Porosity Structure O ﬀ ering Improved Biomechanical Stress Distribution and Enhanced Pain-Relieving Potential

: In this study, we developed a three-dimensional (3D) human body model and a body sculpting clothing (BSC) which was ﬁtted onto that body to simulate the biomechanical stress variations of the BSC with di ﬀ erent porosity structures using the ﬁnite element method. The mechanical properties of the BSC with di ﬀ erent porosity structures were also examined through the tensile testing. Analytical results indicated that the Von Mises stress of the BSC with a porosity structure of 10.28% varied from 0.076 MPa to 337.79 MPa. As compared with a porosity structure of 35.18%, the von Mises stress varied from 0.067 MPa to 207.30 MPa. The von Mises stress decreased as the porosity increasing. Based on the statistical analysis ﬁndings, we obtained a formula to predict the biomechanical relationships (von Mises stress and strain) between the human body and porosity of the BSC. Therefore, these ﬁndings could o ﬀ er potential information in the modiﬁcation of BSC for pain-relieving applications.


Introduction
The textiles and fibers in biomedical development have grown rapidly for therapy applications in recent years [1,2]. The medical textile covers medical products and devices from wound dressings and The commercial nylon fabrics were obtained from Lolinya International Corporation (Taipei, Taiwan). The nylon fiber diameter was almost 20 µm, and these fibers were spun together as loop structure to knit as BSC with different porosity. The warp-knitted BSCs (thickness of 2 mm) were observed by Keyence VHX-2000 digital optical microscope (Taipei, Taiwan). Then, an image processing system (Buehler OmniMet 9.0, Lake Bluff, IL, USA) was employed to calculate the porosity of the warp-knitted BSCs [22]. Subsequently, the digital captured images were converted using Avizo 7.0 software (Thermo Fisher Scientific, Waltham, MA, USA). Afterward, the setting routine of Buehler OmniMet software was used to calculate the percentage of the red area in the capturing images, which also means the porosity of the warp-knitted BSCs. First, set the threshold B/W (0-124) to detect the porosity. However, some pores had poorly detected areas in them, so we filled holes to deal with this problem. Finally, the setting routine gave us the percent area of the pores in the warp-knitted BSCs as a whole (Figure 1). According to their own porosity, the warp-knitted BSCs are named as BSC-1, BSC-2, BSC-3, BSC-4, BSC-5, BSC-6, and BSC-7, respectively (Table 1).

Fabrics Elastic Modulus Measurement
Mechanical properties were obtained via the LFPlus tensile machine (Taipei, Taiwan) with a loading of 1000 N, offering controlled uniformly loading force until sample maximum limitation of proportionality. The sample testing area was set as 1 × 3 cm. The elastic modulus of each sample could be determined. Use these elastic modules; we defined the material properties of the BSCs in later finite element analysis (FEA).

FEA Simulation
Based on the different elastic moduli between the different knitting densities, we tried to figure out how much stresses each sample caused on the human body during the decreasing abdomen circumference by FEA. The 3D human model and BSC model were built by Solidworks 2010 software (SolidWorks, Waltham, MA, USA) and combined together [23]. Then, the 3D models were built through the FEA software (ANSYS Workbench 12.1 version, Canonsburg, PA, USA). The human model takes a 176-cm woman as a basis, with a 29-inch waist circumference, 39-inch abdomen circumference and 41-inch buttocks circumference. The BSC model provided by Lolinya International Corporation and its specialty is abdomen-hugging to rebuild the body's golden ratio. In order to obtain a more accurate analysis, the 3D models' meshes were converted and reinforced (a tetrahedral element with 10 nodes was used for the mesh refinement) to make the FEA models reach to the real state and reliable. The mean numbers of nodes and elements are closed to 62,000 and 32,000, respectively ( Figure 2). The mechanical properties of the BSCs were determined by the tensile testing, and the human model's biomechanical properties were defined as Table 2. Based on the desired abdomen circumference of 27 inches, the original waist circumference was 39 inch. The setting displacement 12 inch was applied on the abdomen portion of the BSC model. The boundary condition was fixed at the base of the human body model. Accordingly, no mutual movement between the human body model and BSC model at their interfaces was allowed. The material was assumed to be linear, isotropic, and homogeneous in the model assembly. Finally, the von Mises stress and stress

Fabrics Elastic Modulus Measurement
Mechanical properties were obtained via the LFPlus tensile machine (Taipei, Taiwan) with a loading of 1000 N, offering controlled uniformly loading force until sample maximum limitation of proportionality. The sample testing area was set as 1 × 3 cm. The elastic modulus of each sample could be determined. Use these elastic modules; we defined the material properties of the BSCs in later finite element analysis (FEA).

FEA Simulation
Based on the different elastic moduli between the different knitting densities, we tried to figure out how much stresses each sample caused on the human body during the decreasing abdomen circumference by FEA. The 3D human model and BSC model were built by Solidworks 2010 software (SolidWorks, Waltham, MA, USA) and combined together [23]. Then, the 3D models were built through the FEA software (ANSYS Workbench 12.1 version, Canonsburg, PA, USA). The human model takes a 176-cm woman as a basis, with a 29-inch waist circumference, 39-inch abdomen circumference and 41-inch buttocks circumference. The BSC model provided by Lolinya International Corporation and its specialty is abdomen-hugging to rebuild the body's golden ratio. In order to obtain a more accurate analysis, the 3D models' meshes were converted and reinforced (a tetrahedral element with 10 nodes was used for the mesh refinement) to make the FEA models reach to the real state and reliable. The mean numbers of nodes and elements are closed to 62,000 and 32,000, respectively ( Figure 2). The mechanical properties of the BSCs were determined by the tensile testing, and the human model's biomechanical properties were defined as Table 2. Based on the desired abdomen circumference of 27 inches, the original waist circumference was 39 inch. The setting displacement 12 inch was applied on the abdomen portion of the BSC model. The boundary condition was fixed at the base of the human body model. Accordingly, no mutual movement between the human body model and BSC model at their interfaces was allowed. The material was assumed to be linear, isotropic, and homogeneous in the model assembly. Finally, the von Mises stress and stress distribution between the human body model and BSC model can be gained and compared in the study.
Appl. Sci. 2020, 10, x FOR PEER REVIEW 4 of 9 distribution between the human body model and BSC model can be gained and compared in the study.

Statistical Analysis
The data were analyzed via the SPSS statistical software (IBM Statistics version 19, Armonk, NY, USA). Data were presented as mean ± standard deviation (p-value of <0.01 was considered significant). Pearson correlation coefficient as a statistical method in tensile testing was utilized to correlate the fabrics porosity parameters with the fabric's elastic modulus (multiple linear regression analysis). In finite element analysis, Pearson correlation coefficient used to correlate the fabrics porosity parameters with the von Mises stress of the human body.

Knitted Structure of the Nylon Fabric
The knitting porosity of the courses and wales knitting structure was observed using the digital optical microscope as shown in Figure 1. The nylon in the knitted BSC follows a tortuous path (a route), forming symmetrical loops above and below the average path of the nylon. These loops can be easily stretched in different directions, which can make BSC more elastic; depending on the bulk of the nylon, knitting patterns, and knitting porosity, the BSC can stretch as much as 500% [24,25]. Therefore, knitting was major using for the BSC that must be elastic or stretch in response to the human body movement [26,27]. Moreover, the courses and wales knitting structure are usually more form-fitting because their elasticity allows them to follow the human body's curvature closely. More extra curvature can be easily introduced into the fabrics without seams, such as the armpit portion, the crotch portion of the clothing can be harvested with short rows or by increasing or decreasing the number of stitches [28].

Statistical Analysis
The data were analyzed via the SPSS statistical software (IBM Statistics version 19, Armonk, NY, USA). Data were presented as mean ± standard deviation (p-value of <0.01 was considered significant). Pearson correlation coefficient as a statistical method in tensile testing was utilized to correlate the fabrics porosity parameters with the fabric's elastic modulus (multiple linear regression analysis). In finite element analysis, Pearson correlation coefficient used to correlate the fabrics porosity parameters with the von Mises stress of the human body.

Knitted Structure of the Nylon Fabric
The knitting porosity of the courses and wales knitting structure was observed using the digital optical microscope as shown in Figure 1. The nylon in the knitted BSC follows a tortuous path (a route), forming symmetrical loops above and below the average path of the nylon. These loops can be easily stretched in different directions, which can make BSC more elastic; depending on the bulk of the nylon, knitting patterns, and knitting porosity, the BSC can stretch as much as 500% [24,25]. Therefore, knitting was major using for the BSC that must be elastic or stretch in response to the human body movement [26,27]. Moreover, the courses and wales knitting structure are usually more form-fitting because their elasticity allows them to follow the human body's curvature closely. More extra curvature can be easily introduced into the fabrics without seams, such as the armpit portion, the crotch portion of the clothing can be harvested with short rows or by increasing or decreasing the number of stitches [28]. The image processing system was used to calculate the BSCs porosity, which is a reliable technique in measuring porosity [22], and the following porosity results were shown in Table 1. To determine the strength of the relationship between the porosity and the elastic modulus of the knitted BSCs, the data were analyzed in two sets and plotted against each other. By the correlation analysis, Pearson correlation coefficient is −0.898 (p < 0.01). In other words, the porosity and the elastic modulus of the knitted BSCs emerge a strong negative relationship. The linear correlation coefficient is R 2 = 0.806 (p < 0.01), and the linear regression Equation (1) and model (Figure 3) can be obtained.
where P is porosity, E BSC is the estimated average elastic modulus of the BSCs, and E BSC is the elastic modulus of the BSCs.
Appl. Sci. 2020, 10, x FOR PEER REVIEW 5 of 9 The image processing system was used to calculate the BSCs porosity, which is a reliable technique in measuring porosity [22], and the following porosity results were shown in Table 1. To determine the strength of the relationship between the porosity and the elastic modulus of the knitted BSCs, the data were analyzed in two sets and plotted against each other. By the correlation analysis, Pearson correlation coefficient is −0.898 (p < 0.01). In other words, the porosity and the elastic modulus of the knitted BSCs emerge a strong negative relationship. The linear correlation coefficient is R 2 = 0.806 (p < 0.01), and the linear regression Equation (1) and model (Figure 3) can be obtained.
where P is porosity, is the estimated average elastic modulus of the BSCs, and is the elastic modulus of the BSCs.

Stress Transfer Behaviors
First, we wanted to investigate the relationship between the porosity of the knitted BSCs and the von Mises stresses of the human body during the BSC decreasing the model's abdomen circumference. Set the boundary conditions as the abdomen circumference decreasing 10 cm, and the following results as shown in Table 3. While the BSC-1 was used as the FEA model, the von Mises stresses were varied from 0.0076 MPa to 337.79 MPa (Figure 4), and most of stresses were concentrated in the crotch portion and the central abdomen portion. In the crotch portion, the BSC has less contact area with the human body. During the abdomen decreasing period, the clothing might cause more stress and pressure on the human body. Therefore, choosing the BSC in the crotch portion should be considered first, and we might choose a more soft and flexible BSC in the crotch portion of the clothing, or change the clothing design, such as the lock using, to prevent the stress concentration.

Stress Transfer Behaviors
First, we wanted to investigate the relationship between the porosity of the knitted BSCs and the von Mises stresses of the human body during the BSC decreasing the model's abdomen circumference. Set the boundary conditions as the abdomen circumference decreasing 10 cm, and the following results as shown in Table 3. While the BSC-1 was used as the FEA model, the von Mises stresses were varied from 0.0076 MPa to 337.79 MPa (Figure 4), and most of stresses were concentrated in the crotch portion and the central abdomen portion. In the crotch portion, the BSC has less contact area with the human body. During the abdomen decreasing period, the clothing might cause more stress and pressure on the human body. Therefore, choosing the BSC in the crotch portion should be considered first, and we might choose a more soft and flexible BSC in the crotch portion of the clothing, or change the clothing design, such as the lock using, to prevent the stress concentration.  After series FEA, the following results were calculated by SPSS. The von Mises stress of the human body was 7.22 ± 0.40 kPa. The relation between the porosity of the BSCs and the von Mises stress of the human body was calculated by the correlation analysis, Pearson correlation coefficient was −0.996 (p < 0.01). In other words, the porosity and the stresses on the human body emerge a strong negative relationship. The linear correlation coefficient is R 2 = 0.991 (p < 0.01), and the linear regression Equation (2) can be gained.

=
(1 − 0.43 ) where P is porosity, is the estimated stresses average of the human body, and is the stresses of the human body.
Then, increased the displacement of the abdomen circumference decreasing until the designed abdomen circumference 27 inch with BSC-1 sample. When the abdomen had decreased 12 inches After series FEA, the following results were calculated by SPSS. The von Mises stress of the human body was 7.22 ± 0.40 kPa. The relation between the porosity of the BSCs and the von Mises stress of the human body was calculated by the correlation analysis, Pearson correlation coefficient was −0.996 (p < 0.01). In other words, the porosity and the stresses on the human body emerge a strong negative relationship. The linear correlation coefficient is R 2 = 0.991 (p < 0.01), and the linear regression Equation (2) can be gained.
where P is porosity, σ body is the estimated stresses average of the human body, and σ body is the stresses of the human body. Then, increased the displacement of the abdomen circumference decreasing until the designed abdomen circumference 27 inch with BSC-1 sample. When the abdomen had decreased 12 inches (about 3-times the 10 cm displacement) (Figure 5), the von Mises stresses varied from 0.0228 MPa to 1032.5 MPa. As result, the following von Mises stresses of the BSC and the human body were growth in multiples with the displacement increased multiples. Therefore, we also used SPSS to conclude the Equation (3) which means the relationship between the porosity of the knitted BSCs (P), the displacement of the abdomen circumference decreasing (∆L), the original length of the abdomen (L 0 ), the von Mises stresses of the human body (σ body ) and the estimated von Mises stresses of the human body (σ body ). Thus, the linear correlation coefficient is R 2 = 0.991 (p < 0.01), and the linear regression Equation (3) and model ( Figure 6) can be harvested.
At the same time, the waist and buttocks circumference of the model would also be decreased, in which the waist circumference was decreased from 29 inch to 23 inch and the buttocks circumference was decreased from 41 inch to 34 inch. No matter how much the porosity of the knitted BSCs was, the same decreasing circumference results occurred.
It is well-known that functional clothing and BSC therapies are a convenient form of treatment used to revitalize the body and tender muscle tissue to bring about a reduction in muscle tension and offer pain-relief [10]. As mentioned above, it was found that there is significant difference in the relationship between the porosity of the BSCs and the stresses on the human body. The stress decreased as the porosity of BSC increasing. Hence, the stress level of the functional clothing or BSC could be adjusted to reduce the pressure of pain on the body. Currently, the latest issue on functional clothing with pain-relieving performance has been discussed using cannabidiol (CBD)-infused clothing. CBD is low tetrahydrocannabinol product derived from Cannabis sativa that has become very popular over the past few years. Patients report relief for a variety of conditions, particularly pain, without the intoxicating adverse effects of medical marijuana [29,30]. Much of the CBD is placed in strategic areas of the functional clothing so that it aligns with specific muscle groups. When wearing the clothes, the CBD releases through the dermal layer and into the pain point of the body. Accordingly, it would be desirable if the BCS could be combined with CBD without sacrificing desirable mechanical and biological properties for pain-relieving applications. Finally, more tests must be conducted to better understand the relationship between the pain-relieving property and BSCs with different porosities in the future.
At the same time, the waist and buttocks circumference of the model would also be decreased, in which the waist circumference was decreased from 29 inch to 23 inch and the buttocks circumference was decreased from 41 inch to 34 inch. No matter how much the porosity of the knitted BSCs was, the same decreasing circumference results occurred.
It is well-known that functional clothing and BSC therapies are a convenient form of treatment used to revitalize the body and tender muscle tissue to bring about a reduction in muscle tension and offer pain-relief [10]. As mentioned above, it was found that there is significant difference in the relationship between the porosity of the BSCs and the stresses on the human body. The stress decreased as the porosity of BSC increasing. Hence, the stress level of the functional clothing or BSC could be adjusted to reduce the pressure of pain on the body. Currently, the latest issue on functional clothing with pain-relieving performance has been discussed using cannabidiol (CBD)-infused clothing. CBD is low tetrahydrocannabinol product derived from Cannabis sativa that has become very popular over the past few years. Patients report relief for a variety of conditions, particularly pain, without the intoxicating adverse effects of medical marijuana [29,30]. Much of the CBD is placed in strategic areas of the functional clothing so that it aligns with specific muscle groups. When wearing the clothes, the CBD releases through the dermal layer and into the pain point of the body. Accordingly, it would be desirable if the BCS could be combined with CBD without sacrificing desirable mechanical and biological properties for pain-relieving applications. Finally, more tests must be conducted to better understand the relationship between the pain-relieving property and BSCs with different porosities in the future.

Conclusions
Through these investigations, first, we used an image processing system to analyze the porosity of the knitted BSCs and calculated the linear regression model. Then, we constructed a biomechanical model in BSCs by the FEA and found that there was significant difference in the relationship between the porosity of the BSCs and the stresses on the human body. Moreover, as the displacement increased in multiples, the stresses on the human body are grew in multiples. Therefore, the present data demonstrated a potential benefit in terms of providing biomechanical behaviors of the BSC for the human body.

Conclusions
Through these investigations, first, we used an image processing system to analyze the porosity of the knitted BSCs and calculated the linear regression model. Then, we constructed a biomechanical model in BSCs by the FEA and found that there was significant difference in the relationship between the porosity of the BSCs and the stresses on the human body. Moreover, as the displacement increased in multiples, the stresses on the human body are grew in multiples. Therefore, the present data demonstrated a potential benefit in terms of providing biomechanical behaviors of the BSC for the human body.