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The Journal of Neuroscience, January 1, 1998, 18(1):521-530
Peripheral Neural Mechanisms Determining the Orientation of
Cylinders Grasped by the Digits
M. J.
Dodson1,
A. W.
Goodwin1,
A. S.
Browning2, and
H. M.
Gehring1
1 Department of Anatomy and Cell Biology, University of
Melbourne, Parkville, Victoria 3052, Australia, and
2 Department of Experimental Psychology, Oxford University,
Oxford OX1 3UD, England
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ABSTRACT |
When a human grasps a cylindrical object, feedback on the
orientation of the cylinder with respect to the axes of the digits is
crucial for successful manipulation of the object. We measured the
ability of humans to discriminate the orientations of cylinders passively contacting the fingerpad. For a cylinder of curvature of 521 m
1 (radius, 1.92 mm) subjects were able to
discriminate, at the 75% level, orientation differences of 5.4°; for
a less curved cylinder (curvature, 172 m1; radius,
5.81 mm) the difference limen decreased to 4.2°. The neural
mechanisms underlying the determination of tactile orientation were
investigated by recording the responses of single slowly adapting type
I afferents (SAIs) innervating the fingerpads of anesthetized monkeys.
When cylinders were stepped across the receptive field of an SAI, the
resulting response profiles were Gaussian in shape; the shape
corresponded to the shape of the cylinder, increasing in height and
decreasing in width for more curved cylinders. All SAIs had the same
underlying profile shape except for a multiplicative constant
determined by the sensitivity of the individual afferent. Thus it was
possible to reconstruct the response of the population of active SAIs
in the fingerpad. Changing the orientation of the cylinder resulted in
a rotation of the population response, but the change in angle of the
population response was greater than the change in orientation of the
cylinder. This discrepancy increased as the orientation of the cylinder
moved closer to the orientation of the axis of the finger and was more
pronounced for the less curved cylinder. Measured contact areas between
the cylinders and the skin were elliptical, with orientations exceeding
those of the cylinder; again the differences were greater for the less curved cylinder and for orientations closer to that of the finger axis.
The human discrimination performance could be explained in terms of the
SAI population responses.
Key words:
tactile orientation; mechanoreceptor; cutaneous afferent; finger; grasp; shape; curvature; cylinder; skin mechanics
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INTRODUCTION |
The evolution of the hand with its
opposable thumb, independent finger movements (Tubiana, 1981
), and high
density of cutaneous innervation (Johansson and Vallbo, 1979) has led
to dexterous manipulations that are of great importance to human
existence. For appropriate motor control of the hand, the brain must
have information about a number of parameters of the object being
manipulated. Cylinders characterize a class of objects that we handle
regularly, e.g., when writing with a pen or eating with chopsticks. A
cylinder is defined completely by two parameters, its orientation and
its curvature. At any one instant of time, the only source of
information about the curvature of the cylinder (local shape), its
position on the digits, and its orientation with respect to the digits is the population of mechanoreceptors in the skin contacting the object
(Goodwin, 1997).
A number of studies have elucidated how the local shape of contacted
objects may be relayed to the brain by the cutaneous mechanoreceptive
afferents. LaMotte and Srinivasan used sinusoidally shaped steps,
indenting them into and scanning them across monkeys' fingerpads
(LaMotte and Srinivasan, 1987a,b; Srinivasan and LaMotte, 1987). They
demonstrated that the shapes of the steps were represented in the
responses of the cutaneous afferents and showed that these responses
could explain the human ability to discriminate such shaped steps.
There have also been studies of the responses of cutaneous afferents to
ellipsoids scanned over the fingerpad (LaMotte et al., 1994) and to
cylindrical wavy surfaces scanned across the fingerpad (LaMotte
and Srinivasan, 1996). Using spherical stimuli, Goodwin et al. (1991,
1995) and Wheat et al. (1995) showed that the reconstructed responses
of the population of active slowly adapting type I afferents (SAIs),
recorded in monkeys, accounted for their psychophysical measurements of
the human capacity to discriminate the curvatures of the spheres and
also their positions on the fingerpad. Determination of local shape,
mainly in the context of robotics has also been the subject of a number
of theoretical studies (Allen and Michelman, 1990; Berkemeier and
Fearing, 1993; Reynaerts and van Brussel, 1993; Hahn, 1994).
Few studies have been related directly to the orientation of grasped
objects. A number of investigators, measuring either human
psychophysical performance or neural responses in monkeys, have
explored the orientation of patterns of vibrating dots (Schneider et
al., 1986; Kops and Gardner, 1996) or the orientation of stimuli scanned across the skin (Costanzo and Gardner, 1980; Warren et al.,
1986; Essick and Edin, 1995; Ruiz et al., 1995). In addition, tactile
resolution is often measured by requiring the subject to distinguish
between two possible orthogonal orientations of edges or gratings
(Essock et al., 1992; Van Boven and Johnson, 1994; Stevens and
Patterson, 1995). Lechelt (1992) investigated cylinder orientation
directly and, using a bimanual comparison task, showed that humans
could discriminate orientation differences of 10°. LaMotte and
Srinivasan (1993) have described the responses of SAIs to cylinders of
different curvature applied to the receptive field center, but there
has been no analysis of cutaneous afferent population responses for
cylindrical stimuli and no study of the representation of the
orientation of the cylinder in the neural responses.
In this paper we measure the ability of humans to discriminate the
orientation of cylinders passively contacting the fingerpad. In
matching single-fiber recordings in anesthetized monkeys, we characterize the responses of the population of SAIs, showing how the
orientation of the stimulus is represented in the neural responses, and
we relate these to the human performance.
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MATERIALS AND METHODS |
Stimulus. The set of stimuli consisted of seven
Delrin cylinders with radii of 1.44, 1.92, 2.94, 3.90, 5.81, and 12.4 mm or 
(flat); the corresponding curvatures, given by the reciprocal of the radii, were 694, 521, 340, 256, 172, 80.6, and 0 m1, respectively. The cylinders were attached to a
stepping motor, which was mounted on the balanced beam of the
stimulator (Fig. 1, top). When
a relay was triggered, the beam was released, and the cylinder was
lowered to contact the fingerpad. Static contact force was set by
counterweights, and a damper ensured smooth motion with a velocity at
contact of 20 mm · sec1. The orientation of
the cylinder 
could be adjusted rapidly under computer control with
a resolution of 0.9°/step (Fig. 1, bottom). A pair of
x-y micrometers and dial indicators, attached to
the stimulator, allowed the position at which the cylinders contacted
the skin to be adjusted with a resolution of 0.01 mm.
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Figure 1.
Balanced beam stimulator (top) and
the coordinate conventions (bottom). A cylinder
(a) was mounted on the stepping motor
(b). Force was set by the weight
(c), and position was adjusted by the micrometers
(d) and dial indicators
(e). Activating relay (f)
released the beam, and damper (g) ensured smooth
motion. The x- and y-axes passed through
the receptive field center and were orthogonal to and parallel to the
axis of the finger, respectively. The orientation of the cylinder was
defined by angle (positive, counterclockwise), and the orientation
of the contact ellipse was defined by angle  .
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Human psychophysics. Six healthy humans (four male and two
female) ranging in age from 22 to 48 years volunteered for these experiments, which were approved by the University of Melbourne Human
Ethics Committee. The subject was seated comfortably with the forearm
supinated, and the index finger of the dominant hand was anchored in a
bed of Plasticine. A curtain prevented the subject from seeing either
the stimulator or his or her finger. The stimulator was positioned with
the surfaces of the cylinders located 1 mm above the skin. At contact,
the line of action of the force was orthogonal to the plane tangential
to the fingerpad. Contact force was set at 40 gm weight (0.392 N). This
force was chosen to allow comparison with previous tactile studies of
shaped stimuli (e.g., Srinivasan and LaMotte, 1987; Goodwin et al.,
1991); it is at the low end of forces generally used by humans in
manipulative tasks (Johansson, 1996) and is particularly pertinent to
"delicate" manipulations such as writing with a pen. In the first
series of experiments, the subject's ability to discriminate the
orientation of the cylinder with curvature of 521 m1 (radius, 1.92 mm) was measured using a forced
choice paradigm. A trial consisted of a pair of stimuli. For the first
stimulus in the pair (the standard) the axis of the cylinder was at
right angles to the axis of the finger ( = 0). In some trials the
second or comparison stimulus was at the same orientation as the
standard (Ss), and for other trials the
comparison stimulus was at a different orientation
(Sd); the change in orientation was in a
clockwise direction so that was negative. The subject's task was
to respond that both stimuli in the pair were the same
(Rs) or that they were different
(Rd). On each day five blocks of trials
were run with the comparison stimulus having an orientation of 
1.8,
3.6, 5.4, 9, or 13.5°, respectively. Each block consisted of
20 trials with 10 Ss and 10 Sd pairs distributed randomly. The order of
presentation of the blocks was varied randomly from day to day and from
subject to subject. Data were collected for 10 d (200 trials at
each orientation). To avoid auditory cues from the stepping motor, it
was always advanced before presentation of either the standard or the
comparison stimulus. For the standard stimuli and the
Ss comparison stimuli, the stepping motor was advanced 180°; for the Sd comparison stimuli
it was advanced 180° plus the desired difference. The stimulus was in
contact with the skin for 1 sec, and the interval between the standard
and comparison stimuli in a trial was ~1.5 sec. The point of contact of each stimulus was varied randomly along the axis of the finger over
a range of ~2 mm. From the conditional probabilities,
P(Rd/Sd) and
P(Rd/Ss),
the bias-free measure d
was calculated (Johnson, 1980).
A second series of experiments was conducted, which was identical to
the first series except that the curvature of the cylinder was 172 m1 (radius, 5.81 mm), and there were six
orientations, which had values of 0.9, 1.8, 3.6, 4.5, 7.2,
and 9° respectively.
Neural recording. Experiments, approved by the University of
Melbourne Animal Ethics Committee, were performed on five Macaca nemestrina monkeys weighing from 2.0 to 8.2 kg. After a dose of ketamine hydrochloride (15 mg/kg, i.m.) plus atropine sulfate (60 µg/kg, i.m.), an endotracheal tube and an intraperitoneal catheter
were inserted. Surgical anesthesia was induced by administration of
sodium pentobarbitone (15-20 mg/kg, i.v.) and was maintained throughout the experiment by sodium pentobarbitone diluted in saline
(15 mg/ml, i.p.) administered hourly through the catheter (dose as
required). The catheter was also used for fluid replacement. Body
temperature was monitored by a rectal thermometer and was maintained at
37°C by a heating blanket. Respiration rate, end-tidal carbon dioxide
level, blood pressure, heart rate, and oxygen saturation levels were
monitored throughout the experiment. Antibiotic cover was provided by
amoxycillin (18 mg/kg, i.m.) every 6 hr and, at the end of the
experiment, by a dose of 50 mg/kg benzathine penicillin, 30 mg/kg
procaine penicillin, and 19 mg/kg benzylpenicillin. In four successive
experiments on a monkey the median nerve was exposed at four sites, and
single fibers were isolated by microdissection. The first two
dissections were in the upper arms, and the last two were in the lower
arms; at least 2 weeks elapsed between experiments. At the end of each
experiment, the dissection was sutured in layers, and the monkey was
returned to a heated, padded cage to recover.
Isolated action potentials recorded from a platinum hook electrode were
amplified, stored on a digital oscilloscope, and passed through a
time-amplitude window discriminator. These signals were sampled at 10 kHz (0.1 msec resolution) and stored on disk for off-line analysis.
Single fibers were classified as SAIs, fast-adapting type I afferents
(FAIs), or FAIIs by the established criteria of responses to static
stimuli, responses to rapidly changing stimuli, and receptive field
size (Vallbo and Johansson, 1984). Initially, receptive field positions
were estimated using von Frey hairs. Only SAIs were studied and only if
the receptive field was located on the central region of a fingerpad.
The finger innervated by the isolated afferent was immobilized in
modeling clay with the nail secured by cotton thread. The center of the
receptive field was then determined more precisely as follows. A sphere with radius of 1.44 mm (curvature, 694 m1) was
attached to the stimulator and applied, with a contact force of 15 gm
weight (0.147 N), to points separated by 0.5 mm along two orthogonal
axes through the estimated receptive field center; one axis was
parallel to the axis of the finger, and the other was at right angles
to it. At each point the total response over 1 sec was measured, and
the point of maximum response was determined. The process was repeated
successively around this point to establish the center of the receptive
field.
Receptive field response profiles were measured for the seven cylinders
with the axis of the cylinder orthogonal to the axis of the finger ( = 0°). One of the cylinders was applied to the receptive field at
points separated by 0.5 mm along the y-axis (Fig. 1). The
surface of the cylinder was positioned 0.5 mm above the skin, and the
line of action of the force was orthogonal to the plane tangential to
the fingerpad at the receptive field center. Contact force was set at
15 gm weight (0.147 N). At each point the stimulus was applied seven
times, contacting the finger for 1.5 sec and then raised off the finger
for 2.5 sec. For analysis, the first application was ignored, and
responses for the last six applications (each preceded by the same
stimulus with the same interstimulus interval) were used. The process
was repeated for the remaining six cylinders with the order of
presentation of the seven cylinders varied randomly from afferent to
afferent. Responses were measured by the number of action potentials
occurring during the first second of response.
For the two cylinders used in the human psychophysics experiments
(curvatures, 521 and 172 m1), response profiles
were measured in both spatial dimensions on the skin at five different
orientations as follows. One of the cylinders was positioned at points
along the y-axis separated by 0.5 mm. At each point the
stimulus was presented in a block of 31 trials. The first trial was
ignored in the analysis, and the remaining 30 trials consisted of six
presentations at each of the five orientations at 0, ±4.5, and ±9°.
The order of the 30 trials was randomized. This process was then
repeated along lines parallel to the axis of the finger at
x = ±1, ±2, and 3 mm. The entire process was then
executed for the second cylinder. The order in which the two cylinders
were selected was randomized from afferent to afferent.
To define the profiles as completely as possible, for each afferent we
examined the maximum number of points located on the relatively flat
central portion of the fingerpad. The proximal limit was determined by
the interphalangeal crease, the distal limit by the curvature of the
fingertip, and the medial and lateral limits by the curvature of the
sides of the finger. A complete matrix took ~7 hr.
The process of manufacturing the cylinders and their attachments to the
stepping motor was such that there was a different small offset in the
y direction for each cylinder. These offsets were measured
with a micrometer and were compensated for in the analysis.
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RESULTS |
Human psychophysics
When a cylinder of curvature of 521 m1
contacted the fingerpad, humans were able to discriminate small
differences in the orientation of the cylinder. In Figure
2A the index of
discriminability d is plotted as a function of the
difference in orientation between the standard and comparison stimuli.
The psychometric function was similar for all six subjects, with
d increasing approximately linearly with an increase in the
orientation difference. For each subject the difference limen was
calculated as follows. Regression of the five data points yielded a
straight line from which the orientation difference corresponding to a
d value of 1.35 could be obtained; this is equivalent to a
difference in orientation that could be discriminated with a
probability of 75%. Table 1 shows these
difference limens. Similar behavior occurred for the cylinder with a
curvature of 172 m1. Comparison of discrimination
for the two cylinders is seen clearly in Figure 2C, which
shows the psychometric functions averaged over the six subjects for
each of the cylinders. At all orientation differences, discrimination
was more acute for the less curved stimulus. For each subject, the
difference limen shown in Table 1 was less for the cylinder with
curvature of 172 m1 than for the cylinder with
curvature of 521 m1 (one-tailed paired
t test, p = 0.001). Because the position of contact of the cylinders on the skin was varied randomly, the discrimination could not have been based on spurious simple cues such
as a shift in position of a single end point of the contact area.
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Figure 2.
Human discrimination of the orientation of a
cylinder contacting the fingerpad. A, Cylinder with
curvature of 521 m1 (radius, 1.92 mm). For five
curves (5 subjects) there are five data
points at orientation differences of 1.8, 3.6, 5.4, 9, and 13.5°. For one subject the data point at 13.5° is not shown,
because d > 4 is not meaningful (Macmillan and Creelman, 1991). At
each data point there are 200 observations.
B, Same six subjects for the cylinder with curvature of
172 m1 (radius, 5.81 mm). For each curve (subject)
there are six data points at orientation differences of
0.9, 1.8, 3.6, 5.4, 7.2, and 9°; at each data point
there are 200 observations C, Data points
show means and unilateral SEMs for psychometric functions averaged over
the six subjects. Lines show linear regression of the
data points.
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Receptive field profiles
Responses of 13 SAIs were measured when cylinders, with their axes
orthogonal to the axis of the finger ( = 0° in Fig. 1), were
placed at various positions in the receptive field. For such a
cylinder, a change of position in the x direction has no
effect on the geometry of contact and thus has no effect on the
response of the afferent. Receptive fields were characterized by
measuring the responses when the cylinder was positioned at points
separated by 0.5 mm along the y-axis. The numbers of
impulses elicited during the first second of response are shown for a
typical SAI in Figure 3A. The
small SEs verify the consistency of the responses. For each cylinder,
the response profile peaked when the cylinder was close to the
receptive field center and decreased as the cylinder was placed more
peripherally in the receptive field. An increase in the curvature of
the cylinder had two effects. The peak value of the profile increased,
and the width of the profile decreased.
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Figure 3.
Response profiles for cylinders with their axes
orthogonal to the axis of the finger. A, Responses of a
single SAI (mean ± SEM, n = 6) to the seven
cylinders positioned at points separated by 0.5 mm along the
y-axis. Numbers indicate the curvature of the cylinder in m1. For clarity, SEMs are only
shown at one point for each line, but
they are similar at all the other points. B, Normalized
profiles for 13 SAIs responding to the cylinder with curvature of 340 m1. The normalizing factor was the average
response over the 49 points that were common to all 13 afferents (7 cylinders by 7 positions about the center).
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All 13 SAIs behaved in the same way, except that some afferents were
more sensitive than others. Thus, for the same stimulus, some afferents
had a greater response than others. The effect of the sensitivity of an
individual fiber was eliminated by normalizing; the responses were
divided by an average response for that fiber. The normalization factor
is a measure of the sensitivity of the afferent. The most responsive
afferent was 5.1 times as sensitive as the least responsive afferent,
and the 13 normalization factors were distributed approximately
normally, with a coefficient of variation of 0.38, a result similar to
that found by Goodwin et al. (1995) for spheres. The normalized
profiles, illustrated in Figure 3B for the cylinder with a
curvature of 340 m1, were consistent from fiber to
fiber, indicating that, apart from the sensitivity factor, all SAIs had
the same underlying stimulus-response characteristics.
Normalized response profiles pooled for the 13 afferents for all seven
cylinders are shown in Figure
4A. It can be seen
clearly that as the curvature of the cylinder increased, the profile
peak increased, and the profile width decreased. There was a small proximal shift in the position of the peak with a decrease in the
curvature of the cylinder, probably related to the curvature of the
finger. In this case the small SEs indicate the consistency of the
underlying profiles from fiber to fiber. For further analysis, which is
described later in the paper, it is useful to define these profiles
mathematically. The profile for each cylinder fits closely to the
function
aeby2.
Table 2 gives the values of the constants
a and b, which were determined by nonlinear
regression using the Levenberg-Marquardt algorithm (Press et al.,
1986). The constant a (the height of the profile) indicates
the dependence on local curvature of the Merkel complexes in
conjunction with skin mechanics. As seen in Figure
4B, for low curvatures responses increased rapidly
with increasing curvature and then started to saturate for higher
curvatures. A commonly used measure of the extent of profiles such as
those in Figure 4A is their width at half-height.
From the equation above, the width at half-height is given by
w = 1.67/
b. This parameter, shown in
Figure 4B, indicates how the "size" of the receptive field decreased as the curvature of the cylinder increased. For comparison, equivalents of the constants a and
w for spherical stimuli, measured by Goodwin et al. (1995),
are shown by the broken lines.
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Figure 4.
Profiles for the pool of SAIs. A,
Normalized profiles (mean ± SEM) for the 13 afferents responding
to all seven cylinders. Numbers indicate the curvature
of the cylinder in m1. Because the profile could
not be measured over the full extent from 3.5 to 3.5 mm for each
afferent, the number of data points is different for different
positions; n = 13 for the more central points and decreases for more peripheral points.
Nevertheless, the single SEM shown for each line is similar for all
points on the line. B, Data points and
solid, splined lines show the height of the receptive
field profile (a) and its width at half-height (w) for all seven cylinders. Broken
lines show equivalent values of the constants a
and w for spherical surfaces from the data of Goodwin et
al. (1995).
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For any stimulus, the receptive field profile of an afferent is defined
by the responses at points in the two-dimensional plane of the
receptive field. For a cylinder, the geometry of which is invariant
along its axis, these profiles are effectively one-dimensional, as
illustrated in Figure 5. Such profiles
can be interpreted as the responses of the population of afferents from
a fingerpad in contact with the cylinder, with the simplifying assumption that all afferents have the same sensitivity.
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Figure 5.
Population response profiles in both spatial
dimensions illustrated for three of the cylinders. The axis of the
cylinder was oriented along the x-axis ( = 0°).
Profiles are plotted from the function
aeby2.
For curvatures of 172, 340, and 521 m1, the
constants a and b determined by
regression are 1.24 and 0.11, 1.69 and 0.25, and 1.97 and 0.30, respectively.
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Change in orientation
If the finger were perfectly flat, and the skin mechanics were
isotropic, then changing the orientation of the cylinder with respect
to the finger would simply result in a rotation of the response profile
through that same angle. Thus, for example, changing the orientation of
the cylinder with curvature of 521 m1 by 9°
would result in the profile shown in Figure 5, right panel, rotating by 9° about the z (normalized response) axis. For
a cylinder at an orientation , the resulting response profile would
be given by
aebu2,
where u = ycos xsin.
However, the finger is not flat, and the analysis of Fearing and
Binford (1991) for a rigid cylinder contacting an elastic cylinder
suggests that the rotation of the population response (
) may not
match the rotation of the cylinder () exactly. Thus we measured
directly the nature and extent of rotation in the population
response.
Responses at a matrix of points separated by 0.5 mm in the y
direction and 1 mm in the x direction were measured for 11 SAIs using the cylinder with curvature of 172 m1
and for 10 SAIs using the cylinder with curvature of 521 m1. As before, all the afferents behaved in the
same way, differing only by a scaling factor proportional to their
sensitivity. Thus, the normalized responses could be combined to show
the underlying rotated profiles common to all afferents. There are two
complementary ways of visualizing rotation in the population response.
In Figure 6, profiles varying in one
spatial dimension (y) are shown along lines parallel
to the axis of the finger. Three characteristics can be seen. First, at
x = 0 (Fig. 6B) the profiles at all
five orientations are coincident. Second, along a line away from the origin (Fig. 6C) the profile shifts with rotation, and the
shift is greater for greater rotations. Third, along a line on the
opposite side of the origin (Fig. 6A) the profile
shifts in the opposite direction. In these figures it is easy to gauge
the magnitude of the shifts, but it is not so easy to visualize the
rotation of the profile in both spatial dimensions. This is more easily seen in Figure 7, which shows the
rotation clearly for both spatial dimensions; the disadvantage here is
that it is not easy to assess small quantitative changes in
three-dimensional plots.
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Figure 6.
Normalized responses averaged over 10 SAIs
responding to the cylinder with a curvature of 521 m1. The x- and
y-axes were orthogonal to and parallel to the axis of
the finger, respectively, and the orientation of the cylinder (angle between its axis and the x-axis) was 0, ±4.5,
or ± 9°. For each profile the curve passes
through data points separated by 0.5 mm.
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Figure 7.
Normalized responses averaged over 10 SAIs
responding to the cylinder with a curvature of 521 m1. Profiles are shown for three orientations of
the cylinder (9, 0, and 9°). Data points are
separated by 1 mm in the x direction and by 0.5 mm in
the y direction.
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Figures 6 and 7 demonstrate a rotation of the response profile. The
extent of the rotation () was estimated by nonlinear regression,
fitting the rotated profiles to the function
aeb(ycos
xsin)2. As seen in Table
3, the orientation of the SAI response
profile was not the same as the orientation of the cylinder. In all
cases the magnitude of the response orientation was greater than the magnitude of the cylinder orientation. Furthermore, the difference in
angle ( ) increased with increasing cylinder orientation, and
the magnitude of the difference was greater for the less curved cylinder (curvature, 172 m1) than for the more
curved cylinder (curvature, 521 m1).
Orientation of contact areas
When a rigid cylinder contacts a finger, which is a curved,
compliant body, the geometry of the contact is complex and depends on
the curvature of the cylinder and on the angle of the cylinder with
respect to the axis of the finger. An idea of the likely nature of this
contact can be obtained from the analysis by Fearing and Binford (1991)
for the contact between a rigid cylinder and a cylindrical elastic
"finger." They showed that the contact area was elliptical and that
the orientation of the major axis of the ellipse (Fig. 1, ) was
related to the orientation of the cylinder by the expression:
where 
c and f are the
curvature of the cylinder and the elastic finger, respectively. The
difference between the two orientations ( ) is shown in Figure
8 as a function of the orientation for the two cylinders with curvature of 521 and 172 m1 for a number of elastic fingers of different
curvature. The magnitude of the orientation of the contact ellipse is
greater than the magnitude of the orientation of the cylinder, and the
difference between them increases as the cylinder is angled closer
toward the axis of the finger (closer to = ±90°). The
difference also increases as the finger becomes more curved, and the
difference is greater for the less curved cylinder (172 m1) than for the more curved cylinder (521 m1).
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Figure 8.
Contact between rigid cylinders and fingers.
A, B, Broken lines show the difference ( )
between the orientation of the contact ellipse (Fig. 1, ) and
cylinder orientation () as a function of cylinder orientation for a
rigid cylinder contacting an elastic finger as derived by Fearing and
Binford (1991). Calculations are shown for both cylinders used by us
(curvatures, 521 and 172 m1) and for fingers
ranging in curvature from 31.3 to 167 m1 (radii
ranging from 32 to 6 mm). Squares show differences ( ) between SAI response profile orientation () and cylinder orientation measured in monkeys. Crosses show
differences ( ) between contact ellipse orientation and
cylinder orientation measured in humans (average of 6 subjects). For
clarity, A and B have different ordinate
scales. C, Fingerprints showing contact areas for a
typical human subject. Both cylinders (curvatures, 521 and 172 m1) were used at orientations of 0° for the
standard (S) and 4.5 and 8.1° for the
comparison (C).
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We estimated the contact areas in our human subjects by inking the
cylinders and applying them to the fingerpads at angles of 0, 4.5,
and 8.1° using the same stimulator and stimulus conditions as used
in the psychophysics experiments. A set of fingerprints from a typical
subject is shown in Figure 8C. The contact areas were
elliptical, and the orientation of the major axis (estimated by eye)
averaged over the six subjects was 6.0 and 9.6° for the cylinder
with curvature of 521 m1 at orientations of 4.5
and 8.1°, respectively and 6.9 and 12.3° for the cylinder
with curvature of 172 m1 at orientations of 4.5
and 8.1°, respectively. These results are shown by
crosses in Figure 8. These measurements are approximate only, and there are only two angles and two cylinders, but they show
similar characteristics to the results of Fearing and Binford (1991):
the magnitude of the difference in orientation was greater for the less
curved cylinder, and the difference increased with orientation for the
less curved cylinder but did not change with orientation for the more
curved cylinder.
When the cylinders were applied to monkeys' fingers, we measured the
orientation of the SAI response profiles directly. The differences
between the orientation of the response profile and the orientation of
the cylinder ( in Table 3) are plotted as open
squares in Figure 8. This difference also increased with increasing orientation of the cylinder and was greater for the cylinder
with the smaller curvature.
Human and monkey fingers are not cylindrical but have a higher
curvature on the sides of the fingers and are flatter at the center of
the fingerpad. Thus the effective curvature of the fingerpad is likely
to be somewhere between flat (0 m1) and the
reciprocal of the radius of the finger (~100 m1
for humans and ~250 m1 for our monkeys). The
crosses and squares in Figure 8 are consistent with this. Taken together, these results show that when cylinders contact the finger, the contact ellipse has a different orientation to
the orientation of the cylinder, and the orientation of the SAI
population response is correspondingly affected. The magnitude of the
response orientation is greater than the magnitude of the cylinder
orientation and is greater for less curved cylinders than for more
curved cylinders, which may explain why the human difference limens
were smaller for the less curved cylinder.
| |
DISCUSSION |
Humans are able to manipulate objects with a high degree of
precision. The hand, which is unique to primates, relies on independent movements of the digits and on an opposable thumb (Tubiana, 1981). The
accuracy of these hand movements depends on feedback of the parameters
of the manipulated object. Such information is relayed by a number of
classes of receptors, including joint receptors, muscle spindle
afferents, and Golgi tendon organs (Gandevia et al., 1992). However,
information about the local shape of a grasped object and its position
of contact on the fingers can only be signaled by the cutaneous
mechanoreceptive afferents (Goodwin, 1997). Cylinders represent an
important class of relatively simple objects, the shape of which is
completely defined by two parameters: the orientation of the axis of
the cylinder, in which direction the curvature is zero, and the
curvature in the orthogonal direction. We have investigated the
representation of the curvature and orientation of a cylinder in the
digital nerve discharge in monkeys and have related this to human
psychophysical performance.
Human performance: neural substrate
When a highly curved cylinder (curvature, 521 m1; radius, 1.92 mm) was applied passively to the
subjects' fingerpads, they were able to discriminate changes in
orientation of 5.4°. For a less curved cylinder (curvature, 172 m1; radius, 5.81 mm), their discrimination
threshold of 4.2° was significantly lower. These values are less than
the 10° difference limen found by Lechelt (1992) for a cylinder of
curvature of 526 m1 (radius, 1.9 mm), probably
because of cognitive factors resulting from the more complex paradigm
of Lechelt (1992), which involved a comparison of four stimuli
presented to both the left and right hands. Other tactile orientation
data, such as the discrimination threshold of 14° for a dot scanned
over the finger at different orientations (Keyson and Houtsma, 1995),
are not directly comparable.
In our experiments, the cylinders were applied passively to the skin
with a constant static contact force and with an initial contact
velocity of 20 mm · sec1. In monkeys, only the
SAIs responded appreciably to such stimuli. All SAIs had the same
underlying stimulus-response characteristics, differing only by a
scaling constant determined by the sensitivity of the afferent; thus it
was possible to reconstruct the responses of a complete ideal SAI
population to any of the cylinders at any orientation. For three
parameters of the cylinder (curvature, position, and orientation), the
only source of information relayed to the brain arises in the
population of cutaneous afferents. The shape (curvature) of the
cylinder is reflected in the shape of the SAI population response,
which increases in magnitude and decreases in width for more curved
cylinders. The position of contact on the skin is represented by the
position of the response profile within the overall SAI population. For
these two parameters of the stimulus, curvature and position, the
results are analogous to our previous observation for spherical stimuli
(Goodwin et al., 1995; Wheat et al., 1995). The dependence of the peak
of the response profiles on curvature (Fig. 4, constant a)
is similar to corresponding measurements made previously by LaMotte and
Srinivasan (1993, 1996). Comparison of profile heights and widths (Fig.
4) for spheres, which have a single curvature in all directions, and
cylinders, which have a single curvature in one direction and zero
curvature in the orthogonal direction, should allow a refinement of
existing skin mechanics models (Phillips and Johnson, 1981; Srinivasan,
1989; Srinivasan and Dandekar, 1996). LaMotte and Srinivasan have also
addressed the representation of the local shape of an object in the
peripheral nerve discharge using sinusoidally shaped steps (LaMotte and
Srinivasan 1987a,b; Srinivasan and LaMotte, 1987).
Changing the orientation of the cylinder resulted in a rotation of the
SAI population response profile from which the brain could, in
principle, easily determine the orientation of the stimulus. From the
widths of the profiles in Figure 4 and the lengths of the fingerprints
in Figure 8, we estimate that SAIs would be active over an area >70
mm2, which, at an innervation density of 0.7 mm2 (Johansson and Vallbo, 1979), comprises about
50 afferents. This is similar to the number of
x-y positions used by us in the regressions determining the orientations of the profiles in Table 3; the resolution
in our estimates exceeds the 4 or 5° human difference limens but
takes no account of two factors that influence resolution. Noise,
particularly in the CNS, is a major factor that increases the
uncertainty in any response measure; we do not know the extent of such
noise. In addition, not all fibers in the population have the same
sensitivity, leading to some "distortion" in the profiles, which
could reduce the resolution depending on how the brain accounts for
this variation in calculating the orientation. An analogous neural
representation of tactile stimulus orientation was demonstrated by
LaMotte et al. (1994) for ellipsoids scanned across monkeys' fingerpads; the ellipsoid orientations, presented at 30° increments, were evident in the spatiotemporal patterns of activity.
There are a number of ancillary tactile cues that could, in principle,
assist in the discrimination of orientation. Because the finger is not
perfectly flat and isotropic, contact areas with cylinders of different
orientation may differ slightly in their lengths, widths, or the
pressure distributions within them; these differences would be
reflected in differences in the SAI population response length, width,
and height. In addition, some members in the population may be active
for one orientation but not for another. However, the signal-to-noise
ratio for these ancillary cues would be much smaller than for the
orientation of the population as a whole, and the resolution would be
correspondingly degraded. Moreover, such cues are confounded by the
multidimensional nature of the stimulus and could only be used in
discrimination tasks in which nothing other than the orientation of the
stimulus changed, a situation that is rare in real life. Random changes in the position of the stimulus along the axis of the finger were introduced in our psychophysics experiments in an attempt to eliminate these cues; randomizing the position in the orthogonal direction as
well would have provided additional safeguards. For similar reasons we
believe that the FAIs and SAIIs do not play a major role in this task.
The responses of the FAIs to our stimuli are low in magnitude, but they
could contribute to ancillary cues such as the "length" of the
response or the location of active units in the population; for the
reasons given above, we do not believe that they play a major role in
determining stimulus orientation. Similarly, although SAIIs will be
activated, including those around the borders of the fingerpads, they
are unlikely to provide a robust signal for the orientation of a
multidimensional stimulus.
Contact mechanics
The mechanics of contact between a rigid cylinder and the
compliant cylinder-like finger is complex and has an important bearing on neural responses and human performance. Studies of human and monkey
skin mechanics have not addressed this issue. The problem is also
crucial in robotics, and in this field, there have been some analyses
for rigid cylinders contacting elastic cylinders, which form the
fingers of the robots. In particular, the study of Fearing and Binford
(1991) showed that the contact area is elliptical, with an orientation
that is different from the orientation of the cylinder. The difference
in orientation is larger for less curved cylinders and for cylinders
that are oriented closer toward the axis of the finger. The situation
in the human is even more complex, because the curvature of the finger
is not uniform, being flatter at the center of the pad and more curved
on the sides of the finger, and also the finger is not a simple elastic
body. Nevertheless, currently the robotic analyses provide the best guide to the behavior of human and monkey fingers with regard to the
orientation of cylinders. The trends in our data in Figure 8 are
consistent with many of the aspects of these simple robotic models. The
estimated contact ellipses in the human behaved in a way similar to
those in the robot elastic finger, and the same trends were also seen
in the orientation of the SAI response profiles recorded in
monkeys.
Our data and the model of Fearing and Binford (1991) suggest that human
performance (both tactile and manipulative) would be degraded as the
orientation of the cylinder deviated further from a line orthogonal to
the finger axis, and would be degraded for less curved cylinders. The
finding of Lechelt (1992) that the difference limen increased from 10 to 15° as the cylinder orientation increased from 0 to 45° is
consistent with this hypothesis. However, there are a number of
complicating factors. First, the finger is not cylindrical toward the
tip but has an appreciable curvature in both directions. This factor
probably accounts for the low thresholds (10°) of subjects
discriminating orientations close to that of the finger axis in the
experiments of Lechelt (1992). Second, during opposition in the human
hand, the axes of the thumb and the index finger are not parallel;
therefore, cylinders oriented close to the axis of one digit will not
be close to the axis of the other digit (Tubiana, 1981). Third, because the SAI population response also contains information about the shape
of the cylinder, it is possible that the brain compensates to some
degree for the alterations caused by contact mechanics. There is
clearly a need for an extension of current primate skin mechanics
models (Phillips and Johnson, 1981; Srinivasan, 1989; Srinivasan and
Dandekar, 1996) to account for the complex shape of the finger.
Comparison with vision
Orientation is a crucial parameter of visual stimuli, and there is
extensive literature, including human psychophysical studies, single-neuron responses, and robotic vision. The orientation
discrimination threshold in humans is different for different stimuli
and different experimental conditions. For long lines, the difference
limen is of the order of 1° but varies with the orientation of the
stimulus (Orban et al., 1984; Heeley and Buchanan-Smith, 1990;
Westheimer and Ley, 1997). Orientation selectivity is a well documented
property of cells in the visual cortex, and there are a number of
models relating single-cell responses to psychophysical measurements (Paradiso, 1988; Vogels, 1990). In the tactile system, we have only
limited data relating the responses of cortical neurons to the
orientation of the stimulus (Pubols and Leroy, 1977; Hyvarinen and
Poranen, 1978). As yet there are no detailed models for the perception
of tactile orientation.
| |
FOOTNOTES |
Received Aug. 1, 1997; revised Oct. 16, 1997; accepted Oct. 20, 1997.
This work was supported by a grant from the National Health and Medical
Research Council of Australia.
Correspondence should be addressed to A. W. Goodwin, Department of
Anatomy and Cell Biology, University of Melbourne, Parkville, Victoria
3052, Australia.
| |
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Top
Abstract
Introduction
