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Biomechanics
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Inertial Sensor Assessment of Human Movement
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Inertial Sensor Assessment of Human Movement

A special issue of Biomechanics (ISSN 2673-7078). This special issue belongs to the section "Gait and Posture Biomechanics".

Deadline for manuscript submissions: 25 May 2025 | Viewed by 7834

Special Issue Editors

Dr. Elissavet Rousanoglou

E-Mail Website
Guest Editor
Sports Biomechanics Lab, Department of Sports Medicine and Biology of Exercise, School of Physical Education and Sports Science, National and Kapodistrian University of Athens, 157 72 Athens, Greece
Interests: biomechanics; rhythmic movement; postural stability; muscle mechanics
Dr. John Buckley

E-Mail Website
Guest Editor
Department of Biomedical & Electronics Engineering, University of Bradford, Bradford BD7 1DP, UK
Interests: clinical biomechanics; locomotion; lower-limb prosthetics; movement control
Dr. Alan Godfrey

E-Mail Website
Guest Editor
Department Computer Science, Northumbria University, Newcastle-upon-Tyne NE1 8ST, UK
Interests: wearable systems; physiological monitoring; digital biomarkers; gait
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The development of low-cost, commercial MEMS inertial sensors has led to rapid growth in research on the application of these sensors for the assessment of daily human movement, sport and exercise.

The incorporation of inertial sensors in smartphones and, more recently, in smartwatches has not only driven research, but it has also broadened their application to detecting a wide range of human movements; for example, they are used in occupational, clinical and rehabilitation settings; movement variability; postural and motor control; and movement entrainment to rhythmic acoustic stimuli.

This Special Issue welcomes original research and review papers covering inertial sensing of the full span of human movement.

Dr. Elissavet Rousanoglou
Dr. John Buckley
Dr. Alan Godfrey
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Biomechanics is an international peer-reviewed open access quarterly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1000 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • inertial sensors
  • gyroscopes
  • accelerometers
  • physical activity
  • clinical applications
  • occupational applications
  • rehabilitation
  • sport applications
  • smartphone sensors
  • postural control
  • balance—postural stability
  • rhythmic movement

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Published Papers (5 papers)

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Research

10 pages, 3594 KiB  
Article
Effects of Gait Speed and Sole Adjustment on Shoe–Floor Angles: Measurement Using Shoe-Type Sensor
by Yu Hashiguchi, Tsuguru Numabe and Ryosuke Goto
Biomechanics 2024, 4(4), 595-604; https://doi.org/10.3390/biomechanics4040042 - 1 Oct 2024
Viewed by 310
Abstract
Background: Assessment of walking with shoes is important for understanding different types of walking in various environments. Methods: In this study, a shoe-type sensor was used to demonstrate the shoe–floor angle in fifteen participants who walked on a treadmill under varying gait speed [...] Read more.
Background: Assessment of walking with shoes is important for understanding different types of walking in various environments. Methods: In this study, a shoe-type sensor was used to demonstrate the shoe–floor angle in fifteen participants who walked on a treadmill under varying gait speed and sole adjustments, lifting one side of the sole. The shoe–floor angle in the sagittal; the angle of toe-up (θTup) and toe-down (θTdown) and frontal planes; and the angle of pronation (θPro) and supination (θSup) were calculated, and angles at the initial contact and maximum angles were extracted. Results: The results showed that most angles significantly increased with an increase in the gait speed (θTup and θTdown; p < 0.01 both, θPro and θSup; p < 0.02 and 0.04). Conversely, only the supination angle at the initial contact changed significantly, owing to the tilt of the sole (p < 0.01). Conclusion: Shoe movements were more strongly affected by gait speed than by sole adjustment. Full article
(This article belongs to the Special Issue Inertial Sensor Assessment of Human Movement)
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Figure 1

Figure 1
<p>(<b>a</b>) A sensor embedded in the shoe midsole; (<b>b</b>) shoes with the sensor.</p> Full article ">Figure 2
<p>Parameters of shoe–floor angle. These parameters demonstrate the angle between the ground and shoe in the sagittal (<b>a</b>) or frontal plane (<b>b</b>) that were calculated through the sensor’s anteroposterior or mediolateral axis and its projection vector to the horizontal plane. The angle of toe-up (<span class="html-italic">θ</span>Tup) and toe-down (<span class="html-italic">θ</span>Tdown) in the sagittal plane, and the angle of supination (<span class="html-italic">θ</span>Sup) and pronation (<span class="html-italic">θ</span>Pro) in the frontal plane were demonstrated.</p> Full article ">Figure 3
<p>Angle changes of each condition are shown. Each waveform was calculated by averaging the angle change over five gait cycles. Angle change among speed conditions in the sagittal plane (<b>a</b>) and frontal plane (<b>c</b>). Angle change among sole adjustment conditions in the sagittal plane (<b>b</b>) and frontal plane (<b>d</b>). <span class="html-italic">θ</span>Tup indicates the angle in the dorsiflexion direction, and <span class="html-italic">θ</span>Tdown indicates the angle in the plantarflexion direction with respect to the floor. (<b>a</b>,<b>b</b>) are shown with <span class="html-italic">θ</span>Tup as positive. <span class="html-italic">θ</span>Pro indicates the angle in the eversion direction, and <span class="html-italic">θ</span>Sup indicates the angle in the inversion direction with respect to the floor. (<b>c</b>,<b>d</b>) are shown with <span class="html-italic">θ</span>Pro as positive.</p> Full article ">Figure 4
<p>Change in shoe–floor angle with gait speed. *: <span class="html-italic">p</span> &lt; 0.05.</p> Full article ">Figure 5
<p>Change in shoe–floor angle with sole adjustment condition. *: <span class="html-italic">p</span> &lt; 0.05.</p> Full article ">
17 pages, 2796 KiB  
Article
Concurrent Validity of Depth-Sensor-Based Quantification of Compensatory Movements during the Swing Phase of Gait in Healthy Individuals
by Kento Kusuda, Shigehito Matsubara, Daisuke Noguchi, Moe Kuwahara, Hiroomi Hamasaki, Toshihiro Miwa, Toru Maeda, Toshihito Nakanishi, Shogo Ninomiya and Keita Honda
Biomechanics 2024, 4(3), 411-427; https://doi.org/10.3390/biomechanics4030028 - 8 Jul 2024
Viewed by 854
Abstract
The advancement in depth-sensor technology increased the potential for the clinical use of markerless three-dimensional motion analysis (3DMA); however, the accurate quantification of depth-sensor-based 3DMA on gait characteristics deviating from normal patterns is unclear. This study investigated the concurrent validity of the measurements [...] Read more.
The advancement in depth-sensor technology increased the potential for the clinical use of markerless three-dimensional motion analysis (3DMA); however, the accurate quantification of depth-sensor-based 3DMA on gait characteristics deviating from normal patterns is unclear. This study investigated the concurrent validity of the measurements of compensatory movements measured by depth-sensor-based 3DMA compared to those measured by marker-based 3DMA. We induced swing-phase compensatory movements due to insufficient toe clearance by restricting unilateral ankle and knee joint movements in healthy individuals. Thirty-two healthy young adults (nineteen males, aged 20.4 ± 2.0 years, height 164.4 ± 9.8 cm, weight 60.0 ± 9.3 kg [average ± standard deviation]) walked the 6 m walkway in slow speed, very slow speed, and knee–ankle–foot orthosis (KAFO; participants wore KAFOs on the right leg) conditions. Gait kinematics were measured with marker-based and depth-sensor-based 3DMA systems. The intraclass correlation coefficient (ICC3,1) was used to measure the relative agreement between depth-sensor-based and marker-based 3DMA and demonstrated good or moderate validity for swing-phase compensatory movement measurement. Additionally, the ICC2,1 measured absolute agreement between the systems and showed lower validity than the ICC3,1. The measurement errors for contralateral vaulting, trunk lateral flexion, hip hiking, swing-side hip abduction, and circumduction between instruments were 0.01 m, 1.30°, 1.99°, 2.37°, and 1.53°, respectively. Depth-sensor-based 3DMA is useful for determining swing-phase compensatory movements, although the possibility of missing a slight measurement error of 1–2° must be considered. Full article
(This article belongs to the Special Issue Inertial Sensor Assessment of Human Movement)
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Figure 1

Figure 1
<p>Overview of the experimental setup.</p> Full article ">Figure 2
<p>Body landmarks derived from the skeletal recognition technology of Azure Kinect.</p> Full article ">Figure 3
<p>Marker locations for marker-based 3D motion analysis.</p> Full article ">Figure 4
<p>Definition of abnormal gait patterns: contralateral vaulting (<b>a</b>), trunk lateral flexion to the stance side (<b>b</b>), hip hiking (<b>c</b>), swing-side hip abduction (<b>d</b>), and circumduction (<b>e</b>).</p> Full article ">Figure 5
<p>Average (thick line) and 1 SD (fine line) of hip and knee extension and ankle plantar flexion angles during gait cycle for each condition as evaluated with marker-based (<b>a</b>) and depth-sensor-based 3DMA (<b>b</b>) systems.</p> Full article ">Figure 6
<p>Summary for the concurrent validity of abnormal gait patterns.</p> Full article ">
11 pages, 1646 KiB  
Article
Mimicking an Asymmetrically Walking Visual Cue Alters Gait Symmetry in Healthy Adults
by Krista G. Clark, Louisa D. Raisbeck, Scott E. Ross and Christopher K. Rhea
Biomechanics 2024, 4(2), 346-356; https://doi.org/10.3390/biomechanics4020024 - 3 Jun 2024
Viewed by 795
Abstract
Gait asymmetries are a common problem in clinical populations, such as those with a history of stroke or Parkinson’s disease. The use of a split-belt treadmill is one way to enhance gait symmetry but relies on specialty (and typically expensive) equipment. Alternatively, visual [...] Read more.
Gait asymmetries are a common problem in clinical populations, such as those with a history of stroke or Parkinson’s disease. The use of a split-belt treadmill is one way to enhance gait symmetry but relies on specialty (and typically expensive) equipment. Alternatively, visual cues have been shown as a method to alter gait mechanics, but their utility in altering gait symmetry has been relatively understudied. Before deploying this method to clinical populations, a proof-of-concept study is needed to explore using visual cues to alter gait symmetry in healthy adults. Therefore, the purpose of this study was to examine the extent to which healthy adults could synchronize to an asymmetric visual cue with a small or large gait asymmetry using wearable sensors to measure gait asymmetries. Seventy-two healthy adults (ages: 23.89 ± 6.08 years) walked on the treadmill for two conditions: with and without the visual cue. Each walking condition lasted 10 min at the participant’s preferred walking speed. Inertial sensors were used to measure gait asymmetries. Some participants did not respond to the visual cue, and groups were separated into responders and non-responders. Participants in the small and large asymmetry-responder groups exhibited statistically significant increased asymmetries in single limb support % (p < 0.01) and step duration (s) (p < 0.05, p < 0.01, respectively). Only the large asymmetry-responder group showed statistically significant (p < 0.01) increased asymmetries in stride length. Overall, asymmetrical walking visual cues can alter gait asymmetries, and inertial sensors were sensitive enough to detect small changes in gait asymmetries. Full article
(This article belongs to the Special Issue Inertial Sensor Assessment of Human Movement)
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Figure 1

Figure 1
<p>Freeze frame of the asymmetrically walking visual cue that shows the pelvis, legs, and feet that presented the motion of asymmetrical walking on a screen in front of the treadmill. Please see the <a href="#app1-biomechanics-04-00024" class="html-app">Supplmentary Materials</a> section for videos of the cues in motion.</p> Full article ">Figure 2
<p>Comparison of baseline to adaptation in the small and large responder groups—means (SE). Note: SLS % = Single limb support %; * indicates <span class="html-italic">p</span> &lt; 0.05; ** indicates <span class="html-italic">p</span> &lt; 0.01.</p> Full article ">Figure 3
<p>Comparison of baseline to adaptation in the small and large asymmetry non-responder groups—means (SE). Note: SLS % = Single limb support %.</p> Full article ">Figure 4
<p>Comparison of small and large asymmetry-responder groups during the adaptation condition. Note: SLS % = Single limb support %.</p> Full article ">Figure 5
<p>Comparison of asymmetries from baseline to adaptation in the control group. Note: SLS % = Single limb support %.</p> Full article ">
21 pages, 3491 KiB  
Article
Inertial Sensing of the Abdominal Wall Kinematics during Diaphragmatic Breathing in Head Standing
by Elissavet Rousanoglou, Apostolina Foskolou, Analina Emmanouil and Konstantinos Boudolos
Biomechanics 2024, 4(1), 63-83; https://doi.org/10.3390/biomechanics4010005 - 2 Feb 2024
Cited by 1 | Viewed by 914
Abstract
Head standing (HS) in concurrence with diaphragmatic breathing is an atypical deviation from daily activity, yet commonly practiced. The study aimed at the inertially sensed effect of diaphragmatic versus normal breathing on the abdomen wall kinematics during HS. Twenty-eight men and women maintained [...] Read more.
Head standing (HS) in concurrence with diaphragmatic breathing is an atypical deviation from daily activity, yet commonly practiced. The study aimed at the inertially sensed effect of diaphragmatic versus normal breathing on the abdomen wall kinematics during HS. Twenty-eight men and women maintained HS and erect standing (ES) under normal and diaphragmatic breathing. An inertial sensor (LORD MicroStrain®, 3DM-GX3®-45, 2 cm above the umbilicus, 100 Hz, MicroStrain, Williston, VT, USA) recorded the 3D abdomen wall angular displacement (AD) (bandpass filter (0.1–0.5 Hz)). ANOVAs (p ≤ 0.05, SPSS 28.0) were applied to the extracted variables (AD path: magnitude, individual variability-%CVind, and diaphragmatic to normal ratio). Reliability measures (ICC and %SEM) and the minimal detectable change (%MDC90) were estimated. Diaphragmatic breathing increased the AD path (p ≤ 0.05) with the diaphragmatic to normal ratio being lower in HS (p ≤ 0.05). The similar AD time series (cross-correlations at p ≤ 0.05) and the ICCs (>0.80) indicated excellent reliability with the similar across conditions %CVind (p ≤ 0.05), further enhancing reliability. The %MDC90 was consistently higher than the %SEM upper boundary, indicating the differences as “real” ones. The results contribute to the limited data concerning a widely practiced atypical deviation from daily activity, as HS in concurrence with diaphragmatic breathing. Full article
(This article belongs to the Special Issue Inertial Sensor Assessment of Human Movement)
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Figure 1

Figure 1
<p>Men and women participants in the head-standing body stance. (<b>A</b>,<b>B</b>) during normal breathing and (<b>C</b>,<b>D</b>) during diaphragmatic breathing where the abdomen wall expansion is visible. The anatomical calibration of the sensor is described in the second paragraph of the data collection section.</p> Full article ">Figure 2
<p>Sample pre- and post-filtering time series signals (raw and filtered, respectively), as well as after the offset removal, for the 3D angular displacement (roll, pitch, and yaw: forward, outward, and downward abdominal expansion, respectively) in erect standing during normal (<b>top</b>) and diaphragmatic (<b>bottom</b>) breathing.</p> Full article ">Figure 3
<p>Sample pre- and post-filtering time series signals (raw and filtered, respectively), as well as after the offset removal, for the 3D angular displacement (roll, pitch, and yaw: forward, outward, and downward abdominal expansion, respectively) in head standing during normal (<b>top</b>) and diaphragmatic (<b>bottom</b>) breathing.</p> Full article ">Figure 4
<p>Mean (SD) of the angular displacement (AD) path length of the roll, pitch, and yaw Euler angles as well as their resultant for each condition of body stance and breathing type. The anatomical expansion of the abdomen wall during diaphragmatic inspiration is noted. The body stance effect and breathing type effect were both significant (<span class="html-italic">p</span> ≤ 0.01 for all), with no significant interaction between them (<span class="html-italic">p</span> &gt; 0.05). EN: Erect standing–Normal breathing, ED: Erect standing–Diaphragmatic breathing, HN: Head standing–Normal breathing, and HD: Head standing–Diaphragmatic breathing.</p> Full article ">Figure 5
<p>Mean (SD) of the individual coefficient of variation (%CVind) (bottom) of the roll, pitch, and yaw Euler angles, as well as their resultant, for each condition of body stance and breathing type. The anatomical expansion of the abdomen wall during diaphragmatic inspiration is noted. Neither the main effects of body stance and breathing type nor their interaction were significant (<span class="html-italic">p</span> &gt; 0.05). EN: Erect standing–Normal breathing, ED: Erect standing–Diaphragmatic breathing, HN: Head standing–Normal breathing, and HD: Head standing–Diaphragmatic breathing.</p> Full article ">Figure 6
<p>Diaphragmatic to normal breathing ratio of the angular displacement (AD) path length in erect standing (E-D/N: black bars) and head standing (H-D/N: grey bars). The anatomical expansion of the abdomen wall during diaphragmatic inspiration is noted. The ratio indicates the times that the AD path was increased in diaphragmatic compared to normal breathing. * significant difference between E-D/N and H-D/N at <span class="html-italic">p</span> ≤ 0.05.</p> Full article ">Figure 7
<p>Boxplots of the mean coefficient of cross-correlation between pairs of trials in each condition. The box indicates the interquartile range of the values (IQR: 50% of the values lie within 0.6745 standard deviation). The horizontal line in the box indicates the median and the x symbol indicates the mean. The whiskers extend up from the top of the box to the largest data element that is less than or equal to 1.5 times the IQR and down from the bottom of the box to the smallest data element that is larger than 1.5 times the IQR. The filled circles indicate values, with those outside the whiskers considered as outliers. The anatomical expansion of the abdomen wall during diaphragmatic inspiration is noted. EN: Erect standing–Normal breathing, ED: Erect standing–Diaphragmatic breathing, HN: Head standing–Normal breathing, and HD: Head standing–Diaphragmatic breathing. Overall, with a very small number of exceptions, the cross-correlations were significant (<span class="html-italic">p</span> ≤ 0.05).</p> Full article ">Figure 8
<p><b>Right</b>: Relative reliability of the AD path length (black squares indicate ICC with the vertical lines denoting the upper and lower bounds of its 95% confidence interval). <b>Left</b>: Absolute reliability of the AD path length (black circles indicate %SEM with the vertical lines denoting the upper and lower bounds of its 95% confidence interval) with the relative minimal detectable change (%MDC90) indicated by the × index. Results are presented for the roll, pitch, and yaw Euler angles as well as their resultants in EN: Erect standing–Normal breathing, ED: Erect standing–Diaphragmatic breathing, HN: Head standing–Normal breathing, and HD: Head standing–Diaphragmatic breathing.</p> Full article ">
13 pages, 2204 KiB  
Article
An Automated Approach to Instrumenting the Up-on-the-Toes Test(s)
by Sarah Aruje Zahid, Yunus Celik, Alan Godfrey and John G. Buckley
Biomechanics 2023, 3(3), 278-290; https://doi.org/10.3390/biomechanics3030024 - 26 Jun 2023
Viewed by 1415
Abstract
Normal ankle function provides a key contribution to everyday activities, particularly step/stair ascent and descent, where many falls occur. The rising to up-on-the-toes (UTT) 30 second test (UTT-30) is used in the clinical assessment of ankle muscle strength/function and endurance and is typically [...] Read more.
Normal ankle function provides a key contribution to everyday activities, particularly step/stair ascent and descent, where many falls occur. The rising to up-on-the-toes (UTT) 30 second test (UTT-30) is used in the clinical assessment of ankle muscle strength/function and endurance and is typically assessed by an observer counting the UTT movement completed. The aims of this study are: (i) to determine whether inertial measurement units (IMUs) provide valid assessment of the UTT-30 by comparing IMU-derived metrics with those from a force-platform (FP), and (ii) to describe how IMUs can be used to provide valid assessment of the movement dynamics/stability when performing a single UTT movement that is held for 5 s (UTT-stand). Twenty adults (26.2 ± 7.7 years) performed a UTT-30 and a UTT-stand on a force-platform with IMUs attached to each foot and the lumbar spine. We evaluate the agreement/association between IMU measures and measures determined from the FP. For UTT-30, IMU analysis of peaks in plantarflexion velocity and in FP’s centre of pressure (CoP) velocity was used to identify each repeated UTT movement and provided an objective means to discount any UTT movements that were not completed ‘fully’. UTT movements that were deemed to have not been completed ‘fully’ were those that yielded peak plantarflexion and CoP velocity values during the period of rising to up-on-the-toes that were below 1 SD of each participant’s mean peak rising velocity across their repeated UTT. The number of UTT movements detected by the IMU approach (23.5) agreed with the number determined by the FP (23.6), and each approach determined the same number of ‘fully’ completed movements (IMU, 19.9; FP, 19.7). For UTT-stand, IMU-derived movement dynamics/postural stability were moderately-to-strongly correlated with measures derived from the FP. Our findings highlight that the use of IMUs can provide valid assessment of UTT test(s). Full article
(This article belongs to the Special Issue Inertial Sensor Assessment of Human Movement)
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Figure 1

Figure 1
<p>(<b>a</b>) Exemplar centre of pressure anteroposterior velocity (CoPyVel) trajectory showing identification of local maxima (circled in red) for each repeated up-on-the-toes (UTT) movement during the UTT-30 s test with peaks falling below 1 SD of the mean (circled in blue). (<b>b</b>) Exemplar CoPyVel trajectory from UTT-stand test, (i) indicates the local maximum in CoPyVel when rising UTT, (j) indicates the beginning of ‘holding’ the UTT position, and (k) indicates the end of ‘holding’ the UTT position. NB, the local minimum in CoPyVel prior to the local maximum indicates the anticipatory postural adjustment (APA) made when initiating the UTT movement.</p> Full article ">Figure 2
<p>Automatic segmentation of up-on-the-toes 30 s test (UTT-30, blue arrows) and UTT-stand test (UTT-stand, red arrows) from right foot (RF) and left foot (LF) inertial measurement units (IMUs). (<b>a</b>) Flow chart of the segmentation algorithm; (<b>b</b>) raw angular velocity signal with specified peaks and tests; (<b>c</b>) processed angular velocity signal; (<b>d</b>) signal after mathematical operations; (<b>e</b>) extracted UTT-30; and (<b>f</b>) extracted UTT-stand.</p> Full article ">Figure 3
<p>Example of raw (example level) inertial measurement unit (IMU, angular velocity, blue line) and force-platform (FP) centre of pressure (CoP, orange line) velocity (m/s) signals from an up-on-the-toes 30 s test (UTT-30).</p> Full article ">Figure 4
<p>(<b>a</b>) The number of up-on-the-toes (UTT) movements each participant completed fully during the UTT-30 test determined using inertial measurement units (IMUs) plotted against a number determined using forceplatform (FP). (<b>b</b>) Each participant’s mean peak plantarflexion angular velocity (from IMU) plotted against their mean peak centre of pressure anteroposterior (CoPy) velocity values (from FP) for the UTT-30 test. ‘r’ is Pearson correlation coefficient. Dotted line in each plot indicates the linear regression line.</p> Full article ">Figure 5
<p>Outcomes for the up-on-the-toes (UTT) stand test: inertial measurement unit (IMU)-derived measures plotted against forceplatform (FP)-derived measures for the period when moving onto the toes. (<b>a</b>) Peak plantarflexion angular velocity (from IMU) plotted against peak centre of pressure anteroposterior (CoPy) velocity (from FP); (<b>b</b>) peak 5th lumbar vertebrae (L5) upward acceleration (from IMU) plotted against peak CoPy acceleration (from FP); (<b>c</b>) peak plantarflexion angular velocity (from IMU) plotted against the vertical ground reaction force (Fz) impulse (from FP) and the period when holding the UTT position; and (<b>d</b>) standard deviation (SD) in L5 acceleration (IMU) plotted against SD in CoPy velocity (FP). ‘r’ is Pearson correlation coefficient. Dotted line in each plot indicates the linear regression line.</p> Full article ">
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