Optimal closed-loop deep brain stimulation using multiple independently controlled contacts.

Deep brain stimulation (DBS) is a well-established treatment option for a variety of neurological disorders, including Parkinson's disease and essential tremor. The symptoms of these disorders are known to be associated with pathological synchronous neural activity in the basal ganglia and thalamus. It is hypothesised that DBS acts to desynchronise this activity, leading to an overall reduction in symptoms. Electrodes with multiple independently controllable contacts are a recent development in DBS technology which have the potential to target one or more pathological regions with greater precision, reducing side effects and potentially increasing both the efficacy and efficiency of the treatment. The increased complexity of these systems, however, motivates the need to understand the effects of DBS when applied to multiple regions or neural populations within the brain. On the basis of a theoretical model, our paper addresses the question of how to best apply DBS to multiple neural populations to maximally desynchronise brain activity. Central to this are analytical expressions, which we derive, that predict how the symptom severity should change when stimulation is applied. Using these expressions, we construct a closed-loop DBS strategy describing how stimulation should be delivered to individual contacts using the phases and amplitudes of feedback signals. We simulate our method and compare it against two others found in the literature: coordinated reset and phase-locked stimulation. We also investigate the conditions for which our strategy is expected to yield the most benefit.

Average beta burst duration profiles provide a signature of dynamical changes between the ON and OFF medication states in Parkinson's disease.

Parkinson's disease motor symptoms are associated with an increase in subthalamic nucleus beta band oscillatory power. However, these oscillations are phasic, and there is a growing body of evidence suggesting that beta burst duration may be of critical importance to motor symptoms. This makes insights into the dynamics of beta bursting generation valuable, in particular to refine closed-loop deep brain stimulation in Parkinson's disease. In this study, we ask the question "Can average burst duration reveal how dynamics change between the ON and OFF medication states?". Our analysis of local field potentials from the subthalamic nucleus demonstrates using linear surrogates that the system generating beta oscillations is more likely to act in a non-linear regime OFF medication and that the change in a non-linearity measure is correlated with motor impairment. In addition, we pinpoint the simplest dynamical changes that could be responsible for changes in the temporal patterning of beta oscillations between medication states by fitting to data biologically inspired models, and simpler beta envelope models. Finally, we show that the non-linearity can be directly extracted from average burst duration profiles under the assumption of constant noise in envelope models. This reveals that average burst duration profiles provide a window into burst dynamics, which may underlie the success of burst duration as a biomarker. In summary, we demonstrate a relationship between average burst duration profiles, dynamics of the system generating beta oscillations, and motor impairment, which puts us in a better position to understand the pathology and improve therapies such as deep brain stimulation.

Predicting the effects of deep brain stimulation using a reduced coupled oscillator model.

Deep brain stimulation (DBS) is known to be an effective treatment for a variety of neurological disorders, including Parkinson's disease and essential tremor (ET). At present, it involves administering a train of pulses with constant frequency via electrodes implanted into the brain. New 'closed-loop' approaches involve delivering stimulation according to the ongoing symptoms or brain activity and have the potential to provide improvements in terms of efficiency, efficacy and reduction of side effects. The success of closed-loop DBS depends on being able to devise a stimulation strategy that minimizes oscillations in neural activity associated with symptoms of motor disorders. A useful stepping stone towards this is to construct a mathematical model, which can describe how the brain oscillations should change when stimulation is applied at a particular state of the system. Our work focuses on the use of coupled oscillators to represent neurons in areas generating pathological oscillations. Using a reduced form of the Kuramoto model, we analyse how a patient should respond to stimulation when neural oscillations have a given phase and amplitude, provided a number of conditions are satisfied. For such patients, we predict that the best stimulation strategy should be phase specific but also that stimulation should have a greater effect if applied when the amplitude of brain oscillations is lower. We compare this surprising prediction with data obtained from ET patients. In light of our predictions, we also propose a new hybrid strategy which effectively combines two of the closed-loop strategies found in the literature, namely phase-locked and adaptive DBS.

Headache: an important symptom possibly linked to white matter lesions in thalassaemia.

Neurological manifestations are reported only occasionally in patients with thalassaemia and are given much less prominence than the complications related to anaemia and iron overload. White matter changes (WMCs) on magnetic resonance imaging (MRI) in patients with thalassaemia were first reported two decades ago but the significance of these lesions remains unclear. We studied the neurological and cognitive manifestations in 82 older patients with thalssaemia [25 Thalassaemia major (TM), 24 thalassaemia intermedia (TI) and 33 haemaglobin E ß thalassaemia (EBT)] and 80 controls, and found that headaches were more common in thalassaemia patients (50/82, 61%) than in controls (18/80, 22·5%: P < 0·001). WMCs on MRI were found in 20/82 (24·3%) patients and 2/29 (6·9%) controls had (P = 0·078). WMC were more common among those with headaches (17/50: 34%) than in those without headache (3/32; 9·3%) (P = 0·023). WMCs were not associated with reduction of cognition. Nevertheless, cognition was lower in the TI and EBT groups compared with those with TM (P = 0·002). The association of headache with WMC in thalassaemia has not been reported before and warrants further study.

How to entrain a selected neuronal rhythm but not others: open-loop dithered brain stimulation for selective entrainment.

Objective.While brain stimulation therapies such as deep brain stimulation for Parkinson's disease (PD) can be effective, they have yet to reach their full potential across neurological disorders. Entraining neuronal rhythms using rhythmic brain stimulation has been suggested as a new therapeutic mechanism to restore neurotypical behaviour in conditions such as chronic pain, depression, and Alzheimer's disease. However, theoretical and experimental evidence indicate that brain stimulation can also entrain neuronal rhythms at sub- and super-harmonics, far from the stimulation frequency. Crucially, these counterintuitive effects could be harmful to patients, for example by triggering debilitating involuntary movements in PD. We therefore seek a principled approach to selectively promote rhythms close to the stimulation frequency, while avoiding potential harmful effects by preventing entrainment at sub- and super-harmonics.Approach.Our open-loop approach to selective entrainment, dithered stimulation, consists in adding white noise to the stimulation period.Main results.We theoretically establish the ability of dithered stimulation to selectively entrain a given brain rhythm, and verify its efficacy in simulations of uncoupled neural oscillators, and networks of coupled neural oscillators. Furthermore, we show that dithered stimulation can be implemented in neurostimulators with limited capabilities by toggling within a finite set of stimulation frequencies.Significance.Likely implementable across a variety of existing brain stimulation devices, dithering-based selective entrainment has potential to enable new brain stimulation therapies, as well as new neuroscientific research exploiting its ability to modulate higher-order entrainment.

Optimizing deep brain stimulation based on isostable amplitude in essential tremor patient models.

OBJECTIVE: Deep brain stimulation is a treatment for medically refractory essential tremor. To improve the therapy, closed-loop approaches are designed to deliver stimulation according to the system's state, which is constantly monitored by recording a pathological signal associated with symptoms (e.g. brain signal or limb tremor). Since the space of possible closed-loop stimulation strategies is vast and cannot be fully explored experimentally, how to stimulate according to the state should be informed by modeling. A typical modeling goal is to design a stimulation strategy that aims to maximally reduce the Hilbert amplitude of the pathological signal in order to minimize symptoms. Isostables provide a notion of amplitude related to convergence time to the attractor, which can be beneficial in model-based control problems. However, how isostable and Hilbert amplitudes compare when optimizing the amplitude response to stimulation in models constrained by data is unknown. APPROACH: We formulate a simple closed-loop stimulation strategy based on models previously fitted to phase-locked deep brain stimulation data from essential tremor patients. We compare the performance of this strategy in suppressing oscillatory power when based on Hilbert amplitude and when based on isostable amplitude. We also compare performance to phase-locked stimulation and open-loop high-frequency stimulation. MAIN RESULTS: For our closed-loop phase space stimulation strategy, stimulation based on isostable amplitude is significantly more effective than stimulation based on Hilbert amplitude when amplitude field computation time is limited to minutes. Performance is similar when there are no constraints, however constraints on computation time are expected in clinical applications. Even when computation time is limited to minutes, closed-loop phase space stimulation based on isostable amplitude is advantageous compared to phase-locked stimulation, and is more efficient than high-frequency stimulation. SIGNIFICANCE: Our results suggest a potential benefit to using isostable amplitude more broadly for model-based optimization of stimulation in neurological disorders.

Phase-dependence of response curves to deep brain stimulation and their relationship: from essential tremor patient data to a Wilson-Cowan model.

Essential tremor manifests predominantly as a tremor of the upper limbs. One therapy option is high-frequency deep brain stimulation, which continuously delivers electrical stimulation to the ventral intermediate nucleus of the thalamus at about 130 Hz. Constant stimulation can lead to side effects, it is therefore desirable to find ways to stimulate less while maintaining clinical efficacy. One strategy, phase-locked deep brain stimulation, consists of stimulating according to the phase of the tremor. To advance methods to optimise deep brain stimulation while providing insights into tremor circuits, we ask the question: can the effects of phase-locked stimulation be accounted for by a canonical Wilson-Cowan model? We first analyse patient data, and identify in half of the datasets significant dependence of the effects of stimulation on the phase at which stimulation is provided. The full nonlinear Wilson-Cowan model is fitted to datasets identified as statistically significant, and we show that in each case the model can fit to the dynamics of patient tremor as well as to the phase response curve. The vast majority of top fits are stable foci. The model provides satisfactory prediction of how patient tremor will react to phase-locked stimulation by predicting patient amplitude response curves although they were not explicitly fitted. We also approximate response curves of the significant datasets by providing analytical results for the linearisation of a stable focus model, a simplification of the Wilson-Cowan model in the stable focus regime. We report that the nonlinear Wilson-Cowan model is able to describe response to stimulation more precisely than the linearisation.

Computational searches for iron oxides at high pressures.

We have used density-functional-theory methods and the ab initio random structure searching (AIRSS) approach to predict stable structures and stoichiometries of mixtures of iron and oxygen at high pressures. Searching was performed for 12 different stoichiometries at pressures of 100, 350 and 500 GPa, which involved relaxing more than 32 000 structures. We find that Fe2O3 and FeO2 are the only phases stable to decomposition at 100 GPa, while at 350 and 500 GPa several stoichiometries are found to be stable or very nearly stable. We report a new structure of Fe2O3 with P2(1)2(1)2(1)2 symmetry which is found to be more stable than the known Rh2O3(II) phase at pressures above ∼233 GPa. We also report two new structures of FeO, with Pnma and R3m symmetries, which are found to be stable within the ranges 195-285 GPa and 285-500 GPa, respectively, and two new structures of Fe3O4 with Pca21 and P21/c symmetries, which are found to be stable within the ranges 100-340 GPa and 340-500 GPa, respectively. Finally, we report two new structures of Fe4O5 with P42/n and [Formula: see text] symmetries, which are found to be stable within the ranges 100-231 GPa and 231-500 GPa, respectively. Our new structures of Fe3O4 and Fe4O5 are found to have lower enthalpies than their known structures within their respective stable pressure ranges.

Compression algorithm for multideterminant wave functions.

A compression algorithm is introduced for multideterminant wave functions which can greatly reduce the number of determinants that need to be evaluated in quantum Monte Carlo calculations. We have devised an algorithm with three levels of compression, the least costly of which yields excellent results in polynomial time. We demonstrate the usefulness of the compression algorithm for evaluating multideterminant wave functions in quantum Monte Carlo calculations, whose computational cost is reduced by factors of between about 2 and over 25 for the examples studied. We have found evidence of sublinear scaling of quantum Monte Carlo calculations with the number of determinants when the compression algorithm is used.

Expectant fathers' knowledge of maternal morbidity: a Sri Lankan experience.

BACKGROUND: Male partners play an important and vital role in the decision-making process regarding pregnant women's health. The purpose of the present study was to assess the knowledge and awareness of expectant fathers about Gestational Diabetes Mellitus (GDM), Pregnancy Induced Hypertension (PIH), and anaemia during pregnancy. METHODS: A cross sectional descriptive study was carried out among expectant fathers whose partners were attending antenatal clinics at the Anuradhapura Teaching Hospital, Sri Lanka. All consenting participants were interviewed by investigators using an interviewer administered questionnaire to collect data on knowledge of risk factors, symptoms, complications and their control. Statistical analysis was performed using the Kruskal Wallis test.  RESULTS: Of the 246 expectant fathers studied, 192 (78%) were aware of GDM, 183 (74.4%) and 154 (62.6%) were aware of PIH and anaemia during pregnancy, respectively. The total number of answers provided by expectant fathers ranged from 0 to 33 (of 41 questions). There were 44 fathers who could not answer even a single question. For GDM, anaemia, and PIH, the percentages of expectant fathers who failed to provide at least a single correct answer were 24.8%, 40.2%, and 31.3%, respectively. The median number of total correct answers provided increased steadily along with the average income (chi-square 31.24, p<0.001) and educational level (chi-square 33.57, p<0.001). Expectant fathers in the 25-34 age group had significantly higher scores, compared to younger and older fathers (chi-square 15.11, p=0.001). Fathers experiencing the second pregnancy of their spouses also had higher scores. CONCLUSIONS: Expectant father's knowledge of the selected morbidities was limited. To improve maternal health, any health promotional programmes should include expectant fathers.