Intralimb gait coordination of individuals with stroke using vector coding

Individuals with stroke often present functional impairment and gait alteration. Among different aspects, intralimb coordination of these individuals is one of the key points that should be considered before implementing any gait intervention protocol. The purpose of this study was to investigate the effects of stroke on intralimb gait coordination of the lower limbs using a vector coding technique. Twenty-five individuals with stroke and 18 non-disabled individuals (control), between 46 and 71 years old, participated in this study. A computerized analysis system registered data from reflective markers placed on specific body landmarks to define thigh, shank, and foot of both body sides, as participants walked at self-selected comfortable speed. Coordination modes, such as in-phase, anti-phase, proximal-segment-phase, and distal-segment-phase, and variability of thigh-shank, and shank-foot were analyzed for the paretic, non-paretic and control limbs during the stance and swing periods, and the entire gait cycle using the vector coding technique. During the stance period, individuals with stroke presented higher frequency of thigh-phase and lower frequency of shank-phase for the thigh-shank coupling and higher frequency of shank-phase for the shank-foot coupling compared to non-disabled controls, indicating that the proximal segment of each pair leads the movement. During the swing period, the paretic limb presented higher frequency for in-phase than non-paretic and control limbs for the thigh-shank coupling. Adaptations in the non-paretic limb were observed in the swing period, with higher frequency than paretic and control limbs in the thigh-phase for the thigh-shank coupling, and higher frequency than the paretic limb in the foot-phase for the shank-foot coupling. No differences in coordination variability were found between paretic, non-paretic, and control limbs. The vector coding technique constitutes a useful tool for identifying gait alterations in intralimb coordination of individuals with stroke. Our coordination results demonstrate a shift from distal to more proximal control during the stance phase in both legs for the individuals with stroke and an inability to decouple segment coordination during the swing phase in the paretic limb. The results indicate that it is more suitable to consider the stance and swing periods separately instead of considering the entire gait cycle to investigate intralimb gait coordination of individuals with stroke.     

Using swing resistance and assistance to improve gait symmetry in individuals post-stroke

A major characteristic of hemiplegic gait observed in individuals post-stroke is spatial and temporal asymmetry, which may increase energy expenditure and the risk of falls. The purpose of this study was to examine the effects of swing resistance/assistance applied to the affected leg on gait symmetry in individuals post-stroke. We recruited 10 subjects with chronic stroke who demonstrated a shorter step length with their affected leg in comparison to the non-affected leg during walking. They participated in two test sessions for swing resistance and swing assistance, respectively. During the adaptation period, subjects counteracted the step length deviation caused by the applied swing resistance force, resulting in an aftereffect consisting of improved step length symmetry during the post-adaptation period. In contrast, subjects did not counteract step length deviation caused by swing assistance during adaptation period and produced no aftereffect during the post-adaptation period. Locomotor training with swing resistance applied to the affected leg may improve step length symmetry through error-based learning. Swing assistance reduces errors in step length during stepping; however, it is unclear whether this approach would improve step length symmetry. Results from this study may be used to develop training paradigms for improving gait symmetry of stroke survivors.     

Exploring gait adaptations to perturbed and conventional treadmill training in Parkinson’s disease: Time-course,sustainability, and transfer

BackgroundGait impairment is a major motor symptom in Parkinson’s disease (PD), and treadmill training is an effective non-pharmacological treatment option.Research questionIn this study, the time course, sustainability and transferability of gait adaptations to treadmill training with and without additional postural perturbations were investigated.Methods38 PD patients (Hoehn & Yahr 1–3.5) were randomly allocated to eight weeks of treadmill training, performed twice-weekly for 40 min either with (perturbation treadmill training [PTT], n = 18) or without (conventional treadmill training [CTT], n = 20) additional perturbations to the treadmill surface. Spatiotemporal gait parameters were assessed during treadmill walking on a weekly basis (T0–T8), and after three months follow-up (T9). Additional overground gait analyses were performed at T0 and T8 to investigate transfer effects.ResultsTreadmill gait variability reduced linearly over the course of 8 weeks in both groups (p < .001; Cohen’s d (range): −0.53 to −0.84). Only the PTT group significantly improved in other gait parameters (stride length/time, stance-/swing time), with stride time showing a significant between-group interaction effect (Cohen’s d = 0.33; p = .05). Additional between-group interactions indicated more sustained improvements in stance (Cohen’s d = 0.85; p = .02) and swing time variability in the PTT group (Cohen’s d = 0.82; p = .03) at T9. Overground gait improvements at T8 existed only in stance (d = -0.73; p = .04) and swing time (d = 0.73; p = .04).DiscussionTreadmill stride-to-stride variability reduced substantially and linearly, but transfer to overground walking was limited. Adding postural perturbations tended to increase efficacy and sustainability of several gait parameters. However, since between-group effects were small, more work is necessary to support these findings.     

State-dependent corrective reactions for backward balance losses during human walking

We investigated corrective reactions for backward balance losses during walking. Several biomechanical studies have suggested that backward falling can be predicted from the horizontal position and velocity of the body center of mass (COM) related to the stance foot. Our hypothesis was that corrective reactions for backward balance losses depend on whether the body moves forward or backward after a perturbation. Using a split-belt treadmill, backward balance losses during walking were induced by rapid decreases of belt speed from 3.5 km/h to 2.5, 2.0, 1.5 and 1.0 km/h. We measured kinematic data and surface electromyography (EMG) during corrective reactions while walking on the treadmill. Phase portrait analysis of COM trajectories revealed that backward balance stability was decreased by the perturbations. When the perturbed belt speed was 1.0 km/h, the COM states at toe-off were significantly lower than the stability limit; a rapid touch-down of the swing foot posterior to the stance foot then occurred, and the gait rhythm was modulated so that the phase advanced. EMG recordings during perturbed steps revealed a bilateral response, including modulation of the swing leg during the recovery. For weaker perturbations, the swing foot placements were anterior to the stance foot and there was a phase delay. In contrast to the bilateral responses for stronger perturbations, unilateral EMG responses were observed for weaker perturbations. The differences in joint kinematics and EMG patterns in the unperturbed swing leg depended on the COM states at toe-off, suggesting the existence of different responses consisting of ongoing swing movements and rapid touch-down. Thus, we conclude that corrective reactions for backward balance losses are not only phase-dependent but also state-dependent. In addition, the control system for backward balance losses predicts the feasibility of forward progression and modulates swing movement and walking rhythm according to backward balance stability.     

Speed-Interactive Treadmill Training Using Smartphone-Based Motion Tracking Technology Improves Gait in Stroke Patients

This study was conducted to investigate the effects of speed-interactive treadmill training (SITT) using smartphone-based motion tracking technology on gait in stroke patients. Thirty-four chronic stroke patients were randomly divided into a SITT group (n = 18) and a standard treadmill training (control) group (n = 16). The SITT group underwent smartphone-based SSIT while the control group underwent standard treadmill training. Both groups performed the training for 35 min per session, 3 times per week, for 6 weeks. Both groups used nonmotorized treadmills so that patients could control the speed. Evaluation was conducted during the week before and after the training. The OptoGait system measured gait spatiotemporal parameters. Both groups showed significant improvement in the temporal and spatial gait parameters (p < .05). In the SITT group, compared to the control group, the two-way analysis of variance with repeated measures showed an improvement in the temporal and spatial gait parameters after the intervention period (p < .05). This study confirmed that SITT improved the gait function of stroke patients. Based on this result, the authors propose that SITT, by improving gait, can be used as an effective training method to improve patients' functional activities in the clinic.     

Changes in lower limb co-contraction and stiffness by toddlers with Down syndrome and toddlers with typical development during the acquisition of independent gait

During gait acquisition, children learn to use their changing resources to meet the requirements of the task. Compared to typically developing toddlers (TD), toddlers with Down syndrome (DS) have functionally different musculoskeletal characteristics, such as hypotonia, and joint and ligament laxity, that could produce a reduced passive stiffness. The interplay between this inherently lower passive stiffness and the demands of walking may result in different strategies during gait acquisition. This study compared normalized global stiffness and lower limb's co-contraction indices (CCI) used by toddlers with TD (n=12) and with DS (n=12), during the early stages of gait acquisition. Stiffness and CCI were normalized by gravitational torque (mLg) in both phases of gait (stance, swing). Five longitudinal evaluations were conducted from the onset of locomotion until three months post-acquisition. All children were video taped and had electromyographic (EMG) recordings from muscle pairs of one leg, which were used to calculate CCI of hip, knee, ankle, and total leg CCI. Body and lower limb stiffness were calculated according to a hybrid pendulum resonance equation. Results from ANOVAs revealed no group differences on stiffness or on CCI's during stance but children with DS showed greater CCI during swing. Despite the structural musculoskeletal differences between toddlers with TD and with DS, the similarities observed in their processes of gait development suggest functional equivalences.     

Distraction Affects the Performance of Obstacle Avoidance During Walking

In this study, dual-task interference in obstacle-avoidance tasks during human walking was examined. Ten healthy young adults participated in the experiment. While they were walking on a treadmill, an obstacle suddenly fell on the treadmill in front of their left leg during either midswing, early stance, or late stance of the ipsilateral leg. Participants were instructed to avoid the obstacle, both as a single task and while they were concurrently performing a cognitive secondary task (dual task). Rates of failure, avoidance strategy, and a number of kinematic parameters were studied under both task conditions. When only a short response time was available, rates of failure on the avoidance task were larger during the dual task than during the single task. Smaller crossing swing velocities were found during the dual task as compared with those observed in the single task. The difference in crossing swing velocities was attributable to increased stiffness of the crossing swing limb. The results of the present study indicated that divided attention affects young and healthy individuals' obstacle-avoidance performance during walking.     

Distraction affects the performance of obstacle avoidance during walking

In this study, dual-task interference in obstacle-avoidance tasks during human walking was examined. Ten healthy young adults participated in the experiment. While they were walking on a treadmill, an obstacle suddenly fell on the treadmill in front of their left leg during either midswing, early stance, or late stance of the ipsilateral leg. Participants were instructed to avoid the obstacle, both as a single task and while they were concurrently performing a cognitive secondary task (dual task). Rates of failure, avoidance strategy, and a number of kinematic parameters were studied under both task conditions. When only a short response time was available, rates of failure on the avoidance task were larger during the dual task than during the single task. Smaller crossing swing velocities were found during the dual task as compared with those observed in the single task. The difference in crossing swing velocities was attributable to increased stiffness of the crossing swing limb. The results of the present study indicated that divided attention affects young and healthy individuals' obstacle-avoidance performance during walking.     

Development of postural adjustment during gait initiation: kinematic and EMG analysis

The authors studied the development of postural adjustments associated with the initiation of gait in children by using kinematic and electromyographic (EMG) analysis. Participants (N = 28) included infants with 1-4 and 9-17 months of walking experience, children 4-5 years of age, and adults. Anticipatory postural adjustments (APA) were present in the youngest age groups, including a clear anticipatory lateral tilt of the pelvis and the stance leg, which enabled the child to unload the opposite leg shortly before its swing phase. An anticipatory activation of the hip abductor of the leg in stance phase prior to heel-off was found, suggesting pelvis stabilization. APA did not appear consistently until 4-5 years of age. A decrease in segmental oscillations occurred across the ages, indicating better control of intersegmental coordination in the frontal and sagittal planes during the postural phase of gait initiation. Young walkers presented APA involving movements of both the upper and the lower parts of the body, whereas, like adults, 4- to 5-year-olds were able to laterally shift only the pelvis and the stance leg. The oldest children and the adults also showed lower activation levels of hip and knee muscles but higher activation at the ankle level. Those kinematic and EMG results taken together suggest a clear developmental sequence from an en bloc operation of the body through an articulated operation with maturation, walking experience, or both.     

Development of Postural Adjustment During Gait Initiation: Kinematic and EMG Analysis

The authors studied the development of postural adjustments associated with the initiation of gait in children by using kinematic and electromyographic (EMG) analysis. Participants (N = 28) included infants with 1-4 and 9-17 months of walking experience, children 4-5 years of age, and adults. Anticipatory postural adjustments (APA) were present in the youngest age groups, including a clear anticipatory lateral tilt of the pelvis and the stance leg, which enabled the child to unload the opposite leg shortly before its swing phase. An anticipatory activation of the hip abductor of the leg in stance phase prior to heel-off was found, suggesting pelvis stabilization. APA did not appear consistently until 4-5 years of age. A decrease in segmental oscillations occurred across the ages, indicating better control of intersegmental coordination in the frontal and sagittal planes during the postural phase of gait initiation. Young walkers presented APA involving movements of both the upper and the lower parts of the body, whereas, like adults, 4- to 5-year-olds were able to laterally shift only the pelvis and the stance leg. The oldest children and the adults also showed lower activation levels of hip and knee muscles but higher activation at the ankle level. Those kinematic and EMG results taken together suggest a clear developmental sequence from an en bloc operation of the body through an articulated operation with maturation, walking experience, or both.     

Adaptation of neuromuscular synergies during intentional constraints of space-time relationships in human gait

Tight frequency-to-amplitude relationships are observed in spontaneous human steady gait. They can be modified, if required; that flexibility forms a fundamental basis of the intentional adaptive capabilities of locomotion. In the present experiments, the processes underlying that flexibility were investigated at both the level of joint kinematics and the level of neuromuscular synergies. Subjects (N = 4) walked at the same speed either with a preferred or a nonpreferred frequency-to-amplitude relationship (i.e., constrained, short steps at a high frequency [COS condition] or constrained, long steps at a low frequency [COL condition]); their swing and stance phases were separately analyzed. In the COS condition, increases in EMG activity were specifically required during the swing phase. In the COL condition, several muscles required increases in EMG activity during the stance phase, but decreases of the hamstring muscles were needed during the swing phase. Whereas, in preferred walking, modification of the frequency affects the EMG patterns globally (the gain increasing with the frequency in both the stance and swing phases), the present results show that changing the frequency in a constrained manner either affects the swing phase specifically or affects both phases, but in the opposite direction. That finding indicates that a separate control is needed in both the swing and the stance phases.     

Adaptation of Neuromuscular Synergies During Intentional Constraints of Space-Time Relationships in Human Gait

Tight frequency-to-amplitude relationships are observed in spontaneous human steady gait. They can be modified, if required; that flexibility forms a fundamental basis of the intentional adaptive capabilities of locomotion. In the present experiments, the processes underlying that flexibility were investigated at both the level of joint kinematics and the level of neuromuscular synergies. Subjects (N = 4) walked at the same speed either with a preferred or a nonpreferred frequency-to-amplitude relationship (i.e., constrained, short steps at a high frequency [COS condition] or constrained, long steps at a low frequency [COL condition]); their swing and stance phases were separately analyzed. In the COS condition, increases in EMG activity were specifically required during the swing phase. In the COL condition, several muscles required increases in EMG activity during the stance phase, but decreases of the hamstring muscles were needed during the swing phase. Whereas, in preferred walking, modification of the frequency affects the EMG patterns globally (the gain increasing with the frequency in both the stance and swing phases), the present results show that changing the frequency in a constrained manner either affects the swing phase specifically or affects both phases, but in the opposite direction. That finding indicates mat a separate control is needed in both the swing and the stance phases.     

Enhanced arm swing alters interlimb coordination during overground walking in individuals with traumatic brain injury

The current study investigated interlimb coordination in individuals with traumatic brain injury (TBI) during overground walking. The study involved 10 participants with coordination, balance, and gait abnormalities post-TBI, as well as 10 sex- and age-matched healthy control individuals. Participants walked 12 m under two experimental conditions: 1) at self-selected comfortable walking speeds; and 2) with instructions to increase the amplitude and out-of-phase coordination of arm swinging. The gait was assessed with a set of spatiotemporal and kinematic parameters including the gait velocity, step length and width, double support time, lateral displacement of the center of mass, the amplitude of horizontal trunk rotation, and angular motions at shoulder and hip joints in sagittal plane. Interlimb coordination (coupling) was analyzed as the relative phase angles between the left and right shoulders, hips, and contralateral shoulders and hips, with an ideal out-of-phase coupling of 180° and ideal in-phase coupling of 0°. The TBI group showed much less interlimb coupling of the above pairs of joint motions than the control group. When participants were required to increase and synchronize arm swinging, coupling between shoulder and hip motions was significantly improved in both groups. Enhanced arm swinging was associated with greater hip and shoulder motion amplitudes, and greater step length. No other significant changes in spatiotemporal or kinematic gait characteristics were found in either group. The results suggest that arm swinging may be a gait parameter that, if controlled properly, can improve interlimb coordination during overground walking in patients with TBI.     

Effects of heel height on knee rotation and gait

A triaxial electrogoniometer was used along with a Locam camera to measure knee rotation and gait characteristics of nineteen female college students while walking on a treadmill under three experimental conditions (barefoot, running shoes and high heels). Range of valgus-varus, flexion-extension and internal-external rotation during the swing and support phases, and maximum flexion during the swing walking step phase were studied. Significant differences (p < 0.01) were found among the three heel height treatments for range of knee flexion-extension during the swing walking phase and for internal-external rotation during the swing walking phase. Significant differences (p < 0.01) were also found between the high heeled swing phase mean value for internal-external rotation and the barefoot treatment mean values. ANOVA indicated a significant difference among the three experimental treatments for all distance and temporal variables studied.     

Three-dimensional joint kinematics of ACL-deficient and ACL-reconstructed knees during stair ascent and descent

Mechanical environmental changes in the knee are induced by altered joint kinematics under cyclic loading during activities of daily living after anterior cruciate ligament (ACL) injury. This is considered a risk factor in progressive cartilage degeneration and the early onset of osteoarthritis following ACL injury and even after reconstructive surgery. The purpose of this study was to examine 3D joint kinematics of ACL-deficient and ACL-reconstructed knees to health controls during stair ascent and descent. A 3D optical video motion capture system was used to record coordinate data from reflective markers positioned on subjects as they ascended and descended a custom-built staircase. Spatiotemporal gait and knee joint kinematic variables were calculated and further analyzed. The ACL-deficient knees exhibited a significant extension deficit compared to the ACL-intact controls. A more varus and internally rotated tibial position was also identified in the ACL-deficient knees during both stair ascent and descent. The ACL-reconstructed knees exhibited less abnormality in both spatiotemporal gait parameters and joint kinematics, but these variables were not fully restored to a normal level. The kinematic profiles of the ACL-reconstructed knees were more similar to those of the ACL-deficient knees when compared to the ACL-intact knees. This suggests that the ACL-reconstructed knees had been "under-corrected" rather than "over-corrected" by the reconstructive surgery procedure. Findings from this study may provide more insight with respect to improving ACL reconstruction surgical techniques, which may aid the early progression of cartilage degeneration in ACL-reconstructed knees.     

Kinematic gait parameters for older adults with Parkinson's disease during street crossing simulation

Safe street crossing is important for older adults' social inclusion. We assessed gait kinematic adaptation under different simulated street crossing conditions in older adults with Parkinson's disease (PD) and made comparisons with older adults without PD to understand how PD interferes in outdoor task performance, helping in the development of strategies to reduce road traffic accident risk. In 20 older adults without PD (control group – CG) and 20 with PD (GPD), we assessed usual gait (C1), gait during street crossing simulation (C2), and gait during reduced-time street crossing simulation (C3). Velocity, step length, and step, swing, stance, and double support time were analyzed. Spatiotemporal differences in gait between groups and conditions were analyzed. The GPD walked 16% slower in C1 and 12% slower in C2 and C3 than the CG. GPD also took 11% shorter steps in C1 and 9.5% shorter steps in C2. The double support time was 8.5% greater in C1. In intragroup comparisons, there were significant differences in all gait conditions. The CG showed increased velocity (C2 15% > C1; C3 13% > C2; C3 26% > C1), step length (C2 8% > C1; C3 5% > C2; C3 13% > C1), and swing time (C2 2% > C1; C3 3.7% > C2; C3 6% > C1), and decreased step time (C2 7.5% < C1; C3 8% < C2; C3 15% < C1), stance time (C2 1.3% < C1; C3 2.5% < C2; C3 3.6% < C1), and double support time (C2 6.3% < C1; C3 10.5% < C2; C3 16% < C1). GPD showed increased velocity (C2 19% > C1; C3 13.5% > C2; C3 29.7% > C1), step length, (C2 6% > C1; C3 7% > C2; C3 16% > C1), and swing time (C2 3% > C1; C3 3% > C2; C3 5.5% > C1) and decreased step time (C2 10.3% < C1; C3 7.7% < C2; C3 17% < C1), stance time (C2 1.7% < C1; C3 1.7% < C2; C3 3.4% < C1), and double support time (C2 7% < C1; C3 9.5% < C2; C3 16% < C1). Kinematic changes observed in the intergroup comparison show that participants with PD had lower velocity in all conditions. However, per the intragroup results, both participants with and without PD managed to significantly modify gait variables to attempt to cross the street in the given time. It is necessary to assess whether this increases fall risk by exposing them to road traffic accidents.     

Common and specific gait patterns in people with varying anatomical levels of lower limb amputation and different prosthetic components

The present study’s aim was to identify the kinematic and kinetic gait patterns and to measure the energy consumption in people with amputation according to both the anatomical level of amputation and the type of prosthetic components in comparison with a control group matched for the gait speed. Fifteen subjects with unilateral transtibial amputation (TTA), forty with unilateral transfemoral amputation (TFA) (9 with mechanical, 17 with CLeg and 14 with Genium prosthesis) and forty healthy subjects were recruited. We computed the time-distance gait parameters; the range of angular motion (RoM) at hip, knee and ankle joints, and at the trunk and pelvis; the values of the 2 peaks of vertical force curve; the full width at half maximum (FWHM) and center of activity (CoA) of vertical force; the mechanical behavior in terms of energy recovery (R-step) and energy consumption. The main results were: i) both TTA and TFA show a common gait pattern characterized by a symmetric increase of step length, step width, double support duration, pelvic obliquity, trunk lateral bending and trunk rotation RoMs compared to control groups. They show also an asymmetric increase of stance duration and of Peak1 in non-amputated side and a decrease of ankle RoM in amputated side; ii) only TFA show a specific gait pattern, depending on the level of amputation, characterized by a symmetric reduction of R-step and an asymmetric decrease of stance duration, CoA and FWHM and an increase of Peak1 in the amputated side and of hip and knee RoM, CoA and FWHM in the non-amputated side; iii) people with amputation with Genium prosthesis show a longer step length and increased hip and knee RoMs compared to people with amputation with mechanical prosthesis who conversely show an increased pelvic obliquity: these are specific gait patterns depending of the type of prosthesis. In conclusion, we identified both common and specific gait patterns in people with amputation, either regardless of, or according to their level of amputation and the type of prosthetic component.     

Spatial and temporal variability of movement parameters in individuals with Down syndrome

This investigation compared spatial and temporal gait movement parameters of a sample of individuals with Down syndrome (n=12) and one of individuals without disabilities (n=12). All participants were evaluated on responses to a preferred pace and fast walk with the GAITRite Electronic Walkway. Spatial outcomes included step and stride length, step and stride width, toe-in/toe-out, and base of support. Temporal outcomes included step time, velocity, single and double leg support time, stance, and swing time. There were significant group differences for step length, step width, stride length, and velocity in the preferred walk condition. Significant group differences for step length, step width, and stride length were observed in the fast walk condition. Percentage differences also indicated lower scores for all spatial and temporal variables in relation to the control group. The ability to control gait movements appears to reflect earlier movement experiences, so it may be possible to use variable sensory feedback and specific training to modify and adjust movement responses and improve gait performance in Down syndrome.     

An Energetic Comparison of Symmetrical and Asymmetrical Human Gait

This article contrasts the mechanical energy profiles of asymmetrical galloping with those of symmetrical running in adult humans. Seven female subjects were filmed while performing overground running and galloping at their preferred velocities. A previous study (Whitall & Caldwell, 1992) showed that kinematic differences between these gait modes included higher preferred velocity for running than galloping, with distinct differences in interlimb coordination but surprisingly similar intralimb patterns. Energetically, in the present study the whole body center of mass during galloping was found to behave much as it does in walking; kinetic and potential energy profiles were out of phase, as compared with running, which exhibited in-phase fluctuations of kinetic and potential energies. The primary reason for these center of mass differences was found in the energetics of the back leg of galloping, which demonstrated alterations in timing of its energy fluctuations and less energy generation than the front leg. Analysis of the power sources underlying the segmental energies during swing phase showed that the back leg's energy changes were accomplished mainly through reduced use of the hip muscles and less interlimb energy transfer. The back leg's energetics during swing also displayed a shift toward greater reliance on nonmuscular energy sources. A pattern of energy inflow during early swing and energy outflow during late swing was common to both running and galloping, although the galloping legs both demonstrated more abrupt transitions between these phases. The possibility is raised that the 67/33 interlimb phasing ratio used in galloping is selected to reduce mechanical energy variations of the total body center of mass. These data suggest that models of asymmetric gait in humans must account for more than merely phase alteration.