Internal models of target motion: expected dynamics overrides

Articles in PresS. J Neurophysiol (November 19, 2003). 10.1152/jn.00862.2003
Internal models of target motion: expected dynamics overrides measured
kinematics in timing manual interceptions
Myrka Zago1, Gianfranco Bosco 1,2, Vincenzo Maffei1 , Marco Iosa1 , Yuri P. Ivanenko1, and
Francesco Lacquaniti1,2
1Sezione di Fisiologia umana, IRCCS Fondazione Santa Lucia, via Ardeatina 306, 00179
Roma (Italy), 2Dipartimento di Neuroscienze and Centro di Biomedicina spaziale, Università di
Roma Tor Vergata, Via Montpellier 1, 00133 Roma (Italy)
running title: Internal models for target interception
Correspondence to:
Dr. Myrka Zago
IRCCS Fondazione Santa Lucia
via Ardeatina 306
00179 Rome (Italy)
ph +39-06-51501478
fax +39-06-51501482
e-mail: [email protected]
Copyright (c) 2003 by the American Physiological Society.
Prevailing views on how we time the interception of a moving object assume that the visual
inputs are informationally sufficient to estimate the time-to-contact from object’s kinematics.
Here we present evidence in favor of a different view: the brain makes the best estimate about
target motion based on measured kinematics and an a priori guess about the causes of motion.
According to this theory, a predictive model is used to extrapolate time-to-contact from
expected dynamics (kinetics). We projected a virtual target moving vertically downward on a
wide screen with different randomized laws of motion. In the first series of experiments,
subjects were asked to intercept this target by punching a real ball that fell hidden behind the
screen and arrived in synchrony with the visual target. Subjects systematically timed their
motor responses consistent with the assumption of gravity effects on an object’s mass, even
when the visual target did not accelerate. With training, the gravity model was not switched
off but adapted to non-accelerating targets by shifting the time of motor activation. In the
second series of experiments, there was no real ball falling behind the screen. Instead the
subjects were required to intercept the visual target by clicking a mouse-button. In this case,
subjects timed their responses consistent with the assumption of uniform motion in the
absence of forces, even when the target actually accelerated. Overall, the results are in accord
with the theory that motor responses evoked by visual kinematics are modulated by a prior of
the target dynamics. The prior appears surprisingly resistant to modifications based on
performance errors.
Key words: visuo-manual coordination, interception, motor timing, time-to-contact, internal
models, gravity
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Introduction
Interception requires precise timing, whether to catch or hit a ball, to jump on land or dive in
water. How do we estimate time-to-contact (TTC) with an approaching object? Most extant theories
posit that all relevant information is present in the visual stimulus without resorting to high-level
computations or internal representations (Gibson 1966; Lee and Reddish 1981; Regan and Gray
2000; Tresilian 1999). However there are limitations in the visual system that raise questions about
the general validity of these theories (Lacquaniti et al 1993a). Although several monocular and
binocular cues can contribute to TTC-estimates, they generally provide only first-order
approximations related to object’s distance and velocity (Lee and Reddish 1981; Rushton and Wann
1999; Regan and Gray 2000; Tresilian 1995). In fact neurophysiology shows that cortical neurons
specialized for visual motion processing accurately encode target velocity and direction, but contain
only partial information about acceleration (Perrone and Thiele 2001). Moreover, psychophysics
indicates that the human visual system poorly estimates image accelerations over short viewing
periods (Bozzi 1959; Brouwer et al 2002; Regan et al 1986; Runeson 1975; Werkhoven et al. 1992).
Accordingly, at the motor level arbitrary accelerations generally are not taken into account in timing
interceptions (Bootsma et al 1997; Engel and Soechting 2000; Gottsdanker et al 1961; Lee et al.
1997; Port et al. 1997). Another problem is that, due to sensorimotor delays, interceptive actions
must be anticipatory, based on information available at least 100-200 ms before contact.
Extrapolation of visual motion information into the future can lead to severe spatial and temporal
misjudgements (Tresilian 1995).
To overcome these problems, it has been hypothesized that on-line visual information is
combined with an a priori representation (called reference model) of target dynamics that depends
on the context of the specific visuomotor task (Lacquaniti et al 1993a). In other words, the brain
could make the best guess about visible or hidden causes of object’s motion at any time, and use a
predictive model to extrapolate TTC from expected dynamics (kinetics) rather than from measured
kinematics. In Newtonian dynamics a free particle moves with constant velocity, unless acted upon
by an accelerative force. If it is difficult to discriminate arbitrary accelerations visually,
gravitational acceleration might be internalized based on lifelong exposure (Hofsten and Lee 1994;
Hubbard 1995; Lacquaniti et al 1993a; Watson et al 1992; Tresilian 1993). Visual signals about
target position and velocity could be combined with an internal estimate of earth gravity, yielding a
second-order dynamic model of TTC for interception of objects whose motion is expected to be
affected by gravity (Lacquaniti and Maioli 1989; Lacquaniti et al 1993a; McIntyre et al 2001). In a
similar vein, it has been suggested that targeted movements are coupled to an intrinsic second-order
guide similar to gravity (Lee 1998). The idea that an internal model of gravity can be used to
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disambiguate sensory information has also been developed in the field of vestibular physiology.
Vestibular otoliths (as all linear accelerometers) measure gravito-inertial forces, but cannot
distinguish linear accelerations from gravity. Based on eye movement responses to combinations of
tilts and rotations, it has been proposed that the brain combines canal signals with otolith signals
and uses an internal model of gravity to estimate linear accelerations and disambiguate tilt from
translation of the head (Hess and Angelaki 1999; Merfeld et al 1999).
Here we show that the timing of responses aimed at intercepting a visual target is very different
depending on the dynamic context. Virtual targets moving vertically downward with different laws
of motion were intercepted with a timing consistent with the assumption of uniform motion in the
absence of forces. In contrast, when the same virtual targets were used to punch a hidden real ball
arriving in synchrony, response timing was consistent with the assumption of gravity effects on an
object’s mass. With training, the gravity model was not switched off, but adapted to nonaccelerating targets by shifting the time for motor activation. The results indicate that responses
evoked by low-level visual inputs change with the context established by dynamic predictive
models from higher-level processing.
Methods
Subjects
In total twenty healthy subjects (12 women and 8 men, 29 ± 5 years old, mean ± SD)
participated in the study receiving modest monetary compensation. All but one subject participated
in one experiment only. The subjects were right-handed (as assessed by a short questionnaire based
on the Edinburgh scale), had normal vision or vision that was corrected for normal, and were naïve
to the purpose of the experiments (except subject G.B.). Experiments were approved by the
Institutional Review Board and conformed to the Declaration of Helsinki on the use of human
subjects in research.
Apparatus
First we describe the setup common to both the punching and the button-press experiments.
Subjects sat on a chair placed in front of a wide vertical screen attached to the ceiling (Fig. 1). The
screen (Video Spectra 1.5-gain) had a pearlescent frontal projection surface of 3.94-m wide, 2.13-m
high. The rear part of the screen was made of black, non-transparent material, preventing the view
of any object through it. The back of the chair supported the head and torso of the subjects without
preventing their motion. The vertical inclination of the back was adjusted at about 40° so as to
allow a comfortable view of the screen with the subjects’ eyes located at 0.5-m horizontal distance
4
from the screen, 1.82-m below the top. In that position subjects could easily reach below and
beyond the lower border of the screen by protracting their arm forward. Images were generated by a
PC and displayed on the screen by a BARCO Graphics 808s (1024x768 pixels, 85-Hz refresh
frequency). A black 9-cm wide box was constantly displayed at the top of the screen against a white
background. In each trial a red 9-cm-diameter target-sphere moved vertically downward; it was
displayed initially as emerging progressively from within the start box at a predefined speed and
acceleration (see protocols) and then shifted with the prescribed law of motion to finally disappear
progressively at the lower border of the screen. The visual angle subtended by the target increased
from 0.8°, when it was first fully visible, to 10.3° when it passed at eye-level. The rest of the room
was dimly illuminated, the only light sources being the BARCO and a PC monitor. Next we
describe the setup specific for each set of experiments.
PUNCHING EXPERIMENTS. A precision laminated electromagnet (G.W. Linsk Co. Inc., Clifton
Springs, N.Y., U.S.A.), attached behind the screen, held a 9-cm-diameter, 70-g-weight inflated
rubber ball. This was a soft ball bought in a children toy-shop, and never caused any discomfort to
the subjects even after several punching trials. A small steel washer (1.4-cm-outer diameter) was
attached to the ball surface to ensure magnetic contact with the electromagnet. The electromagnet
release accuracy was better than 1 ms. Spatial trajectories of the center of the virtual sphere on the
screen and of the real ball were aligned in the vertical plane orthogonal to the seat of the chair,
offset by 7.5-cm in depth. The release time of the real ball and the start time of virtual motion were
set by the computer so as to result in synchronous arrival at an interception point located below the
lower border of the screen. The time of synchronous arrival will be denoted interception time in the
following. Synchronous timing of virtual and real motions was determined by means of an optic
calibration procedure that involved 1-KHz-shuttered video-recordings axially centered on the
interception point. The timing error was always less than the refresh rate of image display for all
tested laws of simulated motion. Because the release of the ball from the electromagnet and its
subsequent fall were noiseless and invisible, the visual information about the virtual motion
provided the only perceptually available TTC-information before the ball contact with the arm.
BUTTON-PRESS
EXPERIMENTS.
Here there was no real ball falling behind the screen. Subjects
sat on the chair as before, grabbing a computer mouse in the right hand. To provide visual feedback
of late interceptions, the screen surface was prolonged downwards with a 0.9-m-long, 0.33-m-wide
strip. A black start box and a blue end box were constantly displayed at the top and bottom of the
regular screen, respectively, the red target-sphere moving downward from the start to the end box.
Recording system
5
PUNCHING EXPERIMENTS. 3D motion of selected body points was recorded at 200 Hz by means
of the Optotrak 3020 system (Northern Digital, Waterloo, Ontario, ± 3SD-accuracy better than 0.2
mm for x,y,z coordinates). Three infrared emitting markers were attached to the skin overlying the
shoulder, elbow, and wrist joint on the right arm. Three additional markers were fixed to the lower
border of the screen to determine the screen plane. A miniature accelerometer (Isotron Endevco),
fixed on the wrist, was sampled at 1 KHz. Electromyographic (EMG) activity of the clavicular
portions of pectoralis (PE) and trapezius (TP), anterior deltoid (AD), posterior deltoid (PD), biceps
(BC), triceps (TR), and flexor carpi radialis (FC) was recorded by means of surface electrodes
(SensorMedics 650414, 2-mm diameter of detection surface) in bipolar configuration (1 cm interelectrode distance). EMG signals were preamplified at the recording site using a pair of matched
FET operational amplifiers to reduce noise, and then differentially amplified (120-dB CMRR),
high-pass filtered (20 Hz), low-pass filtered (200-Hz, 4-pole Bessel), and sampled at 1 KHz.
Sampling of kinematic and EMG data were synchronized with trial start.
BUTTON-PRESS
EXPERIMENTS.
The analog voltage signal from the mouse-button was A/D
converted and sampled at 1 KHz synchronized with trial start.
Experimental procedures and protocols
Before the experiment, subjects received general instructions and familiarized with the set-up
in front of the screen (they could not see behind it). They were informed that in each trial a visual
target-sphere would move vertically downward from the start box at different randomized speeds.
PUNCHING
EXPERIMENTS.
Subjects were asked to intercept the target just below the lower
border of the screen by punching the real soft-ball that would arrive there at the same time as the
visual target. They kept a free relaxed posture between trials. Before trial initiation, an alert signal
instructed the subjects to look at the box on the top of the screen and to recoil their arm in the
starting posture: with the adducted shoulder, the upper arm was roughly vertical, the forearm
horizontal, the wrist mid-pronated, the hand and fingers clenched in a fist. At the beginning of the
trial, an audible attention signal sounded and, after a random delay ranging from 1.2 to 1.7 s, the
virtual sphere exited from the black box. The movement required to punch the ball involved the
forward protraction of the hand by about 20 cm, along a roughly straight-ahead, horizontal
direction. Data were acquired for 5 s, starting 0.4 s before sphere exit. Inter-trial interval was about
14 s. Total duration of each session was about 1h 20 min, with 10-min of rest allowed halfway.
In any given trial the virtual sphere moved from the starting box with randomly assorted initial
speeds (v0 = 0.7, 1, 1.5, 2.5 or 4.5 m s-1) at a constant acceleration (either A = 0 or A = 9.81 m s-2=
1g). The randomization procedure always avoided identical combinations of v0 and A in consecutive
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trials. Subjects were assigned to one of 3 groups (with 5 subjects in each group). In each group,
subjects were exposed to identical sequences of trials.
Subjects of the first 2 groups performed 2 different experiments 24h apart. Each experiment
consisted of 4 identical blocks of 55 trials. In each block, there were 50 test-trials and 5 pseudorandomly interspersed ‘catch-trials’ with unexpectedly altered kinematics. For test-trials, v0 was
pseudo-randomly assigned to one of 5 values, and A was assigned to one fixed value for day 1
experiment (either 0 or 1g depending on the protocol) and the other fixed value on day 2. Thus,
A=1g on day 1 and A=0 on day 2 for group #1 (1g-0g protocol), whereas A=0 on day 1 and A=1g on
day 2 for group #2 (0g-1g protocol). Each catch-trial had the same v0 as the previous test-trial
(catch-1), but different A (A=0 if test-trial was 1g, and A=1g if test-trial was 0g), except for the
catch-trials of day 1 in group #1 that were all trials with A=1g, v0=0 m s-1. Each experiment
therefore consisted of 40 repetitions per 5 test conditions, and 4 repetitions per 5 catch conditions.
The sequence of target v0 was identical in day 1 and day 2. The first through the fifth catch-trials
occurred in the sequence as the 7th , 14th , 27th , 34th, and 54th trials, respectively. Catch-trials were
used to reveal the presence of after-effects due to adaptation (Shadmehr and Mussa-Ivaldi 1994).
Subjects of group #3 (Random protocol) performed a one-day experiment involving 200 testtrials without catch-trials. For each trial, both v0 and A were randomized (20 repetitions per 10
conditions).
BUTTON-PRESS
EXPERIMENTS.
Subjects sat in the same posture as for punching, and kept the
arm still on an arm-rest with the computer mouse grabbed in the right hand. Before trial initiation,
an alert signal instructed the subjects to look at the box on the top of the screen. At the beginning of
the trial, an audible attention signal sounded and, after a random delay ranging from 1.2 to 1.7 s, the
virtual sphere exited from the black box. Subjects were asked to click the mouse-button with the
index finger so as to intercept the descending target just as it reached the center of the end box
(interception point). If they intercepted in the allotted time (±15 ms relative to the exact interception
time), the target-sphere “exploded” blue with a pleasing reward sound. If they intercepted too early
or too late, the target-sphere was flashed red at the point of incorrect interception. Six subjects
performed a one-day experiment involving only test trials whose v0 and A were randomized (as in
Random above). One subject had participated in a punching experiment (Random protocol) about
one year earlier.
General data analysis
7
PUNCHING
EXPERIMENTS.
Rectified EMG and raw kinematic data were numerically low-pass
filtered (bi-directional 20-Hz-cutoff 2nd-order Butterworth filter) to eliminate impact artifacts.
Instantaneous tangential velocity of the hand was computed by numerically differentiating the
recorded x,y,z coordinates of the wrist marker. We measured motor timing based on the time of
occurrence of the first positive peak of hand acceleration, as this parameter was very reliably
derived from the data (see Fig. 3 for examples of acceleration records). The time of this acceleration
peak relative to the interception time will be denoted TTC. We also estimated the onset time (the
time when the acceleration first reached 10% of the first positive peak), and the time of zerocrossing of hand acceleration. Movement duration was defined as the interval between onset time
and zero-crossing time.
Nominally subjects had a timing tolerance of about ± 15 ms around the interception time to
contact the falling ball with the finger knuckles. However, to compute the interception rate we
allowed a wider margin of error, because subjects could effectively contact the ball also with other
parts of the hand (such as the top of the fist). Thus, to determine whether or not the ball was
intercepted in each trial, the time of any measurable contact between the ball and the limb was
determined by the occurrence of specific high-frequency oscillations in the accelerometer signal
(the raw signal was filtered with bi-directional 25-Hz-high-pass Butterworth filter). The ball was
considered intercepted if the contact oscillations occurred between the first positive peak of
acceleration and the first negative peak. Typically, this time interval was about 120 ms independent
of the conditions, implying that we considered as intercepted those trials in which the contact
occurred within ± 60 ms relative to the interception time. Interception rate was then computed as
the percentage of all intercepted trials over the total number of trials of a given condition. We also
verified that subjects intercepted close to the expected interception point by computing the vertical
spatial coordinate of the hand at the time of contact oscillations. This position was not significantly
different from the expected value in any subject. On average it was 0.7 ± 5.7 cm (mean ± SD,
across all trials and subjects) lower than the expected value, equivalent to a time lag of 1.0 ± 11.4
ms relative to the interception time. As a measure of the spatial error, we computed the anteroposterior horizontal spatial coordinate of the hand at the interception time and compared with the
corresponding coordinate of the screen markers.
An exponential function was fitted to the series of repetitions of TTC values for each condition
( v0 , A) to characterize the rate at which subjects adapted. The function has three free parameters:
offset b0 , gain b1 and time-constant b2.
TTCi = b0 + b1 exp(-i/ b2)
(1)
8
where TTCi was the TTC-value on repetition i.
BUTTON-PRESS EXPERIMENTS. TTC was measured as the time of the button-press relative to the
interception time. To calculate interception rate we used two different time windows relative to the
interception time: ± 15 ms or ± 60 ms. The first window corresponds to the time interval used to
provide positive or negative feedback of success to the subjects during the experiments. The second
window corresponds to the time interval that was used to compute interception rate in the punching
experiments. For both time windows, interception rate was derived as the percentage of the trials
whose TTC was included in the window.
STATISTICS. Differences between conditions were assessed using analysis of variance
(ANOVA) followed by Bonferroni-Dunn tests, and using Wilcoxon signed ranks or t-statistics
(p<0.05, level).
Few trials (0.2% of all trials) were excluded from the analysis due to the presence of artifacts
or lack of subject’s attention during the trial as marked in the experiment notebook.
Models of interception timing
Figure 2 defines the critical timing variables for both punching and button-press experiments.
The instantaneous height h (t ) of the virtual target above the interception point is given by the
standard equation of motion:
h (t ) = h0 − v0t − 0.5 At 2
(2)
 0 for 0 g trials
where h0 and v0 are the initial height and velocity, respectively, and A = 
1g for 1g trials
To intercept the target, subjects implicitly solve for h(t)=0 at t=expected interception time (IT).
IT does not necessarily coincide with the true interception time (flight duration of the target),
because the subject’s estimate of target motion might be erroneous. We hypothesize that a motor
response is programmed at a given lead-time LT relative to IT, necessary to compensate for signal
transmission delays. In general, LT will depend on neural and mechanical delays. Thus, LT = PT +
MT, where PT represents the processing time and MT represents the movement time (or the time
epoch of the movement segment under consideration). For causal systems, the future motion of the
target is unknown and can only be extrapolated based on current estimates of h(t) and its time
derivatives. The order of the model used for motion extrapolation refers to the time derivatives that
appear in the describing equation. Thus, a zero-order model includes only position, a first-order
model also includes velocity, and a second-order model also includes acceleration. We have
9
considered models that incorporate visual information about target distance and velocity, because it
is known that these variables can be measured accurately by the visual system (Orban et al. 1984;
Regan 1997). Visual acceleration generally is poorly measured (Regan et al 1986), and we have
considered a second-order model that incorporates an internalized estimate of gravitational
acceleration (Lacquaniti et al 1993a). Our models assume that the response is programmed after a
given visual or internalized variable has reached a critical threshold value at time TT = IT – LT.
This assumption is customary in models of fast interceptions (Lee et al. 1983; Michaels et al 2001;
Port et al 1997; van Donkelaar et al 1992; Wann 1996). A critical test for threshold-based models is
that the threshold value should remain invariant across a number of initial conditions, otherwise
these models would only furnish an ad hoc fitting to a data subset.
In the following, we provide an expression for the time of the motor response from trial onset
predicted by each model (RT*, asterisk denotes prediction) as a function of the initial conditions of
target motion (h0, v0, A) and of the model parameters (PT, and hTT or τ or λ , depending on the
model, see below). In addition, we provide an expression for h*RT (h(t) at RT*) predicted by each
model as a function of v*RT (v(t) at RT*). For these models, h*RT is linearly related to v*RT , with an
intercept (c0) and slope (c1) that differ according to the model and the initial conditions.
h*RT = c0 + c1 v*RT
(3)
All expressions are derived from eq. 2 in a straightforward manner.
DISTANCE−MODEL. It postulates that the response is programmed when the target has reached a
certain threshold-height hTT at t=TT (van Donkelaar et al 1992; Wann 1996). The distance−model
provides a zero-order approximation of target motion, as it incorporates information about current
distance of the target, but ignores velocity and acceleration.
In case of 0g-motion:
RT* = PT + (h0 – hTT)/v0
(4)
and c0 = hTT, c1 = -PT in eq. 3.
In case of 1g-motion:
(
)
RT* = PT + − v 0 + v 02 + 2 g (h0 − hTT ) g
(5)
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and c0 = hTT + 0.5 gPT 2 , c1 = -PT.
τ−MODEL. It postulates that the response is programmed when IT-TT has decreased below a
certain threshold-time τ (Lee and Reddish 1981; Lee et al 1983). By definition:
τ = hTT vTT
(6)
The τ−model provides a first-order approximation of target motion, as it incorporates
information about target distance and velocity, but ignores acceleration. Thus, it represents a 0gmodel.
In case of 0g -motion:
RT* = PT – τ +h0/v0
(7)
and c0 = 0, c1 = (τ − PT) .
In case of 1g motion:
)
(
RT* = PT – τ + − v 0 + g 2τ 2 + v 02 + 2 gh0 g
(8)
and c0 = (0.5PT − τ )gPT , c1 = (τ − PT) .
1G−MODEL. It postulates that the response is programmed when IT-TT has decreased below a
certain threshold-time λ (Lacquaniti and Maioli 1989; Lacquaniti et al 1993a; McIntyre et al 2001).
By definition:
λ= (− vTT + vTT + 2 gˆhTT ) / gˆ
2
(9)
where ĝ is an internalized estimate of gravitational acceleration. In the following we assume
that ĝ =1g (the acceleration of earth’s gravity at sea level). The λ−model provides a second-order
approximation of target motion, as it incorporates information about target distance and velocity,
and always assumes that the target is accelerated by gravity. Thus, it represents a 1g-model.
11
In case of 0g -motion:
RT* = PT – λ + (2h0 − gλ2 ) (2v 0 )
(10)
and c0 = 0.5 gλ2 , c1 = (λ − PT).
In case of 1g motion:
(
)
RT* = PT – λ + − v 0 + v02 + 2 gh0 g
(11)
and c0 = 0.5g(λ − PT)2 , c1 = (λ − PT).
The experimental values of RT (either the times of the positive peak of hand acceleration or the
times of the button-press relative to trial onset) were (least-squares) fitted using eqs. 4-11 to obtain
estimates of the model parameters (PT, and hTT or τ or λ ). To assess the robustness of the
estimates, we followed different fitting procedures. First, the results for 1g-targets and 0g-targets
were fitted simultaneously, using the global model obtained by coupling the eqs. 4 and 5 for the
distance model, eqs. 7 and 8 for the τ−model, and eqs. 10 and 11 for the λ−model. Second, the
results for 1g-targets were fitted separately from those of 0g-targets. This procedure could be used
for both 1g- and 0g-targets in the case of the distance model, only 1g-targets for the τ−model, and
only 0g-targets for the λ−model.
An additional analysis was performed for the punching experiments based on the phase-plots
h,v introduced by Port et al. (1997). Here the experimental values of hRT were linearly regressed
against the corresponding values of vRT using eq. 3 to obtain estimates of the intercept (c0) and slope
(c1). The results for 1g-targets were fitted separately from those for 0g-targets. Several different
temporal landmarks were used for RT, based on the time when hand acceleration first reached a
given percentage level (10%, 25%, 50%, 75% and 100%) of its positive peak. This analysis allows
to discriminate among the various models based on the quadrant where the intercept, slope values
determined from the experimental data fall.
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Results
Intercepting 0g- versus 1g-targets by punching a ball
In all experiments a virtual target-sphere moved vertically downward on the projection screen
with a randomized law of motion. In the first series of experiments, subjects were asked to intercept
this target by punching a real soft-ball (of the same size as the virtual one) that fell hidden behind
the screen. Because the virtual target arrived at the interception point at the same time (interception
time) as the real ball, subjects had to estimate the TTC of the former to punch the latter correctly.
On the first day, one group (#1) of subjects was presented with visual targets moving with 1gacceleration and randomly assorted initial velocities (v0). All subjects punched the ball by
propelling the hand forward with a ballistic, stereotypical movement. The responses were correctly
time-locked to the interception time from the first attempt and varied little in successive trials. The
1st, 2nd and 11th presentation of the same condition from one such experiment are superimposed in
Figure 3 (left, in red, green and blue, respectively). Acceleration and EMG profiles are essentially
indistinguishable among these repetitions.
On average, hand acceleration reached the first positive peak at -64 ± 31 ms (mean ± SD across
all 1g-test-trials of 5 subjects, n=997). Negative (positive) values indicate times before (after) the
interception time. The zero-crossing of hand acceleration occurred at -2 ± 24 ms, indicating that
subjects generated maximum momentum to punch the incoming ball at the right time. Limb
propulsion was determined by a burst of muscle activity of shoulder flexors and elbow extensors,
and it was subsequently braked by shoulder extensors and elbow flexors.
The same group of subjects was trained 24h later with targets at 0g-acceleration and the same
randomly assorted v0 as the previous day. Limb movement and arm muscles activation were similar
to those of the previous day, but their timing was very different (Fig. 3, right). When subjects were
first exposed to each 0g-condition, their responses started too early and the hand passed the
interception point well before the interception time. On average, hand acceleration reached the first
positive peak at -158 ± 83 ms (mean ± SD across the first presentations of each 0g-test-trials of 5
subjects, n=25), 94 ms earlier than for the 1g-targets of the previous day. The zero-crossing of
acceleration occurred at -93 ± 78 ms. As a measure of the spatial error, we computed the difference
between the antero-posterior horizontal spatial coordinate of the hand at the interception time and
the corresponding mean value for the 1g-targets of the previous day. On average, in the first 0g-trial
the hand was 7.3 ± 6.6 cm more anterior than in the 1g-trials. Consequently, it was hit by the ball at
the metacarpus or carpus. With training, the early inappropriate responses were progressively
delayed (compare the 1st, 2nd and 11th presentations in Fig. 3, right), but they remained premature as
compared with 1g-responses.
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The timing but not the waveform of hand acceleration depended on the law of target motion.
All presentations of the same condition from one experiment are superimposed in Fig. 4.
Acceleration profiles for 1g-trials are essentially super imposable for most trials. The positive
component of the acceleration profiles for 0g-trials is very similar to that of 1g-trials, staggered in
time as a function of presentation order. The negative component (braking the movement) tends to
be slightly greater for 0g-trials than for 1g-trials. Several spatio-temporal landmarks of the motor
responses systematically co-varied across trials and conditions. Thus, the time of onset, first
positive peak, and zero-crossing of hand acceleration were always strongly correlated (p<0.001)
between each other. Moreover movement duration varied little across all conditions (on average, its
SD was 32 ± 13 ms). In the following, we mainly concentrate on the TTC of the acceleration peak,
considered as the motor correlate of the time-to-contact of the target estimated by the subject.
The effect of training was tested using three different protocols. Two groups of subjects were
trained with 1g-test-trials on one day (the first and second day in group # 1 and # 2, respectively)
and 0g-test-trials on the other day. Group #3, instead, performed both 1g- and 0g-trials within the
same session, the value of target acceleration being randomized along with the value of initial
velocity (Random protocol). The mean TTC-values (± SEM, n=5), averaged across all subjects of
the latter group, are plotted as a function of repetition number for each initial velocity in Fig. 5 (red
and blue points correspond to 1g- and 0g-trials, respectively). The ensemble average of the data of
all groups is plotted in Fig. 6 along with the best-fitting surfaces.
The general trend of the results was independent of the order with which 1g- and 0g-trials were
practiced. In all groups, TTC of 1g-trials varied little with either repetition or v0. Two-factor
ANOVA showed no significant effect of repetition in any group (p=0.3), and a small but significant
effect of v0 in groups #1-2 (p<0.05) and a non-significant effect in group #3 (p=0.09). The trend
was that TTC for v0=4.5 m s-1 was slightly shorter than that for the other v0. The mean range of
variation of TTC across v0 was 16 ± 8 ms (mean ± SD over all groups).
The TTC-values of 0g-test-trials were significantly (t-test, p<0.001) longer than those of 1gtest-trials: on average, by 114 ± 23 ms (mean ± SEM across all v0-conditions and subjects) in the
first repetition, and by 56 ± 9 ms over the last 5 repetitions. Two-factor ANOVA showed that TTC
of 0g-trials shortened (the time of acceleration peak shifted closer to contact) significantly with both
increasing v0 (p<0.001) and repetition (p<0.001) in all groups. These changes were substantial
resulting in a mean range of variation of 237 ± 44 ms. In general, TTC shortened rapidly with
repetition (within the first 4-5 repetitions) in the conditions with low v0 (0.7, 1 m s-1). Exponential
fitting (eq. 1) of these changes yielded a time constant of 1.8 ± 0.6 (mean ± SEM).
14
We can rule out the hypothesis that subjects synchronized their movements to the start of target
motion by assuming that the real ball was dropped at the same time as the virtual one. This
hypothesis would predict a constant time of the motor response (RT) relative to trial onset. This
hypothesis was rejected because three-factor ANOVA showed a highly significant effect of
acceleration (p<0.001), velocity (p<0.001) and repetition (p<0.005) in all groups.
In contrast with the clear dependency of the timing (TTC) of arm movements on the law of
target motion, their maximum speed showed no systematic relation with target motion. Thus peak
tangential velocity of the hand (vP, occurring close to nominal interception time, see above) did not
depend significantly on target acceleration or v0 in 2 groups, whereas it was slightly but
significantly (p<0.001) higher for 0g-targets than for 1g-targets in group # 1 (on average, vP = 3.54
± 0.96 and 3.25 ± 0.61 m s-1 for 0g- and 1g-targets, respectively, mean ± SD, n=1000). However the
overall range of variation of vP across conditions (v0 and acceleration changes) was always less than
13% of the mean vP.
Consistent with the accurate timing, interception rate of 1g-trials was high from the outset and
improved only slightly with practice. On average, it was 80 ± 16% (mean ± SD) in the first
repetition and 92 ± 10% in the last 5 repetitions of each condition for all subjects and groups.
Instead, interception rate of 0g-trials increased substantially with practice but was always
significantly (t-test, p<0.001) smaller than that of 1g-trials. On average, it was 20 ± 10% in the first
0g-repetition and 59 ± 13% in the last 5 0g-repetitions.
After-effects
Occasional (9%-incidence) trials with unexpectedly altered kinematics, termed ‘catch-trials’,
were interspersed among the test trials of protocols 1-2 to verify for the presence of after-effects due
to adaptation. 1g-catch-trials with v0=0 m s-1, unexpectedly presented during immersive training
with 1g-test-trials with random v0 (day 1 in group #1) did not cause after-effects. TTC of these catch
trials did not differ significantly from that of the preceding trial.
In contrast, the unexpected occurrence of 1g-catch-trials during immersive 0g-training did
cause significant (p<0.001) after-effects in groups #1-2 (Fig. 7). The size of the after-effects did not
change significantly as a function of the time of occurrence during 0g-training, probably because of
the fast time constant of adaptation (the first 1g-catch-trial occurred in the sequence after most
adaptation had occurred). Two-factor ANOVA showed no significant effect of repetition in any
group, and a slight significant effect of v0 (p=0.003) in group #1 but not in #2. When present, the
effect of v0 was small (on average, 6 ms TTC-change per 1 m s-1 velocity change). On average, the
15
interception rate for these 1g-catch-trials was 37 ± 21%, significantly (t-test, p<0.001) lower than
the interception rate of 1g-test-trials.
We also compared the TTC of the 0g-test-trial following a 1g-catch-trial (catch+1) with the
TTC of the previous 0g-test-trial with the same v0 (catch-1). The difference between (catch+1) and
(catch-1) did not deviate significantly from the difference between (catch-1) and (catch-2).
Modeling the data
In theory, subjects might time their responses on the basis of different kinds of TTC-estimate of
the visual target: exact estimates or approximations of different order. Exact estimates would lead to
a correct motor timing for both 1g- and 0g-targets. Zero-order approximations of the distance-model
incorporate information about target distance, but ignore target velocity and acceleration. The
application of this model would overestimate the TTC of targets with shorter flight duration and
underestimate the TTC of targets with longer flight duration. First-order approximations of the
τ−model incorporate information about target distance and velocity, but ignore target acceleration.
Because the τ−model is equivalent to a 0g-model, it would lead to correct TTC-estimates for 0gtargets, but would overestimate TTC of 1g-targets. Finally, second-order approximations based on
an internalized estimate of gravitational acceleration incorporate information about target distance
and velocity, and always assume that the target is accelerated by gravity. Therefore the 1g-model
correctly estimates TTC of 1g-targets, but underestimates TTC of 0g-targets.
The finding that the motor timing was premature and the success rate was low in 0g-test-trial
as compared with 1g-test-trials indicates that the TTC of 0g-targets was underestimated, whereas the
TTC of 1g-targets was estimated correctly. This finding apparently refutes both exact as well as
zero-order and first-order mechanisms, and is compatible instead with a second-order mechanism
based on the 1g-model. However, in line of principle a difference in timing of the motor responses
to either the 0g-targets or the 1g-targets could result from the application of a low-order TTCestimate but with an offset of the motor responses. For instance, subjects could program the
response when the target has traveled a given distance but the response would only occur after a
given delay due to neural and mechanical transmission times. The consequences of a delay are not
intuitive and need to be assessed quantitatively.
To account for transmission delays, we fitted eqs. 4-11 to the experimental RT-values and
obtained the values of RT* and TTC* (= flight duration − RT*) predicted by each model. In a first
analysis, the results for all 1g-targets and for 0g-targets were fitted simultaneously, under the
assumption that the model parameters are invariant across all tested initial conditions. Moreover, a
lower boundary value of 100 ms was imposed to PT, τ and λ in the fitting procedure, in order to
16
avoid unrealistic results (minimum delays for visuo-manual responses are of that order of
magnitude, Carlton 1981). The values of TTC* are plotted as a function of v0, along with the mean
experimental values of TTC for the first repetition of each condition in group # 2 in Fig. 8. The
results were essentially identical for all groups.
The 1g-model (red curve in Fig. 8) reproduced well the trend of the experimental data for all
speeds (v0) and accelerations (1g- and 0g). The best-fit was obtained with a processing time (PT) of
139 ms and a threshold-time (λ) of 202 ms. The linear regression of all predicted TTC* values
versus the corresponding experimental TTC values was highly significant (mean r2=0.87 across
groups, p<0.001), with a slope (0.9) and intercept (-18 ms) that did not differ significantly from
unity and zero, respectively (as expected from a homogeneously good fit).
The distance-model (blue curve) reproduced the experimental data for the lower speed (v0 £ 1.5
m s-1) 0g-targets, but grossly overestimated (on average, by 106 ms) both the values of TTC
experimentally obtained for higher speed 0g-targets, as well as the values for all 1g-targets. The
best-fit was obtained with a PT of 100 ms and a threshold-height (hTT) of 0.39 m. The linear
regression of all predicted TTC* values versus the corresponding experimental TTC values was
significant (mean r2=0.86 across groups), but the slope (1.5) and the intercept (133 ms) were
significantly (p<0.05) greater than unity and zero, respectively.
The τ-model (green curve) reproduced the experimental TTC values for 1g-targets but did not
reproduce those for 0g-targets (mean r2=0.47 across groups). The best-fit was obtained with a
processing time (PT) of 267 ms and a threshold-time (τ) of 476 ms.
Next, we fitted the 1g-targets separately from the 0g-targets. The results did not change
markedly with the 1g-model (mean r2=0.76, PT = 157 ms, λ = 208 ms). The distance-model
reproduced the mean TTC of 1g-data better than before, but overestimated or underestimated the
TTC of targets with shorter or longer flight durations, respectively (mean r = -0.31); its fit of 0gdata did not change appreciably (mean r2=0.76, PT = 100 ms, hTT = 0.36). The τ-model fitted the
data separately worse than before (mean r2=0.08).
Then we removed the boundary values in the fitting procedure. The results for both the 1gmodel and the τ-model remained identical to those obtained under constrained fitting. Instead, the
unconstrained best-fitting of the distance-model yielded negative values incompatible with a causal
system (PT = -121 ms and hTT = -0.40 m).
The second analysis is related to the phase-plots h,v introduced by Port et al. (1997). The
models we are considering predict that the height of the target above the interception point at a
given time after trial onset is linearly related to the corresponding value of target velocity, for all v0
17
at a fixed acceleration (either 1g- or 0g). However, the intercept and slope of the h,v relationship
differ according to the model and the initial conditions (see Models section in Methods). Figure 9
shows the results of simulating the performance of the different models. Each curve in the Figure
corresponds to the locus of all pairs of intercept, slope values obtained by varying model parameters
(see Figure legend for details). Red and blue curves correspond to 1g- and 0g-targets, respectively.
This graphic analysis allows to discriminate among the various models on the basis of the quadrant
where the intercept, slope values fall.
The distance-model predicts h,v relationships with positive intercept and negative slope, for
both 1g- and 0g-targets (orange quadrant in Fig. 9). Instead, the τ-model predicts a positive slope
for all targets, a zero intercept for 0g-targets and a negative intercept for 1g-targets (green
quadrant). Finally, the 1g-model predicts positive intercept and positive slope for all targets (yellow
quadrant).
Predicted curves were compared with the experimental data in the following way. The
experimental values of hRT for the first repetition of each condition were linearly regressed against
the corresponding values of vRT using eq. 2 to obtain estimates of the intercept and slope. Here the
response time RT was varied in steps based on the time of occurrence of different percentage levels
(10%, 25%, 50%, 75% and 100%) of the positive peak of hand acceleration. This allowed to
generalize the results to different temporal landmarks of the response. The results for 1g-targets
were fitted separately from those for 0g-targets.
Experimental values of hRT generally were linearly related to those of vRT (mean r = 0.91). The
estimated pairs of intercept-slope values (black circles in the yellow quadrant of Fig. 9) consistently
satisfied the predictions of 1g-model. Each circle corresponds to a different RT. With decreasing
values of RT, the experimental points shift progressively higher (arrows) along the curves predicted
by the 1g-model. Notice the good agreement between the path described by the experimental points
and the theoretical curves.
The 1g-model also predicts that the pairs of intercept-slope values for 0g-targets becomes
identical to that for 1g-targets when TTC=λ (azure circle). Thus the time-threshold λ can be
estimated independently from 3 parameters of the model: 1) the TTC at which the intercept-slope
curve for 0g-targets intersects that for 1g-targets, 2) the corresponding intercept value (c0 = 0.5gλ2),
and 3) the slope (c1 =λ). In the first repetition, the 3 estimates of λ were 214, 210, and 202 ms,
respectively. Notice the good agreement of the different estimates between each other and with
those derived above. Training with 0g-targets resulted in a systematic decrement of λ-values. This
issue is addressed in the next section.
18
Adaptation of 1g-model to repeated presentations of 0g-trials
We previously showed that the responses to 0g–trials were premature and that with training the
performance improved but there was a consistent residual timing error (Figs. 4-5). Here we show
that this behavior is compatible with the persistent use of the 1g-model throughout practice, with a
progressive adaptation of the threshold-time λ.
The application of the 1g-model leads to predictable differences in timing between 1g- and 0gtargets. A 1g-target arrives at the time predicted by the 1g-model, but a 0g-target arrives later than
expected (Fig. 10A). Thus motor activity triggered by the 1g-model starts earlier than necessary at
0g. For any given value of λ, the timing error (δ) between a 0g–target and a 1g–target decreases
non-linearly with increasing v0 (Fig. 10B). We tested the hypothesis that adaptation reduces δ by
progressively decreasing λ by fitting the prediction of the 1g-model (δ ∗ = gλ2/2v0 ) to the set of
experimental δ −values.
Figure 10C shows examples of the mean δ−values derived from three successive presentations
of each v0 in 0g-test-trials of group # 2. Fitting the prediction of the 1g-model yielded the following
estimates of λ-values: 0.199, 0.180 and 0.132 for the 1st, 2nd and 6th repetition, respectively (r2 =
0.79, 0.91 and 0.97). Figure 11 shows the changes of the estimated λ-values in all repetitions of
group # 2. The results were similar in all groups. In general, each family of experimental δ−values
from a given repetition was adequately fitted by the 1g-model with a given λ-value (p<0.05 for all
subjects). As predicted by the hypothesis of 1g-model adaptation, λ-values tended to decrease
monotonically with 0g-repetitions. λ was 134 ms and PT was 74 ms (r2 = 0.89) in the last repetition,
Exponential fitting (eq. 1) of the changes of λ with repetition showed a rapid decrement (time
constant = 1.8 ± 0.8) from an initial value of 205 ± 23 ms to a steady-state value of 135 ± 28 ms.
Although the 1g-model fitted the data significantly, it did not always reproduce the data at the
highest initial velocity (v0=4.5 m s-1). Thus, the model predicts a monotonic non-linear decrement of
δ −values with increasing v0 (Fig. 10B), but in some cases the δ −values at v0=4.5 m s-1 were
actually slightly greater than those at v0=2.5 m s-1 (see Fig. 5).
Virtual interception
A striking result of the punching experiments was that, even after prolonged exposure, visual
targets moving vertically downward at constant velocity were misrepresented as accelerated by
gravity. To verify whether these illusions depend on the nature of the visual stimuli or they depend
on the dynamic context of interception, we carried out an additional series of experiments. Here the
subjects were presented with targets descending with randomly assorted initial velocities and
19
accelerations as in the Random protocol of punching experiments, but there was no real ball falling
behind the screen. Instead the subjects were required to ‘explode’ the virtual target by clicking the
mouse at the interception time.
For most conditions, the results were the reverse of those of punching, both at a population
level and at an individual level (one subject participated in both sets of experiments at one year
distance). Thus, the responses to slower 0g-targets (that were timed too early in punching) were
correctly time-locked to interception time from the first attempt and varied little in successive trials
in virtual interception (Fig. 12). On average, the TTC of the button-press was 0 ± 31 ms (mean ±
SD, n=720) for all 0g-targets at v0 £ 1.5 m s-1. Conversely, the responses to slower 1g-targets (that
were timed correctly in punching) were slightly but significantly (p<0.001) late in virtual
interception. On average, TTC was 21 ± 40 ms (mean ± SD, n=958) for all 1g-targets at v0 £ 2.5 m
s-1. The timing differences between 0g- and 1g-targets at corresponding v0 were highly significant
(p<0.001). Interception rate computed within ± 15 ms relative to the interception time was not
significantly different between these 0g-targets (39 ± 10%) and 1g-targets (40 ± 12%). However,
interception rate computed within the time window (± 60 ms) comparable to that used for punching
experiments was significantly (t-test, p<0.001) higher for 0g-targets (95 ± 4%) than for 1g-targets
(84 ± 15%).
The responses to faster 0g-targets (v0 ³ 2.5 m s-1) were much more variable across trials than
those of slower targets (the mean SD of the former was twice as large as that of the latter). On
average, they were slightly but significantly (p<0.001) early (TTC = -28 ± 62 ms, n=479).
Three-factor ANOVA showed a significant effect of acceleration (p<0.001) and v0 (p<0.001),
but no significant effect of repetition (p=0.772) when all the trials were pooled together. However,
the mean changes of TTC with repetition were significantly (p<0.05) fitted by an exponential (eq. 1)
in a number of individual 0g- and 1g-conditions (see fitting curves in Fig. 12), indicating the
presence of training effects. The changes were of limited amplitude and could involve either a
decrement or an increment of TTC with repetition. They were rapid for slower targets (time constant
of 1.6 ± 0.9, mean ± SEM), and more gradual for fast targets (15.3 ± 9.9).
The finding that the TTC of most 0g-targets was estimated better than that of most 1g-targets
indicates the use of a dynamic model that assumes uniform motion in virtual interception. This
hypothesis was supported quantitatively by the results of modeling (Fig. 13). The TTC* values
predicted by different interception models are plotted as a function of v0, along with the mean
experimental values of TTC using the same analysis previously applied to punching (see Fig. 8).
The overall best-fit (mean r2=0.61, p<0.01) of the ensemble of all TTC-data was provided by the τ20
model (green curve) with a processing time (PT) and a threshold-time (τ) of 161 ms. As expected,
this model did not accurately reproduce TTC-values corresponding to high initial velocities (v0 = 3.5
or ³ 2.5 m s-1 for 1g- and 0g-trials, respectively). The other two models (1g- and distance-model)
failed to fit the ensemble of data (yielding low, non-significant correlations).
Discussion
We showed that the timing of responses aimed at intercepting a visual target was very different
depending on the dynamic context, virtual interception versus punching. Timing differences
between the two conditions were present from the first trial, before any feedback of performance,
and persisted throughout practice. They were observed both at the population level and at the
individual level of the subject who participated in both sets of experiments. We will argue that they
reflect the operation of predictive models from high-level processing that affect responses evoked
by low-level visual inputs.
Visual information
Although humans are able to analyze visual motion in general scenes, they can easily be
deceived into seeing incorrect motion of simple stimuli (Weiss et al 2002). We must then address
the question of possible perceptual biases arising in the present experiments due to the nature of the
visual stimuli employed. The visual system normally integrates information from multiple sources
to judge the relative position and motion of objects. Changes of retinal image size, binocular
disparity, optical gap between target and interception point, and eye movements are known to
contribute to TTC-estimates under different conditions (Tresilian 1999; Regan and Gray 2000).
These cues are probably combined to generate more robust estimates, as in the dipole model
combining image size and disparity cues (Rushton and Wann 1999).
For bypass approaches such as those of the present experiments, both expansion and translation
of the retinal image are critical cues (Bootsma and Oudejans 1993; Tresilian 1999). It is reasonable
that to achieve best accuracy in ballistic interceptions, visual information is integrated from the
onset up to the latest possible time when the motor response must be centrally triggered (Land and
McLeod 2000). For our experimental conditions we estimate the viewing-time (VT) available to
integrate visual information as VT=TT=IT-LT (see Fig. 2). For punching, the best-fitting model (1gmodel) yielded an estimate for LT (λ) of about 200 ms (before adaptation). For virtual interception,
the best-fitting model (τ-model) yielded an estimate for LT (τ) of about 160 ms. Thus, VT ranged
from about 150 ms (at v0 = 4.5 m s-1) to about 400 ms (at v0 = 0.7 m s-1) for 1g-targets, and from
about 300 ms to about 3 s for 0g-targets (it was about 70 ms longer after adaptation). Based on the
21
geometry of our experimental setup (see Methods), we estimate that a number of the optical
variables that are known to be critical for TTC estimates were in the range of reliable measurement.
Thus the visual angle subtended by the target (θ) varied from 0.8° (at trial onset) to 10.3° (at eyelevel), greater than the 0.7°-size reported to result in accurate estimates of absolute time to collision
for constant velocity approach under binocular conditions (Regan and Gray 2000). We estimate that
image expansion rate (dθ/dt) was always > 0.01 rad/s, and reached values between 0.16 and 0.9
rad/s (depending on the condition) at the end of VT. Vertical angular velocity (dγ/dt) was between 5
and 20 times greater than dθ/dt. It was always > 0.1 rad/s and varied steeply reaching values
between 1.4 and 5 rad/s at the end of VT. The lowest vertical angular velocity (dγ/dt) that is known
to be detected by the visual system is about 0.0003 rad/s, and the discrimination of differences in
dγ/dt is very precise (Weber fraction is about 5%) over a range between 0.03 and 1.2 rad/s (de
Bruyn and Orban 1988; Orban et al. 1984). Outside the optimal range, the Weber fraction increases
steeply. Thus, our targets at lower speeds should have been within the optimal range of
discrimination, but faster targets may have been outside this range.
Clearly, a visual preference for slower speed cannot explain why subjects were much more
accurate at intercepting the fast 1g-targets than the slower 0g-targets in the punching task.
Moreover, the interception performance of our subjects with slow 0g-targets was dramatically
different in the two tasks: so much accurate were subjects in the virtual interception, as much were
they inaccurate when punching. Also this discrepancy cannot be explained by visual psychophysics.
Let us now consider the issue of visual acceleration. Although humans cannot discriminate
accelerations accurately, they are able to detect them by comparing velocities in a 2-stage process
(Werkhoven et al 1992). The first stage involves a low-pass-filter stage (time window of 100-140
ms) and is followed by a discrimination stage sensitive to velocity changes (∆v/v) ³17%
(Werkhoven et al 1992; Brouwer et al 2002). Because VT was longer than 140 ms (see above) and
∆v/v was greater than 17% (it ranged between 26 and 99%), subjects should have been able to
detect the presence or absence of acceleration. Here we have another conundrum for hypotheses
attempting to explain the results based on visual psychophysics. If subjects could detect (if not
measure) visual acceleration, why did they not cope with it for most 1g-targets in the virtual
interception task, while they did so quite accurately in the punching task?
Virtual interception
When our subjects clicked a mouse-button to intercept the descending target, response timing
was consistent with the assumption of uniform motion in the absence of forces. Thus the responses
to most 0g-targets were on time, whereas the responses to most 1g-targets were late. Motor timing
22
was well reproduced by a first-order model (τ-model) that always assumes uniform motion,
irrespective of the law of target motion. The model, however, did not reproduce accurately the
responses to higher velocity targets.
These results with virtual interception are in general agreement with several previous results
obtained with different virtual environments, regardless of the motor modalities involved in the
interception paradigms. In previous studies, a virtual target moved in different directions (including
the vertical) on a 2D-screen with constant velocity or accelerating profiles and subjects were
required either to track it with the finger (Engel and Soechting 2000; Viviani et al 1987) or to hit it
with the hand (van Donkelaar et al 1992) or with a hand-held rod (Brouwer et al 2000) or to
intercept it with a 2D-manipulandum (Lee et al. 1997; Port et al 1997) or with a joystick controlling
the screen cursor (Merchant et al. 2003). In one study, subjects had to squeeze a stationary ball
attached to their hand when they thought that a virtual 3D-ball projected in depth on a headmounted display would hit them (Rushton and Wann 1999). Irrespective of the specific kind of
movement involved, the timing of all motor responses was related to target position and velocity,
but poorly related (if at all) to target acceleration. In particular, Engel and Soechting (2000) were
able to account for all responses with a model including direction and speed aimed at keeping τ
constant. Port et al (1997) reported a dual strategy: the responses to slower targets were well
described by the τ-model, whereas the responses to fast targets were better described by the
distance-model. First-order strategies that ignore online estimates of acceleration also were used in
relative judgement tasks, as when subjects were asked to choose when accelerating or decelerating
objects would collide with a stationary target (Bootsma and Oudejans 1993).
On the whole, it appears that uniform motion is attributed as the default motion of virtual,
mass-less objects, and expected dynamics agrees with first-order visual information about TTC.
However a different dynamic context (for instance, accelerative) can be attributed to virtual targets
under different experimental conditions, as when they are masked for prolonged temporal intervals
(Tresilian 1995). Thus if an observer views a virtual moving object that suddenly disappears,
memory of the object’s final position is shifted forward in the direction of motion, in accord with a
representational momentum (Freyd 1987). Descending motion leads to larger forward displacement
than does ascending motion, and the memory distortion for horizontally moving objects is also
displaced downward below the path of motion, consistent with the hypothesis that the effects of
gravity are internalized (Hubbard 1995).
Punching experiments
23
When punching a hidden real ball arriving in synchrony with the visual target, our subjects
systematically timed their responses consistent with the assumption of gravity effects on an object’s
mass. Thus the responses to 1g-targets were correctly timed, whereas the responses to 0g-targets
were too early. Motor timing was well reproduced by the 1g-model.
The present results for intercepting 1g-targets agree with previous results on catching freefalling balls, where the anticipatory muscle responses were time-locked to contact over a wide
range of drop heights (Bennett et al 1994; Lacquaniti and Maioli 1989; Lacquaniti et al 1993a;
1993b; Lang and Bastian 1999). Present results also can be compared with those of two studies in
which subjects punched balls dropped vertically toward the head (Lee et al 1983; Michaels et al
2001). In those studies (but not here), before punching there was a slow preparatory phase of elbow
flexion. In all studies, the ball was punched by a ballistic limb extension timed independently of
drop duration, as predicted by the 1g-model. TTC was invariant across a 0.35/0.6-s-range of drop
durations here, across a 0.8/1.2-s-range in Lee et al (1983), and across a 0.9/1.3-s-range,
independent of ball size and viewing conditions (monocular/binocular) in Michaels et al (2001).
The present results for intercepting 0g-targets agree with the previous observation that
astronauts continue to anticipate the effects of gravity to time catching movements in microgravity
(McIntyre et al 2001). A ball launcher attached to the ‘ceiling’ of the Spacelab module projected a
0.4 kg ball downward at constant speed from a height of 1.6 m above the hand position, with one of
three different, randomly assorted speeds. The peak of anticipatory biceps EMG occurred earlier
(relative to impact) in microgravity compared to ground (when the ball was accelerated by gravity),
and the time shifts varied non-linearly with v0 as predicted by the 1g-model.
Adaptation of 1g-model
Here we showed that, with training, the gravity model was not switched off, but adapted to
non-accelerating targets by shifting the time for motor activation. We used three different training
protocols and the results were independent of the order with which 1g- and 0g-trials were practiced.
In theory, with practice subjects might have switched off the 1g-model, relying entirely on
visual information to estimate TTC. Motion at constant speed should be accurately measured by the
visual system and used to predict TTC, as it happened in virtual interception. For punching, this
hypothesis is refuted by two observations: the responses to 0g-targets always remained premature,
and the unexpected occurrence of 1g-catch-trials during immersive 0g-training caused significant
after-effects (Shadmehr and Mussa-Ivaldi 1994). Here an after-effect is the response that results
when the subject is expecting a given law of motion but a different law of motion unexpectedly
24
occurs. The response to the unexpected 1g-catch-trial was delayed in time in the opposite direction
to that of the predictable 0g-test-trials (Fig. 7).
The data also refute the alternative hypothesis that subjects develop a new model of target
acceleration, intermediate between 1g and 0g. This hypothesis predicts that the TTC-values of 1gcatch-trials should be much shorter than those found experimentally, and they should be inversely
proportional to v0 (the opposite of the experimental trend). Moreover, it is known that catch-trials
cause errors that interfere with a new internal model and affect future movements (Thoroughman
and Shadmehr 2000). If the changes of TTC with 0g-repetition were achieved through learning a
new internal model, one would expect that the performance error in the 0g-test-trial following a 1gcatch-trial should be greater than in the previous corresponding 0g-test-trial, indicating partial
unlearning of the newly acquired internal model (Thoroughman and Shadmehr 2000). This
prediction was not borne out by the results. The data contradict another outcome predicted by the
hypothesis, namely that when 0g- and 1g-accelerations are equiprobable in the same session as in
the Random protocol, the TTC values of 1g-targets should shift progressively later with training, in
parallel with the TTC-shifts of 0g-targets.
Nature of internal models for interception
Response timing was best explained by the τ-model in virtual interception and by the 1g-model
in punching. By definition τ is the ratio between target distance and velocity at the threshold-time to
generate the motor response within the CNS. Although τ could be an optic variable related to firstorder visual mechanisms (e.g., the inverse of the rate of dilation of the retinal image or the inverse
of the rate of change of relative disparity, Lee and Reddish 1981; Rushton and Wann 1999), it could
also be an internalized control variable related to a 0g-dynamic model of target motion. Contextdependent switching between τ-model and 1g-model, as probably occurs when part of the target
trajectory is masked (see above), favors the view that the τ-model is an internal dynamic model
based on prior expectations.
The 1g-model is related to target distance and velocity at threshold-time, and incorporates an
estimate of gravitational acceleration (Lacquaniti and Maioli 1989; Lacquaniti et al 1993a;
McIntyre et al 2001). This estimate could be an internalized control variable related to a 1gdynamic model. Although presumably it is fed by on-line sensory information (such as that from
vestibular and other graviceptors), it is also independent of that. This hypothesis is supported by the
following arguments. First, the 1g-model was applied here for punching but not for virtual
interception, despite graviceptive information was obviously invariant. Second, the 1g-model has
been shown to be applied for catching a dropped ball in the Spacelab (McIntyre et al 2001). In
25
orbital flight, the spacecraft and its occupants are in free fall so there are no contact forces of
support on an astronaut’s body opposing the action of gravity. This means that there are no gravitydetermined tactile cues related to body orientation and no gravity-determined otolith cues about
head orientation (Lackner and DiZio 2000). One can speculate that a 1g-model can also be applied
to the perception of self-motion, in addition to that of objects’ motion. A dramatic example of the
importance of cognitive context in switching on and off the application of a 1g-model to selfmotion perception again is provided by microgravity observations. Lackner and DiZio (2000) report
that sensations of falling are normally absent in astronauts, presumably because of the stable visual
field, but that they can be elicited by closing the eyes and imagining that one is jumping off a cliff.
In this paper we considered threshold-based models for timing interception. These models
assume that the response is triggered within the CNS when a given visual or internalized variable
has reached a critical threshold value, and then the response proceeds without further corrections till
the end. This assumption is legitimate for ballistic interceptions with a stereotyped waveform, such
as punching or button-press responses or other fast movements (Fitch and Turvey 1978; Lee et al.
1983; Michaels et al 2001; Tyldesley and Whiting 1975; Wollstein and Abernethy 1988). Here we
showed that the waveform of the positive acceleration of the hand in punching was highly
stereotyped, independent of the law of target motion (Fig. 4). The models should incorporate
continuous control to be applied to slower responses developing under on-line sensory feedback till
the end (Brenner et al 1998; Engel and Soechting 2000; Bootsma et al 1997; Viviani et al 1987).
In virtual interception, the threshold-time τ was »160 ms and did not change appreciably with
training. In punching, the threshold-time λ was »200 ms before adaptation and dropped rapidly to
»130 ms with training with 0g-trials. The lower λ-value is close to the estimates of the shortest
visuo-manual delay times (Carlton 1981; Lacquaniti and Maioli 1989; Lee et al 1983; Port et al
1997). This may explain why the adaptation process saturated early on, and the responses to 0gtrials remained premature through the rest of training.
Our models of target dynamics are meant as perceptuo-motor models and do not specify the
implementation. The primate cortical networks involved in visuo-manual coordination have been
extensively investigated for reaching to stationary targets, but much less for interception of moving
targets. Neural correlates of predictive interception have been recently described in motor cortex
and area 7a of monkeys (Merchant et al 2003b). Neural activity in these two areas was associated
with different parameters of target motion (stimulus angle or τ) depending on the visual context
(real or apparent motion, respectively). The parieto-insular vestibular cortex (PIVC, Grusser et al,
1990), instead, could be one substrate of a gravity model. This region receives vestibular
information from the vestibular nuclei via a thalamic relay (VPLo and VPI nuclei), visual
26
information from the accessory optic system and the pulvinar, and somatosensory information from
areas 2v and 3a in primary somatosensory cortex (S1). PIVC is reciprocally connected with
posterior parietal cortex (area 7) and cingulate cortex. Many neurons in PIVC respond to head
accelerations, visual motion and somatosensory stimuli from neck and trunk (Grusser et al. 1990).
Multisensory fusion may then result in a gravicentric code. A gravity model might be encoded in a
distributed network also involving subcortical structures (e.g., the vestibulo-cerebellum) to be used
for different forms of sensorimotor coordination (e.g. eye movements evoked by head tilt and
rotation).
Conclusions
In Helmholtz’s view, our percepts are the best guess as to what is in the world, given both
sensory data and prior experience (Helmholtz 1866). We presented evidence that interceptions of
moving targets are based on visually measured kinematics and an a priori hypothesis about the
causes of target motion. In the language of estimation theory, the posterior probability (the
probability of a target dynamics given the visual measurements of target kinematics) would be
computed from the likelihood of target kinematics and from the prior using Bayes’ rule (Weiss et al
2002). The prior for virtual, mass-less objects is that they are moving freely outside a force field. By
contrast, the prior for a real object is that it moves in the earth gravitational field. We surmise that
while the prior for virtual motion should be susceptible to modification by inserting an artificial but
convincing force field in the scene (people can learn complicated videogames with arbitrary laws of
motion), the prior of earth gravity for real objects should be highly resistant to changes.
Here subjects did not develop a new model appropriate for non-accelerating targets to improve
their chances of success in punching. Instead they stretched the parameters of the pre-existing 1gmodel. This contrasts sharply with the results of most other learning paradigms. Practice with a
novel environment normally leads to formation of the appropriate internal model, and multiple
internal models specific for individual objects can be stored in motor memory (Flanagan and Wing
1997; Gordon et al 1993; Hore et al. 1999; Shadmehr and Mussa-Ivaldi 1994; Wolpert and Kawato
1998). However, while we normally experience many different types of objects, on earth we only
experience one gravity level. The gravity model might be construed as one of the perceptualcognitive universals that according to Shepard (1994) exist in our brain as reflections of world
invariants (such as the period of the terrestrial circadian cycle). In a different perspective, Gibson
(1966) also emphasized the ecological importance that organisms’ perception becomes tuned to
environment invariants (such as gravity) via continuous exposure over thousands of years. Survival
in the forest as on the sports field may take advantage of a single gravity model with fast adaptation
27
of its parameters. Adaptation would be the most parsimonious solution to deal with variable drag
effects. Vertical motion of objects is accelerated by gravity and decelerated to a variable extent by
air (or other fluid) friction depending on the object’s mass, size and fluid viscosity, but falling
objects seldom reach constant velocity. The required adaptation then is generally more limited than
that involved by the present punching experiments, and should be much more successful. But a
falling feather remains difficult to catch for everyone!
Disclosures
The financial support of Italian University Ministry, Italian Health Ministry, and Italian Space
Agency is gratefully acknowledged. We thank Bob Dicker from G.W. Linsk Co. Inc. for generous
assistance with the solenoid, Dr. Andrea d’Avella and Dr. Daniel Wolpert for a critical reading of
an earlier version of the manuscript.
28
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Figure legends
Fig. 1. Experimental set-up. Subjects sat on a chair facing a wide vertical screen. They were
asked to intercept a virtual target-sphere moving vertically downward on the screen when it arrived
at the bottom end of the screen. In the punching experiments, they did so by punching a real softball (of the same size as the virtual one), hidden behind the screen, that arrived in synchrony with
the virtual target. In the button-press experiments, there was no real ball falling behind the screen.
Instead subjects had to ‘explode’ the virtual target by clicking a mouse-button.
Fig. 2. Timing interceptive actions. The instantaneous height h(t) of a target above the
interception point is plotted as a function of time. IT denotes the interception time expected by the
subject, not necessarily coinciding with the true interception time. Our models of interception
assume that, when a visual or internalized variable has reached a critical threshold value, a motor
response is programmed with some lead-time LT relative to IT. LT depends on neural and
mechanical delays. LT = PT + MT, where PT and MT represent the processing time and the
movement time, respectively. RT denotes the response time (time of occurrence of the motor
response relative to trial onset). TT = IT – LT. h0 and v0, hTT and vTT, hRT and vRT denote h(t) and
v(t) at t=0, t=TT, and t=RT, respectively.
Fig. 3. Interception of 1g- versus 0g-targets in a punching experiment. Time profiles of hand
acceleration and rectified EMG activity of the indicated muscles of subject M.A. (protocol 1g-0g)
for three repetitions (1st, 2nd and 11th, in red, green and blue, respectively) of accelerated (left) and
constant velocity (right) targets. Traces are aligned on interception time (dashed lines) and negative
time is before that time.
Fig. 4. Time profiles of hand acceleration for all 40 repetitions of accelerated (upper row) and
constant velocity (lower row) targets from the same subject of Fig. 3. Traces are aligned on
interception time (dashed lines) and negative time is before that time. Each column corresponds to
the indicated initial velocity.
Fig. 5. Effects of training in the Random protocol of punching experiments. The TTC of peak
positive acceleration (time relative to interception time) was averaged across all subjects of group #
3. The mean TTC-values (± SEM, n = 5) are plotted as a function of repetition number for each
initial velocity (red and blue points correspond to 1g- and 0g-trials, respectively. Dark lines through
33
0g-trials correspond to the exponential best fit, whereas dark lines through 1g-trials represent their
mean value over all repetitions.
Fig. 6. Ensemble averages and best-fitting (least-squares) surfaces. TTC-values were averaged
across all subjects and experiments for each repetition to a given target.
Fig. 7. After-effects of 0g-training. Mean (± SEM, n = 5) TTC-values for 1g-catch-trials are
plotted for groups 1-2. The dashed line represents the average value of TTC for 1g-test-trials
presented in the other day of training.
Fig. 8. Predictions of different models for the punching experiments. Dots, mean (n = 5)
experimental TTC-values for the first repetition of each target in group # 2. Red, blue and green
curves, TTC*-values predicted by the 1g-model, the distance-model, and the τ-model, respectively.
Fig. 9. Analysis of h,v relationships for different responses times. The models predict a linear
relationship between the height and the velocity of the target at a given time. Each curve
corresponds to the locus of all pairs of intercept-slope values obtained by varying model parameters
in the following ranges: 0.1<hTT<1.6 m for the distance-model, 100<τ <300 ms for the τ-model, and
100<λ <300 ms for the 1g-model. For all models, 0<PT<300 ms. Red and blue curves correspond to
1g- and 0g-targets, respectively. Intercept-slope values predicted by the 1g-model, distance-model
and τ-model fall in the yellow, orange and green quadrant, respectively. Black circles in the yellow
quadrant correspond to the intercept-slope values estimated from the linear regression of the
experimental values of hRT versus the corresponding values of vRT (first repetition of each target in
group # 2). RT was varied in steps between 100% and 10% of the time of occurrence of the positive
peak of hand acceleration (arrows). The azure circle denotes the time when the pairs of interceptslope values predicted by the 1g-model for 0g-targets becomes identical to that for 1g-targets, and
TTC=λ .
Fig. 10. Adaptation of 1g-model to repeated presentations of 0g-targets. Left: The height of the
0g-target above the interception point is plotted versus time. The 1g-model predicts that a motor
response is programmed when the time remaining before the estimated interception time falls below
a given time-threshold λ (dashed lines). A 0g-target arrives later than predicted by the 1g-model,
and δ is the timing error between 0g- and 1g-conditions. The shorter the λ-value (decreasing from
red to green to blue), the later is the response and the smaller the δ-error. Middle: Each curve
34
depicts the δ−values (as a function of v0) predicted by the three λ-values of Left panel. Right:
Experimental results. Mean (n = 5) δ−values from the 1st, 2nd and 6th repetition of group #
2. δ−values were computed as the difference between the TTC of peak acceleration for individual
0g-test-trials of one day and the mean values for 1g-test-trials of the other day.
Fig. 11. Adaptation of λ across all repetitions of group # 2. λ-values computed over all v0 (n =
5) at incremental repetitions of 0g-trials. Continuous line is exponential fitting function.
Fig. 12. Training in the Random protocol of button-press experiments. The mean TTC-values
(± SEM, n = 6) of button-press are plotted as a function of repetition number for each initial
velocity (red and blue points correspond to 1g- and 0g-trials, respectively). Dark lines through the
conditions A=1g, v0 = 0.7, 4.5 m s-1, A=0g, v0 = 0.7, 1, 4.5 m s-1 correspond to significant
exponential fits, whereas the dark lines through the remaining conditions correspond to their mean
value over all repetitions.
Fig. 13. Predictions of different models for the button-press experiments. Dots, mean (n = 240)
experimental TTC-values for each target. Same format as in Fig. 8.
35
Fig. 1
height
↓
h0
v0
↓
hTT
vTT
↓
hRT
vRT
time
IT
TT
PT
MT
LT
RT
Fig. 2
A = 1g
Day 1
v0 = 0.7 ms−1
Day 2
A = 0g v0 = 0.7 ms−1
150
150
ms−2
Hand acceleration
0
0
−150
−150
1
1
mV
mV
mV
Pectoralis
0.5
0.5
0
0
1
1
Anterior Deltoid
0.5
0.5
0
0
1
1
Triceps
0.5
0
−1000
−500
0
500
0.5
1000
time (ms)
0
−1000
−500
0
time (ms)
Fig. 3
500
1000
ms−2
1g
0
−200
200
ms−2
Hand acceleration
200
0g
0
−200
−400
0
time (ms)
v0 = 0.7 ms−1
400
−400
0
time (ms)
v0 = 1 ms−1
400
−400
0
time (ms)
v0 = 1.5 ms−1
Fig. 4
400
−400
0
time (ms)
v0 = 2.5 ms−1
400
−400
0
time (ms)
v0 = 4.5 ms−1
400
TTC (ms)
100
0
−100
−200
−300
0
5
10
15
20
repetition number
v0 = 0.7 ms−1
0
5
10
15
20
repetition number
v0 = 1 ms−1
0
5
10
15
20
repetition number
v0 = 1.5 ms−1
Fig. 5
0
5
10
15
20
repetition number
v0 = 2.5 ms−1
0
5
10
15
20
repetition number
v0 = 4.5 ms−1
0g-test-trials
1g-test-trials
0
0
-100
-100
-200
-200
-300
-300
TTC
5
5
40
4
30
3
speed
2
20
1
10
40
4
speed
repetition
30
3
2
20
1
10
0
0
Fig. 6
repetition
1g−0g
50
TTC (ms)
Catch trials Day 2
0
−50
−100
0g−1g
50
TTC (ms)
Catch trials Day 1
0
−50
−100
0
50
100
150
trial number
Fig. 7
200
1g−test−trials
0g−test−trials
100
distance
TTC (ms)
0
100
distance
0
1g
τ
−100
−100
1g
−200
−200
τ
−300
−300
−400
−400
−500
0
1
2
3
4
5
−500
0
1
2
3
−1
−1
v0 (ms )
v0 (ms )
Fig. 8
4
5
τ
1g
slope
→
↑
0
−0.2
−0.4
distance
−0.4
−0.2
0
intercept
Fig. 9
0.2
0.4
δ
height
δ
(ms)
300 λ
(ms)
300
1
λ adaptation
200
λ2
100
λ3
0
λ3
time
λ2
λ1
δ3
δ2
0
λ adaptation
200
repetition
100
1
2
3
−1
v0 (ms )
δ1
Fig. 10
4
5
0
0
1
2
3
−1
v0 (ms )
4
5
Lambda (ms)
300
200
100
0
0
5
10
15
20
25
repetition number
Fig. 11
30
35
40
TTC (ms)
100
0
−100
−200
−300
0
10
20
30
repetition number
v0 = 0.7 ms−1
40
0
10
20
30
repetition number
v0 = 1 ms−1
40
0
10
20
30
40
0
10
20
30
40
0
10
20
30
repetition number
repetition number
repetition number
v0 = 1.5 ms−1
v0 = 2.5 ms−1
v0 = 3.5 ms−1
Fig. 12
40
1g−trials
0g−trials
100
100
distance
distance
TTC (ms)
50
50
τ
0
−50
−100
τ
1g
0
1g
−50
0
1
2
3
4
−100
0
1
2
3
−1
−1
v0 (ms )
v0 (ms )
Fig. 13
4