1 Introduction

Digital twins find applications across industries like manufacturing, construction, and healthcare [1,2,3]. Although their potential in healthcare is recognized, the complex nature of personal health information presents challenges for the active implementation of digital twins. Efforts to enhance digital twin-based product development technology can assist medical professionals in subjective and intricate manual design processes, while also reducing product development time and manufacturing costs. By applying a digital twin-based design method, the healthcare industry can automate and digitize the product design process, resulting in personalized design solutions, shorter design times, and lower production costs.

Most studies on digital twin technology in the healthcare industry have focused on data monitoring for health management and prevention purposes. Recently, a plantar pressure monitoring method using a pressure sensor system has been developed, which has been used to treat patients by identifying the pressure pattern of the foot [4, 5]. A patient monitoring system has been developed that transmits the patient's physical characteristics and body changes to a digital environment, enabling accurate diagnosis and appropriate treatment. Furthermore, it monitors, diagnoses, and predicts individual health conditions with the aim of personal health management through a cloud healthcare system based on big data and cloud computing [6, 7]. The development of monitoring and diagnostic technologies must be accompanied by the development of personalized healthcare products for continuous personal health management and prevention. Digital twin-based product development has been widely applied to manufacturing, including assembly data management for complex products such as missiles, aircraft engines, and wind turbines, or optimization of complex product assembly [8, 9]. However, the application of digital twin-based product development technology in the medical field has been limited due to the diverse and complex nature of personal health information compared to the manufacturing sector. Further improvements to digital twin-based product development technology could streamline the subjective and complex manual design process guided by medical professionals; furthermore, it has the potential to shorten product development time and reduce manufacturing costs [10]. Consequently, in the healthcare field, where personal biometric data is crucial, applying a digital twin-based design method can automate and digitize the design process of healthcare products, enabling personalized designs and reducing design time and production costs.

An insole is an insert placed inside a shoe to provide support, cushioning, and enhance foot comfort by redistributing pressure, aligning the foot, absorbing shock, and preventing foot deformities [11, 12]. As each individual's feet have unique shapes and characteristics, customized insole designs can help improve their foot health [13]. Thus, customized insole designs have gained significant attention in recent research. Taha developed a three-dimensional (3D) FEA model based on computed tomography (CT) data to determine sensor placement and accurately measure maximum pressures with minimal sensors [14]. Tang optimized stress distribution in insoles by using FEA and CT data to apply different material properties to each region [15]. Jafarzadeh designed a customized insole by optimizing its strength and shape using a 3D model constructed from CT images [16]. Nouman et al. used 3D FEA foot models to assess pad designs and material stiffness for reducing peak plantar pressure in diabetic feet with neuropathy [17]. While previous studies utilized FEA models based on CT or magnetic resonance imaging (MRI) scans of the foot to simulate insole deformation and stresses, these models are labor-intensive, time-consuming, and lack generalizability, limiting their use in insole design. Hernández-Lara et al. employed metaheuristic algorithms to optimize the thickness and fiber orientation of carbon fiber insoles for lower limb prostheses, utilizing classical lamination theory for their design. [18]. Nevertheless, pads constructed from composite materials present manufacturing challenges and difficulties in designing them to conform to the distinctive features of an individual's foot shape. Therefore, developing a simplified foot model capable of simulating insole deformation and stress across various foot shapes is necessary for an efficient and widely applicable customized insole design [19].

There are currently two methods commonly used for designing and manufacturing customized insoles [20,21,22,23]: The first is manual molding, where experts manually shape the insole based on their subjective opinions. However, this approach can lead to incorrect and inconsistent designs due to individual variances among experts. The second method involves the use of computer numerical control (CNC) or 3D printers to automatically manufacture the insoles. Jonnala et al. developed a computer-aided design (CAD) approach using fused deposition modeling and gyroid structures for designing and manufacturing customized orthotic insoles with enhanced energy absorption capabilities [24]. Rajasrivalli et al. employed topology optimization and 3D printing, achieving improved performance with reduced weight for a customized orthotic insole addressing limb length discrepancy [25]. Guiotto developed a method for producing 3D-printed orthoses using plantar pressure data collected from sensorized insoles during walking [26]. While it offers precise manufacturing, it can be expensive and less accessible for consumers.

Recently, there has been a growing interest in variable insoles, which allow attaching partial insoles to existing insoles and adjusting their position according to the shape and condition of the feet [27]. Variable insoles improve foot balance and comfort by enabling positional adjustments of the partial insole. They can be used with all types of shoes and are cost-effective for consumers. However, despite expert guidance on the location of partial insoles for variable insoles, there is currently no systematic design procedure in place. Therefore, it is necessary to develop a systematic framework for designing customized insoles that considers the material characteristics of variable insoles, based on individual foot pressure data.

This study proposes a digital twin-based design framework for customized insole design as shown in Fig. 1. This framework offers a more efficient alternative to complex 3D foot and insole models by utilizing a simplified FE insole model with a virtual sensor. The incorporation of virtual sensors enables precise adjustments of the material properties within the digital twin model. Individual foot pressure data are analyzed to optimize the positions of partial insoles, resulting in an insole design tailored to each individual's foot shape. The results of the plantar pressure measured from the foot wearing the optimized insole are evaluated to determine if they fall within the range of the AI for normal feet. This evaluation uses AI values that assess the balance of plantar pressure. The optimized insole positions obtained through the framework have the potential to significantly contribute to foot health maintenance. Overall, this study presents a valuable approach using digital twin technology to design customized insoles that enhance comfort and promote foot well-being.

Fig. 1
figure 1

Comparison between existing methods and proposed method

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2 Digital Twin-Based Design Framework

Digital twin technology aims to minimize differences between simulation models and real models by incorporating feedback from the real model. In contrast, traditional simulation primarily focuses on mimicking real models. This study employed digital twin technology to enhance the similarity between the FEA simulation model and the real model with individual's real foot pressure data. By updating the material properties of the FEA model, the digital twin technology was integrated into a design framework for optimizing personalized insole design. The digital twin-based design framework consists of two specific processes, as shown in Fig. 2: (1) The material parameter tuning process enhances the accuracy of the FEA model by establishing a connection between the physical and FEA models. (2) The advanced FEA model-based design process involves designing variable insoles, calculating errors between the physical and FEA models, and validating the final design.

Fig. 2
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Proposed digital twin-based design framework

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In the initial stage, foot pressure data are collected in static postures before and after wearing variable insoles using a plantar pressure measurement device. To simplify the analysis, the barefoot pressure data are transformed and used as an input load in the FEA model, indirectly representing the user's foot shape for analysis and design of the insole. Data preprocessing ensures consistent measurement locations of foot pressure in the collected barefoot data. The maximum pressure data after wearing the variable insole is then used to calculate the difference between the maximum pressure values of the FEA model and the actual maximum pressure values. In this process, a virtual sensor is introduced to optimize the material properties of the insole and virtual sensor (polyurethane foam) to minimize the difference between the maximum pressures of the FEA model and the actual model. Polyurethane foam, exhibiting variations in material properties based on compression deformation, allows for the derivation of suitable material properties that correspond to the user's foot shape. The detailed processes of constructing a physical model and generating an updated FEA model are described in Sects. 3 and 4, respectively.

The updated FEA model is then used to optimize the design of customized variable insoles for individuals. These variable insoles include a partial insole attached to the main insole. Proper positioning of the partial insole can support the foot's arch, distributing load and reducing foot fatigue, maintaining body balance, and minimizing postural sway [28, 29]. Therefore, the horizontal/vertical displacement of the partial insole is considered as the design variable, while the maximum foot pressure is defined as the objective function. A surrogate model for this objective function is generated through a design of experiments. The design process continues until the maximum foot pressure is minimized, determining the optimal position of the partial insoles that best suit the individual's foot. Once the optimal design is achieved, the proposed digital twin-based customized insole design framework is validated. This is done by applying the partial insole's location, as determined by the FEA model, to the physical model and comparing it with experimental data. The optimized partial insole reduces maximum pressure and ensures uniform pressure distribution and good balance across the foot. To validate its performance, the calculated AI values and balances of the feet wearing the optimized insole are compared to the normal range. This comparison confirms whether the optimized insole falls within the expected AI range, further verifying its effectiveness. Detailed results of the optimal design and verification are presented in Sect. 5.

3 Physical Model of Digital Twin

Five research participants with varying foot sizes were selected for data collection using the physical model. Their foot sizes are (1) 230 mm, (2) 240 mm, (3) 250 mm, (4) 260 mm, and (5) 260 mm. Individuals with concave feet, often experiencing discomfort and fatigue while walking and potentially facing long-term foot deformation [30], were specifically recruited for this study. This allowed for the verification of the effect of relieving pressure concentration through changes in the position of the partial insole. The study received approval from the IRB Bioethics Committee of Pusan National University, with all topics pre-agreed upon (PNU IRB/2021_147_HR).

3.1 Experiment and Data Acquisition

Plantar pressure was measured using a plantar pressure measurement device (Ghiwell, GHF-550). This device features a measuring area of 420 mm × 420 mm, equipped with 2304 force-sensitive resistor (FSR) sensors arranged in a 48 × 48 array, and displays pressure in kPa units. To minimize environmental influences, the measurement device was placed on an anti-vibration pad. Vertical and horizontal lines on the upper surface of the device were used to guide the positioning of the inside and heel of the foot, respectively.

Participants positioned their feet within the marked area and placed their arms on the armrest, facing forward to maintain a stable posture. To minimize posture deviation and measurement error, all measurements were repeated five times. The maximum standard deviations for the front, back, left, and right in these measurements were 0.9%, 0.9%, 0.8%, and 0.8% respectively, meeting the acceptable criteria of less than 3% general measurement error [31]. Due to minor variations in foot placement during the repeated measurements, the data underwent a preprocessing step to standardize the position of the measured foot pressure. As depicted in Fig. 3a, a rectangular region of interest (ROI) was identified for five plantar pressure distributions within a 48 × 48 array. The positions of these raw ROIs were then centralized, as shown in Fig. 3b. To apply the participant's foot pressure as an input load condition for the FEA model, the physical and virtual models needed to have the same array structure. However, for more accurate FEA analysis, the virtual model required a higher resolution, which was achieved in this study by increasing the resolution tenfold through linear interpolation as shown in Fig. 3c.

Fig. 3
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Foot pressure data preprocessing

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3.2 Experiments Within the Design Domain

The foot pressure distribution data obtained through the physical model consisted of barefoot data and foot pressure data after wearing a variable insole. The barefoot data served as the input load for the FEA model, while only the maximum pressure from the data collected after wearing a variable insole was utilized to construct the digital twin model. The variable insole employed in this study can be customized to an individual's foot by adjusting the position of the partial insole attached to the ready-made (main) insole. Therefore, to perform the process of upgrading the FEA model and obtaining its optimal design within the design domain, the actual maximum foot pressures for the left and right feet were measured. This was achieved by moving the position of the partial insoles to five points: mid, up, down, in, and out. These actual maximum pressures were then used to evaluate the discrepancies between the physical and FEA models, as illustrated in Fig. 2.

4 FEA Model of Digital Twin

To construct a digital twin model for the variable insole, a simplified FEA model was generated. Given the variations in polyurethane foam material properties based on individual foot shape characteristics, a design optimization process was conducted to enhance the alignment between the real and simulated models.

4.1 FEA Model

The FEA model, created in Ansys Workbench, included a 3D insole model featuring a partial insole attached to the primary insole. As shown in Fig. 4a, a virtual sensor model was introduced to calibrate the difference between the FAE model and actual model. The main insole was modeled as per the size of the actual insole according to the participant’s foot size, positioned between the virtual sensor and partial insole. Since the main and partial insoles adhere to each other, a bonded contact condition was applied to them. The main insole and the virtual sensor were set to have a frictional contact condition, with a friction coefficient of μ = 0.1. This decision was based on a study investigating the effect of insole-ground interface friction on maximum stress/strain [32]. The study was conducted in a static state, and the FEA model was analyzed through linear static analysis. Average barefoot pressure data, repeatedly measured in the physical model, were used as the input load for the FEA model. This load was applied in the direction of the z-axis on the upper surface of the insole model. The initial material properties of the insole were assumed to be representative of polyurethane foam. As shown in Fig. 4b, the maximum pressure was obtained at the location of each partial insole.

Fig. 4
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FEA models of pads based on various partial insole positions

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However, there is a lack of detailed information on the precise material properties of polyurethane foam, and these properties vary with deformation. For example, the Poisson’s ratio of polyurethane foam varies depending on the compressive strain [33]. Similarly, the elastic modulus is affected by the angle of load application, as well as the speed and density of the compression strain [34, 35]. In other words, both the elastic modulus and Poisson’s ratio change with the pressure applied by the foot. To accurately determine the insole’s material properties that vary with foot pressure, it is necessary to tune these properties based on experimental foot pressure data. Therefore, the material properties of the polyurethane foam were chosen as design variables. These properties are tuned by minimizing discrepancies between the results from the physical model and those from the FEA model, effectively creating a digital twin model.

4.2 Material Property Tuning

Four design variables were considered, including the elastic modulus and Poisson's ratio of both the insole and the virtual sensor. The response variable of interest was the maximum pressure obtained in both the physical and FEA models. The ranges for the design variables were determined based on the representative elastic modulus properties of the foam material [36, 37]. The elastic modulus of the insole was set between 0.23 and 4 MPa, while the Poisson's ratio was constrained to the range of 0 to 0.49, which represents the minimum and maximum values of the foam material. For the virtual sensor, the elastic modulus spanned from 0.23 MPa to 10 GPa, wider than the actual range, while the Poisson's ratio was set identical to that of the foam material. A feature importance analysis was conducted to identify the significant variables impacting the response. This analysis divided the design domain of each variable into 50 intervals and employed a random forest (RF) algorithm, known for its high prediction accuracy even with nonlinear data.

The results of this analysis indicated that the elastic modulus of the insole and the Poisson’s ratios of both the insole and virtual sensor (\({E}_{i}\), \({\nu }_{i}\), \({\nu }_{vs}\)) are highly important factors. However, the elastic modulus of the virtual sensor was found to have a negligible impact on the maximum foot pressure. This is attributed to the minimal deformation of the virtual sensor, rendering stiffness changes insignificant in the linear static analysis. Consequently, the elastic modulus of the insole and the Poisson ratios of the insole and virtual sensor were selected as the final design variables.

Following the selection of these variables, the objective function was defined as the sum of errors between the maximum pressures of the physical and FEA models across the five positions of the partial pads. To align the trends in maximum pressure values between the two models for each partial insole position, a Spearman coefficient value constraint of 0.9 was employed. The design optimization problem can be formulated as follows:

$$\begin{array}{*{20}l} {{\text{Find}}} \hfill & {{\mathbf{x}} = \left[ {x_{1} ,x_{2} ,x_{3} } \right]} \hfill \\ {{\text{Minimize}}} \hfill & {f({\mathbf{x}}) = \sum\limits_{i = 1}^{n} {\sqrt {\left( {P_{{\text{max,i}}}^{{{\text{physical}}}} ({\mathbf{x}}) - P_{{\text{max,i}}}^{{{\text{virtual}}}} ({\mathbf{x}})} \right)^{2} } } } \hfill \\ {\text{Subject to}} \hfill & {\left| {g({\mathbf{x}}) = 1 - \frac{{6\sum\limits_{i = 1}^{n} {\left( {R_{{\text{i}}}^{{{\text{physical}}}} ({\mathbf{x}}) - R_{{\text{i}}}^{{{\text{virtual}}}} ({\mathbf{x}})} \right)^{2} } }}{{n(n^{2} - 1)}}} \right| \ge 0.9} \hfill \\ {} \hfill & {\begin{array}{*{20}c} {x_{iL} \le x_{i} \le x_{iU} } & {{\text{for}}\,\,i = 1\sim 3} \\ \end{array} } \hfill \\ \end{array}$$
(1)

where \({x}_{1}\), \({x}_{2}\), and \({x}_{3}\) are \({E}_{i}\), \({\nu }_{i}\), \({\nu }_{vs}\), respectively. \(f(\mathbf{x})\) represents the sum of the errors between the maximum pressures of the physical and FEA models, \({P}_{max,i}^{physical}(\mathbf{x})\) and \({P}_{max,i}^{FEA}(\mathbf{x})\), evaluated at the ith position of the partial insole, where i = 1 ~ n and n = 5. g(x) denotes Spearman’s correlation coefficient between the maximum pressure values of the two models. \({R}_{i}^{physical}(\mathbf{x})\) and \({R}_{i}^{FEA}(\mathbf{x})\) are the ranks of the ith observed maximum pressure values of the physical and FEA models, respectively. The design bound for \({E}_{i}\) is set between 0.23 and 4.0 MPa, and for the Poisson’s ratio \(\nu\), it is between 0 and 0.49.

Surrogate models for both the objective and constraint functions were created using an optimal Latin hypercube design (OLHD) with 120 design of experiments (DOE) points. The Kriging model, known for its excellent predictive performance with highly nonlinear data, was employed as the surrogate model. The accuracy of the surrogate model was assessed by calculating the coefficient of determination (R2) values using an additional set of 120 test data points. The Kriging models for both functions demonstrated high accuracy, with R2 values ranging from 0.891 to 0.971. These models were then utilized to optimize the material properties of the insoles and virtual sensors. An evolutionary algorithm (EA), known for its effectiveness in global optimization, was employed for this optimization process.

Figure 5 shows the maximum pressures obtained from the FEA model before and after material tuning, which were measured from the experiments at five positions of the partial insoles. Due to the variations in foot shape, the maximum pressure values for the left and right feet can significantly differ based on the position of the partial insole. The FEA results, using the material properties before tuning, showed considerable differences from the experimental results. However, after tuning, the similarity and trend between the physical and FEA models became very consistent. The pressure measured from the experiment is directly transferred as an input load to the insole pad, resulting in the experiment and the initial virtual insole showing similar trends in maximum pressure at five locations of the partial insole. The discrepancy between the actual model and the FEA model was minimized by maintaining the trend of maximum pressure values in both models through Spearman’s rho while minimizing their mean squared errors. Consequently, the maximum pressure values using the initial virtual model become almost identical to those obtained using the tuned virtual model. Although the optimized material property values may vary significantly for each individual's foot shape, the tuned virtual model closely resembles the real model after the material tuning.

Fig. 5
figure 5

Changes in maximum pressure according to various partial insole positions before/after material property tuning

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Table 1 presents the numerical results as illustrated in Fig. 5. The optimum material properties for each participant differed from the initial values. The mean errors between the maximum pressures of the physical and FEA models were reduced, from 5.39 to 0.53%. As shown in Fig. 5, the maximum pressure values obtained with the tuned material properties closely matched the experimental data at all five positions, maintaining a consistent trend.

Table 1 Relative errors in the maximum pressure values between virtual models and real models before/after material property tuning
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After the tuning process, a comparison of the elastic modulus and Poisson’s ratio was made between the left and right feet. This was done to ensure the material's physical characteristics remained consistent despite deformation. Figure 6 illustrates that a larger elastic modulus corresponds to lower compression strain, while a smaller elastic modulus is associated with increased compression strain. This observation is in line with previous research. For instance, Widdle noted that the Poisson ratio of polyurethane foam decreases with increasing compression strain [33]. Similarly, Park confirmed through physical experiments that the elastic modulus of polyurethane foam increases with compression strain [38]. In essence, despite variations in the tuned material properties among participants, a consistent pattern was observed: the elastic modulus and Poisson’s ratio of polyurethane foam change in opposite directions in response to compression strain.

Fig. 6
figure 6

Material property tendencies of insole for left/right foot

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5 Insole Design Optimization and Results

The design optimization of the variable insole, consisting of the main and partial insoles, employed an advanced FEA model with tuned material properties. The main insoles were 4 mm thick, while the curved partial insoles were 3 mm thick, providing increased mid-section contact area and designed to match the foot shape. The objective function, estimated using the Kriging model, focused on the maximum pressure variability influenced by foot shape and the positions of the partial insoles. The goal of the optimization was to minimize maximum pressure by identifying the optimal locations for the partial insoles. In this process, the digital twin model was used to evaluate maximum pressure values at these optimized locations, and these values were then compared with experimental results. Additionally, to assess the impact on foot pressure distribution, the Arch Index (AI) and foot pressure imbalance were calculated under different scenarios. These scenarios included the bare foot, using only the main insole, and the variable insole before and after material tuning.

5.1 Insole Design Optimization

Each participant had a different foot size, necessitating individually defined design bounds based on the maximum movement position of the partial insole. Foot sizes with 230 mm, 240 mm, and 250 ~ 260 mm have design bounds of ± 28 mm, ± 29 mm, and ± 31 mm in the X-direction, respectively. The foot sizes with 230 ~ 240 mm and 250 ~ 260 mm have design bounds of ± 53 mm and ± 63 mm in the Y-direction, respectively. Based on the center of the main insole, the X- and Y-directional movements indicate the left and right moving distances, and the vertical moving distance.

The design optimization problem was defined to determine the optimal position of the partial insole in the X- and Y-directions (x and y) by minimizing the maximum pressure, Pmax.

$$\begin{array}{*{20}l} {{\text{Find}}} \hfill & {x,y} \hfill \\ {{\text{Minimize}}} \hfill & {f(x,y) = P_{\max } (x,y)} \hfill \\ {\text{Subject to}} \hfill & {x_{L} \le x \le x_{U} } \hfill \\ {} \hfill & {y_{L} \le y \le y_{U} } \hfill \\ \end{array}$$
(2)

The design bounds for the two design variables are listed in Table 1. The initial design point was (0,0), which was the center of the main insole. OLHD was used to generate the response surface model for the objective function. The total number of DOE points was 80. A Kriging model was generated to predict the maximum pressure and verified using additional 80 test data. Using the actual values, R2 values for all participants are ranged from 0.866 ~ 0.903. The EA was used to find the optimum design points.

Table 2 shows the maximum pressure values obtained from FEA models and experiments at both the initial and optimal design points, before and after tuning the material properties. As shown in Fig. 5, the results from tuning the material properties at the initial design point are very similar to the experimental results, indicating that the FEA model well represents the experimental model. However, when optimizing the position of the partial insole before tuning the material properties, the likelihood of obtaining incorrect optimal design points is high. This is evidenced by the significant differences between the CAE results at the initial optimum point (Initial CAE) and the experimental values (Exp.). As illustrated in Table 2, the maximum pressure values at the optimum points before tuning show a slight reduction compared to those at the initial design points. However, for the fifth participant's left foot, the maximum pressure value is higher than that at the initial point. In contrast, optimizing the position of the partial insole after tuning the material properties leads to increased accuracy in FEA and the attainment of an optimal design point where the maximum pressure is genuinely minimized. For instance, if the average maximum pressure at the initial design point is 122.98 kPa, it decreases by 2.39% to 120.04 kPa at the optimum design point without material parameter tuning. In contrast, with material parameter tuning, this value further decreases by 5.84% to 115.8 kPa at the optimum design point.

Table 2 Initial and optimum positions of partial pads before/after material parameter turning
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Figure 7 displays the positions of the partial insoles at both initial and optimum points, before and after material tuning. The FEA results are color-coded, with green indicating results before tuning and red for those after. These results show that the optimum positions of the partial insole post-tuning are significantly different from those before tuning, for both the left and right feet. This indicates that material tuning substantially impacts the optimal design results. Figure 8 presents the CAE results of foot pressures for all participants. Initially, the middle section of the foot showed minimal pressure distribution. However, wearing a flat (main) insole increased the contact area in this middle section. Positioning the partial insole at the center further enhanced the mid-section area, leading to a reduction in maximum pressure. The optimized insole, when used, showed decreased maximum pressure, particularly in areas where pressure was concentrated. This decrease in maximum pressure led to a wider contact area in the mid-section, resulting in a more even distribution of pressure across the foot compared to other scenarios. Although the difference in pressure values before and after optimization was not substantial, repeated pressure concentrations during walking may contribute to foot deformation. The use of the optimized insole can therefore help in reducing foot fatigue.

Fig. 7
figure 7

Optimized positional changes of the partial insoles before/after material properties tuning

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Fig. 8
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Foot pressure distribution before/after optimized partial insole attachment

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5.2 Arch Index and Balances

To evaluate the effectiveness of the optimized insole in improving foot imbalance, the AI was calculated for three conditions: barefoot, with only the main insole, and with both the initial and optimized insoles for each participant. The foot's length, spanning from the heel to the forefoot, was divided into three equal parts: the forefoot (A), midfoot (B), and heel (C), as depicted in Fig. 9. AI was determined by dividing the area of the midfoot region by the total footprint area. An AI value less than 21% indicates a cavus foot, while a value exceeding 28% suggests a flat foot. The formula for calculating AI is as follows:

$$AI = \frac{B}{A + B + C}$$
(3)
Fig. 9
figure 9

Arch index including reference lines for forefoot, midfoot, and heel foot regions

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Table 3 and Fig. 10 show the AI values calculated for three scenarios: (1) barefoot, (2) wearing only the main insoles, and (3) wearing the initial and optimum designed insoles of the five participants. The AI values for the left and right feet are labeled as AIL and AIR, respectively. Since the experiment involved participants with concave feet, the barefoot AI was less than 0.21, which is below the normal range's lower bound. The study compared results for the following conditions: (1) wearing the main insoles without partial insoles, (2) attaching a partial to the main insole at the initial design point (x = y = 0), and (3) wearing insoles optimized for each participant. When the participants were not wearing the insoles, the foot pressures mainly concentrated in the forefoot area (A) and rearfoot area (C) regions, as shown in Fig. 10, which have very low AI values. Wearing the main insoles led to an increase in AI, yet the values remained outside the normal range, as marked by the shadow region in Fig. 10. Placing the partial insoles at the centers dispersed pressures to the midfoot area, moving the AI values closer to normal.

Table 3 AI results before/after optimization of partial insole positioning
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Fig. 10
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Changes in AI values based on insole attachment conditions

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Even though all participants had concave feet, the specific points where maximum pressures were generated varied due to the differences in foot shapes. As a result, there were instances where wearing partial insoles centered did not bring the AI values into the normal range. In contrast, when the position of the partial insole was optimized, the maximum pressures at these optimal locations were significantly reduced. Consequently, the AI values fell within the normal condition regions. Therefore, appropriately optimizing the position of the partial insole to match individual foot characteristics, using the digital twin model, can lead to improvements in AI. This optimization potentially reduces the concentrated load, thereby decreasing foot fatigue.

6 Conclusion

In this study, a digital twin model was developed to align FEA and real models through material property tuning, providing a novel framework for designing customized insoles. This study achieved three key objectives that distinguish it from previous research.

First, a simplified FEA model was proposed by incorporating a virtual sensor and utilizing measured foot pressures with and without wearing variable insoles. This approach enabled a more accurate representation of real conditions in the FEA model, without the need for complex foot and insole models.

Second, material properties were tuned using approximate models and an optimization method to account for the variable nature of the material properties and minimized discrepancies between the real and FEA models. After tuning the material properties, the average error between the physical model and the CAE model was reduced from 5.39 to 0.53% for five participants’ maximum foot pressures. This material property tuning allowed for accurate predictions of properties suitable for individual foot deformations, thereby enhancing the accuracy of the FEA model.

Third, the digital twin model was used to optimize the position of the partial insole for each individual's foot. Compared to the average maximum pressure at the initial position of the partial insole, the average maximum pressure decreased by 2.39% without material property tuning and further reduced by 5.84% after tuning. For five participants with cavus feet, the AI values fell within the normal range due to the optimization of the partial insole position, compared to conditions of being barefoot, using a flat insole, or the initial insole.

Overall, the proposed design framework offers a valuable tool for insole design, enhancing foot health and presenting broad applicability across various products. Future plans to validate this framework include installing plantar pressure measurement devices in shoe stores or hospitals, collecting extensive foot pressure data, and evaluating the effectiveness of the proposed approach.