On the equivalence of variational problems. II

summary:Elements of general theory of infinitely prolonged underdetermined systems of ordinary differential equations are outlined and applied to the equivalence of one-dimensional constrained variational integrals. The relevant infinite-dimensional variant of Cartan’s moving frame method expressed in quite elementary terms proves to be surprisingly efficient in solution of particular equivalence problems, however, most of the principal questions of the general theory remains unanswered. New concepts of Poincaré-Cartan form and Euler-Lagrange system without Lagrange multiplies appearing as a mere by-product seem to be of independent interest in connection with the 23rd Hilbert problem

Examples from the calculus of variations. III. Legendre and Jacobi conditions

summary:We will deal with a new geometrical interpretation of the classical Legendre and Jacobi conditions: they are represented by the rate and the magnitude of rotation of certain linear subspaces of the tangent space around the tangents to the extremals. (The linear subspaces can be replaced by conical subsets of the tangent space.) This interpretation can be carried over to nondegenerate Lagrange problems but applies also to the degenerate variational integrals mentioned in the preceding Part II

Iodine-125 radiolabeling of silver nanoparticles for in vivo SPECT imaging

Silver nanoparticles are increasingly finding applications in medicine; however, little is known about their in vivo tissue distribution. Here, we have developed a rapid method for radiolabeling of silver nanoparticles with iodine-125 in order to track in vivo tissue uptake of silver nanoparticles after systemic administration by biodistribution analysis and single-photon emission computerized tomography (SPECT) imaging. Poly(N-vinyl-2 -pyrrolidone)-capped silver nanoparticles with an average size of 12 nm were labeled by chemisorption of iodine-125 with a > 80% yield of radiolabeling efficiency. Radiolabeled silver nanoparticles were intravenously injected in Balb/c mice, and the in vivo distribution pattern of these nanoparticles was evaluated by noninvasive whole-body SPECT imaging, which revealed uptake of the nanoparticles in the liver and spleen. Biodistribution analysis confirmed predominant accumulation of the silver nanoparticles in the spleen (41.5%ID/g) and liver (24.5%ID/g) at 24 h. Extensive uptake in the tissues of the reticuloendothelial system suggests that further investigation of silver nanoparticle interaction with hepatic and splenic tissues at the cellular level is critical for evaluation of the in vivo effects and potential toxicity of silver nanoparticles. This method enables rapid iodine-125 radiolabeling of silver nanoparticles with a specific activity sufficient for in vivo imaging and biodistribution analysis

High frequency oscillations in epileptic and non-epileptic human hippocampus during a cognitive task

Hippocampal high-frequency electrographic activity (HFOs) represents one of the major discoveries not only in epilepsy research but also in cognitive science over the past few decades. A fundamental challenge, however, has been the fact that physiological HFOs associated with normal brain function overlap in frequency with pathological HFOs. We investigated the impact of a cognitive task on HFOs with the aim of improving differentiation between epileptic and non-epileptic hippocampi in humans. Hippocampal activity was recorded with depth electrodes in 15 patients with focal epilepsy during a resting period and subsequently during a cognitive task. HFOs in ripple and fast ripple frequency ranges were evaluated in both conditions, and their rate, spectral entropy, relative amplitude and duration were compared in epileptic and non-epileptic hippocampi. The similarity of HFOs properties recorded at rest in epileptic and non-epileptic hippocampi suggests that they cannot be used alone to distinguish between hippocampi. However, both ripples and fast ripples were observed with higher rates, higher relative amplitudes and longer durations at rest as well as during a cognitive task in epileptic compared with non-epileptic hippocampi. Moreover, during a cognitive task, significant reductions of HFOs rates were found in epileptic hippocampi. These reductions were not observed in non-epileptic hippocampi. Our results indicate that although both hippocampi generate HFOs with similar features that probably reflect non-pathological phenomena, it is possible to differentiate between epileptic and non-epileptic hippocampi using a simple odd-ball task

Vztahy mezi oscilacemi a jejich využití u adaptivní hluboké mozkové stimulace

Hluboká mozková stimulace (DBS) patří vedle dopaminergní léčby k nejvýznamnějším terapeutickým přístupům u Parkinsonovy nemoci (PN). Snaha potlačit některé limitace této terapie vede ke zvýšenému zájmu o přístupy jako je adaptivní DBS (aDBS). Stimulace s uzavřenou smyčkou řízená fluktuacemi výkonu v beta pásmu však nemusí být optimální pro všechny pacienty s PN. S cílem nalézt více senzitivní ukazatel než samotnou beta aktivitu byly analyzovány vztahy mezi jednotlivými oscilacemi v kontextu optimální stimulace subthalamického jádra (STN). Vztah fáze beta rytmu a amplitudy vysokofrekvenčních oscilací se jeví jako vhodný parametr pro cílení stimulace

Intraoperative electrophysiological monitoring determines the final electrode position for pallidal stimulation in dystonia patients

BackgroundBilateral deep brain stimulation (DBS) of the globus pallidus internus (GPi) is an effective treatment for refractory dystonia. Neuroradiological target and stimulation electrode trajectory planning with intraoperative microelectrode recordings (MER) and stimulation are used. With improving neuroradiological techniques, the need for MER is in dispute mainly because of the suspected risk of hemorrhage and the impact on clinical post DBS outcome.ObjectiveThe aim of the study is to compare the preplanned GPi electrode trajectories with final trajectories selected for electrode implantation after electrophysiological monitoring and to discuss the factors potentially responsible for differences between preplanned and final trajectories. Finally, the potential association between the final trajectory selected for electrode implantation and clinical outcome will be analyzed.MethodsForty patients underwent bilateral GPi DBS (right-sided implants first) for refractory dystonia. The relationship between preplanned and final trajectories (MicroDrive system) was correlated with patient (gender, age, dystonia type and duration) and surgery characteristics (anesthesia type, postoperative pneumocephalus) and clinical outcome measured using CGI (Clinical Global Impression parameter). The correlation between the preplanned and final trajectories together with CGI was compared between patients 1–20 and 21–40 for the learning curve effect.ResultsThe trajectory selected for definitive electrode implantation matched the preplanned trajectory in 72.5% and 70% on the right and left side respectively; 55% had bilateral definitive electrodes implanted along the preplanned trajectories. Statistical analysis did not confirm any of the studied factors as predictor of the difference between the preplanned and final trajectories. Also no association between CGI and final trajectory selected for electrode implantation in the right/left hemisphere has been proven. The percentages of final electrodes implanted along the preplanned trajectory (the correlation between anatomical planning and intraoperative electrophysiology results) did not differ between patients 1–20 and 21–40. Similarly, there were no statistically significant differences in CGI (clinical outcome) between patients 1–20 and 21–40.ConclusionThe final trajectory selected after electrophysiological study differed from the preplanned trajectory in a significant percentage of patients. No predictor of this difference was identified. The anatomo-electrophysiological difference was not predictive of the clinical outcome (as measured using CGI parameter)

A Novel Statistical Model for Predicting the Efficacy of Vagal Nerve Stimulation in Patients With Epilepsy (Pre-X-Stim) Is Applicable to Different EEG Systems

Background: Identifying patients with intractable epilepsy who would benefit from therapeutic chronic vagal nerve stimulation (VNS) preoperatively remains a major clinical challenge. We have developed a statistical model for predicting VNS efficacy using only routine preimplantation electroencephalogram (EEG) recorded with the TruScan EEG device (Brazdil et al., 2019). It remains to be seen, however, if this model can be applied in different clinical settings. Objective: To validate our model using EEG data acquired with a different recording system. Methods: We identified a validation cohort of eight patients implanted with VNS, whose preimplantation EEG was recorded on the BrainScope device and who underwent the EEG recording according to the protocol. The classifier developed in our earlier work, named Pre-X-Stim, was then employed to classify these patients as predicted responders or non-responders based on the dynamics in EEG power spectra. Predicted and real-world outcomes were compared to establish the applicability of this classifier. In total, two validation experiments were performed using two different validation approaches (single classifier or classifier voting). Results: The classifier achieved 75% accuracy, 67% sensitivity, and 100% specificity. Only two patients, both real-life responders, were classified incorrectly in both validation experiments. Conclusion: We have validated the Pre-X-Stim model on EEGs from a different recording system, which indicates its application under different technical conditions. Our approach, based on preoperative EEG, is easily applied and financially undemanding and presents great potential for real-world clinical use