Properties of mouse cutaneous rapidly adapting afferents: relationship to skin viscoelasticity.
ABSTRACT When skin is stretched, stimuli experienced by a cutaneous mechanoreceptor neuron are transmitted to the nerve ending through the skin. In these experiments, we tested the hypothesis that the viscoelastic response of the skin influences the dynamic response of cutaneous rapidly adapting (RA) neurons. Cutaneous RA afferent neurons were recorded in 3 species of mice (Tsk, Pallid, and C57BL6) whose skin has different viscoelastic properties. Isolated samples of skin and nerve were stimulated mechanically with a dynamic stretch stimulus, which followed a pseudo Gaussian waveform with a bandwidth of 0-60 Hz. The mechanical response of the skin was measured as were responses of single RA cutaneous mechanoreceptor neurons. For each neuron, the strength of association between spike responses and the dynamic and static components of stimuli were determined with multiple logistic regression analysis. The viscoelastic material properties of each skin sample were determined indirectly, by creating a nonlinear (Wiener-Volterra) model of the stress-strain relationship, and using the model to predict the complex compliance (i.e., the viscoelastic material properties). The dynamic sensitivity of RA mechanoreceptor neurons in mouse hairy skin was weakly related to the viscoelastic properties of the skin. Loss modulus and phase angle were lower (indicating a decreased viscous component of response) in Tsk and Pallid than in C57BL6 mice. However, RA mechanoreceptor neurons in Tsk and Pallid skin did not differ from those in C57 skin with regard to their sensitivity to the rate of change of stress or to the rate of change of incremental strain energy. They did have a decreased sensitivity to the rate of change of tensile strain. Thus the skin samples with lower dynamic mechanical response contained neurons with a somewhat lower sensitivity to dynamic stimuli.
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ABSTRACT: Using mixture theory, an axisymmetric continuum model is presented describing the response dynamics of the vestibular semicircular canals to canal-centered head rotation in which the cupula partition is modeled as a poroelastic mixture of interpenetrating solid and fluid constituents. The solid matrix of the cupula is assumed to behave as a linear elastic material, whereas the fluid constituent is assumed to be Newtonian. A regular perturbation analysis of the fluid dynamics in the canal provides a dynamic boundary condition, which acts across the cupula partition. Numerical solution of the coupled system of momentum equations provides the spatio-temporal displacement fields for both the fluid and solid constituents of the cupula. Results indicate that at frequencies above 1 Hz, the fluid constituent is dynamically entrained by the solid matrix such that their motions are bound as if to exist as a single component. The resulting high-frequency response is consistent with the macromechanical response predicted by single-component viscoelastic models of the cupula. Below 1 Hz, the dynamic coupling between the fluid and solid constituents weakens and the transcupular differential pressure is sufficient to force fluid through the mixture with little deformation of the solid matrix. Results are sensitive to the precise value of the cupular permeability. One of the most important distinctions between the present analysis and previous impermeable models of the cupula arises at the micromechanical level in terms of the local fluid flow that is predicted to occur within the cupula and around the ciliary bundles and sensory hair cells. Another important result reveals that the permeation dynamics predicted below 1 Hz gives rise to the same low-frequency macromechanical response as would occur with an impermeable viscoelastic structure having a much greater stiffness. Current estimates of the mechanical stiffness of the cupula, based solely on afferent nerve data, may therefore overestimate the true value intrinsic to the solid matrix by as much as an order of magnitude.Journal of Biomechanical Engineering 11/1999; 121(5):449-61. · 1.52 Impact Factor
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ABSTRACT: 1. Experiments were conducted to test the hypothesis that the responses of joint capsule mechanoreceptors better encode tissue stress or tissue strain. The experimental model was a small ligament from the cat knee capsule, which was stretched uniaxially in vitro. Experiments were done with either force or displacement as the controlled variable, and with steps, sinusoids, or pseudorandom Gaussian noise (PGN) as the input function. 2. The strength of coupling between neural discharge and both strain and stress was quantified during step experiments using linear correlation coefficients. The correlation between the frequency of neural discharge and stress was 0.93 +/- 0.09 (SD). The correlation between frequency of neural discharge and strain was -0.91 +/- 0.06. The magnitudes of these correlation coefficients were not significantly different. 3. The strength of coupling between neural discharge and both strain and stress during sinusoidal and PGN experiments was quantified by the use of an information theoretic statistic, transinformation. Out of 282 sinusoidal runs, transinformation between neural discharge and stress was significantly greater than transinformation between strain and neural discharge 241 times. Transinformation between strain and neural discharge was significantly greater 15 times. 4. During PGN experiments, transinformation between stress and neural discharge was greater than transinformation between strain and neural discharge in all 19 experimental runs. 5. Conditional transinformation between strain and neural discharge, given stress, was calculated for all sinusoidal and pseudorandom experiments. This statistic was greater than zero in 268 out of 289 experimental runs, indicating that a component of strain independent of stress is being signaled in the neural discharge.Journal of Neurophysiology 07/1991; 65(6):1321-8. · 3.30 Impact Factor
- Acta Physiologica Scandinavica 02/1971; 81(1):138-40. · 2.55 Impact Factor
92:1236-1240, 2004. First published 17 March 2004;
P. Grigg, D. R. Robichaud and Z. Del Prete
Afferents: Relationship to Skin Viscoelasticity
Properties of Mouse Cutaneous Rapidly Adapting
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Properties of Mouse Cutaneous Rapidly Adapting Afferents: Relationship to
P. Grigg,1D. R. Robichaud,1and Z. Del Prete2
1Department of Physiology, University of Massachusetts Medical School, Worcester, Massachusetts 01655; and2Department of
Mechanical Engineering, University of Rome “La Sapienza,” 00184 Rome, Italy
Submitted 27 October 2003; accepted in final form 10 March 2004
Grigg, P., D. R. Robichaud, and Z. Del Prete. Properties of mouse
cutaneous rapidlyadapting afferents:
viscoelasticity. J Neurophysiol 92: 1236–1240, 2004. First published
March 17, 2004; 10.1152/jn.01033.2003. When skin is stretched,
stimuli experienced by a cutaneous mechanoreceptor neuron are
transmitted to the nerve ending through the skin. In these experiments,
we tested the hypothesis that the viscoelastic response of the skin
influences the dynamic response of cutaneous rapidly adapting (RA)
neurons. Cutaneous RA afferent neurons were recorded in 3 species of
mice (Tsk, Pallid, and C57BL6) whose skin has different viscoelastic
properties. Isolated samples of skin and nerve were stimulated me-
chanically with a dynamic stretch stimulus, which followed a pseudo
Gaussian waveform with a bandwidth of 0–60 Hz. The mechanical
response of the skin was measured as were responses of single RA
cutaneous mechanoreceptor neurons. For each neuron, the strength of
association between spike responses and the dynamic and static
components of stimuli were determined with multiple logistic regres-
sion analysis. The viscoelastic material properties of each skin sample
were determined indirectly, by creating a nonlinear (Wiener–Volterra)
model of the stress–strain relationship, and using the model to predict
the complex compliance (i.e., the viscoelastic material properties).
The dynamic sensitivity of RA mechanoreceptor neurons in mouse
hairy skin was weakly related to the viscoelastic properties of the skin.
Loss modulus and phase angle were lower (indicating a decreased
viscous component of response) in Tsk and Pallid than in C57BL6
mice. However, RA mechanoreceptor neurons in Tsk and Pallid skin
did not differ from those in C57 skin with regard to their sensitivity to
the rate of change of stress or to the rate of change of incremental
strain energy. They did have a decreased sensitivity to the rate of
change of tensile strain. Thus the skin samples with lower dynamic
mechanical response contained neurons with a somewhat lower sen-
sitivity to dynamic stimuli.
relationship to skin
I N T R O D U C T I O N
Soft tissue structures contain the terminal processes of me-
chanically sensitive afferent neurons. When a soft tissue is
stimulated mechanically, the stimulus to the neuron is some
subset of the local tensile, compressive, and shear stresses and
strains that may be present in the tissue. Because most soft
tissues are viscoelastic, dynamic mechanical stimuli would
result in there being time or rate dependency to the magnitude
of those internal states of stress or strain. Because these states
(or some subset of them) constitute the mechanical stimulus for
mechanoreceptor neurons that innervate the soft tissue struc-
ture, it might be expected that any rate or time dependency in
the mechanoreceptor response would reflect the viscoelastic
mechanical response of the soft tissue structure. There is
evidence both for (Bell and Holmes 1992; Damiano 1999;
Loewenstein and Skalak 1966; Swerup and Rydqvist 1996) and
against (Husmark and Ottoson 1971; Wilkinson and Fukami
1983) a potential role for tissue viscoelasticity in shaping the
dynamic response properties of mechanoreceptors.
However, there have been limitations to the studies address-
ing this issue. First, in seeking relationships between spike
responses and mechanical stimuli, it is necessary to know
which of the many potential component(s) of a mechanical
stimulus actually causes the spike response; in general, this is
unknown. Also, previous investigations have centered mainly
on transient responses (i.e., slow adaptation of responses
evoked by step stimuli). In these studies, parallel behavior has
been observed between the mechanical relaxation of input
stimuli and the slow adaptation of a neuronal response. The
potential problem with this approach is that the 2 processes
may, in fact, be independent of each other.
In this communication, we used a new approach to address
the question of whether tissue viscoelasticity influences the
properties of mechanoreceptors. We used dynamic stimuli to
study rapidly adapting (RA) cutaneous mechanoreceptor affer-
ents in several strains of mice that have different skin vis-
coelasticities. RA afferents respond only to dynamic compo-
nents of stimuli and are not sustained in response to static
stimuli. If skin viscoelasticity is a determinant of the dynamic
response of cutaneous mechanoreceptors, then afferents in the
most viscoelastic samples should have a greater dynamic
response than afferents in the least viscoelastic samples. In a
recent paper (Del Prete et al. 2004) we showed significant
differences in the viscous properties of skin from Tsk mice and
wild-type (C57BL6) mice; Tsk skin had a lesser dynamic
response to dynamic stretch stimuli than skin from C57BL6
mice. In the current experiment we used Tsk and C57BL6
mice; as an additional control we included Pallid mice, which
are breeding colony controls for Tsk. We measured the vis-
coelastic properties of skin samples in each mouse phenotype
by determining the complex compliance. The complex com-
pliance includes measures of the loss modulus and the phase
angle, both of which reflect the viscous component of response
of a sample. In each sample we also determined the sensitivity
of afferents to static versus dynamic components of stimuli.
Using mice also solves the problem of not knowing what
components of a complex stimulus are acting on the neuron. In
a recent paper from this laboratory (Del Prete et al. 2003) we
identified the components of mechanical stimuli signaled by
Address for reprint requests and other correspondence: P. Grigg, Depart-
ment of Physiology S4-245, University of Massachusetts Medical School, 55
Lake Ave., Worcester, MA 01655 (E-mail: Peter.Grigg@umassmed.edu).
The costs of publication of this article were defrayed in part by the payment
of page charges. The article must therefore be hereby marked “advertisement”
in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
J Neurophysiol 92: 1236–1240, 2004.
First published March 17, 2004; 10.1152/jn.01033.2003.
1236 0022-3077/04 $5.00 Copyright © 2004 The American Physiological Societywww.jn.org
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RA mechanoreceptor afferents in mouse skin: RA cutaneous
mechanoreceptor afferents were strongly associated with the
rate of change of tensile stress, the rate of change of tensile
strain, and to tissue stress.
M E T H O D S
The preparation, apparatus, and experimental methods for record-
ing afferent neurons were, with a few exceptions, identical to those
described in the recent communication from this laboratory (Del Prete
et al. 2003).
Adult (Fbn1tsk), Pallid (PldnPa), and wild-type (C57BL/6) mice
were obtained from Jackson Laboratories (Bar Harbor, ME). Tsk mice
were the experimental group; Pallid mice are controls from the colony
in which the spontaneous Tsk mutation is maintained; and C57BL/6
mice are the background strain for Tsk.
Mice were anesthetized with IP Nembutal, 45 mg/kg, in a Univer-
sity of Massachusetts IACUC approved protocol. A specimen of skin
and the sensory nerve innervating it were removed from the ventral
surface of the hindlimb (Fig. 1A). The sample was fashioned as a “?,”
approximately 14 mm from end to end. A 5-mm-wide plastic tab was
glued to each edge of the sample while the skin was in situ, and the
specimen was then excised by cutting around its margins. The tabs
were subsequently used to couple the skin to the apparatus. The skin
was maintained in vitro, outside surface up, in a bath of HEPES-
buffered artificial interstitial fluid (Koltzenburg et al. 1997), at pH 7.4
and at room temperature (20°C), in the apparatus depicted in Fig. 1B.
Two tabs were coupled to the actuating arms of linear actuators
(Aurora Scientific 300B lever systems) by means of strings with
hooks on their ends engaged in holes in the tabs. The other 2 tabs were
coupled to the sides of the apparatus. The tabs served to distribute the
applied load over the entire width of the tab.
The nerve innervating the skin sample was pulled into a small
oil-filled chamber and dissected into small filaments for recording.
Individual filaments were placed on a platinum wire recording elec-
trode; the indifferent electrode was placed in the bath. Neuronal
activity was amplified and spike responses were discriminated using a
template-matching algorithm (SPS; Prospect, S. Australia). The cri-
teria for identifying single-neuron activity were the constant size and
shape of the action potential. Individual afferents were classified as
RA by their transient response (usually consisting of 1–2 action
potentials) to manual stretch or to stroking the skin surface with a
polished glass rod.
The skin was stretched following the procedure used by Grigg and
Robichaud (2004). One actuator was used to stretch the sample; it was
operated in force control mode with a pseudo Gaussian noise (PGN)
command signal. The orthogonal actuator was operated in position
control; loads were recorded along this direction but the length of the
sample was fixed. In separate tests, each sample was actuated uniax-
ially along the X- and the Y-axes, where X and Y directions refer to
along (X) and perpendicular to (Y) the long axis of the leg. Two
amplitudes of stress stimuli were used: they had mean values of either
17 or 35 kPa. The range of values in the sequence was approximately
twice the mean value. Stimulus bandwidth was 0–60 Hz, which
matched the mechanical bandwidth of the actuators.
Data collection runs were 30 s in duration. Loads were measured
along both directions, and displacements were measured along the
actuated direction. They were sampled at 500/s, and stored in data
files. Runs with fewer than 50 spikes were excluded from analysis.
Loads were converted to stresses (?) by normalizing to the cross-
sectional area of the sample, which was taken as the product of tab
width and the thickness. We measured thickness by fixing skin
samples in formalin while they were held at their in situ length, cutting
40-?m frozen sections normal to the skin surface, and measuring the
thickness of the dermal layer using polarizing microscopy. The width
of each specimen was measured from digital photographs of the
Strain could not be directly determined using actuator displace-
ments in this experiment. When a skin sample is actuated along some
direction, as depicted in Fig. 1B, local strain in the central region of
the skin is smaller than that in the tabs. Displacements were converted
to a pseudostrain variable (E) using the expression E ? ?L/L0, where
?L is the measured tab displacement and L0is the distance between
the tabs in the unloaded state. E is not a true strain because the
displacements are different along the length of the sample. Hence we
use the symbol E rather than ?, which would denote a true strain.
However, given that all our specimens had the same geometry, the
variable E allowed us to make comparisons between them.
The relationship between spike responses and mechanical variables
was determined using multiple logistic regression (MLR). MLR is a
multiple correlation method used in models with multiple predictor
variables and a binary outcome event (Hosmer and Lemeshow 1989).
In this application there were 10 predictors: measured values of stress
(?), pseudostrain (E), their rates of change (d?/dt and dE/dt), and the
6 first-order interactions between them. The interaction terms included
? ? E, which would be proportional to strain energy density, and ? ?
d?/dt and E ? dE/dt, which are proportional to the rate of change of
strain energy density. The use of MLR in this application is described
in detail in Del Prete et al. (2003). The outcome of MLR analysis is
an odds ratio, whose magnitude reflects the strength of the association
between the measured mechanical stimuli (predictors) and binary
spike events. The predictors of interest in MLR analyses were stress
and pseudostrain, their rates of change, and the first-order interactions
between them, along the direction the skin was actuated. Loads
measured along the orthogonal direction were ignored because of our
finding (Grigg and Robichaud 2004) that there was no significant
association between them and spike responses.
In RA cutaneous afferents, there are memory effects between
stimuli and responses. A stimulus applied at a particular time has an
effect that is observable later in time. Our prior report (Del Prete et al.
2003) shows in detail how memory effects can be quantified by “lag”
analysis, in which the apparent time of occurrence of spikes is
systematically shifted with respect to predictors, and the strength of
association between predictors and spikes is determined. Odds ratios
were calculated between spikes and all 10 predictors, for memory
times from 0 to 50 ms. This required 26 MLR analyses: one for each
2-ms memory interval from 0 to 50 ms (Fig. 3A).
To characterize skin viscoelasticity, we measured the complex
compliance of each skin sample. The complex compliance is a
property that is measured using sinusoidal inputs. It shows the
relationship between sinusoidal frequency and the storage compliance
(inversely proportional to stiffness), the loss compliance (energy loss
per cycle), and the phase angle between stress and strain. We deter-
mined the complex compliance indirectly, using a systems identifica-
tion approach, described in detail in Hoffman and Grigg (2002). Stress
and strain data collected in uniaxial data collection runs were used to
create a constitutive model of the material properties of the tissue
indicate the location on the leg from which the skin samples were taken. B:
apparatus for stretching the skin in 2 directions. S: skin sample, with plastic
tabs (T) glued to each margin. Plastic tabs are coupled to actuators (MX, MY)
that stretch the skin along the X and Y directions, respectively. Other tabs are
coupled to the apparatus.
Sketch of mouse preparation and testing apparatus. A: shaded areas
1237MOUSE CUTANEOUS RA AFFERENTS
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sample. An individual model took the form of a set of Wiener–
Volterra kernels (Marmarelis 1994, 1993; Marmarelis and Marmarelis
1978). The model for a particular tissue specimen was calculated from
PGN load–displacement data collected from that specimen, using
Lysis 7 software (Biomedical Simulations Resource, Univ. Southern
California). The Wiener–Volterra kernels, embodying the constitutive
relationship for that specimen, were used to predict the specimen’s
strain responses to a set of mathematically derived sinusoidal inputs
with frequencies ranging from 0.1 to 25 Hz. The result of this process
was an ideal (mathematically generated) sinusoidal stress input, and a
strain output predicted by the Wiener–Volterra model. These were
used to make a strain–stress Lissajous figure that was used, in turn, to
compute the complex compliance (storage and loss compliances and
the phase angle) at each frequency.
Differences in viscoelastic properties between the 3 mouse
phenotypes were analyzed using a repeated-measures ANOVA, in
which frequency was the repeated measure. Comparisons of odds
ratios between mouse phenotypes were done with a repeated-
measures ANOVA, in which loading treatments were the repeated
measures. Homogeneity of variance was tested using Levene’s test of
equality of error variances. In analyses where the data suffered from
inhomogeneity of variance, we performed a logarithmic transformation
on the data. All analyses were done using SPSS version 11.5.
R E S U L T S
Twenty neurons were recorded in 7 specimens taken from 6
Tsk mice, 18 neurons were recorded in 7 samples from 7
C57BL6 mice, and 25 neurons were recorded in 5 specimens
from 5 Pallid mice. Although all the animals were of approx-
imately the same age, they differed with respect to body mass.
At the time of use their approximate body masses were:
C57BL/6: 28 g; Tsk: 20 g; Pallid: 22 g.
Skin thickness was measured in several specimens for
each phenotype and was approximately 0.2 mm in each
Load and displacement data were used to determine the
complex compliance for both the X and the Y directions. The
skin was slightly orthotropic, being somewhat stiffer along the
Y than the X direction. LC and phase angles also differed
slightly between X and Y directions. Because none of these
differences was statistically significant, the complex compli-
ances measured along the X and Y directions were averaged
together (Fig. 2). The 3 skin phenotypes differed significantly
with relation to SC, LC, and phase. C57BL/6 samples had
significantly greater LCs and phase angles than Tsk and Pallid
samples at almost all frequencies. Phenotypic differences in
SC, although significant, were small and were observed only at
MLR analysis was used to determine the strength of asso-
ciation between spikes and all 10 predictors, for memory times
between 0 and 50 ms (Fig. 3A). These analyses revealed no
differences between the responses to loading along the X and
Y directions. Therefore as with the mechanical data, the results
from the tests in which the skin was stretched along the X and
Y directions were lumped together. Odds ratios for all the
neurons studied in each stimulus condition were averaged
together for each skin phenotype, yielding an aggregate, mean
odds ratio for each memory time for each loading paradigm for
each of the 3 mouse phenotypes.
There were similarities in the response of neurons in all
loading paradigms in all 3 phenotypes: there was a consistent,
strong association between spike responses and d?/dt, similar
to that shown in Fig. 3A. The association with d?/dt had a peak
at memory times ranging from 10 to 16 ms. In addition, there
was a single interaction term, ? ? d?/dt, whose odds ratios and
mice. Because strain measurements in these experiments are not true strain,
these values are for comparing phenotypes and are not true material properties.
A: storage compliance (reciprocal of stiffness). B: loss compliance. C: phase
Complex compliance of skin samples from C57, Pallid, and Tsk
1238P. GRIGG, D. R. ROBICHAUD, AND Z. DEL PRETE
J Neurophysiol • VOL 92 • AUGUST 2004 • www.jn.org
by guest on May 30, 2013
memory time were roughly equal in all groups. Associations with
dE/dt, however, appeared to differ between mouse phenotypes.
To compare odds ratios between uniaxial and biaxial stimuli,
and across mouse phenotypes, we normalized the magnitudes
of odds ratios to the peak odds ratio for d?/dt. We chose d?/dt
as the norm because it was the most consistent component of
response in all groups, and because the odds ratios and memory
times for this variable did not differ between skin phenotypes.
Figure 3, B–D shows the normalized odds ratios for mechan-
ical variables of interest, contrasted between mouse pheno-
types. Odds ratios for dE/dt differed between the 3 types of
mice: spikes were more strongly associated with dE/dt in
wild-type mice than in Tsk or Pallid (Fig. 3B). Odds ratios for
? and ? ? d?/dt (Fig. 3, D and E) did not differ significantly
between mouse phenotypes. No comparisons are reported for
d?/dt because those values were the norm and are therefore
equal in the graph of Fig. 3C.
Differences in odds ratios in the data of Fig. 3, B–E were
analyzed using analyses of variance. Levene’s test revealed
inhomogeneity of variance between the 3 mouse types in the
data for dE/dt and ? (Fig. 3, B and D). In both cases
performing a log transformation on the data made the
variances homogeneous, and repeated-measures ANOVAs
were run on the transformed data. Post hoc comparisons
revealed that odds ratios for dE/dt in Tsk neurons were
significantly smaller than in C57 neurons. Pallid neurons
had lower odds ratios for ?. The odds ratios for ? ? d?/dt
did not differ between phenotypes.
D I S C U S S I O N
The results support the hypothesis that the viscous component
of skin’s mechanical response contributes to the dynamic sensi-
tivity of mechanoreceptors. However, of the 3 predictors (d?/dt,
dE/dt, and ? ? d?/dt) that have dynamic components, and that
were significantly associated with spikes, only one (dE/dt) was
different between the 3 skin phenotypes. Thus although the data
do support the hypothesis, they do so only moderately.
data collection run in a single neuron, to illustrate the rela-
tionship of odds ratios for main factors (left panel) and
interactions (right panel). B–D: normalized odds ratios for
single factors, to illustrate the differences between mouse
phenotypes. Odds ratios in each experimental group were
normalized to the maximal value of odds for d?/dt in that
group. B: dE/dt; C: d?/dt; D: ?; E: ? ? d?/dt.
Odds ratios vs. memory time. A: data from a single
1239MOUSE CUTANEOUS RA AFFERENTS
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There were significant differences in the dynamic properties
of the 3 skin phenotypes. The greater loss compliance and
phase angle of C56BL/6 skin can be conceptualized as an
increase in the dashpot component in a spring–dashpot (i.e., a
Voigt) model of a soft tissue. A tissue with a greater dashpot
component will, when stretched, have a greater dynamic (i.e.,
viscous) component to its mechanical response. C57BL/6 skin
had a significantly greater dynamic response than did skin from
Tsk or Pallid mice. Nonetheless, the corresponding dynamic
components of neuronal response were mixed. The association
between spikes and d?/dt and d?/dt ? ? did not vary between
phenotypes, and only the association with dE/dt was enhanced
in C57 mice. Thus the results can be considered to be only
weakly supportive of the hypothesis.
When, as with RA afferents, there are multiple variables that
occur at different memory times, and that are positively asso-
ciated with spikes, there is a question as to how they individ-
ually relate to the process of spike initiation. Schafer et al.
(1999) deduced that spikes were initiated with zero delay with
respect to muscle displacement, which is equivalent to strain.
In the current experiments, the variable dE/dt was relatively
strongly associated with spikes at 0-ms memory time, similar
to the findings of Schafer et al. (1999). However, spike initi-
ation in cutaneous RAs is presumably caused by the summed
influences of all the variables that were positively associated
with spikes. Indeed Del Prete et al. (2003) found that a
prediction model that used the variables and the memory times
revealed by logistic regression was able to predict the occur-
rence of spikes with very high accuracy.
Del Prete et al. (2003) suggested that memory effects in RA
afferents might have a basis in the viscoelastic response of
skin. That now seems to be an unlikely explanation because the
times at which the effects of predictors were observed did not
vary between skin phenotypes.
The odds ratios in these experiments were much smaller than
those reported in Del Prete et al. (2003). This is likely attrib-
utable to the fact that we collected data in very short collection
runs with low stimulus levels. This was done because these
preparations tended to become poorly responsive with pro-
longed exposure to stretch stimuli. The precision with which
the logistic function is known determines the goodness of likeli-
hood estimation and therefore the magnitude of the odds ratios.
Tissue viscoelasticity might also influence neuron sensi-
tivity in ways other than those we describe: viscoelasticity
has been suggested to be a determinant of a slowly adapting
component of mechanoreceptor adaptation. After a step
change in displacement, both tissue stress and neural re-
sponse decay with a common time constant. This has been
observed in muscle spindles (Boyd et al. 1977; Hunt and
Wilkinson 1980), baroreceptors (Xavier-Neto et al. 1996),
invertebrate stretch receptors (Rydqvist et al. 1990), tendon
organs (Houk et al. 1981), and joint afferents (Grigg 1975;
Grigg and Greenspan 1977). Similarities of the time con-
stant for stress relaxation and neural adaptation suggest the
slowest component of adaptation is attributed to viscoelastic
relaxation of stress. In such analyses, however, it is neces-
sary that the response clearly be caused by the stimulus.
Among the mechanoreceptors mentioned earlier, a specific
role for tissue stress in driving a neuron has been shown
only for cat joint afferents (Fuller et al. 1991).
As in other experiments addressing the role of tissue vis-
coelasticity, one should note that this experiment does not
preclude the possibility that the relationship between tissue
response and neuronal response may not be a causative one;
neuronal dynamic responses and skin viscoelasticity may be
independent of each other and simply covary.
A C K N O W L E D G M E N T S
We thank S. Baker for advice with statistics.
G R A N T S
This work was supported by National Institute of Neurological Disorders
and Stroke Grant NS-10783.
R E F E R E N C E S
Bell J and Holmes M. Model of the dynamics of receptor potential in a
mechanoreceptor. Math Biosci 110: 139–174, 1992.
Boyd IA, Gladden MH, McWilliam PN, and Ward J. Control of dynamic
and static nuclear bag fibres and nuclear chain fibres by gamma and beta
axons in isolated cat muscle spindles. J Physiol 265: 133–162, 1977.
Damiano ER. A poroelastic continuum model of the cupula partition and the
response dynamics of the vestibular semicircular canal. J Biomech Eng 121:
Del Prete Z, Baker SP, and Grigg P. Stretch responses of cutaneous RA
afferent neurons in mouse hairy skin. J Neurophysiol 89: 1649–1659, 2003.
Fuller MS, Grigg P, and Hoffman AH. Response of joint capsule neurons to
axial stress and strain during dynamic loading in cat. J Neurophysiol 65:
Grigg P. Mechanical factors influencing response of joint afferent neurons
from cat knee. J Neurophysiol 38: 1473–1484, 1975.
Grigg P and Greenspan BJ. Response of primate joint afferent neurons to
mechanical stimulation of knee joint. J Neurophysiol 40: 1–8, 1977.
Grigg P and Robichaud DR. Rat cutaneous RA afferents activated by two
dimensional skin stretch. J Neurophysiol In press.
Hoffman AH and Grigg P. Using uniaxial pseudorandom stress stimuli to
develop soft tissue constitutive equations. Ann Biomed Eng 30: 44–53, 2002.
Hosmer DW and Lemeshow S. Applied Logistic Regression. New York:
Houk JC, Rymer WZ, and Crago PE. Dependence of dynamic response of
spindle receptors on muscle length and velocity. J Neurophysiol 46: 143–
Hunt CC and Wilkinson RS. An analysis of receptor potential and tension of
isolated cat muscle spindles in response to sinusoidal stretch. J Physiol 302:
Husmark I and Ottoson D. Is the adaptation of the muscle spindle of ionic
origin? Acta Physiol Scand 81: 138–140, 1971.
Koltzenburg M, Stucky CL, and Lewin GR. Receptive properties of mouse
sensory neurons innervating hairy skin. J Neurophysiol 78: 1841–1850, 1997.
Loewenstein WR and Skalak R. Mechanical transmission in a Pacinian
corpuscle. An analysis and a theory. J Physiol 182: 346–378, 1966.
Marmarelis PZ and Marmarelis VZ. Analysis of Physiological Systems.
New York: Plenum, 1978.
Marmarelis VZ. Identification of nonlinear biological systems using Laguerre
expansions of kernels. Ann Biomed Eng 21: 573–589, 1993.
Marmarelis VZ. Advanced Methods of Physiological System Modeling. New
York: Plenum, 1994.
Rydqvist B, Swerup C, and Lannergren J. Viscoelastic properties of the
slowly adapting stretch receptor muscle of the crayfish. Acta Physiol Scand
139: 519–527, 1990.
Schafer SS, Dadfar F, Hartel J, Haupts S, and Fischer M. The period of
latency before a muscle receptor generates an action potential as a response
to a muscle stretch. Brain Res 843: 36–47, 1999.
Swerup C and Rydqvist B. A mathematical model of the crustacean stretch
receptor neuron. Biomechanics of the receptor muscle, mechanosensitive
ion channels, and macrotransducer properties. J Neurophysiol 76: 2211–
Wilkinson RS and Fukami Y. Responses of isolated Golgi tendon organs of
cat to sinusoidal stretch. J Neurophysiol 49: 976–988, 1983.
Xavier-Neto J, Moreira ED, and Krieger EM. Viscoelastic mechanisms of
aortic baroreceptor resetting to hypotension and to hypertension. Am J
Physiol Heart Circ Physiol 271: H1407–H1415, 1996.
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