Search

This study aimed to assess the responsiveness to the rehabilitation of three trunk acceleration-derived gait indexes, namely the harmonic ratio (HR), the short-term longest Lyapunov's exponent (sLLE), and the step-to-step coefficient of variation (CV), in a sample of subjects with primary degenerative cerebellar ataxia (swCA), and investigate the correlations between their improvements (∆), clinical characteristics, and spatio-temporal and kinematic gait features. The trunk acceleration patterns in the antero-posterior (AP), medio-lateral (ML), and vertical (V) directions during gait of 21 swCA were recorded using a magneto-inertial measurement unit placed at the lower back before (T0) and after (T1) a period of inpatient rehabilitation. For comparison, a sample of 21 age- and gait speed-matched healthy subjects (HS matched ) was also included. At T1, sLLE in the AP (sLLE AP ) and ML (sLLE ML ) directions significantly improved with moderate to large effect sizes, as well as SARA scores, stride length, and pelvic rotation. sLLE ML and pelvic rotation also approached the HS matched values at T1, suggesting a normalization of the parameter. HRs and CV did not significantly modify after rehabilitation. ∆sLLE ML correlated with ∆ of the gait subscore of the SARA scale (SARA GAIT ) and ∆stride length and ∆sLLE AP correlated with ∆pelvic rotation and ∆SARA GAIT . The minimal clinically important differences for sLLE ML and sLLE AP were ≥ 36.16% and ≥ 28.19%, respectively, as the minimal score reflects a clinical improvement in SARA scores. When using inertial measurement units, sLLE AP and sLLE ML can be considered responsive outcome measures for assessing the effectiveness of rehabilitation on trunk stability during walking in swCA., (© 2024. The Author(s).)

The interpretability of gait analysis studies in people with rare diseases, such as those with primary hereditary cerebellar ataxia (pwCA), is frequently limited by the small sample sizes and unbalanced datasets. The purpose of this study was to assess the effectiveness of data balancing and generative artificial intelligence (AI) algorithms in generating synthetic data reflecting the actual gait abnormalities of pwCA. Gait data of 30 pwCA (age: 51.6 ± 12.2 years; 13 females, 17 males) and 100 healthy subjects (age: 57.1 ± 10.4; 60 females, 40 males) were collected at the lumbar level with an inertial measurement unit. Subsampling, oversampling, synthetic minority oversampling, generative adversarial networks, and conditional tabular generative adversarial networks (ctGAN) were applied to generate datasets to be input to a random forest classifier. Consistency and explainability metrics were also calculated to assess the coherence of the generated dataset with known gait abnormalities of pwCA. ctGAN significantly improved the classification performance compared with the original dataset and traditional data augmentation methods. ctGAN are effective methods for balancing tabular datasets from populations with rare diseases, owing to their ability to improve diagnostic models with consistent explainability.

The aim of this consensus paper is to discuss the roles of the cerebellum in human gait, as well as its assessment and therapy. Cerebellar vermis is critical for postural control. The cerebellum ensures the mapping of sensory information into temporally relevant motor commands. Mental imagery of gait involves intrinsically connected fronto-parietal networks comprising the cerebellum. Muscular activities in cerebellar patients show impaired timing of discharges, affecting the patterning of the synergies subserving locomotion. Ataxia of stance/gait is amongst the first cerebellar deficits in cerebellar disorders such as degenerative ataxias and is a disabling symptom with a high risk of falls. Prolonged discharges and increased muscle coactivation may be related to compensatory mechanisms and enhanced body sway, respectively. Essential tremor is frequently associated with mild gait ataxia. There is growing evidence for an important role of the cerebellar cortex in the pathogenesis of essential tremor. In multiple sclerosis, balance and gait are affected due to cerebellar and spinal cord involvement, as a result of disseminated demyelination and neurodegeneration impairing proprioception. In orthostatic tremor, patients often show mild-to-moderate limb and gait ataxia. The tremor generator is likely located in the posterior fossa. Tandem gait is impaired in the early stages of cerebellar disorders and may be particularly useful in the evaluation of pre-ataxic stages of progressive ataxias. Impaired inter-joint coordination and enhanced variability of gait temporal and kinetic parameters can be grasped by wearable devices such as accelerometers. Kinect is a promising low cost technology to obtain reliable measurements and remote assessments of gait. Deep learning methods are being developed in order to help clinicians in the diagnosis and decision-making process. Locomotor adaptation is impaired in cerebellar patients. Coordinative training aims to improve the coordinative strategy and foot placements across strides, cerebellar patients benefiting from intense rehabilitation therapies. Robotic training is a promising approach to complement conventional rehabilitation and neuromodulation of the cerebellum. Wearable dynamic orthoses represent a potential aid to assist gait. The panel of experts agree that the understanding of the cerebellar contribution to gait control will lead to a better management of cerebellar ataxias in general and will likely contribute to use gait parameters as robust biomarkers of future clinical trials., (© 2022. The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.)

This study aimed to assess the ability of 25 gait indices to characterize gait instability and recurrent fallers among persons with primary degenerative cerebellar ataxia (pwCA), regardless of gait speed, and investigate their correlation with clinical and kinematic variables. Trunk acceleration patterns were acquired during the gait of 34 pwCA, and 34 age- and speed-matched healthy subjects (HS matched ) using an inertial measurement unit. We calculated harmonic ratios (HR), percent recurrence, percent determinism, step length coefficient of variation, short-time largest Lyapunov exponent (sLLE), normalized jerk score, log-dimensionless jerk (LDLJ-A), root mean square (RMS), and root mean square ratio of accelerations (RMSR) in each spatial direction for each participant. Unpaired t-tests or Mann-Whitney tests were performed to identify significant differences between the pwCA and HS matched groups. Receiver operating characteristics were plotted to assess the ability to characterize gait alterations in pwCA and fallers. Optimal cutoff points were identified, and post-test probabilities were calculated. The HRs showed to characterize gait instability and pwCA fallers with high probabilities. They were correlated with disease severity and stance, swing, and double support duration, regardless of gait speed. sLLEs, RMSs, RMSRs, and LDLJ-A were slightly able to characterize the gait of pwCA but failed to characterize fallers., (© 2021. The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.)

The aim of this study was to investigate the time-varying multi-muscle coactivation function (TMCf) in the lower limbs during gait and its relationship with the biomechanical and clinical features of patients with cerebellar ataxia. A total of 23 patients with degenerative cerebellar ataxia (16 with spinocerebellar ataxia, 7 with adult-onset ataxia of unknown etiology) and 23 age-, sex-, and speed-matched controls were investigated. The disease severity was assessed using the Scale for the Assessment and Rating of Ataxia (SARA) in all patients. During walking, simultaneous acquisition of kinematic, kinetic, and electromyography data was performed using a motion analysis system. The coactivation was processed throughout the gait cycle using the TMCf, and the following parameters were measured: synthetic coactivation index, full width at half maximum, and center of activity. Spatiotemporal (walking speed, stance duration, swing duration, first and second double-support durations, step length, step width, stride length, Center of Mass displacement), kinetic (vertical component of GRFs), and energy consumption (total energy consumption and mechanical energy recovered) parameters were also measured. The coactivation variables were compared between patients and controls and were correlated with both clinical and gait variables. A significantly increased global TMCf was found in patients compared with controls. In addition, the patients showed a significant shift of the center of activity toward the initial contact and a significant reduction in energy recovery. All coactivation parameters were negatively correlated with gait speed, whereas the coactivation index and center of activity were positively correlated with both center-of-mass mediolateral displacement values and SARA scores. Our findings suggest that patients use global coactivation as a compensatory mechanism during the earliest and most challenging subphase (loading response) of the gait cycle to reduce the lateral body sway, thus improving gait stability at the expense of effective energy recovery. This information could be helpful in optimizing rehabilitative treatment aimed at improving lower limb muscle control during gait in patients with cerebella ataxia.

Background: Patients with degenerative neurological diseases such as cerebellar ataxia, spastic paraplegia, and Parkinson's disease often display progressive gait function decline that inexorably impacts their autonomy and quality of life. Therefore, considering the related social and economic costs, one of the most important areas of intervention in neurorehabilitation should be the treatment of gait abnormalities. This study aims to determine whether an entire dataset of gait parameters recorded in patients with degenerative neurological diseases can be clustered into homogeneous groups distinct from each other and from healthy subjects. Patients affected by three different types of primary degenerative neurological diseases were studied. These diseases were: i) cerebellar ataxia (28 patients), ii) hereditary spastic paraplegia (31 patients), and iii) Parkinson's disease (70 patients). Sixty-five gender-age-matched healthy subjects were enrolled as a control group. An optoelectronic motion analysis system was used to measure time-distance parameters and lower limb joint kinematics during gait in both patients and healthy controls. When clustering single parameters, step width and ankle joint range of motion (RoM) in the sagittal plane differentiated cerebellar ataxia group from the other groups. When clustering sets of two, three, or four parameters, several pairs, triples, and quadruples of clusters differentiated the cerebellar ataxia group from the other groups. Interestingly, the ankle joint RoM parameter was present in 100% of the clusters and the step width in approximately 50% of clusters. In addition, in almost all clusters, patients with cerebellar ataxia showed the lowest ankle joint RoM and the largest step width values compared to healthy controls, patients with hereditary spastic paraplegia, and Parkinson's disease subjects. This study identified several clusters reflecting specific gait patterns in patients with degenerative neurological diseases. In particular, the specific gait pattern formed by the increased step width, reduced ankle joint RoM, and increased gait variability, can differentiate patients with cerebellar ataxia from healthy subjects and patients with spastic paraplegia or Parkinson's disease. These abnormal parameters may be adopted as sensitive tools for evaluating the effect of pharmacological and rehabilitative treatments., (Copyright © 2017 Elsevier B.V. All rights reserved.)

Background: The harmony of the human gait was recently found to be related to the golden ratio value (ϕ). The ratio between the duration of the stance and that of the swing phases of a gait cycle was in fact found to be close to ϕ, which implies that, because of the fractal property of autosimilarity of that number, the gait ratios stride/stance, stance/swing, swing/double support, were not significantly different from one another. We studied a group of patients with cerebellar ataxia to investigate how the differences between their gait ratios and the golden ratio are related to efficiency and stability of their gait, assessed by energy expenditure and stride-to-stride variability, respectively., Methods: The gait of 28 patients who were affected by degenerative cerebellar ataxia and of 28 healthy controls was studied using a stereophotogrammetric system. The above mentioned gait ratios, the energy expenditure estimated using the pelvis reconstructed method and the gait variability in terms of the stride length were computed, and their relationships were analyzed. Matching procedures have also been used to avoid multicollinearity biases., Findings: The gait ratio values of the patients were farther from the controls (and hence from ϕ), even in speed matched conditions (P=0.011, Cohen's D=0.76), but not when the variability and energy expenditure were matched between the two groups (Cohen's D=0.49). In patients with cerebellar ataxia, the farther the stance-swing ratio was from ϕ, the larger the total mechanical work (R 2 adj =0.64). Further, a significant positive correlation was observed between the difference of the gait ratio from the golden ratio and the severity of the disease (R=0.421, P=0.026)., Interpretation: Harmony of gait appears to be a benchmark of physiological gait leading to physiological energy recovery and gait reliability. Neurorehabilitation of patients with ataxia might benefit from the restoration of harmony of their locomotor patterns., (Copyright © 2017. Published by Elsevier Ltd.)

In the present study, the progression of gait impairment in a group of patients with primary degenerative cerebellar ataxias was observed over a period of 4 years. A total of 30 patients underwent an initial gait analysis study, and thereafter only 12 were evaluated because they completed the 2- and 4-year follow-up evaluations. Time-distance parameters, trunk and joint range of motion (RoM), and variability parameters (e.g., coefficients of variation) were measured at the baseline and at each follow-up evaluation. The scale for the assessment and rating of ataxia (SARA) was used to evaluate disease severity. We found a significant increase in the SARA score at both the 2- and 4-year follow-up evaluations. Almost all the gait variables changed significantly only at the 4-year follow-up. Particularly, we found a significant decrease in the step length and in the hip, knee, and ankle joint RoM values and noted a significant increase in the trunk rotation RoM and stride-to-stride and step length variability. Furthermore, a significant difference in ankle joint RoM was found between spinocerebellar ataxia and sporadic adult-onset ataxia patients, with the value being lower in the former group of patients. Our findings suggest that patients with degenerative cerebellar ataxias exhibit gait decline after 4 years from the baseline. Moreover, patients try to maintain an effective gait by adopting different compensatory mechanisms during the course of the disease in spite of disease progression.

This study aims to evaluate trunk local stability in a group of patients with degenerative primary cerebellar ataxia and to correlate it with spatio-temporal parameters, clinical variables, and history of falls. Sixteen patients affected by degenerative cerebellar ataxia and 16 gender- and age-matched healthy adults were studied by means of an inertial sensor to measure trunk kinematics and spatio-temporal parameters during over-ground walking. Trunk local dynamic stability was quantified by the maximum Lyapunov exponent with short data series of the acceleration data. According to this index, low values indicate more stable trunk dynamics, while high values denote less stable trunk dynamics. Disease severity was assessed by means of International Cooperative Ataxia Rating Scale (ICARS) according to which higher values correspond to more severe disease, while lower values correspond to less severe disease.Patients displayed a higher short-term maximum Lyapunov exponent than controls in all three spatial planes, which was correlated with the age, onset of the disease, and history of falls. Furthermore, the maximum Lyapunov exponent was negatively correlated with ICARS balance, ICARS posture, and ICARS total scores.These findings indicate that trunk local stability during gait is lower in patients with cerebellar degenerative ataxia than that in healthy controls and that this may increase the risk of falls. Local dynamic stability of the trunk seems to be an important aspect in patients with ataxia and could be a useful tool in the evaluation of rehabilitative and pharmacological treatment outcomes.

Although abnormal oscillations of the trunk are a common clinical feature in patients with cerebellar ataxia, the kinematic behaviour of the upper body in ataxic patients has yet to be investigated in quantitative studies. In this study, an optoelectronic motion analysis system was used to measure the ranges of motion (ROMs) of the head and trunk segments in the sagittal, frontal and yaw planes in 16 patients with degenerative cerebellar ataxia during gait at self-selected speed. The data obtained were compared with those collected in a gender-, age- and gait speed-matched sample of healthy subjects and correlated with gait variables (time-distance means and coefficients of variation) and clinical variables (disease onset, duration and severity). The results showed significantly larger head and/or trunk ROMs in ataxic patients compared with controls in all three spatial planes, and significant correlations between trunk ROMs and disease duration and severity (in sagittal and frontal planes) and time-distance parameters (in the yaw plane), and between both head and trunk ROMs and swing phase duration variability (in the sagittal plane). Furthermore, the ataxic patients showed a flexed posture of both the head and the trunk during walking. In conclusion, our study revealed abnormal motor behaviour of the upper body in ataxic patients, mainly resulting in a flexed posture and larger oscillations of the head and trunk. The results of the correlation analyses suggest that the longer and more severe the disease, the larger the upper body oscillations and that large trunk oscillations may explain some aspects of gait variability. These results suggest the need of specific rehabilitation treatments or the use of elastic orthoses that may be particularly useful to reduce trunk oscillations and improve dynamic stability.

Increased antagonist muscle co-activation, seen in motor-impaired individuals, is an attempt by the neuromuscular system to provide mechanical stability by stiffening joints. The aim of this study was to investigate the co-activation pattern of the antagonist muscles of the ankle and knee joints during walking in patients with cerebellar ataxia, a neurological disease that strongly affects stability. Kinematic and electromyographic parameters of gait were recorded in 17 patients and 17 controls. Ankle and knee antagonist muscle co-activation indexes were measured throughout the gait cycle and during the sub-phases of gait. The indexes of ataxic patients were compared with those of controls and correlated with clinical and gait variables. Patients showed increased co-activity indexes of both ankle and knee muscles during the gait cycle as well as during the gait sub-phases. Both knee and ankle muscle co-activation indexes were positively correlated with disease severity, while ankle muscle co-activation was also positively correlated with stance and swing duration variability. Significant negative correlations were observed between the number of self-reported falls per year and knee muscle co-activation. The increased co-activation observed in these cerebellar ataxia patients may represent a compensatory strategy serving to reduce gait instability. Indeed, this mechanism allows patients to reduce the occurrence of falls. The need for this strategy, which results in excessive muscle co-contraction, increased metabolic costs and cartilage degeneration processes, could conceivably be overcome through the use of supportive braces specially designed to provide greater joint stability.

Stopping during walking, a dynamic motor task frequent in everyday life, is very challenging for ataxic patients, as it reduces their gait stability and increases the incidence of falls. This study was conducted to analyse the biomechanical characteristics of upper and lower body segments during abrupt stopping in ataxic patients in order to identify possible strategies used to counteract the instability in the sagittal and frontal plane. Twelve patients with primary degenerative cerebellar ataxia and 12 age- and sex-matched healthy subjects were studied. Time-distance parameters, dynamic stability of the centre of mass, upper body measures and lower joint kinematic and kinetic parameters were analysed. The results indicate that ataxic patients have a great difficulty in stopping abruptly during walking and adopt a multi-step stopping strategy, occasionally with feet parallel, to compensate for their inability to coordinate the upper body and to generate a well-coordinated lower limb joint flexor-extensor pattern and appropriate braking forces for progressively decelerating the progression of the body in the sagittal plane. A specific rehabilitation treatment designed to improve the ability of ataxic patients to transform unplanned stopping into planned stopping, to coordinate upper body and to execute an effective flexion-extension pattern of the hip and knee joints may be useful in these patients in order to improve their stopping performance and prevent falls.

Cerebellar ataxia is associated with unsteady, stumbling gait, and affected patients report a high rate of falls, particularly during locomotor tasks. U-turns (180° turns while walking) require a high level of coordination in order to completely reverse the body trajectory during ongoing motion, and they are particularly challenging for patients with cerebellar ataxia. The aim of this study was to investigate the kinematic strategies adopted by ataxic patients when performing U-turns. Nine ataxic patients and ten controls were analysed as they performed 180° turns to the right while walking. We evaluated the following aspects: centre of mass velocity, body rotation, number of steps needed to complete the task, step length and step width, lower limb joint kinematics and segmental reorientation. Compared with controls, the ataxic patients showed slower deceleration and re-acceleration of the body, needed more steps to complete the U-turn, showed markedly reduced step length and were unable to modulate step width between steps. Furthermore, the patients adopted an extended joint rather than a flexed joint turning strategy, and the degree of knee flexion was found to be negatively correlated with the number of falls. Ataxic patients show an abnormal U-turn in comparison to age-matched healthy subjects. Some of the observed alterations are indicative of a primary deficit in limb-joint coordination, whereas others suggest that patients choose a compensatory strategy aimed at reducing the instability.

This study set out to characterise the pattern of planned gait termination in a sample of patients with cerebellar diseases. The gait termination phase was recorded, using a motion analysis system, in ten patients with primary degenerative cerebellar disease and in ten controls. The subjects were instructed to walk at different gait speeds and to stop in response to an acoustic signal. Time-distance parameters (step length, step width, double support duration, time-to-slow, stopping time, centre of mass velocity and number of steps) and stability index-related parameters (distance between the "extrapolated centre of mass" (XCoM) and centre of pressure (CoP)) were measured at both matched and self-selected gait speeds. At matched speed the patients, compared with the controls, showed a reduced step length, a greater first and second step width and used more steps to stop. At self-selected speed, almost all the parameters differed from those of the controls. Furthermore, the patients showed an increased stability index, suggesting that they need to maintain a "safety margin" between the XCoM and CoP during the gait termination. Patients develop a series of compensatory strategies in order to preserve balance during planned gait termination, e.g. increasing their step width and number of steps. Ataxic patients need to maintain a safety margin in order to avoid instability when stopping. Given the potential risk of falls when stopping, walking ataxic patients may benefit from a rehabilitation treatment focused on preserving and improving their ability to terminate gait safely.

Turning while walking is a common but demanding task requiring modification of the motor program from linear walking to lateral turning and it is associated with a high risk of falls. Patients with cerebellar ataxia have unstable gait and report a high incidence of falls. In the present study, we investigated the motor strategies adopted by ataxic patients when performing turns of different degrees and directions of rotation. Ten ataxic patients and 10 controls were analyzed while performing 30°/90° turns to the right/left. We recorded the number of completed turn tasks, the number of steps needed, and the time taken to complete the task, time-distance parameters and the onset of head, trunk and pelvis reorientation. The ataxic patients were less able to complete 90° turns, displayed a greater stride width, shorter step length, and greater number of steps when turning, and were unable to flexibly adjust their stride width across the turning task. The duration of the turning task and of the segmental reorientation did not differ from control values. Our findings indicate that ataxic patients have more difficulties in performing large turns and adopt a series of compensatory strategy aimed at reducing the instability associated with turning, such as enlarge the base of support, shorten the step length, increase the number of steps, and use the "multi-step" rather than the "spin-turn" strategy. Given the high risk of falls related to this task, it would be useful to include turning training in the rehabilitation protocol of ataxic patients.

Our aim was to perform a comprehensive analysis of the global and segmental features of gait in patients with genetically confirmed inherited ataxias. Sixteen patients with autosomal dominant (spinocerebellar ataxia, SCA1 or 2) or recessive (Friedreich's ataxia, FRDA) ataxia were studied. We used a motion analysis system to record gait kinematic and kinetic data. We measured the mean values of global (time-distance parameters, COM displacement, support moment) and segmental gait parameters (joint displacement and inter-joint coordination), as both discrete and continuous variables, and their variability and correlations with International Cooperative Ataxia Rating Scale (ICARS) scores. We found a marked difference in all global gait parameters between the ataxic patients and the controls and close correlations between longer stride and stance duration and lower gait, posture and total ICARS scores. The only difference between the two patient groups was a shorter step length in the FRDA patients. As regards the segmental features, we found a significantly different waveform shape for all continuous kinematic and kinetic measures between the ataxic patients and the healthy controls, but only minor differences for the discrete measures. Intersegmental coordination evaluated using the continuous relative phase method revealed an irregular alternating joint behaviour without clear evidence of the synchronous pattern of alternating proximal/distal joint seen in healthy subjects. For almost all gait parameters we observed a markedly higher intra-subject variability in the ataxic patients versus the controls, which was strongly related to the clinical ICARS scores. Patients with chronic, progressive inherited ataxias lose the ability to "stabilize" a walking pattern that can be repeated over time. The most peculiar aspect of the gait of inherited ataxia patients, regardless the different genetic forms, seems to be the presence of increased variability of all global and segmental parameters rather than an invariant abnormal gait pattern.

The motor features of people with cerebellar ataxia suggest that locomotion is substantially impaired due to incoordination of the head, trunk, and limbs. The purpose of this study was to investigate how well a wearable soft passive exoskeleton worked for motor coordination in these patients. We used an optoelectronic system to examine the gait of nine ataxic people in three different conditions: without an exoskeleton and with two variants of the exoskeleton, one less and the other more flexible. We investigated kinematics using trunk ranges of motion, the displacement of the center of mass in the medio-lateral direction, and the parameters of mechanical energy consumption and recovery. Furthermore, we investigated the lower limb and trunk muscle coactivation. The results revealed a reduction of the medio-lateral sway of the center of mass, a more efficient behavior of the body in the antero-posterior direction, an energy expenditure optimization, a reduction of muscle coactivation and a better coordination between muscle activations. As a result, the findings laid the groundwork for the device to be used in the rehabilitation of individuals with cerebellar ataxia. [ABSTRACT FROM AUTHOR]

The aim of this study was to assess the ability of multiscale sample entropy (MSE), refined composite multiscale entropy (RCMSE), and complexity index (CI) to characterize gait complexity through trunk acceleration patterns in subjects with Parkinson's disease (swPD) and healthy subjects, regardless of age or gait speed. The trunk acceleration patterns of 51 swPD and 50 healthy subjects (HS) were acquired using a lumbar-mounted magneto-inertial measurement unit during their walking. MSE, RCMSE, and CI were calculated on 2000 data points, using scale factors (τ) 1–6. Differences between swPD and HS were calculated at each τ, and the area under the receiver operating characteristics, optimal cutoff points, post-test probabilities, and diagnostic odds ratios were calculated. MSE, RCMSE, and CIs showed to differentiate swPD from HS. MSE in the anteroposterior direction at τ4 and τ5, and MSE in the ML direction at τ4 showed to characterize the gait disorders of swPD with the best trade-off between positive and negative posttest probabilities and correlated with the motor disability, pelvic kinematics, and stance phase. Using a time series of 2000 data points, a scale factor of 4 or 5 in the MSE procedure can yield the best trade-off in terms of post-test probabilities when compared to other scale factors for detecting gait variability and complexity in swPD. [ABSTRACT FROM AUTHOR]