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At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1995

Is walking a random walk? Evidence for long-range correlations in stride interval of human gait

Complex fluctuation of unknown origin appear in the normal gait pattern. These fluctuations might be described as being (1) uncorrelated white noise, (2) short-range correlations, or (3) long-range correlations with power-law scaling. To test these possibilities, the stride interval of 10 healthy young men was measured as they walked for 9 min at their usual rate. From these time series we calculated scaling indexes by using a modified random walk analysis and power spectral analysis. Both indexes indicated the presence of long-range self-similar correlations extending over hundreds of steps; the stride interval at any time depended on the stride interval at remote previous times, and this dependence decayed in a scale-free (fractallike) power-law fashion. These scaling indexes were significantly different from those obtained after random shuffling of the original time series, indicating the importance of the sequential ordering of the stride interval. We demonstrate that conventional models of gait generation fail to reproduce the observed scaling behavior and introduce a new type of central pattern generator model that sucessfully accounts for the experimentally observed long-range correlations.

Hausdorff, Jeffrey M.↗
NASA NTRSDate not supplied

The Instrumented Walking and Turning Test to Evaluate Suited Gait Dynamics and Performance in Extravehicular Activity Training Environments

Background and aims: Walking will be required for many exploration tasks on the Moon during the Artemis program. Walking in a straight line on the confined floorspace of a testing area, and repetitive treadmill walking that requires no change in direction may not adequately reflect the balance and coordination required during ambulation. Also, performance of turning maneuvers may be affected differently in different extravehicular activity (EVA) training facilities that simulate partial gravity. For example, the Neutral Buoyancy Lab (NBL) simulates lunar gravity by adding weight to underwater subjects to alter buoyancy and achieve the equivalent ground reaction force of 1/6 of Earth’s gravity (1/6G), whereas the Active Response Gravity Offload System (ARGOS) uses a computer controlled overhead suspension system programmed to continuously offload a percentage of a subject’s weight to simulate 1/6G. The degree to which dynamic movements such as turning are comparable across these EVA training facilities has not yet been evaluated. The instrumented gait test helps NASA scientists and engineers evaluate gait dynamics and performance in suited conditions, and this test demonstrates the unique characteristics and limitations of EVA training facilities. We developed an instrumented walking and turning test using inertial measurement units (IMUs) and conducted the test at NASA’s EVA training facilities. Results were used to compare suited walking and turning characteristics in the ARGOS and the NBL. Methods: Subjects donned the Mark III space suit during offloading with the ARGOS spreader bar gimbal and donned the Z2.5 space suit while underwater in the NBL with weights and floatation added to achieve realistic suit center of gravity. The test team securely attached three Opal (APDM, OR, USA) wireless IMUs on the space suit for each test run: one on the middle of the hard upper torso, and one on the left and on the right ankle bearings. During the NBL tests, the IMUs were encased in a waterproof housing (GoPro) with foam added to create a tighter fit. At both testing facilities, 6.3 m x 1.0 m (LxW) walking lines were marked, and a cone for turning or walking around was located at the end of the walking path with another line on the other side of the cone to indicate the stopping point after walking around the cone. Under simulated 1/6G, subjects began by standing at the marked line with their arms folded across the chest, they then walked at a preferred speed along the straight walking path until they reached the end, turned 180 degrees around the cone, and finally stopped at the marked stopping point. All IMU data recorded during testing were automatically saved to the internal memory. Then, raw IMU signals were processed using custom MATLAB (Mathworks, MA, USA) code to compare gait parameters during both the walking and the turning components of the task. These parameters included time (s), speed (m/s for walking and rad/s for turning), step number (n) and walk:turn time ratio (% time spent straight walking versus turning). Results: Less time, faster gait, fewer steps, and higher walk:turn ratio during both walking and turning components were exhibited during tests performed at the ARGOS versus those performed at the NBL. During the NBL tests, the slower walking speed continued at the same rate throughout a U-shape turn. During the ARGOS tests, the subjects performed shorter and tighter turns at 4 times the speed of the NBL turns because they walked 30% faster and the vertical offloading system gave them more support. Conclusion: Our data show that the differences in walking and turning parameters during the NBL tests may be due to the high viscosity in the water environment where the motion of the lower limbs was slow and did not reach full flexion and extension. These tests improve the current knowledge of testing environments in preparation for EVAs on the lunar surface.

Kyoung Jae Kim↗
NASA NTRS1999

Effects of walking velocity on vertical head and body movements during locomotion

Trunk and head movements were characterized over a wide range of walking speeds to determine the relationship between stride length, stepping frequency, vertical head translation, pitch rotation of the head, and pitch trunk rotation as a function of gait velocity. Subjects (26-44 years old) walked on a linear treadmill at velocities of 0.6-2.2 m/s. The head and trunk were modeled as rigid bodies, and rotation and translation were determined using a video-based motion analysis system. At walking speeds up to 1.2 m/s there was little head pitch movement in space, and the head pitch relative to the trunk was compensatory for trunk pitch. As walking velocity increased, trunk pitch remained approximately invariant, but a significant head translation developed. This head translation induced compensatory head pitch in space, which tended to point the head at a fixed point in front of the subject that remained approximately invariant with regard to walking speed. The predominant frequency of head translation and rotation was restricted to a narrow range from 1.4 Hz at 0.6 m/s to 2.5 Hz at 2.2 m/s. Within the range of 0.8-1.8 m/s, subjects tended to increase their stride length rather than step frequency to walk faster, maintaining the predominant frequency of head movement at close to 2.0 Hz. At walking speeds above 1.2 m/s, head pitch in space was highly coherent with, and compensatory for, vertical head translation. In the range 1.2-1.8 m/s, the power spectrum of vertical head translation was the most highly tuned, and the relationship between walking speed and head and trunk movements was the most linear. We define this as an optimal range of walking velocity with regard to head-trunk coordination. The coordination of head and trunk movement was less coherent at walking velocities below 1.2 m/s and above 1.8 m/s. These results suggest that two mechanisms are utilized to maintain a stable head fixation distance over the optimal range of walking velocities. The relative contribution of each mechanism to head orientation depends on the frequency of head movement and consequently on walking velocity. From consideration of the frequency characteristics of the compensatory head pitch, we infer that compensatory head pitch movements may be produced predominantly by the angular vestibulocollic reflex (aVCR) at low walking speeds and by the linear vestibulocollic reflex (1VCR) at the higher speeds.

NASA Discipline Neuroscience↗
NASA NTRS2014

Validity and Reliability of Dynamic Visual Acuity (DVA) Measurement During Walking

DVA is primarily subserved by the vestibulo‐ocular reflex mechanism. Individuals with vestibular hypofunction commonly experience highly debilitating illusory movement or blurring of visual images during daily activities possibly, due to impaired DVA. Even without pathologies, gradual age‐related morphological deterioration is evident in all components of the vestibular system. We examined the construct validity to detect age‐related differences and test‐retest reliability of DVA measurements performed during walking. METHODS: Healthy adults were recruited into 3 groups: 1. young (20‐39years, n=18), 2. middle‐aged (40‐59years, n=14), and 3. older adults (60‐80years, n=15). Randomly selected seven participants from each group (n=21) participated in retesting. Participants were excluded if they had a history of vestibular or neuromuscular pathologies, dizziness/vertigo or >1 falls in the past year. Older persons with MMSE scores <29/30 were excluded to minimize cognitive errors. Participants' age, height, weight and normal walking speed were recorded. The binocular DVA was measured while walking on a treadmill at 0.8 m/s, 1.0 m/s and 1.2 m/s speeds. The walking speeds chosen represent a range of slow to moderate walking speeds for adult life span in participants who have no current mobility problems. The monitor that displayed Landolt 'C' optotypes was placed at 50 cm from the eyes for nearDVA (primary compensation by otolith organs) and at 3.0 m for farDVA (primary compensation by semicircular canals). A mixed factor ANOVA (age group x speed) was performed separately for the Near and FarDVA for detecting group differences. Intraclass correlation coefficients (ICCs) were calculated for each condition to determine test‐retest reliability. RESULTS: The three age groups were not different in their height, weight and normal walking speed (p>0.05). The post hoc analyses for DVA measurements demonstrated that each group was significantly different from the other two groups for Near as well as FarDVA (p<0.001‐p=0.031). The effect of speed was significant for both NearDVA (p=0.012) and FarDVA (p=0.014), however, there was no age group x speed interaction (FarDVA p=0.607, NearDVA p=0.343). The ICCs for Near and FarDVA ranged between 0.85‐ 0.88 and 0.71‐0.87, respectively. CONCLUSIONS: Differences in DVA between the three age groups were detected by using both Near and FarDVA protocols irrespective of the walking speed. Therefore, age group‐specific reference values should be used for detecting malfunction. Further, consistency in walking speed is critical for comparing between studies. NearDVA at all walking speeds and FarDVA at the speed of 1.2 m/s demonstrated excellent testretest reliability. FarDVA at 0.8 m/s and 1.0 m/s demonstrated good test‐retest reliability (ICCs 0.71 and 0.77, respectively).

Deshpande, Nandini↗
NASA NTRS1997

Effect of reduced gravity on the preferred walk-run transition speed

We investigated the effect of reduced gravity on the human walk-run gait transition speed and interpreted the results using an inverted-pendulum mechanical model. We simulated reduced gravity using an apparatus that applied a nearly constant upward force at the center of mass, and the subjects walked and ran on a motorized treadmill. In the inverted pendulum model for walking, gravity provides the centripetal force needed to keep the pendulum in contact with the ground. The ratio of the centripetal and gravitational forces (mv2/L)/(mg) reduces to the dimensionless Froude number (v2/gL). Applying this model to a walking human, m is body mass, v is forward velocity, L is leg length and g is gravity. In normal gravity, humans and other bipeds with different leg lengths all choose to switch from a walk to a run at different absolute speeds but at approximately the same Froude number (0.5). We found that, at lower levels of gravity, the walk-run transition occurred at progressively slower absolute speeds but at approximately the same Froude number. This supports the hypothesis that the walk-run transition is triggered by the dynamics of an inverted-pendulum system.

Non-NASA Center↗
NASA NTRS1994

Increased walking variability in elderly persons with congestive heart failure

OBJECTIVES: To determine the effects of congestive heart failure on a person's ability to walk at a steady pace while ambulating at a self-determined rate. SETTING: Beth Israel Hospital, Boston, a primary and tertiary teaching hospital, and a social activity center for elderly adults living in the community. PARTICIPANTS: Eleven elderly subjects (aged 70-93 years) with well compensated congestive heart failure (NY Heart Association class I or II), seven elderly subjects (aged 70-79 years) without congestive heart failure, and 10 healthy young adult subjects (aged 20-30 years). MEASUREMENTS: Subjects walked for 8 minutes on level ground at their own selected walking rate. Footswitches were used to measure the time between steps. Step rate (steps/minute) and step rate variability were calculated for the entire walking period, for 30 seconds during the first minute of the walk, for 30 seconds during the last minute of the walk, and for the 30-second period when each subject's step rate variability was minimal. Group means and 5% and 95% confidence intervals were computed. MAIN RESULTS: All measures of walking variability were significantly increased in the elderly subjects with congestive heart failure, intermediate in the elderly controls, and lowest in the young subjects. There was no overlap between the three groups using the minimal 30-second variability (elderly CHF vs elderly controls: P < 0.001, elderly controls vs young: P < 0.001), and no overlap between elderly subjects with and without congestive heart failure when using the overall variability. For all four measures, there was no overlap in any of the confidence intervals, and all group means were significantly different (P < 0.05).

NASA Discipline Cardiopulmonary↗
NASA NTRS2016

Field Test: Results of Tandem Walk Performance Following Long-Duration Spaceflight

BACKGROUND: Coordinated locomotion has proven to be challenging for many astronauts following long duration spaceflight. As NASA's vision for spaceflight points toward interplanetary travel, we must prepare for unassisted landings, where crewmembers may need to perform mission critical tasks within minutes of landing. Thus, it is vital to develop a knowledge base from which operational guidelines can be written that define when astronauts can be expected to safely perform certain tasks. Data obtained during the Field Test experiment (FT) will add important insight to this knowledge base. Specifically, we aim to develop a recovery timeline of functional sensorimotor performance during the first 24 hours and several days after landing. METHODS: FT is an ongoing study of 30 long-duration ISS crewmembers. Thus far, 9 have completed the full FT (5 U.S. Orbital Segment [USOS] astronauts and 4 Russian cosmonauts) and 4 more consented and launching within the next year. This is in addition to the eighteen crewmembers that participated in the pilot FT (11 USOS and 7 Russian crewmembers). The FT is conducted three times preflight and three times during the first 24 hours after landing. All crewmembers were tested in Kazakhstan in either the medical tent at the Soyuz landing site (~one hour post-landing), or at the airport (~four hours post-landing). The USOS crewmembers were also tested at the refueling stop (~12 hours post-landing) and at the NASA Johnson Space Center (~24 hours post-landing) and a final session 7 days post-landing. Crewmembers are instrumented with 9 inertial measurement unit sensors that measure acceleration and angular displacement (APDM's Emerald Sensors) and foot pressure-sensing insoles that measure force, acceleration, and center of pressure (Moticon GmbH, Munich, Germany) along with heart rate and blood pressure recording instrumentation. The FT consists of 12 tasks, but here we will focus on the most challenging task, the Tandem Walk, which was also performed as part of pilot FT. To perform the Tandem Walk, subjects begin with their feet together, their arms crossed at their chest and eyes closed. When ready, they brought one foot forward and touched the heel of their foot to their toe, repeating with the other foot, and continuing for about 10 steps. Three trials were collected with the eyes closed and a fourth trial was collected with eyes open. There are four metrics which are used to determine the performance level of the Tandem Walk. The first is percent correct steps. For a step to be counted as correct, the foot could not touch the ground while bringing it forward (no side stepping), eyes must stay closed during the eyes closed trials, the heel and toe should be touching, or almost touching (no large gaps) and there shouldn't be more than a three second pause between steps. Three judges score each step and the median of the three scores is kept. The second metric is the average step speed, or the number of steps/time to complete them. Thirdly, the root mean squared (RMS) error in the resultant trunk acceleration is used to determine the amount of upper body instability observed during the task. Finally, the RMS error of the mediolateral center of pressure as measured by the Moticon insoles is used to determine the mediolateral instability at the foot level. These four parameters are combined into a new overall Tandem Walk Parameter. RESULTS: Preliminary results show that crewmembers perform the Tandem Walk significantly worse the first 24 hours after landing as compared to their baseline performance. We find that each of the four performance metrics is significantly worse immediately after landing. We will present the results of tandem walk performance during the FT thus far. We will also combine these with the 18 crewmembers that participated in the pilot FT, concentrating on the level of performance and recovery rate. CONCLUSION: The Tandem Walk data collected as part of the FT experiment will provide invaluable information on the performance capabilities of astronauts during the first 24 hours after returning from long-duration spaceflight that can be used in planning future Mars, or other deep-space missions with unassisted landings. FT will determine the average sensorimotor recovery timeline and inform return-to-duty guidelines for unassisted landings.

Rosenberg, M. J. F.↗
NASA NTRS1995

Head perturbations during walking while viewing a head-fixed target

Inexpensive, head-fixed computer displays are now available that subjects can wear during locomotion. Our hypothesis is that viewing a head-fixed visual display will change the character- istics of rotational head perturbations during natural walking. Using a 3-axis angular rate sensor, we measured head rotations during natural or treadmill walking, in 10 normal subjects and 2 patients with deficient vestibular function, as they attempted to view (1) a stationary target at optical infinity; and (2) a target at a distance of 20 cm rigidly attached to the head. Normal subjects and patients showed no significant change in the predominant frequency of head rotations in any plane (ranging 0.7-5.7 Hz) during the two different viewing tasks. Mean peak head velocities also showed no difference during the two viewing conditions except in the yaw plane, in which values were greater while viewing the near target. Predominant frequencies of head rotations were similar in the pitch plane during natural or treadmill walking; however, peak velocities of pitch head rotations were substantially greater during natural walking. One vestibular patient showed modest increases of head velocity during natural walking compared with normal subjects. Rotational head perturbations that occur during natural walking are largely unaffected when subjects view a head-fixed target. There is need to study how such perturbations, which induce vestibular eye movements, affect vision of head-fixed displays.

Das, Vallabh E.↗
NASA NTRS2001

Interaction of the body, head, and eyes during walking and turning

Body, head, and eye movements were measured in five subjects during straight walking and while turning corners. The purpose was to determine how well the head and eyes followed the linear trajectory of the body in space and whether head orientation followed changes in the gravito-inertial acceleration vector (GIA). Head and body movements were measured with a video-based motion analysis system and horizontal, vertical, and torsional eye movements with video-oculography. During straight walking, there was lateral body motion at the stride frequency, which was at half the frequency of stepping. The GIA oscillated about the direction of heading, according to the acceleration and deceleration associated with heel strike and toe flexion, and the body yawed in concert with stepping. Despite the linear and rotatory motions of the head and body, the head pointed along the forward motion of the body during straight walking. The head pitch/roll component appeared to compensate for vertical and horizontal acceleration of the head rather than orienting to the tilt of the GIA or anticipating it. When turning corners, subjects walked on a 50-cm radius over two steps or on a 200-cm radius in five to seven steps. Maximum centripetal accelerations in sharp turns were ca.0.4 g, which tilted the GIA ca.21 degrees with regard to the heading. This was anticipated by a roll tilt of the head of up to 8 degrees. The eyes rolled 1-1.5 degrees and moved down into the direction of linear acceleration during the tilts of the GIA. Yaw head deviations moved smoothly through the turn, anticipating the shift in lateral body trajectory by as much as 25 degrees. The trunk did not anticipate the change in trajectory. Thus, in contrast to straight walking, the tilt axes of the head and the GIA tended to align during turns. Gaze was stable in space during the slow phases and jumped forward in saccades along the trajectory, leading it by larger angles when the angular velocity of turning was greater. The anticipatory roll head movements during turning are likely to be utilized to overcome inertial forces that would destabilize balance during turning. The data show that compensatory eye, head, and body movements stabilize gaze during straight walking, while orienting mechanisms direct the eyes, head, and body to tilts of the GIA in space during turning.

Non-NASA Center↗
NASA NTRS2001

Soleus H-reflex gain in humans walking and running under simulated reduced gravity

The Hoffmann (H-) reflex is an electrical analogue of the monosynaptic stretch reflex, elicited by bypassing the muscle spindle and directly stimulating the afferent nerve. Studying H-reflex modulation provides insight into how the nervous system centrally modulates stretch reflex responses.A common measure of H-reflex gain is the slope of the relationship between H-reflex amplitude and EMG amplitude. To examine soleus H-reflex gain across a range of EMG levels during human locomotion, we used simulated reduced gravity to reduce muscle activity. We hypothesised that H-reflex gain would be independent of gravity level.We recorded EMG from eight subjects walking (1.25 m s-1) and running (3.0 m s-1) at four gravity levels (1.0, 0.75, 0.5 and 0.25 G (Earth gravity)). We normalised the stimulus M-wave and resulting H-reflex to the maximal M-wave amplitude (Mmax) elicited throughout the stride to correct for movement of stimulus and recording electrodes relative to nerve and muscle fibres. Peak soleus EMG amplitude decreased by ~30% for walking and for running over the fourfold change in gravity. As hypothesised, slopes of linear regressions fitted to H-reflex versus EMG data were independent of gravity for walking and running (ANOVA, P > 0.8). The slopes were also independent of gait (P > 0.6), contrary to previous studies. Walking had a greater y-intercept (19.9% Mmax) than running (-2.5% Mmax; P < 0.001). At all levels of EMG, walking H-reflex amplitudes were higher than running H-reflex amplitudes by a constant amount. We conclude that the nervous system adjusts H-reflex threshold but not H-reflex gain between walking and running. These findings provide insight into potential neural mechanisms responsible for spinal modulation of the stretch reflex during human locomotion.

Non-NASA Center↗
NASA NTRS2000

Calcaneal loading during walking and running

PURPOSE: This study of the foot uses experimentally measured kinematic and kinetic data with a numerical model to evaluate in vivo calcaneal stresses during walking and running. METHODS: External ground reaction forces (GRF) and kinematic data were measured during walking and running using cineradiography and force plate measurements. A contact-coupled finite element model of the foot was developed to assess the forces acting on the calcaneus during gait. RESULTS: We found that the calculated force-time profiles of the joint contact, ligament, and Achilles tendon forces varied with the time-history curve of the moment about the ankle joint. The model predicted peak talocalcaneal and calcaneocuboid joint loads of 5.4 and 4.2 body weights (BW) during walking and 11.1 and 7.9 BW during running. The maximum predicted Achilles tendon forces were 3.9 and 7.7 BW for walking and running. CONCLUSIONS: Large magnitude forces and calcaneal stresses are generated late in the stance phase, with maximum loads occurring at approximately 70% of the stance phase during walking and at approximately 60% of the stance phase during running, for the gait velocities analyzed. The trajectories of the principal stresses, during both walking and running, corresponded to each other and qualitatively to the calcaneal trabecular architecture.

NASA Center ARC↗
NASA NTRS1992

A new technique for simultaneous monitoring of electrocardiogram and walking cadence

A new technique for simultaneously recording continuous electrocardiographic (ECG) data and walking step rate (cadence) is described. The ECG and gait signals are recorded on 2 channels of an ambulatory Holter monitor. Footfall is detected using ultrathin, force-sensitive foot switches and is frequency modulated. The footfall signal provides an indication of the subject's activity (walking or standing), as well as the instantaneous walking rate. Twenty-three young and elderly subjects were studied to demonstrate the use of this ECG and gait recorder. High-quality gait signals were obtained in all subjects, and the effects of walking on the electrocardiogram were assessed. Initial investigation revealed the following findings: (1) Although walking rates were similar in young and elderly subjects, the elderly had both decreased heart rate (HR) variability (p < 0.005) and increased cadence variability (p < 0.0001). (2) Overall, there was an inverse relation between HR and cadence variability (r = -0.73). Three elderly subjects with no known cardiac disease had HR and cadence variability similar to those of the young, whereas elderly subjects with history of congestive heart failure were among those with the lowest HR variability and the highest cadence variability. (3) Low-frequency (approximately equal to 0.1 Hz) HR oscillations (frequently observed during standing) persisted during walking in all young subjects. (4) In some subjects, both step rate and HR oscillated at the same low frequency (approximately equal to 0.1 Hz) previously identified with autonomic control of the baroreflex.(ABSTRACT TRUNCATED AT 250 WORDS).

NASA Discipline Cardiopulmonary↗
NASA NTRS2006

Effects of Walking Speed and Visual-Target Distance on Toe Trajectory During Swing Phase

After spaceflight, astronauts experience disturbances in their ability to walk and maintain postural stability (Bloomberg, et al., 1997). One of the post-flight neurovestibular assessments requires that the astronaut walk on a treadmill at 1.8 m/sec (4.0 mph), while performing a visual acuity test, set at two different distances ( far and near ). For the first few days after landing, some crewmembers can not maintain the required pace, so a lower speed may be used. The slower velocity must be considered in the kinematic analysis, because Andriacchi, et al. (1977) showed that in clinical populations, changes in gait parameters may be attributable more to slower gait speed than pathology. Studying toe trajectory gives a global view of control of the leg, since it involves coordination of muscles and joints in both the swing and stance legs (Karst, et al., 1999). Winter (1992) and Murray, et al. (1984) reported that toe clearance during overground walking increased slightly as speed increased, but not significantly. Also, toe vertical peaks in both early and late swing phase did increase significantly with increasing speed. During conventional testing of overground locomotion, subjects are usually asked to fix their gaze on the end of the walkway a far target. But target (i.e., visual fixation) distance has been shown to affect head and trunk motion during treadmill walking (Bloomberg, et al., 1992; Peters, et al., in review). Since the head and trunk can not maintain stable gaze without proper coordination with the lower body (Mulavara & Bloomberg, 2003), it would stand to reason that lower body kinematics may be altered as well when target distance is modified. The purpose of this study was to determine changes in toe vertical trajectory during treadmill walking due to changes in walking speed and target distance.

Miller, Chris↗
NASA NTRS1973

Monte-Carlo analysis of rarefied-gas diffusion including variance reduction using the theory of Markov random walks

Molecular diffusion through a rarefied gas is analyzed by using the theory of Markov random walks. The Markov walk is simulated on the computer by using random numbers to find the new states from the appropriate transition probabilities. As the sample molecule during its random walk passes a scoring position, which is a location at which the macroscopic diffusing flow variables such as molecular flux and molecular density are desired, an appropriate payoff is scored. The payoff is a function of the sample molecule velocity. For example, in obtaining the molecular flux across a scoring position, the random walk payoff is the net number of times the scoring position has been crossed in the positive direction. Similarly, when the molecular density is required, the payoff is the sum of the inverse velocity of the sample molecule passing the scoring position. The macroscopic diffusing flow variables are then found from the expected payoff of the random walks.

Perlmutter, M.↗
NASA NTRS2006

"Far" and "Near" Visual Acuity While Walking and the Collective Contributions of Non-Ocular Mechanisms to Gaze Stabilization

Gaze stabilization was quantified in subjects (n=11) as they walked on a motorized treadmill (1.8 m/s) and viewed visual targets at two viewing distances. A "far" target was positioned at 4 m (FAR) in front of the subject and the "near" target was placed at a distance of 0.5 m (NEAR). A direct measure of visual acuity was used to assess the overall effectiveness of the gaze stabilization system. The contributions of nonocular mechanisms to the gaze goal were also quantified using a measure of the distance between the subject and point in space where fixation of the visual target would require the least eye movement amplitude (i.e. the head fixation distance (HFD)). Kinematic variables mirrored those of previous investigations with the vertical trunk translation and head pitch signals, and the lateral translation and head yaw signals maintaining what appear as antiphase relationships. However, an investigation of the temporal relationships between the maxima and minima of the vertical translation and head pitch signals show that while the maximum in vertical translation occurs at the point of the minimum head pitch signal, the inverse is not true. The maximum in the head pitch signal lags the vertical translation minimum by an average of greater than 12 percent of the step cycle time. Three HFD measures, one each for data in the sagittal and transverse planes, and one that combined the movements from both planes, all revealed changes between the FAR and NEAR target viewing conditions. This reorganization of the nonocular degrees of freedom while walking was consistent with a strategy to reduce the magnitude of the eye movements required when viewing the NEAR target. Despite this reorganization, acuity measures show that image stabilization is not occurring while walking and viewing the NEAR target. Group means indicate that visual acuity is not affected while walking in the FAR condition, but a decrement of 0.15 logMAR (i.e. 1.5 eye chart lines) exists between the standing and walking acuity measures when viewing the NEAR target.

Peters, Brian T.↗
NASA NTRS2008

Near-Infrared Spectroscopic Measurements of Calf Muscle during Walking at Simulated Reduced Gravity - Preliminary Results

Consideration for lunar and planetary exploration space suit design can be enhanced by investigating the physiologic responses of individual muscles during locomotion in reduced gravity. Near-infrared spectroscopy (NIRS) provides a non-invasive method to study the physiology of individual muscles in ambulatory subjects during reduced gravity simulations. PURPOSE: To investigate calf muscle oxygen saturation (SmO2) and pH during reduced gravity walking at varying treadmill inclines and added mass conditions using NIRS. METHODS: Four male subjects aged 42.3 +/- 1.7 years (mean +/- SE) and weighing 77.9 +/- 2.4 kg walked at a moderate speed (3.2 +/- 0.2 km/h) on a treadmill at inclines of 0, 10, 20, and 30%. Unsuited subjects were attached to a partial gravity simulator which unloaded the subject to simulate body weight plus the additional weight of a space suit (121 kg) in lunar gravity (0.17G). Masses of 0, 11, 23, and 34 kg were added to the subject and then unloaded to maintain constant weight. Spectra were collected from the lateral gastrocnemius (LG), and SmO2 and pH were calculated using previously published methods (Yang et al. 2007 Optics Express ; Soller et al. 2008 J Appl Physiol). The effects of incline and added mass on SmO2 and pH were analyzed through repeated measures ANOVA. RESULTS: SmO2 and pH were both unchanged by added mass (p>0.05), so data from trials at the same incline were averaged. LG SmO2 decreased significantly with increasing incline (p=0.003) from 61.1 +/- 2.0% at 0% incline to 48.7 +/- 2.6% at 30% incline, while pH was unchanged by incline (p=0.12). CONCLUSION: Increasing the incline (and thus work performed) during walking causes the LG to extract more oxygen from the blood supply, presumably to support the increased metabolic cost of uphill walking. The lack of an effect of incline on pH may indicate that, while the intensity of exercise has increased, the LG has not reached a level of work above the anaerobic threshold. In these preliminary studies, 30% incline walking at reduced gravity may not require anaerobic LG activity due to the low exercise intensity (42.8 +/- 1.6% of VO(sub 2max)). It is also possible that at reduced gravity additional work is being done by muscle groups other than the calf.

Ellerby, Gwenn E. C.↗
NASA NTRS1993

Generalized Levy-walk model for DNA nucleotide sequences

We propose a generalized Levy walk to model fractal landscapes observed in noncoding DNA sequences. We find that this model provides a very close approximation to the empirical data and explains a number of statistical properties of genomic DNA sequences such as the distribution of strand-biased regions (those with an excess of one type of nucleotide) as well as local changes in the slope of the correlation exponent alpha. The generalized Levy-walk model simultaneously accounts for the long-range correlations in noncoding DNA sequences and for the apparently paradoxical finding of long subregions of biased random walks (length lj) within these correlated sequences. In the generalized Levy-walk model, the lj are chosen from a power-law distribution P(lj) varies as lj(-mu). The correlation exponent alpha is related to mu through alpha = 2-mu/2 if 2 < mu < 3. The model is consistent with the finding of "repetitive elements" of variable length interspersed within noncoding DNA.

NASA Discipline Number 14-10↗
DOE OSTI2026

Powers of magnetic graph matrix: Fourier spectrum, walk compression, and applications

Magnetic graphs, originally developed to model quantum systems under magnetic fields, have recently emerged as a powerful framework for analyzing complex directed networks. Existing research has primarily used the spectral properties of the magnetic graph matrix to study global and stationary network features. However, their capacity to model local, nonequilibrium behaviors, often described by matrix powers, remains largely unexplored. We present a combinatorial interpretation of the magnetic graph matrix powers through directed walk profiles—counts of graph walks indexed by the number of edge reversals. Crucially, we establish that walk profiles correspond to a Fourier transform of magnetic matrix powers. The connection allows exact reconstruction of walk profiles from magnetic matrix powers at multiple discrete potentials, and more importantly, an even smaller number of potentials often suffices for accurate approximate reconstruction in real networks. This shows the empirical compressibility of the information captured by the magnetic matrix. This fresh perspective suggests further applications; for example, we illustrate how powers of the magnetic matrix can identify frustrated directed cycles (e.g., feedforward loops) and can be effectively employed for link prediction by encoding local structural details in directed graphs.

complex networks↗