Kinematic Symmetry Research Articles

Performance Evaluation of Jaipur Knee Joint through Kinematics and Kinetics Gait Symmetry with Unilateral Transfemoral Indian Amputees

Gait analysis is considered as the most systematic study of human motion. The analysis of gait includes visual and analytical perception of the individual, augmentation of various mechanical instrumentations for measuring movement of body, muscles activity and body mechanics. Past study focused on gait analysis of various animal locomotion and humans mainly on sports biomechanics. This paper aims to quantify the gait performance with Jaipur Knee, which is one of the most widely used prosthesis in Indian population. Gait data with Jaipur knee joint is not available till date. The proposed study targets to predict the performance of Jaipur knee joint in terms of gait symmetry with transfemoral Indian amputees. Gait symmetry may be the basis of recommendation of knee joint to prosthetic patients. This study used kinematics and kinetics parameters together to quantify the performance of Jaipur knee joint to evaluate gait symmetry. This research will be helpful for clinician to predict and further to prevent the degenerated musculoskeletal effects generally seen in unilateral transfemoral amputees.

Clustering of Self-Organizing Maps as a means to support gait kinematics analysis and symmetry evaluation

Gait analysis is relevant for the functional diagnostic of several musculoskeletal disorders. Walking patterns can be analyzed using techniques such as video processing and inertial measurement units (IMU). In this work, a Self-Organizing Maps (SOM) algorithm is applied to reduce the complexity of kinematic features obtained by IMU sensors of a sample of 40 individuals. Our system provides a simpler data representation (2-D graphic) than conventional methods, which often applies statistical analysis. We have tested the proposed method to analyze typical and simulated limping gait pattern under well-controlled conditions. Based on kinematic parameters and symmetry-related features, SOM algorithm was able to organize the sample in groups of subjects with three different gait patterns, normal and limping with each lower limb. Moreover, our system may be used to evaluate the recovery of a patient, offering intuitive information of his walking pattern in an assessment report. However, further research with atypical-gait subjects is necessary before applying such method as a clinical tool.

The comparison of transfemoral amputees using mechanical and microprocessor- controlled prosthetic knee under different walking speeds: A randomized cross-over trial.

The microprocessor-controlled prosthetic knees have been introduced to transfemoral amputees due to advances in biomedical engineering. A body of scientific literature has shown that the microprocessor-controlled prosthetic knees improve the gait and functional abilities of persons with transfemoral amputation. The aim of this study was to propose a new microprocessor-controlled prosthetic knee (MPK) and compare it with non-microprocessor-controlled prosthetic knees (NMPKs) under different walking speeds. The microprocessor-controlled prosthetic knee (i-KNEE) with hydraulic damper was developed. The comfortable self-selected walking speeds of 12 subjects with i-KNEE and NMPK were obtained. The maximum swing flexion knee angle and gait symmetry were compared in i-KNEE and NMPK condition. The comfortable self-selected walking speeds of some subjects were higher with i-KNEE while some were not. There was no significant difference in comfortable self-selected walking speed between the i-KNEE and the NMPK condition (P= 0.138). The peak prosthetic knee flexion during swing in the i-KNEE condition was between sixty and seventy degree under any walking speed. In the NMPK condition, the maximum swing flexion knee angle changed significantly. And it increased with walking speed. There is no significant difference in knee kinematic symmetry when the subjects wear the i-KNEE or NMPK. The results of this study indicated that the new microprocessor-controlled prosthetic knee was suitable for transfemoral amputees. The maximum swing flexion knee angle under different walking speeds showed different properties in the NMPK and i-KNEE condition. The i-KNEE was more adaptive to speed changes. There was little difference of comfortable self-selected walking speed between i-KNEE and NMPK condition.

Energy-Optimal Human Walking With Feedback-Controlled Robotic Prostheses: A Computational Study

Lower-limb amputees typically experience reduced mobility and higher metabolic rates than non-amputees. It may be possible to improve their mobility and metabolic rate with an optimized robotic prosthesis. Here, we use large-scale trajectory optimization on a simulated transtibial amputee with a robotic prosthesis to obtain metabolic energy-minimizing walking gaits with multiple prosthesis feedback controllers. Using such optimizations, we obtained trends in the energetics and kinematics for various prosthesis work levels. We find that the net metabolic rate has a non-monotonic relationship with the net prosthesis work rate: too much or too little prosthesis work results in higher metabolic rates. We predict that metabolic rate could be reduced below that of a non-amputee, although such gaits are highly asymmetric and not seen in experiments with amputees wearing robotic prostheses. We predict higher metabolic rates with SACH foot, a passive prosthesis. Walking gaits with left-right symmetry in kinematics or ground reaction forces have higher metabolic rates than asymmetric gaits, suggesting a potential reason for asymmetries in amputee walking. Our findings suggest that a computational framework such as the one presented here could augment the experimental approaches to prosthesis design iterations, although quantitatively accurate simulation-based prediction of experiments remains an open problem.

Load exposure of osseointegrated implants for transfemoral limb prosthesis during running.

Direct skeletal attachment of lower limb prostheses ensures direct load transfer between the prosthetic leg and the skeleton. Knowledge of the load characteristics at the boneimplant interface during high-loading activities is needed to understand the limitations of current implant systems, as well as to inform their future development. The present study estimates the load scenario at the bone-implant interface of a transfemoral amputee while running with kinematic symmetry between the prosthetic and the intact limbs corresponding to that of an ablebodied subject. Kinematic symmetry was used as this represents the ultimate aim of advanced bionic legs. Kinematic data and ground reaction forces from a running trial of an able-bodied subject were matched to a musculoskeletal model of a transfemoral amputee. The joint reaction forces at the boneimplant interface were calculated using inverse dynamics. The normalized peak forces and moments during a single gait cycle were calculated to 153 % BW (body weight) / -14.8 % BWm, 186 % BW / 16.2 % BWm and 56.8 % BW / -18.7 % BWm for the x- (anterior), y- (longitudinal), and z-axis (lateral-medial), respectively. These findings can potentially be used as design input for future implant systems and external safety devices.

1. Investigating the Link Between Kinematic, Kinetic and Muscular Symmetry in Young Adults 12 or More Months post-ACL Reconstruction

Anterior cruciate ligament (ACL) injury after primary reconstruction and return-to-sport clearance is common. Since research indicates asymmetry as a valid predictor of injury, it is proposed that inter-limb asymmetry following ACL reconstruction contributes to the elevated incidence of re-injury in this population. Current return-to-sport protocol include objective tests such as joint laxity and strength tests, as well as single leg hop and drop landing tests. Since these assessments are based on visual observation, or simple kinematics measurements, it is unclear how visual asymmetry reflects the underlying joint forces and muscular effort responsible for the performance in these tasks. This study aims to assess the asymmetry present at the kinematic, kinetic, and motor control levels to clarify the after-effects of ACL reconstruction. This pilot study will help us appreciate if additional work exploring screening measures as effective tools for predicting ACL injury following primary reconstruction is warranted. Standard techniques will be used to measure the kinematics, joint kinetics and muscle activation during this 25-repetition squat protocol. Correlations will compare the left and right lower limbs for joint angular displacement, joint angular velocity, joint power, vertical ground reaction forces, and muscle activation amplitude.

A Kinematic Symmetry Index of Gait Patterns Between Older Adults With and Without Low Back Pain.

Cross-sectional study. To investigate the symmetry index for limb support patterns in right limb-dominant older adults with and without low back pain (LBP). The effects of bilateral asymmetry on gait performance were reported; however, there is a lack of understanding on kinematic symmetry to assess subjects with LBP. This asymmetry might be related to increased compensatory patterns to the dominant side in subjects with LBP. Eighty-two right limb-dominant older adults (45 control subjects and 37 subjects with LBP) participated in the study. A three-dimensional motion capture system was used to measure temporal-spatial gait parameters (cadence, speed, stride length, step length, and limb support times). The symmetry index was the ratio of the gait cycle between the limbs to compare the dominance pattern between groups. Although the symmetry index was not different between groups, the initial limb support (t = 2.07, P = 0.04) and terminal limb support (t = -2.26, P = 0.02) times were significantly different. The LBP group demonstrated significantly greater nondominant initial support times and dominant terminal support times. The single-limb support was not different between groups (t = 1.72, P = 0.09). The limb support pattern demonstrated a significant interaction between groups (F = 4.72, P = 0.03) regardless of gait speed (F = 0.91, P = 0.34). An asymmetrical gait pattern was evident in the LBP group as they demonstrated a longer double-limb support pattern due to a possible pain avoidance strategy. The control group demonstrated a symmetrical pattern for limb support in the stance phase. Clinicians need to consider asymmetric limb support patterns of gait modification similar to the control group when developing rehabilitation strategies for patients with LBP. 3.

Curved momentum spaces from quantum groups with cosmological constant

We bring the concept that quantum symmetries describe theories with nontrivial momentum space properties one step further, looking at quantum symmetries of spacetime in presence of a nonvanishing cosmological constant Λ. In particular, the momentum space associated to the κ-deformation of the de Sitter algebra in (1+1) and (2+1) dimensions is explicitly constructed as a dual Poisson–Lie group manifold parametrized by Λ. Such momentum space includes both the momenta associated to spacetime translations and the ‘hyperbolic’ momenta associated to boost transformations, and has the geometry of (half of) a de Sitter manifold. Known results for the momentum space of the κ-Poincaré algebra are smoothly recovered in the limit Λ→0, where hyperbolic momenta decouple from translational momenta. The approach here presented is general and can be applied to other quantum deformations of kinematical symmetries, including (3+1)-dimensional ones.

Wigner functions for gauge equivalence classes of unitary irreducible representations of noncommutative quantum mechanics

While Wigner functions forming phase space representation of quantum states is a well-known fact, their construction for noncommutative quantum mechanics (NCQM) remains relatively lesser known, in particular with respect to gauge dependencies. This paper deals with the construction of Wigner functions of NCQM for a system of 2-degrees of freedom using 2-parameter families of gauge equivalence classes of unitary irreducible representations (UIRs) of the Lie group $\g$ which has been identified as the kinematical symmetry group of NCQM in an earlier paper. This general construction of Wigner functions for NCQM, in turn, yields the special cases of Landau and symmetric gauges of NCQM.

Noncommutative coherent states and related aspects of Berezin–Toeplitz quantization**Dedicated by the first and the third authors to the memory of the second author, with gratitude for his friendship and for all they learnt from him.

In this paper, we construct noncommutative coherent states using various families of unitary irreducible representations (UIRs) of , a connected, simply connected nilpotent Lie group, which was identified as the kinematical symmetry group of noncommutative quantum mechanics for a system of two degrees of freedom in an earlier paper. Similarly described are the degenerate noncommutative coherent states arising from the degenerate UIRs of . We then compute the reproducing kernels associated with both these families of coherent states and study the Berezin–Toeplitz quantization of the observables on the underlying 4-dimensional phase space, analyzing in particular the semi-classical asymptotics for both these cases.

Prosthetic model, but not stiffness or height, affects the metabolic cost of running for athletes with unilateral transtibial amputations.

Running-specific prostheses enable athletes with lower limb amputations to run by emulating the spring-like function of biological legs. Current prosthetic stiffness and height recommendations aim to mitigate kinematic asymmetries for athletes with unilateral transtibial amputations. However, it is unclear how different prosthetic configurations influence the biomechanics and metabolic cost of running. Consequently, we investigated how prosthetic model, stiffness, and height affect the biomechanics and metabolic cost of running. Ten athletes with unilateral transtibial amputations each performed 15 running trials at 2.5 or 3.0 m/s while we measured ground reaction forces and metabolic rates. Athletes ran using three different prosthetic models with five different stiffness category and height combinations per model. Use of an Ottobock 1E90 Sprinter prosthesis reduced metabolic cost by 4.3 and 3.4% compared with use of Freedom Innovations Catapult [fixed effect (β) = -0.177; P < 0.001] and Össur Flex-Run (β = -0.139; P = 0.002) prostheses, respectively. Neither prosthetic stiffness (P ≥ 0.180) nor height (P = 0.062) affected the metabolic cost of running. The metabolic cost of running was related to lower peak (β = 0.649; P = 0.001) and stance average (β = 0.772; P = 0.018) vertical ground reaction forces, prolonged ground contact times (β = -4.349; P = 0.012), and decreased leg stiffness (β = 0.071; P < 0.001) averaged from both legs. Metabolic cost was reduced with more symmetric peak vertical ground reaction forces (β = 0.007; P = 0.003) but was unrelated to stride kinematic symmetry (P ≥ 0.636). Therefore, prosthetic recommendations based on symmetric stride kinematics do not necessarily minimize the metabolic cost of running. Instead, an optimal prosthetic model, which improves overall biomechanics, minimizes the metabolic cost of running for athletes with unilateral transtibial amputations.NEW & NOTEWORTHY The metabolic cost of running for athletes with unilateral transtibial amputations depends on prosthetic model and is associated with lower peak and stance average vertical ground reaction forces, longer contact times, and reduced leg stiffness. Metabolic cost is unrelated to prosthetic stiffness, height, and stride kinematic symmetry. Unlike nonamputees who decrease leg stiffness with increased in-series surface stiffness, biological limb stiffness for athletes with unilateral transtibial amputations is positively correlated with increased in-series (prosthetic) stiffness.

Nonlinear dynamics induced by linear wave interactions in multilayered flows

Using simple kinematics, we propose a general theory of linear wave interactions between the interfacial waves of a two-dimensional (2D), inviscid, multilayered fluid system. The strength of our formalism is that one does not have to specify the physics of the waves in advance. Wave interactions may lead to instabilities, which may or may not be of the familiar ‘normal-mode’ type. Contrary to intuition, the underlying dynamical system describing linear wave interactions is found to be nonlinear. Specifically, a saw-tooth jet profile with three interfaces possessing kinematic and geometric symmetry is explored. Fixed points of the system for different ranges of a Froude number like control parameter $\unicode[STIX]{x1D6FE}$ are derived, and their stability evaluated. Depending upon the initial condition and $\unicode[STIX]{x1D6FE}$, the dynamical system may reveal transient growth, weakly positive Lyapunov exponents, as well as different nonlinear phenomena such as the formation of periodic and pseudo-periodic orbits. All these occur for those ranges of $\unicode[STIX]{x1D6FE}$ where normal-mode theory predicts neutral stability. Such rich nonlinear phenomena are not observed in a 2D dynamical system resulting from the two-wave problem, which reveals only stable and unstable nodes.

THE SYNTHESIS OF THE PLANAR LINKAGES WITH SYMMETRICAL CONFIGURATIONS

The mechanisms that employ symmetrical configurations can be found in the steering mechanisms, double open refrigerator, roof boxes, and double open windows, among others. They are useful for some special applications with kinematic symmetry. There have been studies about the linkage synthesis, especially in the research of planar closed chains, from as early as 1960s. However, no study has focused on the symmetry of planar linkages. Thus, the purpose of this paper is to present a methodology to synthesize the configurations of planar linkages. The systematic methodology can be divided into structure synthesis, configuration synthesis and results produced from three major processes. Finally, four suitable results of up to six-bar linkages can be obtained, for example. The four results include one four-bar linkage and three six-bar linkages.

Early Changes in Knee Center of Rotation During Walking After Anterior Cruciate Ligament Reconstruction Correlate With Later Changes in Patient-Reported Outcomes

Background: Altered knee kinematics after anterior cruciate ligament injury and reconstruction (ACLR) have been implicated in the development of posttraumatic osteoarthritis (PTOA), leading to poor long-term clinical outcomes. Purpose: This study was conducted to determine (1) whether the average knee center of rotation (KCOR), a multidimensional metric of knee kinematics, of the ACL-reconstructed knee during walking differs from that of the uninjured contralateral knee; (2) whether KCOR changes between 2 and 4 years after surgery; and (3) whether early KCOR changes predict patient-reported outcomes 8 years after ACLR. Study Design: Descriptive laboratory study. Methods: Twenty-six human participants underwent gait analysis with calculation of bilateral KCOR during walking at 2 and 4 years after unilateral ACLR. Knee injury and Osteoarthritis Outcome Score (KOOS) and Lysholm score results were collected at 2, 4, and 8 years after ACLR in 13 of these participants. Results: The ACL-reconstructed knee showed greater medial compartment motion because of pivoting about a more lateral KCOR (P = .03) than the contralateral knee at 2 years. KCOR became less lateral over time (P = .047), with values approaching those of the uninjured knee by 4 years (P = .55). KCOR was also more anterior in the ACL-reconstructed knee at 2 years (P = .02). Between 2 and 4 years, KCOR moved posteriorly in 16 (62%) and anteriorly in 10 (38%) participants. Increasing the anterior position of KCOR in the ACL-reconstructed knee from 2 to 4 years correlated with worsening clinical outcomes at 4 years (KOOS–Quality of Life, R2 = 0.172) and more strongly at 8 years (Lysholm score, R2 = 0.41; KOOS-Pain, R2 = 0.37; KOOS-Symptoms, R2 = 0.58; and KOOS–Quality of Life, R2 = 0.50). Conclusion: The observed changes to KCOR during walking between 2 and 4 years after ACLR show progressive improvement toward kinematic symmetry over the 2-year follow-up. The correlation between increasingly abnormal kinematics and worsening clinical outcomes years later in a subset of participants provides a potential explanation for the incidence of PTOA after ACLR.

Deformation of noncommutative quantum mechanics

In this paper, the Lie group $G_{NC}^{\alpha,\beta,\gamma}$, of which the kinematical symmetry group $G_{NC}$ of noncommutative quantum mechanics (NCQM) is a special case due to fixed nonzero $\alpha$, $\beta$ and $\gamma$, is three-parameter deformation quantized using the method suggested by Ballesteros and Musso in "Quantum Algebras as Quantizations of Dual Poisson-Lie Groups" [J. Phys. A: Math. Theor., 46 (2013), 195203]. A certain family of QUE algebras, corresponding to $G_{NC}^{\alpha,\beta,\gamma}$ with two of the deformation parameters approaching zero, is found to be in agreement with the existing results of the literature on quantum Heisenberg group. Finally, we dualize the underlying QUE algebra to obtain an expression for the underlying star-product between smooth functions on $G_{NC}^{\alpha,\beta,\gamma}$.

An OSp extension of the canonical tensor model

Tensor models are generalizations of matrix models, and are studied as discrete models of quantum gravity for arbitrary dimensions. Among them, the canonical tensor model (CTM for short) is a rank-three tensor model formulated as a totally constrained system with a number of first-class constraints, which have a similar algebraic structure as the constraints of the ADM formalism of general relativity. In this paper, we formulate a super-extension of CTM as an attempt to incorporate fermionic degrees of freedom. The kinematical symmetry group is extended from $O(N)$ to $OSp(N,\tilde N)$, and the constraints are constructed so that they form a first-class constraint super-Poisson algebra. This is a straightforward super-extension, and the constraints and their algebraic structure are formally unchanged from the purely bosonic case, except for the additional signs associated to the order of the fermionic indices and dynamical variables. However, this extension of CTM leads to the existence of negative norm states in the quantized case, and requires some future improvements as quantum gravity with fermions. On the other hand, since this is a straightforward super-extension, various results obtained so far for the purely bosonic case are expected to have parallels also in the super-extended case, such as the exact physical wave functions and the connection to the dual statistical systems, i.e. randomly connected tensor networks.

Wigner functions for noncommutative quantum mechanics: A group representation based construction

This paper is devoted to the construction and analysis of the Wigner functions for noncommutative quantum mechanics, their marginal distributions, and star-products, following a technique developed earlier, viz, using the unitary irreducible representations of the group GNC, which is the three fold central extension of the Abelian group of ℝ4. These representations have been exhaustively studied in earlier papers. The group GNC is identified with the kinematical symmetry group of noncommutative quantum mechanics of a system with two degrees of freedom. The Wigner functions studied here reflect different levels of non-commutativity—both the operators of position and those of momentum not commuting, the position operators not commuting and finally, the case of standard quantum mechanics, obeying the canonical commutation relations only.

Conserved integrals for inviscid compressible fluid flow in Riemannian manifolds

An explicit determination of all local conservation laws of kinematic type on moving domains and moving surfaces is presented for the Euler equations of inviscid compressible fluid flow in curved Riemannian manifolds in n &gt;1 dimensions. All corresponding kinematic constants of motion are also determined, along with all Hamiltonian kinematic symmetries and kinematic Casimirs which arise from the Hamiltonian structure of the inviscid compressible fluid equations.

One-Dimensional Traps, Two-Body Interactions, Few-Body Symmetries. II. N Particles

This is the second in a pair of articles that classify the configuration space and kinematic symmetry groups for N identical particles in one-dimensional traps experiencing Galilean-invariant two-body interactions. These symmetries explain degeneracies in the few-body spectrum and demonstrate how tuning the trap shape and the particle interactions can manipulate these degeneracies. The additional symmetries that emerge in the non-interacting limit and in the unitary limit of an infinitely strong contact interaction are sufficient to algebraically solve for the spectrum and degeneracy in terms of the one-particle observables. Symmetry also determines the degree to which the algebraic expressions for energy level shifts by weak interactions or nearly–unitary interactions are universal, i.e. independent of trap shape and details of the interaction. Identical fermions and bosons with and without spin are considered. This article analyzes the symmetries of N particles in asymmetric, symmetric, and harmonic traps; the prequel article treats the one, two and three particle cases.

One-Dimensional Traps, Two-Body Interactions, Few-Body Symmetries: I. One, Two, and Three Particles

This is the first in a pair of articles that classify the configuration space and kinematic symmetry groups for $N$ identical particles in one-dimensional traps experiencing Galilean-invariant two-body interactions. These symmetries explain degeneracies in the few-body spectrum and demonstrate how tuning the trap shape and the particle interactions can manipulate these degeneracies. The additional symmetries that emerge in the non-interacting limit and in the unitary limit of an infinitely strong contact interaction are sufficient to algebraically solve for the spectrum and degeneracy in terms of the one-particle observables. Symmetry also determines the degree to which the algebraic expressions for energy level shifts by weak interactions or nearly-unitary interactions are universal, i.e.\ independent of trap shape and details of the interaction. Identical fermions and bosons with and without spin are considered. This article sequentially analyzes the symmetries of one, two and three particles in asymmetric, symmetric, and harmonic traps; the sequel article treats the $N$ particle case.