Discrete and Rhythmic Dynamics as Units of Coordinated Action: Behavioral Data, a Model,

1. Discrete and Rhythmic Dynamics as Units of Coordinated Action: Behavioral Data, a Model, and Brain Imaging Results Dagmar Sternad Pennsylvania State University In collaboration with: Aymar de Rugy, Kunlin Wei, William Dean

2. Everyday behaviors consist of both discrete and rhythmic elements, in parallel or insequence ! TheQuestion: What are the units or primitives that are underlying in the formation of complex actions and sequences?

3. Division into Rhythmic and Discrete Actions Different Control Strategies ? Literature is divided into studies on rhythmic and discrete actions: • Computational and cognitiveapproaches typically focus on discrete reaching or pointing movements or sequencing of action elements (e.g., Morasso, Flash, Ghez, Rosenbaum) • Equilibrium-point model proposes “discrete” virtual trajectories (e.g. Feldman, Latash) • Rhythmic movements are a concatenation of discrete elements or “strokes” • Research on Central Pattern Generators places emphasis on rhythm generation (e.g., Grillner, Delcomyn, Selverston) • Dynamical systems approach emphasizes rhythmic movements typically in bimanual and locomotory actions, “primacy of rhythms” (e.g., Turvey, Kelso, Beek, Schöner) • Discrete movements are aborted limit cycles What are the primitives that are underlying in the formation of behavioral sequences?

4. Some Recent Exceptions: Staude and colleagues (1998, 2000, 2002): Initiation of a discrete movement at the background of tremor and voluntary oscillations, work on signal onset detection Smits-Engelmann et al. (2002) and Buchanan et al. (2003): Discrete and rhythmic performance of a Fitts task Ivry and colleagues (2002, 2003): Distinction into continuous and discrete movements with explicit temporal or spatial goal Criterion: Difference in timing variability Selective impairment in cerebellar patients and split-brain patients in discrete movements Jirsa and Kelso (submitted): Topological argument for existence of two movement primitives Sternad and colleagues (2000, 2001, 2002, 2003): Discrete and rhythmic movements in single-limb, intralimb, interlimb movements And not so recent: Wacholder (1928): ”Willkürliche Haltung und Bewegung”

5. The Big Picture Theoretical Backdrop: • Movement trajectories are the outcome of a high-dimensional nonlinear dynamical system • “Units” of this dynamical system are fixed point and limit cycle attractors • For complex behaviors these units are coupled

6. Hypothesis and Questions Discrete and rhythmic actions are two units of action ! • A limb can oscillate and/or translate around each joint df • Discrete movements are changes between positions (in extrinsic space) • Oscillations are back and forth movements around a fixed midpoint (in intrinsic space) • What kind of oscillators can be conceived? • How could a discrete dynamics look like? • How do they interact?

7. A Three-Tiered Strategy 1) Behavioral experiments 2) Modeling 3) Brain imaging Let’s start with a behavioral experiment:

8. EXPERIMENT 1: A SIMPLE COMPLEX TASK T1 • Instruction: • “Move rhythmically around the target according to the period prescribed by a metronome. Upon another metronome signal, shift to the second target. Do this either as fast as possible without stopping the oscillation or whenever you want.” T2 T3 T4 • Experimental Design: • Three tasks: MID, AMP, MID+AMP • 2 instructions: Self-paced and reaction time • All conditions were initially paced at 2Hz • 15 trials per condition, tasks were conducted in 3 blocks • 6 participants

9. The Three Tasks Change in the amplitude of the oscillation, no discrete movement Change in both amplitude and midpoint of oscillation Discrete change in the midpoint of the oscillation, no change in oscillation

10. Kinematics and EMG Data Dependent Measures:Phase of Discrete Movement Initiation: fonset and fdisc Reaction Time: RTpremotor and RTCOM fonset fdisc • Also: • Expected phase of initiation: • fexp =fexp +RT • Phase shift of oscillation • - Peak velocity of discrete movement

11. 1. Phase of the Discrete Initiation fdisc fonset • - fonsetandfdiscare limited to subsets of phases, but mode is shifted by 1/4 cycle • Resultsoffdisc are centered around 0 and 2π rad and are more pronounced • No difference between tasks within an instruction condition

12. 1. Phase of the Discrete Initiation fdisc shows nonuniform distribution, while fexp is uniformly distributed When fonset was plotted in the same fashion against fexp, the pattern disappeared almost completely. fdisc is the more relevant measure This expresses synchronization rather than a threshold mechanism

13. 2. Reaction Time: Distributions Using the threshold method by Abbink et al. (1998) Too many unrealistic values Using the center of mass of the discrete burst Potentially overestimation but no unrealistically short values

14. 2. Reaction Time as a Function of Expected Phase RT is either shortened or lengthened in order to synchronize the discrete burst with one of the ongoing rhythmic bursts. No asymmetry in the distribution.

15. 3. Differences between Tasks: Reaction Time Average RTCOM for: MID: 275 ms AMP: 290 ms MID+AMP: 330 ms Longest time for most complex task! Implicit support for the conceptual distinction into discrete and rhythmic units

16. A MODEL WITH TWO UNITS – A LIMIT-CYLCE OSCILLATOR AND A FIXED-POINT ATTRACTOR The oscillator is motivated by neuronal, half-center oscillator models (Matsuoka, 1985): Two mutually inhibiting neurons with tonic input

17. RHYTHMIC PATTERN GENERATOR Output of the oscillator yi yj Input to the oscillator SR

18. The neural output drives a limb: Joint angle displacement q Antagonistic torques are linear functions of the output of the oscillator Limb dynamics driven by torques:

19. DISCRETE PATTERN GENERATOR SD tonset yi yj

20. ACTIVATION AND OUTPUT SIGNALS Input to the oscillator yi yi yj Output of the oscillator yj Joint angle displacement Desired position

21. COMBINATION OF DISCRETE AND RHYTHMIC UNITS IN 3 TASKS Unweighted superposition of the two activation signals: sRD = sD + sR Increase in oscillatory amplitude is achieved by an increase in sR

22. How it works at 6 different onset times t0 between 0 and 2π rad : Center of mass merges with its closest burst, producing a discontinuous shift from 0 to 2π rad

23. SIMULATION RESULTS: PHASE AND REACTION TIME IN 3 TASKS

24. 2. Reaction Time as a Function of Expected Phase RT is either shortened or lengthened in order to synchronize the discrete burst with one of the ongoing rhythmic bursts. No asymmetry in the distribution

25. First Summary of Results of the Unimanual Task A clear set of results: Replication: Discrete initiation and reaction time is constrained by the rhythmic movement. Measures on the basis of center of burst activity give clearer results, speaking to synchronization rather than a threshold mechanism underlying the interaction of the two units. Differences in reaction times between tasks indicate that MID+AMP is the most complex task => indirect support for distinction into rhythmic and discrete units. How else can the hypothesis of rhythmic and discrete movement primitives be tested? Brain imaging

26. EXPERIMENT 2: CORTICAL ACTIVITY DURING RHYTHMIC AND DISCRETE MOVEMENTS - fMRI Hypothesis: If discrete and rhythmic actions are different behavioral units, different brain activity should be observed. Task: Subjects perform self-paced rhythmic and discrete wrist actions, randomly initiated.

27. Methods 4T fMRI scanner • Visual signaling of experimental conditions • Video-based monitoring of subjects • Anatomical (T1) scan before and after sessions • One full brain scan every 5 seconds (24 slices, 6mm apart) • Voxel dimensions 3.5 x 3.5 x 6.0 [mm3]

28. Experimental Design • Conditions: • Rhythmic wrist movements • Discrete self-initiated wrist movements • Rest condition • 30 seconds with 6 scans per condition • 4 repetitions per session presented in randomized order • Two 6-min sessions per subject • Anatomical (T1) scan before and after sessions • 11 subjects

29. RESULTS AVERAGES OF 11 SUBJECTS Rhythmic – Rest Confined to contralateral primary and supplementary motor cortex, and ipsilateral cerebellum Discrete – Rest Additional activation of contralateral premotor and parietal areas, and other ipsilateral areas

30. Discrete versus Rhythmic Parietal cortex Premotor cortex discrete rhythmic rest

31. CONTROL EXPERIMENT Possible alternative explanations for results: • Higher effort in discrete movements due to accelerations and decelerations • More start-and-stops, i.e., movement initiation and termination • Control Conditions: • Continuously rhythmic wrist movements • Rhythmic movements with 6 stops • 6 discrete movements • Rest • 30 seconds per condition, 4 repetitions per session, randomized order • 2 sessions per subject • 6 subjects • Anatomical scan before and after sessions

32. Experiment 1 Discrete – Rhythmic Experiment 2 Discrete.stop – Rhythmic.stop

33. Experiment 1 Experiment 2 Rhythmic.stop – Rhythmic.cont Discrete – Rhythmic Inferior parietal cortex Superior parietal cortex Parietal cortex: Start and stops use another area

34. Experiment 2 Experiment 1 Rhythmic.stop – Rhythmic.cont Discrete – Rhythmic

35. THE POINT IS THAT: There is support for our starting hypothesis ! We started with the hypothesis: • Movement systems are nonlinear dynamical systems with two fundamental attractor types: Point attractor and limit cycle attractor • Behavioral sequences are generated by oscillatory and discrete “primitives” • The two units exert specific constraints onto each other when they co-exist Behavioral experiments: • Kinematic data provide data basis for formulation of a model Modeling experimental results: • Using a neural model with activation/parameter dynamics Brain imaging study: • Discrete and rhythmic movements engage different brain areas

36. More Questions: Two different units of actions that are multiply coupled to produce complex behaviors !? Can we generalize these results to combinations across joints?

37. EXPERIMENT 3: "CLEANING THE TABLE" • Instruction: • “Move your hand rhythmically around one target at the given frequency. Upon a trigger signal, shift to the second target as fast as possiblewithout stopping the oscillation.” • Experimental Design: • Two directions: T1 -> T2, adduction • T2 -> T1, abduction • Trigger tone at randomized phases • 10 trials per condition, randomized order

38. Two Hypotheses The constraints between rhythmic and discrete elements occur at a neural level. Hence, similar interactions should be observed as found in single-joint movements. Passive torques across the limb segments become the dominant factor. Exploitation of interaction torques becomes the constraining factor for the coupling between limb segments.

39. RESULTS: ENDPOINT TRAJECTORIES Exemplary trial: T1 -> T2 Onset of discrete movement is at ~ 3π/2 rad (maximal elbow flexion is π rad). *

40. RESULTS: JOINT TRAJECTORIES AND EMG SIGNALS Onset of discrete movement Trigger Elbow joint angle Shoulder joint angle • Oscillations were performed only in the elbow joint. • Discrete displacement was performed only in the shoulder joint. • Amplitude and frequency of oscillation is maintained before and after the discrete movement. • Little perturbation of the steady state oscillation. Brachioradialis Lateral triceps Anterior deltoid Posterior deltoid

41. PAIRWISE RELATIVE PHASE BETWEEN RHYTHMIC EMG ACTIVITY Relative phase between brachioradialis anterior and posterior deltoid is antiphasic, implying co-contraction to stabilize the shoulder joint during elbow oscillation.

42. ONSET OF THE DISCRETE MOVEMENT Histogram Onset as a phase of the agonist EMG (shoulder cycle): Activity of posterior deltoid facilitates the initiation of the discrete movement. Replication of single-joint results. 0 π 2π

43. ONSET OF THE DISCRETE MOVEMENT Onset as a phase of the elbow cycle: Discrete onsets prevail at phases between π and 2π rad of the elbow cycle.

44. JOINT TORQUE ANALYSIS: AVERAGE TORQUE PATTERNS PER CYCLE Adduction Are phase preferences coincident with phases where torques assist the movement? Steady state torque patterns during oscillations at T1 and T2: Shoulder adduction is assisted by interaction torque in the middle part of the elbow cycle. Elbow extension flexion

45. JOINT TORQUES AT ONSET Peak Acceleration Onset Time profiles of shoulder torques at abduction onset (4.83 rad): Muscle and net torques are opposing the discrete initiation. During the first discrete interval the signs of all torque profiles change.

46. MY MAIN POINTS • Cleaning a table: A task that explicitly cuts across the distinction between rhythmic and discrete movements. • Complex endpoint trajectory can be parsed into simpler units at the joint level. • Replication of single-joint results: The simultaneous coordination of discrete and rhythmicactions in uni- and multijoint actions imposesspecific constraints on the coordination. • Constraints appear to arise at the local level while central signals remain independent. Where to go from here?

47. EXPERIMENT 4: Discrete and Rhythmic Actions in Bimanual Movements • Are the same mutual interactions also seen when discrete and rhythmic movements are performed in two mechanically separate joints? • Are these features more central neural interactions rather than mechanical effects?

48. Experimental Task • Instruction: • “Move your right arm rhythmically between T1 and T2 according to the period prescribed by the metronome. Upon another metronome signal, shift your left arm from T3 to T4as fast as possible, without stopping the oscillation. • Two blocks: 1) Initiation of a discrete movement. • 2) Initiation of a rhythmic movement. • Experimental Design: • Metronome periods: 250ms, 350ms, 450ms, 550ms • Rhythmic and discrete initiation • 15 trials per condition per period, randomized order

49. KINEMATICS AND EMG DATA

50. Timing and Resonance Properties in Rhythmic Coordination Dagmar Sternad Hong Yu, Aymar de Rugy, Daniel Russell The Pennsylvania State University Department of Kinesiology