# Information processing via human soft tissue

Yo Kobayashi<EMAIL_ADDRESS>Graduate School of Engineering
Science, Osaka University, Osaka, Japan

###### Abstract

This study demonstrates that the soft biological tissues of humans can be used
as a type of soft body in physical reservoir computing. Soft biological
tissues possess characteristics such as stress-strain nonlinearity and
viscoelasticity that satisfy the requirements for physical reservoir
computing, including nonlinearity and memory. The aim of this study was to
utilize the dynamics of human soft tissues as a physical reservoir for the
emulation of nonlinear dynamical systems. To demonstrate this concept, joint
angle data during motion in the flexion-extension direction of the wrist
joint, and ultrasound images of the muscles associated with that motion, were
acquired from human participants. The input to the system was the angle of the
wrist joint, while the deformation field within the muscle (obtained from
ultrasound images) represented the state of the reservoir. The results
indicate that the dynamics of soft tissue have a positive impact on the
computational task of emulating nonlinear dynamical systems. This research
suggests that the soft tissue of humans can be used as a potential
computational resource.

##  I Introduction

Reservoir computing is an information processing technique that exploits the
input-driven transient behavior of a high-dimensional system known as a
reservoir, and serves as a framework for recurrent neural network learning
jaeger2002tutorial ; maass2002real ; goto2021twin . Reservoir computing is
particularly well-suited for real-time computing with time-varying inputs, and
is therefore highly effective for emulating complex temporal computations
maass2002real ; jaeger2002tutorial ; jaeger2004harnessing ; buonomano2009state
; verstraeten2007experimental ; nakajima2015information . A reservoir
computing approach has been proposed to overcome the limitations of
conventional neural networks, which take a considerable amount of time to
converge to an attractor state and are not ideal for real-time computation
nakajima2015information . Complex nonlinear dynamical systems can be
effectively emulated by incorporating linear and static readouts from the
reservoir’s high-dimensional state space, provided that the reservoir dynamics
exhibit sufficient nonlinearity and memory. This technique offers the
advantage of maintaining low computational costs for both learning and
computation, which is achieved by adjusting the linear and static readout
weights from the reservoir. Various abstract dynamical systems have been
proposed for reservoir applications, including neural models for echo state
networks jaeger2002tutorial ; jaeger2004harnessing  and liquid state machines
maass2002real , water flow states fernando2003pattern ; goto2021twin , and
nonlinear mass spring systems hauser2011towards ; hauser2012role .

A recent development in reservoir computing is the use of physical system
dynamics as a reservoir, a technique referred to as physical reservoir
computing tanaka2019recent ; nakajima2020physical . It has been suggested that
a physical system with nonlinearity and memory could serve as an alternative
to traditional computational frameworks like the Turing machine
nakajima2014exploiting . Examples of implementation have been reported in a
variety of physics fields, including photonics vandoorne2008toward ;
larger2012photonic ; brunner2013parallel , spin torrejon2017neuromorphic ;
tsunegi2019physical , and quantum fujii2017harnessing ; nakajima2019boosting ,
with each platform demonstrating particular computational properties intrinsic
to its respective spatio-temporal scale goto2021twin . These examples
demonstrate that the suitability of a system for use as a reservoir is not
contingent upon its specific implementation, but rather relies on system
properties such as input separability and fading memory
nakajima2015information .

Several studies have demonstrated that soft body dynamics can be used as a
physical reservoir nakajima2015information ; nakajima2014exploiting ;
nakajima2018exploiting . In these studies, the mechanical system of a soft
body composed of a rubber material, designed to mimic the legs of an octopus
operating underwater, functions as a reservoir. The dynamics resulting from
the interaction between the soft body and the water acted as a reservoir,
confirming that the viscous damping caused by the water was necessary to
preserve the memory for the calculations kagaya2022echo . The kinematics and
material nonlinearity of the soft body were also utilized to act as a
reservoir nakajima2013soft .

This study demonstrates that the soft biological tissue of humans can be
utilized as a physical reservoir for information processing. Soft biological
tissues exhibit stress-strain nonlinearity and possess viscoelastic properties
fung2013biomechanics ; kobayashi2017simple ; kobayashi2020non . Therefore, the
dynamics of soft tissue satisfy the system requisites, including nonlinearity
and memory, necessary for physical reservoir computing. The specific objective
of this study is to utilize the dynamics of soft human tissues as a physical
reservoir to emulate nonlinear dynamical systems. Soft tissues are found
throughout the human body; therefore, if computational processing can be
delegated to biological tissues, it could lead to a distributed computation
system for human-assisted devices. To the best of our knowledge, this is the
first study to discuss the capability of in vivo human tissue to act as a
physical reservoir.

Figure 1:  Experimental setup and information processing scheme using human
soft tissue. (a) Photograph illustrating the experimental setup employed in
this study. The wrist joint angle (a-2) and ultrasound images (a-3) of the
muscles associated with the movement in the flexion-extension direction of the
wrist joint were acquired from human participants (a-1). The objective of this
experiment was to generate muscle deformation dynamics though wrist joint
movement and to use the deformation as a physical reservoir for information
processing. (b) Schematic representation of an analogy between a conventional
reservoir computing system (b-1) and our system (b-2) used in this study. In
conventional reservoir systems, randomly coupled abstract computational units
are used as reservoirs (b-1). In our system, the deformation fields (positions
of feature points) inside the muscle, obtained from image processing of
ultrasound images, are used as computational units (b-2). The focus of this
study is to investigate if this physical reservoir can effectively emulate
nonlinear dynamical systems often targeted by conventional reservoir computing
systems.

##  II  Methods

The experimental concept for this study is illustrated in Fig. 1. The joint
angle during motion in the flexion-extension direction of the wrist joint and
ultrasound images (echo movies) of the muscles associated with that motion
were acquired from human participants. This experiment aims to generate muscle
deformation dynamics by varying the wrist joint angle and utilize the
resulting deformation field as a physical reservoir for information
processing. The input to the system is the wrist joint angle, and the state
variable of the reservoir is the deformation field within the muscle. To
successfully emulate nonlinear dynamical systems within this setup, the
dynamics of the soft tissue must provide the necessary nonlinearity and
memory, because reservoir computing relies solely on static and linear
readouts during the learning process.

Data were collected from 10 young, healthy participants aged 20 years or
older, who had completed their growth spurts. This research was approved by
the ethical committee for human studies at the Graduate School of Engineering
Science, Osaka University. The experimental procedure was identical for all
participants. The experimental setup is shown in Fig. 1 (a). A goniometer
(SG110/A, Biometrics Ltd) was attached to the wrist joint. The probe
(LF11-5H60-A3, Telemed Medical Systems) of the ultrasound imaging device
(ArtUS EXT-1H, Telemed Medical Systems) was attached to the position where a
large muscle deformation was observed near the elbow joint during flexion and
extension of the wrist joint, and was secured in place with a band (ProbeFix
Dynamic T, Telemed Medical Systems). The ultrasound probe was positioned to
extensor carpi radialis brevis muscle and its surrounding muscles
(approximately 5[cm] from the elbow joint toward the wrist joint). The
extensor carpi radialis brevis muscle is a muscle that contributes to flexion
and extension of the wrist joint.

Participants performed wrist joint extension motion along the target line,
displayed on screen as the target joint angle. A sinusoidal curve was selected
to specify the target joint angle (ref: Fig. 2(a)), with 0 [deg] used as a
reference position, and either 20[deg], 40[deg], or 60[deg] randomly selected
as the amplitude of the sinusoidal curve. The period of the target joint angle
was 4 seconds. During each experiment, 18 cycles of the specified motion was
measured. Taking into account that noise was likely to occur at the beginning
and end of each experiment, the data from 15 cycles were used for analysis
(the initial two cycles and final cycle of each data set was removed). The
data used in the evaluation phase described below included joint angles of all
amplitudes (20[°], 40[°], and 60[°]) (ref: Fig. 2(a)). Five sets of
experiments were performed per participant, resulting in a total of 50
experiments from the 10 participants.

Time series data of the wrist joint angles acquired during the experiment were
used to calculate the input joint angle vector
$\bm{\theta}=\left(\theta_{1},\theta_{2},\cdots\right)$ where $\theta_{k}$ is
the joint angle at the k-th time data point. Ultrasound images of the muscle
were acquired and feature points were extracted by image processing at each
time point. To determine the initial positions of the feature points, Shi-
Tomasi corner detection shi1994good  was used for the first frame of the
ultrasound image. The coordinates of each feature point extracted by corner
detection were tracked using optical flow lucas1981iterative  to obtain their
x, y coordinate data
$\mathbf{\bar{s}}=\left(\bar{x}^{1},\bar{y}^{1},\bar{x}^{2},\bar{y}^{2},\cdots\right)^{T}$,
where ($\bar{x}^{i}$, $\bar{y}^{i}$ ) is the coordinate of the i-th feature
point. These data were used to calculate the reservoir state vector
$\mathbf{s_{k}}=\left(s^{1}_{k},s^{2}_{k},s^{3}_{k},s^{4}_{k},\cdots\right)^{T}$
at each time point k. See Appendix A for details of this data preprocessing.

To evaluate the computational capability of our system, we used a nonlinear
autoregressive moving average (NARMA) model as an emulation task for nonlinear
dynamical systems, which are the standard benchmark tasks in the field of
machine learning, in particular for recurrent neural network learning. This
task presents a challenging problem for any computational system due to its
dependence on nonlinearity and long time lags hochreiter1997long . The first
NARMA system is the following second-order nonlinear dynamical system. This
system was introduced in atiya2000new  and was used as an example in
hauser2011towards ; nakajima2013soft ; nakajima2015information ; goto2021twin
. Hereafter we refer to this system as NARMA2.

$\displaystyle o_{k+1}=0.4o_{k}+0.4o_{k}o_{k-1}+0.6(r_{k})^{3}+0.1$ (1)

where $r_{k}$ and $o_{k}$ are input and system output at k-th time point. The
next NARMA system is a nonlinear dynamical system of order N, represented as
follows:

$\displaystyle
o_{k+1}=0.3o_{k}+0.05o_{k}\left(\sum_{j=1}^{N-1}o_{k-j}\right)+1.5r_{k-N+1}r_{k}+0.1$
(2)

The value of N ranges from 3 to 15, and each corresponding system is denoted
as NARMA N (e.g., when N = 10, it is referred to as NARMA10). Notably, NARMA10
with this particular parameter setting was first introduced in atiya2000new
and has been widely used in various studies, such as
verstraeten2007experimental ; hauser2011towards ; nakajima2013soft ;
nakajima2015information ; goto2021twin . The aim of these emulation tasks is
to test the system’s ability to process input histories with nonlinearity. A
key aspect of the NARMA model is to include the long-term dependence of the
system with an N-th time lag, which requires that the learning system have
some degree of nonlinearity and memory to emulate it goto2021twin . The input
vector $\mathbf{r}=(r_{1},r_{2},\cdots)$ was calculated from the input joint
angle vector $\bm{\theta}$ using the equation $r_{k}=0.2\times\theta_{k}/60$
to scale linearly to the approximate range [0, 0.2], based on previous studies
goto2021twin .

Thus, we applied this input $r_{k}$ to NARMA2 through NARAMA15 models and
obtained the target output $o_{k}$. The readout was implemented using a linear
model commonly used in reservoir computing. The system output
$\mathbf{\hat{o}}=(\hat{o}_{1},\hat{o}_{2},\cdots)$ is then defined as
follows:

$\displaystyle\hat{o}_{k}=\sum_{i}w^{i}s^{i}_{k}$ (3)

To emulate the desired nonlinear dynamical system in this framework, we adjust
only the linear readout weights $\mathbf{w}=(w^{1},w^{2},\cdots)$, which are
fixed after learning. Ridge regression hastie2009elements  was used to learn
these weights $\mathbf{w}$. See Appendix B for details on the learning process
using ridge regression.

A total of 15 cycles (60 seconds) of data were used for the analysis, which
was divided into a training phase and an evaluation phase. The training phase
consisted of the first 12 cycles (48 seconds) and the evaluation phase
encompassed the remaining 3 cycles (12 seconds). The first 1.5 seconds of the
training data was omitted from the training dataset because it contained the
initial transient response of the nonlinear equations. During the training
phase, linear readouts were trained for each task using the aforementioned
ridge regression procedure. In the evaluation phase, trained linear readouts
were used to generate system outputs $\mathbf{\hat{o}}$.

During the evaluation phase of this study, the normalized mean square error
(NMSE
$=\sum_{k}\left(o_{k}-\hat{o}_{k}\right)^{2}/\sum_{k}\left(o_{k}\right)^{2}$ )
was calculated for the target and system outputs to assess the performance of
the system output. For each of the 50 experimental data runs, the NMSE was
calculated for each of the NARMA2 to NARMA15 emulation tasks. From these
results, we calculated the means and variances of the NMSE.

To characterize biological soft tissue as a physical reservoir, we also
computed task performance using a simple linear regression (LR) model
nakajima2015information ; goto2021twin . A simple LR model is represented by
the equation $\hat{o}^{LR}_{k}=w^{\prime\prime}\times r_{k}+w^{\prime}$. It is
important to note that this model assumes the absence of soft tissue dynamics
and only considers the raw inputs for information processing; therefore, we
can conclude that soft tissue contributes to the emulation task of the
nonlinear equation if our system demonstrates superior computational
performance when compared with the simple LR model. In the accuracy validation
of these simple LR models , the training data, training method, and training
procedure were the same for those used in our system, to ensure fair
comparison.

##  III  Result

Representative examples of the performance of the inputs and the NARMA2, 3, 5,
10, and 15 tasks during the evaluation phase are presented in Fig. 2, along
with the performance of the simple LR model for comparison purposes. It is
evident that our system outperforms the simple LR model in all NARMA tasks.
The emulation results using our system closely approximate the target
dynamics. In contrast, the simple LR models based on raw inputs, which do not
account for the dynamics of soft tissue, fail to emulate the target dynamical
system. These results suggest that the dynamics of soft tissue contribute to
the successful emulation of the nonlinear equation.

The mean and variance of the NMSE for the NARMA tasks at each N are presented
in Figure 3. Figure 3 (a) presents the results of our system incorporating the
dynamics of soft tissues, while Fig. 3 (b) presents the results of the simple
LR model. In all NARMA tasks, the NMSE values achieved by our system were
consistently lower than those of the simple LR model. A statistical comparison
using the paired t-test between our system and the simple LR model reveals
significant differences ($p<0.01$) for all NARMA tests. The performance of our
system gradually decreases as N increases (Fig. 3(a)), indicating a limitation
in the memory capacity of the soft tissue dynamics.

These results demonstrate that our system successfully performs its task by
exploiting the nonlinearity and memory derived from the dynamics of soft
tissues.

Figure 2:  Representative examples of time series data of the input and
outputs from the evaluation phase. Time series data are presented for (a) the
input (and joint angle) and the outputs for (b) NARMA2, (c) NARMA3, (d)
NARMA5, (e) NARMA10, and (f) NARMA15. The plots for each output (b)-(f) are
overlaid with the time series of the target output $\mathbf{o}$ (dashed red
line), the system output $\mathbf{\hat{o}}$ (blue line), and the output of the
simple LR model $\hat{o}^{LR}$ (doted green line) for comparison. The system
outputs demonstrate superior performance compared with the simple LR model
across all NARMA tasks. These results indicate that the dynamics of human soft
tissue play a significant role in emulating the nonlinear equations.  Figure
3:  Comparison of the mean error and mean variation of the NMSE for each NARMA
task. (a) The NMSE of the system output $\mathbf{\hat{o}}$ using the dynamics
of human soft tissue. (b) The NMSE of the simple linear regression model of
the input $\hat{o}^{LR}$. The horizontal axis represents the order N of the
NARMA model. Note that the vertical axes of (a) and (b) have different scales.
For all the NARMA tasks, the NMSE of our system is lower than that of the
simple LR model. These results demonstrate the potential for using human soft
tissue as a computational resource.

##  IV  Discussion

In this study, we demonstrated that the dynamics of soft biological tissue can
be exploited to emulate nonlinear dynamical systems. A comparative analysis of
task performance with the simple LR model established the superior performance
of our system across all tasks. These results demonstrate the positive impact
of soft tissue dynamics on the computational task. Moreover, these results
suggest that human soft tissue can potentially be used as a computational
resource. In other words, with appropriate input sets and computational tasks
defined, soft biological tissue can be utilized as part of a computational
device. Unlike other conventional computers based on the Turing machine, our
system does not require an explicit storage device and assumes that memory is
implicit in the transient dynamics of soft tissues. By assigning tasks to the
system that require memory (NARMA tasks) and evaluating its performance, we
could confirm the memory capacity of our system. In this study, joint motion
was used as the method to induce muscle deformation, but external actuator
devices could also be used in such applications. Since biological soft tissue
is present throughout the human body, this system has the potential to
eliminate or reduce the computational requirements for devices in close
proximity to humans by delegating the computational load to human soft tissue.

Our approach is capable of simultaneously emulating multiple nonlinear
dynamical systems (NARMA2 to NARMA15) using the dynamics of the same soft
tissue by adjusting the weight of the read out. This means that the physical
reservoir of soft tissues (the single data series of the deformation field
$\mathbf{S}$) can compute multiple tasks simultaneously, a concept known as
multitasking hauser2011towards ; nakajima2014exploiting . This suggests that
when soft tissue is used as a physical reservoir, it is not necessary to have
a different physical system for each computational task; instead, a single
physical system can perform multiple computational tasks.

In reservoir computing research, it has been established that for a reservoir
to have strong computational power, it needs to possess input separability and
fading memory maass2002real ; nakajima2014exploiting . In the case of a soft
tissue physical reservoir, it is believed that these properties are inherent
in its dynamics because of the viscoelasticity and nonlinear stress-strain
properties of soft biological tissue. Input separability is usually
accomplished by nonlinear mapping from low-dimensional inputs to higher
dimensional state spaces. The body dynamics of soft materials tend to be
underactuated systems tedrake2009underactuated , which would allow input
signals to naturally map to higher dimensions of the soft body, thus achieving
input separability nakajima2014exploiting . The non-uniformity and diverse
mechanical properties of soft biological tissues potentially facilitate input
separability. Fading memory is a property that preserves the effects of recent
input sequences in the system, allowing the integration of input information
over time. This ensures a reproducible computation, where the recent history
of the input signal is important. In our system, the slow relaxation of the
dynamics to the input signal, due to the damping effect caused by the
viscoelastic properties of soft tissue, is believed to help achieve fading
memory. Previous studies on physical reservoirs using rubber materials for
soft bodies operating in water nakajima2015information ;
nakajima2014exploiting , have indicated that the interaction between the soft
body and water is essential for computational tasks kagaya2022echo . However,
in our study, physical reservoir computing with soft tissue successfully
performed computational tasks without an underwater environment. This could be
attributed to the unique viscoelastic properties of soft tissues, which
exhibit a power law dependence on time and frequency kobayashi2017simple ;
kobayashi2020non ; bonfanti2020fractional , leading to long term damping
effects.

These findings pave the way to successfully exploit the dynamics of human
tissue for a wide range of computational tasks and applications. The
miniaturization and flexibility of the sensors used in our method (for
example, wang2022bioadhesive ), coupled with novel technology to implement
linear readouts as devices, enables information processing using human tissue,
eliminating the need for other computers based on the Turing machine. Thus,
this technology holds potential for a diverse range of applications such as
human-machine interaction technology, medical devices, life support devices,
and wearable devices. Utilizing human tissue as a computational resource
enables control and information processing to be implemented in targeted areas
of the body, which could lead to the distribution of computational devices. It
could also be applied to small-scale devices that perform information
processing internally or in close proximity to the body, at the edge and
locally. In addition, we expect our approach to inspire further research in
novel concepts for computing across a wide range of fields.

The framework presented in this study may also help shed light on the role of
the human body and other living organisms. Physical reservoir computing can be
regarded as an attempt to harness the inherent computational capability of
living organisms. Exploring what kind of computational tasks can be performed
using living bodies could provide a new perspective on understanding questions
such as why living organisms possess their particular morphologies. There have
been discussions concerning whether the body of a living organism could serve
as a physical reservoir and function as a computational resource for
perception and motor control of the organism nonaka2020locating . The delay
observed in the NARMA3 task, approximately 50 [ms], is comparable to the time
required for reflection. Similarly, the delay of the NARMA10 system is
approximately 150 [ms], which is comparable to the time taken for voluntary
motor responses. These findings indicate that it is possible, from a timescale
perspective, for soft tissue in living organisms to act as a physical
reservoir and computational resource for perception and motor control. These
insights highlight interesting research directions that warrant further
exploration.

###### Acknowledgements.

The authors would like to thank Y. Katagi for assistance with the experiments.
This work was supported in part by a Grant-in-Aid for Scientific Research from
the Ministry of Education, Culture, Sports, Science and Technology (MEXT)
(19H02112 and 19K22878), Japan.

##  Appendix A  Data preprocessing

Time series data of wrist joint angles were acquired at 1000 [Hz] using a
goniometer. These data were resampled to 63 [Hz] to match the frame rate of an
ultrasound image. A low-pass filter (Butterworth filter butterworth1930theory
) was applied to the data to remove noise. These data were used as the input
joint angle vector $\bm{\theta}=\left(\theta_{1},\theta_{2},\cdots\right)$
where $\theta_{k}$ is the joint angle at k-th time data point. Ultrasound
images of the wrist joint were acquired at 63[Hz] when the wrist was flexed
and extended, and feature points in the ultrasound images were extracted by
image processing at each time point. In determining the initial positions of
the feature points, we first used Shi-Tomasi corner detection shi1994good  for
the first frame of the ultrasound image. The coordinates of each feature point
extracted by corner detection were tracked using optical flow
lucas1981iterative  to obtain their x, y coordinate data. We used the
coordinates of feature points that could be tracked to the end by optical flow
$\mathbf{\bar{s}}=\left(\bar{x}^{1},\bar{y}^{1},\bar{x}^{2},\bar{y}^{2},\cdots\right)^{T}$,
where ($\bar{x}^{i}$, $\bar{y}^{i}$ ) is the coordinate of i-th feature point.
Then, a standardization and low-pass filter (Butterworth filter
butterworth1930theory ) was applied to the time series data of each
coordinates $\mathbf{\bar{s}}^{i}=(\bar{s}^{i}_{1},\bar{s}^{i}_{2},\cdots)$.
These data were used as the reservoir state vector
$\mathbf{s_{k}}=\left(s^{1}_{k},s^{2}_{k},s^{3}_{k},s^{4}_{k},\cdots\right)^{T}$
at each time point k and the reservoir state matrix
$\mathbf{S}(=\mathbf{s_{1}},\mathbf{s_{2}},\cdots)$. Note that the mean number
of feature points used for the reservoir state vector was 995.

##  Appendix B  Ridge regression

Ridge regression is a method used to calculate the weight
$\mathbf{w}(=(w^{1},w^{2},\cdots))$ that minimizes the following loss function
with the residual sum of squares term and the L2 regularization term.

$\displaystyle
L=\sum_{k}\left(o_{k}-\hat{o}_{k}\right)^{2}+\frac{1}{2}\lambda\sum_{i}(w^{i})^{2}$
(4)

The weight $\mathbf{w}$ that minimizes the loss function was determined
analytically using the following equation.

$\displaystyle\mathbf{w}=\mathbf{o}\mathbf{S}^{\mathrm{T}}\left(\mathbf{S}\mathbf{S}^{\mathrm{T}}+\lambda\mathbf{I}\right)^{-1}$
(5)

where $\mathbf{S}$ is the reservoir state matrix, which summarizes the
reservoir state vectors described above
$\mathbf{S}(=\mathbf{s_{1}},\mathbf{s_{2}},\cdots)$, $\mathbf{w}$ is the
weight of the corresponding linear readout, $\lambda$ is a hyperparameter and
$\mathbf{I}$ is the identity matrix. The hyperparameter $\lambda$ was
determined by trial and error, and the same value ($\lambda=10$) was used for
all training.

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