectories. Total white matter T(1) was sampled by defining white matter masks on axial slices of the T(1) maps. Median T(1) in the pyramidal tracts, corpus callosum and total white matter of MS patients was significantly longer than in controls (p < 0.0001). Median pyramidal tract T(1) correlated significantly with the pyramidal Kurtzke Functional Systems Score (r = 0.64, p = 0.0007) and the Expanded Disability Status Scale (r = 0.55, p = 0.005). By contrast, no correlation with disability was observed for corpus callosum T(1) or total white matter T(1). Our findings show that quantifying pathology within the pyramidal tracts, by utilizing T(1), provides a strong correlate of disability compared with the overall white matter burden of disease. Pyramidal tract T(1) may also provide an objective, sensitive measure for monitoring the progression of motor deficits and disability.

White matter T(1) relaxation time histograms and cerebral atrophy in multiple sclerosis

T(1) relaxation time (T(1)) provides a quantitative magnetic resonance imaging (MRI) parameter for evaluating tissue damage in the brain. We aimed to measure T(1) in the white matter of patients with multiple sclerosis (MS) and study relationships with cerebral atrophy, T(2) lesion load and clinical parameters. Twenty-six patients with relapsing-remitting MS and sixteen healthy controls were scanned with dual-echo T(2)-weighted, 3-dimensional (3-D) magnetization-prepared rapid acquisition gradient echo and whole brain, multi-slice inversion recovery (IR) sequences. White matter masks were defined on axial T(1) map slices using semi-automated seed growing and normalized 'total white matter' T(1) histograms generated. Atrophy data was obtained using the Cavalieri method of modern design stereology. T(2) lesion volume was also determined using seed growing.T(1) histogram-derived measures (median, peak height, peak position and standard deviation) in MS patients were significantly different (p < 0.0001) from controls. Median T(1) correlated significantly with supratentorial (r = 0.42, p = 0.036), lateral ventricle (r = 0.55, p = 0.004), and T(2) lesion volumes (r = 0.84, p < 0.0001), but not with clinical parameters. Total white matter T(1) provides a robust, quantitative measure of global disease burden in MS, and also correlates significantly with cerebral atrophy. Serial studies are required to determine its potential role as a surrogate marker of disease progression.

White matter mapping using diffusion tensor MRI

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.

Compact fourth-order finite difference method for solving differential equations

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.

Effects of stochastic webs on chaotic electron transport in semiconductor superlattices

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.