Spatiotemporal Asymmetry Research Articles

Encoding spatiotemporal asymmetry in artificial cilia with a ctenophore-inspired soft-robotic platform

A remarkable variety of organisms use metachronal coordination (i.e., numerous neighboring appendages beating sequentially with a fixed phase lag) to swim or pump fluid. This coordination strategy is used by microorganisms to break symmetry at small scales where viscous effects dominate and flow is time-reversible. Some larger organisms use this swimming strategy at intermediate scales, where viscosity and inertia both play important roles. However, the role of individual propulsor kinematics-especially across hydrodynamic scales-is not well-understood, though the details of propulsor motion can be crucial for the efficient generation of flow. To investigate this behavior, we developed a new soft robotic platform using magnetoactive silicone elastomers to mimic the metachronally coordinated propulsors found in swimming organisms. Furthermore, we present a method to passively encode spatially asymmetric beating patterns in our artificial propulsors. We investigated the kinematics and hydrodynamics of three propulsor types, with varying degrees of asymmetry, using Particle Image Velocimetry and high-speed videography. We find that asymmetric beating patterns can move considerably more fluid relative to symmetric beating at the same frequency and phase lag, and that asymmetry can be passively encoded into propulsors via the interplay between elastic and magnetic torques. Our results demonstrate that nuanced differences in propulsor kinematics can substantially impact fluid pumping performance. Our soft robotic platform also provides an avenue to explore metachronal coordination at the meso-scale, which in turn can inform the design of future bioinspired pumping devices and swimming robots.

Assessing framework of rainfall-induced landslide hazard considering spatiotemporal asymmetry in extreme precipitation indices under climate change

Assessing framework of rainfall-induced landslide hazard considering spatiotemporal asymmetry in extreme precipitation indices under climate change

Theta Phase Precession and the Dynamics of Spatiotemporal Asymmetry in Hippocampal Place Fields

A consistently observed characteristic of hippocampal place fields is the shifting of the field's center of mass and the subsequent development of asymmetry. This is evidenced by the expansion of the place field in an asymmetric manner over repeated traversals, wherein a rat's initial entry into the field prompts a low firing rate that substantially increases as it exits. Our study delves deeper into these spatiotemporal asymmetries of place field spiking, specifically examining their relationship with theta oscillations and disentangling the effects from environmental factors. Analysis of neuronal data from a T-maze alternation task revealed a distinct non-uniform firing pattern of place cells. This pattern was markedly skewed in relation to the phases of theta cycles, indicating a phase precession effect. We found that as the rat navigates through the place field, there is a systematic advancement of spike timing, with action potentials tending to cluster in the early phases of theta during the exit phase of the field. Such temporal coordination of spikes suggests that the timing of neural activity within theta cycles is as integral as spatial location, influencing the dynamics of place field expansion and potentially affecting the hippocampal local field potential. This discovery underscores the role of theta phase precession in spatial encoding, proposing a novel temporal component that could underpin the cognitive map within the hippocampus. R01 MH126236 R01 AG055544. This is the full abstract presented at the American Physiology Summit 2024 meeting and is only available in HTML format. There are no additional versions or additional content available for this abstract. Physiology was not involved in the peer review process.

The influence of sensitizer on spatiotemporal asymmetry in gait: a comparison of fallers and non-fallers

Aim To compare spatiotemporal parameters of asymmetry in gait between fallers and non-fallers in the age group of 50–79 years under the influence of different sensitisers. Settings and design Convenience sampling. Cross-sectional observational study. Methods and material A cross-sectional study was conducted on a cohort of seventy-two healthy adults within the age range of 50–79 years. The participants were segregated into two distinct groups: fallers, who had experienced falls within the past year and achieved a John Hopkins score exceeding 6, and non-fallers, characterised by an absence of falls in the preceding year and a John Hopkins score lower than 6. Gait analysis was performed using a pressure-sensitive walkway system known as GaitRite. Subjects were asked to walk two times on the walkway under five different conditions (slow walking, fast, walking, fixed gaze walking, dual-task walking, and walking with weights). Data were analysed. Results A Mann–Whitney U Test was employed to statistically compare gait asymmetry between fallers and non-fallers, revealing a significant difference. This dissimilarity in gait asymmetry was further magnified under varying sensitising conditions. Temporal parameters demonstrated more pronounced asymmetry when compared to spatial parameters. Conclusions The result shows that sensitisers influence the asymmetry in fallers more when compared to non-fallers. The sensitisers which increased asymmetry compared to non-fallers were slow walking, fast walking, fixed gaze, dual-task, and walking with weights. This study observed that all the temporal parameters are sensitive towards asymmetry when subjects were asked to walk under different sensitisers.

Facilitation of motor adaptation using multiple gait rehabilitation interventions.

The rate of adjustment in a movement, driven by feedback error, is referred to as the adaptation rate, and the rate of recovery of a newly adapted movement to its unperturbed condition is called the de-adaptation rate. The rates of adaptation and de-adaptation are dependent on the training mechanism and intrinsic factors such as the participant's sensorimotor abilities. This study investigated the facilitation of the motor adaptation and de-adaptation processes for spatiotemporal features of an asymmetric gait pattern by sequentially applying split-belt treadmill (SBT) and asymmetric rhythmic auditory cueing (ARAC). Two sessions tested the individual gait characteristics of SBT and ARAC, and the remaining four sessions consisted of applying the two interventions sequentially during training. The adjustment process to the second intervention is referred to as "re-adaptation" and is driven by feedback error associated with the second intervention. Ten healthy individuals participated in the randomized six-session trial. Spatiotemporal asymmetries during the adaptation and post-adaptation (when intervention is removed) stages were fitted into a two-component exponential model that reflects the explicit and implicit adaptation processes. A double component was shown to fit better than a single-component model. The decay constants of the model were indicative of the corresponding timescales and compared between trials. Results revealed that the explicit (fast) component of adaptation to ARAC was reduced for step length and step time when applied after SBT. Contrarily, the explicit component of adaptation to SBT was increased when it was applied after ARAC for step length. Additionally, the implicit (slow) component of adaptation to SBT was inhibited when applied incongruently after ARAC for step time. These outcomes show that the role of working motor memory as a translational tool between different gait interventions is dependent on (i) the adaptation mechanisms associated with the interventions, (ii) the targeted motor outcome of the interventions; the effects of factors (i) and (ii) are specific to the explicit and implicit components of the adaptation processes; these effects are unique to spatial and temporal gait characteristics.

A novel simulation based approach for user-based redistribution in bike-sharing system

The increased demand for a safe, reliable, cost-effective, clean, and social distancing-friendly mode of commuting in the post-COVID world has motivated the transportation research community to closely analyse and optimise the operations of the existing Bike-Sharing Systems (BSS). One of the key elements in BSS operation is the redistribution of bicycles to cope with the spatiotemporal asymmetry in the demands across the docking stations. Operators usually employ trucks to do the rebalancing at regular intervals. Alternatively, strategies encouraging user-based rebalancing that allow the continuous redistribution of bicycles can be implemented. Dynamic user-based rebalancing strategies are often considered a feasible approach to improve the reliance and performance of the BSS and have been gaining prominence. This paper presents a simulation-driven dynamic user-based redistribution framework using the novel Distance-Willingness-Reward (DWR) matrix method. The framework shows the capability to generate dynamic incentives for the users, motivating them to participate in the rebalancing process, leading to the continuous redistribution of bicycles at each station. The Distance-Willingness-Reward (DWR) matrix method generates the required dynamic incentives for each user, and the bike requirements at each docking station are evaluated using an improved suggestion measure, the Station Impact Index (SII). Simulation experiments are designed and run for 30 days of operation considering 30 stations. Results show that the proposed approach gives better performance compared to the existing operator-based rebalancing and no rebalancing approaches.

Reducing Knee Hyperextension With an Exoskeleton in Children and Adolescents With Genu Recurvatum: A Feasibility Study.

Genu recurvatum, or knee hyperextension, is a complex gait pattern with a variety of etiologies, and is often connected with knee weakness, lack of motor control, and spasticity. Because of the atypical forces placed on the soft tissues, early treatment or prevention of knee hyperextension may help prevent further degradation of the knee joint. In this study, we assessed the feasibility of a knee exoskeleton to mitigate hyperextension and increase swing range of motion in five children/adolescents who presented with unilateral genu recurvatum. Over the course of three visits, each participant practiced walking with the exoskeleton, which provided torque assistance during both stance and swing based on an impedance control law. In final validation trials, the exoskeleton was effective in reducing knee hyperextension (0.2 ± 4.7° average peak knee extension without exo to 9.9 ± 10.3° with exo) and improving swing range of motion by 14.0 ± 4.5° increase on average. However, while the exoskeleton was effective in normalizing the kinematics, it did not lead to improved spatio-temporal asymmetry measures. This work showcases a promising potential application of a robotic knee exoskeleton for improving the kinematic characteristics of genu recurvatum gait.

Insufficiencies in sensory systems reweighting is associated with walking impairment severity in chronic stroke: an observational cohort study.

Walking and balance impairment are common sequelae of stroke and significantly impact functional independence, morbidity, and mortality. Adequate postural stability is needed for walking, which requires sufficient integration of sensory information between the visual, somatosensory, and vestibular centers. "Sensory reweighting" describes the normal physiologic response needed to maintain postural stability in the absence of sufficient visual or somatosensory information and is believed to play a critical role in preserving postural stability after stroke. However, the extent to which sensory reweighting successfully maintains postural stability in the chronic stages of stroke and its potential impact on walking function remains understudied. In this cross-sectional study, fifty-eight community-dwelling ambulatory chronic stroke survivors underwent baseline postural stability testing during quiet stance using the modified Clinical test of Sensory Interaction in Balance (mCTSIB) and assessment of spatiotemporal gait parameters. Seventy-six percent (45/58) of participants showed sufficient sensory reweighting with visual and somatosensory deprivation for maintaining postural stability, albeit with greater postural sway velocity indices than normative data. In contrast, survivors with insufficient reweighting demonstrated markedly slower overground walking speeds, greater spatiotemporal asymmetry, and limited acceleration potential. Adequate sensory system reweighting is essential for chronic stroke survivors' postural stability and walking independence. Greater emphasis should be placed on rehabilitation strategies incorporating multisensory system integration testing and strengthening as part of walking rehabilitation protocols. Given its potential impact on outcomes, walking rehabilitation trials may benefit from incorporating formal postural stability testing in design and group stratification.

Patterns of asymmetry and energy cost generated from predictive simulations of hemiparetic gait

Hemiparesis, defined as unilateral muscle weakness, often occurs in people post-stroke or people with cerebral palsy, however it is difficult to understand how this hemiparesis affects movement patterns as it often presents alongside a variety of other neuromuscular impairments. Predictive musculoskeletal modeling presents an opportunity to investigate how impairments affect gait performance assuming a particular cost function. Here, we use predictive simulation to quantify the spatiotemporal asymmetries and changes to metabolic cost that emerge when muscle strength is unilaterally reduced and how reducing spatiotemporal symmetry affects metabolic cost. We modified a 2-D musculoskeletal model by uniformly reducing the peak isometric muscle force unilaterally. We then solved optimal control simulations of walking across a range of speeds by minimizing the sum of the cubed muscle excitations. Lastly, we ran additional optimizations to test if reducing spatiotemporal asymmetry would result in an increase in metabolic cost. Our results showed that the magnitude and direction of effort-optimal spatiotemporal asymmetries depends on both the gait speed and level of weakness. Also, the optimal speed was 1.25 m/s for the symmetrical and 20% weakness models but slower (1.00 m/s) for the 40% and 60% weakness models, suggesting that hemiparesis can account for a portion of the slower gait speed seen in people with hemiparesis. Modifying the cost function to minimize spatiotemporal asymmetry resulted in small increases (~4%) in metabolic cost. Overall, our results indicate that spatiotemporal asymmetry may be optimal for people with hemiparesis. Additionally, the effect of speed and the level of weakness on spatiotemporal asymmetry may help explain the well-known heterogenous distribution of spatiotemporal asymmetries observed in the clinic. Future work could extend our results by testing the effects of other neuromuscular impairments on optimal gait strategies, and therefore build a more comprehensive understanding of the gait patterns observed in clinical populations.

Manual stabilization reveals a transient role for balance control during locomotor adaptation.

A fundamental feature of human locomotor control is the need to adapt walking patterns in response to changes in the environment. For example, when people walk on a split-belt treadmill, which has belts that move at different speeds, they adapt to the asymmetric speed constraints by reducing spatiotemporal asymmetry. Here, we aim to understand the role of balance control as a potential factor driving this adaptation process. We recruited 24 healthy, young adults to adapt to walking on a split-belt treadmill while either holding on to a handrail or walking with free arm swing. We measured whole body angular momentum and step length asymmetry as measures of dynamic balance and spatiotemporal asymmetry, respectively. To understand how changes in intersegmental coordination influenced whole body angular momentum, we also measured segmental angular momenta and the coefficient of cancellation. When participants were initially exposed to the asymmetry in belt speeds, we observed an increase in whole body angular momentum that was due to both an increase in the momentum of individual segments and a reduction in the coefficient of cancellation. Holding on to a handrail reduced the perturbation to asymmetry during the early phase of adaptation and resulted in a smaller aftereffect during early postadaptation. In addition, the stabilization provided by holding on to a handrail led to reductions in the coupling between angular momentum and asymmetry. These results suggest that regulation of dynamic balance is most important during the initial, transient phase of adaptation to walking on a split-belt treadmill.NEW & NOTEWORTHY We investigated the role of dynamic balance during adaptation to a split-belt treadmill by measuring whole body angular momentum with or without holding on to a handrail. The initial step length asymmetry and associations between balance and asymmetry reduced when holding on to a handrail during early adaptation. These findings indicate that dynamic balance mostly contributes to the initial phase of adaptation when people are exposed to an asymmetric walking constraint.

A Systematic Review of Non-Pharmacological Interventions to Improve Gait Asymmetries in Neurological Populations

Gait asymmetries are commonly observed in neurological populations and linked to decreased gait velocity, balance decrements, increased fall risk, and heightened metabolic cost. Interventions designed to improve gait asymmetries have varying methods and results. The purpose of this systematic review was to investigate non-pharmacological interventions to improve gait asymmetries in neurological populations. Keyword searches were conducted using PubMed, CINAHL, and Academic Search Complete. The search yielded 14 studies for inclusion. Gait was assessed using 3D motion capture systems (n = 7), pressure-sensitive mats (e.g., GAITRite; n = 5), and positional sensors (n = 2). The gait variables most commonly analyzed for asymmetry were step length (n = 11), stance time (n = 9), and swing time (n = 5). Interventions to improve gait asymmetries predominantly used gait training techniques via a split-belt treadmill (n = 6), followed by insoles/orthoses (n = 3). The literature suggests that a wide range of methods can be used to improve spatiotemporal asymmetries. However, future research should further examine kinematic and kinetic gait asymmetries. Additionally, researchers should explore the necessary frequency and duration of various intervention strategies to achieve the greatest improvement in gait asymmetries, and to determine the best symmetry equation for quantifying gait asymmetries.

Spatiotemporal strategies adopted to walk at fast speed in high- and low-functioning individuals post-stroke: a cross-sectional study

ABSTRACT Background Walking at fast speed is a gait training strategy post-stroke. It is unknown how faster-than-preferred pace impacts spatiotemporal gait characteristics in survivors with different functional abilities. Objective To test the hypothesis that compared to high-functioning individuals, low-functioning individuals will be limited in modifying spatiotemporal gait parameters for walking at faster-than-preferred speed, and these limitations are associated with fear of falling. Methods Forty-two adults, 17.6 ± 14.6 months post-stroke, traversed an instrumented walkway at preferred and fast speeds. Participants were categorized to a low-functioning group (LFG) (n = 20; <0.45 m/s) and high-functioning group (HFG) (n = 22; ≥0.45 m/s). Cadence, step length, stance time and spatiotemporal asymmetry measures were calculated. The Modified Falls-efficacy Scale examined fear of falling. Multivariate and correlational analysis tested hypotheses. Results Increased speed from preferred to fast pace was significantly greater for HFG (0.27 ± 0.03 m/s) than LFG (0.10 ± 0.02 m/s) (p ≤ 0.001). Cadence gain from preferred to fast pace did not differ between groups. However, HFG exhibited greater change in paretic (∆6.1 ± 1.37 cm; p < .001) and non-paretic step lengths (∆4.5 ± 1.37 cm; p = .003) than LFG. Spatiotemporal asymmetry did not change for either group. Fear of falling had moderately positive correlation with ∆paretic step length (r = 0.43; p = .004) and ∆non-paretic step length (r = 0.32; p = .035). Conclusions While both low- and high-functioning individuals used a step-lengthening strategy to walk at faster-than-preferred speeds, the gain in step lengths was limited in low-functioning individuals and was partially explained by falls-efficacy.

An observational study of hydrodynamic impact on water mass transport due to tidal power generation

The world's largest Sihwa Tidal Power Plant (TPP), located on the west coast of Korea, was built in 2011 for the purpose of improving water quality and producing renewable energy. After several years of actual operation, most of the original purpose was achieved, but unexpected coastal environmental changes such as tidal flat damage and sediment accumulation also occurred. In this study, in order to understand the causes of these environmental changes, field observations were conducted near TPP, and spatial and temporal variability of flow structure and water exchange process were investigated. Three-dimensional velocity data were collected along the closed line surrounding the outside of the TPP for 11 h during spring tide and analyzed according to two discharge phases: power generation phase (PGP) and drainage phase (DP). The results show that the depth-averaged maximum current velocity was more than three times greater at DP than at PGP. Jet-like flow during DP caused very high horizontal shear, whereas vertical shear was relatively weak, indicating that the horizontal and vertical flow structures were very different. The most notable result is that the mass transport patterns between PGP and DP are significantly different, i.e., during PGP, mass transport is dominated on the left side of the TPP, whereas during DP, it occurs at the front of the TPP. This means that there is a strong spatiotemporal asymmetry between the inflow from the downstream (outside of the TPP) during PGP and the outflow from the upstream (inside of the TPP) during DP. These asymmetric processes can have a significant impact on the material exchange and sediment transport near the TPP. Since observational studies on TPP are extremely rare, this study is expected to contribute to future TPP related research, such as numerical modeling.

Spatiotemporal Asymmetry in Metachronal Rowing at Intermediate Reynolds Numbers.

In drag-based swimming, individual propulsors operating at low Reynolds numbers (where viscous forces dominate over inertial forces) must execute a spatially asymmetric stroke to produce net fluid displacement. Temporal asymmetry (that is, differing duration between the power vs. recovery stroke) does not affect the overall generated thrust in this time-reversible regime. Metachronal rowing, in which multiple appendages beat sequentially, is used by a wide variety of organisms from low to intermediate Reynolds numbers. At the upper end of this range, inertia becomes important, and increasing temporal asymmetry can be an effective way to increase thrust. However, the combined effects of spatial and temporal asymmetry are not fully understood in the context of metachronal rowing. To explore the role of spatiotemporal asymmetry in metachronal rowing, we combine laboratory experiments and reduced-order analytical modeling. We measure beat kinematics and generated flows in two species of lobate ctenophores across a range of body sizes, from 7 to 40 mm in length. We observe characteristically different flows in ctenophores of differing body size and Reynolds number, and a general decrease in spatial asymmetry and increase in temporal asymmetry with increasing Reynolds number. We also construct a one-dimensional mathematical model consisting of a row of oscillating flat plates whose flow-normal areas change with time, and use it to explore the propulsive forces generated across a range of Reynolds numbers and kinematic parameters. The model results show that while both types of asymmetry increase force production, they have different effects in different regions of the parameter space. These results may have strong biological implications, as temporal asymmetry can be actively controlled while spatial asymmetry is likely to be partially or entirely driven by passive fluid-structure interaction.

Changes in Walking Speed After High-Intensity Treadmill Training Are Independent of Changes in Spatiotemporal Symmetry After Stroke.

Objectives: Decreased walking speeds and spatiotemporal asymmetry both occur after stroke, but it is unclear whether and how they are related. It is also unclear whether rehabilitation-induced improvements in walking speed are associated with improvements in symmetry or greater asymmetry. High-intensity speed-based treadmill training (HISTT) is a recent rehabilitative strategy whose effects on symmetry are unclear. The purpose of this study was to: (1) assess whether walking speed is cross-sectionally associated with spatiotemporal symmetry in chronic stroke, (2) determine whether HISTT leads to changes in the spatiotemporal symmetry of walking, and (3) evaluate whether HISTT-induced changes in walking speed are associated with changes in spatiotemporal symmetry.Methods: Eighty-one participants with chronic stroke performed 4 weeks of HISTT. At pre, post, and 3-month follow-up assessments, comfortable and maximal walking speed were measured with the 10-meter walk test, and spatiotemporal characteristics of walking were measured with the GAITRite mat. Step length and swing time were expressed as symmetry ratios (paretic/non-paretic). Changes in walking speed and symmetry were calculated and the association was determined.Results: At pre-assessment, step length and swing time asymmetries were present (p < 0.001). Greater temporal symmetry was associated with faster walking speeds (p ≤ 0.001). After HISTT, walking speeds increased from pre-assessment to post-assessment and follow-up (p ≤ 0.002). There were no changes in spatiotemporal symmetry (p ≥ 0.10). Change in walking speed was not associated with change in spatial or temporal symmetry from pre- to post-assessment or from post-assessment to follow-up (R2 ≤ 0.01, p ≥ 0.37).Conclusions: HISTT improves walking speed but does not systematically improve or worsen spatiotemporal symmetry. Clinicians may need to pair walking interventions like HISTT with another intervention designed to improve walking symmetry simultaneously. The cross-sectional relation between temporal symmetry and walking speed may be mediated by other factors, and not be causative.

Distal Bias of Meiotic Crossovers in Hexaploid Bread Wheat Reflects Spatio-Temporal Asymmetry of the Meiotic Program.

Meiotic recombination generates genetic variation and provides physical links between homologous chromosomes (crossovers) essential for accurate segregation. In cereals the distribution of crossovers, cytologically evident as chiasmata, is biased toward the distal regions of chromosomes. This creates a bottleneck for plant breeders in the development of varieties with improved agronomic traits, as genes situated in the interstitial and centromere proximal regions of chromosomes rarely recombine. Recent advances in wheat genomics and genome engineering combined with well-developed wheat cytogenetics offer new opportunities to manipulate recombination and unlock genetic variation. As a basis for these investigations we have carried out a detailed analysis of meiotic progression in hexaploid wheat (Triticum aestivum) using immunolocalization of chromosome axis, synaptonemal complex and recombination proteins. 5-Bromo-2′-deoxyuridine (BrdU) labeling was used to determine the chronology of key events in relation to DNA replication. Axis morphogenesis, synapsis and recombination initiation were found to be spatio-temporally coordinated, beginning in the gene-dense distal chromosomal regions and later occurring in the interstitial/proximal regions. Moreover, meiotic progression in the distal regions was coordinated with the conserved chromatin cycles that are a feature of meiosis. This mirroring of the chiasma bias was also evident in the distribution of the gene-associated histone marks, H3K4me3 and H3K27me3; the repeat-associated mark, H3K27me1; and H3K9me3. We believe that this study provides a cytogenetic framework for functional studies and ongoing initiatives to manipulate recombination in the wheat genome.

The spatiotemporal spread of cervical spinal cord contusion injury pathology revealed by 3D in-line phase contrast synchrotron X-ray microtomography

Extensive structural changes occur within the spinal cord following traumatic injury. Acute tissue debris and necrotic tissue are broken down, proliferating local glia and infiltrating leukocytes remodel tissue biochemical and biophysical properties, and a chronic cavity surrounded by a scar forms at the injury epicentre. Serial-section 2D histology has traditionally assessed these features in experimental models of spinal cord injury (SCI) to measure the extent of tissue pathology and evaluate efficacy of novel therapies. However, this 2D snapshot approach overlooks slice intervening features, with accurate representation of tissue compromised by mechanical processing artefacts. 3D imaging avoids these caveats and allows full exploration of the injured tissue volume to characterise whole tissue pathology. Amongst 3D imaging modalities, Synchrotron Radiation X-ray microtomography (SRμCT) is advantageous for its speed, ability to cover large tissue volumes at high resolution, and need for minimal sample processing. Here we demonstrate how extended lengths of formalin-fixed, paraffin-embedded (FFPE) rat spinal cord can be completely imaged by SRμCT with micron resolution. Label-free contrast derived from X-ray phase interactions with low-density soft tissues, reveals spinal cord white matter, gray matter, tissue damage and vasculature, with tissue still viable for targeted 2D-histology after 3D imaging. We used SRμCT to quantify tissue pathology after a midline, cervical level (C6), 225 kDyne contusion injury over acute-to-chronic (24 h to 5 weeks) post injury time points. Quantification revealed acute tissue swelling prior to chronic atrophy across the whole imaged region (spanning 2 spinal segments above and below injury), along with rostro-caudal asymmetries in white and gray matter volume loss. 3D volumes revealed satellite damage in tissue far removed from the epicentre, and extensive rostro-caudal spread of damage through the base of the dorsal columns at 24 h post injury. This damage overlapped regions of vasogenic oedema, confirmed with subsequent histology. Tissue damage at later time points in border regions was most prominent in the dorsal columns, where it overlapped sites of damaged venous vasculature. Elaborating rostro-caudal and spatiotemporal asymmetries in reduced traumatic injury models centred on these regions may inform future treatments that seek to limit the spread of tissue pathology to these ‘at-risk’ regions.

Generalization of the k coefficient method in relativity to an arbitrary angle between the velocity of an observer (source) and the direction of the light ray from (to) a faraway source (observer) at rest

The k coefficient method proposed by Bondi is extended to the general case where the angle α between the velocity of a signal from a distant source at rest and the velocity of the observer does not coincide with 0 or π, as considered by Bondi, but takes an arbitrary value in the interval 0 ⩽ α ⩽ π, and to the opposite case where the source is moving and the observer is at rest, while the angle α between the source velocity and the direction of the signal to the observer takes any value between 0 and π. Functions k*(β, α) and k+(β, α) of the angle and relative velocity are introduced for the ratio ω / ω′ of proper frequencies of the source and observer. Their explicit expressions are obtained without using Lorentz transformations, from the condition that the coherence of a bunch of rays is preserved in passing from the source frame to the observer frame. Owing to the analyticity of these functions in α, the ratio of frequencies in the cases mentioned is given by the formulas ω / ω′ = k*(β, α) and ω / ω′ = k+(β, π – α) ≡ 1 / k*(β, α), which coincide with those for the Doppler effect, in which the angle α, the velocity β, and one of the frequencies are measured in the rest frame. A ray emitted by the source at an angle α to the observer’s velocity in the source frame is directed at an angle α′ to the same velocity in the observer frame. Owing to light aberration, the angles α and α′ are functionally related through k*(β, α) = k+(β, β′). The functions α′(α, β) and α (α′,β) are expressed as antiderivatives of k*(β, α) and k*(β, π – α′). The analyticity of the functions k*(β, z) and k+(β, z) in z ≡ α in the interval 0 ⩽ z ⩽ π is extended to the entire plane of complex z, where k* has poles at i ln cos α1 (see ()), and k+ has zeros at the same points shifted by π. The spatiotemporal asymmetry of the Doppler and light aberration effects is explained by the closeness of these singularities to the real axis.

Spatiotemporal Gait Asymmetry Distinguishes Fallers And Non-fallers In Below-knee Amputees

Introduction: Below-knee-amputees (BKA) are at a higher risk of falling compared to non-amputee controls. Gait patterns have been reported to be an important risk factor of falls: in particular, great disparity in asymmetry of kinematic parameters between lower limbs are observed in BKA. PURPOSE: To investigate differences between spatiotemporal symmetry gait patterns, functional mobility and balance confidence among unilateral BKA fallers and non-fallers. Method: Twenty-six unilateral BKA (14 fallers: 47.5±8.6 yrs; 29.5±4.5 kg/m2 and 12 non-fallers: 47.5±8.6 yrs; 31.1±5.5 kg/m2) completed 5 walking trials, at a self-selected pace, on a 4.3 m GaitRite system. Step length, swing time, and stance time for each limb was collected. Symmetry ratios between limbs were calculated. Self-reported falls within the past 12 months, Timed Up and Go (TUG) Test and the Activity-Specific Balance Confidence (ABC) questionnaire were also collected. Independent t-tests were performed to compare the fallers with the non-fallers. RESULTS: The fallers had significantly lower functional mobility (12.1±2.7 v. 8.5±1.1 sec) and reported lower balance confidence (77.4±10.9 v. 87.7±13.7) than the non-fallers (p < 0.05). The fallers also had significantly larger step length (1.12±0.05 v. 1.01±0.05), stance time (10.6±0.03 v. 1.02±0.02) and swing time (1.11±0.05 v. 1.04±0.05) asymmetries (p < 0.05). Discussion: These results suggest that spatiotemporal asymmetry could be useful in distinguishing prospective fallers from non-fallers among BKA. BKA fallers had increased gait asymmetry compared to the non-fallers, which may be attributed to prosthetic alignment, as well as acquired gait changes because of pain, and diminished strength and range of motion. These findings should be used by clinicians to identify BKA at a greater risk of falling, and specific functional and psychological interventions should be considered for these individuals to improve gait asymmetry, functional mobility, and balance confidence.

Improving Spatiotemporal Gait Asymmetry Has Limited Functional Benefit for Individuals Poststroke

Prior literature suggests a relationship between spatiotemporal gait asymmetry and metabolic cost of walking, balance, endurance, quality of life, and physical activity in people with chronic stroke. Our purpose was to determine whether targeting spatiotemporal gait symmetry would concomitantly improve these measures. This study represents secondary outcome measures from a trial in which 48 participants with chronic stroke were randomized to groups that all targeted spatiotemporal gait asymmetry. Measures of balance, daily step count, endurance (6-minute walk test [6MWT), metabolic cost of walking, quality of life (Stroke Impact Scale [SIS]), and overground spatiotemporal asymmetries were collected 1 week prior to and following training. Separate analyses were performed for those who trained for spatial versus temporal asymmetry. The effect of time (pre/post) was examined for all measures and correlational analyses evaluated the potential relationships between changes in spatiotemporal asymmetry and all other measures. Individuals who trained to target step length asymmetry improved balance, 6MWT distance, metabolic cost of walking, and SIS-Mobility. Individuals who trained to target stance time asymmetry improved balance, 6MWT distance, SIS-Mobility, and SIS-Global recovery scores. However, step length asymmetry improvements were only related to improved 6MWT distance (P = 0.025; r = -0.49). Stance time asymmetry improvements were only related to improved metabolic cost of walking (P = 0.031; r = 0.558). Despite a targeted training approach and noted improvements in most measures, these changes did not appear to arise from improved spatiotemporal gait asymmetry. Furthermore, improvements in gait function observed in the laboratory setting did not appear to translate to increased community mobility.Video Abstract available for more insights from the authors (see the Video, Supplemental Digital Content 1, available at: http://links.lww.com/JNPT/A316).