Design and procedure

As described in the introduction, the aim of the study was to investigate the effects of predictive and non-predictive tracking modes on movement performance and control. To achieve this, various 2D target trajectories were generated with a pseudo-random shape.

One of these trajectories (TR1) was only presented in periodic repetitions, whereas the other trajectories (TR2, TR3, TR4) were presented in a random order without repeti-tions. Moreover, in order to further stimulate predictive tracking of TR1, subjects were familiarized with this trajectory during an initial training block (seeMeasurement blocks for further details of the experimental design).

Trajectories

The 2D-velocities of the generated trajectories were based on sums of 5 harmonics with random phase and a base frequency corresponding to a period of 4 s. The 5 harmonics had frequencies of 0.25, 1, 1.75, 2.5, and 3.25 Hz. The peak velocities of the compo-nents were proportional to a Gaussian envelope with a value 1 at 0 Hz and decayed for higher frequencies. The decay of 3 dB was reached at 0.75 Hz. The frequency and magnitude values of the summed components were selected after visual inspection of various parameter combinations. Bothx and y velocities were generated independently.

Integrating these velocities yielded the 2D trajectories. These trajectories were then re-sampled nonlinearly to adjust the sampling distance (sd) according to (2.4), where V denotes the tangential velocity, r is the radius of curvature, and K and α are two free parameters [23]. This method is known as the two-thirds power law that describes an empirical relationship between the shape and the kinematics of free-hand and manual tracking movements [24,25], and it was applied here to assure that the subjects perceive the generated trajectories as natural as possible to avoid trajectory-induced error factors during the analyzed tracking movements.

1http://www.qnx.com/products/neutrino-rtos/neutrino-rtos.html?lang=en

sd

∆t =V =K r

1 +α·r ¹₃

(2.4)

The variable ∆t specifies the sampling interval for the generated movement trace. The parameters K andαwere adjusted to achieve a mean tangential velocity of 10 cm/s and a ratio between the maximum and minimum tangential velocity of 2.

In this way 14 different random trajectories were generated independently from each other. Figure 2.2shows the 4 trajectories (TR1 to TR4) used for repeated presentation, as described in the next section. The remaining 10 trajectories (uniformly denoted as TRU) were used to introduce ”unpredictable” sections, as described below.

-15 -10 -5 0 5 10 15

-15 -10 -5 0 5 10 15

TR1 TR2 TR3 TR4

Vertical position (cm)

Horizontal position (cm)

Figure 2.2: The presented target trajectories. Closed traces were generated by integrating sums of 5 harmonics with a random phase and a base frequency correspond-ing to a period of 4 s. Labels (TR1-TR4) were assigned randomly to the generated

trajectories.

Measurement blocks

The smallest unit of the design was one presentation of a generated trajectory, which is referred to as a ”trial”. Trials were grouped into so-called ”sub-blocks”, followed by a pause of 4 s. The initial trials of these sub-blocks were not included in the analysis because they differed from the other continuation trials in the movement initiation required after the 4 s pause (see alsoData exclusion). The main experiment was composed of 6 blocks, each consisting of several sub-blocks as described below (for a graphical representation, see Figure 2.3). Blocks were separated by a break of about 5 minutes.

(1) In the first block, only the trajectory TR1 was presented in the so-called periodic training presentation mode as follows. The block consisted of 10 sub-blocks each con-taining 4 trials with periodic presentation of TR1. The purpose of this block was to make the subject familiar with the selected trajectory without introducing unwanted fatigue effects (pauses between sub-block executions). From the 40 presented trials, 30 continuation trials were analyzed.

(2) The periodic training block was followed by 5 test blocks, each presenting 12 sub-blocks. Six of these sub-blocks showed the non-periodic test presentation mode and contained the three trajectories TR2, TR3 and TR4 in a random order led by one of the unpredictable sections (TRU). Each of these 6 sub-blocks contained one of 6 possible permutations of TR2, TR3 and TR4. Alternating with the non-periodic test sub-blocks, 6 sub-blocks were inserted with TR1 in the so-called periodic test presentation mode.

This presentation mode was – apart from the vicinity to thenon-periodic test sub-blocks – identical to the periodic training mode. After exclusion of the initial trials of the periodic test sub-blocks and the initial, unpredictable sections of the non-periodic test sub-blocks, the five test blocks provided in total 90 trials (5 blocks ×6 sub-blocks ×3 trials) of periodic test trials (TR1), and 90 trials (5 blocks× 6 sub-blocks×3 trials) of non-periodic test trials (TR2, TR3 and TR4).

The specific structure of the non-periodic sub-blocks kept the subjects under the illusion of path randomness despite repetitive presentations of TR2-TR4. These repetitions were necessary to calculate joint angle variance-covariance which is the basis for the Uncontrolled Manifold Method.

TRAINING pause (4 s) pause (4 s)

...

pause (4 s)

TR1TR1TR1TR11 TR1TR1TR1TR12 TR1TR1TR1TR110

pause (4 s)

TRUTR3TR4TR21 pause (4 s)

TR1TR1TR1TR12 TRUTR3TR4TR23 pause (4 s) TR1TR1TR1TR14

...

pause (4 s) pause (4 s) TRUTR3TR4TR211 pause (4 s) TR1TR1TR1TR112

TEST (x5) Measurement block Periodic training / test sub-block Non-periodic test sub-block Non-periodic control sub-block

CONTROL pause (4 s) pause (4 s)

...

pause (4 s)

1TR1TR3TR4TR2TRU 2TRUTR4TR1TR2TR3 10TRUTR1TR3TR4TR2 Figure2.3:Measurementblocksoftheexperiment.Thesmallestunitofthedesignwasonepresentationofageneratedtrajectory,which isreferredtoasa”trial”.Trialsweregroupedintoso-called”sub-blocks”,followedbyapauseof4s.Themainexperimentwascomposedof6 blocks(TRAINING+5xTEST),eachconsistingofseveralsub-blocksofselectedtrajectories.ThemeasurementwiththeCONTROLblockwas performedafterthemainexperimenttotestwhetherdifferencesbetweenperiodicandnon-periodicpresentationswererelatedtothepresentation modesandnottodifferencesbetweenthetrajectories.ThebordersofthegraphicalboxesdenotingTR1-TR4refertothecorrespondingtrajectories showninFigure2.2

To test whether effects of periodic or non-periodic presentations were related to differ-ences between the trajectories rather than to the presentation modes a control experiment was performed on a different day, at least five weeks after the main experiment. This control consisted of a single ”non-periodic” block with 10 sub-blocks, each starting with one of the ”unpredictable” sections (TRU) followed by TR1, TR2, TR3 and TR4 in a random order. Thus, each trajectory was presented 10 times.