Citation for published version (APA): Donker, S. F. (2002). Flexibility of human walking: a study on interlimb coordination Groningen: s.n.

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1 University of Groningen Flexibility of human walking Donker, Stella Franciscus IMPORTANT NOTE: You are advised to consult the publisher's version (publisher's PDF) if you wish to cite from it. Please check the document version below. Document Version Publisher's PDF, also known as Version of record Publication date: 2002 Link to publication in University of Groningen/UMCG research database Citation for published version (APA): Donker, S. F. (2002). Flexibility of human walking: a study on interlimb coordination Groningen: s.n. Copyright Other than for strictly personal use, it is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license (like Creative Commons). Take-down policy If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. Downloaded from the University of Groningen/UMCG research database (Pure): For technical reasons the number of authors shown on this cover page is limited to 10 maximum. Download date:

2 Flexibility of Human Walking: A study on Interlimb Coordination Stella Donker

3 Flexibility of Human Walking: A study on Interlimb Coordination To Frank & Rens

4 The research presented in this dissertation was conducted at the Sint Maartenskliniek-research, Nijmegen. Financial support was provided by the Foundation for Behavioral Sciences of the Netherlands Organization for Scientific Research (NWO), grant number: Cover photo: Patrick Demarchelier, Publisher: PrintPartners Ipskamp B.V., Enschede, the Netherlands An electronic version of this thesis is available at Stella Donker

5 RIJKSUNIVERSITEIT GRONINGEN FLEXIBILITY OF HUMAN WALKING: A study on interlimb coordination Proefschrift ter verkrijging van het doctoraat in de Medische Wetenschappen aan de Rijksuniversiteit Groningen op gezag van de Rector Magnificus, dr. F. Zwarts, in het openbaar te verdedigen op woensdag 30 oktober 2002 om 14:15 uur door Stella Franciscus Donker geboren op 2 november 1969 te Utrecht

6 Promotores: Prof. dr. Th. Mulder Prof. dr. P. J. Beek Prof. dr. J. Duysens Beoordelingscommissie: Prof. dr. S. Swinnen Prof. dr. ir. P. Veltink Prof. dr. A. Gramsbergen ISBN

7 You're walking. And you don't always realize it, but you're always falling With each step, you fall forward slightly And then catch yourself from falling Over and over, you're falling And then catching yourself from falling And this is how you can be walking and falling at the same time. Laurie Anderson; Walking and falling, Big Science, 1982

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9 Index Chapter 1 Introduction and outline 9 Chapter 2 Coordination between arm and leg movements during locomotion 21 Chapter 3 Effects of limb loading and velocity on the relative phasing between arm and leg movements during walking 53 Chapter 4 Adaptations in arm movements for added mass to wrist or ankle during walking 81 Chapter 5 Interlimb coordination in prosthetic walking: Effects of asymmetry and walking velocity 97 Chapter 6 General discussion and summary 123 References 135 Nederlandse samenvatting (Dutch summary) 149 Dankwoord (Acknowledgements) 155 About the author 159

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11 Chapter 1 Introduction & Outline According to the dictionary 1 to walk is to move along on foot, that is, advance by steps. In spite of this concise and compact definition, and in spite of the fact that walking is one of the most basic human motor activities, little is known about how this progression of steps is controlled. Hence, it is not surprising that the majority of studies on walking is still very much concerned with unraveling the mechanisms governing the stepping movements of the legs. To this end, the leg movements are often simplified in that the main focus of study becomes the stride 2 (Inman, Ralston, & Todd, 1981). As a result of this practice, stride parameters such as stride length, step width, cadence, swing time, double support phase, knee, hip and ankle angle are widely used, not only to determine gait but also to distinguish among different forms of pathological gait (cf. Whittle, 1998). Clearly, biomechanical analyses have contributed considerably to the understanding of the ability to move one foot in front of the other in a rapid and orderly progression. By studying the mechanical properties of the musculoskeletal system substantial insight has been gained into how the human body interacts with the environment. By approximating human walking as a mechanical process controlled solely by Newton s laws, simple walking robots have been built that are able to walk down a shallow slope without using any internal power. These so-called passive walkers illustrate that, in principle, the interaction between gravity and inertia alone is sufficient to explain the movements of the legs (e.g., McGeer, 1990, 1993; Mochon & McMahon, 1980). Elaborating on this insight, Holt, Hamill, and Andres (1990) argued that the basic goal of all biological locomotor systems is to achieve optimization in the form of minimal muscular requirements or minimal metabolic cost, and that this is achieved by moving the limbs at their eigenfrequencies (or resonant frequencies). The preferred walking velocity in individuals (in the order of about 4 to 5 km/h) is viewed as the result of this principle (Holt et al., 1990). This is not to deny, of course, that in cluttered environments the flow of energy (and hence the associated metabolic costs) may be uneven due to necessary variations in walking velocity. As McGeer (1993) already emphasized,

12 efferent and afferent motor signals are always necessary for starting and stopping, for navigating over irregular terrain and for supplying energy when needed. Besides its operationalization in terms of eigenfrequencies and preferred walking velocities (cf. Clark & Phillips, 1993; Warren, Kay, & Yilmaz, 1996), the principle of minimizing energy consumption has also been associated with the symmetry of gait (cf. Czerniecki & Gitter, 1996). As a consequence of these ideas, energy consumption and its determinants (i.e., walking velocity and symmetry) are widely used to describe and evaluate gait patterns. Whereas biomechanics elucidated how forces act upon bone structures and how gravity constrains movement, neurophysiology highlighted the dazzling complexity of gait control due to its intrinsic focus on the planning, execution and adaptation of movements by the central nervous system. By now, it is more or less accepted that there are specialized neuronal circuits in the human spinal cord that organize the characteristic cyclical movements of the legs during locomotion (for a review see Duysens & van de Crommert, 1998). A compelling illustration of the presence of such central pattern generators (CPGs) is the observation that newborn babies show stepping behavior when adequately stimulated. In spite of these central controllers afferent input is essential for the timing and shaping of locomotor patterns, as well as for reflex adjustments of the program to compensate for changing environmental conditions (Clarac, 1991; Duysens, Clarac, & Cruse, 2000). For example, a newborn baby is capable of making stepping movements, but it takes about a year for a baby to stand upright and even longer to walk independently. Moreover, it takes six years or longer after the onset of independent walking for the neurocontrol system to reach the same level of expediency and maturation as observed in adults. Evidence for this was obtained in terms of the kinematics of the leg movements (Berger, Altenmueller, & Dietz, 1984; Stolze et al., 1997; Sutherland, Olshen, Cooper, & Woo, 1980), EMG recordings of the leg muscles (Berger, Quintern, & Dietz, 1987; Okamoto & Kumamoto, 1972), and postural control (Brenière & Bril, 1998; Ledebt, Bril, & Brenière, 1998). Whereas both biomechanics and physiology provide explanations of basic walking patterns, the necessity to integrate the knowledge accumulated in different disciplines becomes apparent when studying walking as a whole body activity, that is, as a dynamically stable behavior that is robust to perturbations. While being engaged in the regulation of walking, neural control systems are continuously challenged by changes in the environment, such as obstacles or events, as well as by changes in the body itself (e.g., 10 Chapter 1

13 impairment, pain, fatigue, mechanical constraints). In order to maintain (or regain) a stable gait, the human locomotor system (i.e., the musculoskeletal, the neuromuscular and the central control system), is forced to react adequately (i.e., flexibly) to both types of changes. For instance, Patla and coworkers (see Patla, 1991, for review) performed a lot of research on the adaptation to environmental perturbations and showed that humans use various strategies to solve these problems, depending on the situation at hand. Indeed, the human locomotor system has a great capacity to adapt to changing circumstances, as is demonstrated, for example, by a patient s ability to walk with a leg-prosthesis. Hence, the study of locomotion should not only concern the basic stepping movements of the legs but should also focus on the control of balance during locomotion and the adaptation of basic patterns to the goals and changes in the environment, including both anticipatory and reactive responses (Grillner & Wallen, 1985). Indeed, human walking entails much more than merely advancing by steps. Pathological gait The complexity of human locomotion is particularly striking in pathological walking in that biomechanical principles that apply to healthy walking are not always adequate to explain the phenomena observed in pathological gait. Pathological gait is often characterized by asymmetries, low preferred walking speeds, shortened stride lengths and longer double support times (e.g., Dingwell, Cusumano, Sternad, & Cavanagh, 2000; Mattes, Martin, & Royer, 2000), all of which are accompanied by an increase in energy consumption (e.g., the selected frequencies of the movements of the limbs may deviate considerably from their eigenfrequencies and symmetry may be abandoned see, e.g., Murray, Sepic, Gardner, & Downs, 1978). It is conceivable that in many instances of pathological gait, the principle of minimizing energy consumption is obscured because other factors and concerns have become (or are) much more important, such as fear of falling (enhanced controllability), pain avoidance (fear of pain) and other functional compensations. These considerations suggest that the traditional approach to human gait, with its emphasis on walking velocity and symmetry, may be incomplete and limited. It therefore seems relevant to search for determinants of walking that reflect qualities of coordination and the Chapter 1 11

14 changes therein that are brought about by both internal (e.g., pathology) and external (i.e., environmental) factors. Patently, walking, be it healthy or pathological, is a highly adaptive, flexible activity that is continuously altered so as to meet environmental and internal requirements, and should be investigated accordingly. Interlimb coordination and Dynamical Systems Theory (DST) A promising approach in studying human walking in terms of stability and flexibility is to examine the coordination between multiple cyclically moving segments and their interaction with the environment. Indeed, in this approach the locomotor system is being considered as a complex ensemble of interacting components instead of a system existing mainly of two individual legs. Moreover, this approach provides tools to describe human locomotion in terms of relevant and quantifiable macroscopic variables instead of a wide range of stride parameters, as will be explained in the following. As already stated, a basic feature of human walking is the placement of one leg in front of the other, implying the occurrence of cyclical leg movements. In fact, such repetitive, cyclical movements of the limbs are a universal feature of many forms of locomotion (flying, swimming, and walking). An important aspect of the coordination of rhythmic movements is the tendency to move the limbs (wings, fins, legs, and arms) at a common frequency and at a certain phase relation. In studying the phase relations of fin movements, Von Holst (1939/1979) distinguished between two forms of interlimb coordination, which he called absolute and relative coordination, respectively. Whereas absolute coordination is characterized by a highly regular and stable phase relation between two limb movements, this relation is markedly less regular and stable in relative coordination. Put differently, phase locking (absolute coordination) refers to a situation in which the phases of two component oscillators (e.g., limbs) are related linearly, that is, θ 2 (t) = θ 1 (t) + a constant. In contrast, phase entrainment (relative coordination) refers to a situation in which θ 2 completes one full cycle in the time that θ 1 completes one full cycle but in the absence of a fixed magnitude of θ 2 - θ 1. Whereas absolute coordination is rarely found in nature, phase entrainment is the rule rather than the exception in biological movement systems and depends on the strength of the coupling between the oscillating components. If the coupling decreases, so that it drops outside 12 Chapter 1

15 the entrainment zone, new coordinative modes may arise due to reentrainment in other attractor zones such as superharmonic entrainment (e.g., from 1:1 to 2:1 frequency relation). This implies that variations in coupling strength may allow for spontaneous changes between coordinative patterns. During the last two decades or so, rhythmic interlimb coordination has been investigated extensively, particularly from the perspective of Dynamical Systems Theory (or DST, cf. Haken, Kelso, & Bunz, 1985). This theory is concerned with the mathematical description and formal analysis of the stability properties of dynamical systems, as well as qualitative changes in these properties due to continuous variations in system parameters. When applied to human movement, DST leads to the point of view that stable patterns of coordination can be understood mathematically (and hence may be studied accordingly) as attractors in lowdimensional state spaces. This point of view further implies that the abrupt transitions in coordination that may occur as a result of gradual changes in a movement parameter, such as frequency or (walking) speed, may be conceived as phase transitions, that is, as shifts from one attractor to another, often due to loss of stability and subsequent disappearance of the previously occupied attractor (e.g., Kelso & Ding, 1993). Consequently, this principle gives rise to flexible behavior in that coordinative patterns (called gaits in studies of locomotion) may disappear and give rise to new ones as a result of variations in the prevailing internal or external constraints. The strength of applications of DST to the study of movement resides in the strictly operational character of the approach: key concepts such as stability and phase transitions are defined precisely, so that theory and data may be brought in close contact to one another. For example, in the context of the study of rhythmic interlimb coordination, the standard deviation of relative phase and the coherence between the power spectra of the limb movements are used as exact, theoretically motivated measures of pattern stability (cf. Schöner, Kelso, & Haken, 1986). Thus, the effects of specific changes in internal and external parameters may be measured quantitatively, allowing for rigorous study of both the stability and flexibility of the movement system. Adaptation and arm movements A main entry point in identifying determinants of functionally adequate Chapter 1 13

16 locomotion is to examine the ability to adapt adequately to internal and external changes. In more classical studies on animal locomotion the adaptation of the animal to alterations has been studied in terms of the coordination between limb movements, in particular their relative phasing (e.g., Stein, 1974; Von Holst, 1939/1973). Perturbation studies in which a mass was added to paws, wings or fins, or in which limbs were amputated, invariably resulted in new behavioral patterns, demonstrating the remarkable capability of the (animal) locomotor system to flexibly adapt to new conditions. In contrast, the (few) attempts that have been made to capture the determinants of the adaptability of human walking have focused predominantly on changes within the stride, that is, within the movements of a single leg (e.g., Nilsson & Thorstensson, 1987; Patla, 1991; Zijlstra, 1997). Changes in the coordination between the leg movements have hardly been investigated in this context, let alone changes in the coordination of the upper body. In line with traditional gait analysis, if mentioned at all, the upper body is mostly referred to as a single unit (HAT: head, arms, and trunk). The legs carry and displace the body whereby the whole body is conceived as an inverted pendulum (Dingwell, 1998; MacKinnon & Winter, 1993). The arms are thought to behave like passive pendulums and their function would merely be to counteract the rotation of the trunk. However, if human locomotion would not involve active participation of the arms, their motion would vary greatly for various cadences and contribute to a considerable jerkiness in locomotion (Jackson, Joseph, & Wyard, 1978). Hogue (1969) argued that the arms do act as pendulums but that their pendular action is caused by both gravity and muscular activity, which he found to increase with increasing cadence. However, as early as the late 1930s, Elftman (1939) realized that the swinging of the arms is not a purely incidental accompaniment of forward movement but rather an integral part of the dynamics of progression. The ability to change behavioral patterns according to environmental requirements or to-be-learned tasks is an essential feature of functionally adequate human locomotion. By studying human locomotion in terms of interlimb coordination, including both arm and leg movements, a theoretically adequate and significant opportunity is created to answer the question how the stability properties of these behavioral patterns emerge and how they vary as a result of fluctuations in both internal and external parameters. 14 Chapter 1

17 Outline of this thesis The goal of the present thesis is to gain insight into the flexible nature of human locomotion by focusing on the coordination between arm and leg movements during walking. As already indicated in the preceding, this focus will be based on DST because this theory provides expedient tools and strictly defined concepts for studying and evaluating the stability and flexibility of walking. It is expected that this type of analysis will enable a more direct and revealing assessment of the structure of different control strategies and their relative effectiveness, as compared to studies of single leg movements. First of all, locomotor patterns such as walking, running, and hopping are characterized by specific phase and frequency relations between cyclical arm and leg movements. It may be assumed that the stability of gait patterns is reflected in the interactions (or couplings) between these cyclical arm and leg movements. Second, it follows from the fact that man possesses multiple gait patterns that, under certain circumstances, shifts will occur from one pattern to another. For example, a walker who gradually increases speed may, at a certain speed, exhibit a transition from walking to running. Such transitions bear the characteristics of phase transitions and may be studied accordingly (cf. Diedrich & Warren, 1995). The occurrence of such transitions implies that the coordination between the limb movements can be adapted flexibly to the prevailing circumstances. To gain more insight into the flexibility of walking, or the lack thereof in specific groups of patients, it seems worthwhile to study interlimb coordination during walking in detail. Additionally, there is an important theoretical motive for focusing on interlimb coordination during walking that requires some further explanation. The current insights into the stability and the formation of patterns of interlimb coordination have largely been obtained in experimental studies that were explicitly directed at deriving and testing formal model constructs. At first, these experiments pertained invariably to finger and hand movements. Later, the experimental approach was extended to arm and leg movements performed by subjects who were seated in specially designed chairs, such that the mechanical interaction with the ground and balance control played no role. Although a few studies have been conducted on the coordination between arm and leg movements during walking, the differences between experimental tasks aimed at the construction of formal models and an everyday, mechanically complex activity such as walking, have hardly been investigated to date. An in-depth study of the coordination between arm and leg movements during walking would allow one to Chapter 1 15

18 examine to what extent the current, formalized insights into rhythmic interlimb coordination, as obtained in experimental studies that were specifically designed for that purpose, also apply to human walking. In line with this last motive, the research reported in the present thesis focuses on the effects of two (independent) factors on interlimb coordination, namely walking velocity and the degree of (a)symmetry between the limbs. Moreover, as pointed out earlier in this chapter, both movement frequency and (a)symmetry play important roles in the study of walking, particularly in the study of pathological gait patterns. Examining the effect of walking velocity and (a)symmetry on the coordination between arm and leg movements allows for studying the adaptation to changes in walking velocity and in the degree of (a)symmetry of the participating components. First, in chapter 2, the effect of walking velocity on the coordination between arm and leg movements was studied in detail. From previous research it was known that at low walking velocities the frequencies of the arm and leg movements often relate as 2:1, whereby the arms swing in unison, whereas at higher walking velocities they invariably relate as 1:1 (Craik, Herman, & Finley, 1976). In the research reported in this chapter it was examined whether this behavioral phenomenon is better explained from a biomechanical perspective (cf. Webb, Tuttle, & Baksh, 1994) or from a dynamical systems perspective. The experiment reported in chapter 3 focused on the effect of adding a mass to arm or leg on interlimb coordination during healthy human walking. The overall question being asked was to what extent the human movement system is robust to such a perturbation. Specifically, we elaborated on the effects of both symmetry and walking velocity. In chapter 2 strong indications were found that the arm movements may not simply be considered as passive pendulums. Instead, it was argued that although passive properties do play a role, the observed coordination patterns are part of a complex dynamic behavior. Indeed, in chapter 3 it was found that the coordination between arm and leg movements was quite robust to the mass perturbations. Therefore, in chapter 4 the contribution of the arms during walking was examined in greater detail, again under manipulation of walking velocity and limb loading. In the research reported in this chapter, the question of interest was whether adaptations to local perturbations are restricted to the perturbed limb or whether they induce a reorganization of all co-moving limbs so as to preserve coordinative stability as was observed in chapter 3. The observations and conclusions of chapters 2, 3 and 4, in which specific manipulations were performed in healthy participants, were 16 Chapter 1

19 validated in chapter 5. In this chapter the influence of a prosthetic leg with inertial properties that differ from that of the healthy leg (cf. chapter 4) on the coordination between arm and leg movements was investigated. Specifically, both issues of symmetry and walking velocity were studied. The thesis concludes with a summary and a general discussion in chapter 6. Notes 1. Merriam-Webster Advanced Dictionary & Thesaurus, Merriam - Webster and Franklin Electronic Publishers, Note that two successive steps (e.g., from heel contact of one foot to heel contact of the other foot) define a stride (e.g., from heel contact of one foot to heel contact of the same foot). Chapter 1 17

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23 Chapter 2 Coordination between arm and leg movements during locomotion Previous studies examining the effect of walking velocity on the coordination between arm and leg movements have reported the occurrence of 2:1 frequency coordination at low walking velocities and of 1:1 frequency coordination at higher walking velocities. On the one hand, this phenomenon has been interpreted from a biomechanical perspective in terms of the tendency of the arms to move at, or close to, their resonance frequency. On the other hand, it has been interpreted from a dynamical systems perspective in terms of two stable regimes of frequency and phase locking between arm and leg movements, and in terms of velocity-induced phase transitions between these regimes due to loss of stability of the alternate coordination mode. To evaluate these contrasting interpretations, we conducted an experiment to quantify the effect of walking velocity on the stability of the frequency and phase coordination between the individual limb movements. Spectral analyses revealed the presence of 2:1 frequency coordination between arm and leg movements as a consistent feature of the data in only 3 out of 8 participants at walking velocities ranging from 1.0 to 2.0 km/h, in spite of the fact that the eigenfrequencies of the arms were rather similar across participants. The degree of interlimb coupling, as indexed by weighted coherence and variability of relative phase, was lower for the arm movements and for ipsilateral and diagonal combinations of arm and leg movements than for the leg movements. Furthermore, the coupling within all pairs of limb movements was found to increase with walking velocity, whereas no clear signs were observed that the switches from 2:1 to 1:1 frequency coordination and vice versa were preceded by loss of stability. Therefore, neither a purely biomechanical nor a purely dynamical model is optimally suited to explain these results. Instead, an integrative model involving elements of both approaches seems to be required. Stella Donker, Peter Beek, Robert Wagenaar, & Theo Mulder Journal of Motor Behavior, 33, , 2001

24 Introduction Human walking is a complex activity involving a large number of cyclically moving components, that is, legs, pelvis, trunk, arms, and head. Recently, the study of human walking has clearly gone beyond simple analyses of leg movements in terms of the absolute and relative timing of the various phases of Phillipson s step cycle (cf. Shapiro, Zernicke, Gregor, & Diestel, 1981), indirect coordination measures such as bipedal contact time (Marey, 1874; Rozendal, 1968), and the kinetics of the muscles and joints in the legs (Vaughan, Davis, & O'Connor, 1992). It is now more and more recognized that, in order to understand the dynamics of walking, one cannot restrict the system under study to an isolated pair of walking legs; head, arm, and trunk movements should also be included. A rapidly increasing number of studies testify to this development (e.g., Capozzo, 1982; Clark & Phillips, 1993; Elftman, 1939; Ledebt, Bril, & Wiener-Vacher, 1995; Murray, Sepic, Gardner, & Downs, 1978; Nashner & Forssberg, 1986; Thorstensson, Nilsson, Carlson, & Zomlefer, 1984; Van Emmerik & Wagenaar, 1996a, 1996b; Wagenaar & Beek, 1992; Wagenaar & Van Emmerik, 1994; Warren, Kay, & Yilmaz, 1996). 1 In the present article, we focus on a very basic and common property of human walking, namely, the coordination between arm and leg movements. Our specific interest is in the effect of walking velocity on interlimb coordination. This interest was motivated by current theoretical considerations and developments, although potential practical implications are recognized. For instance, in the field of applied movement science, walking velocity has been postulated to be a relevant (control) parameter for inducing or promoting desired coordination patterns and avoiding undesired coordination patterns (cf. Van Emmerik, Wagenaar, & Wolters, 1993). Such a theoretically motivated application, however, requires thorough empirical knowledge of the effects of velocity on the dynamics of walking. Movement velocity is an important parameter that plays an essential role in various models of rhythmically coordinated movements. In the literature, the effects of movement velocity on interlimb coordination have been studied from two contrasting theoretical approaches, the biomechanical approach and the dynamical systems approach. We briefly discuss each approach and, in doing so, explain our motivation for conducting the present study. In the biomechanical approach to movement coordination, an understanding of the patterns of coordinated movements is sought in terms of the underlying forces and moments that give rise to those patterns. A 22 Chapter 2

25 commonly applied strategy in studying rhythmic movements from this perspective is to treat the moving limbs as force-driven pendulums and to explain the observed movement patterns in terms of the physical properties of the pendulums and their muscular forcing (cf. Holt, Hamill, & Andres, 1990; Schot & Decker, 1998). An example of such an approach is the study of Webb, Tuttle, and Baksh (1994) on the pendular activity of the upper limbs during slow and normal walking. They started from the observation (cf. Craik, Herman, & Finley, 1976; Webb & Tuttle, 1989) that at customary walking velocities the upper limbs swing in alternation, with each limb swinging forward and backward in phase with the diagonal lower limb, whereas at lower walking velocities the upper limbs swing in phase at a frequency twice as high as the stride frequency of the legs. Those studies advanced the hypothesis that the stride frequency at which single swinging changes to double swinging occurs at or slightly below the natural pendular frequency of the upper limbs. Webb et al. (1994) explained the occurrence of the observed coordination modes (i.e., single swinging or double swinging) in terms of the biomechanical properties of one of the two components (legs and arms) participating in the coordination. This explanation, however, is somewhat unsatisfactory in that it explains why the arms show a tendency to move at a certain frequency but not why particular, functionally stable forms of coordination between the movements of the arms and the legs are preferred. This restriction may reflect a general limitation of the biomechanical approach to understanding coordinative phenomena. Biomechanical properties play a role in coordinative phenomena, but coordinative structures are functional units of organization that are based foremost on informational rather than on biomechanical principles. As Kelso (1994) pointed out, biomechanical properties may shape the dynamical properties of coordination but they do not determine them. On the other hand, the degree to which the biomechanical properties of the effector system shape the coordination dynamics may vary from task to task. Evidently, biomechanical principles are likely to play a more prominent role in walking than in the coordination of rhythmic finger movements. Therefore, in studying human locomotion, it will be particularly useful to consider, and if possible to explicitly model, the biomechanical constraints in conjunction with the informational constraints. The expediency of such an approach was aptly argued and demonstrated by Taga (1994). Taga modeled the control of walking as a form of self-organization, in which a rhythmic spatiotemporal pattern is generated through the multilink dynamics of the musculoskeletal system and the nonlinear dynamics of the (central) nervous system, conceived as a Chapter 2 23

26 collection of neural oscillators or central pattern generators. Contrary to the biomechanical approach, the main focus in the dynamical systems approach is on the stability properties of spatiotemporal patterns of bodily parts coordinated with each other and the environment (see, e.g., Beek, Peper, & Stegeman, 1995; Kelso, 1995; Schöner & Kelso, 1988). Qualitative changes or phase transitions are a special entry point in studying the stability properties of coordination patterns because they are associated with an enormous reduction of information, allowing for the identification of the relevant collective variables or order parameters for describing the coordination patterns over which the transition is defined (Haken, 1977, 1983). The core of the approach as it has evolved to date is formed by a large number of studies on rhythmically coordinated movements, which build on Kelso s (1981, 1984), by now paradigmatic, experiment on frequency-induced transitions from antiphase to in-phase coordination in rhythmic finger movements and the so-called Haken, Kelso, and Bunz (1985), or HKB, model for this phenomenon. In the HKB model, Haken and his colleagues capitalized on the mathematical theory of nonlinear oscillations by modeling the rhythmic finger movements in terms of nonlinearly coupled nonlinear oscillators. A key feature of this model is the decrease of the interaction or coupling strength between the fingers with increasing frequency, resulting in loss of stability of the antiphase coordination at a particular frequency. The purpose of this kind of nonlinear oscillator models is to find general formal analogies for complex dynamical phenomena that occur quite generally in biological systems displaying oscillatory behavior, no matter their precise material composition or instantiation. Thus, instead of analyzing highly task-dependent (neuro-) physiological mechanisms and biomechanical properties, in the dynamical systems approach, one seeks to identify general, dynamical principles of coordination in the form of frequency and phase attraction, nonequilibrium phase transitions, phase wandering, chaos, and the like. Thus, in contrast to the biomechanical approach, the thrust of the dynamical systems approach is to understand (rhythmic interlimb) coordination as a form of dynamic pattern formation or self-organization, involving the emergence and annihilation of stable spatiotemporal patterns that can be described mathematically as attractors. According to this perspective, single swinging and double swinging are viewed as coordinative patterns resulting from frequency and phase locking. The switch from single swinging to double swinging in the coordination between arm and leg movements, and vice versa, is viewed as a nonequilibrium phase transition between these two regimes of frequency and phase 24 Chapter 2

27 locking (Van Emmerik & Wagenaar, 1996b; Wagenaar & Van Emmerik, 1994). According to this interpretation, the behavioral switch in question should be characterized by loss of stability of the frequency- and phaselocking regime prior to the switch and the subsequent entering of a stable frequency- and phase-locking regime after the switch. Particularly, for the switching behavior of interest to constitute a genuine phase transition, one would expect to observe catastrophe flags such as hysteresis, that is, the occurrence of jumps at distinct values of the control parameter as a function of the history of the system, and critical fluctuations, that is, enhanced variability resulting from loss of stability of a previously stable mode (cf. Gilmore, 1981). So far, the stability properties of the coordinative modes between arm and leg movements during walking referred to as single swinging and double swinging have been studied and analyzed in some detail, but conclusive evidence for the occurrence of frequency and phase locking and for the presence or absence of phase transitions has not yet been obtained. Wagenaar and Van Emmerik (1994, 2000) reported evidence for the presence of 2:1 and 1:1 frequency coordination between arm and leg movements during walking at low and customary velocities, respectively, by showing that the frequency ratios in question were close to 2 and 1. The velocity-dependent effects on the stability of the observed coordination patterns was assessed only in terms of the variability of relative phase (which is a valid index of coordinative stability only if relative phase is a point attractor), however, and not in terms of spectral analyses addressing the stability of the frequency coordination. Using variability of relative phase, they found no convincing evidence for the theoretical interpretation that the switches from single swinging to double swinging and vice versa constitute genuine phase transitions in that they are characterized by catastrophe flags such as hysteresis and critical fluctuations (cf. Gilmore, 1981). Although Wagenaar and Beek (1992) reported a hysteresis effect for stride frequency, and Wagenaar and Van Emmerik (2000) observed hints of increased fluctuations in the relative phasing between the arms at intermediate velocities ( m/s), no hysteresis and critical fluctuations effects have been reported to date for the coordination between arm and leg movements. All in all, the present state of affairs justifies further experimental and numerical analyses of this type of coordination. Thus, we conducted the present experiment to examine in detail the coordination between arm and leg movements by using a combination of methods to study the observed frequency and phase relations. Our specific aims in the present study were the following: Chapter 2 25

28 1. (a) To replicate the basic findings of Craik et al. (1976), Webb et al. (1994), and Wagenaar and Van Emmerik (1994, 2000) regarding the two forms of frequency coordination between arm and leg movements, that is, 2:1 at low walking velocities and 1:1 at customary walking velocities; and (b) to determine whether those frequency relations are instances of frequency locking. 2. To examine the extent to which the observed coordination patterns and switches therein might be related to the eigenfrequencies of the arms. 3. To analyze in detail the relative phasing between arm and leg movements and to examine the possibility of phase locking and its quantitative properties. 4. To establish the effect of walking velocity on the degree of (frequency and phase) coupling between arm and leg movements as compared to other limb combinations. 5. To determine whether qualitative changes in the coordination between arm and leg movements are characterized by hysteresis and critical fluctuations. The findings with regard to these goals allow one to evaluate the relative merits of the current biomechanical (Aims 1 and 2) and dynamical (Aims 1, 3, 4 and 5) accounts of the effect of walking velocity on the coordination between arm and leg movements. Method Participants Three women and 5 men (mean age = 29 years; range = years) participated in the experiment. All participants were naive with regard to our purposes in the experiment. All participants gave their written informed consent and the study was approved by the local Medical Ethics Committee. Materials The participants walked on a walking belt (Enraf Nonius, model Entred Reha; Bonto BV, Zwolle, The Netherlands) with a computer-controlled velocity (the time to change the velocity by 0.5 km/h was about 1.5 s). Small lightweight triangular frames with a reflective spherical marker (diameter 15 mm) on each corner were attached to the upper arms, forearms, upper legs and lower legs by means of Velcro strips, as shown in Figure 1A. Two additional markers were placed on the heels. The positions of the 26 markers were recorded at a sampling rate of 100 Hz by means of a 26 Chapter 2

29 three-dimensional (3D) passive registration system called PRIMAS (Furnée, 1989). Four video cameras were placed around the walking belt, two on each side so that at all times the markers were in view of at least two cameras, as was required for the successful 3D reconstruction of their position. The 3D reconstruction error was about 1 mm. Y upper arm marker frame lower arm upper leg lower leg heel Z X A. B. Figure 1. (A) Sagittal view of the marker configuration (black circles). Marker frames (each holding three markers) were placed on the upper arms, forearms, upper legs and lower legs. A single marker was attached on each of the heels. (B) The coordinate axes x, y, and z. The sagittal plane was defined by the xy plane. In this study, only the rotational movements (in degrees) of the limbs around the z-axis (i.e., the rotational movements in the sagittal plane, represented by white the arrow around the z-axis in the figure) are discussed. Procedure and Design Before each experimental session, participants were acquainted with walking on a walking belt at different velocities. This familiarization process took about 5 minutes. Subsequently, a reference measurement was taken during which the positions of the marker frames in space were recorded for future reference. Participants walked barefooted on the belt and were instructed to walk as naturally as possible. No specific instructions regarding the movements of the arms were given. Each participant took part in a single measurement session, consisting of one large trial. During this trial, walking velocity was gradually increased in steps of 0.5 km/h from 1.0 km/h up to 4.0 km/h and subsequently decreased from 4.0 km/h to 1.0 km/h, Chapter 2 27

30 yielding two observations at the walking velocities km/h and a single observation for 4.0 km/h. About 10 s after changing the velocity of the walking belt, the position data of the markers were recorded for 15 stride cycles. Consequently, the recording time varied from 40 s at the lowest velocity to 30 s at the highest velocity. A session (i.e., recording the entire trial) took about 20 min. At the end of the session, anthropometric measures were taken of the arms of the participant while he or she stood in the anatomical position. Those measures included (a) upper arm length (acromion to epicondylus lateralis), (b) lower arm length (epicondylus lateralis to processus styloideus ulnae), and (c) hand length (processus styloideus ulnae to the tip of the middle finger). In addition, body height and body weight were measured. Data Collection and Compression Initial processing. From the reference measures, a 3D coordinate system (x-, y-, and z-axis) was defined that coincided with the sagittal, frontal, and transverse plane for each participant as depicted in Figure 1B (cf. Veldpaus, Woltring, & Dortmans, 1988). We calculated and then filtered the rotation (in degrees) of the marker frames around the three axes by means of a lowpass linear phase FIR filter, cut-off frequency 5 Hz (which eliminated the noise from the data while leaving the characteristic frequencies of the movement, which were all lower than 2 Hz, unaffected). The analyses were restricted to the rotational movements of the lower legs and the forearms in the sagittal plane (i.e., rotation around the z-axis). 2 To center the time series around the origin of the z-axis, we subtracted the mean rotation of each time series in this coordinate from the position signal at each sample. Thus, the movements of the arms and the legs were expressed as rotational movements (in degrees) around the z-axis. Spectral analysis. To determine whether different frequency-locked patterns of coordination were present between the arm and leg movements, we analyzed the collected data in three steps. First, we determined the dominant frequency of each limb movement by applying a Fast Fourier Transform (FFT) algorithm to the position data. On the basis of the output of the FFT, we defined the dominant frequency of the limb movement as the frequency at which the largest peak was present in the power spectrum. This peak had to be larger than the mean power plus twice its standard deviation. Second, we calculated the ratio between the dominant frequencies for the arm and leg movements at each side of the body. Similarly, we calculated the ratio between the dominant frequency for the arm movement and the second significant frequency (first super harmonic) 28 Chapter 2

31 of the leg movement. Third, we established whether the calculated frequency ratios were at or near the integers 1 or 2. Given the accuracy of estimating the dominant frequencies of the individual limb movements, and in view of the theoretical consideration that 1:1 frequency locking is typically more stable than 2:1 frequency locking (e.g., Serrien & Swinnen, 1997), a tolerance region of 10% was accepted for frequency locks around 1 and a tolerance region of 5% for frequency locks around 2 (i.e., 1 ± 0.1 and 2 ± 0.1). (A sharper criterion was used for the less stable frequency mode because the smaller the region of parametric resonance the greater the probability that the measured value in fact belongs to a neighboring region of parametric resonance of higher order, e.g., 2:3 is closer to 1:2 than to 1:1; for details see Treffner & Turvey, 1993). In addition to the FFT of the time series of the limb movements, we correlated in pairs (i.e., right leg/left leg, left arm/right arm, right arm/right leg, left arm/left leg, right arm/left leg and left arm/right leg) the power spectra of the individual limb movements by using a special kind of crossspectral analysis, called weighted coherence (Porges & Bohrer, 1980). This analysis was performed to evaluate and compare the shared rhythmicity (i.e., the degree of coupling) between pairs of limb movements and to assess the effect of walking velocity in that regard. First, the coherence, Cxy, between the power spectra of two signals x and y was calculated as follows: Pxy( ω) Cxy( ω) =, Pxx( ω) Pyy( ω) where Pxy(ω) is the cross-spectral density of signal x and y at frequency ω and Pxx(ω) and Pyy(ω) are the power spectral density of signal x and y at frequency ω. In the case of nonhomologous limb pairs, the leg movement was defined as signal x, and in the case of homologous limb pairs the left limb was defined as signal x. The weighted coherence or C w was then calculated across the frequency band of Hz, 3 according to the following formula: Cw = 2.0 ω= 0.1 Cxy( ω) Pxx( ω). 2.0 Pxx( ω) ω= 0.1 For each participant, the weighted coherence was calculated for all six limb pairs and for each walking velocity. 2 Chapter 2 29

32 Eigenfrequency. The eigenfrequencies of the arms were estimated according to the commonly used pendulum equation for animal locomotion (Holt et al., 1990; Holt, Jeng, Ratcliffe, & Hamill, 1995; Kugler & Turvey, 1987; Wagenaar & Van Emmerik, 2000): 1 ω0 = L 2π 2g, where ω 0 = eigenfrequency, π = , L = simple pendulum equivalent length, and g = 9.81 m/s 2. The simple pendulum equivalent length (L) was calculated from the three segments of the arm (upper arm, lower arm, and hand), according to the following formula: L = I / (M D), where I = moment of inertia, M = mass, D = distance from acromion to the center of mass of the arm. Moments of inertia were estimated from anthropomorphic data (Winter, 1990). t limbx(i) t limbx(i+1) t limby(i) t limby(i+1) Arm movement rotation around z-axis Leg movement time Figure 2. Example of an experimental trial in which the frequency of the arm movements (upper trace) was twice as high as that of the leg movements (lower trace). For such trials, the relative phase was calculated on the basis of the first maxima of the arm movement subsequent to the maxima of the leg movement. See text for abbreviations. Point estimates of relative phase. For the 1:1 frequency coordination, point estimates of relative phase were calculated using the moments (t limbx and t limby ) at which the positive maxima were reached in the angular position data of the limbs: 30 Chapter 2

33 φ (i) t = t limby( i) t t limbx( i) limbx( i+ 1) limbx( i) 360, where limby and limbx were the right and left limbs, respectively, when calculating the point estimate of relative phase between homologous limb movements. In the case of nonhomologous limb pairs, limby and limbx were the arm and leg movements, respectively. In the case of 2:1 frequency coordination, the maximum of the arm movement subsequent to the maximum of the leg movement was used for calculating the relative phase and the second maximum was ignored (see Figure 2 for an example). We assessed the stability of the coordination between the limbs by calculating the standard deviation of the mean relative phase (SDφ) for all six pairs of limb movements for each participant and for each walking velocity. We calculated means and standard deviations of relative phases by means of directional (or circular) statistics to avoid artifacts caused by phase wrapping (Batchelet, 1981; Burgess-Limerick, Abernethy, & Neal, 1991). Continuous estimates of relative phase. To examine the continuous aspects of the phase progression of the individual limb movements, we differentiated the angular position time series and projected the angular position time series and the calculated angular velocity time series in the phase plane to obtain the phase angle ϕ (i). After normalization of the angular position and velocity time series to their respective maxima and minima, the phase angles were calculated as follows: ϕ tan 1 ( i) = [( dx / dt) / x]. We determined discrete values of the continuous estimate of relative phase at the peaks (moment of maximum forward extension of the limb) and valleys (moment of maximal backward extension of the limb) of the time series by subtracting the phase angles of two limb movements, as follows: θ n: m = nϕs mϕf, where n:m represent the found dominant frequency ratios (1:1 or 2:1). The phase angle of the slower limb, ϕ S, was multiplied by n (1 or 2) and the phase angle of the faster limb, ϕ F, was multiplied with m (i.e., 1). Hence, we generalized the relative phase to n:m rhythm. In line with the procedure of the point estimate of relative phase, the phase of the arm movement was subtracted from the phase of the leg movement, or, in the case of homologous limb pairs, the phase of the left limb movement was subtracted Chapter 2 31