Skin Comfort Sensation with Mechanical Stimulus from Electronic Skin

The field of electronic skin has received considerable attention due to its extensive potential applications in areas including tactile sensing and health monitoring. With the development of electronic skin devices, electronic skin can be attached to the surface of human skin for long-term health monitoring, which makes comfort an essential factor that cannot be ignored in the design of electronic skin. Therefore, this paper proposes an assessment method for evaluating the comfort of electronic skin based on neurodynamic analysis. The holistic analysis framework encompasses the mechanical model of the skin, the modified Hodgkin–Huxley model for the transduction of stimuli, and the gate control theory for the modulation and perception of pain sensation. The complete process, from mechanical stimulus to the generation of pain perception, is demonstrated. Furthermore, the influence of different factors on pain perception is investigated. Sensation and comfort diagrams are provided to assess the mechanical comfort of electronic skin. The comfort assessment method proposed in this paper provides a theoretical basis when assessing the comfort of electronic skin.

The development of electronic skin has led to the necessity of long-term conformally attached devices to collect physiological information [31,33,34], which has highlighted the importance of comfort in the design of electronic skin [35].The uncomfortable sensations induced by electronic skin can be attributed to the mechanical [36][37][38][39], thermal [40][41][42][43][44][45][46], and electrical [47,48] stimuli during operation.On the one hand, these stimuli comprise the on-demand therapeutics applied by the electronic skin, which is able to reduce long-term medical costs and health risks.On the other hand, the stimuli come from the inevitable accumulation of Joule heat and mechanical differences compared to human skin [49].
A significant number of researchers have concentrated their efforts on the comfort of electronic skin, conducting investigations from a variety of vantage points.Some researchers attempted to bridge the gap between electronic skin devices and human skin by modifying the structural design [36,37,[50][51][52].The utilization of the horseshoe topology and the control of the geometric parameters of the structure has enabled the minimization of the mechanical difference between electronic skin and human skin, resulting in the realization of mechanical stealth during the working process of the electronic skin, and has effectively improved the comfort perceived by the human skin.Other researchers have studied the sensations experienced by the skin under thermo-mechanical coupling stimuli from electronic skin, proposing a thermal comfort assessment method consisting of a stimulation and perception evaluation [53][54][55][56][57][58][59][60][61].This method allows for the quantification of the sensation of pain perceived by the skin under the combined action of mechanical, thermal, and chemical stimuli caused by the electronic skin.However, there is a paucity of studies analyzing the comfort of electronic skin considering mechanical stimuli.
This paper presents an assessment method for evaluating comfort when wearing electronic skin devices.The method encompasses the mechanical model of skin, the transduction model of stimuli, and the modulation and perception model of pain sensation.The mechanical model of skin is established to obtain the theoretical stress distribution, which is verified through comparison using the finite element analysis (FEA).Subsequently, the nerve impulse under mechanical stimuli is acquired through the modified Hodgkin-Huxley model, and the sensation is evaluated based on a mathematical model of gate control theory.Additionally, the factors that influence the comfort of the electronic skin, including the magnitude of mechanical stimuli and the location of the nociceptor, are also discussed.

Analysis of Skin Sensation
The process of skin sensations is schematically illustrated in Figure 1.A sensation is induced by the mechanical stimuli from the thermal management electronic skin device, namely, a thermal protecting substrate [41], and transduced to the nervous impulses by the nociceptors on the skin.The signal is then transmitted to the central nervous system, where it is modulated and precepted by the mid-brain and spinal cord.The following section will present a detailed analysis of each step in this process.term medical costs and health risks.On the other hand, the stimuli come from the inev table accumulation of Joule heat and mechanical differences compared to human skin [4 A significant number of researchers have concentrated their efforts on the comfort electronic skin, conducting investigations from a variety of vantage points.Some researc ers attempted to bridge the gap between electronic skin devices and human skin by mo ifying the structural design [36,37,[50][51][52].The utilization of the horseshoe topology an the control of the geometric parameters of the structure has enabled the minimization the mechanical difference between electronic skin and human skin, resulting in the rea zation of mechanical stealth during the working process of the electronic skin, and h effectively improved the comfort perceived by the human skin.Other researchers ha studied the sensations experienced by the skin under thermo-mechanical coupling stimu from electronic skin, proposing a thermal comfort assessment method consisting of a stim ulation and perception evaluation [53][54][55][56][57][58][59][60][61].This method allows for the quantification the sensation of pain perceived by the skin under the combined action of mechanical, the mal, and chemical stimuli caused by the electronic skin.However, there is a paucity studies analyzing the comfort of electronic skin considering mechanical stimuli.
This paper presents an assessment method for evaluating comfort when weari electronic skin devices.The method encompasses the mechanical model of skin, the tran duction model of stimuli, and the modulation and perception model of pain sensatio The mechanical model of skin is established to obtain the theoretical stress distributio which is verified through comparison using the finite element analysis (FEA).Subs quently, the nerve impulse under mechanical stimuli is acquired through the modifi Hodgkin-Huxley model, and the sensation is evaluated based on a mathematical mod of gate control theory.Additionally, the factors that influence the comfort of the electron skin, including the magnitude of mechanical stimuli and the location of the nocicepto are also discussed.

Analysis of Skin Sensation
The process of skin sensations is schematically illustrated in Figure 1.A sensation induced by the mechanical stimuli from the thermal management electronic skin devic namely, a thermal protecting substrate [41], and transduced to the nervous impulses the nociceptors on the skin.The signal is then transmitted to the central nervous syste where it is modulated and precepted by the mid-brain and spinal cord.The followi section will present a detailed analysis of each step in this process.
Figure 1.Schematic of the skin sensation procedure, which is induced by the mechanical stimul caused by electronic skin: a thermal protecting substrate [41] is transduced to the nervous impuls by the nociceptor on the skin, and then modulated and perceived by the central nervous system.Figure 1.Schematic of the skin sensation procedure, which is induced by the mechanical stimulus caused by electronic skin: a thermal protecting substrate [41] is transduced to the nervous impulses by the nociceptor on the skin, and then modulated and perceived by the central nervous system.

Stress Distribution on the Skin
As the largest organ of the human body, skin generally consists of three layers: the epidermis, dermis, and subcutis.For the simplicity of analysis, each layer is considered to be isotropic [62].Considering the mechanical loading applied by the electronic skin, an axisymmetric model of skin is established, as illustrated in Figure 2a.The mechanical loading from electronic skin is denoted by p(r).The zero-displacement boundary condition Materials 2024, 17, 2920 3 of 16 is assumed at the bottom surface of the skin.The stress components satisfy the equilibrium equations and constitutive equations: Here, λ and G are the Lame constants, which are linked with the Young's modulus E and Poisson's ratio ν by the following: taken as examples, as demonstrated in Figure 2b,c.Figure 2b shows a wearable bilateral vibrotactile (BV) actuator-based virtual reality (VR) interface targeting the palms [63].The hemispherical BV actuator is tightly mounted on the skin, and the mechanical stimulus is denoted by p1(r) in this paper.p1(r) and ̂  can be expressed as follows: ( ) Figure 2c demonstrates a thermal protecting substrate, consisting of a phase change material with a metal film on the top of the soft polymer [41].The mechanical stimulus from the planar-shaped thermal protecting substrate is denoted as p2(r).According to our previous research [64], the mechanical stimulus induced by the rigid metal film p2(r) and corresponding Hankel transform ̂  can be expressed as follows: ( )  The mechanical model of skin, which consists of three layers: the epidermis, dermis and subcutis.Two types of mechanical loading are analyzed, including (b) a hemispherical mechanical stimulus p 1 (r) induced by the wearable bilateral-vibrotactile-actuator-based virtual reality interface targeting the palms [63], and (c) the mechanical stimulus induced by the thermal protecting substrate p 2 (r) [41].
Setting u* = 2Gu, w* = 2Gw and utilizing the Hankel transform leads to the following: (5) In this paper, H i and H i −1 are the i-order Hankel transform and reversed Hankel transform.The solution of Equation ( 4) is as follows: The matrix Ψ(ξ, z) is detailed in Appendix A. Considering that the Lame constants are different in each layer of skin, u* and w* are substituted with u and w in Equation ( 6): The matrix N(ξ, z) is detailed in Appendix B. Due to the fact that each layer of skin has different mechanical properties, Equation ( 7) becomes: σ z and τ zr can be obtained by utilizing the reversed Hankel transform.The other stress components, except σ z and τ zr , can be obtained through the constitutive equations.The complete Ŷ(ξ, 0) is obtained by utilizing the zero-displacement boundary condition at the bottom surface of the skin: where p(ξ) is the 0-order Hankel transform of p(r).
As mentioned before, the p(r) is the mechanical stimulus induced by the electronic skin.The electronic skins have different forms according to their different functions, leading to different mechanical loadings on the skin.Two typical electronic skin devices were taken as examples, as demonstrated in Figure 2b,c.Figure 2b shows a wearable bilateral vibrotactile (BV) actuator-based virtual reality (VR) interface targeting the palms [63].The hemispherical BV actuator is tightly mounted on the skin, and the mechanical stimulus is denoted by p 1 (r) in this paper.p 1 (r) and p1 (ξ) can be expressed as follows: Figure 2c demonstrates a thermal protecting substrate, consisting of a phase change material with a metal film on the top of the soft polymer [41].The mechanical stimulus from the planar-shaped thermal protecting substrate is denoted as p 2 (r).According to our previous research [64], the mechanical stimulus induced by the rigid metal film p 2 (r) and corresponding Hankel transform p2 (ξ) can be expressed as follows:

Model of Transduction
Nervous impulses originate from the current, which is induced by the opening of the ion channels of the nociceptors.According to previous research [58], the ion channels are generally gated by three kinds of stimuli: thermal, mechanical, and chemical stimuli.The total stimulus-induced current consists of three components: All of these current components need to be considered in the analysis of thermomechanical coupling stimuli to account for the effect of temperature, thermal stress, and thermal burn damage, respectively.For the skin sensations encountered under mechanical stimuli, the temperature change can be ignored [65]; thus, only the I mech needs to be considered: Here, H(x) is the Heaviside function.Three mechanical-stimulus-related parameters are given by C m1 = 1 µA/cm 2 , C m2 = 3, and C m3 = −1 µA/cm 2 .The mechanical threshold of pain sensation is given by σ t = 0.2 MPa [54].Here, σ max represents the stress level on the nociceptor, which is defined as follows: The intensity of the external stimulus is determined through the frequency of the nerve impulses.The modified Hodgkin-Huxley (H-H) model is utilized to describe the generation of action potentials [54], which is schematically shown in Figure 3: Here, C m = 1 µF/cm 2 is the capacitance of the membrane, and V m is the membrane potential.I shift = 8.1 mA is the current used to guarantee the potentials.I Na , I K , and I A are the ion current components corresponding to the sodium ion (Na + ), potassium ion (K + ), and additional K + .I L is the leakage current component.I Na , I K , I L , and I A are related to the membrane potential and corresponding ionic conductance: Materials 2024, 17, x FOR PEER REVIEW 6 of 17

Model of Modulation and Perception
The mathematical model of gate control theory (GCT) proposed by Britton et al. is introduced to describe the modulation and perception procedure of skin sensations [67][68][69], and is schematically shown in Figure 4.According to Connor's research [66], the ionic conductance is given by κ Na = 120 ms/cm 2 , κ K = 20 ms/cm 2 , κ L = 0.3 ms/cm 2 , and κ A = 47.7 ms/cm 2 in this paper.Furthermore, E Na = 55 mV, E K = −72 mV, E L = −17.15mV, and E A = −75 mV are the corresponding reversal ionic potentials, as shown in Figure 3. m, h, n, A, B are the gating variables, and their details can be found in Appendix C. The action potential V m can be integrated by combining Equations ( 13)-( 16).

Model of Modulation and Perception
The mathematical model of gate control theory (GCT) proposed by Britton et al. is introduced to describe the modulation and perception procedure of skin sensations [67][68][69], and is schematically shown in Figure 4.

Model of Modulation and Perception
The mathematical model of gate control theory (GCT) proposed by Britton et al. is introduced to describe the modulation and perception procedure of skin sensations [67][68][69], and is schematically shown in Figure 4.According to Britton's theory, the information about noxious stimulus is transmitted through small fibers (C and Aδ), and the information of less intense stimuli is transmitted through the large fiber (Aβ).The stimulus information undergoes inhibitory and excitory modulation when routed through substantia gelatinosa (SG) cells to the central transmission cell (T-cell).This procedure can be expressed by the following equations: According to Britton's theory, the information about noxious stimulus is transmitted through small fibers (C and Aδ), and the information of less intense stimuli is transmitted through the large fiber (Aβ).The stimulus information undergoes inhibitory and excitory modulation when routed through substantia gelatinosa (SG) cells to the central transmission cell (T-cell).This procedure can be expressed by the following equations: Equation ( 17) is the general form of the modulation procedure described in GCT, where the subscripts i, e, t, b, s, and l denote the inhibitory SG cells, excitatory SG cells, T-cell, midbrain, small fibers, and large fibers, respectively.The subscript 0 stands for the initial state.V and stands for the potential of different cells.τ = 0.7, which is a time constant in the equation.x l and x s are the impulse frequencies transmitted through large and small fibers, respectively.x k is linked with V k by the following: Here, k = i, e, t, b, V k0 = −70 mV, and V thr = −55 mV is the threshold for pain sensation.The function g li represents the modulation on cell i from cell l.Equation ( 17) requires function g, a monotonically increasing convergence function.Therefore, the specific expression for Equation ( 17) is obtained by introducing the hyperbolic tangent function for g: θ se and θ li stand for the proportion of the signal that is transmitted through SG cells, which are both taken to be 0.8 in this paper.In this paper, x s is taken as the frequency of V m , and x l is taken to be 0. The signal would be transmitted to the midbrain once the output of T-cell V t exceeds the V thr , meaning that V t is directly related with the level of pain sensation.

Verification of the Distribution of Stress on Skin
Firstly, the mechanical model of skin is verified by comparing the stress distribution with the finite element analysis (FEA).By utilizing the commercialized software ABAQUS 6.14, a 6 mm × 2.5 mm axisymmetric model of skin is established.The Young's moduli and the thickness of the dermis, epidermis, and subcutis are listed in Table 1 [70].The bottom surface of the model is fixed.A p = 20 Pa, δ = 1 mm hemispherical loading p 1 (r) is applied to the top surface of the model.The model is discretized with 0.005 mm CAX4R mesh, which is enough to guarantee the convergency of the FEA.The variations in two normal stress components, σ z and σ r , along the z-axis and r-axis are denoted by the dots in Figure 5.The theoretical results, shown as the lines in Figure 5, were numerically obtained through the reversed Hankel transform, where the parity of the function is utilized in the integration.In Figure 5a,b, it can be observed that both σ z and σ r dramatically decrease when z is in the range of the dermis and epidermis, and they converge to 0 at the subcutis.However, σ r shows a discontinuous change at the interface.Figure 5c demonstrates that the variation in σ z is consistent with the stress boundary condition, and the Figure 5d shows that σ r gradually decreases to 0 along the r-axis.In addition, the finite element results of the stress distribution under the action of the rigid plate load p 2 (r) were compared with the theoretical results shown in Figure 6.As shown in Figure 6a,b, the changes in the two normal stress components σ z and σ r along the z-axis are plotted.Similar to the hemispherical load p 1 (r), σ z converges to 0 instantaneously as coordinate z increases, and σ r shows discontinuous changes at the interface of the different layers of the skin.Figure 6c,d show the changes in normal stress components σ z and σ r along the r-axis.The change in σ z on the r-axis completely corresponds to the stress boundary condition.As it leaves the loading area, σ r instantaneously converges to 0 along the r-axis.The theoretically solved theoretical stress distribution is in good agreement with the FEA results, and the theoretical model of the skin is perfectly verified.In addition, the finite element results of the stress distribution under the action of the rigid plate load p2(r) were compared with the theoretical results shown in Figure 6.As shown in Figure 6a,b, the changes in the two normal stress components σz and σr along the z-axis are plotted.Similar to the hemispherical load p1(r), σz converges to 0 instantaneously as coordinate z increases, and σr shows discontinuous changes at the interface of the different layers of the skin.Figure 6c,d show the changes in normal stress components σz and σr along the r-axis.The change in σz on the r-axis completely corresponds to the stress boundary condition.As it leaves the loading area, σr instantaneously converges to 0 along the r-axis.The theoretically solved theoretical stress distribution is in good agreement with the FEA results, and the theoretical model of the skin is perfectly verified.

Case Study
Firstly, the skin sensations experienced under an increasing mechanical stimulus are completely demonstrated in Figure 7.A hemispherical loading with δ = 1 mm and an increasing amplitude p = 0.4 × 10 6 t (Pa) is applied, where the kinetic effects can be ignored.The nociceptor is assumed to be z = 0.5 mm on the z-axis.Figure 7a shows the membrane potential induced by the mechanical stimulus; the nerve impulses start after the mechanical stimulus reaches the threshold for pain sensations, σt.The frequency of the

Case Study
Firstly, the skin sensations experienced under an increasing mechanical stimulus are completely demonstrated in Figure 7.A hemispherical loading with δ = 1 mm and an increasing amplitude p = 0.4 × 10 6 t (Pa) is applied, where the kinetic effects can be ignored.The nociceptor is assumed to be z = 0.5 mm on the z-axis.Figure 7a shows the membrane potential induced by the mechanical stimulus; the nerve impulses start after the mechanical stimulus reaches the threshold for pain sensations, σ t .The frequency of the nerve impulses also increases with the increase in mechanical loading (Figure 7a,b).The output of T-cell V t , which is directly related to skin sensation, is plotted in Figure 7c.After the formation of nerve impulses gradually increases, uncomfortable pain sensations are perceived after 1500 ms, when V t exceeds the threshold.The effects of different parameters on skin sensation are studied.Firstly, the influ of loading amplitude p is analyzed, as demonstrated in Figure 8.A hemispherical loa p1(r) with fixed radius δ = 1 mm is applied.In Figure 8a, the variations in Vm with diff loading amplitude p (0.5 MPa, 1 MPa, and 1.5 MPa) are plotted.It is clear tha amplitude of Vm remains stable, but the frequency gradually increases with the loa amplitude.Thus, the relationship between the frequency of Vm, steady state value (Vt ∞ ) and the loading amplitude p are plotted as the black line and the red line in Fi 8b.The frequency of Vm monotonically increases with p, which means the intensity o outside stimuli is carried through the frequency of Vm [54,71].Similarly, the Vt is positively correlated with p, suggesting that the pain perception induced by the elect skin intensifies with increasing mechanical stimuli.The effects of different parameters on skin sensation are studied.Firstly, the influence of loading amplitude p is analyzed, as demonstrated in Figure 8.A hemispherical loading p 1 (r) with fixed radius δ = 1 mm is applied.In Figure 8a, the variations in V m with different loading amplitude p (0.5 MPa, 1 MPa, and 1.5 MPa) are plotted.It is clear that the amplitude of V m remains stable, but the frequency gradually increases with the loading amplitude.Thus, the relationship between the frequency of V m , steady state value of V t (V t ∞ ) and the loading amplitude p are plotted as the black line and the red line in Figure 8b.The frequency of V m monotonically increases with p, which means the intensity of the outside stimuli is carried through the frequency of V m [54,71].Similarly, the V t is also positively correlated with p, suggesting that the pain perception induced by the electronic skin intensifies with increasing mechanical stimuli.
amplitude.Thus, the relationship between the frequency of Vm, steady state value of Vt (Vt ∞ ) and the loading amplitude p are plotted as the black line and the red line in Figure 8b.The frequency of Vm monotonically increases with p, which means the intensity of the outside stimuli is carried through the frequency of Vm [54,71].Similarly, the Vt is also positively correlated with p, suggesting that the pain perception induced by the electronic skin intensifies with increasing mechanical stimuli.showing that pain perception intensifies with increasing mechanical stimuli.
Secondly, the effect of the nociceptor's location is analyzed.It is clear that the stress level is different in different locations.A hemisphere loading is applied to the surface of the skin with p = 0.5 MPa and δ = 1 mm.The variation in σ max along the z-axis is demonstrated in Figure 9a.The σ max shows a dramatic decrease in epidermis, followed by a slight descent and then ascent in the dermis, before finally converging to 0 in the subcutis.According to previous research, the nociceptor is mainly located at the dermis and epidermis [72].Thus, in Figure 9b, we show the variation in frequency and V t ∞ as the nociceptor varies across the dermis.As the nociceptor gradually deepens in the z direction, it can be seen that the frequency, which represents the intensity of the external stimuli, first decreases and then increases, which represents the degree of pain sensation, also showing the same trend.Secondly, the effect of the nociceptor's location is analyzed.It is clear that the stress level is different in different locations.A hemisphere loading is applied to the surface of the skin with p = 0.5 MPa and δ = 1 mm.The variation in σmax along the z-axis is demonstrated in Figure 9a.The σmax shows a dramatic decrease in epidermis, followed by a slight descent and then ascent in the dermis, before finally converging to 0 in the subcutis.According to previous research, the nociceptor is mainly located at the dermis and epidermis [72].Thus, in Figure 9b, we show the variation in frequency and Vt ∞ as the nociceptor varies across the dermis.As the nociceptor gradually deepens in the z direction, it can be seen that the frequency, which represents the intensity of the external stimuli, first decreases and then increases, which represents the degree of pain sensation, also showing the same trend.

Phase Diagram of Comfortable Electronic Skin Design
In order to guide and optimize the design of electronic skin and ensure the comfort of potential users, the stress level and the steady state potentials of T cell Vt ∞ under different loading amplitudes and different nociceptor locations are calculated and summarized.The mechanical loading radius of p1(r) and p2(r) are fixed at δ = 1 mm. Figure 10 shows the variation in stress level σmax with the depth of the nociceptor and the load amplitude p under (a) p1(r) and (b) p2(r), respectively.Different colors represent different stress levels of σmax.It can be seen from Figure 10 that σmax first decreases and then increases along the z direction, and is linearly positively correlated with load amplitude p.The maximum value of σmax appears at z = 0.1 mm, p = 0.6 MPa.The interval where σmax < σt is marked with a blank area in Figure 10.In the blank interval, the stress level of the nociceptor is less than the stress-sensing threshold, meaning that the mechanically related current component Imech would not be induced in the transduction process.And the external mechanical stimuli cannot be sensed by human skin in the blank area in Figure 10.

Phase Diagram of Comfortable Electronic Skin Design
In order to guide and optimize the design of electronic skin and ensure the comfort of potential users, the stress level and the steady state potentials of T cell V t ∞ under different loading amplitudes and different nociceptor locations are calculated and summarized.The mechanical loading radius of p 1 (r) and p 2 (r) are fixed at δ = 1 mm. Figure 10 shows the variation in stress level σ max with the depth of the nociceptor and the load amplitude p under (a) p 1 (r) and (b) p 2 (r), respectively.Different colors represent different stress levels of σ max .It can be seen from Figure 10 that σ max first decreases and then increases along the z direction, and is linearly positively correlated with load amplitude p.The maximum value of σ max appears at z = 0.1 mm, p = 0.6 MPa.The interval where σ max < σ t is marked with a blank area in Figure 10.In the blank interval, the stress level of the nociceptor is less than the stress-sensing threshold, meaning that the mechanically related current component I mech would not be induced in the transduction process.And the external mechanical stimuli cannot be sensed by human skin in the blank area in Figure 10.
< σt is marked with a blank area in Figure 10.In the blank interval, the stress level o nociceptor is less than the stress-sensing threshold, meaning that the mechanically rel current component Imech would not be induced in the transduction process.And external mechanical stimuli cannot be sensed by human skin in the blank area in Fi 10.Different colors correspond to different stress levels σ max on the nociceptor.In the blank area, σ max is smaller than the stress perception threshold σ t , meaning that the human body cannot feel the corresponding mechanical stimulation from the electronic skin.
Figure 11 shows how the steady-state potential V t ∞ on T cells changes with the nociceptor depth z and load amplitude p under the mechanical stimuli of p 1 (r) and p 2 (r), respectively.Different colors correspond to different V t ∞ sizes.The colored intervals surrounded by black solid lines denote the comfort sensation intervals of human skin under mechanical stimulation from an electronic skin, corresponding to a V t ∞ less than the pain threshold V thr (−55 mV).It can be seen that V t ∞ in the color interval in Figure 11 is consistent with the change trend of stress level σ max in Figure 10; that is, there is a positive correlation between human comfort perception (V t ∞ ) and σ max on nociceptors.
In Figure 11, the V t ∞ in the gray shaded area is greater than the pain perception threshold V thr .Mechanical stimulation from electronic skin that falls within the shaded range would lead the human body to experience mechanical pain perception.By combining Figures 10 and 11, the comfort phase diagram that was used to guide the electronic skin design in this article can be obtained.The mechanical comfort of electronic skin could be achieved by controlling the mechanical stimulation amplitude and rationally planning the position where the electronic skin device will be worn.Different colors correspond to different stress levels σmax on the nociceptor.In the blank area, σmax is smaller than the stress perception threshold σt, meaning that the human body cannot feel the corresponding mechanical stimulation from the electronic skin.
Figure 11 shows how the steady-state potential Vt ∞ on T cells changes with the nociceptor depth z and load amplitude p under the mechanical stimuli of p1(r) and p2(r), respectively.Different colors correspond to different Vt ∞ sizes.The colored intervals surrounded by black solid lines denote the comfort sensation intervals of human skin under mechanical stimulation from an electronic skin, corresponding to a Vt ∞ less than the pain threshold Vthr (−55 mV).It can be seen that Vt ∞ in the color interval in Figure 11 is consistent with the change trend of stress level σmax in Figure 10; that is, there is a positive correlation between human comfort perception (Vt ∞ ) and σmax on nociceptors.In Figure 11, the Vt ∞ in the gray shaded area is greater than the pain perception threshold Vthr.Mechanical stimulation from electronic skin that falls within the shaded range would lead the human body to experience mechanical pain perception.By combining Figure 10 and Figure 11, the comfort phase diagram that was used to guide the electronic skin design in this article can be obtained.The mechanical comfort of electronic skin could be achieved by controlling the mechanical stimulation amplitude and rationally planning the position where the electronic skin device will be worn.

Conclusions
This paper presents a novel method for assessing the comfort of electronic skin devices, taking mechanical stimuli into account.The proposed method comprises the following steps:

Conclusions
This paper presents a novel method for assessing the comfort of electronic skin devices, taking mechanical stimuli into account.The proposed method comprises the following steps: (1) a mechanical model of skin is constructed, where the stress distribution on the skin is obtained theoretically based on elastic theory; (2) the transduction model is developed, where the nervous impulses induced by the mechanical stimuli are acquired through the modified H-H model; (3) the model of modulation and perception is introduced, where the mathematical model of GCT theory is introduced to evaluate the relationship between the nerve impulse and the skin sensation.A mechanical model of skin is verified through a comparison of the theoretical stress distribution and the FEA results.Factors that influence how comfortable an electronic skin are also investigated, including the compression amplitude and the location of the nociceptor.Comfort diagrams are provided to guide the design of electronic skin.

Figure 2 .
Figure 2. (a) The mechanical model of skin, which consists of three layers: the epidermis, dermis and subcutis.Two types of mechanical loading are analyzed, including (b) a hemispherical

Figure 2 .
Figure 2. (a)The mechanical model of skin, which consists of three layers: the epidermis, dermis and subcutis.Two types of mechanical loading are analyzed, including (b) a hemispherical mechanical stimulus p 1 (r) induced by the wearable bilateral-vibrotactile-actuator-based virtual reality interface targeting the palms[63], and (c) the mechanical stimulus induced by the thermal protecting substrate p 2 (r)[41].

Figure 3 .
Figure 3.The schematic of the modified Hodgkin and Huxley model.Different ionic current components, including INa, IK, IL, and IA, are related to the membrane potential Vm and corresponding reversal ionic potentials and ionic conductances [54].

Figure 3 .
Figure 3.The schematic of the modified Hodgkin and Huxley model.Different ionic current components, including I Na , I K , I L , and I A , are related to the membrane potential V m and corresponding reversal ionic potentials and ionic conductances [54].

Figure 3 .
Figure 3.The schematic of the modified Hodgkin and Huxley model.Different ionic current components, including INa, IK, IL, and IA, are related to the membrane potential Vm and corresponding reversal ionic potentials and ionic conductances [54].

Figure 4 .
Figure 4.The mathematical model of GCT [67-69].The nerve impulses transmitted through large fibers (Aβ) and small fibers (C and Aδ), with inhibitory and excitatory modulation in SG cells.E, I, and T denote the inhibitory SG cells, excitatory SG cells, and central transmission cells.Symbols "+" and "-" represent excitatory and inhibitory modulation to corresponding cells, respectively.

Figure 4 .
Figure 4.The mathematical model of GCT [67-69].The nerve impulses transmitted through large fibers (Aβ) and small fibers (C and Aδ), with inhibitory and excitatory modulation in SG cells.E, I, and T denote the inhibitory SG cells, excitatory SG cells, and central transmission cells.Symbols "+" and "-" represent excitatory and inhibitory modulation to corresponding cells, respectively.

Figure 5 .
Figure 5.The stress distribution under p1(r) for σz, and σr along the z axis (a,b) and r axis (c,d).The theoretical and FEA results are shown as lines and dots, respectively.The dash line in (a,b) represent the boundaries of different layers of skin.And the dash lin in (c,d) delineate the mechanicallystimulated area.The agreement between the theoretical and FEA data verifies the elastic model of the skin.

Figure 5 . 17 Figure 6 .
Figure 5.The stress distribution under p 1 (r) for σ z , and σ r along the z axis (a,b) and r axis (c,d).The theoretical and FEA results are shown as lines and dots, respectively.The dash line in (a,b) represent the boundaries of different layers of skin.And the dash lin in (c,d) delineate the mechanically-stimulated area.The agreement between the theoretical and FEA data verifies the elastic model of the skin.Materials 2024, 17, x FOR PEER REVIEW 9 of 17

Figure 6 .
Figure 6.The stress distribution under p 2 (r) for σ z , and σ r along the z axis (a,b) and r axis (c,d).

Materials 2024 , 10 Figure 7 .
Figure 7.The perception procedure is demonstrated through the application of an incre hemispherical loading with p = 0.4 × 10 6 t (Pa).(a) The action potential Vm, (b) the frequency o and (c) the output of T-cell Vt increase with increasing loading amplitude.

Figure 7 .
Figure 7.The perception procedure is demonstrated through the application of an increasing hemispherical loading with p = 0.4 × 10 6 t (Pa).(a) The action potential V m , (b) the frequency of V m , and (c) the output of T-cell V t increase with increasing loading amplitude.

Figure 8 .
Figure 8. Variations in skin pain sensation under hemispherical loading with different amplitude p; (a) the variation in membrane potential Vm; (b) the variation in Vm frequency (grey); the Vt ∞ with p, showing that pain perception intensifies with increasing mechanical stimuli.

Figure 8 .
Figure 8. Variations in skin pain sensation under hemispherical loading with different amplitude p; (a) the variation in membrane potential V m ; (b) the variation in V m frequency (grey); the V t ∞ with p,

Figure 9 .
Figure 9. Influence of nociceptor location on skin pain sensation.A hemisphere loading with p = 0.5 MPa and δ = 1 mm is applied; (a) the variation in σmax with the depth of the nociceptor in the skin; (b) the variation in Vm frequency (grey) and the Vt ∞ with z.

Figure 9 .
Figure 9. Influence of nociceptor location on skin pain sensation.A hemisphere loading with p = 0.5 MPa and δ = 1 mm is applied; (a) the variation in σ max with the depth of the nociceptor in the skin; (b) the variation in V m frequency (grey) and the V t ∞ with z.

Figure 10 .
Figure10.The sensation diagram of human skin under different load sizes and at different nociceptor depths with different mechanical loadings from electronic skins: (a) p 1 (r) and (b) p 2 (r).Different colors correspond to different stress levels σ max on the nociceptor.In the blank area, σ max is smaller than the stress perception threshold σ t , meaning that the human body cannot feel the corresponding mechanical stimulation from the electronic skin.

Figure 10 .
Figure 10.The sensation diagram of human skin under different load sizes and at different nociceptor depths with different mechanical loadings from electronic skins: (a) p1(r) and (b) p2(r).Different colors correspond to different stress levels σmax on the nociceptor.In the blank area, σmax is smaller than the stress perception threshold σt, meaning that the human body cannot feel the corresponding mechanical stimulation from the electronic skin.

Figure 11 .
Figure 11.A comfort diagram of human skin under different load sizes and at different nociceptor depths with different mechanical loadings from electronic skins: (a) p1(r) and (b) p2(r).The potential level steady-state values Vt ∞ of T cell are denoted by different colors.Vt ∞ in the shaded area is greater than the pain perception threshold Vthr, exceeding the human pain sensation threshold.
(1) a mechanical model of skin is constructed, where the stress distribution on the skin is obtained theoretically based on elastic theory; (2) the transduction model is developed, where the nervous impulses induced by the mechanical stimuli are acquired through the modified H-H model; (3) the model of modulation and perception is introduced, where the mathematical model of GCT theory is introduced to

Figure 11 .
Figure 11.A comfort diagram of human skin under different load sizes and at different nociceptor depths with different mechanical loadings from electronic skins: (a) p 1 (r) and (b) p 2 (r).The potential level steady-state values V t ∞ of T cell are denoted by different colors.V t ∞ in the shaded area is greater than the pain perception threshold V thr , exceeding the human pain sensation threshold.

Table 1 .
Mechanical properties and thicknesses for each layer of skin.

Table 1 .
Mechanical properties and thicknesses for each layer of skin.