Consideration of mechanical filtering systemof the Meissner corpuscle
Shinobu Kuroki1 , Hiroyuki Kajimoto2, Takaaki Nara3 , Naoki Kawakami1 and Susumu Tachi1
1Graduate School of Information Science and Technology, The University of Tokyo, Tokyo, Japan(Tel : +81-3-5841-6917; E-mail: Shinobu Kuroki@ipc.i.u-tokyo.ac.jp, kawakami, tachi@star.t.u-tokyo.ac.jp )2
Department of Human Communication, The University of Electro-Communications, Tokyo, Japan(Tel : +81-42-443-5445; E-mail: kajimoto@hc.uec.ac.jp)
3
Department of Mechanical Engineering and Intelligent Systems, The University of Electro-Communications, Tokyo,
Japan(Tel : +81-42-484-3327; E-mail: nara@mce.uec.ac.jp)
Abstract: We are researching the natural timing of mechanoreceptor activity with the aim of developing improved
artificial tactile presentation systems. In order to develop strategies for manufacturing noninvasive devices, we focusedon peripheral level. We have presented a hypothesis on the energy conversion system of the Meissner corpuscle, a type of
mechanoreceptor. It was proposed that these corpuscles encode the normal strain, especially by detecting the horizontal
normal strain. We also observed an experimental evidence consistent with our hypothesis. In this study, we focusedon the virtual stiffness of the mechanoreceptors and developed a motion model to verify why the horizontal stretching
preferentially induces activity in the Meissner corpuscle.
Keywords: Mechanoreceptor, strain, nerve activity, human information processing

1. INTRODUCTION
To provide natural sensation by artificial means, manykinds of displays were developed to date. One of themost important point of the design of devices and signals is spatiotemporal densities. In tactile fields, this kindof problem is not quite as simple as those in other senses.
Here, all we know is two-point discrimination threshold.
The problem is that we don’t even know the requirementsof designing; the parameters of the major proportions oftactile informations cannot be determined yet. As a result, we were unable to demonstrate sensations clearly.
Consequently, ad hoc stimulations have been used for thetactile devices. To somehow break through this situation, we intend to figure out the human tactile perceptual
mechanisms partially.
To make noninvasive devices, we focused on peripheral level. When you touch an object with your finger,
the skin surface is deformed, the mechanoreceptor deformation is followed, and then nerve activities arise. By using a simulation of dynamics of elasticity, the predictionof elastic transfer property from skin to mechanoreceptor
already has a certain accuracy. The left-behind subject isthe relation between mechanoreceptor modification andnerve activity.
We have been proposing an explanation for the energy
conversion system of Meissner corpuscles which exist in
the superficial layer of the skin as shown in Fig. 1. The
response of this receptor is supposed to be important especially for active touch. Our proposed explanation was
experimentally-supported in our previous work. In thispaper, we tried to describe this explanation i.e. the relation between the skin modification and a nerve activity of
Meissner corpuscle by using a spring model. This discussion will help us determine an effective strategy for signal

limiting ridges

papillameissner
corpuscle

epidermis

merkel’s disk
ruffini ending

intermediate ridges dermis

pacinian corpuscle

subcutaneous
tissueFig. 1 pattern diagrams of the finger skin (reconstructedfrom [1])design of tactile displays.

2. RELATED RESEARCH
Tactile sensations are generated by mechanoreceptor
units. Mechanoreceptors are classified into four groups
based on their receptive fields and speeds of adaptation.
Meissner corpuscles are known to have small receptive
fields and to be rapidly adapting mechanoreceptors. It is
well known that they have a relatively low characteristic frequency of around 40 Hz, localized in the papillary
dermis with lengths of around 150 µm and diameters of
40-70 µm.
Many electrophysiological experiments involving theapplication of vibration to a fingertip have been conducted [2]. Fig.2 shows the RA nerve activity recordedin the arm on the application of a sinewave vibration to athe skin is pulled or shrunk (lower diagram), the collagen fibrils bend, and as a result, the deformation of theskin surface will not reach the Meissner corpuscles directly. Sripati et al. recorded nerve activity with 15 can-Fig. 2 Nerve activity of a single RA skin afferent fiber
to mechanical vibration (reconstructed from [2])fingertip. The nerve activity is synchronized with the mechanical vibration. It occurs in a specific phase with one
or two pulses per cycle of the applied vibration. Since
the interval of the nerve activity is sufficiently long, it
is considered that this synchronization is not caused by arefractory period. This receptor is offset-compensated receptor, so this finding suggests that Meissner corpuscles
must have some mechanical filtering system. This suggestion is a good basis for analyzing the nerve activation
timing of Meissner corpuscles.

3. HYPOTHESISWe reviewed the structure of the Meissner corpuscle
and presented a hypothesis on the strength of two structural reasons [3].
3.1 Axonal structure
Generally, when using the finite element method,mechanoreceptors are approximated to encode the strainenergy density of the skin. This approximation is reasonable if the receptor is an ideal elastic body with axons thatspread omnidirectionally such that they become equallysensitive in all directions. However, observations haverevealed that some part of an axon runs tangential to theskin surface, most of it is regarded to run parallel to theskin surface. We consider that if nerves encode the line
integral of the strain, horizontal stretching should preferentially generate nerve activity.
3.2 Periaxonal structure
Iwanaga et al. reported that each corpuscle is linked
with the basal aspect of the epidermis by dermal collagen fibers[4]. Their findings indicated a deformationin the epidermis is followed by a distortion of the dermal collagen fibers, which continue into the corpuscles.
With existence of these fibers, skin can expand and contact nonlinearly. Motivated by Iwanaga’s findings and her
hypothesis of Meissner corpuscles, we proposed a detection mechanism, which is illustrated in Fig. 3. (The top
and middle diagrams are based on Iwanaga’s hypothesis.)If the skin surface is pushed in or if it is stretched fromits basal phase (middle diagram), the epidermal basement membrane under the stimulated point will open and
the Meissner corpuscles will be extended along their minor axes. As a result, nerve axons are stretched, whichleads to nerve activity. In contrast, when some part of

Fig. 3 Proposed nerve activity mechanism of the Meissner corpuscle
didate variables for the relevant receptor deformation [5].
They concluded that maximum tensile strain likely drives
SAI mechanotransduction, whereas changes in receptor
surface area drive RA transduction. However, we propose that Meissner corpuscles encode the normal strain;that is, tensile strain likely drives RA transconduction.
Still, their finding that the physical quantities closely related to local membrane stretching were most predictiveof the observed afferent responses is consistent with ours.
According to this hypothesis, nerve activity does not occur when the skin surface is shrunk, but when the skin is
stretched. Thus, it is possible to realize nerve activation
in a specific phase that is synchronized with mechanicalvibration.
With these two reasons, we proposed the following hypothesis: Meissner corpuscles encode the normal strain, particularly detecting the horizontal normal
strain. To verify the proposed detection mechanism for
the Meissner corpuscle, we took experimental approachand reached a positive conclusion. In next section we developed a motion model to verify why horizontal stretching preferentially induces activity in the Meissner corpuscle.

4. MODEL
Here, we use a spring model to describe the stretching mechanism of an axon. In order to discuss the significance of collagen fibrils in this mechanism, we describe the relation between the deformation of the finger skin and the stretching of an axon. We attempt tomodel the nonlinearity between the direction of the ex-ternal force and the structural stiffness of an elastic body.
Consider how a small volume under only a vibrator deforms when perpendicular vibrations are introduced in anelastic body. For the sake of simplicity, we consider anelastic truss in two-dimensional space. Small rotations
and small strains are assumed.
The Meissner corpuscle, dermal layer, epidermal layer
as a bridge girder, and collagen fibril are partially modeled. Consider the cell as an existence region of the
Meissner corpuscle. In a cell that is surrounded by the
epidermal layer as a bridge girder, the collagen fibrils link
the corpuscle and epidermis, as shown in Fig. 4. This cell

placed along the X-axis only.
(u1 , v1 ) = (0, 0)(u3 , v3 ) = (U + δU, 0)(u4 , v4 ) = (U, 0)

Here, u and v represent the displacement of each node
along the X- and Y- axes, respectively. We set different
displacements for nodes 3 and 4. This displacement describes the elastic body depth difference between these
two nodes. Node 3 is shallower than node 4; therefore,
it will be stretched horizontally to a greater extent by avertical force.
In this model, node 2 is not externally forced.
(p2 , q2 ) = (0, 0)

Fig. 4 Modeled cell region (surrounded by red box)
elongates and contracts with the deformation of the skinsurface. In this section, the changing of the virtual stiffness of this cell is predicted. There are three components
in the cell,-the Meissner corpuscle and dermal layer havea relatively soft stiffness;, while the collagen fibril has
a hard stiffness. Naturally, these materials stiffnesses do
not change; however, the virtual stiffness of the entire cellstructure can change. We predict that the collagen fibril
has two modes, namely, rotation and translation, and thatthe virtual stiffness changes due to the switching between
these modes.
4.1 Three-element model
Consider a plane three-bar truss with the geometry
shown in Fig. 5. This model comprises three elements infour nodes. Elements A, B, and C are springs represent-

(1)
(2)
(3)

(4)

Assume U > 0, considering a horizontally stretched dermal papilla. Set the default positions of elements A and C
to the horizontal, with element B angled at θb . Applying
Eqs. (1),(2),(3), and (4) to the equilibrium equations ofnode 2, the displacement of node 2 (u2 , v2 ) is given by
1
U
2(U + 2δU ) cos θbv2 =2 sin θb

u2 =

(5)
(6)

When nodes 3 and 4 are moved in the positive direction,
node 2 exhibits a positive displacement along both axes.
Note that u2 < U . This shows that both elements A
and B rotate so that θa asymptotically approaches θb . As
a result, the corpuscle (element A) runs parallel to thecollagen (element B). Conversely, when adding(u3 , v3 ) = (−U − δU, 0)(u4 , v4 ) = (−U, 0)

(7)
(8)

we anticipate symmetrical results.
1
u2 = − U
2(−U − 2δU ) cos θbv2 =2 sin θb
Fig. 5 Three-element modeling the axon terminus, collagen fibril, and dermal layer,
respectively. The X-and Y-axes are considered to be parallel and perpendicular to the skin surface, respectively.
We extend this model by U along the X-axis and calculate the stretching of element A. In other words, node 1 as
the center of the Meissner corpuscle is a fixed end while
nodes 3 and 4 as the epidermal basement membrane (i.e.,at the boundary of the dermis and the epidermis) are dis-

(9)
(10)

It shows that both elements A and B rotate such that they
are orthogonal to each other. As a result, the corpuscle(element A) is at right angles to the collagen (element B).
In the following truss analysis, only small rotations
and small strains are assumed. The next step is to consider element A as an angled bar. We vary the angle andcheck the resulting effect. Here, we set the default position of element C to the horizontal, and elements A and
B are angled at θa and θb to the horizontal. The displacement of node 2 (u2 , v2 ) is given by the equilibrium equa-tion.


K s2b + s2a + s2b−a + 2ks2a


U
u2 =
2K s2b + s2b−a + 2ks2a
K −s2b + s2a + s2b−a

 2
+
δU
2K sb + s2b−a + 2ks2a
v2 =

(11)

K (sb cb − sa ca + sb−a cb−a ) − 2ksa caU
2K s2b + s2b−a + 2ks2a+

K (3sb cb − sa ca + sb−a cb−a )δU2K s2b + s2b−a + 2ks2a(12)where ca and sa represent cos a and sin a, (ka , kb , kc ) =(k, K, k), and k < K. Here, elements A and C have thesame spring constant and the fibril has sufficient stiffness.
First, we assume that θa is small. We set the approximate values of cos a · sin a = 1 and sin2 a = 0 in theequilibrium equation.
1
u2 = U2−s2 − s2
 δU
 b2 b−a
2 sb + s2b−a
K s2b − sa + s2(b−a) − 2ksa


v2 =
U
2K s2b + s2b−a3s2b − sa + s2(b−a)
 δU+2 s2b + s2b−a

(13)

(14)

K (3s2b − s2a + sb−a )δU
2Ks2b + 2ks2as2 − s2 − s2
 2a 2b  b−a}U + αδU
2
2 sb + sb−a + 2k
K sa

u2 =
(16)

In this equation, v2 becomes negative when θa becomeslarger than θb . As a result, θa becomes smaller and approaches θb again.
These equations indicate that when U > 0 is added tothis cell, θa approximates θb and the mode of the collagen fibril switches from rotation to translation. Next, we
attempt to describe an axon elongation with this model(18)

When adding U > 0, θa asymptotically approaches
θb so that sa increase while sb and sb−a decrease. Assume that K is sufficiently larger than k, then the denominator of the first term in Eq.(18) decreases. On theother hand, considering the numerator of the first term inEq.(18), s2a − s2b − s2b−a increases. Note that θb must be
smaller than π2 and it must decrease, while θa increases
from zero. Because the rate of increase of s2a is larger
than that of −s2b−a , s2a − s2b + s2b−a increases on the addition of U > 0. Therefore, the coefficient value of u2
now increases monotonically when adding U > 0, andθa asymptotically approaches θb . With this tendency, thehorizontal displacement U is converted to u2 efficiently
on the addition of U > 0 as opposed to the addition of
U < 0.
If there is no fibril in the skin-mechanoreceptor system, node 2 would not be displaced along the Y-axis.
With input (u4 , v4 ) = (U, 0),U2v2 = 0K (s2b − s2a + sb−a ) − 2ks2a
U
2K s2b + s2b−a + 2ks2a+

Among the axon elongation characteristics that one may
consider, a controversial characteristic is the coefficientvalue of u2 . Therefore, we restrict the argument to thecoefficient value of u2 . Here, we focused on the major
displacement U ’s coefficient value. From Eq.(11), it canbe written as
K s2b + s2a + s2b−a + 2ks2a
U + αδUu2 =2K s2b + s2b−a + 2ks2a={1 +Here, v2 > 0 because K  k, and u2 < U so that
θa approaches θb . At the default position, the corpuscle(element A) is parallel to the collagen (element B). By
inputting −U to this expression, symmetrical results canbe calculated.
Second, consider the situation where θa is nearly equalto θb . We set the approximate values of cos(b − a) = 1
and sin2 (b − a) = 0 in the equilibrium equation.

K s2b + s2a + 2ks2a
U
u2 =2Ks2b + 2ks2a 2
K sb − s2a
δU
(15)
−
2Ks2b + 2ks2av2 =and verify the effectiveness of these mode conversions.
If an axon elongation δL is much smaller than the naturallength of an axon (i.e.; element A) L, it can be describedas such2
δL = (L + u2 ) + v22 − Lu2 2  v2 2
1+
+
−1
=L
L
L


2u2
.
−1
=L
1+
L
u2
.
−1
=L 1 +
L
(17)
=u2

(19)
(20)

This u2 without collagen is smaller than u2 with collagen.

5. DISCUSSION
After the skin surface has been pushed, the axon endings, which were horizontal by default, run parallel to theangled collagen fibril. It was shown that this tendency is
not disrupted by an additional displacement. Conversely,
after the skin surface has been pulled, the axon endings

run at right angles to the collagen fibril. It was shown thatthe coefficient value of axon elongation monotonicallyincreases on the addition of a horizontal stretch deformation. Since the collagen fibril has two modes, namely,
rotation and translation, the virtual stiffness changes dueto the switching between these modes. The elongation
increases on stretching and decreases on shrinking. Pushing deformation results in direct stretching from the epidermis to the mechanoreceptor. With this tendency, anaxon that is sufficiently softer than the collagen fibrils
will distend suitably when stretched horizontally. As aresult, an external force is converted to axon elongation
efficiently on pushing as opposed to pulling. This effectleads to a nonlinearity in the displacement magnitude andhorizontal elasticity of the mechanoreceptor.
The axon endings are folded along the minor axis.
This changing of the virtual stiffness corresponds to alengthening of the minor axis of the mechanoreceptor,
i.e., when calculating the strain of the axon not relative tothe length of the mechanoreceptor minor axis but relative
to the size of the dermal papilla on stretching. In otherwords, the integral strain along the width of the axon increases when it is stretched horizontally.

6. CONCLUSION
The objective of this study was to determine the mechanisms behind human tactile perception. We focused on
the transitive problem and attempted to describe the timing of nerve activity. In this study, we verified a mechanical filtering system for Meissner corpuscles by using a
structural model.
Based on a previous research, we considered that the
Meissner corpuscles tend to stretch in the horizontal direction, and proposed the following hypothesis: Meissnercorpuscles encode the normal strain, especially by detecting the horizontal normal strain.
To explain our hypothesis, we predict the changing of
the virtual stiffness of a cell, which is existence regionof the Meissner corpuscle. In order to describe the relation between the deformation of the finger skin and thestretching of an axon, we created a spring model. Although the materials stiffnesses do not change, the virtual stiffness of the entire cell structure can be changed.
This changing may be due to the switching of the twomodes of the collagen fibril, namely, rotation and translation. The virtual stiffness of the dermis increases anddecreases on stretching and shrinking, respectively. An
external force is converted to axon elongation efficiently
on pushing as opposed to pulling. This effect leads toa nonlinearity in the nerve activity-, as explained by ournormal strain hypothesis. A design is required to verify
this model. Once the physical quantity that is encodedby the mechanoreceptors has been clarified, we can easily calculate that quantity either by a theoretical formulaor by means of simulation. If it becomes possible to describe the spatiotemporal distribution of the activity oftactile receptors, it will be possible to obtain a signal design that exhibits a natural tactile sense. This will lead tothe development of better tactile displays.

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