MOVE

94. S Houweling, BW van Dijk, PJ Beek and A Daffertshofer (2009). Cortico-spinal synchronization reflects changes in performance when learning a complex bimanual task. NeuroImage. doi: S1053-8119(09)01201-4 [pii] 10.1016/j.neuroimage.2009.11.017

Motor performance is accompanied by neural activity in various cortical and sub-cortical areas. This intricate network has to be delicately orchestrated. We analyzed the role of beta synchronization in motor learning using magneto-encephalography combined with electromyography. Cortico-spinal synchronization in the beta band was found to be of particular importance in establishing bimanual movement patterns in the context of a 3:2 polyrhythmic (isometric) force production task. Its dynamics correlated highly with the learning of this complex bimanual motor skill. We submit that the cortical dynamics entrains the spinal motor system by which cortico-spinal beta synchrony serves higher-level motor control functions as primary means of information transfer along the neural axis.

93. SC Ponten, A Daffertshofer, A Hillebrand and CJ Stam (2009). The relationship between structural and functional connectivity: Graph theoretical analysis of an EEG neural mass model. NeuroImage. doi: S1053-8119(09)01120-3 [pii] 10.1016/j.neuroimage.2009.10.049

We investigated the relationship between structural network properties and both synchronization strength and functional characteristics in a combined neural mass and graph theoretical model of the electroencephalogram (EEG). Thirty-two neural mass models (NMMs), each representing the lump activity of reasonably large groups of interacting excitatory and inhibitory neurons, were reciprocally and excitatory coupled using random rewiring as described by Watts and Strogatz. Numerical analysis of the network revealed an abrupt transition towards a synchronized state as a function of increasing coupling strength alpha. Synchronization increased with increasing degree and decreasing regularity of the network. Parameters of the functional network showed a diverse dependency on structural connectivity: normalized clustering coefficient gamma and path length lambda increased with increasing alpha. For sufficiently large alpha, however, gamma decreased with increasing rewiring probability p, while lambda increased. Hence, a structured functional network exists despite the randomness of the underlying structural network. That is, patterns of functional connectivity are influenced by patterns of the corresponding structural level but do not necessarily agree with those.

92. D Staudenmann, I Kingma, A Daffertshofer, DF Stegeman and JH van Dieen (2009). Heterogeneity of muscle activation in relation to force direction: A multi-channel surface electromyography study on the triceps surae muscle. Journal of Electromyography and Kinesiology 19(5): 882. doi:10.1016/j.jelekin.2008.04.013

Several skeletal muscles can be divided into sub-modules, called neuromuscular compartments (NMCs), which are thought to be controlled independently and to have distinct biomechanical functions. We looked for distinct muscle activation patterns in the triceps surae muscle (TS) using surface electromyography (EMG) during voluntary contraction. Nine subjects performed isometric and isotonic plantar flexions combined with forces along pre-defined directions. Besides the forces under the ball of the foot, multi-channel surface EMG was measured with electrodes homogeneously distributed over the entire TS. Using principal component analysis, common (global) components were omitted from the EMG signals, thereby estimating muscle activity sufficiently accurate to track fine fluctuations of force during an isotonic contraction (r = 0.80 +/- 0.09). A subsequent cluster analysis showed a topographical organization of co-activated parts of the muscle that was different between subjects. Low and negative correlations between the EMG activity within clusters were found, indicating a substantial heterogeneity of TS activation. The correlations between cluster time series and forces at the foot in specific directions differed substantially between clusters, showing that the differentially activated parts of the TS had specific biomechanical functions.

91. A Daffertshofer, S Houweling, B van Dijk and P Beek (2009). Learning-related changes of beta-activity in motor areas. International Journal of Bioelectromagnetism 11(3): 116.

Motor control is accompanied by activity in specialized areas with a continuous adjustment of the flow of information. We studied interactions between hemispheres during the learning of a bimanual polyrhythmic movements during which the left and right fingers moved at a fixed frequency ratio. In the course of learning performance improved as revealed by an increased frequency locking. The improvement was primarily achieved through an adjusted timing of the slow finger. Accompanying brain activity was localized using synthetic aperture magnetometry of whole-head MEG that revealed significant changes in bilateral motor areas and cerebellum. As expected, the adapted motor output was reflected in the overall timing of and in motor areas. In particular in motor areas contralateral to the adapted finger the beta-modulation was significantly tightened.

90. TW Boonstra, A Daffertshofer, M Roerdink, I Flipse, K Groenewoud and PJ Beek (2009). Bilateral motor unit synchronization of leg muscles during a simple dynamic balance task. European Journal of Neuroscience 29(3): 613. doi:10.1111/j.1460-9568.2008.06584.x

To handle the rich repertoire of behavioural goals, the CNS has to control the many degrees of freedom of the musculoskeletal system in a flexible manner. This problem can be drastically simplified if muscle synergies serve as the to-be-controlled building blocks of motor performance, instead of the individual degrees of freedom. Muscle synergies have been identified as coherent activation patterns of a group of muscles in space or time, but the neural mechanisms underlying their formation remain largely unknown. Here we evaluated the hypothesis that synergies are reflected in common input to different contributing muscles, and investigated modulations in motor unit (MU) synchronization of homologous muscles during a rhythmic balance task. If common input is related to muscle synergies, the resultant MU synchronization should not be static but task dependent and, in the present context, vary in time. Coherence between surface electromyographic signals of bilateral leg muscles revealed MU synchronization in two distinct frequency bands. MU synchronization was not constant but modulated within a movement cycle, and its time course resembled the activation patterns of the muscles. These results are congruent with a linkage between MU synchronization and muscle synergies, and suggest that MU synchronization provides an expedient method for studying synergy-related neural mechanisms.

89. TW Boonstra, BCM van Wijk, P Praamstra and A Daffertshofer (2009). Corticomuscular and bilateral EMG coherence reflect distinct aspects of neural synchronization. Neuroscience Letters 463(1): 17. doi:10.1016/j.neulet.2009.07.043

Using electroencephalography (EEG) and electromyography (EMG), corticomuscular and bilateral motor unit synchronization have been found in different frequency bands and under different task conditions. These different types of long-range synchrony are hypothesized to originate from distinct mechanisms. We tested this by comparing time-resolved EEG-EMG and EMG-EMG coherence in a bilateral precision-grip task. Bilateral EMG activity was synchronized between 7 and 13 Hz for about 1 s when force output from both hands changed from an increasing to a stable force production. In contrast, EEG-EMG coherence was statistically significant between 15 and 30 Hz during stable force production. The disparities in their time-frequency profiles accord with the existence of distinct underlying processes for corticomuscular and bilateral motor unit synchronization. In addition, the absence of synchronization between cortical activity and common spinal input at 10 Hz renders a cortical source unlikely.

88. HH Chen and A Daffertshofer (2009). Changing degrees of freedom and degeneracy in the process of motor learning. Journal of Sport & Exercise Psychology 31: S52.

87. MJ Breakspear, A Daffertshofer and P Ritter (2009). BrainModes: A principled approach to modeling and measuring large-scale neuronal activity. Journal of Neuroscience Methods 183(1): 1. doi:10.1016/j.jneumeth.2009.07.008

Complex systems, such as the brain, exhibit multiple levels of organization due to processes which support the separation of scales across time and/or space. That is, cooperative phenomena – or "modes" of activity – occurring at one scale give rise to coherent spatiotemporal structures at a coarser scale. In turn, structures at the coarser scale constrain – and hence influence – emerging activity at a finer scale. BrainModes is an annual scientific summit which seeks to bring together experimental, computational and theoretical neuroscientists engaged at different levels of organization, with the goal of advancing a principled approach to understanding brain function based on the concept of cooperative phenomena in complex systems. Phenomena of particular interest include synchronization, stochastic influences, and spatiotemporal processes in both healthy and pathological states such as seizures. This Special Issue reports the 2008 BrainModes Workshop, held in Amsterdam (December 2008) which focused on the application of this framework to the analysis of brain oscillations and synchronization phenomena across time scales.

86. CJC Lamoth, A Daffertshofer, R Huys and PJ Beek (2009). Steady and transient coordination structures of walking and running. Human Movement Science 28(3): 371. doi:10.1016/j.humov.2008.10.001

We studied multisegmental coordination and stride characteristics in nine participants while walking and running on a treadmill. The study’s main aim was to evaluate the coordination patterns of walking and running and their variance as a function of locomotion speed, with a specific focus on gait transitions and accompanying features like hysteresis and critical fluctuations. Stride characteristics changed systematically with speed in a gait-dependent fashion, but exhibited no hysteresis. Multisegmental coordination of walking and running was captured by four principal components, the first two of which were present in both gaits. Locomotion speed had subtle yet systematic differential effects on the relative phasing between the identified components in both walking and running and its variance, in particular in the immediate vicinity of gait transitions. Unlike the stride characteristics, the identified coordination patterns revealed clear evidence of both hysteresis and critical fluctuations around transition points. Overall, the results Suggest that walking and running entail similar, albeit speed- and gait-dependent, coordination structures, and that gait transitions bear signatures of nonequilibrium phase transitions. Application of multivariate analyses of whole-body recordings appears crucial to detect these features in a reliable fashion.

85. M Muskulus, S Houweling, S Verduyn-Lunel and A Daffertshofer (2009). Functional similarities and distance properties. Journal of Neuroscience Methods 183(1): 31. doi:10.1016/j.jneumeth.2009.06.035

The analysis of functional and effective brain connectivity forms an important tool for unraveling structure-function relationships from neurophysiological data. It has clinical applications, supports the formulation of hypotheses regarding the role and localization of functional processes, and is often an initial step in modeling. However, only a few of the commonly applied connectivity measures respect metric properties: reflexivity, symmetry, and the triangle inequality. This may hamper interpretation of findings and subsequent analysis. Connectivity indices obtained by metric measures can be seen as functional distances, and may be represented in Euclidean space by the methods of multidimensional scaling. We sketch some classes of measures that do allow for such a reconstruction, in particular the class of Wasserstein distances, and discuss their merits for interpreting cortical activity assessed by magnetoencephalography. In an application to magnetoencephalographic recordings during the execution of a bimanual task, the Wasserstein distances between relative circular variances indicated cortico-muscular synchrony as well as cross-talk between bilateral primary motor areas in the beta-band.

84. CJ Stam, W de Haan, A Daffertshofer, BF Jones, I Manshanden, AM van Cappellen van Walsum, T Montez, JP Verbunt, JC de Munck, BW van Dijk, HW Berendse and P Scheltens (2009). Graph theoretical analysis of magnetoencephalographic functional connectivity in Alzheimer’s disease. Brain 132(Pt 1): 213.

In this study we examined changes in the large-scale structure of resting-state brain networks in patients with Alzheimer’s disease compared with non-demented controls, using concepts from graph theory. Magneto-encephalograms (MEG) were recorded in 18 Alzheimer’s disease patients and 18 non-demented control subjects in a no-task, eyes-closed condition. For the main frequency bands, synchronization between all pairs of MEG channels was assessed using a phase lag index (PLI, a synchronization measure insensitive to volume conduction). PLI-weighted connectivity networks were calculated, and characterized by a mean clustering coefficient and path length. Alzheimer’s disease patients showed a decrease of mean PLI in the lower alpha and beta band. In the lower alpha band, the clustering coefficient and path length were both decreased in Alzheimer’s disease patients. Network changes in the lower alpha band were better explained by a ‘Targeted Attack’ model than by a ‘Random Failure’ model. Thus, Alzheimer’s disease patients display a loss of resting-state functional connectivity in lower alpha and beta bands even when a measure insensitive to volume conduction effects is used. Moreover, the large-scale structure of lower alpha band functional networks in Alzheimer’s disease is more random. The modelling results suggest that highly connected neural network ‘hubs’ may be especially at risk in Alzheimer’s disease.

83. AL van Delden, CL Peper, J Harlaar, A Daffertshofer, NI Zijp, K Nienhuys, P Koppe, G Kwakkel and PJ Beek (2009). Comparing unilateral and bilateral upper limb training: the ULTRA-stroke program design. BMC Neurol 9: 57. doi: 1471-2377-9-57 [pii] 10.1186/1471-2377-9-57

BACKGROUND: About 80% of all stroke survivors have an upper limb paresis immediately after stroke, only about a third of whom (30 to 40%) regain some dexterity within six months following conventional treatment programs. Of late, however, two recently developed interventions–constraint-induced movement therapy (CIMT) and bilateral arm training with rhythmic auditory cueing (BATRAC)–have shown promising results in the treatment of upper limb paresis in chronic stroke patients. The ULTRA-stroke (acronym for Upper Limb TRaining After stroke) program was conceived to assess the effectiveness of these interventions in subacute stroke patients and to examine how the observed changes in sensori-motor functioning relate to changes in stroke recovery mechanisms associated with peripheral stiffness, interlimb interactions, and cortical inter- and intrahemispheric networks. The present paper describes the design of this single-blinded randomized clinical trial (RCT), which has recently started and will take several years to complete. METHODS/DESIGN: Sixty patients with a first ever stroke will be recruited. Patients will be stratified in terms of their remaining motor ability at the distal part of the arm (i.e., wrist and finger movements) and randomized over three intervention groups receiving modified CIMT, modified BATRAC, or an equally intensive (i.e., dose-matched) conventional treatment program for 6 weeks. Primary outcome variable is the score on the Action Research Arm test (ARAT), which will be assessed before, directly after, and 6 weeks after the intervention. During those test sessions all patients will also undergo measurements aimed at investigating the associated recovery mechanisms using haptic robots and magneto-encephalography (MEG). DISCUSSION: ULTRA-stroke is a 3-year translational research program which aims (1) to assess the relative effectiveness of the three interventions, on a group level but also as a function of patient characteristics, and (2) to delineate the functional and neurophysiological changes that are induced by those interventions. The outcome on the ARAT together with information about changes in the associated mechanisms will provide a better understanding of how specific therapies influence neurobiological changes, and which post-stroke conditions lend themselves to specific treatments. TRIAL REGISTRATION: The ULTRA-stroke program is registered at the Netherlands Trial Register (NTR, http://www.trialregister.nl, number NTR1665).

82. MR van den Heuvel, R Balasubramaniam, A Daffertshofer, A Longtin and PJ Beek (2009). Delayed visual feedback reveals distinct time scales in balance control. Neuroscience Letters 452(1): 37.

We performed an experiment in which we challenged postural stability in 12 healthy subjects by providing artificial delayed visual feedback. A monitor at eye-height presented subjects with a visual representation of the location of their center-of-pressure (COP) and they were instructed to position their COP as accurately as possible on a small target. Visual feedback of the COP was displayed either in real-time, or delayed by 250, 500, 750, or 1000 ms. In a control condition, no visual feedback was provided. As expected, stability increased during real-time visual feedback compared to when feedback was absent. To identify time scales at which postural control during quiet stance takes place we sought to distinguish between different frequencies. Low frequencies, i.e. slow components of postural sway, showed a monotonic increase in sway amplitude with increasing delay, whereas high frequencies, i.e. fast components of postural sway, showed significantly reduced sway amplitude for delays of 500-750 ms compared to the other delay conditions. Low- and high-frequency components of postural sway thus exhibited differential susceptibility to artificial delays, thereby supporting the notion of postural control taking place on two distinct time scales.

81. BC van Wijk, A Daffertshofer, N Roach and P Praamstra (2009). A role of beta oscillatory synchrony in biasing response competition? Cerebral Cortex 19(6): 1294. doi: bhn174 [pii] 10.1093/cercor/bhn174

Beta-range oscillatory activity measured over the motor cortex and beta synchrony between cortex and spinal cord can be up- or downregulated in anticipation of a postural challenge or the initiation of movement. Based on these properties of beta activity in the preparation for future events, the present investigation addressed whether simultaneous up- and downregulation of beta activity might act as an online mechanism to suppress and select competing responses. Measures of local and long-range beta synchrony were obtained from electroencephalographic and electromyographic signals recorded during a cued choice reaction task. Analyses focused on task-related changes in beta synchrony during a 2-s delay period between cue and response signal. Analyzed separately, none of the beta measures (spectral power, corticospinal coherence, corticospinal phase synchronization) showed simultaneous up- and downregulation over opposite hemispheres controlling the competing responses. However, the combined pattern of beta measures showed beta power desynchronization associated with selection of a response and increased corticospinal coherence and phase synchronization associated with suppression of a response. These results indicate that concurrent up- and downregulation of different components of beta oscillatory activity is likely to have a functional role in response selection, resembling attentional modulation of alpha activity in visual selection.

80. AN Vardy, A Daffertshofer and PJ Beek (2009). Tapping with intentional drift. Experimental Brain Research 192(4): 615. doi: 10.1007/s00221-008-1576-5

When tapping a desired frequency, subjects tend to drift away from this target frequency. This compromises the estimate of the correlation between inter-tap intervals (ITIs) as predicted by the two-level model of Wing and Kristofferson which consists of an internal timer (‘clock’) and motor delays. Whereas previous studies on the timing of rhythmic tapping attempted to eliminate drift, we compared the production of three constant frequencies (1.5, 2.0, and 2.5 Hz) to the production of tapping sequences with a linearly decreasing inter-tap interval (ITI) (corresponding to an increase in tapping frequency from 1.5 to 2.5 Hz). For all conditions a synchronization-continuation paradigm was used. Tapping forces and electromyograms of the index-finger flexor and extensor were recorded and ITIs were derived yielding interval variability and model parameters, i.e., clock and motor variances. Electromyographic recordings served to study the influence of tapping frequency on the peripheral part of the tap event. The condition with an increasing frequency was more difficult to perform, as evidenced by an increase in deviation from the intended ITIs. In general, tapping frequency affected force level, inter-tap variability, model parameters, and muscle co-activation. Parameters for the condition with a decreasing ITI were comparable to those found in the constant frequency conditions. That is, although tapping with an intentional drift is different from constant tapping and more difficult to perform, the timing properties of both forms of tapping are remarkably similar and described well by the Wing and Kristofferson model.

79. M Zeitler, A Daffertshofer and CC Gielen (2009). Asymmetry in pulse-coupled oscillators with delay. Phys Rev E Stat Nonlin Soft Matter Phys 79(6 Pt 2): 065203.

We studied the dynamics of synchronization in asymmetrically coupled neural oscillators with time delay. Stability analysis revealed that symmetric excitatory coupling results in synchrony at multiple phase relations. Asymmetry yields two saddle-node bifurcations of the stable states when coupling is asymmetric. By contrast, with inhibitory coupling only in phase or antiphase is stable as long as coupling is symmetric. Otherwise, these stable states shift or even vanish. The reduced bistability range suggests the beneficial role of asymmetric coupling for reliable neural information transfer.

78. NR van Ulzen, CJ Lamoth, A Daffertshofer, GR Semin and PJ Beek (2008). Characteristics of instructed and uninstructed interpersonal coordination while walking side-by-side. Neuroscience Letters 432(2): 88.

We examined how people synchronize their leg movements while walking side-by-side on a treadmill. Walker pairs were either instructed to synchronize their steps in in-phase or in antiphase or received no coordination instructions. Frequency and phase analysis revealed that instructed in-phase and antiphase coordination were equally stable and independent of walking speed and the difference in individually preferred stride frequencies. Without instruction we found episodes of frequency locking in three pairs and episodes of phase locking in four pairs, albeit not always at (or near) 0 degrees or 180 degrees. Again, we found no difference in the stability of in-phase and antiphase coordination and no systematic effects of walking speed and the difference in individually preferred stride frequencies. These results suggest that the Haken-Kelso-Bunz model for rhythmic interlimb coordination does not apply to interpersonal coordination during gait in a straightforward manner. When the typically involved parameter constraints are relaxed, however, this model may largely account for the observed dynamical characteristics.

77. S Curilef, AR Plastino, RS Wedemann and A Daffertshofer (2008). Landauer’s principle and non-equilibrium statistical ensembles. Physics Letters A 372(14): 2341.

Landauer’s principle is fundamental for the physics of information. It establishes the least amount of energy that needs to be dissipated in order to erase a bit of information. Using the Beck-Cohen representation of statistical ensemble distributions, we explore an extension of Landauer’s principle to systems out of equilibrium.

76. A Daffertshofer (2008). How do ensembles occupy space? European Physical Journal-Special Topics 157: 79.

To find an answer to the title question, an attractiveness function between agents and locations is introduced yielding a phenomenological but generic model for the search for optimal distributions of agents over space. Agents can be seen as, e.g., members of biological populations like colonies of bacteria, swarms, and so on. The global attractiveness between agents and locations is maximized causing (self-propelled) `motion’ of agents and, eventually, distinct distributions of agents over space. At the same token spontaneous changes or `decisions’ are realized via competitions between agents as well as between locations. Hence, the model’s solutions can be considered a sequence of decisions of agents during their search for a proper location. Depending on initial conditions both optimal as well as suboptimal configurations can be reached. For the latter early decision-making are important for avoiding possible conflicts: if the proper moment is missed, then only a few agents can find an optimal solution. Indeed, there is a delicate interplay between the values of the attractiveness function and the constraints as can be expressed by distinct terms of a potential function containing different Lagrange parameters. The model should be viewed as a top-down approach as it describes the dynamics of order parameters, i.e. macroscopic variables that reflect affiliations between agents and locations. The dynamics, however, is modified via so-called cost functions that are interpreted in terms of affinity levels. This interpretation can be seen as an original step towards an understanding of the dynamics at the underlying microscopic level. When focusing on the agent, one may say that the dynamics of an order parameter shows the evolution of an agent’s intrinsic `map’ for solving the problem of space occupation. Importantly, the dynamics does not necessarily distinguish between evolving (or moving) agents and evolving (or moving) locations though agents are more likely to be actors than the locations. Put differently, an order parameter describes an internal map which is linked to the expectation of an agent to find a certain location. Owing to the dynamical representation, we can therefore follow up the change of these maps over time leading from uncertainty to certainty.

75. S Houweling, A Daffertshofer, BW van Dijk and PJ Beek (2008). Neural changes induced by learning a challenging perceptual-motor task. NeuroImage 41(4): 1395.

We studied the neural changes accompanying the learning of a perceptual-motor task involving polyrhythmic bimanual force production. Motor learning was characterized by an increase in stability of performance. To assess after-effects in the corresponding neural network, magnetoencophalographic and electromyographic signals were recorded and analyzed in terms of (event-related) amplitude changes and synchronization patterns. The topology of the network was first identified using a beamformer analysis, which revealed differential effects of activation in cortical areas and cerebellar hemispheres. We found event-related (de-)synchronization of beta-activity in bilateral cortical motor areas and alpha-modulations in the cerebellum. The alpha-modulation increased after learning and, simultaneously, the bilateral M1 coupling increased around the movement frequency reflecting improved motor timing. Furthermore, the inter-hemispheric gamma-synchronization between primary motor areas decreased, which may reflect a reduced attentional demand after learning.

74. A Plastino and A Daffertshofer (2008). Classical typicality of the canonical distribution. Europhysics Letters 84(3): 30006.

We consider the typicality of the canonical ensemble’s probability distribution from a classical perspective, resuming recent discussions on quantum-mechanical aspects of canonical typicality. In the conventional derivation of the classical canonical distribution for a system S that is weakly coupled to a heat bath B, it is assumed that the composite S + B is represented by the microcanonical ensemble i.e., by a uniform probability distribution on an energy shell of the composite S + B. Here we show that for a very large heat bath almost all probability distributions defined on this energy shell behave according to the microcanonical ensemble, yielding a marginal probability distribution for S of the canonical form. Consequently, the classical canonical distribution can be regarded as much more "typical" than suggested by the standard derivation.

73. MM Ponsen, A Daffertshofer, E Wolters, PJ Beek and HW Berendse (2008). Impairment of complex upper limb motor function in de novo Parkinson’s disease. Parkinsonism & Related Disorders 14(3): 199.

The aim of the present study was to evaluate complex upper limb motor function in newly diagnosed, untreated Parkinson’s disease (PD) patients. Four different unimanual upper limb motor tasks were applied to 13 newly diagnosed, untreated PD patients and 13 age- and sex-matched controls. In a handwriting task, PD patients had significantly reduced sentence length and writing velocity, and decreasing letter height in the course of writing. Furthermore, PD patients performed an aiming task slower with than without target, and showed increased transposition in a pointing task. The results of this study extend previous observations of impaired complex upper limb movements to newly diagnosed, untreated PD patients.

72. A van Londen, M Herwegh, CH van der Zee, A Daffertshofer, CA Smit, A Niezen and TW Janssen (2008). The effect of surface electric stimulation of the gluteal muscles on the interface pressure in seated people with spinal cord injury. Archives of Physical Medicine and Rehabilitation 89(9): 1724.

OBJECTIVE: To study effects of surface electric stimulation of the gluteal muscles on the interface pressure in seated persons with spinal cord injury (SCI). DESIGN: One session in which alternating and simultaneous surface electric stimulation protocols were applied in random order. SETTING: Research laboratory of a rehabilitation center. PARTICIPANTS: Thirteen subjects with SCI. INTERVENTION: Surface electric stimulation of the gluteal muscles. MAIN OUTCOME MEASURES: Interface pressure, maximum pressure, pressure spread, and pressure gradient for the stimulation measurement. Variables were compared using 2-tailed paired t tests. RESULTS: Alternating and simultaneous stimulation protocol caused a significant (P<.01) decrease in interface pressure (-17+/-12 mmHg, -19+/-14 mmHg) and pressure gradient (-12+/-11 mmHg, -14+/-12 mmHg) during stimulation periods compared with rest periods. There was no significant difference in effects between the 2 protocols. CONCLUSIONS: Surface electric stimulation of the gluteal muscles in persons with SCI causes a decrease in interface pressure. This might restore blood flow in compressed tissue and help prevent pressure ulcers.

71. TW Boonstra, A Daffertshofer, JC van Ditshuizen, MR van den Heuvel, C Hofman, NW Willigenburg and PJ Beek (2008). Fatigue-related changes in motor-unit synchronization of quadriceps muscles within and across legs. Journal of Electromyography and Kinesiology 18(5): 717.

Two experiments were conducted to examine effects of muscle fatigue on motor-unit synchronization of quadriceps muscles (rectus femoris, vastus medialis, vastus lateralis) within and between legs. We expected muscle fatigue to result in an increased common drive to different motor units of synergists within a leg and, hence, to increased synchronization, i.e., an increased coherence between corresponding surface EMGs. We further expected fatigue-related motor overflow to cause motor-unit synchronization of homologous muscles of both legs, although to a lesser extent than for synergists within a leg. In the first experiment, different levels of fatigue were induced by varying posture (knee angle), whereas in the second experiment fatigue was induced in a fixed posture by instructing participants to produce different force levels. EMG coherence was found in two distinct frequency bands (6-11 and 13-18 Hz) and was higher within a leg than between legs. The fatigue-related increase of 6-11 Hz inter-limb synchronization resembled the increased motor overflow during unimanual contractions and thus hinted at an increase in bilateral coupling. Synchronization at 13-18 Hz was clearly different and appeared to be related to posture.

70. TW Boonstra, M Roerdink, A Daffertshofer, B van Vugt, G van Werven and PJ Beek (2008). Low-alcohol doses reduce common 10- to 15-Hz input to bilateral leg muscles during quiet standing. Journal of Neurophysiology 100(4): 2158.

The effects of low doses of alcohol on neural synchronization in muscular activity were investigated in ten participants during quiet standing with eyes open or closed. We focused on changes in common input to bilateral motor unit pools as evident in surface electromyographic (EMG) recordings of lower leg extensor and flexor muscles. The extensor muscles exhibited bilateral synchronization in two distinct frequency bands (i.e., 0-5 and 10-15 Hz), whereas synchronization between flexor muscles was minimal. As expected, alcohol ingestion affected postural sway, yielding increased sway at higher blood-alcohol levels. Whereas vision affected bilateral synchronization only at 0-5 Hz, alcohol ingestion resulted in a progressive decrease of synchronization at 10-15 Hz between the EMG activities of the extensor muscles. The decrease in common bilateral input is most likely related to reduced reticulospinal activity with alcohol ingestion.

69. AM van Mourik, A Daffertshofer and PJ Beek (2008). Extracting global and local dynamics from the stochastics of rhythmic forearm movements. Journal of Motor Behavior 40(3): 214.

The authors examined the dynamics governing rhythmic forearm movements that 9 participants performed under a variety of task constraints by using a generic, unbiased analysis technique for extracting the drift coefficients of Fokker-Planck equations from stochastic data. From those coefficients, they reconstructed and analyzed vector fields and phase portraits to identify characteristic, task-dependent kinematic and dynamical features. They first directly estimated the parameters of weakly nonlinear self-sustaining oscillators from the extracted drift coefficients. The estimated parameters that the authors had selected instinctively and then particularized by using averaging methods largely confirmed previously derived limit-cycle models. Next, they ventured beyond limit-cycle models to examine global and local dynamical features that those models cannot adequately address, particularly task-dependent changes in flow strength and curvature and distinct dynamical features associated with flexion and extension. The authors argue that those features should be focal points of researchers’ future modeling efforts to formulate a more adequate and encompassing account of the dynamics of rhythmic movement.

68. D Staudenmann, A Daffertshofer, I Kingma, DF Stegeman and JH van Dieen (2007). Independent component analysis of high-density electromyography in muscle force estimation. IEEE Transactions On Biomedical Engineering 54(4): 751.

Accurate force prediction from surface electromyography (EMG) forms an important methodological challenge in biomechanics and kinesiology. In a previous study (Staudenmann et al., 2006), we illustrated force estimates based on analyses lent from multivariate statistics. In particular, we showed the advantages of principal component analysis (PCA) on monopolar high-density EMG (HD-EMG) over conventional electrode configurations. In the present study, we further improve force estimates by exploiting the correlation structure of the HD-EMG via independent component analysis (ICA). HD-EMG from the triceps brachii muscle and the extension force of the elbow were measured in 11 subjects. The root mean square difference (RMSD) and correlation coefficients between predicted and measured force were determined. Relative to using the monopolar EMG data, PCA yielded a 40% reduction in RMSD. ICA yielded a significant further reduction of up to 13% RMSD. Since ICA improved the PCA-based estimates, the independent structure of EMG signals appears to contain relevant additional information for the prediction of muscle force from surface HD-EMG.

67. A Daffertshofer and CJ Stam (2007). Influences of volume conduction on phase distributions. International Congress Series 1300: 209.

We investigated the influence of common sources on the distribution of relative phases between encephalographic signals. We found that common sources may only change the real part of the correlation between two analytical signals. This result implies that, in general, volume conduction has only symmetric effects on the (relative) phase distribution in that unimodal phase distributions become centered around 0 or ± π. Hence, asymmetries and/or shifts of the relative phase distribution indicate non-trivial correlations in the generating sources

66. TW Boonstra, A Daffertshofer, E van As, S van der Vlugt and PJ Beek (2007). Bilateral motor unit synchronization is functionally organized. Experimental Brain Research 178(1): 79.

To elucidate the neural interactions underlying bimanual coordination, we investigated in 11 participants the bilateral coupling of homologous muscles in an isometric force production task involving fatiguing elbow flexion and extension. We focused on changes in motor unit (MU) synchronization as evident in EMG recordings of relevant muscles. In contrast to a related study on leg muscles, the arm muscles did not exhibit MU synchronization around 16 Hz, consistent with our hypothesis that 16 Hz MU synchronization is linked to balance maintenance. As expected, bilateral MU synchronization was apparent between 8 and 12 Hz and increased with fatigue and more strongly so for extensor than for flexor muscles. MU synchronization in that frequency band is interpreted in terms of common bilateral input and substantiates the idea that common input is functionally organized. Since these findings are consistent with the literature on mirror movements, they suggest that both phenomena may be related.

65. TW Boonstra, JF Stins, A Daffertshofer and PJ Beek (2007). Effects of sleep deprivation on neural functioning: an integrative review. Cellular and Molecular Life Sciences 64(7-8): 934.

Sleep deprivation has a broad variety of effects on human performance and neural functioning that manifest themselves at different levels of description. On a macroscopic level, sleep deprivation mainly affects executive functions, especially in novel tasks. Macroscopic and mesoscopic effects of sleep deprivation on brain activity include reduced cortical responsiveness to incoming stimuli, reflecting reduced attention. On a microscopic level, sleep deprivation is associated with increased levels of adenosine, a neuromodulator that has a general inhibitory effect on neural activity. The inhibition of cholinergic nuclei appears particularly relevant, as the associated decrease in cortical acetylcholine seems to cause effects of sleep deprivation on macroscopic brain activity. In general, however, the relationships between the neural effects of sleep deprivation across observation scales are poorly understood and uncovering these relationships should be a primary target in future research.

64. F Buma, A Daffertshofer, G Kwakkel and EEH Van Wegen (2007). External cueing and activity in the Parkinsonian brain: Development of a motor paradigm. Parkinsonism & Related Disorders 13: S180.

Objective: External rhythms (cues) are known for their capacity to improve motor performance (e.g. gait) in patients with Parkinson’s disease (PD). The neurophysiological mechanisms behind this phenomenon are largely unidentified. Nonetheless it has been suggested that external cueing may allow for bypassing deficient brain circuitry. In a MEG pilot study with healthy subjects, we developed a protocol to investigate the brain activity accompanying self-paced and externally paced hand movements by means of its location and timing. The results show that the protocol can be readily applied to study brain dynamics during cued movements in PD patients. Method: Subjects (N = 4) performed 3 conditions under rhythmic somato-sensory stimulation (80 bpm) in the MEG: move on cue, feel the cue, and move without cue, with restperiods before and after. The movement task involved rhythmically squeezing a rubber balloon. Synthetic aperture magnetometry (SAM) was used to localize sources of motor-related brain activity. In two sources (~ M1 left and right) we found altered brain activity by comparing first and last resting state. Changes occurred primarily in the mu (7−11 Hz) and beta (13−30 Hz) frequency range. Results: The movement protocol was clearly visible in the spectrograms of motor cortex activity. Power in the beta and mu frequency bands decreased during cued movement compared to rest conditions. In addition, a significant increase of power in mu and beta bands in the final rest period compared to the initial baseline was observed. Conclusion: The power increase after a bout of movement activity suggests that rhythmic movement alone causes a (transient) increase in brain resting state in the healthy brain. Comparing these results with pathological data may help to unravel the dynamics of the (cortical) organization during voluntary cued and self-paced movement in PD.

63. A Daffertshofer, TW Boonstra and PJ Beek (2007). Cortical beta synchronization is related to low-order motor parameters. International Congress Series 1300: 329.

To study the possible functional role of event-related de-synchronization in the beta band we altered various motor parameters in order to challenge the level of synchronization. We recorded whole-head MEG, bilateral EMG, and force during a rhythmic motor task, in which participants had to produce isometric forces paced by acoustic stimuli. Movement rate, force level, and task difficulty (synchronization vs. syncopation) were manipulated and changes in synchronization were analyzed. The results indicated that beta amplitude was mainly affected by ‘low-order’ motor parameters, such as force level and movement rate.

62. A Daffertshofer and AR Plastino (2007). Forgetting and gravitation: From Landauer’s principle to Tolman’s temperature. Physics Letters A 362(4): 243.

The erasure of a bit of information requires the dissipation of a minimal amount of energy as being formulated in Landauer’s principle. We show that for an information processing device in a static gravitational field Landauer’s lower energy bound is determined by Tolman’s temperature relation.

61. JC Dessing, A Daffertshofer, CE Peper and PJ Beek (2007). Pattern stability and error correction during in-phase and antiphase four-ball juggling. Journal of Motor Behavior 39(5): 433.

The authors studied pattern stability and error correction during in-phase and antiphase 4-ball fountain juggling. To obtain ball trajectories, they made and digitized high-speed film recordings of 4 highly skilled participants juggling at 3 different heights (and thus different frequencies). From those ball trajectories, the authors determined and analyzed critical events (i.e., toss, zenith, catch, and toss onset) in terms of variability of point estimates of relative phase and temporal correlations. Contrary to common findings on basic instances of rhythmic interlimb coordination, in-phase and antiphase patterns were equally variable (i.e., stable). Consistent with previous findings, however, pattern stability decreased with increasing frequency. In contrast to previous results for 3-ball cascade juggling, negative lag-one correlations for catch-catch intervals were absent, but the authors obtained evidence for error corrections between catches and toss onsets. That finding may have reflected participants’ high skill level, which yielded smaller errors that allowed for corrections later in the hand cycle.

60. S Houweling, A Daffertshofer, BW van Dijk and PJ Beek (2007). Synchronization in perceptual motor integration. International Congress Series 1300: 333.

We studied changes in neural synchronization during the learning and stabilization in a perceptual motor task involving polyrhythmic bimanual force production. Effects of inter-hemispheric synchronization, captured in terms of changes in time-resolved phase synchrony, were clearly related to the stability of motor performance and could be interpreted as a result of altered transcallosal crosstalk.

59. AA Post, G de Groot, A Daffertshofer and PJ Beek (2007). Pumping a playground swing. Motor Control 11(2): 136.

In mechanical studies of pumping a playground swing, two methods of energy insertion have been identified: parametric pumping and driven oscillation. While parametric pumping involves the systematic raising and lowering of the swinger’s center of mass (CM) along the swing’s radial axis (rope), driven oscillation may be conceived as rotation of the CM around a pivot point at a fixed distance to the point of suspension. We examined the relative contributions of those two methods of energy insertion by inviting 18 participants to pump a swing from standstill and by measuring and analyzing the swing-swinger system (defined by eight markers) in the sagittal plane. Overall, driven oscillation was found to play a major role and parametric pumping a subordinate role, although the relative contribution of driven oscillation decreased as swinging amplitude increased, whereas that of parametric pumping increased slightly. Principal component analysis revealed that the coordination pattern of the swing-swinger system was largely determined (up to 95%) by the swing’s motion, while correlation analysis revealed that (within the remaining 5% of variance) trunk and leg rotations were strongly coupled.

58. CJ Stam, G Nolte and A Daffertshofer (2007). Phase lag index: Assessment of functional connectivity from multi channel EEG and MEG with diminished bias from common sources. Human Brain Mapping 28: 1178.

OBJECTIVE: To address the problem of volume conduction and active reference electrodes in the assessment of functional connectivity, we propose a novel measure to quantify phase synchronization, the phase lag index (PLI), and compare its performance to the well-known phase coherence (PC), and to the imaginary component of coherency (IC). METHODS: The PLI is a measure of the asymmetry of the distribution of phase differences between two signals. The performance of PLI, PC, and IC was examined in (i) a model of 64 globally coupled oscillators, (ii) an EEG with an absence seizure, (iii) an EEG data set of 15 Alzheimer patients and 13 control subjects, and (iv) two MEG data sets. RESULTS: PLI and PC were more sensitive than IC to increasing levels of true synchronization in the model. PC and IC were influenced stronger than PLI by spurious correlations because of common sources. All measures detected changes in synchronization during the absence seizure. In contrast to PC, PLI and IC were barely changed by the choice of different montages. PLI and IC were superior to PC in detecting changes in beta band connectivity in AD patients. Finally, PLI and IC revealed a different spatial pattern of functional connectivity in MEG data than PC. CONCLUSION: The PLI performed at least as well as the PC in detecting true changes in synchronization in model and real data but, at the same token and like-wise the IC, it was much less affected by the influence of common sources and active reference electrodes.

57. TW Boonstra, A Daffertshofer, M Breakspear and PJ Beek (2007). Multivariate time-frequency analysis of electromagnetic brain activity during bimanual motor learning. NeuroImage 36(2): 370.

Although the relationship between brain activity and motor performance is reasonably well established, the manner in which this relationship changes with motor learning remains incompletely understood. This paper presents a study of cortical modulations of event-related beta activity when participants learned to perform a complex bimanual motor task: 151 channel MEG data were acquired from nine healthy adults whilst learning a bimanual 3:5 polyrhythm. Sources of MEG activity were determined by means of synthetic aperture magnetometry that yielded locations and time courses of beta activities. The relationship between changes in performance and corresponding changes in event-related power were assessed using partial least squares. Behavioral data revealed that participants successfully learned to perform the 3:5 polyrhythm and that performance improvement was mainly achieved through the proper timing of the finger producing the slow rhythm. We found event-related modulation of beta power in the contralateral motor cortex that was inversely related to force output. The degree of beta modulation increased during the experiment – although the force level remained constant – and was positively correlated with motor performance, in particular for the motor cortex contralateral to the slow hand. These electrophysiological findings support the view that activity in motor cortex co-varies closely with behavioral changes over the course of learning.

56. AN Vardy, A Daffertshofer, A Ridderikhoff and PJ Beek (2007). Differential after-effects of bimanual activity on mirror movements. Neuroscience Letters 416(2): 117.

Using a rhythmic isometric force production paradigm, we investigated the after-effects of in-phase and antiphase bimanual performance on the unintended recruitment of the homologous muscles of the opposite limb during subsequent performance of tasks that were unimanual by design. Electromyograms obtained from the muscles of the opposite limb were analyzed in terms of their amplitude and the distribution of their phase relative to that of the intended movements. Preceding bimanual activity had distinct effects on the relative phase (mean and uniformity) of the structured electromyograms. These were particularly pronounced following performance of the in-phase pattern. These findings are discussed in terms of interhemispheric excitation and inhibition.

55. CJ Lamoth, A Daffertshofer, OG Meijer and PJ Beek (2006). How do persons with chronic low back pain speed up and slow down? Trunk-pelvis coordination and lumbar erector spinae activity during gait. Gait Posture 23(2): 230. doi: S0966-6362(05)00029-9 [pii] 10.1016/j.gaitpost.2005.02.006

In healthy walking, the timing between trunk and pelvic rotations, as well as erector spinae (ES) activity varies systematically with walking velocity, whereas a comparable velocity-dependent adaptation of trunk-pelvis coordination is often reduced or absent in persons with low back pain (LBP). Based on the hypothesis that trunk-pelvis coordination is linked to overall gait stability, persons with LBP can be expected to have difficulties in dealing with perturbations. We examined the ability of 12 persons with LBP and 12 controls to adapt trunk and pelvis rotations and ES activity to sudden changes in velocity. 3D angular movements of thoracic, lumbar, and pelvic segments and surface EMG were recorded during treadmill walking at six different velocities, which increased or decreased unexpectedly. Relative phases of segmental rotations were determined and (in-)variant properties of kinematics and ES activity were studied using principal component analysis. Compared to healthy controls, persons with LBP exhibited a reduced ability to adapt trunk-pelvis coordination and ES muscle activity to changes in velocity. Altered coordination and muscular control may reflect an attempt to stabilise the spine and prevent the occurrence of unexpected perturbations. The assessment of gait patterns in terms of coordination may help clinicians to quantify movement impairments and may suggest interventions aimed at facilitating the emergence of desired coordination patterns.

54. TW Boonstra, A Daffertshofer, CE Peper and PJ Beek (2006). Amplitude and phase dynamics associated with acoustically paced finger tapping. Brain Research 1109(1): 60. doi: S0006-8993(06)01801-4 [pii] 10.1016/j.brainres.2006.06.039

To gain insight into the brain activity associated with the performance of an acoustically paced synchronization task, we analyzed the amplitude and phase dynamics inherent in magnetoencephalographic (MEG) signals across frequency bands in order to discriminate between evoked and induced responses. MEG signals were averaged with respect to motor and auditory events (tap and tone onsets). Principal component analysis was used to compare amplitude and phase changes during listening and during paced and unpaced tapping, allowing a separation of brain activity related to motor and auditory processes, respectively. Motor performance was accompanied by phasic amplitude changes and increased phase locking in the beta band. Auditory processing of acoustic stimuli resulted in a simultaneous increase of amplitude and phase locking in the theta and alpha band. The temporal overlap of auditory-related amplitude changes and phase locking indicated an evoked response, in accordance with previous studies on auditory perception. The temporal difference of movement-related amplitude and phase dynamics in the beta band, on the other hand, suggested a change in ongoing brain activity, i.e., an induced response supporting previous results on motor-related brain dynamics in the beta band.

53. AM van Mourik, A Daffertshofer and PJ Beek (2006). Estimating Kramers-Moyal coefficients in short and non-stationary data sets. Physics Letters A 351(1-2): 13.

To reliably estimate the dynamics of diffusive Markov processes, we combine statistically independent empirical data. Since commutative statistics do not affect fundamental Markov properties, they provide robust estimators for Kramers–Moyal coefficients even when registration time and sampling frequency of individual recordings are rather limited. We also show how the results of the method can be further improved and extended in order to apply it in the non-stationary regime.

52. CJ Lamoth, OG Meijer, A Daffertshofer, PI Wuisman and PJ Beek (2006). Effects of chronic low back pain on trunk coordination and back muscle activity during walking: changes in motor control. European Spine Journal 15(1): 23. doi: 10.1007/s00586-004-0825-y

Low back pain (LBP) is often accompanied by changes in gait, such as a decreased (preferred) walking velocity. Previous studies have shown that LBP diminishes the normal velocity-induced transverse counter-rotation between thorax and pelvis, and that it globally affects mean erector spinae (ES) activity. The exact nature and causation of these effects, however, are not well understood. The aim of the present study was to examine in detail the effect of walking velocity on global trunk coordination and ES activity as well as their variability to gain further insights into the effects of non-specific LBP on gait. The study included 19 individuals with non-specific LBP and 14 healthy controls. Gait kinematics and ES activity were recorded during treadmill walking at (1) a self-selected (comfortable) velocity, and (2) sequentially increased velocities from 1.4 up to maximally 7.0 km/h. Pain intensity, fear of movement and disability were measured before the experiment. The angular movements of thorax, lumbar and pelvis were recorded in three dimensions. ES activity was recorded with pairs of surface electrodes. Trunk-pelvis coordination and mean amplitude of ES activity were analyzed. In addition, invariant and variant properties of trunk kinematics and ES activity were studied using principal component analysis (PCA). Comfortable walking velocity was significantly lower in the LBP participants. In the transverse plane, the normal velocity-induced change in pelvis-thorax coordination from more in-phase to more antiphase was diminished in the LBP participants, while lumbar and pelvis rotations were more in-phase compared to the control group. In the frontal plane, intersegmental timing was more variable in the LBP than in the control participants, with additional irregular movements of the thorax. Rotational amplitudes were not significantly different between the LBP and control participants. In the LBP participants, the pattern of ES activity was affected in terms of increased (residual) variability, timing deficits, amplitude modifications and frequency changes. The gait of the LBP participants was characterized by a more rigid and less variable kinematic coordination in the transverse plane, and a less tight and more variable coordination in the frontal plane, accompanied by poorly coordinated activity of the lumbar ES. Pain intensity, fear of movement and disability were all unrelated to the observed changes in coordination, suggesting that the observed changes in trunk coordination and ES activity were a direct consequence of LBP per se. Clinically, the results imply that conservative therapy should consider gait training as well as exercises aimed at improving both intersegmental and muscle coordination.

51. MM Ponsen, A Daffertshofer, E van den Heuvel, E Wolters, PJ Beek and HW Berendse (2006). Bimanual coordination dysfunction in early, untreated Parkinson’s disease. Parkinsonism Relat Disord 12(4): 246. doi: S1353-8020(06)00028-9 [pii] 10.1016/j.parkreldis.2006.01.006

Bimanual coordination involves the simultaneous performance of either symmetrical (in-phase) or asymmetrical (anti-phase) movements with both hands and is known to be impaired in Parkinson’s disease (PD). At present, it is unclear whether this aspect of motor function is already impaired in early stage, untreated PD patients. Therefore, we investigated the accuracy of bimanual coordination in 13 early stage, untreated PD patients and 13 age- and sex-matched healthy controls. Each subject performed bimanual coordination tasks at two different movement frequencies (1 and 1.75 Hz) and with two different phase relationships (in-phase and anti-phase). The percentage of unsuccessful trials (as a measure of overall task performance) in PD patients was significantly higher than in healthy subjects. PD patients performed high frequency in-phase and anti-phase bimanual coordination tasks less accurately with their non-dominant hand than healthy subjects. Furthermore, PD patients had more difficulty than healthy subjects in maintaining a constant phase relationship between the hands in the anti-phase condition at low movement frequency. This study demonstrates that bimanual coordination dysfunction is a very early sign of PD. Bimanual coordination tasks, in particular those involving high frequency anti-phase movements, might prove useful in the early diagnosis of PD.

50. M Roerdink, M De Haart, A Daffertshofer, SF Donker, AC Geurts and PJ Beek (2006). Dynamical structure of center-of-pressure trajectories in patients recovering from stroke. Experimental Brain Research 174(2): 256. doi: 10.1007/s00221-006-0441-7

In a recent study, De Haart et al. (Arch Phys Med Rehabil 85:886-895, 2004) investigated the recovery of balance in stroke patients using traditional analyses of center-of-pressure (COP) trajectories to assess the effects of health status, rehabilitation, and task conditions like standing with eyes open or closed and standing while performing a cognitive dual task. To unravel the underlying control processes, we reanalyzed these data in terms of stochastic dynamics using more advanced analyses. Dimensionality, local stability, regularity, and scaling behavior of COP trajectories were determined and compared with shuffled and phase-randomized surrogate data. The presence of long-range correlations discarded the possibility that the COP trajectories were purely random. Compared to the healthy controls, the COP trajectories of the stroke patients were characterized by increased dimensionality and instability, but greater regularity in the frontal plane. These findings were taken to imply that the stroke patients actively (i.e., cognitively) coped with the stroke-induced impairment of posture, as reflected in the increased regularity and decreased local stability, by recruiting additional control processes (i.e., more degrees of freedom) and/or by tightening the present control structure while releasing non-essential degrees of freedom from postural control. In the course of rehabilitation, dimensionality stayed fairly constant, whereas local stability increased and regularity decreased. The progressively less regular COP trajectories were interpreted to indicate a reduction of cognitive involvement in postural control as recovery from stroke progressed. Consistent with this interpretation, the dual task condition resulted in less regular COP trajectories of greater dimensionality, reflecting a task-related decrease of active, cognitive contributions to postural control. In comparison with conventional posturography, our results show a clear surplus value of dynamical measures in studying postural control.

49. D Staudenmann, I Kingma, A Daffertshofer, DF Stegeman and JH van Dieen (2006). Improving EMG-based muscle force estimation by using a high-density EMG grid and principal component analysis. IEEE Transactions On Biomedical Engineering 53(4): 712.

The accuracy of predictions of muscle force based on electromyography (EMG) is an important issue in biomechanics and kinesiology. Since human skeletal muscles show a high diversity and heterogeneity in their fiber architecture, it is difficult to properly align electrodes to the muscle fiber direction. Against this background, we analyzed the effect of different bipolar configuration directions on EMG-based force estimation. In addition, we investigated whether principal component analysis (PCA) can improve this estimation. High-density surface-EMG from the triceps brachii muscle and the extension force of the elbow were measured in 11 subjects. The root mean square difference (RMSD) between predicted and measured force was determined. We found the best bipolar configuration direction to cause a 13% lower RMSD relative to the worst direction. Optimal results were obtained with electrodes aligned with the expected main muscle fiber direction. We found that PCA reduced RMSD by about 40% compared to conventional bipolar electrodes and by about 12% compared to optimally aligned multiple bipolar electrodes. Thus, PCA contributes to the accuracy of EMG-based estimation of muscle force when using a high-density EMG grid.

48. AM van Mourik, A Daffertshofer and PJ Beek (2006). Deterministic and stochastic features of rhythmic human movement. Biological Cybernetics 94(3): 233.

The dynamics of rhythmic movement has both deterministic and stochastic features. We advocate a recently established analysis method that allows for an unbiased identification of both types of system components. The deterministic components are revealed in terms of drift coefficients and vector fields, while the stochastic components are assessed in terms of diffusion coefficients and ellipse fields. The general principles of the procedure and its application are explained and illustrated using simulated data from known dynamical systems. Subsequently, we exemplify the method’s merits in extracting deterministic and stochastic aspects of various instances of rhythmic movement, including tapping, wrist cycling and forearm oscillations. In particular, it is shown how the extracted numerical forms can be analysed to gain insight into the dependence of dynamical properties on experimental conditions.

47. A Ridderikhoff, A Daffertshofer, CL Peper and PJ Beek (2005). Mirrored EMG activity during unimanual rhythmic movements. Neuroscience Letters 381(3): 228.

We studied instances of mirror movements–in the form of coherent EMG activity of the muscles in the arm not intended to move–during the performance of a unimanual rhythmic task in healthy adults. Epochs of involuntary muscle activity were detected and analyzed using time-resolved spectral methods. The observed frequency and phase locking between EMG patterns derived from homologous extensor muscles indicated the presence of neural cross-talk, which is relevant to the study of interlimb coordination.

46. SF Donker, A Daffertshofer and PJ Beek (2005). Effects of velocity and limb loading on the coordination between limb movements during walking. Journal of Motor Behavior 37(3): 217.

The authors investigated the effects of velocity (increasing from 0.5 to 5.0 km/hr in steps of 0.5 km/hr) and limb loading on the coordination between arm and leg movements during treadmill walking in 7 participants. Both the consistency of the individual limb movements and the stability of their coordination increased with increasing velocity; the frequency coordination between arm and leg movements was 2:1 at the lower velocities and 1:1 at the higher velocities. The mass manipulation affected the individual limb movements but not their coordination, indicating that a stable walking pattern was preserved. The results differed qualitatively from those obtained in studies on bimanual interlimb coordination, implying that the dynamical principles identified therein are not readily applicable to locomotion.

45. BPLM den Brinker and A Daffertshofer (2005). The IDED method to measure the visual accessibility of the built environment. International Congress Series 1282: 992.

In view of an increasing support for the “human right” of low vision people to use vision for independent traveling, architects have to reckon with this target group’s visual needs when planning and designing. We recommend a visual acuity > 3/60 as the premier inclusion criterion to define the target group ‘low vision’ for whom principles of ‘design for all’ can be applied. An image processing method is presented to illustrate what is visible for people belonging to the target group. The method incorporates ‘image degeneration’ and ‘edge detection’. The method is demonstrated in an analysis of a hazardous stairway descent situation.

44. A Daffertshofer, CE Peper and PJ Beek (2005). Stabilization of bimanual coordination due to active interhemispheric inhibition: a dynamical account. Biological Cybernetics 92(2): 101.

Based on recent brain-imaging data and congruent theoretical insights, a dynamical model is derived to account for the patterns of brain activity observed during stable performance of bimanual multifrequency patterns, as well as during behavioral instabilities in the form of phase transitions between such patterns. The model incorporates four dynamical processes, defined over both motor and premotor cortices, which are coupled through inhibitory and excitatory inter- and intrahemispheric connections. In particular, the model underscores the crucial role of interhemispheric inhibition in reducing the interference between disparate frequencies during stable performance, as well as the failure of this reduction during behavioral transitions. As an aside, the model also accounts for in- and antiphase preferences during isofrequency movements. The viability of the proposed model is illustrated by magnetoencephalographic signals that were recorded from an experienced subject performing a polyrhythmic tapping task that was designed to induce transitions between multifrequency patterns. Consistent with the model’s dynamics, contra- and ipsilateral cortical areas of activation were frequency- and phase-locked, while their activation strength changed markedly in the vicinity of transitions in coordination.

43. TW Boonstra, A Daffertshofer and PJ Beek (2005). Effects of sleep deprivation on event-related fields and alpha activity during rhythmic force production. Neuroscience Letters 388(1): 27.

The influence of sleep deprivation (SD) on event-related fields and the distribution of power over the scalp of MEG imaged brain activity was studied during acoustically paced rhythmic force production. At the behavioral level, SD resulted in a reduction of the lag (negative asynchrony) between produced forces and acoustic stimuli at higher movement tempos. Principal component analysis of the accompanying MEG activity showed that auditory- and motor-evoked fields were attenuated after SD and revealed an anterior shift of power towards more frontal channels. These results were interpreted in terms of a change of central processing of afferent sensory input due to SD.

42. TW Boonstra, HE Clairbois, A Daffertshofer, J Verbunt, BW van Dijk and PJ Beek (2005). MEG-compatible force sensor. Journal of Neuroscience Methods 144(2): 193.

By use of an insulating material we constructed a strain gauge based sensor to measure isometric forces in parallel with magneto-encephalographic recordings (i.e. without interference). The sensor can be used in different geometries to measure force production in different dimensions. Furthermore, it can easily be adapted or modified for specific experimental applications. Finally, on-line processing of the recorded forces, e.g., for the purpose of feedback, can be realized using standard MEG equipment.

41. AV Barbosa, HC Yehia, A Daffertshofer and E Vatikiotis-Bateson (2005). Synthesizing speech acoustics from head and face motion. The Journal of the Acoustical Society of America 117(4): 2542.

This work outlines a quantitative analysis of the relation between speech acoustics and the face and head motions that occur simultaneously [A. V. Barbosa, Ph.D. thesis, Universidade Federal de Minas Gerais, Belo Horizonte, Brazil, 2004]. 2-D motion data is obtained by means of a video camera. An algorithm has been developed for tracking markers on the speaker’s face from the acquired video sequence [A. V. Barbosa, E. Vatikiotis-Bateson, and A. Daffertshofer, in Proceedings of the 8th ICSLP Interspeech 2004, Korea, 2004]. The motion domain is represented by the 2-D marker trajectories, whereas line spectrum pairs (LSP) coefficients and the fundamental frequency F0 are used to represent the speech acoustics domain. Mathematical models are trained to estimate the acoustic parameters (LSPs + F0) from the motion parameters (2-D marker positions). The estimated acoustic parameters are then used to synthesize the acoustic speech signal. Cross-domain analysis for undecomposed (i.e., full head + face) and decomposed (i.e., separated head and face) normalized 2-D motions is performed. Syntheses from each method using intelligibility tests and qualitative comparison of the original and synthesized utterances are being evaluated.

40. A Daffertshofer and AR Plastino (2005). Landauer’s principle and the conservation of information. Physics Letters A 342(3): 213.

Erasure of information requires the dissipation of a minimal amount of energy as being formulated in Landauer’s principle. This profound concept in information processing has recently been derived by use of basic dynamical principles of statistical mechanics. We present an alternative derivation of Landauer’s principle based on dynamical principles and certain properties of the Shannon-Gibbs-Boltzmann entropy, in particular, (sub-)additivity.

39. CL Peper, A Ridderikhoff, A Daffertshofer and PJ Beek (2004). Explanatory limitations of the HKB model: incentives for a two-tiered model of rhythmic interlimb coordination. Human Movement Science 23(5): 673. doi: S0167-9457(04)00085-5 [pii] 10.1016/j.humov.2004.10.007

The HKB model for rhythmic interlimb coordination has highlighted the importance of coordinative stability and loss of stability, and introduced, with this focus, a new set of explanatory constructs. However, the phenomenological character of both parts of this model (i.e., the potential and the associated system of coupled oscillators) precludes an understanding of how the observed stability characteristics are related to more specific (e.g., biomechanical and neurophysiological) aspects of the movement system. A two-tiered model (involving a distinction between ‘neural’ and ‘effector‘ dynamics) is discussed that offers handles for addressing such underpinnings of the identified coordination dynamics. The promise of the model in this regard is illustrated by two recent studies showing how explicit accounts of the effector dynamics may help disclose why (and how) particular properties of the peripheral system affect the overall coordination dynamics.

38. A Wing, A Daffertshofer and J Pressing (2004). Multiple time scales in serial production of force: A tutorial on power spectral analysis of motor variability. Human Movement Science 23(5): 569.

We present a tutorial on a power spectral approach to variability in serial motor performance, describing as a case study two experiments on the form of the variance in two force production tasks. In Experiment I we examine grip force and load force in repetitive unimanual pulling; in Experiment 2, we describe repetitive bimanual pressing. In both experiments log-log plots of power spectral density of peak force of the responses in each stream against frequency (i.e. periodicity or repetition cycle defined with respect to the ordered succession of responses) were approximately linear with negative slopes which varied systematically with test conditions. We propose the two response streams in each experiment are associated with different levels of sustained attention and state a simple model involving summation of moving average processes on multiple time scales as a qualitative account of the changes in 1/f slope.

37. AR Plastino and A Daffertshofer (2004). Liouville dynamics and the conservation of classical information. Physical Review Letters 93(13).

We show that the invariance of entropic distances under Liouville dynamics yields classical analogues of information-related, quantum mechanical impossible operations. By recourse to Fisher’s information measure, we also establish a connection between such classically forbidden operations and statistical estimation theory.

36. R Balasubramaniam, AM Wing and A Daffertshofer (2004). Keeping with the beat: movement trajectories contribute to movement timing. Experimental Brain Research 159(1): 129.

Previous studies of paced repetitive movements with respect to an external beat have either emphasised (a) the form of movement trajectories or (b) timing errors made with respect to the external beat. The question of what kinds of movement trajectories assist timing accuracy has not previously been addressed. In an experiment involving synchronisation or syncopation with an external auditory metronome we show that the nervous system produces trajectories that are asymmetric with respect to time and velocity in the out and return phases of the repeating movement cycle. This asymmetry is task specific and is independent of motor implementation details (finger flexion vs. extension). Additionally, we found that timed trajectories are less smooth (higher mean squared jerk) than unpaced ones. The degree of asymmetry in the flexion and extension movement times is positively correlated with timing accuracy. Negative correlations were observed between synchronisation timing error and the movement time of the ensuing return phase, suggesting that late arrival of the finger is compensated by a shorter return phase and conversely for early arrival. We suggest that movement asymmetry in repetitive timing tasks helps satisfy requirements of precision and accuracy relative to a target event.

35. A Daffertshofer, R Huys and PJ Beek (2004). Dynamical coupling between locomotion and respiration. Biological Cybernetics 90(3): 157.

In search of the formative principles underwriting locomotor-respiratory coupling, we reanalyzed and modeled the data collected by Siegmund and coworkers (1999) on the synchronization of respiration during rowing. Apart from the frequency doubling in respiration reported earlier, detailed time-resolved spectral analyses revealed decreasing stability of entrainment close to abrupt changes in frequency relations as well as switches in the relative phase between respiration and locomotion. A single physiological, albeit mechanically constrained, quantity sufficed to explain the observed frequency and phase locking phenomena: the effective value of oxygen volume in the lungs. The cyclic abdominal pressure modulates the self-sustaining rhythmic respiration, modifies the total lung pressure, and causes (local) maxima at frequency ratios between movement and respiration that are composed of small integers. Hence, optimizing the effective oxygen volume can be seen as the mechanism that drives respiration to synchronize with locomotion.

34. A Daffertshofer, CJ Lamoth, OG Meijer and PJ Beek (2004). PCA in studying coordination and variability: a tutorial. Clinical Biomechanics (Bristol, Avon) 19(4): 415.

OBJECTIVE: To explain and underscore the use of principal component analysis in clinical biomechanics as an expedient, unbiased means for reducing high-dimensional data sets to a small number of modes or structures, as well as for teasing apart structural (invariant) and variable components in such data sets. DESIGN: The method is explained formally and then applied to both simulated and real (kinematic and electromyographic) data for didactical purposes, thus illustrating possible applications (and pitfalls) in the study of coordinated movement. BACKGROUND: In the sciences at large, principal component analysis is a well-known method to remove redundant information in multidimensional data sets by means of mode reduction. At present, principal component analysis is starting to penetrate the fundamental and clinical study of human movement, which amplifies the need for an accessible explanation of the method and its possibilities and limitations. Besides mode reduction, we discuss principal component analysis in its capacity as a data-driven filter, allowing for a separation of invariant and variant properties of coordination, which, arguably, is essential in studies of motor variability. METHODS: Principal component analysis is applied to kinematic and electromyographic time series obtained during treadmill walking by healthy humans. RESULTS: Common signal structures or modes are identified in the time series that turn out to be readily interpretable. In addition, the identified coherent modes are eliminated from the data, leaving a filtered, residual pattern from which useful information may be gleaned regarding motor variability. CONCLUSIONS: Principal component analysis allows for the detection of modes (information reduction) in both kinematic and electromyographic data sets, as well as for the separation of invariant structure and variance in those data sets. RELEVANCE: Principal component analysis can be successfully applied to movement data, both as feature extractor and as data-driven filter. Its potential for the (clinical) study of human movement sciences (e.g., diagnostics and evaluation of interventions) is evident but still largely untapped.

33. R Huys, A Daffertshofer, P Beek, D Sanderson and G Siegmund (2004). Locomotion-respiration coupling: an account of the underlying dynamics. Journal of Applied Physiology 96(6): 2341.

Ventilation and locomotion coupling (entrainment) has been observed and described in rowers during incremental exercise protocols but not during simulated race conditions. The purpose of this descriptive study was to examine ventilation and locomotion entrainment on a breath-by-breath and stroke-by-stroke basis in varsity male rowers during a maximal 2,000-m ergometer test. Eight of eleven rowers entrained ventilation at integral multiples of stroke rate (1:1, 2:1, or 3:1) for at least 120 consecutive seconds, with a 2:1 entrainment pattern being most common. In all 2:1-entrained subjects, inspiration occurred at catch and finish and expiration occurred during the latter portions of drive and recovery. In entrained and unentrained breaths from all rowers, peak flow rates and tidal volumes varied depending on when the breath was initiated during the stroke cycle. Entrained rowers made use of these differences and breathed in a pattern by which they avoided initiating breaths that resulted in reduced tidal volumes. The present data indicated that ventilation was impaired at stroke finish and not at catch, as hypothesized by some previous researchers. Ventilation also appeared to be subordinate to consistent locomotive patterns under race conditions.

32. R Huys, A Daffertshofer and PJ Beek (2004). Multiple time scales and subsystem embedding in the learning of juggling. Human Movement Science 23(3-4): 315.

To gain insight into the multiform dynamics and integration of remote yet pertinent subsystems into the performance of complex perceptual-motor skills, we recently conducted a series of longitudinal and cross-sectional experiments on the acquisition of 3-ball cascade juggling in which we measured, next to the ball trajectories, postural sway, eye and head movements and respiration. The aim of the present paper is to review the main results and theoretical implications of these experimental studies for understanding skill acquisition. As regards the evolution of the quality of the juggling itself, we found that only certain aspects of throwing and catching were adjusted, while the goal behavior of sustained juggling (operationalized as the number of consecutive throws) and the degree of frequency and phase locking between the ball trajectories, indexing pattern stability, increased monotonically. The latter three aspects evolved at different rates, reflecting the existence of a temporal hierarchy in learning. Postural sway exhibited initial manifestations of task-specific, possibly mechanically induced, modes of 3:1 and 3:2 frequency locking with the ball trajectories and only few transitions between those modes. Functional stability appeared to be enhanced during practice by minimizing the sway amplitudes rather than by adjusting the sway dynamics itself. Eye and point-of-gaze movements also showed instances of 3:1 and 3:2 frequency locking with the ball trajectories; especially establishing a 3:1 locking (horizontal eye movements) appeared to be important. Expert behavior suggested that extended practice promotes reliance on multiple sources of information, allowing the proficient juggler to switch adaptively between functional organizations involving distinct perceptual systems. No consistent coordination between breathing and juggling was found. It was concluded that multiform dynamics, involving hierarchically ordered time scales, underlie the acquisition of complex skills and that the subsystems subserving realization of the task goal become assembled and embedded in a task- and subsystem-specific manner.

31. R Huys, A Daffertshofer and PJ Beek (2004). Multiple time scales and multiform dynamics in learning to juggle. Motor Control 8(2): 188.

To study the acquisition of perceptual-motor skills as an instance of dynamic pattern formation, we examined the evolution of postural sway and eye and head movements in relation to changes in performance, while 13 novices practiced 3-ball cascade juggling for 9 weeks. Ball trajectories, postural sway, and eye and head movements were recorded repeatedly. Performance improved exponentially, both in terms of the number of consecutive throws and the degree of frequency and phase locking between the ball trajectories. These aspects of performance evolved at different time scales, indicating the presence of a temporal hierarchy in learning. Postural sway, and eye and head movements were often 3:2 and sometimes 3:1 frequency locked to the ball trajectories. As a rule, the amplitudes of these oscillatory processes decreased exponentially at rates similar to that of the increase in the degree of phase locking between the balls. In contrast, the coordination between these oscillatory processes evolved exponentially at different time scales, apart from some erratic evolutions. Collectively, these findings indicate that skill acquisition in the perceptual-motor domain involves multiple time scales and multiform dynamics, both in terms of the development of the goal behavior itself and the evolution of the processes subserving this goal behavior.

30. CJ Lamoth, A Daffertshofer, OG Meijer, G Lorimer Moseley, PI Wuisman and PJ Beek (2004). Effects of experimentally induced pain and fear of pain on trunk coordination and back muscle activity during walking. Clinical Biomechanics (Bristol, Avon) 19(6): 551.

OBJECTIVE: To examine the effects of experimentally induced pain and fear of pain on trunk coordination and erector spinae EMG activity during gait. DESIGN: In 12 healthy subjects, hypertonic saline (acute pain) and isotonic saline (fear of pain) were injected into erector spinae muscle, and unpredictable electric shocks (fear of impending pain) were presented during treadmill walking at different velocities, while trunk kinematics and EMG were recorded. BACKGROUND: Chronic low back pain patients often have disturbed trunk coordination and enhanced erector spinae EMG while walking, which may either be due to the pain itself or to fear of pain, as is suggested by studies on both low back pain patients and healthy subjects. METHODS: The effects of the aforementioned pain-related manipulations on trunk coordination and EMG were examined. Results. Trunk kinematics was not affected by the manipulations. Induced pain led to an increase in EMG variability and induced fear of pain to a decrease in mean EMG amplitude during double stance. CONCLUSIONS: Induced pain and fear of pain have subtle effects on erector spinae EMG activity during walking while leaving the global pattern of EMG activity and trunk kinematics unaffected. This suggests that the altered gait observed in low back pain patients is probably a complex evolved consequence of a lasting pain, rather than a simple immediate effect. RELEVANCE: Variability of EMG data and kinematics may explain pain-dependent alterations of motor control, which in turn might contribute to a further understanding of the development of movement impairments in low back pain.

29. R Huys, A Daffertshofer and PJ Beek (2003). Learning to juggle: on the assembly of functional subsystems into a task-specific dynamical organization. Biological Cybernetics 88(4): 302.

We examined the development of task-specific couplings among functional subsystems (i.e., ball circulation, respiration, and body sway) when learning to juggle a three-ball cascade, with a focus on learning-induced changes in the coupling between ball movements and respiration and the coupling between ball movements and body sway. Six novices practiced to juggle three balls in cascade fashion for one hour per day for twenty days. On specific days (7 in total), ball movements, center-of-pressure (CoP) trajectories and respiration traces were measured simultaneously. Discrete, time-continuous and spectral analyses revealed that the spatio-temporal variability of the juggling patterns decreased with practice and that the degree to which the task constraints were satisfied increased gradually. No conclusive evidence was found for ball movement-respiration coupling. In contrast, clear-cut evidence was found for the presence of 1:3 and 2:3 frequency locking between the vertical component of the ball trajectories and both the anterior-posterior and the medio-lateral components of the CoP. Incidence and expression of these mode locks varied across individuals and altered in the course of learning. Gradual changes in locking strength, appearances and disappearances of mode locks, as well as abrupt transitions between coupled states were observed. These results indicate that dissimilar learning dynamics may arise in the functional embedding of subsystems into a task-specific organization and that motor equivalence is an inherent property of such emerging task-specific organizations.

28. A Hutt, A Daffertshofer and U Steinmetz (2003). Detection of mutual phase synchronization in multivariate signals and application to phase ensembles and chaotic data. Physical Review E 68(3).

This work presents a method for the detection of mutual phase synchronization in nonstationary time series. We show how the application of a cluster algorithm that considers spatiotemporal structures of data follows from the general condition of phase-synchronized data. In view of the topology of phasic data, we reformulate the K-means cluster algorithm on a flat torus and apply a segmentation index derived in an earlier work [A. Hutt and H. Riedel, Physica D 177, 203 (2003)]. This index is extended by means of averaging in order to reflect phase synchronization in ensembles of multivariate time series. The method is illustrated using simulated multivariate phase dynamics and arrays of chaotic systems, in which temporal segments of phase-synchronized states are registered. A comparison with results from an existing bivariate synchronization index reveals major advantages of our method.

27. TD Frank, A Daffertshofer and PJ Beek (2002). Impacts of statistical feedback on the flexibility-accuracy trade-off in biological systems. Journal of Biological Physics 28(1): 39.

Biological systems possess the ability to adapt quickly and adequately to both environmental and internal changes. This vital ability cannot be explained in terms of conventional stochastic processes because such processes are characterized by a trade-off between flexibility and accuracy, that is, they either show short transition times (large Kramers escape rates) to broad steady-state distributions or long transition times to sharply peaked distributions. To develop a stochastic theory for systems exhibiting both flexibility and accuracy, we study systems under the impact of white noise multiplied with an accordant statistical measure, here the probability density. This results in negative feedback and circular causality: the more probable a stable state the less it will be affected by noise and, conversely, the less a stable state is affected by noise the more probable it is. Using nonlinear Fokker-Planck equations, steady states are computed via transformations of solutions of the corresponding linear Fokker-Planck equations. Transients reveal rapidly evolving and sharply peaked probability densities and thus mimic systems characterized by both flexibility and accuracy.

26. A Daffertshofer, AR Plastino and A Plastino (2002). Classical no-cloning theorem. Physical Review Letters 88(21): 210601.

A classical version of the no-cloning theorem is discussed. We show that an arbitrary probability distribution associated with a (source) system cannot be copied onto another (target) system while leaving the original distribution of the source system unperturbed. For classical dynamical systems such a perfect cloning process is not permitted by the Liouvillian (ensemble) evolution associated with the joint probability distribution of the composite source-target-copying machine system.

25. PJ Beek, CE Peper and A Daffertshofer (2002). Modeling rhythmic interlimb coordination: Beyond the Haken-Kelso-Bunz model. Brain and Cognition 48(1): 149.

Although the Haken-Kelso-Bunz (HKB) model was originally formulated to account for phase transitions in bimanual movements, it evolved, through experimentation and conceptual elaboration, into a fundamental formal construct for the experimental study of rhythmically coordinated movements in general. The model consists of two levels of formalization: a potential defining the stability properties of relative phase and a system of coupled limit cycle oscillators defining the individual limb movements and their interactions. Whereas the empirical validity of the potential is well established, the validity of the formalization in terms of coupled oscillators is questionable, both with regard to the asumption that individual limb movements are limit cycle oscillators with (only) two active degrees of freedom and with regard to the postulated coupling. To remedy these limitations a more elaborate system of coupled oscillators is outlined, comprising two coupled limit cycle oscillators at the neural level, each of which is coupled to a linearly damped oscillator, representing the end-effectors.

24. TD Frank and A Daffertshofer (2001). Multivariate nonlinear Fokker-Planck equations and generalized thermostatistics. Physica A-Statistical Mechanics and Its Applications 292(1-4): 392.

Multivariate nonlinear Fokker-Planck equations are derived which are solved by equilibrium distributions of generalized thermostatistics. The multivariate Fokker-Planck equations proposed by Kaniadakis and by Borland et al. are re-obtained as special cases. Furthermore, a Kramers equation is derived for particles obeying the nonextensive thermostatistics proposed by Tsallis.

23. TD Frank and A Daffertshofer (2001). H-theorem for nonlinear Fokker-Planck equations related to generalized thermostatistics. Physica A-Statistical Mechanics and Its Applications 295(3-4): 455.

In correspondence to conventional thermostatistics we formulate an H-theorem showing that transients solutions of nonlinear Fokker-Planck equations related to generalized thermostatistics converge to stationary probability densities. The H-theorem is applied to relaxation processes of classical bosons and fermions as proposed by Kaniadakis and Quarati, diffusion processes consistent with the generalized thermostatistics proposed by Tsallis, and stochastic processes with statistical feedback. (C) 2001 Elsevier Science B,V. All rights reserved.

22. A Daffertshofer, H Haken and J Portugali (2001). Self-organized settlements. Environment and Planning B-Planning & Design 28(1): 89.

In the present study we address the question of how persons or families occupy specific locations according to an attractiveness function between persons and flats. We suggest a mathematically formulated model in order to find optimal distributions of persons over flats. The model maximizes the global attractiveness of the ensemble and accounts for various conflicting situations. Its solutions show that, depending on initial conditions, both optimal as well as suboptimal configurations can be reached. An interpretation of the approach in terms of mental maps is offered.

21. TD Frank, A Daffertshofer, CE Peper, PJ Beek and H Haken (2001). H-theorem for a mean field model describing coupled oscillator systems under external forces. Physica D-Nonlinear Phenomena 150(3-4): 219.

This article studies the asymptotic behavior of solutions of Fokker-Planck equations describing mean field approximations of weakly coupled oscillator systems subjected to external forces. Using an H-theorem we show that transient probability densities converge to stationary ones. Furthermore, stability criteria are derived for the stationary solutions of these Fokker-Planck equations. The obtained results are applied to a model that combines the Haken-Kelso-Bunz model and the models of weakly coupled oscillators proposed by Winfree and Kuramoto. The stability criteria based on the H-theorem agree with those derived in our earlier analyses.

20. TD Frank, A Daffertshofer and RJ Beek (2001). Interpreting screw displacement apparent motion as a self-organizing process. Behavioral and Brain Sciences 24(4): 668.

Based on concepts of self-organization, we interpret apparent motion as the result of a so-called non-equilibrium phase transition of the perceptual system with the stimulus-onset asynchrony (SOA) acting as a control parameter. Accordingly, we predict a significantly increasing valiance of the quality index of apparent motion close to critical SOAs.

19. TD Frank, A Daffertshofer and PJ Beek (2001). Multivariate Ornstein-Uhlenbeck processes with mean-field dependent coefficients: Application to postural sway. Physical Review E 6301(1).

We study the transient and stationary behavior of many-particle systems in terms of multivariate Ornstein-Uhlenbeck processes with friction and diffusion coefficients that depend nonlinearly on process mean fields. Mean-held approximations of this kind of system are derived in terms of Fokker-Planck equations. In such systems, multiple stationary solutions as well as bifurcations of stationary solutions may occur. In addition, strictly monotonically decreasing steady-state autocorrelation functions that decay faster than exponential functions are found, which are used to describe the erratic motion of the center of pressure during quiet standing.

18. AA Post, CE Peper, A Daffertshofer and PJ Beek (2000). Relative phase dynamics in perturbed interlimb coordination: stability and stochasticity. Biological Cybernetics 83(5): 443.

Various stability features of bimanual rhythmic coordination. including phase transitions, have been modeled successfully by means of a one-dimensional equation of motion for relative phase obeying a gradient dynamics, the Haken-Kelso-Bunz model. The present study aimed at assessing pattern stability for stationary performance and estimating the model parameters (a, b, and Q) for the stochastic extension of this model. Estimates of a and b allowed for reconstruction of the potential defining the gradient dynamics. Two coordination patterns between the forearms (in-phase, antiphase) were performed at seven different frequencies. model parameters were estimated on the basis of an exponential decay parameter describing the relaxation behavior of continuous relative phase following a mechanical perturbation. Variability of relative phase and relaxation time provided measures of pattern stability. Although the predicted inverse relation between pattern stability and movement frequency was observed for the lower tempo conditions, it was absent for the higher tempos, reflecting the influence of task constraints. No statistically significant differences in stability were observed between the two coordination modes, indicating the influence of intention. The reconstructed potential reflected the observed stability features, underscoring the adequacy of the parameter estimations. The relaxation process could not be captured adequately by means of a simple exponential decay function but required an additional oscillatory term. In accordance with previous assumptions, noise strength Q did not vary as a function of movement frequency. However, systematic differences in Q were observed between the two coordination modes. The advantages and (potential) pitfalls of using stationary performance of single patterns to examine the stability features of a bistable potential were discussed.

17. A Daffertshofer, TD Frank, CE Peper and PJ Beek (2000). Three pertinent issues in the modeling of brain activity: Nonlinearities, time scales, and neural underpinnings. Behavioral and Brain Sciences 23(3): 400.

A critical discussion is provided of three central assumptions underlying Nunez’s approach to modeling cortical activity. A plea is made for neurophysiologically realistic models involving nonlinearities, multiple time scales, and stochasticity.

16. A Daffertshofer, CE Peper and PJ Beek (2000). Spectral analyses of event-related encephalographic signals. Physics Letters A 266(4-6): 290.

Recently, phase transitions (i.e. abrupt changes between different coordinative modes) have been used as a window into the relation between electro-magnetic activity in the brain and the performance of a perceptual-motor task. The present article reports an experiment similar to a pioneering study in this area, published in Phys. Lett. A 169 (1992) 134-144, which focused on tempo-induced transitions from syncopation to synchronization in a unimanual tapping task. In line with the original study, such transitions were found to be a consistent feature of the data and accompanying analyses of the MEG and EEG patterns revealed both in-phase and anti-phase frequency locking between the events, i.e., taps and acoustic stimuli and the corresponding brain activities. In contrast with the original study, however, no transitions were observed from the basic frequency to twice the basic frequency in the MEG and EEG recordings during synchronization. This discrepancy motivated a discussion of some potential problems in the spectral analysis of event-related encephalographic signals.

15. A Daffertshofer, CE Peper, TD Frank and PJ Beek (2000). Spatio-temporal patterns of encephalographic signals during polyrhythmic tapping. Human Movement Science 19(4): 475.

Interactions between limbs play an essential role in the formation of coherent macroscopic configurations during the bimanual performance of rhythmic movements. To uncover possible cortical aspects of these interactions, we study the relation between magneto-encephalo graphic signals and behavioral data during polyrhythmic tapping. In general, an explicit description of the relevant couplings requires a reliable quantification of phenomena like frequency and phase locking, Therefore, we first discuss a new cross-spectral measure that allows for the determination of frequency-locked areas in spatio-temporal signals. Subsequently, we estimate the corresponding generalized phase dynamics based on a system of two non-linearly coupled self-sustaining oscillators, The implications of these results for quantitative estimates of the functional coupling between hands/cortical areas in terms of distinct regimes of phase locking are discussed.

14. TD Frank and A Daffertshofer (2000). Exact time-dependent solutions of the Renyi Fokker-Planck equation and the Fokker-Planck equations related to the entropies proposed by Sharma and Mittal. Physica A-Statistical Mechanics and Its Applications 285(3-4): 351.

Exact time-dependent solutions representing generalized one-dimensional Ornstein-Uhlenbeck processes are derived from nonlinear Fokker-Planck equations and the corresponding diffusion processes are studied. The corresponding systems are related to the Renyi entropy and entropies proposed by Sharma and Mittal. In the former case normal diffusion is found with a diffusion late depending on the order of the Renyi entropy. In the latter case we find anomalous diffusion processes.

13. TD Frank, A Daffertshofer, CE Peper, PJ Beek and H Haken (2000). Towards a comprehensive theory of brain activity: Coupled oscillator systems under external forces. Physica D-Nonlinear Phenomena 144(1-2): 62.

Recently, Jirsa et al. and Haken discussed a theory comprising the brain wave equation proposed by Nunez, the Wilson-Cowan/Ermentrout-Cowan model, and Hopfield networks. This theory was applied to model findings obtained in an experiment that relates brain activity and behavior, the so-called Julliard experiment. In previous works of Jirsa et al. and Frank et al. the focus was on the brain wave aspect. Recently, we conducted similar experiments. The results obtained are modeled in this paper in terms of coupled oscillator systems. Coupled oscillator systems are considered to represent the Wilson-Cowan/Ermentrout-Cowan-model aspect of the unifying theory. Building on a model proposed by Haken, Kelso, and Bunt and the theory of weakly coupled oscillators established by Winfree and by Kuramoto, we derive a nonlinear Fokker-Planck equation whose stationary solutions mimic the neocortical brain activity observed in our experiments.

12. AA Post, A Daffertshofer and PJ Beek (2000). Principal components in three-ball cascade juggling. Biological Cybernetics 82(2): 143.

To uncover the underlying control structure of three-ball cascade juggling, we studied its spatiotemporal properties in detail. Juggling patterns, performed at fast and preferred speeds, were recorded in the frontal plane and subsequently analyzed using principal component analysis and serial correlation techniques. As was expected on theoretical grounds, the principal component analysis revealed that maximally four instead of the original six dimensions (3 balls x 2 planar coordinates) are sufficient for describing the juggling dynamics. Juggling speed was shown to affect the number of dimensions (four for the fast condition, two for the preferred condition) as well as the smoothness of the time evolution of the eigenvectors of the principal component analysis? particularly around the catches. Contrary to the throws and the zeniths, and regardless of juggling speed, consecutive catches of the same hand showed a markedly negative lag-one serial correlation, suggesting that the catches are timed so as to preserve the temporal integrity of the juggling act.

11. A Daffertshofer, C van den Berg and PJ Beek (1999). A dynamical model for mirror movements. Physica D-Nonlinear Phenomena 132(1-2): 243.

In an experiment involving the unimanual performance of rhythmic movements about the elbow joint, mirror movements (MM ) (i.e,, unintended, associated movements) were observed in the arm not instructed to move. The amplitude of these movements was small relative to that of the intended movements (in the order of 0.5 to 5%). Complex patterns of relative phasing were observed between the intended movements and the MM that were characterized by the presence of higher harmonics in the oscillating units. The patterns in question depended on the frequency of the intended movements, which was varied from 0.5 to 3 Hz. At low frequencies, cases of both in- and anti-phase coordination were observed amidst various other instances of phase locking. MM were smaller in the anti-phase than in the in-phase coordination. At higher frequencies, the occurrence of in-phase coordination was most common while instances of anti-phase coordination were absent. To account for these properties, a dynamical model for the coordination between large-amplitude intended movements and small-amplitude MM? was derived in the form of a model of nonlinearly coupled nonlinear oscillators with unequal amplitudes. The derived model was shown to correspond well with many quantitative and qualitative features of the observed dynamics of MM, including frequency locking, stable in-phase and anti-phase coordination, coordination-dependency of mirror movement amplitudes. and the presence of higher harmonics. The implications of the obtained experimental and analytical results and numerical parameter optimizations for the study of MM were discussed.

10. TD Frank and A Daffertshofer (1999). Nonlinear Fokker-Planck equations whose stationary solutions make entropy-like functionals stationary. Physica A-Statistical Mechanics and Its Applications 272(3-4): 497.

The present study extends the correspondence principle of Martinet et al. that establishes a link between nonlinear Fokker-Planck equations (NLFPEs) and the variational principle approach of the theory of canonical ensembles. By virtue of the extended correspondence principle we reobtain results of Kaniadakis and Quarati for Bose and Fermi systems and find relations similar to those derived by Plastino and Plastino and recently by Borland concerning the entropy of nonextensive thermostatistics introduced in physics by Tsallis. Moreover, we propose NLFPEs related to the Renyi entropy and to the entropy proposed by Sharma and Mittal. The latter comprises Tsallis‘ entropy and the Renyi entropy.

9. TD Frank, A Daffertshofer, PJ Beek and H Haken (1999). Impacts of noise on a field theoretical model of the human brain. Physica D-Nonlinear Phenomena 127(3-4): 233.

Salient properties of the spatio-temporal patterns in MEG recordings of human brain activity, such as macroscopic coherence of a limited number of modes and the occurrence of phase transitions, have been successfully described with the help of field theoretical models for the dendritic currents in the cortex. So far, however, these models have ignored the effects of noise which play an important role in the emergence of such properties. The present article provides a formal treatment of the effects of stochastic fluctuations in the vicinity of the phase transitions that were observed by Kelso in his so-called Julliard experiment [Fuchs et al., Phase transition in the human brain: spatial mode dynamics, Int. J. Bifurcation and Chaos 2 (1992) 917-939; H. Haken, Principles of Brain Functioning, Springer, Berlin, 1996; J.A.S. Kelso, Dynamic Patterns - The Self-organization of Brain and Behavior, MIT Press, Cambridge, 1995]. To describe and examine these effects, the field theoretical model proposed by Jirsa and Haken [A field theory of electromagnetic brain activity, Phys. Rev. Lett. 77 (1996) 960-963; A derivation of a macroscopic field theory of the brain from the quasi-microscopic neural dynamics, Physica D 99 (1997) 503-526] was extended by incorporating Gaussian white noise. The extended model describes the stochastic properties of the most dominant spatio-temporal components, including stochastic variations of the amplitudes of the extracted spatial modes. Furthermore, the model captures critical phenomena such as critical slowing down and critical fluctuations, which are derived analytically. These theoretical results are generalized by means of numerical simulations of amplitude and phase dynamics.

8. A Daffertshofer (1998). Effects of noise on the phase dynamics of nonlinear oscillators. Physical Review E 58(1): 327.

Various properties of human rhythmic movements have been successfully modeled using nonlinear oscillators. However, despite some extensions towards stochastical differential equations, these models do not comprise different statistical features that can be explained by nondynamical statistics. For instance, one observes certain lag one serial correlation functions for consecutive periods during periodic notion. This work aims at an extension of dynamical descriptions in terms of stochastically forced nonlinear oscillators such as.. xi+omega(0)(2)xi= n(xi,xi)+q(xi,xi)Psi(t), were the nonlinear function n(xi,xi) generates a limit cycle and Psi(t) denotes colored noise that is multiplied via q(xi,xi). Nonlinear self-excited systems have been frequently investigated, particularly emphasizing stability properties and amplitude evolution. Thus, one can focus on the effects of noise on the frequency or phase dynamics that can be analyzed by use of time-dependent Fokker-Planck equations. It can be shown that noise multiplied via polynoms of arbitrary finite order cannot generate the desired period correlation but predominantly results in phase diffusion. The system is extended in terms of forced oscillators in order to find a minimal model producing the required error correction.

7. M Agu, M Yamada and A Daffertshofer (1998). A field theory of pattern identification using the concept of gauge fields. IEICE Transactions on Information and Systems E81D(2): 206.

A held theory for geometrical pattern identification is developed based on the postulate that various modified patterns are identified via invariant characteristics of pattern transformations. The invariant characteristics of geometrical patterns are written as the functional of the light intensity distribution of pattern, its spatial gradient, and also its spatial curvature. Some definite expressions of the invariant characteristic functional for two dimensional linear transformation are derived, and their invariant and Feature extracting property are examined numerically. It is also shown that the invariant property is conserved even when patterns are deformed locally by introducing a "gauge field" as new degree of freedom in the functional in form of a covariant derivative. Based on this idea. we discuss a field theoretical model for pattern identification performed in biological systems.

6. H Gang, A Daffertshofer and H Haken (1996). Diffusion of periodically forced Brownian particles moving in space-periodic potentials. Physical Review Letters 76(26): 4874.

The diffusion properties of overdamped particles moving in spatially symmetrical periodic potentials subject to both symmetrical time-periodic driving and stochastic forcing are investigated [the typical model formally reads x = -V'(x) + U(t) + Gamma(t), V(L +/- x) = V(x), U(T + t) = U(t), [Gamma(t)] = 0, [Gamma(t)Gamma(tau)] = 2D delta(t – tau)]. It is found that the diffusion rate can be greatly enhanced if the various forcings are chosen in an optimal matching. In particular, we may get a diffusion rate larger than the rate of free diffusion.

5. H Haken, CE Peper, PJ Beek and A Daffertshofer (1996). A model for phase transitions in human hand movements during multifrequency tapping (vol 90, pg 179, 1996). Physica D-Nonlinear Phenomena 92(3-4): 260.

4. H Haken, CE Peper, PJ Beek and A Daffertshofer (1996). A model for phase transitions in human hand movements during multifrequency tapping. Physica D-Nonlinear Phenomena 90(1-2): 179.

In bimanual tapping, abrupt transitions between frequency ratios were observed when movement frequency was gradually increased. The transition routes showed individual tendencies, not necessarily in agreement with predictions derived from the sine circle map. Therefore, a more detailed theoretical model of coupled oscillators was developed. In the model the interaction function is a polynomial of coupling terms which allow for specific frequency locks. The magnitudes of these coupling terms are related to the amplitude of oscillation and the order of the frequency lock. Because increase in movement frequency is associated with a drop in amplitude, it results in differential loss of stability of the allowed frequency ratios. New frequency-locked states may be attained by detuning the stiffness parameters of the component oscillators. The model accounts for both free-running solutions and individual tendencies in transition routes. The relative weights of the coupling terms are influenced by practice and intention.

3. A Daffertshofer and H Haken (1995). Adaptive hierarchical structures. From Natural to Artificial Neural Computation 930: 76.

The construction of a hierarchical system to distinguish classes of patterns can be improved by the combination of a dynamical elastic matching with a time dependent image resolution. Using the elastic matching as a preprocessing for synergetic computers one achieves an invariant perception by means of arbitrary spatial transformations. On the other hand a time dependent resolution, realized with a Gaussian distribution, can be interpreted as a dynamical change of the available image information. The coupling of these two dynamics results in a hierarchy of locality of pattern transformations. Therefore this system utilizes a dynamical feature extraction and implies the definition several classes of patterns.

2. EW Lang, M Daffertshofer, A Daffertshofer, SB Wirth, RM Chesnut and M Hennerici (1995). Variability of vascular territory in stroke. Pitfalls and failure of stroke pattern interpretation. Stroke 26(6): 942.

BACKGROUND AND PURPOSE: We investigated the efficacy and feasibility of determining infarction mechanisms and underlying embolic or hemodynamic pathologies from topographical patterns of ischemic damage seen on computed tomography or magnetic resonance imaging. METHODS: Infarction patterns from 22 patients with ipsilateral severe, hemodynamically relevant carotid stenosis (n = 6) or occlusions (n = 16) were superimposed, using two matching algorithms, onto maps showing the variability of the cerebral vascular territories as determined from recent cadaver studies. These images were used to classify the infarctions as border-zone or territorial for the two conditions of minimal and maximal middle cerebral artery distribution. RESULTS: Classification of infarction patterns resulting from carotid stenosis was independent of the territorial extension map chosen: 83% were classified as territorial. Classification of patterns due to carotid occlusion, however, varied highly; 81% of infarctions were considered territorial when the maximal middle cerebral artery distribution map was used, whereas only 19% were when the minimal territorial extension map was used. CONCLUSIONS: The current concept that stroke mechanisms can be inferred from the interpretation of stroke patterns seen on computed tomography scans or magnetic resonance imaging is significantly confounded by the demonstrated variability in intracranial vascular distributions. Stroke pattern interpretation appears to be highly dependent on the in vivo vascular tree of the individual, which is unknown to the examiner. This calls into question the reliability of classifying infarction patterns as border-zone or territorial. Determination of true underlying stroke mechanisms requires a comprehensive approach and cannot be based solely on stroke pattern interpretation.

1. A Daffertshofer and H Haken (1994). A New Approach to Recognition of Deformed Patterns. Pattern Recognition 27(12): 1697.

By introducing a distance between original and deformed patterns and an adequate cost function we derive a gradient dynamics for transformation functions that transform one pattern into another one. In its simplest form the cost function is lent from an elastic medium but in further improvements the corresponding lame constants are chosen pattern dependent. In the case of line patterns a smearing out by means of a Gaussian distribution is introduced and made time dependent. The numerical simulations show the feasibility of the present approach, for instance, for the recognition of handwritten characters or of faces showing different facial expressions.