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Marguerite Gilbeau

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Aug 3, 2024, 5:39:12 PM8/3/24

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Background: With the increase in the use of soft-tissue fillers worldwide, there has been a rise in the serious adverse events such as vascular compromise and blindness. This article aims to review the role of fillers in causing blindness and the association between hyaluronic acid (HA) filler and blindness.

Conclusions: Autologous fat was the most common filler associated with blindness despite HA fillers being the most commonly used across the globe. However, the blindness caused by other soft-tissue fillers like collagen and calcium hydroxylapatite was represented. It was also evident through the review that the treatment of HA-related blindness was likely to have better outcomes compared with other fillers due to hyaluronidase use.

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Recently, soft machines have attracted attention in a number of research fields. Their soft bodies can undergo dramatic changes in their morphologies to adapt to various environments1,2. They deliver vital applications for carrying fragile objects, for human-robot interaction and for search and rescue in emergency situations, mostly due to their inherent softness that results in increased adaptivity and less damage during contact3,4. Furthermore, their production costs are relatively low, so they can be easily incorporated into a wide range of machines for various purposes5.

Concomitant to these benefits is a great challenge in controlling their body dynamics. Generally, soft body dynamics exhibit a variety of properties, including nonlinearity, memory and potentially infinitely many degrees of freedom1,4. In addition, their degrees of freedom are often larger than the number of actuators (i.e., underactuated systems), which leads to well-known difficulties in controlling them6.

Here, we demonstrate that these seemingly undesired properties can in fact be highly beneficial in that they allow us to use soft bodies as computational resources. Our approach is based on a machine learning technique called reservoir computing, which has a particular focus on real-time computing with time-varying inputs and is suited to emulate complex temporal computations7,8,9,10,11. Its framework has been proposed to overcome a limitation in the conventional attractor-based neural networks that takes a certain amount of time to converge to an attractor state, which is less suitable for real-time computing. Our approach places more emphasis on the transient dynamics of high-dimensional dynamical systems9,10,11,12, which are typically referred to as the reservoir. To have computational capabilities, a reservoir should have the properties of input separability and fading memory9. Input separability is usually achieved by nonlinear mapping of the low-dimensional input to a high-dimensional state space, similar to the function of a kernel in machine learning13. Fading memory is a property of a system that retains the influence of a recent input sequence within the system, which permits the integration of stimulus information over time. This enables reproducible computation for which the recent history of the signal is significant. If the dynamics of the reservoir involve enough nonlinearity and memory, emulating complex, nonlinear dynamical systems only requires adding a linear, static readout from the high-dimensional state space of the reservoir. A number of different implementations for reservoirs have been proposed, such as abstract dynamical systems for echo state networks7,8 or models of neurons for liquid state machines9, the surface of water in a laminar state14 and nonlinear mass spring systems15,16,17,18,19. Lately, electronic and optical implementations have also been reported20,21,22,23. These examples clearly illustrate that the prerequisites to be a reservoir do not depend on the specific implementation of the system but rather on the properties of the system (i.e., input separability and fading memory).

In this study, we use a simple but powerful physical platform with a soft silicone arm to demonstrate that soft body dynamics can be used as a reservoir. Previously, we showed that the body dynamics generated by this soft silicone arm can be used to emulate functions that require short-term memory and embed robust closed-loop control into the arm on the basis of a Boolean function24. In this study, we extend our previous approaches and aim to emulate nonlinear dynamical systems based on continuous functions, which are more frequently used in real-world applications. For example, controllers, which are often defined as continuous dynamical systems, are particularly interesting target systems for such an emulation25. This would imply that we can use the physical body of a soft machine to carry out computations needed to calculate complex time-dependent control actions and embed motor programs into the body through feedback loops. By comparing with standard machine learning techniques, we systematically characterize the information processing capacity of the soft body dynamics and show that the soft body dynamics can be exploited as a part of computational device.

(a) Schematics showing a scheme using the soft silicone arm as a part of a computational device. The arm embeds 10 bend sensors and is immersed underwater. Inputs are motor commands that generate arm motions and the embedded bend sensors reflect the arm posture for each timestep. Corresponding system outputs are generated by the weighted sum of the sensory values. (b) Picture showing the soft silicone arm used in this study. (c) Schematics expressing an analogy between a conventional reservoir computing system and our system. In a conventional reservoir system, randomly coupled abstract computational units are used for the reservoir, whereas our system exploits a physical reservoir whose units are sensors that are coupled through a soft silicone material. Our question here is whether our physical reservoir can perform tasks of nonlinear dynamical systems emulations, which are often targeted with conventional reservoir computing systems and are useful in the context of control.

By generating passive body dynamics resulting from the interaction between the water and the soft silicone material29,30, we will show that the sensory time series reflected in the body dynamics can be used to emulate the desired nonlinear dynamical systems, which are often targeted with a recurrent neural network learning or reservoir computing approach Fig. 1(c). For this purpose, we first need to define how to provide inputs to the system and how to generate corresponding outputs . In this study, we apply the motor command as an input and the output is generated by a weighted sum of the 10 sensory values and a constant valued bias set to Fig. 1(a). The output is defined as follows:

To evaluate the computational power of our system, we use the emulation tasks of nonlinear dynamical systems, called nonlinear auto-regressive moving average (NARMA) systems, which are standard benchmark tasks in the context of machine learning (e.g., recurrent neural network learning). This task presents a challenging problem for any computational system because of its nonlinearity and dependence on long time lags31. The first NARMA system is the following second-order nonlinear dynamical system:

From the upper to the lower plots, the time series of the motor command, the corresponding sensory values (odd-numbered sensors and even-numbered sensors) and the outputs for NARMA2, NARMA5, NARMA10, NARMA15 and NARMA20 are depicted. For each plot of the output, the time series for the system output as well as the target output and the output for the LR model is overlaid for comparison. Note that the output of the LR model, especially in NARMA5, NARMA10, NARMA15 and NARMA20, is not a constant but a scaled version of the input with an offset (see the inset that scales up the output for the LR model from timestep 6300 to 6400 in each plot).

To further characterize the computational power of our system, we have compared our system performance with that of conventional reservoir system called a leaky integrator echo state network (LESN), introduced in33. Like other reservoir systems, LESN has input and output layers and a reservoir, whose computational unit is equipped with a leaky integrator. Because we use a superimposed sine wave for the input time series, the NARMA systems to be emulated here tend to have slow dynamics, as shown in Fig. 2. LESN is better suited for these slow dynamics than the conventional ESN because the reservoir unit has individual state dynamics33. This is the reason for the choice of LESN for our comparisons (similar discussions can be found in34,35,36). For effective comparisons with our system, we investigate the performance of LESN with the same number of computational nodes (10 fully coupled reservoir nodes with one bias term), the same input time series and the same training and evaluation data sets.

In this study, we have systematically demonstrated that body dynamics originating from a soft silicone arm can be exploited to emulate nonlinear dynamical systems. We confirmed this by comparing the task performance with that of the LR model, from which we found that in all our tasks and for any settings of T for the input, our system outperformed the LR model. Hence, the body dynamics contributed positively to all computational tasks. Our scheme enabled us to emulate multiple nonlinear dynamical systems simultaneously by using the dynamics generated from a single soft body. We further characterized the performance of our system by comparing it with that of LESN. As expected, our physical system performed worse than an artificially optimized LESN. However, our setup had a performance comparable to or even better than that of LESN, whose parameters (a,ρ) were chosen randomly under various experimental conditions. Our results suggest that the incorporation of soft materials into the body of machines or robots also represents the addition of potential computational resources that can be exploited. If the appropriate conditions for the actuations are set and the appropriate computational tasks are defined, the soft body can even be successfully exploited as a part of a computational device. Considering that the body has primary functions other than computation, we could even argue that this feature comes along with soft bodies for free.