Exotic complex Hadamard matrices, and their equivalence

In this paper we use a design theoretical approach to construct new, previously unknown complex Hadamard matrices. Our methods generalize and extend the earlier results of de la Harpe--Jones and Munemasa--Watatani and offer a theoretical explanation for the existence of some sporadic examples of complex Hadamard matrices in the existing literature. As it is increasingly difficult to distinguish inequivalent matrices from each other, we propose a new invariant, the fingerprint of complex Hadamard matrices. As a side result, we refute a conjecture of Koukouvinos et al. on (n-8)x(n-8) minors of real Hadamard matrices.Comment: 10 pages. To appear in Cryptography and Communications: Discrete Structures, Boolean Functions and Sequence

On quaternary complex Hadamard matrices of small orders

One of the main goals of design theory is to classify, characterize and count various combinatorial objects with some prescribed properties. In most cases, however, one quickly encounters a combinatorial explosion and even if the complete enumeration of the objects is possible, there is no apparent way how to study them in details, store them efficiently, or generate a particular one rapidly. In this paper we propose a novel method to deal with these difficulties, and illustrate it by presenting the classification of quaternary complex Hadamard matrices up to order 8. The obtained matrices are members of only a handful of parametric families, and each inequivalent matrix, up to transposition, can be identified through its fingerprint.Comment: 7 page

Optimization of extracranial stereotactic radiation therapy of small lung lesions using accurate dose calculation algorithms

BACKGROUND: The aim of this study was to compare and to validate different dose calculation algorithms for the use in radiation therapy of small lung lesions and to optimize the treatment planning using accurate dose calculation algorithms. METHODS: A 9-field conformal treatment plan was generated on an inhomogeneous phantom with lung mimics and a soft tissue equivalent insert, mimicking a lung tumor. The dose distribution was calculated with the Pencil Beam and Collapsed Cone algorithms implemented in Masterplan (Nucletron) and the Monte Carlo system XVMC and validated using Gafchromic EBT films. Differences in dose distribution were evaluated. The plans were then optimized by adding segments to the outer shell of the target in order to increase the dose near the interface to the lung. RESULTS: The Pencil Beam algorithm overestimated the dose by up to 15% compared to the measurements. Collapsed Cone and Monte Carlo predicted the dose more accurately with a maximum difference of -8% and -3% respectively compared to the film. Plan optimization by adding small segments to the peripheral parts of the target, creating a 2-step fluence modulation, allowed to increase target coverage and homogeneity as compared to the uncorrected 9 field plan. CONCLUSION: The use of forward 2-step fluence modulation in radiotherapy of small lung lesions allows the improvement of tumor coverage and dose homogeneity as compared to non-modulated treatment plans and may thus help to increase the local tumor control probability. While the Collapsed Cone algorithm is closer to measurements than the Pencil Beam algorithm, both algorithms are limited at tissue/lung interfaces, leaving Monte-Carlo the most accurate algorithm for dose prediction

Basal Ganglia Pathways Associated With Therapeutic Pallidal Deep Brain Stimulation for Tourette Syndrome

BACKGROUND: Deep brain stimulation (DBS) targeting the globus pallidus internus (GPi) can improve tics and comorbid obsessive-compulsive behavior (OCB) in patients with treatment-refractory Tourette syndrome (TS). However, some patients’ symptoms remain unresponsive, the stimulation applied across patients is variable, and the mechanisms underlying improvement are unclear. Identifying the fiber pathways surrounding the GPi that are associated with improvement could provide mechanistic insight and refine targeting strategies to improve outcomes. METHODS: Retrospective data were collected for 35 patients who underwent bilateral GPi DBS for TS. Computational models of fiber tract activation were constructed using patient-specific lead locations and stimulation settings to evaluate the effects of DBS on basal ganglia pathways and the internal capsule. We first evaluated the relationship between activation of individual pathways and symptom improvement. Next, linear mixed-effects models with combinations of pathways and clinical variables were compared in order to identify the best-fit predictive models of tic and OCB improvement. RESULTS: The best-fit model of tic improvement included baseline severity and the associative pallido-subthalamic pathway. The best-fit model of OCB improvement included baseline severity and the sensorimotor pallidosubthalamic pathway, with substantial evidence also supporting the involvement of the prefrontal, motor, and premotor internal capsule pathways. The best-fit models of tic and OCB improvement predicted outcomes across the cohort and in cross-validation. CONCLUSIONS: Differences in fiber pathway activation likely contribute to variable outcomes of DBS for TS. Computational models of pathway activation could be used to develop novel approaches for preoperative targeting and selecting stimulation parameters to improve patient outcomes

Proceedings of the Fourth Annual Deep Brain Stimulation Think Tank: A Review of Emerging Issues and Technologies

This paper provides an overview of current progress in the technological advances and the use of deep brain stimulation (DBS) to treat neurological and neuropsychiatric disorders, as presented by participants of the Fourth Annual DBS Think Tank, which was convened in March 2016 in conjunction with the Center for Movement Disorders and Neurorestoration at the University of Florida, Gainesveille FL, USA. The Think Tank discussions first focused on policy and advocacy in DBS research and clinical practice, formation of registries, and issues involving the use of DBS in the treatment of Tourette Syndrome. Next, advances in the use of neuroimaging and electrochemical markers to enhance DBS specificity were addressed. Updates on ongoing use and developments of DBS for the treatment of Parkinson’s disease, essential tremor, Alzheimer’s disease, depression, post-traumatic stress disorder, obesity, addiction were presented, and progress toward innovation(s) in closed-loop applications were discussed. Each section of these proceedings provides updates and highlights of new information as presented at this year’s international Think Tank, with a view toward current and near future advancement of the field

Human pallidothalamic and cerebellothalamic tracts: anatomical basis for functional stereotactic neurosurgery

Anatomical knowledge of the structures to be targeted and of the circuitry involved is crucial in stereotactic functional neurosurgery. The present study was undertaken in the context of surgical treatment of motor disorders such as essential tremor (ET) and Parkinson’s disease (PD) to precisely determine the course and three-dimensional stereotactic localisation of the cerebellothalamic and pallidothalamic tracts in the human brain. The course of the fibre tracts to the thalamus was traced in the subthalamic region using multiple staining procedures and their entrance into the thalamus determined according to our atlas of the human thalamus and basal ganglia [Morel (2007) Stereotactic atlas of the human thalamus and basal ganglia. Informa Healthcare Inc., New York]. Stereotactic three-dimensional coordinates were determined by sectioning thalamic and basal ganglia blocks parallel to stereotactic planes and, in two cases, by correlation with magnetic resonance images (MRI) from the same brains prior to sectioning. The major contributions of this study are to provide: (1) evidence that the bulks of the cerebellothalamic and pallidothalamic tracts are clearly separated up to their thalamic entrance, (2) stereotactic maps of the two tracts in the subthalamic region, (3) the possibility to discriminate between different subthalamic fibre tracts on the basis of immunohistochemical stainings, (4) correlations of histologically identified fibre tracts with high-resolution MRI, and (5) evaluation of the interindividual variability of the fibre systems in the subthalamic region. This study should provide an important basis for accurate stereotactic neurosurgical targeting of the subthalamic region in motor disorders such as PD and ET

Image-based analysis and long-term clinical outcomes of deep brain stimulation for Tourette syndrome: a multisite study

BACKGROUND: Deep brain stimulation (DBS) can be an effective therapy for tics and comorbidities in select cases of severe, treatment-refractory Tourette syndrome (TS). Clinical responses remain variable across patients, which may be attributed to differences in the location of the neuroanatomical regions being stimulated. We evaluated active contact locations and regions of stimulation across a large cohort of patients with TS in an effort to guide future targeting. METHODS: We collected retrospective clinical data and imaging from 13 international sites on 123 patients. We assessed the effects of DBS over time in 110 patients who were implanted in the centromedial (CM) thalamus (n=51), globus pallidus internus (GPi) (n=47), nucleus accumbens/anterior limb of the internal capsule (n=4) or a combination of targets (n=8). Contact locations (n=70 patients) and volumes of tissue activated (n=63 patients) were coregistered to create probabilistic stimulation atlases. RESULTS: Tics and obsessive-compulsive behaviour (OCB) significantly improved over time (p0.05). The median time was 13 months to reach a 40% improvement in tics, and there were no significant differences across targets (p=0.84), presence of OCB (p=0.09) or age at implantation (p=0.08). Active contacts were generally clustered near the target nuclei, with some variability that may reflect differences in targeting protocols, lead models and contact configurations. There were regions within and surrounding GPi and CM thalamus that improved tics for some patients but were ineffective for others. Regions within, superior or medial to GPi were associated with a greater improvement in OCB than regions inferior to GPi. CONCLUSION: The results collectively indicate that DBS may improve tics and OCB, the effects may develop over several months, and stimulation locations relative to structural anatomy alone may not predict response. This study was the first to visualise and evaluate the regions of stimulation across a large cohort of patients with TS to generate new hypotheses about potential targets for improving tics and comorbidities

A Network Model of Local Field Potential Activity in Essential Tremor and the Impact of Deep Brain Stimulation

Essential tremor (ET), a movement disorder characterised by an uncontrollable shaking of the affected body part, is often professed to be the most common movement disorder, affecting up to one percent of adults over 40 years of age. The precise cause of ET is unknown, however pathological oscillations of a network of a number of brain regions are implicated in leading to the disorder. Deep brain stimulation (DBS) is a clinical therapy used to alleviate the symptoms of a number of movement disorders. DBS involves the surgical implantation of electrodes into specific nuclei in the brain. For ET the targeted region is the ventralis intermedius (Vim) nucleus of the thalamus. Though DBS is effective for treating ET, the mechanism through which the therapeutic effect is obtained is not understood. To elucidate the mechanism underlying the pathological network activity and the effect of DBS on such activity, we take a computational modelling approach combined with electrophysiological data. The pathological brain activity was recorded intra-operatively via implanted DBS electrodes, whilst simultaneously recording muscle activity of the affected limbs. We modelled the network hypothesised to underlie ET using the Wilson-Cowan approach. The modelled network exhibited oscillatory behaviour within the tremor frequency range, as did our electrophysiological data. By applying a DBS-like input we suppressed these oscillations. This study shows that the dynamics of the ET network support oscillations at the tremor frequency and the application of a DBS-like input disrupts this activity, which could be one mechanism underlying the therapeutic benefit