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INTRODUCTION: Gait and mobility impairment are pivotal signs of parkinsonism, and they are particularly severe in atypical parkinsonian disorders including multiple system atrophy (MSA) and progressive supranuclear palsy (PSP). A pilot study demonstrated a significant improvement of gait in patients with MSA of parkinsonian type (MSA-P) after physiotherapy and matching home-based exercise, as reflected by sensor-based gait parameters. In this study, we aim to investigate whether a gait-focused physiotherapy (GPT) and matching home-based exercise lead to a greater improvement of gait performance compared with a standard physiotherapy/home-based exercise programme (standard physiotherapy, SPT). METHODS AND ANALYSIS: This protocol was deployed to evaluate the effects of a GPT versus an active control undergoing SPT and matching home-based exercise with regard to laboratory gait parameters, physical activity measures and clinical scales in patients with Parkinson's disease (PD), MSA-P and PSP. The primary outcomes of the trial are sensor-based laboratory gait parameters, while the secondary outcome measures comprise real-world derived parameters, clinical rating scales and patient questionnaires. We aim to enrol 48 patients per disease group into this double-blind, randomised-controlled trial. The study starts with a 1 week wearable sensor-based monitoring of physical activity. After randomisation, patients undergo a 2 week daily inpatient physiotherapy, followed by 5 week matching unsupervised home-based training. A 1 week physical activity monitoring is repeated during the last week of intervention. ETHICS AND DISSEMINATION: This study, registered as 'Mobility in Atypical Parkinsonism: a Trial of Physiotherapy (Mobility_APP)' at clinicaltrials.gov (NCT04608604), received ethics approval by local committees of the involved centres. The patient's recruitment takes place at the Movement Disorders Units of Innsbruck (Austria), Erlangen (Germany), Lausanne (Switzerland), Luxembourg (Luxembourg) and Bolzano (Italy). The data resulting from this project will be submitted to peer-reviewed journals, presented at international congresses and made publicly available at the end of the trial. TRIAL REGISTRATION NUMBER: NCT04608604.
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Terapia por Ejercicio , Trastornos Parkinsonianos , Modalidades de Fisioterapia , Humanos , Terapia por Ejercicio/métodos , Trastornos Parkinsonianos/rehabilitación , Trastornos Parkinsonianos/terapia , Método Doble Ciego , Ensayos Clínicos Controlados Aleatorios como Asunto , Marcha , Enfermedad de Parkinson/rehabilitación , Enfermedad de Parkinson/terapia , Atrofia de Múltiples Sistemas/rehabilitación , Atrofia de Múltiples Sistemas/terapia , Parálisis Supranuclear Progresiva/terapia , Parálisis Supranuclear Progresiva/rehabilitación , Servicios de Atención de Salud a Domicilio , Anciano , Masculino , Femenino , Trastornos Neurológicos de la Marcha/rehabilitación , Trastornos Neurológicos de la Marcha/etiologíaRESUMEN
Nanoparticles, exhibiting functionally relevant structural heterogeneity, are at the forefront of cutting-edge research. Now, high-throughput single-particle imaging (SPI) with X-ray free-electron lasers (XFELs) creates opportunities for recovering the shape distributions of millions of particles that exhibit functionally relevant structural heterogeneity. To realize this potential, three challenges have to be overcome: (1) simultaneous parametrization of structural variability in real and reciprocal spaces; (2) efficiently inferring the latent parameters of each SPI measurement; (3) scaling up comparisons between 105 structural models and 106 XFEL-SPI measurements. Here, we describe how we overcame these three challenges to resolve the nonequilibrium shape distributions within millions of gold nanoparticles imaged at the European XFEL. These shape distributions allowed us to quantify the degree of asymmetry in these particles, discover a relatively stable "shape envelope" among nanoparticles, discern finite-size effects related to shape-controlling surfactants, and extrapolate nanoparticles' shapes to their idealized thermodynamic limit. Ultimately, these demonstrations show that XFEL SPI can help transform nanoparticle shape characterization from anecdotally interesting to statistically meaningful.
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Goal: Gait analysis using inertial measurement units (IMUs) has emerged as a promising method for monitoring movement disorders. However, the lack of public data and easy-to-use open-source algorithms hinders method comparison and clinical application development. To address these challenges, this publication introduces the gaitmap ecosystem, a comprehensive set of open source Python packages for gait analysis using foot-worn IMUs. Methods: This initial release includes over 20 state-of-the-art algorithms, enables easy access to seven datasets, and provides eight benchmark challenges with reference implementations. Together with its extensive documentation and tooling, it enables rapid development and validation of new algorithm and provides a foundation for novel clinical applications. Conclusion: The published software projects represent a pioneering effort to establish an open-source ecosystem for IMU-based gait analysis. We believe that this work can democratize the access to high-quality algorithm and serve as a driver for open and reproducible research in the field of human gait analysis and beyond.
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Falls are an eminent risk for older adults and especially patients with neurodegenerative disorders, such as Parkinson's disease (PD). Recent advancements in wearable sensor technology and machine learning may provide a possibility for an individualized prediction of fall risk based on gait recordings from standardized gait tests or from unconstrained real-world scenarios. However, the most effective aggregation of continuous real-world data as well as the potential of unsupervised gait tests recorded over multiple days for fall risk prediction still need to be investigated. Therefore, we present a data set containing real-world gait and unsupervised 4x10-Meter-Walking-Tests of 40 PD patients, continuously recorded with foot-worn inertial sensors over a period of two weeks. In this prospective study, falls were self-reported during a three-month follow-up phase, serving as ground truth for fall risk prediction. The purpose of this study was to compare different data aggregation approaches and machine learning models for the prospective prediction of fall risk using gait parameters derived either from continuous real-world recordings or from unsupervised gait tests. The highest balanced accuracy of 74.0% (sensitivity: 60.0%, specificity: 88.0%) was achieved with a Random Forest Classifier applied to the real-world gait data when aggregating all walking bouts and days of each participant. Our findings suggest that fall risk can be predicted best by merging the entire two-week real-world gait data of a patient, outperforming the prediction using unsupervised gait tests (68.0% balanced accuracy) and contribute to an improved understanding of fall risk prediction.
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Enfermedad de Parkinson , Dispositivos Electrónicos Vestibles , Humanos , Anciano , Estudios Prospectivos , Marcha , CaminataRESUMEN
Gait analysis using foot-worn inertial measurement units has proven to be a reliable tool to diagnose and monitor many neurological and musculoskeletal indications. However, only few studies have investigated the robustness of such systems to changes in the sensor attachment and no consensus for suitable sensor positions exists in the research community. Specifically for unsupervised real-world measurements, understanding how the reliability of the monitoring system changes when the sensor is attached differently is from high importance. In these scenarios, placement variations are expected because of user error or personal preferences. In this manuscript, we present the largest study to date comparing different sensor positions and attachments. We recorded 9000 strides with motion-capture reference from 14 healthy participants with six synchronized sensors attached at each foot. Spatial gait parameters were calculated using a double-integration method and compared to the reference system. The results indicate that relevant differences in the accuracy of the stride length exists between the sensor positions. While the average error over multiple strides is comparable, single stride errors and variability parameters differ greatly. We further present a physics model and an analysis of the raw sensor data to understand the origin of the observed differences. This analysis indicates that a variety of attachment parameters can influence the systems' performance. While this is only the starting point to understand and mitigate these types of errors, we conclude that sensor systems and algorithms must be reevaluated when the sensor position or attachment changes.
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Pie , Caminata , Algoritmos , Marcha , Análisis de la Marcha , Humanos , Reproducibilidad de los ResultadosRESUMEN
Falls are among the leading causes of injuries or death for the elderly, and the prevalence is especially high for patients suffering from neurological diseases like Parkinson's disease (PD). Today, inertial measurement units (IMUs) can be integrated unobtrusively into patients' everyday lives to monitor various mobility and gait parameters, which are related to common risk factors like reduced balance or reduced lower-limb muscle strength. Although stair ambulation is a fundamental part of everyday life and is known for its unique challenges for the gait and balance system, long-term gait analysis studies have not investigated real-world stair ambulation parameters yet. Therefore, we applied a recently published gait analysis pipeline on foot-worn IMU data of 40 PD patients over a recording period of two weeks to extract objective gait parameters from level walking but also from stair ascending and descending. In combination with prospective fall records, we investigated group differences in gait parameters of future fallers compared to non-fallers for each individual gait activity. We found significant differences in stair ascending and descending parameters. Stance time was increased by up to 20 % and gait speed reduced by up to 16 % for fallers compared to non-fallers during stair walking. These differences were not present in level walking parameters. This suggests that real-world stair ambulation provides sensitive parameters for mobility and fall risk due to the challenges stairs add to the balance and control system. Our work complements existing gait analysis studies by adding new insights into mobility and gait performance during real-world gait.
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Enfermedad de Parkinson , Anciano , Marcha/fisiología , Humanos , Equilibrio Postural/fisiología , Estudios Prospectivos , Caminata/fisiologíaRESUMEN
One of the outstanding analytical problems in X-ray single-particle imaging (SPI) is the classification of structural heterogeneity, which is especially difficult given the low signal-to-noise ratios of individual patterns and the fact that even identical objects can yield patterns that vary greatly when orientation is taken into consideration. Proposed here are two methods which explicitly account for this orientation-induced variation and can robustly determine the structural landscape of a sample ensemble. The first, termed common-line principal component analysis (PCA), provides a rough classification which is essentially parameter free and can be run automatically on any SPI dataset. The second method, utilizing variation auto-encoders (VAEs), can generate 3D structures of the objects at any point in the structural landscape. Both these methods are implemented in combination with the noise-tolerant expand-maximize-compress (EMC) algorithm and its utility is demonstrated by applying it to an experimental dataset from gold nanoparticles with only a few thousand photons per pattern. Both discrete structural classes and continuous deformations are recovered. These developments diverge from previous approaches of extracting reproducible subsets of patterns from a dataset and open up the possibility of moving beyond the study of homogeneous sample sets to addressing open questions on topics such as nanocrystal growth and dynamics, as well as phase transitions which have not been externally triggered.
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Single-particle X-ray diffractive imaging (SPI) of small (bio-)nanoparticles (NPs) requires optimized injectors to collect sufficient diffraction patterns to allow for the reconstruction of the NP structure with high resolution. Typically, aerodynamic lens-stack injectors are used for NP injection. However, current injectors were developed for larger NPs (>100â nm), and their ability to generate high-density NP beams suffers with decreasing NP size. Here, an aerodynamic lens-stack injector with variable geometry and a geometry-optimization procedure are presented. The optimization for 50â nm gold-NP (AuNP) injection using a numerical-simulation infrastructure capable of calculating the carrier-gas flow and the particle trajectories through the injector is also introduced. The simulations were experimentally validated using spherical AuNPs and sucrose NPs. In addition, the optimized injector was compared with the standard-installation 'Uppsala injector' for AuNPs. Results for these heavy particles showed a shift in the particle-beam focus position rather than a change in beam size, which results in a lower gas background for the optimized injector. Optimized aerodynamic lens-stack injectors will allow one to increase NP beam density, reduce the gas background, discover the limits of current injectors and contribute to structure determination of small NPs using SPI.
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Driven by the advancements of wearable sensors and signal processing algorithms, studies on continuous real-world monitoring are of major interest in the field of clinical gait and motion analysis. While real-world studies enable a more detailed and realistic insight into various mobility parameters such as walking speed, confounding and environmental factors might skew those digital mobility outcomes (DMOs), making the interpretation of results challenging. To consider confounding factors, context information needs to be included in the analysis. In this work, we present a context-aware mobile gait analysis system that can distinguish between gait recorded at home and not at home based on Bluetooth proximity information. The system was evaluated on 9 healthy subjects and 6 Parkinsons disease (PD) patients. The classification of the at home/not at home context reached an average F1-score of 98.2 ± 3.2 %. A context-aware analysis of gait parameters revealed different walking bout length distributions between the two environmental conditions. Furthermore, a reduction of gait speed within the at home context compared to walking not at home of 8.9 ± 9.4 % and 8.7 ±5.9 % on average for healthy and PD subjects was found, respectively. Our results indicate the influence of the recording environment on DMOs and, therefore, emphasize the importance of context in the analysis of continuous motion data. Hence, the presented work contributes to a better understanding of confounding factors for future real-world studies.
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Análisis de la Marcha , Enfermedad de Parkinson , Marcha , Humanos , Caminata , Velocidad al CaminarRESUMEN
Gait tests as part of home monitoring study protocols for patients with movement disorders may provide valuable standardized anchor-points for real-world gait analysis using inertial measurement units (IMUs). However, analyzing unsupervised gait tests relies on reliable test annotations by the patients requiring a potentially error-prone interaction with the recording system. To overcome this limitation, this work presents a novel algorithmic pipeline for the automated detection of unsupervised standardized gait tests from continuous real-world IMU data. In a study with twelve Parkinson's disease patients, we recorded real-world gait data over two weeks using foot-worn IMUs. During continuous daily recordings, the participants performed series of three consecutive 4×10 -Meters-Walking-Tests ( 4×10 MWTs) at different walking speeds, besides their usual daily-living activities. The algorithm first detected these gait test series using a gait sequence detection algorithm, a peak enhancement pipeline, and subsequence Dynamic Time Warping and then decomposed them into single 4×10 MWTs based on the walking speed. In the evaluation with 419 available gait test series, the detection reached an F1-score of 88.9% and the decomposition an F1-score of 94.0%. A concurrent validity evaluation revealed very good agreement between spatio-temporal gait parameters derived from manually labelled and automatically detected 4×10 MWTs. Our algorithm allows to remove the burden of system interaction from the patients and reduces the time for manual data annotation for researchers. The study contributes to an improved automated processing of real-world IMU gait data and enables a simple integration of standardized tests into continuous long-term recordings. This will help to bridge the gap between supervised and unsupervised gait assessment.
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Enfermedad de Parkinson , Pie , Marcha , Análisis de la Marcha , Humanos , Enfermedad de Parkinson/diagnóstico , Velocidad al CaminarRESUMEN
Climbing stairs is a fundamental part of daily life, adding additional demands on the postural control system compared to level walking. Although real-world gait analysis studies likely contain stair ambulation sequences, algorithms dedicated to the analysis of such activities are still missing. Therefore, we propose a new gait analysis pipeline for foot-worn inertial sensors, which can segment, parametrize, and classify strides from continuous gait sequences that include level walking, stair ascending, and stair descending. For segmentation, an existing approach based on the hidden Markov model and a feature-based gait event detection were extended, reaching an average segmentation F1 score of 98.5% and gait event timing errors below ±10ms for all conditions. Stride types were classified with an accuracy of 98.2% using spatial features derived from a Kalman filter-based trajectory reconstruction. The evaluation was performed on a dataset of 20 healthy participants walking on three different staircases at different speeds. The entire pipeline was additionally validated end-to-end on an independent dataset of 13 Parkinson's disease patients. The presented work aims to extend real-world gait analysis by including stair ambulation parameters in order to gain new insights into mobility impairments that can be linked to clinically relevant conditions such as a patient's fall risk and disease state or progression.
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Análisis de la Marcha , Caminata , Algoritmos , Pie , Marcha , HumanosRESUMEN
BACKGROUND: To objectively assess a patient's gait, a robust identification of stride borders is one of the first steps in inertial sensor-based mobile gait analysis pipelines. While many different methods for stride segmentation have been presented in the literature, an out-of-lab evaluation of respective algorithms on free-living gait is still missing. METHOD: To address this issue, we present a comprehensive free-living evaluation dataset, including 146.574 semi-automatic labeled strides of 28 Parkinson's Disease patients. This dataset was used to evaluate the segmentation performance of a new Hidden Markov Model (HMM) based stride segmentation approach compared to an available dynamic time warping (DTW) based method. RESULTS: The proposed HMM achieved a mean F1-score of 92.1% and outperformed the DTW approach significantly. Further analysis revealed a dependency of segmentation performance to the number of strides within respective walking bouts. Shorter bouts ([Formula: see text] strides) resulted in worse performance, which could be related to more heterogeneous gait and an increased diversity of different stride types in short free-living walking bouts. In contrast, the HMM reached F1-scores of more than 96.2% for longer bouts ([Formula: see text] strides). Furthermore, we showed that an HMM, which was trained on at-lab data only, could be transferred to a free-living context with a negligible decrease in performance. CONCLUSION: The generalizability of the proposed HMM is a promising feature, as fully labeled free-living training data might not be available for many applications. To the best of our knowledge, this is the first evaluation of stride segmentation performance on a large scale free-living dataset. Our proposed HMM-based approach was able to address the increased complexity of free-living gait data, and thus will help to enable a robust assessment of stride parameters in future free-living gait analysis applications.
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Enfermedad de Parkinson , Algoritmos , Marcha , Análisis de la Marcha , Humanos , CaminataRESUMEN
Wearable sensor technology already has a great impact on the endurance running community. Smartwatches and heart rate monitors are heavily used to evaluate runners' performance and monitor their training progress. Additionally, foot-mounted inertial measurement units (IMUs) have drawn the attention of sport scientists due to the possibility to monitor biomechanically relevant spatio-temporal parameters outside the lab in real-world environments. Researchers developed and investigated algorithms to extract various features using IMU data of different sensor positions on the foot. In this work, we evaluate whether the sensor position of IMUs mounted to running shoes has an impact on the accuracy of different spatio-temporal parameters. We compare both the raw data of the IMUs at different sensor positions as well as the accuracy of six endurance running-related parameters. We contribute a study with 29 subjects wearing running shoes equipped with four IMUs on both the left and the right shoes and a motion capture system as ground truth. The results show that the IMUs measure different raw data depending on their position on the foot and that the accuracy of the spatio-temporal parameters depends on the sensor position. We recommend to integrate IMU sensors in a cavity in the sole of a running shoe under the foot's arch, because the raw data of this sensor position is best suitable for the reconstruction of the foot trajectory during a stride.
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Pie , Carrera , Zapatos , Dispositivos Electrónicos Vestibles , Fenómenos Biomecánicos , Humanos , Resistencia Física , Análisis Espacio-TemporalRESUMEN
Aim: This paper introduces Apkinson, a mobile application for motor evaluation and monitoring of Parkinson's disease patients. Materials & methods: The App is based on previously reported methods, for instance, the evaluation of articulation and pronunciation in speech, regularity and freezing of gait in walking, and tapping accuracy in hand movement. Results: Preliminary experiments indicate that most of the measurements are suitable to discriminate patients and controls. Significance is evaluated through statistical tests. Conclusion: Although the reported results correspond to preliminary experiments, we think that Apkinson is a very useful App that can help patients, caregivers and clinicians, in performing a more accurate monitoring of the disease progression. Additionally, the mobile App can be a personal health assistant.
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Aplicaciones Móviles , Enfermedad de Parkinson/fisiopatología , Teléfono Inteligente , Anciano , Anciano de 80 o más Años , Femenino , Marcha , Humanos , Masculino , Persona de Mediana Edad , Movimiento , Índice de Severidad de la Enfermedad , HablaRESUMEN
X-ray free-electron lasers promise diffractive imaging of single molecules and nanoparticles with atomic spatial resolution. This relies on the averaging of millions of diffraction patterns of identical particles, which should ideally be isolated in the gas phase and preserved in their native structure. Here, we demonstrated that polystyrene nanospheres and Cydia pomonella granulovirus can be transferred into the gas phase, isolated, and very quickly shock-frozen, i.e., cooled to 4 K within microseconds in a helium-buffer-gas cell, much faster than state-of-the-art approaches. Nanoparticle beams emerging from the cell were characterized using particle-localization microscopy with light-sheet illumination, which allowed for the full reconstruction of the particle beams, focused to < 100 µ m , as well as for the determination of particle flux and number density. The experimental results were quantitatively reproduced and rationalized through particle-trajectory simulations. We propose an optimized setup with cooling rates for particles of few-nanometers on nanosecond timescales. The produced beams of shock-frozen isolated nanoparticles provide a breakthrough in sample delivery, e.g., for diffractive imaging and microscopy or low-temperature nanoscience.
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To advance microfluidic integration, we present the use of two-photon additive manufacturing to fold 2D channel layouts into compact free-form 3D fluidic circuits with nanometer precision. We demonstrate this technique by tailoring microfluidic nozzles and mixers for time-resolved structural biology at X-ray free-electron lasers (XFELs). We achieve submicron jets with speeds exceeding 160 m s-1, which allows for the use of megahertz XFEL repetition rates. By integrating an additional orifice, we implement a low consumption flow-focusing nozzle, which is validated by solving a hemoglobin structure. Also, aberration-free in operando X-ray microtomography is introduced to study efficient equivolumetric millisecond mixing in channels with 3D features integrated into the nozzle. Such devices can be printed in minutes by locally adjusting print resolution during fabrication. This technology has the potential to permit ultracompact devices and performance improvements through 3D flow optimization in all fields of microfluidic engineering.
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Microfluídica/instrumentación , Impresión Tridimensional/instrumentación , Biología Sintética/instrumentación , Hemo/química , Hemoglobinas/química , Humanos , Rayos Láser , Microfluídica/métodos , Biología Sintética/métodos , Microtomografía por Rayos XRESUMEN
Hereditary spastic paraplegias (HSP) represents a group of orphan neurodegenerative diseases with gait disturbance as the predominant clinical feature. Due to its rarity, research within this field is still limited. Aside from clinical analysis using established scales, gait analysis has been employed to enhance the understanding of the mechanisms behind the disease. However, state of the art gait analysis systems are often large, immobile and expensive. To overcome these limitations, this paper presents the first clinically relevant mobile gait analysis system for HSP patients. We propose an unsupervised model based on local cyclicity estimation and hierarchical hidden Markov models (LCE-hHMM). The system provides stride time, swing time, stance time, swing duration and cadence. These parameters are validated against a GAITRite system and manual sensor data labelling using a total of 24 patients within 2 separate studies. The proposed system achieves a stride time error of -0.00 ± 0.09 s (correlation coefficient, r = 1.00) and a swing duration error of -0.67 ± 3.27 % (correlation coefficient, r = 0.93) with respect to the GAITRite system. We show that these parameters are also correlated to the clinical spastic paraplegia rating scale (SPRS) in a similar manner to other state of the art gait analysis systems, as well as to supervised and general versions of the proposed model. Finally, we show a proof of concept for this system to be used to analyse alterations in the gait of individual patients. Thus, with further clinical studies, due to its automated approach and mobility, this system could be used to determine treatment effects in future clinical trials.
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Análisis de la Marcha/métodos , Procesamiento de Señales Asistido por Computador , Paraplejía Espástica Hereditaria , Adulto , Algoritmos , Femenino , Marcha/fisiología , Humanos , Masculino , Cadenas de Markov , Persona de Mediana Edad , Reproducibilidad de los Resultados , Paraplejía Espástica Hereditaria/diagnóstico , Paraplejía Espástica Hereditaria/fisiopatología , Aprendizaje Automático SupervisadoRESUMEN
Imaging biological molecules in the gas-phase requires novel sample delivery methods, which generally have to be characterized and optimized to produce high-density particle beams. A non-destructive characterization method of the transverse particle beam profile is presented. It enables the characterization of the particle beam in parallel to the collection of, for instance, x-ray-diffraction patterns. As a rather simple experimental method, it requires the generation of a small laser-light sheet using a cylindrical telescope and a microscope. The working principle of this technique was demonstrated for the characterization of the fluid-dynamic-focusing behavior of 220 nm polystyrene beads as prototypical nanoparticles. The particle flux was determined and the velocity distribution was calibrated using Mie-scattering calculations.
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Mobile gait analysis systems using wearable sensors have the potential to analyze and monitor pathological gait in a finer scale than ever before. A closer look at gait in Parkinson's disease (PD) reveals that turning has its own characteristics and requires its own analysis. The goal of this paper is to present a system with on-shoe wearable sensors in order to analyze the abnormalities of turning in a standardized gait test for PD. We investigated turning abnormalities in a large cohort of 108 PD patients and 42 age-matched controls. We quantified turning through several spatio-temporal parameters. Analysis of turn-derived parameters revealed differences of turn-related gait impairment in relation to different disease stages and motor impairment. Our findings confirm and extend the results from previous studies and show the applicability of our system in turning analysis. Our system can provide insight into the turning in PD and be used as a complement for physicians' gait assessment and to monitor patients in their daily environment.
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Algoritmos , Monitoreo Fisiológico/instrumentación , Enfermedad de Parkinson/fisiopatología , Zapatos , Dispositivos Electrónicos Vestibles , Adulto , Anciano , Anciano de 80 o más Años , Estudios de Casos y Controles , Diseño de Equipo , Femenino , Trastornos Neurológicos de la Marcha/diagnóstico , Trastornos Neurológicos de la Marcha/fisiopatología , Humanos , Masculino , Persona de Mediana Edad , Monitoreo Fisiológico/métodos , Monitoreo Fisiológico/normas , Reproducibilidad de los Resultados , Análisis Espacio-TemporalRESUMEN
The original article [1] contained an error whereby Fig. 6 contained a minor shading glitch affecting its presentation. This has now been corrected.