Explaining Machine Learning Models for Clinical Gait Analysis

Machine Learning (ML) is increasingly used to support decision-making in the healthcare sector. While ML approaches provide promising results with regard to their classification performance, most share a central limitation, their black-box character. This article investigates the usefulness of Explainable Artificial Intelligence (XAI) methods to increase transparency in automated clinical gait classification based on time series. For this purpose, predictions of state-of-the-art classification methods are explained with a XAI method called Layer-wise Relevance Propagation (LRP). Our main contribution is an approach that explains class-specific characteristics learned by ML models that are trained for gait classification. We investigate several gait classification tasks and employ different classification methods, i.e., Convolutional Neural Network, Support Vector Machine, and Multi-layer Perceptron. We propose to evaluate the obtained explanations with two complementary approaches: a statistical analysis of the underlying data using Statistical Parametric Mapping and a qualitative evaluation by two clinical experts. A gait dataset comprising ground reaction force measurements from 132 patients with different lower-body gait disorders and 62 healthy controls is utilized. Our experiments show that explanations obtained by LRP exhibit promising statistical properties concerning inter-class discriminativity and are also in line with clinically relevant biomechanical gait characteristics.

Indices of Loading and Propulsive Ability in the Gait of Patients With Chronic Stroke With Equinus Foot Deviation: A Correlation Study

In literature, indices of overall walking ability that are based on ground reaction forces have been proposed because of their ease of administration with patients. In this study, we analyzed the correlation between the indices of dynamic loading and propulsion ability of 40 chronic hemiparetic post-stroke patients with equinus foot deviation and a set of clinical assessments of ankle joint deviations and walking ability. Ankle passive and active range of motion (ROM) and triceps surae spasticity were considered, along with walking speed and three complementary scales of walking ability focusing respectively on the need for assistance on functional mobility, including balance and transfers, and the limitation in social participation. The correlation between the ground reaction force-based indices and both clinical and functional variables was carried out using the non-parametric Spearman correlation coefficient. Both indices were correlated to 8 of the 10 investigated variables, thus supporting their use. In particular, the dynamic propulsive ability was correlated with all functional scales (rho = 0.5, p < 0.01), and has the advantage of being a continuous variable. Among clinical assessments, limited ankle ROM affected walking ability the most, while spasticity did not. Since the acquisition of ground reaction forces does not require any patient prepping, the derived indices can be used during the rehabilitation period to quickly detect small improvements that, over time, might lead to the broad changes detectable by clinical scales, as well as to immediately highlight the lack of these improvements, thus suggesting adjustments to the ongoing rehabilitation approach.

Study on synergistic system of energy-absorbing yielding anti-impact supporting structure and surrounding rock

Through the improvement of supporting structure and the utilization of the interaction between surrounding rock and supporting structure, the synergistic system of energy-absorbing yielding anti-impact supporting structure and surrounding rock is established. The process of energy absorption device, energy-absorbing yielding anti-impact supporting structure and synergistic system under impact is simulated to analyze the properties of them. The following conclusions could be drawn. The deformation and yielding process under compression of energy absorption device is divided into five stages. Compared with the traditional supporting structure, the energy-absorbing yielding anti-impact supporting structure has the reaction force with lower value and smaller fluctuation range before the deformation of the energy absorption device reaches the third ascending section. The synergy between surrounding rock and supporting structure plays an important role in roadway support. Compared with the supporting structure without surrounding rock, the reaction force of the supporting structure in the synergistic system is lower, and a stationary stage is added in the early stage of the reaction force curve.

Short-term results of gait analysis with the Heidelberg foot measurement method and functional outcome after operative treatment of ankle fractures

Background Ankle fractures are common fractures in trauma surgery. Several studies have compared gait patterns between affected patients and control groups. However, no one used the Heidelberg Foot Measurement Method in combination with statistical parametric mapping of the entire gait cycle in this patient cohort. We sought to identify possible mobility deficits in the tibio-talar joint and medial arch in patients after ankle fractures as a sign of stiffness and pain that could result in a pathological gait pattern. We focused on the tibio-talar flexion as it is the main movement in the tibio-talar joint. Moreover, we examined the healing progress over time. Methods Fourteen patients with isolated ankle fractures were included prospectively. A gait analysis using the Heidelberg Foot Measurement Method was performed 9 and 26 weeks after surgery to analyse the tibio-talar dorsal flexion, the foot tibia dorsal flexion, the subtalar inversion and the medial arch as well as the cadence, the walking speed and the ground reaction force. The American Orthopedic Foot & Ankle Society ankle hindfoot score was used to obtain clinical data. Results were compared to those from 20 healthy participants. Furthermore, correlations between the American Orthopedic Foot & Ankle Society hindfoot score and the results of the gait analysis were evaluated. Results Statistical parametric mapping showed significant differences for the Foot Tibia Dorsal Flexion for patients after 9 weeks (53–75%: p = 0.001) and patients after 26 weeks (58–70%: p = 0.011) compared to healthy participants, respectively. Furthermore, significant differences regarding the tibio-talar dorsal flexion for patients 9 weeks after surgery (15–40%: p < 0.001; 56,5–70%: p = 0.007; 82–88%: p = 0.033; 97–98,5%: p = 0.048) as well as patients after 26 weeks (62,5–65%: p = 0.049) compared to healthy participants, respectively. There were no significant differences looking at the medial arch and the subtalar inversion. Moreover, significant differences regarding the ground reaction force were found for patients after 9 weeks (0–17%: p < 0.001; 21–37%: p < 0.001; 41–54%: p < 0.001; 60–64%: p = 0.013) as well as patients after 26 weeks (0–1,5%: p = 0.046; 5–15%: p < 0.001; 27–33%: p = 0.001; 45–49%: p = 0.005; 57–59%: p = 0.049) compared to healthy participants, respectively. In total, the range of motion in the tibio-talar joint and the medial arch was reduced in affected patients compared to healthy participants. Patients showed significant increase of the range of motion between 9 and 26 weeks. Conclusions This study shows, that patients affected by ankle fractures show limited mobility in the tibio-talar joint and the medial arch when compared to healthy participants. Even though the limitation of motion remains at least over a period of 26 weeks, a significant increase can be recognized over time. Furthermore, if we look at the absolute values, the patients’ values tend to get closer to those of the control group. Trial registration This study is registered at the German Clinical Trials Register (DRKS00023379).

Maxwell-Lorentz without self-interactions: Conservation of energy and momentum

Since a classical charged point particle radiates energy and momentum it is argued that there must be a radiation reaction force. Here we present an action for the Maxwell-Lorentz without self interactions model, where each particle only responds to the fields of the other charged particles. The corresponding stress-energy tensor automatically conserves energy and momentum in Minkowski and other appropriate spacetimes. Hence there is no need for any radiation reaction.

Effects of Hinged versus Floor-Reaction Ankle-Foot Orthoses on Standing Stability and Sit-to-Stand Performance in Children with Spastic Diplegic Cerebral Palsy

Hinged ankle-foot orthoses (HAFOs) and floor reaction ankle-foot orthoses (FRAFOs) are frequently prescribed to improve gait performance in children with spastic diplegic cerebral palsy (CP). No study has investigated the effects of FRAFO on sit-to-stand (STS) performance nor scrutinized differences between the application of HAFOs and FRAFOs on postural control. This study compared the effects of HAFOs and FRAFOs on standing stability and STS performance in children with spastic diplegic CP. Nine children with spastic diplegic CP participated in this crossover repeated-measures design research. Kinematic and kinetic data were collected during static standing and STS performance using 3-D motion analysis and force plates. Wilcoxon signed ranks test was used to compare the differences in standing stability and STS performance between wearing HAFOs and FRAFOs. The results showed that during static standing, all center of pressure (COP) parameters (maximal anteroposterior/mediolateral displacement, maximal velocity, and sway area) were not significantly different between FRAFOs and HAFOs. During STS, the floor reaction force in the vertical direction was significantly higher with FRAFOs than with HAFOs (p = 0.018). There were no significant differences in the range of motion in the trunk, knee, and ankle, the maximal velocity of COP forward displacement, completion time, and the force of hip, knee, and ankle joints between the two orthoses. The results suggest both FRAFOs and HAFOs have a similar effect on standing stability, while FRAFOs may benefit STS performance more compared to HAFOs.

Analytical model of bolt shear resistance considering progressive yield of surrounding material

Existing analytical models usually fail to match with the actual conditions due to ignoring the nonlinear behavior of the surrounding material reaction force, which changes progressively with the joint shear displacement from elastic stage to yield stage. To tackle this problem, this study proposes a new analytical model to describe the bolt deformation and bolt contribution from elastic stage to plastic stage. The developed model is verified by available experimental direct shear tests of bolted joints and compared with existing models. Then, based on this model, the effects of the joint dilation angle, the bolt installation angle, the friction angle, and the surrounding material strength on bolt contribution are also analyzed and its implication is further discussed. Our results show that the proposed model can precisely describe the evolution of bolt contribution from elastic stage to plastic stage. Compared with surrounding material strength, the augmentation of the joint dilation angle and friction angle is more beneficial to increase the bolt contribution and the optimal installation angle. The work presented is to attempt to provide a reference for the understanding of bolting mechanism of jointed rock mass, the development of bolting theories and the practice of bolting engineering.

Accelerometer-based prediction of ground reaction force in head-out water exercise with different exercise intensity countermovement jump

Background Water jumping exercise is an alternative method to achieve maintenance of bone health and reduce exercise injuries. Clarifying the ground reaction force (GRF) of moderate and high cardiopulmonary exercise intensities for jumping movements can help quantify the impact force during different exercise intensities. Accelerometers have been explored for measuring skeletal mechanical loading by estimating the GRFs. Predictive regression equations for GRF using ACC on land have already been developed and performed outside laboratory settings, whereas a predictive regression equation for GRF in water exercises is not yet established. The purpose of this study was to determine the best accelerometer wear-position for three exercise intensities and develop and validate the ground reaction force (GRF) prediction equation. Methods Twelve healthy women (23.6 ± 1.83 years, 158.2 ± 5.33 cm, 53.1 ± 7.50 kg) were recruited as participants. Triaxial accelerometers were affixed 3 cm above the medial malleolus of the tibia, fifth lumbar vertebra, and seventh cervical vertebra (C7). The countermovement jump (CMJ) cadence started at 80 beats/min and increased by 5 beats per 20 s to reach 50%, 65%, and 80% heart rate reserves, and then participants jumped five more times. One-way repeated analysis of variance was used to determine acceleration differences among wear-positions and exercise intensities. Pearson’s correlation was used to determine the correlation between the acceleration and GRF per body weight on land (GRFVLBW). Backward regression analysis was used to generate GRFVLBW prediction equations from full models with C7 acceleration (C7 ACC), age, percentage of water deep divided by body height (PWDH), and bodyweight as predictors. Paired t-test was used to determine GRFVLBW differences between values from the prediction equation and force plate measurement during validation. Lin’s CCC and Bland–Altman plots were used to determine the agreement between the predicted and force plate-measured GRFVLBW. Results The raw full profile data for the resultant acceleration showed that the acceleration curve of C7 was similar to that of GRFv. The predicted formula was − 1.712 + 0.658 * C7ACC + 0.016 * PWDH + 0.008 * age + 0.003*weight. Lin’s CCC score was 0.7453, with bias of 0.369%. Conclusion The resultant acceleration measured at C7 was identified as the valid estimated GRFVLBW during CMJ in water.

Sensor-based skeleton modeling and MVEEs approach of the redundant manipulator for reaction motion

With the wide application of redundant manipulators, sharing a working space with humans and dealing with uncertainty seems an inevitable problem, especially in the dynamic and unstructured domain. How to deal with obstacle avoidance is of particular importance that robots and humans/environments are safe interactions to fulfill the complex cooperating tasks. This paper aimed at solving the problem of multiple points avoidance for the reaction motion based on the skeleton algorithm in unstructured and dynamic environments. A method named “sensor-based skeleton modeling and MVEEs approach of the redundant manipulator for the reaction motion” is proposed. The extraction of skeleton information from image is obtained to calculate the distances of the multiple control points and establish the repulsion in this method. Afterward, the force Jacobian related to the priority weighting factors is calculated and then a reaction force with damping term is established, which is corresponding nominal torque commands. For the redundant manipulator, the joint angles are obtained through torque iteration instead of inverse kinematics to reduce calculation cost. Finally, the method was tested by a 7-DOF manipulator in the ROS framework. The obtained results indicate that the method in this method can realize dynamic obstacle avoidance and time cost reduction.

Prediction and investigation between impeller blade shape parameters and performance parameters in CFD and ANN

The blade shape parameters have a remarkable effect on the centrifugal pump performance. In order to reveal the relationship between these parameters and pump performance, a single channel was regarded as the research object to calculate its performance by numerical simulation, and the performance was measured on an experimental rig. The optimized ANN is proposed, and it is proved to be highly accurate. The ANN correlation coefficient of the total response could be above 0.997 after thousands of retaining. The sorts and degrees affecting performance parameters were found out by gray relation analysis. It was found that the blade angles at the leading edge were more influential for reaction force, head and minimum pressure, while the wrap angles had greater impact for efficiency. Furthermore, a multiple linear regression model was established to quantify the weight and trend of the influence of blade shape parameters on performance. The results provide a reference guide for the optimized design of centrifugal impeller to improve pump performance.