Synergy Structure Research Articles

Assortment optimization under the multinomial logit model with product synergies

In synergistic assortment optimization, a product’s attractiveness changes as a function of which other products are offered. We represent synergy structure graphically. Vertices denote products. An edge denotes synergy between two products, which increases their attractiveness when both are offered. Finding an assortment to maximize retailer’s expected profit is NP-hard in general. We present efficient algorithms when the graph is a path, a tree, or has low treewidth. We give a linear program to recover the optimal assortment for paths.

Modular organization of murine locomotor pattern in the presence and absence of sensory feedback from muscle spindles.

Locomotion on land and in water requires the coordination of a great number of muscle activations and joint movements. Constant feedback about the position of own body parts in relation to the surrounding environment and the body itself (proprioception) is required to maintain stability and avoid failure. The central nervous system may follow a modular type of organization by controlling muscles in orchestrated groups (muscle synergies) rather than individually. We used this concept on genetically modified mice lacking muscle spindles, one of the two main classes of proprioceptors. We provide evidence that proprioceptive feedback is required by the central nervous system to accurately tune the modular organization of locomotion. For exploiting terrestrial and aquatic locomotion, vertebrates must build their locomotor patterns based on an enormous amount of variables. The great number of muscles and joints, together with the constant need for sensory feedback information (e.g. proprioception), make the task of controlling movement a problem with overabundant degrees of freedom. It is widely accepted that the central nervous system may simplify the creation and control of movement by generating activation patterns common to muscle groups, rather than specific to individual muscles. These activation patterns, called muscle synergies, describe the modular organization of movement. We extracted synergies through electromyography from the hind limb muscle activities of wild-type and genetically modified mice lacking sensory feedback from muscle spindles. Muscle spindle-deficient mice underwent a modification of the temporal structure (motor primitives) of muscle synergies that resulted in diminished functionality during walking. In addition, both the temporal and spatial (motor modules) components of synergies were severely affected when external perturbations were introduced or when animals were immersed in water. These findings show that sensory feedback from group Ia/II muscle spindles regulates motor function in normal and perturbed walking. Moreover, when group Ib Golgi tendon organ feedback is lacking due to enhanced buoyancy, the modular organization of swimming is almost completely compromised.

Influence of fatigue on running coordination: A UCM analysis with a geometric 2D model and a subject-specific anthropometric 3D model

Although fatigue is a central issue in endurance sports little is known about the effects of fatigue on coordination. The uncontrolled manifold (UCM) approach has been widely used in recent studies to examine coordination in human movement; however, it has not been used to study the effects of fatigue on running. Therefore, the aim of this study was to analyze the effects of fatigue on the synergy structure stabilizing the center of mass (CoM) trajectory in experienced runners during high-intensity running using the UCM approach.A total of 13 healthy young experienced runners participated in the study. Based on a lactate threshold testing undertaken one week prior to the measurements, participants were asked to run on a treadmill at their individual “fatigue-speed” until exhaustion. The kinematics of 20 consecutive gait cycles were recorded at the beginning (rested) and at the end (fatigue) of the protocol. The effects of fatigue on the synergy structure were investigated using a geometric 2D model and a subject-specific anthropometric 3D model. Specifically, the variance affecting the CoM trajectory (UCM⊥), the variance not affecting the CoM trajectory (UCM‖), and their ratio (UCMRatio) were analyzed for different gait cycle phases (absorption, propulsion and flight phase).Three-way repeated-measures ANOVA tests revealed differences between the two models. Fatigue-induced changes in the UCM structure could only be detected using the 3D model. UCMRatio did not change, but UCM⊥ increased during flight phase. In the 2D model, UCMRatio and both components were higher during the propulsion phase than during the absorption phase in both the rested and the fatigued state.Using a current concept for analyzing motor coordination, the UCM approach, only minor changes with fatigue were detected using the 3D subject-specific model. This indicates that the runners were able to control the trajectory of their CoM when fatigued. As the 2D model was not able to detect these changes, our study emphasizes that future studies on the effects of fatigue should focus on 3D analyses.

Gait synergetic neuromuscular control in children with cerebral palsy at different gross motor function classification system levels.

Cerebral palsy (CP) is a neural developmental disease featured with gait abnormalities. CP gait assessment is usually performed with the Gross Motor Function Classification System (GMFCS) in clinics, which does not involve a thorough assessment of neuromuscular control. To understand how the neuromuscular control disorders lead to gait abnormalities, we explored the relationship between GMFCS levels and the gait synergetic control characteristics in this study. In total, 18 children with CP at different GMFCS levels (mean age: 4.41±1.30 yr) and 8 age-matched typically developing (TD) children (mean age: 4.43±1.36 yr) were recruited to perform a straight walking task, and the surface electromyographic (sEMG) signals from eight lower limb muscles on each side and accelerometer data were collected. A nonnegative matrix factorization method was applied to obtain the muscle synergies from the sEMG signals. Next, synergy structures were projected onto the basic gait synergies to test the completeness of those structures. Subsequently, synergy activation parameters, including total activation duration and coactivation index, were compared across the participants. This study showed that children with CP at GMFCS levels I and II and the TD children had similar synergy structures, but the synergy activations of these children with CP were different from those of TD children. In addition, similar to previous research, we also found that children with CP at GMFCS level III could not access all four basic synergies on both sides. Based on the synergy analysis results, a gait assessment paradigm was proposed to facilitate the clinical CP gait evaluation. NEW & NOTEWORTHY Understanding the mechanism of gait abnormality has important clinical significance for the diagnosis, prognosis, and possible treatment of motor dysfunction in children with cerebral palsy (CP). In this study, the comparisons of the lower limb muscle synergies among different groups of children with CP at different Gross Motor Function Classification System levels might provide some new insight into the mechanism underlying the gait disorder. In particular, the discrepancies of gait synergy structure and activation patterns across the study groups may indicate different neurophysiological and pathological attributes in different groups of patients.

Coordinated activities of trunk and upper extremity muscles during walker-assisted paraplegic gait: A synergy study

Individuals with spinal cord injury (SCI) at lower thoracic levels might walk independently with the aid of mechanical orthoses and walker by using their unimpaired trunk and upper extremity muscles (TUEM). The required motor skills and the associated subtasks of the paraplegic locomotion, however, have not been well understood yet. The purpose of this study was to investigate the coordination of the TUEM activities throughout the paraplegic gait cycle using synergy analysis. For eight paraplegic individuals (30.6 ± 11.6 years; SCI level: T12), the kinematics data and the surface electromyography (EMG) signals of TUEM were recorded during 15 gait cycles. Non-negative matrix factorization method was used to extract muscle synergies from the EMG results, which were time normalized in association with four stages of each gait step. For each subject, the number, structures and activation profiles of the muscle synergies across different gait cycles were highly similar, resulting in three subject-specific templates of synergy structure and activation profile with mean intra-subject similarity scores of 0.94 ± 0.02 (p < 0.037) and 0.90 ± 0.06 (p < 0.001), respectively. Hierarchical clustering of the subject-specific templates revealed five representative templates for all subjects, among which, three that were in common for at least six subjects were considered as the characteristic synergies of paraplegic locomotion. The first and second characteristic synergies (inter-subject similarity scores >0.91, p < 0.037) composed mainly of the pectoralis major, latissimus dorsi, longissimus, iliocostalis quadratus lumborum, and the triceps, posterior deltoid and lower trapezius muscles, respectively, and were activated during the ipsilateral and the contralateral leg raising and swing stages. The third characteristic synergy, (inter-subject similarity scores >0.95, p < 0.02), contained mainly the abdominal and lumbopelvic muscles and was activated during the balance adjustment and walker propulsion stages of the gait cycle. These results provide more insight into the motor skills and the associated subtasks of the paraplegic locomotion.

Alterations of Muscle Synergies During Voluntary Arm Reaching Movement in Subacute Stroke Survivors at Different Levels of Impairment

Motor system uses muscle synergies as a modular organization to simplify the control of movements. Motor cortical impairments, such as stroke and spinal cord injuries, disrupt the orchestration of the muscle synergies and result in abnormal movements. In this paper, the alterations of muscle synergies in subacute stroke survivors were examined during the voluntary reaching movement. We collected electromyographic (EMG) data from 35 stroke survivors, ranging from Brunnstrom Stage III to VI, and 25 age-matched control subjects. Muscle synergies were extracted from the activity of 7 upper-limb muscles via nonnegative matrix factorization under the criterion of 95% variance accounted for. By comparing the structure of muscle synergies and the similarity of activation coefficients across groups, we can validate the increasing activation of pectoralis major muscle and the decreasing activation of elbow extensor of triceps in stroke groups. Furthermore, the similarity of muscle synergies was significantly correlated with the Brunnstrom Stage (R = 0.52, p < 0.01). The synergies of stroke survivors at Brunnstrom Stage IV–III gradually diverged from those of control group, but the activation coefficients remained the same after stroke, irrespective of the recovery level.

Effect of Physical Therapy on Muscle Synergy Structure During Standing-Up Motion of Hemiplegic Patients

Stroke patients suffer from declined physical ability, and it is important to analyze rehabilitation intervention and clarify its effect on the motion of patients. In this study, the effect of intervention on the standing-up motion of stroke patients is investigated. First, the intervention timing of a physical therapist (PT) is analyzed quantitatively from the muscle activity of upper limbs during therapy. Next, the intervention effect is evaluated based on body kinematics and muscle synergy. In this study, twenty trials are conducted, in which the standing-up motion of hemiplegic patients (n=12) is measured with and without the intervention by a PT. The results show that PTs teach hemiplegic patients the timing of lifting their buttocks during standing-up motion. Furthermore, it has been found that this intervention could improve the standing-up motion, although stroke patients had inadequate muscle synergy structure. In particular, some patients had delayed activation of the synergy and they could only stood up after they moved their center of mass toward their feet. However, the intervention by PTs could induce earlier activation of the synergy. Moreover, the intervention could properly shorten the activation duration of muscle synergy for those who had unusually inappropriate longer activation of synergy. These results imply that disordered and inadequate muscle synergy structure can be improved by proper intervention, and this study contributes to the further development of new rehabilitation methodologies.

Fatigue Influences the Recruitment, but Not Structure, of Muscle Synergies.

The development of fatigue elicits multiple adaptations from the neuromuscular system. Muscle synergies are common patterns of neuromuscular activation that have been proposed as the building blocks of human movement. We wanted to identify possible adaptations of muscle synergies to the development of fatigue in the upper limb. Recent studies have reported that synergy structure remains invariant during the development of fatigue, but these studies did not examine isolated synergies. We propose a novel approach to characterise synergy adaptations to fatigue by taking advantage of the spatial tuning of synergies. This approach allows improved identification of changes to individual synergies that might otherwise be confounded by changing contributions of overlapping synergies. To analyse upper limb synergies, we applied non-negative matrix factorization to 14 EMG signals from muscles of 11 participants performing isometric contractions. A preliminary multidirectional task was used to identify synergy directional tuning. A subsequent fatiguing task was designed to fatigue the participants in their synergies’ preferred directions. Both tasks provided virtual reality feedback of the applied force direction and magnitude, and were performed at 40% of each participant’s maximal voluntary force. Five epochs were analysed throughout the fatiguing task to identify progressive changes of EMG amplitude, median frequency, synergy structure, and activation coefficients. Three to four synergies were sufficient to account for the variability contained in the original data. Synergy structure was conserved with fatigue, but interestingly synergy activation coefficients decreased on average by 24.5% with fatigue development. EMG amplitude did not change systematically with fatigue, whereas EMG median frequency consistently decreased across all muscles. These results support the notion of a neuromuscular modular organisation as the building blocks of human movement, with adaptations to synergy recruitment occurring with fatigue. When synergy tuning properties are considered, the reduction of activation of muscle synergies may be a reliable marker to identify fatigue.

Assessment of ankle muscle activation by muscle synergies in healthy and post-stroke gait

Objective: Impaired ankle dorsal and plantar flexor function is a frequent sequela of stroke. A better assessment of ankle muscle activation would be highly significant for stroke rehabilitation. The challenge in implementing current electromyography (EMG)-based assessments is due to problems with the variability and individuality of ankle muscle EMG profiles during walking. We have been studying a new technique using the muscle synergy method to quantify the characteristics that underlie ankle muscle activation to address this issue. Approach: We processed surface EMG signals from ankle muscles and gait parameters collected from 20 healthy and 22 post-stroke subjects during walking. A non-negative matrix factorization algorithm was used to extract muscle synergies. Main results: Our results suggest a featured muscle synergy structure (R = 0.84, 95% CI: 0.83–0.85) underlying ankle muscle activation in both healthy and post-stroke subjects. The structure of the featured muscle synergy was robust in the same subjects across different conditions in the healthy group (R = 0.97, 95% CI: 0.96–0.98) and the post-stroke group (R = 0.95, 95% CI: 0.88–0.97). Compared to the stroke group, the synergy patterns of healthy subjects showed better regularity and higher inter-subject similarity (P = 0.001). In addition, the results of muscle synergies were indicative of locomotor performance. Significance: The innovative quantitative results of this study can help us to better understand ankle muscle activation and will be a reference for clinical assessments and intervention studies.

An inquiry of synergy structure and its effect on ill-structured problem solving

An inquiry of synergy structure and its effect on ill-structured problem solving

Contralesional Hemisphere Regulation of Transcranial Magnetic Stimulation-Induced Kinetic Coupling in the Poststroke Lower Limb.

The neural constraints underlying hemiparetic gait dysfunction are associated with abnormal kinetic outflow and altered muscle synergy structure. Recent evidence from our lab implicates the lesioned hemisphere in mediating the expression of abnormally coupled hip adduction and knee extension synergy, suggesting a role of cortical networks in the regulation of lower limb motor outflow poststroke. The potential contribution of contralesional hemisphere (CON-H) in regulating paretic leg kinetics is unknown. The purpose of this study is to characterize the effect of CON-H activation on aberrant across-joint kinetic coupling of the ipsilateral lower-extremity muscles poststroke. Amplitude-matched adductor longus motor-evoked potentials were elicited using single pulse transcranial magnetic stimulation (TMS) of the lesioned (L-H) and CON-Hs during an isometric adductor torque matching task from 11 stroke participants. For 10 control participants, TMS of the contralateral and ipsilateral hemisphere were given during the same task. TMS-induced torques were characterized at the hip and knee joints to determine the differential regulation of abnormal kinetic synergies by each motor cortices. The TMS-induced ratio of knee extension/hip adduction torques was quantified during 40 and 20% of maximum adduction torque. For both the 40 and 20% target adduction tasks, we find that contralesional stimulation significantly reduced but did not eliminate the TMS-induced ratio of knee extension/hip adduction torques for the stroke group (p = 0.0468, p = 0.0396). In contrast, the controls did not present a significantly different TMS-evoked torque following stimulation (p = 0.923) of the hemisphere ipsilateral to the test leg. The reduced expression of abnormal across-joint kinetic coupling suggests that the CON-H may contribute an adaptive role in lower limb control poststroke. Future study of neuromodulation paradigms that leverage adaptive CON-H activation may yield clinically relevant gains in lower limb motor function poststroke.

Study of Intellectual Capital Dimensions in IT Industry Using DEMATEL Method

The purpose of this paper is to analyse the causal relation structure among the dimensions of Intellectual Capital (IC) by using the DEMATEL method. In this study, the dimensions of IC comprise human, structural, and relational capital. This study empirically analyses the causal relation structure with a sample of 18 (12 national and 6 multi-national) Information Technology (IT) firms operating in India. The respondents were the experts from IT firms encompassing chief executive officers, general managers, Human Resource (HR) managers, senior managers, and the IT consultants. Decision-Making Trial and Evaluation Laboratory (DEMATEL) method is used for the statistical treatment of the data. On the human, structural, and relational capital fronts, findings of the study suggest that “motivation of the personnel”, “operation process”, “brand value”, respectively, have the maximum causing properties. The study is limited to IT industry of India only. The dimensions of IC will differently trigger the attitude and behaviours of employees relevant for the parent organisation that helps the management to deal with different dynamic circumstances resulting in different outcomes. Study empirically assessed that there are synergy and causal relation structure between the dimensions. Present study contributes to retention and engagement of human capital and prefers potentially important policy implications. Examining the interrelationship among the dimensions of IC in the context of Indian IT is the novel contribution of the present study. Theoretically and empirically assessing the causal interrelationship and addressing the research gaps summarised from the literature will contribute to the IC research.

Clarification of muscle synergy structure during standing-up motion of healthy young, elderly and post-stroke patients.

Standing-up motion is an important daily activity. It has been known that elderly and post-stroke patients have difficulty in performing standing-up motion. The standing-up motion is retrained by therapists to maximize independence of the elderly and post-stroke patients, but it is not clear how the elderly and post-stroke patients control their redundant muscles to achieve standing-up motion. This study employed the concept of muscle synergy to analyze how healthy young adults, healthy elderly people and post-stroke patients control their muscles. Experimental result verified that four muscle synergies can represent human standing-up motion. In addition, it indicated that the post-stroke patients shift the weights of muscle synergies to finish standing-up motion comparing to healthy subjects. Moreover, different muscle synergy structures were associated with the CoM and joint kinematics.

Investigation of the Intra- and Inter-Limb Muscle Coordination of Hands-and-Knees Crawling in Human Adults by Means of Muscle Synergy Analysis

To investigate the intra- and inter-limb muscle coordination mechanism of human hands-and-knees crawling by means of muscle synergy analysis, surface electromyographic (sEMG) signals of 20 human adults were collected bilaterally from 32 limb related muscles during crawling with hands and knees at different speeds. The nonnegative matrix factorization (NMF) algorithm was exerted on each limb to extract muscle synergies. The results showed that intra-limb coordination was relatively stable during human hands-and-knees crawling. Two synergies, one relating to the stance phase and the other relating to the swing phase, could be extracted from each limb during a crawling cycle. Synergy structures during different speeds kept good consistency, but the recruitment levels, durations, and phases of muscle synergies were adjusted to adapt the change of crawling speed. Furthermore, the ipsilateral phase lag (IPL) value which was used to depict the inter-limb coordination changed with crawling speed for most subjects, and subjects using the no-limb-pairing mode at low speed tended to adopt the trot-like mode or pace-like mode at high speed. The research results could be well explained by the two-level central pattern generator (CPG) model consisting of a half-center rhythm generator (RG) and a pattern formation (PF) circuit. This study sheds light on the underlying control mechanism of human crawling.

Assessment of Upper Limb Motor Dysfunction for Children with Cerebral Palsy Based on Muscle Synergy Analysis

Muscle synergies are considered to be building blocks underlying motor behaviors. The goal of this study is to explore an objective and effective method to assess the upper limb motor dysfunction of cerebral palsy (CP) children from the aspect of muscle synergy analysis. Fourteen CP children and 10 typically developed (TD) children were recruited to perform three similar upper limb motion tasks related to the movements of elbow and shoulder joints, and surface electromyographic (sEMG) signals were recorded from 10 upper arm and shoulder muscles involved in the defined tasks. Non-negative matrix factorization algorithm was used to extract muscle synergies and the corresponding activation patterns during three similar tasks. For each subject in TD group, four muscle synergies were extracted in each task. Whereas, fewer mature synergies were recruited in CP group, and many abnormal synergy structures specific to CP group appeared. In view of neuromuscular control strategy differences, three synergy-related parameters were proposed and synergy structure similarity coefficient was found to have high ability in depicting the inter-subject similarity within task and the intra-subject similarity between tasks. Seven upper limb assessment (UPA) metrics, which were defined as the combinations of synergy structure similarity coefficients of three tasks, were proposed to assess the upper limb motor function of CP children. The experimental results demonstrated that these UPA metrics were able to assess upper limb motor function comprehensively and effectively. The proposed assessment method can serve as a promising approach to quantify the abnormality of muscle synergies, thus offering potential to derive a physiologically based quantitative index for assessing upper limb motor function in CP clinical diagnosis and rehabilitation.

On identifying kinematic and muscle synergies: a comparison of matrix factorization methods using experimental data from the healthy population.

Literature on comparing factorization methods in identifying motor synergies using numerically generated, simulation, and muscle activation data from animal studies already exists. We present an empirical evaluation of the performance of three of these methods on muscle activation and joint angles data from human reaching motion: principal component analysis, nonnegative matrix factorization, and independent component analysis. Using numerical simulation, we also studied the meaning and differences in the synergy structures returned by each method. The results can be used to unify approaches in identifying and interpreting motor synergies.

Muscle synergies during bench press are reliable across days

Muscle synergies have been investigated during different types of human movement using nonnegative matrix factorization. However, there are not any reports available on the reliability of the method. To evaluate between-day reliability, 21 subjects performed bench press, in two test sessions separated by approximately 7days. The movement consisted of 3 sets of 8 repetitions at 60% of the three repetition maximum in bench press. Muscle synergies were extracted from electromyography data of 13 muscles, using nonnegative matrix factorization. To evaluate between-day reliability, we performed a cross-correlation analysis and a cross-validation analysis, in which the synergy components extracted in the first test session were recomputed, using the fixed synergy components from the second test session. Two muscle synergies accounted for >90% of the total variance, and reflected the concentric and eccentric phase, respectively. The cross-correlation values were strong to very strong (r-values between 0.58 and 0.89), while the cross-validation values ranged from substantial to almost perfect (ICC3, 1 values between 0.70 and 0.95). The present findings revealed that the same general structure of the muscle synergies was present across days and the extraction of muscle synergies is thus deemed reliable.

M&amp;A Synergies in Domestic M&amp;A Deals in Russia in 2006–2014

This article aims to develop econometric model suitable for valuation of synergies in Russian domestic M&A deals. The authors test several empirical hypotheses about factors of synergy creation in 2006–2014. The article looks into various ways to estimate synergies based on financial statements of companies that participated in the deal. Success rate of deals and synergy structure is estimated for the whole sample and for growth and crisis periods. Most important factors of synergy are estimated, and robustness of these factors during growth and crisis periods is analyzed.

Repeatability of muscle synergies within and between days for typically developing children and children with cerebral palsy

Muscle synergies are typically calculated from electromyographic (EMG) signals using nonnegative matrix factorization. Synergies identify weighted groups of muscles that are commonly activated together during a task, such as walking. Synergy analysis has become an emerging tool to evaluate neuromuscular control; however, the repeatability of synergies between trials and days has not been evaluated. The goal of this study was to evaluate the repeatability of synergy complexity and structure in unimpaired individuals and individuals with cerebral palsy (CP). EMG data were collected from eight lower-limb muscles during gait for six typically developing (TD) children and five children with CP on two separate days, over three walking speeds. To evaluate synergy complexity, we calculated the total variance accounted for by one synergy (tVAF1). On a given day, the average range in tVAF1 between gait cycles was 18.2% for TD and 19.1% for CP. The average standard deviation in tVAF1 between gait cycles was 4.9% for TD and 5.0% for CP. Average tVAF1 calculated across gait cycles was not significantly different between days for TD or CP participants. Comparing synergy structure, the average (standard deviation) within day correlation coefficients of synergy weights for two or more synergies were 0.89 (0.15) for TD and 0.88 (0.15) for CP. Between days, the average correlation coefficient of synergy weights for two or more synergies was greater than 0.89 for TD and 0.74 for CP. These results demonstrate that synergy complexity and structure averaged over multiple gait cycles are repeatable between days in both TD and CP groups.

Merging and Fractionation of Muscle Synergy Indicate the Recovery Process in Patients with Hemiplegia: The First Study of Patients after Subacute Stroke.

Loss of motor coordination is one of the main problems for patients after stroke. Muscle synergy is widely accepted as an indicator of motor coordination. Recently, the characteristics of muscle synergy were quantitatively evaluated using nonnegative matrix factorization (NNMF) with surface electromyography. Previous studies have identified that the number and structure of synergies were associated with motor function in patients after stroke. However, most of these studies had a cross-sectional design, and the changes in muscle synergy during recovery process are not clear. In present study, two consecutive measurements were conducted for subacute patients after stroke and the change of number and structure of muscle synergies during gait were determined using NNMF. Results showed that functional change did not rely on number of synergies in patients after subacute stroke. However, the extent of merging of the synergies was negatively associated with an increase in muscle strength and the range of angle at ankle joint. Our results suggest that the neural changes represented by NNMF were related to the longitudinal change of function and gait pattern and that the merging of synergy is an important marker in patients after subacute stroke.