INTRODUCTION
Lower limb prostheses are vital for restoring mobility and quality of life for those with amputated limbs or natural disability. The prosthetic socket is a key interface that influences comfort, stability, and functionality but needs to be designed with a uniform stress distribution. Recent advancements have focused on elastomeric liners, essential for pressure distribution and cushioning. Improving these liners’ mechanical properties is crucial for enhancing user comfort and prosthetic performance. Finite element analysis (FEA) is a crucial tool for assessing the mechanical behavior of prosthetic sockets and liners. It simulates the interaction between the residual limb and the socket, enabling evaluation of stress distribution, deformation patterns, and performance under various loads. This approach offers valuable insights for optimizing prosthetic components. Recent studies have utilized FEA to examine transtibial prosthetic sockets with elastomeric liners. Cagle et al. (2018) investigated stress distribution and load transfer mechanisms, while Meng et al. (2020) analyzed compression/release stabilized transfemoral sockets, highlighting socket design’s role in reducing tissue deformation and improving comfort. Boudjemaa et al. (2021) explored the impact of multi-layer prosthetic foam liners on stress distribution at the stump–prosthetic interface, showcasing the potential benefits of layered liner structures in optimizing load distribution and alleviating pressure points, thereby enhancing user comfort and prosthetic functionality.
Furthermore, personalized prosthetic liner design has emerged as a promising avenue for optimizing interface mechanics. Sahli et al. (2024) explored the impact of personalized liner thickness on stress distribution at the stump–prosthesis interface. Their research underscored the importance of individualized fitting in improving comfort and functionality, highlighting the potential of personalized prosthetic solutions. Mbithi et al. (2019) focused on predictive control strategies for active prosthetic sockets, and Chillale et al. (2019) studied an orthopedic implant to improve weight-bearing capability. Vélez Zea et al. (2015) analyzed residual limb length and stress distribution. Further contributions to the understanding of prosthetic socket dynamics have been made by Zhang et al. (2013), Lacroix and Ramírez Patiño (2011), and Ramírez and Vélez (2012), who investigated the contact interface between the transfemoral stump and the prosthetic socket, the donning procedure of a prosthetic transfemoral socket, and the boundary condition between bone and soft tissue in FEA of a transfemoral amputee, respectively. Moreover, studies by Lee et al. (2004), Lin et al. (2004), and Jia et al. (2004) have provided significant insights into the contact interface between the transtibial residual limb and the prosthetic socket, as well as the effects of liner stiffness and dynamic load transfer mechanics. Most of these studies did not offer clear methodologies for addressing high-stress areas at the stump–prosthetic interface, instead making general suggestions. In contrast, our study focuses on predicting stress concentration areas and proposing a comprehensive methodology to reduce them. Considering these advancements, this study aims to contribute to the progression of prosthetic socket design by conducting a comprehensive analysis of elastomeric liners’ mechanical performance. By harnessing advanced computational methodologies and integrating novel design, we emphasize the comfort, stability, and overall satisfaction of individuals with disability utilizing lower limb prostheses. This study aims to propose an innovative liner designed to enhance patient comfort by reducing stress levels at the stump–prosthetic interface. The study is conducted in two stages. In the first stage, FEA is employed to predict the areas that will experience the highest levels of stress at the interface under a load simulating a natural standing state. In the second stage, specific measures are taken to reduce stress in these identified areas. This involves designing personalized liners tailored to the unique characteristics of each patient’s residual limb. By considering the shape, size, and nature of the residual limb, the proposed liners are customized to address the high-stress areas effectively. This methodology not only improves comfort and functionality but also enables the creation of individualized liners that cater to the specific needs of each patient, ensuring optimal load distribution and minimizing pressure points. By focusing on personalized solutions, this approach advances prosthetic liner technology and enhances the overall patient experience.
METHOD
Geometry and material properties
The finite element model developed in this study is crucial for simulating the biomechanical interactions at the stump–prosthesis interface, providing insights into stress distribution and potential areas for intervention. The model’s construction involved several sophisticated stages. First, three-dimensional (3D) modeling of the residual limb was carried out, where high-resolution computed tomography (CT) scans were used to capture detailed anatomical features of the residual limb, including the tibia, fibula, and surrounding muscle tissues. These images served as the foundation for creating a highly accurate 3D model. Using 3D Slicer software (Harvard University, USA), renowned for its precision in medical image processing, we converted the two-dimensional CT images into a comprehensive 3D representation of the residual limb (Lin et al., 2004). In the second stage, the prosthetic socket and liner were designed. The 3D model was subsequently imported into Autodesk Meshmixer (Autodesk, Inc., USA). This software enabled the customization of the prosthetic socket and liner designs to precisely fit the unique contours of the residual limb. Special attention was paid to adjusting the contact surfaces to accommodate and smooth any cavities or irregularities, ensuring an optimal fit and comfort (Tobushi et al., 2001; Stevens and Wurdeman, 2019). In the third stage, conversion and integration of the components were carried out. After the initial design and adaptations, the model components (socket and liner) were converted from the stereolithography format to initial graphics specification using MIMICS 3-MATIC software (Materialise NV, Belgium). This conversion was essential for ensuring that the models were suitable for advanced engineering analyses and seamlessly integrated into the finite element simulation environment (Ramos and Simões, 2006).
Figure 1 illustrates the complete finite element model, showcasing the integration of the residual limb with the tailored prosthetic socket and liner, emphasizing the precision and adaptability of our modeling approach. By harnessing these advanced technological tools and methodologies, the development of the finite element model not only reflects cutting-edge practices in biomedical engineering but also establishes a benchmark for crafting personalized prosthetic solutions that are scientifically accurate and highly tailored to individual needs. Table 1 provides all the detailed information regarding Young’s modulus and Poisson’s ratio values utilized in the FEA for each respective material (bone, muscle, gel liner, and socket) (Jia et al., 2004; Lin et al., 2004; Dickinson et al., 2017).
Detailed material properties for the finite element model.
| Material | Young’s modulus | Poisson’s ratio |
|---|---|---|
| Bone (Lin et al., 2004) | 10 GPa | 0.3 |
| Muscle (Lin et al., 2004) | 0.2 MPa | 0.49 |
| Gel liner (Jia et al., 2004) | 0.38 MPa | 0.39 |
| Socket (Dickinson et al., 2017) | 1.5 GPa | 0.3 |
In the stress prediction phase, a gel liner was utilized (referenced in Table 1). In the subsequent phase, two types of polymeric foam, namely flexible polyurethane foam and polyurethane shape-memory polymer foam, were employed for the development of the innovative personalized liner. Both foams were considered hyper-elastic materials. The flexible polyurethane foam was characterized by the hyper-elastic Ogden’s model parameters: μ1 = 7.27, α1 = 1.63, μ2 = −7.2, α2 = 1.63, μ3 = 8.5E-4, α3 = 45.75 (Ju, 2014). The mechanical properties of the polyurethane shape-memory polymer foam, as depicted in Figure 2, were utilized (Tobushi et al., 2001).
Compressive stress–strain relationship of polyurethane shape-memory polymer foam (Tobushi et al., 2001).
Boundary conditions and mesh model
In this investigation, the interfaces between bone and soft tissue were considered fixed, while the physical interaction between the stump and the liner was modeled utilizing surface-to-surface contact. To simulate the frictional dynamics between the liner and soft tissues, a coefficient of friction of 0.5 was adopted. This coefficient governs the resistance to sliding between the two surfaces, with a higher value indicating increased frictional force (refer to Fig. 3a). Regarding the loading conditions, a static vertical load equivalent to half of the body weight (350 N) was applied to the apex of the tibial bone (Slifka and Whitton, 2000; Ramos and Simões, 2006; Dickinson et al., 2017). The necessity to simulate a realistic loading scenario that an amputee would encounter led to the decision to employ half of the body weight. Although it is acknowledged that physiological loading varies, the model is made simpler and a consistent basis for assessing stress distribution at the stump–prosthetic interface is provided by using this assumption. This method provides a useful trade-off between FEA representativeness and complexity while adhering to accepted biomechanical principles. Additionally, the distal end of the socket was fixed. Tetrahedral meshes were selected for all components, including bone, soft tissue, socket, and liner. The mesh model is presented in Figure 3b. Tetrahedral meshes are typically favored over hexahedral meshes for intricate, free-formed geometries due to their computational efficiency (Ramos and Simões, 2006).
The mesh convergence process was specifically applied to the residual limb, as it is expected to experience the highest deformation and is therefore the primary volume of interest. For other components such as the femur, liner, and socket, an element size of 5 mm was utilized. The mesh convergence study involved applying a fixed vertical load to the top of the residual limb and constraining its bottom. This iterative analysis was conducted by maintaining a constant applied load and consistent boundary conditions while varying the mesh size. This approach ensured the accuracy and reliability of the simulation results by identifying the optimal mesh size for capturing the mechanical behavior of the residual limb under load; the mesh details of the finite element model are shown in Table 2.
Mesh details of the finite element model.
| Material | Elements size (mm) | Number of element |
|---|---|---|
| Bone | 5 | 28,224 |
| Muscle | 3 | 282,195 |
| Gel liner | 5 | 30,036 |
| Socket | 5 | 28,184 |
However, this study has few limitations. First, the FEA simulations are based on idealized models that may not capture the full complexity of real-life conditions. Variations in individual limb geometry, material properties, and daily activities can significantly affect the results. Second, the study assumes a simplified loading condition of a fixed vertical load, which might not fully represent the dynamic and variable forces experienced during different movements and activities. Additionally, the mesh convergence process was applied primarily to the residual limb, potentially overlooking fine details in the femur, liner, and socket regions.
RESULTS AND DISCUSSION
The simulation process consisted of two primary stages. Initially, we simulated the application of the patient’s weight on the prosthesis using a conventional gel liner. The aim was to predict the areas experiencing peak stresses at the stump/liner interface. Subsequently, in the second stage, we devised an innovative 3D liner. This involved strategically cushioning the areas identified with peak stresses using memory foam. The objective was to absorb and diminish these stresses effectively.
Prediction of peak stress areas
At this juncture, subsequent to applying half of the patient’s weight to the amputated limb while wearing the prosthesis equipped with a gel liner, our employment of the FEA enabled us to pinpoint the regions with the highest contact pressure (CPRESS) and shear stress. Notably, the CPRESS exhibited concentration in three distinct areas: the lateral area of the tibia head (LTH), the tibia end area (TE), and the fibular end (FE). Figures 4 and 5 present a visualization from FEA illustrating the distribution of CPRESS on a residual limb enveloped in a prosthetic socket with a silicone liner interface. The color gradient, denoting varying pressure levels, reveals a peak CPRESS of 72.3 kPa. This peak pressure potentially localizes over bone prominences or regions with insufficient soft tissue cushioning, rendering them more susceptible to heightened stress from the prosthesis load. Areas exhibiting the highest pressure, depicted in red, necessitate meticulous consideration in prosthetic design to reduce user discomfort or skin irritation.
The areas with the greatest normal stress (contact pressure) intensity at the stump/prosthetic interface after the predicting stage.
Conversely, regions shaded in blue signify lower pressure zones, warranting evaluation to ensure a snug prosthetic fit and to avert socket movement. In summary, this pressure mapping serves as a valuable tool for pinpointing areas necessitating potential modifications in the prosthetic liner to augment wearer comfort and optimize prosthesis functionality.
Figure 6 exhibits the distribution of circumferential shear stress at the stump/prosthetic interface. The color-coded map delineates areas of varying shear stress, with the highest absolute stress levels peaking at 13.6 kPa. Remarkably, stress concentrations are evident around the LTH, TE, and FE. These regions of elevated stress play a pivotal role in prosthetic fitting, as neglecting them could result in discomfort or skin complications unless adequately cushioned or accommodated within the design of the prosthetic socket and liner.
Figure 7 depicts an FEA output illustrating longitudinal shear stress at the stump/prosthetic interface. The shear stress is quantified and color-coded, with the legend “frictional shear stress component in the second local tangent direction (CSHEAR2)” ranging from approximately −0.0132 to +0.0122 MPa. In this analysis, the peak longitudinal shear stress occurring parallel to the surface of the limb and the direction of limb length is shown to reach up to 13.2 kPa. The image provides two views of the residual limb within the prosthetic socket, highlighting regions of heightened shear stress in bright red. These areas predominantly cluster around the LTH, TE, and FE. Longitudinal shear stresses of such magnitude indicate potential sites where friction between the limb and the socket might induce skin irritation or discomfort, particularly during movement activities such as walking or adjusting posture. Understanding the distribution of these stresses is pivotal for designing prosthetic liners aimed at minimizing frictional forces, thereby mitigating the risk of shear-related skin injuries and enhancing the overall comfort of the prosthesis for the user.
Innovative prosthetic liner
Following the identification of regions subjected to the highest pressures during prosthetic use, we have engineered a novel, personalized liner to address these critical areas. This innovative liner integrates flexible polyurethane foam at targeted stress points to provide cushioning. Additionally, the foundational structure of the liner incorporates polyurethane shape-memory polymer foam, selected for its ability to conform to the limb’s morphology while effectively distributing and reducing CPRESS.
Figure 8 illustrates the model of innovative prosthetic liner. The model distinctly showcases the placement of flexible polyurethane foam (highlighted in green) at strategic locations, designed to alleviate pressure by absorbing and dispersing forces that would otherwise be concentrated on the limb. The remainder of the liner is constructed from polyurethane shape-memory polymer foam (indicated in red), chosen for its unique viscoelastic properties which enable it to mold to the user’s anatomy under body temperature, thus providing a custom-fit that maintains its shape over time. This dual-material approach aims to not only enhance the comfort and fit of the prosthetic liner but also to mitigate the adverse effects of prolonged pressure, which can lead to skin breakdown and discomfort. By leveraging advanced materials and tailored design, the liner represents a significant advancement in prosthetic technology, prioritizing both user comfort and limb health.
Stresses at the stump/prosthetic interface after wearing the innovative liner
The distribution of normal stress, known as CPRESS, at the interface between a residual limb and its corresponding prosthetic liner following the application of the innovative liner design is presented in Figure 9. This FEA visualization employs a color gradient to represent stress across the limb’s surface, with the legend “CPRESS” indicating pressures ranging from 0 to 42.24 kPa. The depicted pressure distribution demonstrates a significant reduction in stress intensity, particularly in regions previously identified as experiencing the highest pressures during the predictive phase of the analysis. Specific areas of interest and their respective pressures are as follows:
The LTH region now exhibits a reduced CPRESS of 10 kPa, representing a substantial improvement from initial estimates. This suggests that the innovative liner effectively relieves stress in this area. The pressure in the TE region has decreased to 28 kPa, marking a considerable reduction from pre-intervention levels. This reduction indicates the liner’s ability to redistribute forces away from vulnerable regions. The pressure at the FE end is about 14 kPa, also indicating a reduction in stress. This reduction is critical in preventing skin breakdown and discomfort around the fibula. These results underscore the effectiveness of the innovative prosthetic liner in reducing the intensity of CPRESS across the residual limb, potentially leading to improvements in prosthetic comfort and functionality. Such advancements are vital for enhancing the quality of life for individuals reliant on prosthetic limbs, offering promising directions for future prosthetic design and material science research. This analysis not only validates the innovative liner’s design strategy but also underscores the importance of personalized pressure management in prosthetic development.
Figure 10 demonstrates the longitudinal shear stress profiles at the stump/prosthetic interface. The color mapping, guided by the legend “frictional shear stress component in the first local tangent direction,” spans from a negative −8.963e-03 MPa to a positive +8.338e-03 MPa, representing the directional forces acting parallel to the limb’s length. The color gradation reflects the distribution and magnitude of the shear stresses experienced by the residual limb within the prosthetic socket. Areas depicted in red and orange indicate zones of higher shear stress, which are of particular interest as they may be locations where internal friction is greatest, potentially leading to skin shear and discomfort for the prosthetic wearer. The analysis presents different perspectives—plantar, lateral, and frontal views—providing a comprehensive understanding of stress dynamics around the limb. These insights are crucial for the iterative process of prosthetic design, allowing for the refinement of liner materials and structural characteristics to minimize potential shear-induced tissue trauma and enhance prosthesis comfort. Such information is paramount for improving the wearer’s experience and ensuring the long-term viability of the prosthetic solution.
Figure 11 presents a comprehensive visualization of the circumferential shear stress distribution at the stump–liner interface using FEA. The results indicate that the LTH experienced a shear stress of 1.7 kPa, TE of 2.5 kPa, and FE of 5.4 kPa. These findings underscore the effectiveness of the innovative liner design in mitigating peak circumferential shear stresses in these critical areas. The color-coded map within the figure illustrates a spectrum of shear stresses, with the legend “CSHEAR2” specifying a range from −10.26 to +11.57 kPa, indicative of the rotational forces exerted on the skin surrounding the residual limb. Areas depicted in red represent the highest shear stress zones, suggesting potential areas of concern for skin irritation or discomfort, thereby identifying opportunities for further refinement of the liner design to enhance user comfort.
By providing a visual representation from various angles, Figure 11 serves as an essential tool in the prosthetic design process. It allows for the precise localization of high-stress regions and guides the targeted enhancement of the prosthetic liner. The goal is to reduce shear forces that could lead to skin damage, thereby improving the overall fit and comfort of the prosthesis for the wearer.
In Figure 12a, overall peak stress values across the stump–prosthetic interface are delineated for two different liner materials, referred to as Liner A and Liner B. The first bar illustrates a CPRESS of 72.3 kPa with Liner A, notably reduced to 42.2 kPa when using Liner B. Similarly, circumferential shear stress is reduced from 13.6 kPa in Liner A to 11.5 kPa in Liner B, while longitudinal shear stress decreases from 13.2 kPa with Liner A to 8.96 kPa with Liner B. These values suggest that Liner B has a significant dampening effect on both CPRESS and shear stress compared to Liner A. A segmented analysis of stress across three distinct areas of the stump–prosthetic interface: the LTH, TE, and FE, for both Liner A and Liner B, is demonstrated in Figure 12b. In all three regions, Liner B exhibits lower stress measurements than Liner A, highlighting the effectiveness of Liner B in stress reduction. For instance, the LTH region shows a CPRESS of 55 kPa with Liner A and a reduced pressure of 10 kPa with Liner B. Similarly, the TE region’s CPRESS decreases from 60 kPa with Liner A to 28 kPa with Liner B, and the FE region from 72.3 to 14 kPa. Circumferential and longitudinal shear stresses in these localized areas also exhibit reductions with Liner B, indicating a more favorable biomechanical interaction between the stump and the prosthetic interface when Liner B is used. These findings are crucial for the ongoing enhancement of prosthetic liners, providing clear evidence that Liner B’s material composition and structural design are more effective in reducing the stresses that can lead to discomfort and potential skin damage for the prosthetic user. The data from Figure 12a and b will be instrumental in guiding the development of prosthetic liners that offer improved comfort and safety for users.
(a) Peak contact pressure and shear stresses at the stump–prosthetic interface for Liners A and B; (b) contact pressure and shear stresses at the stump–prosthetic interface in three areas—LTH, TE, and FE for Liners A and B. Abbreviations: FE, the fibular end; LTH, lateral area of the tibia head; TE, tibia end area.
The anatomical features of the residual limb, such as bony prominences and soft tissue thickness, significantly influence stress distribution at the stump–prosthetic interface. In areas with less soft tissue, like the lateral tibia head and tibia end, higher stress concentrations were observed due to minimal cushioning. Our new liner design effectively reduced these stresses by incorporating customized thickness and advanced elastomeric materials, tailored to match the residual limb’s contours. This improved fit and cushioning distributed loads more evenly, reducing peak stresses and enhancing patient comfort. These findings underscore the importance of considering anatomical characteristics in prosthetic liner design for optimal functionality and comfort.
In the first phase of this study, we observed that the results for both normal stresses and shear stresses were consistent with findings from several previous studies (Lin et al., 2004; Lacroix and Ramírez Patiño, 2011; Zhang et al., 2013; Cagle et al., 2018). This consistency enhances the reliability of our results, suggesting that our simulation model and methodology are robust and valid. By corroborating our findings with established research, we can be more confident in the accuracy of our stress distribution predictions at the stump–prosthetic interface. In the second phase, we focused on implementing a new design aimed at reducing stress concentrations identified in the first phase. The new design significantly decreased the stress levels compared to those reported in the referenced studies (Lin et al., 2004; Lacroix and Ramírez Patiño, 2011; Zhang et al., 2013; Cagle et al., 2018). Specifically, our design modifications led to a substantial reduction in both normal and shear stresses at critical points of the residual limb–prosthetic interface. This reduction was achieved by optimizing the liner’s material properties and geometry to better distribute the applied loads and alleviate pressure points.
Our findings demonstrate the efficacy of the proposed design in enhancing comfort and potentially reducing the risk of skin irritation and other complications associated with high-stress areas. This approach underscores the importance of targeted interventions based on precise stress analysis, paving the way for more personalized and effective prosthetic solutions. Future studies should build upon these findings by incorporating real-world patient data and conducting clinical trials to further validate and refine the design improvements.
CONCLUSION
This research harnesses the precision of FEA to pioneer an innovative prosthetic liner that effectively alleviates interface stresses between the residual limb and the prosthetic socket. Our investigation comprised two critical stages: initially, we utilized a standard silicone liner to identify regions prone to high stresses at the stump–liner interface, particularly the LTH, TE, and FE. In the subsequent phase, our efforts were focused on creating an innovative foam liner, thoughtfully designed to cushion and diminish stresses in regions identified during the predictive stage. The liner’s implementation led to remarkable stress reductions in these focal areas: LTH (from 55 to 10 kPa), TE (from 60 to 28 kPa), and FE (from 72.3 to 14 kPa), establishing the liner’s potential to significantly enhance prosthetic comfort. Our study’s findings underscore the successful application of FEA in advancing prosthetic technology. The developed liner not only confirms the potential to substantially lower peak stress regions but also highlights the pivotal role of personalized pressure management in prosthetic development. The comfort-oriented liner design, substantiated by empirical evidence, emerges as a promising solution poised to transform prosthetic design, promising a future where custom comfort is the standard, thereby significantly elevating the quality of life for individuals with limb loss. This study contributes to the ongoing discourse on enhancing healthcare outcomes for disabled individuals, and the broader implications of our findings suggest that the integration of sophisticated FEA, innovative materials, and personalized design is a stride toward transforming the landscape of prosthetic technology.