Changes to gait speed and the walk ratio with rhythmic auditory cuing

Brief High-Velocity Motor Skill Training Increases Step Frequency and Improves Length/Frequency Coordination in Slow Walkers With Chronic Motor-Incomplete Spinal Cord Injury

OBJECTIVE

To quantify spatiotemporal coordination during overground walking among persons with motor-incomplete spinal cord injury (PwMISCI) by calculating the step length (SL)/step frequency (SF) ratio (ie, the Walk Ratio [WR]) and to examine the effects of motor skill training (MST) on the relationship between changes in these parameters and walking speed (WS).

DESIGN

Between-day exploratory analysis.

SETTING

Research laboratory in a rehabilitation hospital PARTICIPANTS: PwMISCI (N=26).

INTERVENTIONS

3-day high-velocity MST.

MAIN OUTCOME MEASURES

Overground WS, SL, SF, and WR measured during the 10-Meter Walk Test.

RESULTS

Among the full sample, MST was associated with increases in WS, SL, SF, and a decrease in the WR. Relative change in WS and SF was higher among slow (ΔWS=↑46%, ΔSF=↑28%) vs fast (ΔWS=↑16%, ΔSF=↑8%) walkers. Change in the WR differed between groups (slow: ΔWR=↓10%; fast: ΔWR=0%). Twenty-six percent of the variability observed in ΔWR among slow walkers could be explained by ΔSF, while ΔSL did not contribute to ΔWR. Among fast walkers, ΔSL accounted for more than twice the observed ΔWR (43%) compared to ΔSF (15%).

CONCLUSIONS

On the whole, WR values among PwMISCI are higher than previous reports in other neurologic populations; however, values among fast walkers were comparable to noninjured adults. Slow walkers demonstrated greater variability in the WR, with higher values associated with slower WS. Following MST, increases in WS coincided with a decrease in the WR among slow walkers, mediated primarily through an effect on SF. This finding may point to a specific mechanism by which MST facilitates improvements in WS among PwMISCI with greater mobility deficits.

On the relation between gait speed and gait cycle duration for walking on even ground

Gait models and reference motions are essential for the objective assessment of walking patterns and therapy progress, as well as research in the field of wearable robotics and rehabilitation devices in general. A human can achieve a desired gait speed by adjusting stride length and/or stride frequency. It is hypothesized that sex, age, and physique of a person have a significant influence on the combination of these parameters. A mathematical description of the relation between gait speed and its determinants is presented in the form of a parameterized analytic function. Based on the statistical significance of the parameters, three models are derived. The first two models are valid for slow to fast walking, which is defined as the interval of approximately 0.6-2.0ms-1, assuming a linear relation of gait speed and stride length, and a non-linear relation of gait speed and stride duration, respectively. The third model is valid for a defined range of walking speed centered at a certain (preferred or spontaneous) gait speed. The latter assumes a constant walk ratio, i.e. the ratio between step or stride length and step or stride frequency, and is recommended for walking at a speed of 1.0-1.6ms-1. On the basis of a large pool of gait datasets, regression coefficients with significance for age and/or body mass index are identified. The presented models allow to estimate the gait cycle duration based on gait speed, sex, age and body mass index of healthy persons walking on even ground.

Cadence-based classification of moderate-intensity overground walking in 41- to 85-year-old adults

BACKGROUND

Walking cadence (steps/min) has emerged as a valid proxy of physical activity intensity, with consensus across numerous laboratory-based treadmill studies that ≥100 steps/min approximates absolutely defined moderate intensity (≥3 metabolic equivalents; METs). We recently reported that this cadence threshold had a classification accuracy of 73.3% for identifying moderate intensity during preferred pace overground walking in young adults. The purpose of this study was to evaluate and compare the performance of a cadence threshold of ≥100 steps/min for correctly classifying moderate intensity during overground walking in middle- and older-aged adults.

METHODS

Participants (N = 174, 48.3% female, 41-85 years of age) completed laboratory-based cross-sectional study involving an indoor 5-min overground walking trial at their preferred pace. Steps were manually counted and converted to cadence (total steps/5 min). Intensity was measured using indirect calorimetry and expressed as METs. Classification accuracy (sensitivity, specificity, accuracy) of a cadence threshold of ≥100 steps/min to identify individuals walking at ≥3 METs was calculated.

RESULTS

The ≥100 steps/min threshold demonstrated accuracy of 74.7% for classifying moderate intensity. When comparing middle- vs. older-aged adults, similar accuracy (73.4% vs. 75.8%, respectively) and specificity (33.3% vs. 34.5%) were observed. Sensitivity was high, but was lower for middle- vs. older-aged adults (85.2% vs. 93.9%, respectively).

CONCLUSION

A cadence threshold of ≥100 steps/min accurately identified moderate-intensity overground walking. Furthermore, accuracy was similar when comparing middle- and older-aged adults. These findings extend our previous analysis in younger adults and confirm the appropriateness of applying this cadence threshold across the adult lifespan.

Effects of rhythmic auditory cueing on gait variability and voluntary control of walking -a cross-sectional study

Temporal gait variability is strongly associated with motor function and falls in the context of numerous diseases. Rhythmic auditory cueing (RAC) can influence stride-to-stride time, although its effects on temporal gait variability remain unclear. Therefore, the aim of the present cross-disease study was to examine the effects of RAC on stride time variability (STV), as well as the factors affecting changes in STV during walking with RAC. Participants with post-stroke (n = 12) and orthopedic disease (n = 23) performed a random block design under four conditions: comfortable walking speed (CWS) and walking with RAC (RAC 0%, RAC +10%, RAC -10%). STV was measured along with co-contraction and inter-muscular coherence of the shank muscles during walking for each condition. The contributions of the muscle activity pattern and voluntary control to the change in STV between the CWS and RAC 0% conditions were examined using hierarchical multiple regression analysis. STV was significantly lower in the RAC 0% condition than in the CWS condition (p = 0.03). Hierarchical multiple regression analysis revealed that the change in STV was explained by STV in the CWS condition (β = -0.36) and by changes in co-contraction (β = 0.43) and inter-muscular coherence (β = 0.38) during the stance phase between the CWS and RAC 0% conditions (R² = 0.56, p < 0.001). These findings indicate that walking training with RAC is effective in reducing gait variability and immediately improves muscle activity patterns and excessive corticospinal activity.

Classification of moderate-intensity overground walking speed in 21- to 85-year-old adults

The Compendium of Physical Activities reports that walking at 2.5 mph associates with absolutely-defined moderate intensity (i.e., ≥3 metabolic equivalents [METs]). However, it is unclear whether this speed threshold is accurate during overground walking and/or across the adult age-span. This study aimed to identify optimal and heuristic speed thresholds associated with 3 METs during overground walking across age groups. Healthy adults (n = 248, 21-85 years old, 49% women) performed a 5-minute self-paced overground walking trial. Speed was measured using an electronic gait mat, and oxygen uptake was measured using indirect calorimetry and converted to METs. Optimal and heuristic thresholds and classification accuracy metrics were determined and compared using ROC curve analyses. Speed thresholds (95% CIs) associated with 3 METs for the whole sample, young (21-40 years), middle-aged (41-60 years) and older-aged (61-85 years) groups were 1.29 (1.25, 1.33), 1.30 (1,26, 1,35), and 1.25 (1.21, 1.29) m/s, respectively. Overall, 3 mph and 5 km/h performed better than 2.5 mph and 4.5 km/h in balancing both sensitivity and specificity (higher Youden's Indices). Overground walking speeds associated with 3 METs were similar across age groups. A heuristic threshold of 3 mph or 5 km/h may better identify absolutely-defined moderate intensity overground walking.

Synchronization performance affects gait variability measures during cued walking

BACKGROUND

Incorporating variability within gait rehabilitation offers a promising approach to restore functional capacity. However, it's success requires adequate synchronization, a parameter that lacks report in most of the literature regarding cued gait training.

RESEARCH QUESTION

How changes to synchronization performance during fractal-like and isochronous cueing impacts gait variability measures?

METHODS

We asked twelve young male participants to walk in synchronization to two different temporally structure cueing (isochronous [ISO] and fractal [FRC]). We have also manipulated the cueing's tempo by increasing and decreasing it by 5% to manipulate synchronization, resulting in six conditions (stimuli [ISO,FRC] x tempo [SLOW, NORMAL, FAST]). The normal condition was set from an uncued trial through the participant's self-paced stride time. Synchronization performance (ASYNC) and gait variability (fractal scaling and coefficient of variation) were calculated from stride time data ( -ISIs,CV-ISIs). Repeated measures analysis of variance or Aligned Rank Transform were conducted to determine significant differences between metronome tempo and stimuli for the dependent variables RESULTS: Our results showed a FAST tempo decreases synchronization performance (ASYNC) and leads to lower -ISIs, for both ISO and FRC stimuli. This indicates that when an individual exhibits poor synchronization during cued gait training, his/her gait variability patterns will not follow the temporal structure of the presented metronome. Specifically, if the individual poorly synchronizes to the cues, the gait patterns become more random, a condition typically observed in older adults and neurological patients, which runs contrary to the hypothesis when using fractal-like metronomes.

SIGNIFICANCE

This study provides supporting evidence that measuring synchronization performance in cued training is fundamental for a proper clinical interpretation of its effects. This is particularly relevant for the recent and ongoing clinical research using fractal-like metronomes since the expected gait patterns are dependent on the synchronization performance. Randomized control trials must incorporate synchronization performance related measures.

Association between temporal asymmetry and muscle synergy during walking with rhythmic auditory cueing in stroke survivors living with impairments

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We examined the effect of temporal gait asymmetry on muscle synergy post stroke.

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In our design, the temporal asymmetry during gait was experimentally modulated.

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The temporal asymmetry was modulated using rhythmic auditory cueing.

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Rhythmic auditory cueing with gait immediately improved temporal asymmetry and muscle synergy deficits.

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The temporal asymmetry affected muscle synergy more than kinematics.

Objective

To examine the relationship between temporal asymmetry and complexity of muscle synergy during walking using rhythmic auditory cueing (RAC) and the factors related to changes in muscle synergy during walking with RAC in survivors of stroke.

Design

Cross-sectional study.

Setting

Wards at 2 medical corporation hospitals.

Participants

Forty survivors of stroke (N=40; mean age, 70.4±10.3 years; time since stroke, 72.2±32.3 days) who could walk without physical assistance.

Interventions

Not applicable.

Main Outcome Measures

The participants were assessed in a random block design under 2 conditions: comfortable walking speed (CWS) and walking with RAC. Single-leg support time, kinematics, and electromyograms were measured. Factors related to the complexity of muscle synergy (variance accounted for by 1 synergy [VAF1]) between the walking conditions were examined using hierarchical multiple regression analysis.

Results

In the RAC condition, lower limb flexion and knee flexion angles, single-leg support time on the paretic side, and the symmetry index of single-leg support time were increased compared with those in the CWS condition. VAF1 was decreased in the RAC condition (73.9±0.15) compared with that in the CWS condition (76.9±0.13, P=.002). Hierarchical multiple regression analysis revealed that the change in VAF1 was explained by change in single-leg support time (R²=0.43, P=.002).

Conclusions

The RAC condition demonstrated a more complex representation of muscle synergy than the CWS condition; the change in single-leg support time on the paretic side related to the changes in muscle synergy more than changes in lower limb angle. These findings can help in the walking-training concept to improve muscle synergy deficits in survivors of stroke.

The effects of different frequencies of rhythmic acoustic stimulation on gait stability in healthy elderly individuals: a pilot study

The efficacy of rhythmic acoustic stimulation (RAS) to improve gait and balance in healthy elderly individuals is controversial. Our aim was to investigate, through 3D gait analysis, the effect of different types of RAS (fixed frequency and based on subject-specific cadence), using conventional gait parameters and the trunk displacement as readouts. Walking at a fixed frequency of 80 bpm, the subjects showed extended duration of gait cycle and increased gait variability while the same individuals, walking at a fixed frequency of 120 bpm, showed reduced trunk sway and gait cycle duration. With regard to the RAS at subject-specific frequencies, walking at 90% of the subject-specific average cadence did not significantly modify the gait parameters, except for the speed, which was reduced. In contrast, walking at 100% and 110% of the mean cadence caused increased stride length and a slight reduction of temporal parameters and trunk sway. In conclusion, this pilot study shows that using RAS at fixed frequencies might be an inappropriate strategy, as it is not adjusted to individual gait characteristics. On the other hand, RAS frequencies equal to or slightly higher than each subject's natural cadence seem to be beneficial for gait and stability.

Walking cadence (steps/min) and intensity in 61-85-year-old adults: the CADENCE-Adults study

BACKGROUND

Heuristic (i.e., evidence-based, rounded) cadences of ≥100 and ≥ 130 steps/min have consistently corresponded with absolutely-defined moderate (3 metabolic equivalents [METs]) and vigorous (6 METs) physical activity intensity, respectively, in adults 21-60 years of age. There is no consensus regarding similar thresholds in older adults.

PURPOSE

To provide heuristic cadence thresholds for 3, 4, 5, and 6 METs in 61-85-year-old adults.

METHODS

Ninety-eight community-dwelling ambulatory and ostensibly healthy older adults (age = 72.6 ± 6.9 years; 49% women) walked on a treadmill for a series of 5-min bouts (beginning at 0.5 mph with 0.5 mph increments) in this laboratory-based cross-sectional study until: 1) transitioning to running, 2) reaching ≥75% of their age-predicted maximum heart rate, or 3) reporting a Borg rating of perceived exertion > 13. Cadence was directly observed and hand-tallied. Intensity (oxygen uptake [VO2] mL/kg/min) was assessed with indirect calorimetry and converted to METs (1 MET = 3.5 mL/kg/min). Cadence thresholds were identified via segmented mixed effects model regression and using Receiver Operating Characteristic (ROC) curves. Final heuristic cadence thresholds represented an analytical compromise based on classification accuracy (sensitivity, specificity, positive and negative predictive value, and overall accuracy).

RESULTS

Cadences of 103.1 (95% Prediction Interval: 70.0-114.2), 116.4 (105.3-127.4), 129.6 (118.6-140.7), and 142.9 steps/min (131.8-148.4) were identified for 3, 4, 5, and 6 METs, respectively, based on the segmented regression. Comparable values based on ROC analysis were 100.3 (95% Confidence Intervals: 95.7-103.1), 111.5 (106.1-112.9), 116.0 (112.4-120.2), and 128.6 steps/min (128.3-136.4). Heuristic cadence thresholds of 100, 110, and 120 were associated with 3, 4, and 5 METs. Data to inform a threshold for ≥6 METs was limited, as only 6/98 (6.0%) participants achieved this intensity.

CONCLUSIONS

Consistent with previous data collected from 21-40 and 41-60-year-old adults, heuristic cadence thresholds of 100, 110, and 120 steps/min were associated with 3, 4, and 5 METs, respectively, in 61-85-year-old adults. Most older adults tested did not achieve the intensity of ≥6 METs; therefore, our data do not support establishing thresholds corresponding with this intensity level.

TRIAL REGISTRATION

Clinicaltrials.gov NCT02650258 . Registered 24 December 2015.

Locomotion Mode Recognition Algorithm Based on Gaussian Mixture Model Using IMU Sensors

The number of elderly people has increased as life expectancy increases. As muscle strength decreases with aging, it is easy to feel tired while walking, which is an activity of daily living (ADL), or suffer a fall accident. To compensate the walking problems, the terrain environment must be considered, and in this study, we developed the locomotion mode recognition (LMR) algorithm based on the gaussian mixture model (GMM) using inertial measurement unit (IMU) sensors to classify the five terrains (level walking, stair ascent/descent, ramp ascent/descent). In order to meet the walking conditions of the elderly people, the walking speed index from 20 to 89 years old was used, and the beats per minute (BPM) method was adopted considering the speed range for each age groups. The experiment was conducted with the assumption that the healthy people walked according to the BPM rhythm, and to apply the algorithm to the exoskeleton robot later, a full/individual dependent model was used by selecting a data collection method. Regarding the full dependent model as the representative model, the accuracy of classifying the stair terrains and level walking/ramp terrains is BPM 90: 98.74%, 95.78%, BPM 110: 99.33%, 95.75%, and BPM 130: 98.39%, 87.54%, respectively. The consumption times were 14.5, 21.1, and 14 ms according to BPM 90/110/130, respectively. LMR algorithm that satisfies the high classification accuracy according to walking speed has been developed. In the future, the LMR algorithm will be applied to the actual hip exoskeleton robot, and the gait phase estimation algorithm that estimates the user’s gait intention is to be combined. Additionally, when a user wearing a hip exoskeleton robot walks, we will check whether the combined algorithm properly supports the muscle strength.

Superposition principle applies to human walking with two simultaneous interventions

Gait rehabilitation therapies provide adjusted sensory inputs to modify and retrain walking patterns in an impaired gait. Asymmetric walking is a common gait abnormality, especially among stroke survivors. Physical therapy interventions using adaptation techniques (such as treadmill training, auditory stimulation, visual biofeedback, etc.) train gait toward symmetry. However, a single rehabilitation therapy comes up short of affecting all aspects of gait performance. Multiple-rehabilitation therapy applies simultaneous stimuli to affect a wider range of gait parameters and create flexible training regiments. Understanding gait responses to individual and jointly applied stimuli is important for developing improved and efficient therapies. In this study, 16 healthy subjects participated in a four-session experiment to study gait kinetics and spatiotemporal outcomes under training. Each session consisted of two stimuli, treadmill training and auditory stimulation, with symmetric or asymmetric ratios between legs. The study hypothesizes a linear model for gait response patterns. We found that the superposition principle largely applies to the gait response under two simultaneous stimuli. The linear models developed in this study fit the actual data from experiments with the r-squared values of 0.95 or more.

Development of a Cadence-based Metabolic Equation for Walking

PURPOSE

This study aimed to develop cadence-based metabolic equations (CME) for predicting the intensity of level walking and evaluate these CME against the widely adopted American College of Sports Medicine (ACSM) Metabolic Equation, which predicts walking intensity from speed and grade.

METHODS

Two hundred and thirty-five adults (21-84 yr of age) completed 5-min level treadmill walking bouts between 0.22 and 2.24 m·s, increasing by 0.22 m·s for each bout. Cadence (in steps per minute) was derived by dividing directly observed steps by bout duration. Intensity (oxygen uptake; in milliliters per kilogram per minute) was measured using indirect calorimetry. A simple CME was developed by fitting a least-squares regression to the cadence-intensity relationship, and a full CME was developed through best subsets regression with candidate predictors of age, sex, height, leg length, body mass, body mass index (BMI), and percent body fat. Predictive accuracy of each CME and the ACSM metabolic equation was evaluated at normal (0.89-1.56 m·s) and all (0.22-2.24 m·s) walking speeds through k-fold cross-validation and converted to METs (1 MET = 3.5 mL·kg·min).

RESULTS

On average, the simple CME predicted intensity within ~1.8 mL·kg·min (~0.5 METs) at normal walking speeds and with negligible (<0.01 METs) bias. Including age, leg length, and BMI in the full CME marginally improved predictive accuracy (≤0.36 mL·kg·min [≤0.1 METs]), but may account for larger (up to 2.5 mL·kg·min [0.72 MET]) deviations in the cadence-intensity relationships of outliers in age, stature, and/or BMI. Both CME demonstrated 23%-35% greater accuracy and 2.2-2.8 mL·kg·min (0.6-0.8 METs) lower bias than the ACSM metabolic equation's speed-based predictions.

CONCLUSIONS

Although the ACSM metabolic equation incorporates a grade component and is convenient for treadmill-based applications, the CME developed herein enables accurate quantification of walking intensity using a metric that is accessible during overground walking, as is common in free-living contexts.

Walking cadence (steps/min) and intensity in 41 to 60-year-old adults: the CADENCE-adults study

BACKGROUND

In younger adults (i.e., those < 40 years of age) a walking cadence of 100 steps/min is a consistently supported threshold indicative of absolutely-defined moderate intensity ambulation (i.e., ≥ 3 metabolic equivalents; METs). Less is known about the cadence-intensity relationship in adults of middle-age.

PURPOSE

To establish heuristic (i.e., evidence-based, practical, rounded) cadence thresholds for absolutely-defined moderate (3 METs) and vigorous (6 METs) intensity in adults 41 to 60 years of age.

METHODS

In this cross-sectional study, 80 healthy adults of middle-age (10 men and 10 women representing each 5-year age-group between 41 to 60 years; body mass index = 26.0 ± 4.0 kg/m2) walked on a treadmill for 5-min bouts beginning at 0.5 mph and increasing in 0.5 mph increments. Performance termination criteria included: 1) transitioning to running, 2) reaching 75% of age-predicted maximum heart rate, or 3) reporting a Borg rating of perceived exertion > 13. Cadence was directly observed (i.e., hand tallied). Intensity (i.e., oxygen uptake [VO2] mL/kg/min) was assessed with an indirect calorimeter and converted to METs (1 MET = 3.5 mL/kg/min). A combination of segmented regression and Receiver Operating Characteristic (ROC) modeling approaches was used to identify optimal cadence thresholds. Final heuristic thresholds were determined based on an evaluation of classification accuracy (sensitivity, specificity, positive and negative predictive value, overall accuracy).

RESULTS

The regression model identified 101.7 (95% Predictive Interval [PI]: 54.9-110.6) and 132.1 (95% PI: 122.0-142.2) steps/min as optimal cadence thresholds for 3 METs and 6 METs, respectively. Corresponding values based on ROC models were 98.5 (95% Confidence Intervals [CI]: 97.1-104.9) and 117.3 (95% CI: 113.1-126.1) steps/min. Considering both modeling approaches, the selected heuristic thresholds for moderate and vigorous intensity were 100 and 130 steps/min, respectively.

CONCLUSIONS

Consistent with our previous report in 21 to 40-year-old adults, cadence thresholds of 100 and 130 steps/min emerged as heuristic values associated with 3 and 6 METs, respectively, in 41 to 60-year-old adults. These values were selected based on their utility for public health messaging and on the trade-offs in classification accuracy parameters from both statistical methods. Findings will need to be confirmed in older adults and in free-living settings.

Immediate effect of individual bars of insoles and their combination on gait parameters in asymptomatic healthy adults

Objective: The way how individual bars of sensorimotor insoles influence the gait kinematics is not fully understood yet. Therefore, this study aimed to explore the effect of three sensorimotor orthotic conditions (the medial calcaneal and retrocapital lateral bars and their combination) on the gait parameters in healthy adults during the stance phase of gait cycle.Materials and methods: Twenty-six young adults performed 20 gait cycles in each condition using their self-selected cadence and provided standardised shoes with the base-sole and the three types of orthotics. A three-dimensional motion analysis system (8 cameras; 200 Hz) was used and a six-degrees of freedom model was applied. The cadence, the stride length, the first peaks of foot external rotation, eversion and dorsal flexion as well as the first peak of hip adduction were analysed.Results: Significant differences (p < 0.05) were found for all parameters between the orthotic conditions, except the cadence. Significant difference in the first peak of hip adduction (p = 0.008) was found between the dominant and non-dominant leg. There were no significant interactions between the factors of condition and leg dominance (p > 0.05).Conclusions: There seems to be overall tendencies in immediate changes in ankle joint kinematics caused by all three sensorimotor orthotic conditions and besides the mechanical principles, also 'proprioceptive mechanism' seems to play a role. However, maximum observed average angular change was 2° and some variability in reactions to each orthotic condition exists among the individuals. Therefore, clinical relevance of such changes remains unclear and careful analysis of expected outcomes should be the common part of every orthotic intervention.

Using Music-Based Cadence Entrainment to Manipulate Walking Intensity

BACKGROUND

While previous studies indicate an auditory metronome can entrain cadence (in steps per minute), music may also evoke prescribed cadences and metabolic intensities.

PURPOSE

To determine how modulating the tempo of a single commercial song influences adults' ability to entrain foot strikes while walking and how this entrainment affects metabolic intensity.

METHODS

Twenty healthy adults (10 men and 10 women; mean [SD]: age 23.7 [2.7] y, height 172.8 [9.0] cm, mass 71.5 [16.2] kg) walked overground on a large circular pathway for six 5-min conditions; 3 self-selected speeds (slow, normal, and fast); and 3 trials listening to a song with its tempo modulated to 80, 100, and 125 beats per minute. During music trials, participants were instructed to synchronize their step timing with the music tempo. Cadence was measured via direct observation, and metabolic intensity (metabolic equivalents) was assessed using indirect calorimetry.

RESULTS

Participants entrained their cadences to the music tempos (mean absolute percentage error = 5.3% [5.8%]). Entraining to a music tempo of 100 beats per minute yielded ≥3 metabolic equivalents in 90% of participants. Trials with music entrainment exhibited greater metabolic intensity compared with self-paced trials (repeated-measures analysis of variance, F1,19 = 8.05, P = .01).

CONCLUSION

This study demonstrates the potential for using music to evoke predictable metabolic intensities.