Introduction

The application of parametric design and additive manufacturing in footwear production enables the creation of forms, lattice structures, and material textures. The pressure-relief performance and conformability of auxetic lattice structures in shoe soles contribute to enhanced footwear comfort 1. The Thiessen polygon, also known as the Voronoi diagram, appears frequently in nature, such as in dragonfly wings and gourd veins, representing a morphological logic rule based on natural evolution 2. Research indicates that porosity increases with the scaling factor, showing an approximately linear relationship. Materials made using this lattice structure exhibit a negative Poisson’s ratio, expanding laterally under tension and densifying under compression.

3D-printed footwear reduces material waste, enhances structural stability, and improves comfort while also meeting consumers’ personalized needs. A variety of materials suitable for this manufacturing technology, including thermoplastic polyurethane (TPU), widely used in the footwear industry, are increasingly being utilized. 3D-printed TPU shoe soles are known for their wear resistance and deformation stability. Zhou et al. 3 investigated the biomechanical changes and parameter differences between regular shoes and biomimetic shoes during the running stance phase. The results highlighted the effective foot stability provided by biomimetic shoes, offering valuable insights for this study. Previous studies introduced an innovative midsole design method utilizing auxetic structures to enhance comfort and performance 4. However, 3D-printed midsole structures feature parallel upper and lower surfaces, which are inconsistent with the typical curved shapes of conventional midsoles and do not conform well to the foot’s surface.

Comfort is a crucial element of midsole design, as any discomfort can change a runner’s biomechanics, affect balance, and increase the risk of injury5. There are differences in plantar pressure, pressure trajectory center, 3D ankle kinematics, and gait dynamics when wearing different printed midsoles6. However, some studies have shown that 3D-printed shoes do not improve running economy7. These controversies indicate that while considering the impact of peak pressure and force when addressing potential injuries like stress fractures is important, it is also crucial to consider the force–time integral, as it measures how long an area endures stress8. A previous study focused on evaluating the cushioning performance of different midsoles19. This study aims to quantitatively analyze the effects of various 3D-printed midsoles on balance and stability throughout the gait cycle, which is crucial for developing footwear that minimizes injury risks in athletes.

Wearing these shoe midsoles shows differences in plantar pressure, pressure trajectory center, 3D ankle kinematics, and gait dynamics. While peak pressure and force values are important for assessing potential injuries like stress fractures, the force–time integral is also crucial as it indicates how long a region experiences stress. Comfort is critical in midsole design, as any discomfort can alter biomechanics, affect balance, and increase injury risk 8. A previous study evaluated the cushioning performance of different midfoot soles 19. This study aims to investigate how different 3D-printed midsoles impact balance and stability during the entire gait cycle, which is key to preventing sports injuries. Especially, the gait ratio is a key metric for analyzing gait characteristics, primarily used to evaluate pressure distribution and performance across different phases or regions of gait. Gait ratio reflects the uniformity of pressure or time distribution across different regions or phases. The gait ratio, as an indicator of gait analysis, is closely related to foot pressure measurements. By calculating the pressure ratio of different areas, it can quantify the balance and stability of gait, thereby providing data support for foot health and performance optimization in different movement states.

In this study, we propose three different lattice patterns designed with the same wall thickness and fused deposition modeling (FDM) 3D printing material. The midsoles are positioned according to the foot to create specific designs for evaluating the efficiency of viscoelastic lattice designs in stress distribution. The contributions of this research are as follows:

  1. (a)

    Introducing three custom 3D-printed Thiessen polygon structures (TS), considering the material properties.

  2. (b)

    Proposing a method for assessing midsole balance using the gait ratio and designing 3D-printed midsoles based on activity type.

  3. (c)

    Using a single material (TPU) to minimize cost and material usage.

The focus of this study is optimizing midsole stability and exploring how different midsole structures adapt to various activities. This innovative approach not only addresses gaps in previous research but also lays the foundation for a comprehensive exploration of how advanced midsole designs can revolutionize the stability performance of running shoes. Based on biomechanical principles, it is hypothesized that different 3D-printed biomimetic midsole structures influence gait phases and gait ratios. H1: Different midsole structures (1TS, 2TS, 3TS) have a significant effect on the gait ratio. H2: During running, the gait ratio of 1TS differs significantly from barefoot.

In addition, in this paper, gait ratios play a key role, mainly in the following aspects. Specifically, gait ratios reveal different dynamic patterns of the foot during walking by comparing the pressure differences between the medial and lateral parts of the foot, especially regarding rearfoot, midfoot, and forefoot balance. The study uses gait ratio analysis to determine how to assess an individual’s injury risk under dynamic conditions, rather than traditional static methods. Gait ratio analysis allows for accurate assessment of support needs in different foot areas, enabling the customization of more suitable orthotic support for individuals. By using plantar pressure test software to compare gait ratio graphs of different footwear, the study evaluates the supportiveness of the shoes. This allows for the selection of footwear that provides optimal support, helping to reduce the occurrence of sports injuries.

Results and discussion

Compressive properties of five types of cube samples applied biomimetic structures.

Figure 1 illustrates the compression displacement-compression stress (strain–stress, S–S) curves of five types of 3D-printed biomimetic cubes, while Table 1 summarizes key mechanical properties, including the initial compressive modulus, compressive strength at 25% and 50% strain, and compressive toughness of each sample.

Fig. 1
figure 1

Compressive S–S curve of five types of cubes applied biomimetic structure.

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Table 1 Compressive properties of five types of cube samples.
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From the S–S curves, it was evident that among the five biomimetic cubes, honeycomb (HN) and horseshoe (HS) exhibited the highest rigidity, while 1TS, 2TS, and 3TS demonstrate softer and more elastic characteristics. Specifically, the HN and HS samples show a significant increase in stress, exceeding 5 kN at approximately 35% displacement. Conversely, tyson polygon 1 (1TS) exhibited a yield point at approximately 10% strain, while tyson polygon 2 (2TS) and tyson polygon 3 (3TS) displayed yield points at approximately 20% strain, confirming their elastic structural properties. Despite having internal voids, the HN and HS samples maintained high compressive strength due to the uniform stacking of repeating unit structures.

The compressive properties of the samples are as follows. For the initial compressive modulus, HN and HS displayed high values of 7.59 ± 0.66 MPa and 6.73 ± 0.59 MPa, respectively, while 1TS, 2TS, and 3TS exhibited lower values of 1.66 ± 0.04 MPa, 1.04 ± 0.20 MPa, and 2.69 ± 0.04 MPa, respectively. At 30% strain, the compressive strength of HN and HS was 1.76 ± 0.02 MPa and 1.76 ± 0.13 MPa, significantly higher than that of 1TS (0.12 ± 0.03 MPa), 2TS (0.18 ± 0.03 MPa), and 3TS (0.47 ± 0.05 MPa), showing more than a fourfold difference. At 50% strain, the compressive strength of 1TS, 2TS, and 3TS was 0.19 ± 0.01 MPa, 0.28 ± 0.05 MPa, and 0.65 ± 0.01 MPa, respectively. The compressive toughness values were 41.08 ± 4.33 J for HN, 40.92 ± 0.82 J for HS, 10.85 ± 0.43 J for 1TS, 14.20 ± 2.58 J for 2TS, and 34.42 ± 0.47 J for 3TS.

These findings confirmed that the compressive properties vary significantly depending on the design of the biomimetic patterns. When applied to midsoles, HN and HS were deemed unsuitable due to their excessive rigidity, which compromises cushioning functionality. In contrast, 1TS, 2TS, and 3TS, with their porous structures, provide sufficient internal voids to facilitate compression. The irregularly connected struts of these designs not only offer effective foot support but also contribute to enhanced elasticity and cushioning. Based on these properties, the 1TS, 2TS, and 3TS designs were incorporated into midsoles, manufactured using 3D printing, and subsequently evaluated through gait ratio measurements.

Gait ratio analysis of midsole foot pressure for three different structures

Measurements of plantar pressure provide an indication of foot and ankle functions during gait and other functional activities, because the foot and ankle provide both the necessary support and flexibility for weight bearing and weight shifting while performing these activities9. The use of force platforms is the method most commonly used to assess the interaction of the foot and supporting surface. The gait ratios analysis provides specific calculations about different aspects of the roll off. The gait ratios are calculated by analyzing the progression of pressure under each of the zones of the feet and by comparing the medial part of the foot with its lateral part. As the correlation between static foot posture parameters and dynamics is not confirmed, the aim of this study was to determine relevant parameters to describe the risk on injury as well as the optimal orthotic support for an individual based on dynamic plantar pressure measurements (in contrast to the conventional static techniques used). This study focuses on dynamic foot pressure ratios during the stance phase: rearfoot balance (0–15%), midfoot balance (25–40%), and forefoot balance (50–80%). Footscan 9 software compares gait ratio graphs across footwear designs to assess supportiveness. In this study, the gait ratio was utilized to test Hypothesis 1 by comparing the performance of different midsole designs.

Figure 2 illustrates the gait ratio results for different motions, focusing on heel rotation (HR), foot balance (FB), and forefoot balance (FFB). The results for each motion and midsole design are as follows. For HR, during walking, 1TS decreased by 3.32% compared to 2TS and by 4.87% compared to 3TS. Additionally, 2TS decreased by 1.54% compared to 3TS. The statistical analysis showed significant differences with F = 195.6 and P < 0.0001, and the order of performance was 2TS > 1TS > 3TS. During running, 1TS showed a 2.21% decrease compared to 2TS and a 0.91% decrease compared to 3TS, while 2TS was 1.30% higher than 3TS. These differences were statistically significant, with F = 47.57 and P < 0.0001, and the order of performance was 1TS > 3TS > 2TS. During jumping, 1TS showed a 1.23% decrease compared to 2TS and a 0.63% decrease compared to 3TS, while 2TS was 0.59% higher than 3TS. These results were also statistically significant, with F = 39.43 and P < 0.0001, and the performance order was 1TS > 3TS > 2TS. For FB, during walking, 1TS decreased by 3.15% compared to 2TS and by 2.70% compared to 3TS. These differences were statistically significant, with F = 33.74 and P < 0.0001, and the order of performance was 2TS > 3TS > 1TS. During running, 1TS was 7.53% lower than 2TS, while 2TS was 6.71% higher than 3TS. These differences were significant, with F = 158.7 and P < 0.0001, and the order of performance was 1TS > 3TS > 2TS. During jumping, 1TS showed a 5.02% decrease compared to 2TS and a 2.21% decrease compared to 3TS, while 2TS was 2.81% higher than 3TS. The differences were significant, with F = 88.82 and P < 0.0001, and the performance order was 1TS > 3TS > 2TS. For FFB, during walking, 1TS decreased by 0.13% compared to 2TS and increased by 1.66% compared to 3TS, while 2TS decreased by 1.80% compared to 3TS. These differences were statistically significant, with F = 18.17 and P < 0.0001, and the order of performance was 1TS > 2TS > 3TS. During running, 1TS was 3.66% lower than 2TS, while 2TS was 4.67% higher than 3TS. The analysis showed significant differences, with F = 88.06 and P < 0.0001, and the performance order was 3TS > 1TS > 2TS. During jumping, 1TS showed a 4.08% decrease compared to 2TS and a 1.41% decrease compared to 3TS, while 2TS was 2.66% higher than 3TS. These differences were significant, with F = 108.7 and P < 0.0001, and the order of performance was 1TS > 3TS > 2TS.

Fig. 2
figure 2

Gait ratio of three types of midsole applied biomimetic structure during different dynamic motions (walking, running, jumping). (a) Heel rotation, (b) Foot balance ratio, and (c) Forefoot balance ratio.

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This study compared the performance of three different midsoles, namely 1TS, 2TS, and 3TS, across walking, running, and jumping motions. The results revealed significant differences in their effects on HR, FB, and FFB. The midsole 1TS consistently outperformed the other two designs, 2TS and 3TS, in controlling HR, maintaining foot balance, and minimizing forefoot load across all types of motion. In contrast, 2TS demonstrated the weakest performance, particularly in foot balance and forefoot load distribution. The midsole 3TS showed intermediate results, performing better than 2TS but worse than 1TS. In summary, while 2TS shows a more even medial–lateral pressure distribution during walking and lower heel pronation-supination compared to other midsoles, 1TS performs better during running and jumping with reduced foot inversion-eversion and closer medial–lateral pressure balance. Specifically, 1TS offered better stability and balance control, with reductions in foot balance of 7.53% compared to 2TS during running and 5.02% during jumping. The results for forefoot load distribution varied depending on the type of motion, with 1TS excelling during walking and 2TS performing better during jumping. Studies on footwear design, including those focusing on futsal and running shoes11, highlight the importance of midsole composition, arch support, and shoe shape in influencing plantar pressure distribution during movement. These findings align with the current study, where 1TS consistently outperformed the other midsoles in controlling heel rotation, maintaining foot balance, and distributing forefoot load, thereby supporting its superior stability and load management capabilities12.

Figure 3 illustrates the gait ratio results for different motions, highlighting the performance of three midsoles (1TS, 2TS, 3TS) in terms of hallux stiffness (HS), medial forefoot balance (MFB), and meta loading (ML). The detailed findings are as follows. For HS (Fig. 3a), during walking, 1TS decreased by 0.72% compared to 2TS and by 0.45% compared to 3TS, while 2TS decreased by 0.27% compared to 3TS. The differences were not statistically significant (F = 0.73, P = 0.48), and the order of performance was 2TS > 1TS > 3TS. During running, 1TS was 2.35% higher than 2TS, and 2TS was 2.31% lower than 3TS. Although the differences were statistically significant (F = 4.23, P < 0.01), there was no significant difference between 1 and 3TS (P = 0.99). The order of performance was 1TS > 3TS > 2TS. During jumping, 1TS was 1.12% higher than 2TS and 0.21% higher than 3TS, while 2TS was 0.90% lower than 3TS. The differences were not significant (F = 3.00, P = 0.0501), and the order was 1TS > 3TS > 2TS. For MFB (Fig. 3b), during walking, 1TS decreased by 0.008% compared to 2TS and by 0.46% compared to 3TS. The differences were not statistically significant (F = 1.56, P = 0.21), and the order of performance was 3TS > 1TS > 2TS. During running, 1TS was 1.20% higher than 2TS, while 2TS was 0.27% higher than 3TS but also 0.92% lower than 3TS. These differences were not significant (F = 2.99, P = 0.53), and the order was 1TS > 3TS > 2TS. During jumping, 1TS was 0.58% higher than 2TS, and 2TS was 0.60% higher than 3TS. Although the differences were not statistically significant (F = 5.79, P = 0.23), 1TS showed a 1.19% improvement over 3TS (F = 2.99, P = 0.002). The order of performance was 1TS > 2TS > 3TS. For ML (Fig. 3c), during walking, 1TS decreased by 2.01% compared to 2TS and by 2.81% compared to 3TS, while 2TS decreased by 0.78% compared to 3TS. The differences were statistically significant for 1TS and 3TS (F = 15.33, P < 0.0001) but not for 2TS and 3TS (P = 0.29). The order of performance was 3TS > 2TS > 1TS. During running, 1TS was 0.14% higher than 2TS and 0.73% higher than 3TS, while 2TS was 0.59% higher than 3TS. The differences were not statistically significant (F = 0.606, P = 0.54), and the order was 1TS > 3TS > 2TS. During jumping, 1TS was 1.40% lower than 2TS and 2.05% higher than 3TS. These differences were statistically significant for 1TS and 2TS (F = 8.08, P = 0.01) and for 1TS and 3TS (F = 8.08, P = 0.0003), but not for 2TS and 3TS (P = 0.41). The order of performance was 2TS > 1TS > 3TS.

Fig. 3
figure 3

Gait ratio of three types of midsole applied biomimetic structure during different dynamic motions (walking, running, jumping). (a) Hallux stiffness ratio, (b) Medial forefoot balance ratio, and (c) Meta loading ratio.

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This study compared the performance of three different midsoles—1TS, 2TS, and 3TS—across walking, running, and jumping, revealing significant differences in HS, MFB, and ML. During walking, the impact on HS was minimal, with 2TS showing the highest stiffness. In running, 1TS exhibited the highest stiffness, contributing to better control. For jumping, 1TS outperformed the other midsoles, though the differences were not statistically significant. Regarding MFB, 3TS demonstrated the highest load during walking, while 1TS performed better during running and jumping, offering improved load distribution. For ML, 3TS showed the highest values during walking, indicating better shock absorption, whereas 1TS was slightly better during running. During jumping, 2TS displayed the highest ML, suggesting enhanced cushioning.

In summary, 1TS consistently performed well in terms of stability and control, making it ideal for dynamic movements. It demonstrated superior HS (P < 0.01) and MFB (F = 2.99, P = 0.53) in most conditions. However, 3TS provided better shock absorption during walking, with a higher ML of 2.81% compared to 1TS (F = 15.33, P < 0.0001). In contrast, 2TS generally underperformed, particularly during jumping, where its higher Meta Loading (F = 8.08, P = 0.01) resulted in uneven load distribution.

Midsole design played a critical role in dynamic movements, especially with harder materials or a forefoot plate to enhance load distribution. Sun et al. 13 indicate that stiffer midsoles, like 3TS, improve forefoot load distribution during walking, reducing energy loss and enhancing stability. Similarly, the rigidity of 1TS contributes to reduced energy waste during running and jumping, supporting its superior stability and control. These findings align with Honert et al.14, which highlights the role of midsole stiffness in minimizing energy loss at foot joints and improving overall performance in dynamic activities like running and jumping.

Differences midsole of different structures gait ratio and gait phase during running

The three metatarsals exhibited an upward orientation during the first 20% of the stance phase, continuing until full foot contact was achieved15. This provides a theoretical basis for observing the gait ratio during the first 20% of the gait cycle in running posture in this study. The gait ratio was analyzed at 200 ms, and the results are presented in Fig. 4a.

Fig. 4
figure 4

(a) Differences gait ratios (heel rotation, foot balance, forefoot balance, hallux stiffness, medial forefoot balance, and meta loading) of three types of midsole applied biomimetic structure during running motion. (b) Gait phase comparison of three types of midsole applied biomimetic structure during running motion.

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The results are as follows. In the analysis of HR, the peak occurred at 100 ms, and a statistically significant difference was observed between the 1TS and 2TS midsoles. The results showed that 1TS outperformed 2TS in this metric, with P = 0.008 and R = 0.2041. For FB, the peak also occurred at 100 ms, but no statistically significant difference was found between the 1TS and 3TS midsoles. This suggests that these two midsoles perform similarly in maintaining foot balance at the observed peak. In the analysis of FFB, a significant difference was observed between the 1TS and 2TS midsoles, with P = 0.01 and R = 0.19, indicating that 1TS provides better forefoot stability compared to 2TS. However, about ratio of HS, MFB and ML, no significant findings were reported, suggesting that the differences in midsole performance for these specific conditions were not statistically meaningful.

The overall results indicated that the 1TS midsole performs better than the 2TS midsole in both heel balance and forefoot balance, which enhances stability during running. In contrast, the 2TS midsole shows noticeable pronation during forefoot landing, which negatively impacts stability. The study also reveals that peak gait ratios typically occur within the first 100–200 ms of running. These findings demonstrate that different midsole structures—specifically 1TS, 2TS, and 3TS—have a significant impact on foot balance and stability during running. Among these, the 1TS structure provides the best performance in heel and forefoot balance, offering superior stability. On the other hand, the 2TS structure exhibits increased pronation during forefoot landing, which reduces overall stability.

Figure 4b illustrates the gait phases during running under different footwear conditions. The single foot timing analysis presents the distinct events and phases occurring during the foot roll-off process for the selected right foot. These gait phases outline the sequential events and stages during the rolling motion of the right foot while running. For each phase, the duration is provided in both milliseconds (ms) and percentage (%). The following gait phases are identified. About initial contact phase (ICP), the duration between the initial foot contact event and the initial metatarsal contact event. Regarding forefoot contact phase (FFCP), the duration between the initial metatarsal contact event and the initial forefoot contact event. In case of foot flat phase (FFP), the duration between the initial forefoot contact event (the moment when all metatarsal zones are visible) and the heel off event (the moment when no pressure is detected under the heel). About forefoot push-off phase (FFOP), the duration between the heel off event and the last foot contact event (the moment when no pressure is detected under any foot zone). This structured analysis allows for a detailed comparison of gait phases across different footwear conditions.

The ICP and FFCP phases, which are the weight-bearing phases of the gait cycle, showed the shortest durations in barefoot conditions. Both 1TS and 2TS midsoles exhibited significantly shorter durations in these phases compared to 3TS (F = 1.38, P = 0.02). In the FFP phase, the 1TS and 2TS midsole conditions showed significantly longer durations compared to barefoot (F = 5.98, P = 0.001). Changes in midsole structures were found to significantly affect the gait phases, particularly in the FFCP and FFP phases. As midsole hardness increased, female runners experienced longer forefoot landing phases, while the duration of the full-foot landing phase decreased. The longer FFCP phase observed in 3TS compared to 1TS and 2TS may be attributed to the harder midsole material, which reduces foot plantar flexion during walking. Conversely, the increased duration of the FFP in the 1TS midsole suggests enhanced stability during the support phase. This increased stability in the 1TS midsole helps to distribute pressure more evenly across the foot, thereby minimizing the risk of localized pressure overload and reducing the potential for injury. These findings are consistent with Hamedi et al. 16, which underscores the significant influence of midsole hardness on running gait, particularly during the forefoot and full-foot landing phases. Harder midsoles can alter foot flexion, impacting gait stability and efficiency. Additionally, prolonged FFOP time may indicate reduced gait efficiency, suggesting insufficient effectiveness during the support or propulsion phases of the gait cycle.

Comparative analysis of gait ratios of barefoot to midsoles

In this study, we investigated the effects of different test conditions—1TS, 2TS, 3TS, and barefoot (BF)—on gait ratio and stability. The comparison between BF and midsoles was used to test Hypothesis 2. Figure 5 presents the gait ratios of the foot during running, providing a comparative analysis of the gait ratios between BF and the various midsole conditions.

Fig. 5
figure 5

Differences in gait ratios between barefoot and midsole-supported running (a) heel rotation, (b) foot balance, (c) forefoot balance, (d) hallux stiffness, (e) medial forefoot balance, and (f) meta loading.

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The results are as follows. In the analysis of HR (Fig. 5a), the 1TS condition exhibited a significantly lower value compared to the BF condition, with a reduction of 1.57%. This difference was statistically significant, with p < 0.0001 and F = 11.6. Conversely, the 2TS condition showed a slight increase of 0.15% compared to BF; however, this difference was not statistically significant (p = 0.96, F = 11.6). Based on the analysis of stability, the performance order for HR was ranked as follows: 1TS > 3TS > BF > 2TS. In terms of FB (Fig. 5b), the 1TS condition demonstrated a significantly lower value compared to BF, with a reduction of 3.46%. This result was statistically significant, with p < 0.0001 and F = 32.81. In contrast, the 2TS condition showed a minimal increase of 0.11% compared to BF, but this difference was not statistically significant (p = 0.99, F = 32.81). The ranking of stability performance for foot balance was determined to be 1TS > 3TS > 2TS > BF. For FFB (Fig. 5c), the 1TS condition exhibited a significant reduction of 2.02% compared to BF (p < 0.0001, F = 20.68). Similarly, the 3TS condition also showed a significant reduction compared to BF, with a decrease of 2.55% (p < 0.0001, F = 20.68). In contrast, the 2TS condition displayed an increase of 0.83% compared to BF, but this difference was not statistically significant (p = 0.13, F = 20.68). The ranking of stability for FFB was found to be 3TS > 1TS > BF > 2TS. In the evaluation of HS (Fig. 5d), the 1TS condition showed a significant reduction of 2.16% compared to BF, with the difference being statistically significant (p < 0.0001, F = 46.73). Conversely, the 2TS condition displayed a significant increase of 2.21% compared to BF (p < 0.0001, F = 46.73). The 3TS condition demonstrated a significant reduction of 1.92% compared to BF (p < 0.0001, F = 20.68). The stability ranking for HS was as follows: 1TS > 3TS > BF > 2TS. In the analysis of MFB (Fig. 5e), the 1TS condition showed a significant reduction of 0.66% compared to BF (p < 0.0001, F = 10.02). Similarly, the 3TS condition exhibited a significant reduction of 0.95% compared to BF (p < 0.0001, F = 10.02). On the other hand, the 2TS condition showed a significant increase of 0.61% compared to BF (p < 0.0001, F = 10.02). The ranking of stability performance for MFB was determined to be 1TS > 3TS > BF > 2TS. In the evaluation of ML (Fig. 5f), the 1TS condition exhibited a significant reduction of 1.72% compared to BF (p < 0.0001, F = 33.29). Similarly, the 3TS condition showed a significant reduction of 1.64% compared to BF (p < 0.0001, F = 33.29). Conversely, the 2TS condition displayed a significant increase of 1.27% compared to BF (p < 0.0001, F = 33.29). The stability ranking for ML was found to be 1TS > 3TS > BF > 2TS.

1TS showed superior stability in HR, FB, FFB, HS, MFB, and ML, with significant reductions compared to BF, indicating better gait stability and pressure distribution. 2TS showed minor, mostly insignificant changes, with poorer performance in some metrics. 3TS performed better than BF and 2TS in specific areas but was slightly inferior to 1TS overall. In conclusion, 1TS is the optimal midsole for enhancing gait stability and pressure uniformity.

As shown in Fig. 5a, the analysis of HR revealed that the 1TS midsole was more effective than BF in controlling HR, with superior performance in providing better rotational control. The 2TS midsole, on the other hand, exhibited a slightly higher HR than BF, suggesting that 2TS and BF had similar effectiveness in controlling HR. Among the tested conditions, the 1TS midsole offered the highest stability, providing more balanced foot support during the running support phase. In contrast, the 2TS midsole demonstrated the lowest stability, indicating a need for further optimization to enhance its performance under dynamic conditions. The analysis of FB in Fig. 5b showed that the 1TS midsole performed exceptionally well, offering significant advantages in controlling foot tilt and enhancing overall stability. This superior performance makes the 1TS midsole particularly suitable for activities requiring robust foot support and balance. In contrast, there was no statistically significant difference in FB between the 2TS midsole and BF. However, the 2TS midsole slightly outperformed BF in terms of stability. Therefore, the 1TS midsole is the most suitable option for scenarios requiring enhanced foot balance and support, while the 2TS midsole may require further optimization to improve its balance capabilities. The analysis of FFB in Fig. 5c indicated that the 1TS and 3TS midsoles exhibited similar performance in controlling forefoot support and stability. Although the 3TS midsole slightly outperformed the 1TS midsole in terms of balance, the difference was not statistically significant. From a design perspective, 1TS and 3TS performed similarly in forefoot support, with 3TS excelling in stability and 1TS demonstrating greater efficiency in stride frequency. For example, as shown in Fig. 2c, the support phase of running was completed in 0.5 s, suggesting that the 1TS midsole was more suitable for athletic footwear. As shown in Fig. 5d, in the evaluation of HS, the 1TS midsole reduced stiffness by 2.16%, while the 3TS midsole reduced stiffness by 1.92%. In contrast, the 2TS midsole increased stiffness by 2.21%. Moderate increases in stiffness, as observed in 2TS, can improve support, but excessive stiffness may limit flexibility. Stability rankings showed that the 1TS midsole was the most stable, followed by 3TS, BF, and finally 2TS. These findings suggested that moderate reductions in stiffness, such as those seen in 1TS and 3TS, enhance balance, while excessive stiffness, as in 2TS, can reduce overall stability. This had important implications for improving foot stability and flexibility. In the analysis of MFB in Fig. 5e, the 1TS midsole reduced stiffness by 0.66%, while the 3TS midsole reduced stiffness by 0.95%, both contributing to more even load distribution and improved flexibility. In contrast, the 2TS midsole increased stiffness by 0.61%, which may lead to a more concentrated load on the medial forefoot. While this could enhance support, it may also limit flexibility and reduce overall stability. The softer characteristics of the 1TS midsole help disperse pressure effectively, offering higher stability even during light-load gait. The analysis of ML in Fig. 5f showed that the 1TS midsole reduced metatarsal load by 1.72%, while the 3TS midsole showed a reduction of 1.64%, compared to BF. In contrast, the 2TS midsole increased metatarsal load by 1.27%. These changes were statistically significant (p < 0.0001, F = 33.29). Stability rankings indicated that the 1TS midsole was the most stable, followed by 3TS, BF, and 2TS. The lower load ratios observed in 1TS and 3TS suggest that these midsoles more effectively control pressure distribution in the metatarsal area. In particular, the 1TS midsole significantly reduces metatarsal load, demonstrating optimal stability and potentially minimizing discomfort and injury risk from pressure during running. Conversely, the higher metatarsal load observed in 2TS indicates less effective load control in this area.

According to Cai et al.7, differences in the height between the inner and outer forefoot areas of running shoes can significantly influence lower limb joint dynamics during the standing phase of the gait cycle. A slightly higher outer forefoot has been shown to reduce the risk of knee injuries and improve gait performance, particularly for individuals with excessive inward rotation. In this study, the 2TS midsole exhibited significant outward tilt in the forefoot region. This tilt may be attributed to the incomplete removal of the outer support component during the 3D printing process, resulting in uneven density between the inner and outer sides of the structure. This study also observed that midsoles with varying levels of hardness performed similarly in terms of load-bearing function, a finding that contradicts with Zhou et al.17. Earlier studies suggested that harder midsoles are better at transmitting dynamic changes during movement, while softer midsoles provide greater comfort and cushioning. However, the current study found minimal differences in load control across the different midsole designs. This discrepancy is likely due to the specific structural characteristics of the shoes and the conditions under which movement occurred. These findings suggest that the load-bearing function of a midsole is influenced not solely by its hardness but also by other structural factors. Zhou et al. 18 highlights the importance of forefoot function during running, noting that this area is a primary focus for force distribution. Proper shoe design can mitigate metatarsal stress, potentially reducing the risk of injury. Bionic shoe designs, for example, have been shown to alleviate metatarsal stress. Previous research from our team indicated that midsoles with greater hardness may provide better efficiency in transferring kinematic changes, but this comes at the cost of increased joint stress, potentially leading to pain. The motion control mechanism of running shoes is largely determined by the deformation rate of the outsole. Similar observations were made in this study. The bionic 1TS midsole created a slightly unstable plane, which helped reduce excessive supination and pronation. This structural feature contributed to improved joint control during dynamic movements.

Overall, the results of this study indicate that the 1TS midsole is more suitable for enhancing full-foot stability, while the 3TS midsole is better at providing dynamic control in the forefoot region. Depending on specific gait requirements, these midsole designs can be selected to improve gait control and stability. These findings have practical applications in improving shoe and orthotic designs, particularly in the context of sports and rehabilitation. In conclusion, this study demonstrates clear differences between the tested midsoles in terms of foot stability and rotation control. These insights can be used to optimize shoe designs, enhancing both comfort and safety for wearers. By tailoring midsole designs to address specific biomechanical needs, future innovations in footwear design may further improve performance and reduce the risk of injuries.

Conclusions

In this study, three different 3D-printed midsole structures were analyzed, and a total of 15 female participants were recruited for foot pressure testing. The results of the study are summarized as follows. Firstly, based on the comparison of data, the highest frequency of walking was observed with the 2TS midsole, while the highest frequencies for running and jumping were associated with the 1TS midsole. This indicates that the 2TS midsole may be more suitable for walking, while the 1TS midsole is better suited for dynamic activities such as running and jumping. Secondly, the analysis of peak values during the running gait phase, specifically between 0.1 and 0.2 s, showed that the 1TS midsole performed exceptionally well in terms of heel balance. Regarding foot balance, there was no statistically significant difference between the 1TS and 3TS midsoles, although the 1TS midsole was significantly better than the 2TS midsole. For forefoot balance, the 1TS midsole demonstrated significantly better performance compared to the 2TS midsole. Lastly, wearing the 1TS midsole significantly improved the balance of the forefoot, heel, and the entire foot compared to the BF condition. These results highlight the superior stability and balance provided by the 1TS midsole across various gait parameters.

These findings have important implications for the sneaker and footwear industry. The application of 3D-printed midsoles shows great potential for development and practical use, particularly in enhancing foot stability and performance. Moreover, this study provides valuable insights into the role of midsole design in optimizing gait balance and stability. However, this study has several limitations. These include potential ethnic and regional differences among participants, variability in the duration of wearing the test footwear, measurement techniques, and other influencing factors. Future research could address these limitations by exploring the use of different 3D printing technologies or conducting tests with athlete populations to further evaluate midsole performance in dynamic and high-stress conditions.

Methods

Materials

In this study, to manufacture the cube and midsole, TPU filament (eTPU-95A, eSun, China) was used. The specifications of the filament are as follows. The diameter was 1.75 mm, density was 1.43 g/cm , and hardness was Shore 95 A. Also, it was manufactured using an FDM 3D printer (Cubicon single plus, Cubicon Co. Ltd., Korea).

Preparation of five types of cube samples applied biomimetic structure

The Voronoi component in Rhino’s plugin Grasshopper was utilized to generate basic Thiessen polygons. As part of the biomimetic design process, five different structures were modeled using Rhino software (Robert McNeel & Associates, USA), each with dimensions of 50 × 50 × 50 mm3. The five biomimetic structures were inspired by three natural elements: mammals, herbivores, and aquatic plants. These structures were developed as Honeycomb (HN), Horseshoe (HS), Tyson Polygon 1 (1TS), Tyson Polygon 2 (2TS), and Tyson Polygon 3 (3TS). Detailed specifications of the structures are presented in Fig. 6a. The modeled biomimetic structure was 3D printed using the slicing program Cubicreatore 4 V4.4.0 (Cubicon Co. Ltd., Korea). The slicing program status is appeared in Fig. 6b. And the five types of modeled cubes were manufactured using FDM 3D printing. The 3D printing processing conditions were as follows. The nozzle temperature was 225℃, bed temperature was 65℃, printing speed was 60 mm/s, infill density was 100%, and an infill pattern was Zig Zag. The printed biomimetic structure is shown in Fig. 6c.

Fig. 6
figure 6

Process of preparation of the cube samples. (a) 3D modeling, (b) Slicing program, and (c) Sample image.

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Preparation of 3D printed midsole samples applied biomimetic structures

The design process illustrates the gradual optimization from basic cube testing to complex midsole structures, establishing a reliable experimental foundation for the research. The three types of 3D-printed running shoe midsoles incorporating biomimetic structures were designated as 1TS, 2TS, and 3TS, respectively. The material and 3D printing process conditions were the same as for the cube. And To ensure consistent recovery performance of the bottom material during the experiments, three pairs of midsoles were prepared for each type. The images of the samples are presented in Fig. 7a.

Fig. 7
figure 7

(a) Wearing images of BF, 1TS, 2TS, and 3TS. (b) The plantar pressure test methods for the three types of dynamic motions (walking, running, jumping).

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Characterizations

The characteristic analysis was conducted as follows. First, about compressive property of cube samples, each structure’s deformation performance was evaluated. Compression tests were conducted on different cube samples, and performance metrics were recorded. This step helped identify suitable biomimetic structures for midsoles. To confirm the compressive properties of 3D printed cube, it was measured according to the KS M ISO 604 standard. Experiments were implemented using a 5KN load cell in the universal testing machine (AGS-X, Shimadzu Co., Kyoto, Japan). The samples were compressed in the -z direction and at a speed of 25 mm/min. The maximum strain was limited to 50% depends on the samples. Each sample was compressed three times and the obtained average value was used to analyze the compressive strength at 50% strain, initial modulus, and toughness10.

Second, the contents related to plantar pressure are as follows. In this study, to calculate the number of subjects, the G*Power 3.1 (Franz Faul, Germany) was used with a two-tailed test, an effect size (dz) of 0.8, an α error probability of 0.05, and a power (1 − β) of 0.8, resulting in a minimum requirement of 15 participants. After screening, 15 healthy female runners were recruited for the experiment. The participants had an average age of 28.8 ± 7.95 years, an average height of 157.92 ± 4.89 cm, an average weight of 53.16 ± 4.95 kg, and an average foot size of 232.19 ± 2.56 mm. The inclusion criteria for participants required them to be between 19 and 40 years old, female, and without any health issues, neuromuscular diseases, or known gait abnormalities. Participants also needed to have no lower limb injuries in the past six months, regularly engage in running activities, and have a body mass index (BMI) between 18.5 and 24 with a foot length between 230 and 235 mm. And the reasons for selecting female runners may include the following. Women are more prone to injuries than men in running sports. The selection of participants may be limited by available resources, such as sample size, difficulty in recruiting participants, or experimental setting, which could lead to a preference for selecting female participants. Without the interference of gender variables, researchers can focus more on analyzing the effects of other factors (such as running shoes, gait patterns, etc.) on female runners, reducing external influences. Before the experiment, all participants received detailed information about the study and signed an informed consent form approved by the Institutional Review Board (IRB). This study received ethical approval from Dong-A University’s Institutional Review Board (IRB No. 2–1,040,709-AB-N-01–202,311-HR-048–03). All experiments were performed in accordance with relevant guidelines and regulations.

The plantar pressure analysis was conducted using a plantar pressure analyzer (Materialise, Belgium) with an 8-m mat and a foot scanner (Alchemaker, Korea). The participants performed the experiment wearing 3D-printed midsoles along with socks (JT Co., Korea). The experiment included four conditions: barefoot (BF), 1TS, 2TS, and 3TS. To assess the plantar pressure under different dynamic motions, the study evaluated walking, running, and jumping. For the measurement method of walking and running, participants walked or ran back and forth five cycles on an 8-m mat at a constant speed of 100 bpm for walking and 150 bpm for running. In the experimental design, participants were given a fixed rate, and the metronome was used to control the step frequency during the test. During each cycle, the plantar pressure of the entire sole was measured once for both the left and right foot, resulting in a total of five data points for each foot (left and right). The average of these measurements was used for analysis. For jumping motion, participants jumped from a 20 cm high box with speed of 105 bpm onto the plantar pressure analyzer using one foot. And this was measured five times for each foot. Similar to the walking and running motions, the plantar pressure of the entire sole was measured five times for each foot (left and right) to obtain the data. The 20 cm jump height was chosen for its balance of safety, moderate difficulty, and compatibility with the Footscan device. It ensures participant safety by minimizing the risk of injury, provides an appropriate challenge without causing fatigue or distortion, and meets the height requirements of the testing equipment for accurate data collection. The dynamic motion during plantar pressure test methods are illustrated in Fig. 7b. The plantar pressure experiment method was conducted in the same manner as in previous studies 19.

The plantar pressure data was collected as a complete dataset of the entire plantar and was analyzed by dividing it into ten distinct zones. These zones were classified as follows: Toe part (T1, T2-5), Metatarsal part (M1, M2, M3, M4, M5), Midfoot part (MF), and Heel part (ML, HL). This classification allowed for a more detailed examination of the pressure distribution across different areas of the foot. The obtained plantar pressure data was utilized to derive six types of gait ratio data. The gait ratios analysis provides specific calculations about different aspects of the roll off. The gait ratios are calculated by analyzing the progression of pressure under each of the zones of the feet and by comparing the medial part of the foot with its lateral part. The gait ratios were derived from Footscan 9 data, as outlined in Table 2. Each gait ratio analysis focuses on a different and specific property of the roll-off. First, about heel rotation (HR), hallux stiffness was calculated by comparing the pressure underneath the first toe with the pressure underneath the first metatarsal head. A positive value indicated a higher load on the first toe, a negative value indicates a higher load on M1. Second, in terms of foot balance (FB), mediolateral foot balance was defined as the mediolateral pressure distribution of the entire foot during stance phase. A higher pressure underneath the medial aspect of the foot suggested a pronation of the foot, a higher pressure underneath the lateral aspect of the foot suggested a supination of the foot. Third, regarding forefoot balance (FFB), mediolateral forefoot distribution was defined as the pressure distribution at the level of the forefoot during stance phase. An increased pressure underneath the medial aspect of the forefoot suggested a pronation of the forefoot, an increased pressure underneath the lateral aspect of the forefoot suggested a supination of the forefoot. Fourth, about hallux stiffness (HS), hallux stiffness was calculated by comparing the pressure underneath the first toe with the pressure underneath the first metatarsal head. A positive value indicated a higher load on the first toe, a negative value indicated a higher load on M1. Fifth, concerning medial forefoot balance (FB), The medial forefoot distribution was calculated by comparing the pressure underneath M1 and M2. A positive value indicated a higher load on metatarsal 2, a negative value indicated a higher load on metatarsal 1. A high value indicated a large difference in load between metatarsal 1 and 2. Sixth, about meta loading (ML), meta loading is defined as the pressure distribution between the inner metatarsal heads and the outer metatarsal heads during stance phase. A positive value indicated a higher load on the inner metatarsal heads, a negative value indicated a higher load on the outer metatarsal heads. A high value for meta loading indicated a large difference in load on the inner metatarsal heads compared to the outer metatarsals. The gait ratios analysis can be available in the clinical and scientific package. Footscan 9 software allows for the comparison of gait ratio graphs across different footwear designs to evaluate their supportiveness20,21.

Table 2 Explanatory note Gait ratio.
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Third, in case of statistical analysis, statistical analysis was conducted using SPSS 26.0 and PRISM 10 software. Descriptive statistics, including mean and standard deviation, were calculated for the gait ratio parameters. A one-way ANOVA was performed to evaluate changes in gait ratios across different midsole structures, with the significance level set at α = 0.05 (p < 0.05 was considered statistically significant). During the experiment, participants wore shoes equipped with various 3D-printed midsoles, and data on gait ratios (heel rotation, foot balance, forefoot balance, hallux stiffness, medial forefoot balance, and meta loading) and gait phases (forefoot off phase, foot flat phase, forefoot contact phase, and initial contact phase) were collected using a gait analysis system. The Shapiro–Wilk test was used to assess the normality of the data. If the data were not normally distributed, appropriate data transformations or non-parametric tests, such as the Kruskal–Wallis test, were applied. Foot gait ratios are crucial for analyzing an individual’s gait balance, particularly the ratio between the stance and swing phases. By evaluating whether the gait ratio falls within the normal range, potential gait imbalances or instability can be identified. Although the normal range for gait ratios varies depending on the specific metrics used, a ratio close to 1:1 is generally considered symmetric and indicative of normal gait. Repeated measures ANOVA and t-tests were conducted to compare gait ratios across the three midsole conditions, using data from the right foot as a reference. A significance level of p < 0.05 was used to determine whether the midsole structure had a significant effect on the gait ratio. When significant differences were observed, post-hoc tests with Bonferroni correction were applied to identify specific group differences. Additionally, effect sizes (Cohen’s d) were calculated to quantify the magnitude of these differences.