A Digital Twin System for the Sitting-to-Standing Motion of the Knee Joint

Abstract

(1) Background: A severe decline in knee joint function significantly affects the mobility of the elderly, making it a key concern in the field of geriatric health. To alleviate the pressure on the knee joints of the elderly during daily movements such as sitting and standing, effective biomechanical solutions are required. (2) Methods: In this study, a biomechanical framework was established based on mechanical analysis to derive the transfer relationship between the ground reaction force and the knee joint moment. Experiments were designed to collect knee joint data on the elderly during the sit-to-stand process. Meanwhile, magnetic resonance imaging (MRI) images were processed through a medical imaging control system to construct a detailed digital 3D knee joint model. A finite element analysis was used to verify the model to ensure the accuracy of its structure and mechanical properties. An improved radial basis function was used to fit the pressure during the entire sit-to-stand conversion process to reduce the computational workload, with an error of less than 5%. In addition, a small-target human key point recognition network was developed to analyze the image sequences captured by the camera. The knee joint angle and the knee joint pressure distribution during the sit-to-stand conversion process were mapped to a three-dimensional interactive platform to form a digital twin system. (3) Results: The system can effectively capture the biomechanical behavior of the knee joint during movement and shows high accuracy in joint angle tracking and structure simulation. (4) Conclusions: This study provides an accurate and comprehensive method for analyzing the biomechanical characteristics of the knee joint during the movement of the elderly, laying a solid foundation for clinical rehabilitation research and the design of assistive devices in the field of rehabilitation medicine.

1. Introduction

Elderly individuals perform a large number of sitting-to-standing motions daily, and they commonly face difficulties in these movements. Compared to younger people, they require special attention to factors related to knee joint health [1]. The degree of knee joint degradation varies among elderly individuals with different physical fitness levels, they cannot avoid the prolonged duration of sitting-to-standing actions. This leads to the knee joint enduring sustained pressure over time, increasing the risk of developing knee joint diseases [2]. In-depth research on the force distribution of the knee joint during the sitting-to-standing process is of great significance for improving the quality of life of elderly individuals, reducing the likelihood of knee joint diseases, and advancing the treatment of such conditions.

Scholars have conducted in-depth studies on the anatomical structure and biomechanical properties of the knee joint. Blankevoort et al. examined the knee joint’s anatomical structure, providing a detailed description of the interaction between the joint ligaments, cartilage, and bones, as well as its dynamic performance during the sitting-to-standing motion [3]. Fukubayashi et al. investigated the biomechanical properties of the knee joint, revealing the stress distribution and deformation when the knee joint is subjected to different types of loading [4]. Andriacchi et al. focused on the biomechanical role of the knee ligaments during the sitting-to-standing motion, highlighting the crucial role of ligaments in regulating joint stability and alleviating loading stresses [5].

While significant progress has been made in understanding knee joint biomechanics, current computational models for knee joint analysis exhibit distinct limitations affecting clinical applicability. Research on the mechanical performance of the knee joint primarily focuses on its anatomical structure, with recent attention shifting toward motion patterns related to the knee joint. However, studies specifically examining the actual loading conditions of the knee joint during sit-to-stand movements remain relatively scarce [6,7]. Recent systematic reviews have highlighted the diverse modeling strategies and their specific constraints in knee joint applications, particularly in addressing the biomechanical challenges faced by older elderly populations during daily activities [8,9].

Knee-specific musculoskeletal modeling approaches, predominantly utilizing multibody dynamic platforms, have shown considerable variability in biomechanical predictions. Abdullah et al. (2024) conducted a comprehensive systematic review of 116 studies, revealing significant differences between multibody dynamics-based musculoskeletal modeling platforms in gait analysis, with particular challenges in elderly populations where anatomical variations are more pronounced [10]. These platforms, while computationally efficient, often rely on generic anatomical templates that fail to capture individual knee joint characteristics. Finite element models for knee joint analysis offer superior mechanical accuracy by incorporating detailed material properties of cartilage, meniscus, and ligaments. Yan et al. (2024) systematically reviewed various finite element modeling strategies for knee joints, summarizing different approaches and their clinical applications [8]. However, recent developments by Esrafilian et al. (2024) demonstrated that despite advances in automated segmentation tools for knee joint modeling, these approaches remain computationally intensive and require simplified loading conditions that may not reflect real-world movement patterns [11]. The integration of finite element models with musculoskeletal simulations shows promise but remains challenging for real-time clinical applications [12].

Digital twin systems represent an emerging paradigm for knee joint modeling that addresses many limitations of traditional approaches. Since Michael Grieves (2014) first introduced the concept of digital twins [13], this technology has been widely applied across various fields, including smart manufacturing, energy management, and intelligent transportation [14]. In recent years, the application of digital twin technology in the healthcare sector has achieved remarkable progress [15,16]. Saxby et al. (2023) proposed a comprehensive digital twin framework for precision neuromusculoskeletal healthcare, building upon international standards to enable personalized biomechanical analysis [17]. Recent developments in image-based musculoskeletal models have demonstrated the ability to accurately predict knee extension torques, showing improved accuracy over traditional generic models [18]. However, integrating multiscale biomechanical data with computational modeling remains challenging, particularly for elderly populations where knee tissue properties vary significantly from those of healthy young adults. The latest advances in 2025 have significantly enhanced the clinical applicability of digital twin systems. Hoyer et al. (2025) established foundations for knee joint digital twins using quantitative MRI (qMRI) biomarkers, demonstrating the potential for precision health strategies in managing osteoarthritis and predicting knee replacement outcomes [19]. Andres et al. (2025) explored the advantages of digital twin technology in orthopedic trauma surgery, highlighting its benefits in predicting improvements in implant stress distribution and fracture strain states [20]. Furthermore, recent comprehensive reviews have demonstrated that digital twin systems for musculoskeletal applications leverage computational models such as multibody dynamics and finite element analysis to simulate mechanical behavior, with the integration of wearable technologies enabling real-time monitoring and feedback for preventive measures and adaptive care strategies [21].

The anatomical structure of the knee joint serves as the foundation for biomechanical analysis, with finite element analysis being used to study stress distribution during sit-to-stand movements. These findings offer scientific support for designing rehabilitation aids and provide a basis for the diagnosis and treatment of joint disorders. He et al. (2021) performed finite element analysis on the human lumbar spine and employed neural networks for the real-time prediction of its mechanical properties, with the digital twin system developed through this method laying a research foundation for related fields [22]. Recent advances in biomechanical modeling have demonstrated the importance of considering sample geometry and joint-specific characteristics, as shown by studies examining the effects of foot orthoses on lower limb joint angles and moments in adults with flat feet [23] and investigations into how articular cartilage sample geometry influences mechanical response and properties using finite element simulation [24]. The limitations of existing knee modeling approaches highlight the need for personalized strategies that integrate individual knee anatomical data with functional analysis. MRI-based digital twin systems for knee joints address these constraints by providing patient-specific geometries while maintaining computational efficiency for real-time applications, particularly valuable for elderly knee rehabilitation where individualized assessment is crucial. For elderly knee mechanics research, a digital twin model enables the real-time visualization of stress distribution during sit-to-stand transitions, clarifying the biomechanical challenges faced by the elderly and providing a scientific basis for designing specialized rehabilitation devices and therapeutic interventions.

2. Materials and Methods

2.1. Analysis of Relationship Between Knee Joint Torque and Posture

According to human anatomy, movements in the coronal, sagittal, and transverse planes can be simplified to the sagittal plane. Since the knee joint primarily operates within the sagittal plane, this simplification is crucial for analyzing knee joint torque. By simplifying the human body into three segments—trunk, thigh, and lower leg—mechanical analysis can be focused on the knee and hip joints. A simplified model of the human body for sit-to-stand motion is established using these three segments. The specific simplified model is shown in Figure 1.

In this simplified model, the lengths of the lower leg, thigh, and trunk are denoted as l₁, l₂, and l₃, respectively, while their corresponding weights are denoted as m₁, m₂, and m₃. The simplified joint angles are denoted as α, β, and θ. Specifically, α represents the angle between the trunk and the thigh; β is the angle between the thigh and the lower leg; θ₁ is the angle between the lower leg and the ground; and θ₂ and θ₃ are the angles between the thigh, upper trunk, and the vertical direction, respectively. Based on the joint angle relationships in the sagittal plane, the following joint angle conversion relations can be obtained:

θ₂ = 0.5π + θ₁ − β

(1)

θ₃ = π − θ₂ − α

(2)

To calculate the knee joint torque, it is essential to first analyze the forces acting on the hip joint. A two-dimensional Cartesian coordinate system is established with the ankle joint as the origin, the direction from the ankle joint to the foot as the x-axis, and the vertical direction of the body as the y-axis. A torque balance equation is established with the hip joint as the origin. The derived dynamic equation for the hip joint is as follows:

J₃α₃ + F_1xl₃ sin(θ₃) − F_1yl₃ cos(θ₃) = M₁

(3)

In this equation, J₃ represents the moment of inertia of the trunk segment; a_3x and a are the accelerations of the trunk along the x-axis and y-axis, respectively; F_1x and F_1y are the forces acting on the hip joint along the x-axis and y-axis; and M₁ is the hip joint torque. A torque balance equation is then established with the knee joint as the origin. The derived dynamic equation for the knee joint is as follows:

J₂α₂ + F_2xl₂ sin(θ₂) − F_2yl₂ cos(θ₂) = M₂

(4)

In this equation, J₂ represents the moment of inertia of the thigh segment; a_2x and a_2y are the accelerations of the thigh along the x-axis and y-axis, respectively; F_2x and F_2y are the forces acting on the knee joint; and M₂ is the knee joint torque. By combining the dynamic equations for the hip joint and the knee joint, the knee joint torque model is established as follows:

M₂ = J₂α₂ +0.5l₂(F_2x cos(θ₂) + F_2y sin(θ₂) − 0.5F_1y sin(θ₂) − 2F_1x sin(θ₂))

(5)

Some of the variables in this equation are related to the analysis subjects. By using a dynamic capture system to track body posture, information such as the lengths of the lower leg, thigh, and trunk, as well as the angles and angular accelerations of each joint, can be analyzed. Through force measurement experiments, the required reaction force values can be obtained. The weights of the lower leg, thigh, and trunk are calculated based on the average weight distribution of each body part. By designing an experiment that combines the dynamic capture system with a six-dimensional force and torque system, the torque generated by the knee joint during the sit-to-stand transition can be analyzed. This allows for the study of the knee joint’s mechanical behavior.

During the experiment, the optical motion capture system is used to obtain real-time posture data on the volunteer. This data is then used to establish the relationship between knee joint torque and posture. The experiment involves 10 healthy adults, all of whom have no significant knee joint disorders or history of athletic activity. Before the experiment, each volunteer underwent a detailed physical examination, and the experimental procedure and safety precautions were explained. All volunteers agreed to participate and signed an informed consent form.

The detailed demographic and anthropometric characteristics of the participants are summarized in

Table 1. Participant demographics and characteristics.

Parameter	Mean ± SD	Range
Age (years)	48.7 ± 16.2	25–75
Height (cm)	170.3 ± 8.1	158–185
Weight (kg)	71.2 ± 12.5	55–92
BMI (kg/m2)	24.8 ± 3.7	20.1–30.8
Gender (Male/Female)	6/4	-

. The participant cohort included individuals across a wide age range (25–75 years) to investigate age-related biomechanical differences and validate the digital twin system’s applicability for diverse populations.

The wide age range (25–75 years) was selected to investigate age-related biomechanical differences during sit-to-stand motions. Participants were categorized into three age groups for comparative analysis:

• Young adults (25–35 years): n = 4.
• Middle-aged adults (36–55 years): n = 3.
• Older adults (56–75 years): n = 3.

For the digital twin model’s development and validation, one representative young adult participant (height: 175 cm; weight: 65 kg) was selected to establish the personalized biomechanical framework and demonstrate the digital twin system’s capabilities. The remaining participants (n = 9) were used for comprehensive joint torque analysis to validate the system’s applicability across different demographic groups and investigate correlations between anthropometric characteristics and biomechanical parameters.

During the experiment, volunteers were required to perform the sit-to-stand movement multiple times in order to obtain high-quality experimental data. At the start of the experiment, volunteers sat naturally on a chair with their backs against the chair’s backrest. Their arms hung naturally at their sides, and their feet were placed flat on the multi-dimensional force measurement system. After maintaining the sitting posture for ten seconds, the volunteer naturally rises to a standing position. After holding the standing posture for ten seconds, they return to the initial sitting position, completing one full sit-to-stand movement. After repeating the sit-to-stand movement five times, the data collection process for one volunteer is completed. After the sensors stop for two minutes, the volunteer is replaced, and the sit-to-stand experiment is repeated five times with the new volunteer. During this period, the multi-dimensional force measurement system recorded the ground reaction force data at different time points, while the optical motion capture system tracked the volunteer’s posture at those same time points. The time synchronization between the multi-dimensional force measurement system and the optical motion capture system was maintained. At this point, the basic data collection process is complete. The specific experimental setup is shown in Figure 2. The experimental setup consisted of a motion capture system (MARS2H, Nokov Inc., Beijing, China) with 7 cameras positioned around the measurement area at a 100 Hz sampling frequency, providing a 3D tracking accuracy of ±0.1 mm. The multi-dimensional force measurement system (Bioforcen, Eliwise Inc., Hefei, China) was synchronized with the motion capture system for comprehensive data collection, with a force measurement accuracy of ±0.1 N and a sampling rate of 1000 Hz. Reflective markers were placed according to the Helen Hayes model with 16 marker points on key anatomical landmarks. System calibration was performed using the six-dimensional force platform surface as the reference plane to establish the experimental coordinate system, with a temporal synchronization accuracy of ±1 ms maintained between all measurement systems.

2.2. Knee Joint Finite Element Model Construction

To validate the experimental data and the knee joint torque model, finite element analysis software is needed to simulate the loading conditions of the knee joint during sit-to-stand movements. The accuracy of the finite element analysis results depends on the model’s accuracy. Using multiple modeling software tools to construct the knee joint model improves its precision. This enhances the reliability of the finite element analysis results.

While generic knee models are readily available on simulation platforms, this study requires individualized knee joint models to accurately capture the biomechanical behavior during sit-to-stand movements. Elderly individuals often exhibit significant anatomical variations due to age-related changes including cartilage degeneration, bone remodeling, and ligament laxity, which can substantially affect load distribution patterns and biomechanical behavior. However, even among healthy adults, considerable variations exist in knee joint geometry, including bone contours, joint space dimensions, and cartilage thickness, which directly influence biomechanical responses during functional movements. Previous research has demonstrated that subject-specific models predict biomechanical parameters with a greater degree of accuracy than generic models [25], which is particularly important for the precise finite element analysis and digital twin system development required in this study. The MRI-based individualized modeling approach ensures that the digital twin system accurately represents the specific anatomical and biomechanical characteristics of each participant, providing high-fidelity biomechanical modeling essential for the accurate real-time visualization of knee joint forces and stress distributions during sit-to-stand movements.

The knee joint is composed of complex surfaces, and even with advanced surface modeling software, constructing an accurate knee joint model remains challenging. By analyzing MRI images through a medical imaging control system, an accurate knee joint model can be established. The created model, using Materialise Mimics Innovation Suite Research 21.0, is then imported into Geomagic 2021 for optimization, resulting in a more precise 3D model of the knee joint. This optimized model is then modified in SolidWorks 2021 SP5.1, where geometric repair and simplification are performed to reduce computational complexity and enhance efficiency, followed by finite element analysis in ANSYS 17.0.

After processing the knee joint model, it is imported into finite element analysis software for the final parameter settings. The knee joint model is discretized into a finite element model through mesh generation, converting the continuous geometric structure into discrete elements. Next, the physical properties of each component are integrated to assign different material properties to the knee joint finite element model. Additionally, based on human anatomy, appropriate boundary conditions are set to simulate real physiological constraints for the model. The applied constraints mainly involve the distal tibia and proximal femur, restricting the tibia from moving along the X-, Y-, and Z-axes and the femur from moving along the Y- and Z-axes. The femur is allowed to freely slide along the X-axis, simulating the flexion process of the knee joint. This completes the construction of the knee joint finite element model. In subsequent analysis, finite element analysis software is used to perform static and dynamic simulations of the model, assessing the distribution of physical quantities such as stress and displacement in the knee joint during the sit-to-stand movement.

In finite element analysis, selecting appropriate knee flexion key points is essential for accurate surrogate model fitting. In addition to significant maxima, minima, and inflection points, using Latin hypercube sampling to increase key points enhances the significance of the analysis results.

Latin hypercube sampling is a statistical sampling technique that efficiently generates representative samples within a given design space. Four main steps are involved in using this method to supplement key points. First, the knee joint angles are divided into equal intervals, where each dimension is partitioned into an equal number of non-overlapping subintervals, and one sample point is chosen in each subinterval. Then, a random position is selected in each dimension to place a sample point, ensuring that there is exactly one sample point in each subinterval. Finally, the sample points in each dimension are randomly arranged to generate the Latin hypercube samples. This method ensures the uniform distribution of sample points across each dimension, with only one point per subinterval, avoiding repetition within the same interval. As a result, it provides a more comprehensive coverage of the design space with minimal additional computation, enhancing the representativeness of the finite element analysis results.

A point selection analysis of the finite element model can effectively reduce the computational load, but the results from this analysis do not meet continuity requirements, so data fitting is needed for the finite element analysis results. To improve the comprehensiveness of the fitting results, an improved radial basis function is used to fit the finite element data of knee flexion. First, the finite element data of the knee at different angles is preprocessed, and then the improved radial basis function is used to fit the preprocessed data, obtaining the force distribution of the knee throughout the flexion process.

Before fitting the finite element data, preprocessing is required to eliminate the effects of noise and outliers. Standardizing the finite element data eliminates the influence of dimensional units. The data is then mean-centered and divided by its standard deviation, ensuring a mean of 0 and a standard deviation of 1, completing the standardization process. To address the impact of outliers in the fitting data, an outlier detection method is used to filter the data. The interquartile range of the data is calculated, and data outside this range are considered outliers and removed to eliminate their influence.

After preprocessing, the improved radial basis function is used to fit the finite element data of knee flexion. The use of the commonly used radial basis function is a widely applied method for interpolation and function approximation. Its basic principle is to use a set of basis functions to map points from high-dimensional space to low-dimensional space, thereby fitting the data. The mathematical expression of the radial basis function is as follows:

$$\mathsf{\phi }(\mathrm{x})={\sum }_{i=1}^N{\omega }_i·\phi \left(‖x-x_i‖\right)$$

(6)

During the adaptive basis function selection process, cross-validation is used to assess the performance of different basis functions, and the optimal basis function is selected based on the evaluation results.

In the cross-validation method, the dataset is divided into a training set and a test set. The improved radial basis function is applied to fit the training set, and the fitting performance is evaluated on the test set. By adjusting the basis functions and the basic parameter settings, different fitting outcomes are generated. The optimal basis function and parameters are determined by analyzing these results, followed by a final fitting. The fitting with the improved radial basis function resulted in a continuous force distribution of the knee joint throughout the entire flexion process, providing a basis for the further study of the biomechanical characteristics during knee joint flexion.

2.3. Digital Fusion and Visualization

Based on the continuous finite element analysis results, a knee joint animation model is constructed using 3D modeling software. The finite element data is used as cloud map data to support the animation display of the knee joint, and appropriate color schemes are applied for visualization, ultimately creating a digital twin system.

To build a digital twin model of the knee joint in real-time 3D interactive software, it is necessary to create an anatomical model of the knee joint, including the femur, tibia, meniscus, and cartilage. Similarly, medical imaging control systems are used to analyze MRI images and construct models for all the bones in the knee joint anatomical structure. These models are then optimized in 3D modeling software and converted into formats compatible with real-time 3D interactive software, such as OBJ, FBX, or STL. A new project is then created in the real-time 3D interactive software, and the optimized knee joint 3D model is imported into the project’s resources. An empty game object is created in the scene, and the knee joint 3D model is added as a child object. The position, scale, and rotation are adjusted to ensure the correct anatomical structure is displayed.

To import finite element data as contour data into real-time 3D interactive software, an improved radial basis function is used to fit the finite element data for knee joint flexion, obtaining force data at each node for different angles, thus generating continuous finite element data. Additionally, the force value data for each node is mapped to a predefined RGB color scale, where red represents high-stress regions, green denotes moderate-stress regions, and blue indicates low-stress regions. The specific color scale range is determined based on the pressure value intervals, ensuring that the pressure values are displayed with appropriate resolution in the animation.

Therefore, a real-time 3D interactive software script is written to apply the read contour data file to the knee joint model. During the reading process, the maximum and minimum values in the data are used to define the RGB color scale range, with each node assigned a material and its color set according to the contour data. Simultaneously, a data input interface is set up, requiring real-time updates of the contour map on the knee joint model based on the input angle values. The input interface is implemented via sliders or other controls in the real-time 3D interactive software user interface, facilitating the simulation of actual inputs and adjusting the knee joint model’s angle. Finally, to enhance the real-time display in the 3D interactive software, a light source is added to the knee joint model to more clearly observe the changes in the contour map.

2.4. Real-Time Data Acquisition

During the development of both the front-end and back-end of the digital twin system, interfaces were provided for data input, enabling diverse input methods. Currently, there are many sensors available for real-time data acquisition, and when the accuracy requirements for recognition are not high, cameras are a convenient and simple option. Additionally, the application of the knee joint digital twin model targets the human body, involving the identification of the hip, knee, and ankle joints in RGB animated images. The recognition of these joints has been well-developed in the field of machine vision. By using a monocular camera, it is possible to quickly obtain human posture data and analyze the angles of the hip, knee, and ankle joints in the 2D plane, which can be used as input for constructing a complete digital twin system [26].

One of the main factors influencing the accuracy and speed of monocular camera recognition is the network architecture. The identification of the knee joint angle can be accomplished based on human key point recognition. Human key point recognition is a small object recognition task, and enhancing the network’s sensitivity to small objects can significantly improve recognition accuracy. The High-Resolution Network preserves more feature information from the original data throughout the network by integrating downsampling networks [27].

Among the two types of layers mentioned above, there is also a feature layer (feature map) that maintains the same size as the high-resolution layer. This feature layer, not processed by the bottleneck layer, retains more spatial feature information. Additionally, since its size matches that of the high-resolution layer, it does not require upsampling or downsampling during the feature fusion process, thus reducing the computational time of the network model. Before the fully connected processing of the high-resolution feature layer, the retained feature layer is directly fused with the final high-resolution feature layer. The size of the retained feature layer is 64 × 48, thus forming the fusion network model, as shown in Figure 3.

Common feature fusion methods include stacking fusion, averaging fusion, weighted fusion, and deep fusion. Among these, the weighted fusion method allows for adjusting the weight parameters to increase the contribution of important fusion layers, offering high flexibility [28]. Stacking fusion, on the other hand, retains all information from the fused feature layers, and its proper use can enhance the final recognition performance. To ensure the network retains more shallow feature information, the constructed network uses stacking fusion for feature layer integration.

3. Results

Based on the derived force conversion equations and pose–force experiments, the knee joint moments of ten volunteers during multiple sit-to-stand movements can be calculated. It was observed that the knee joint moment variation curves of the ten volunteers during the sit-to-stand movements were similar and closely related to the volunteers’ body weight. For example, for a 175 cm tall, 65 kg male adult, the joint moments, forces (F₁, F₂, F₃), and ground reaction force corresponding to the positions and angles of different joints (θ₁, θ₂, θ₃) are shown in

Table 2. Knee joint torque calculation data.

Knee Angle (β)	F1/N	F2/N	F3/N	Knee Joint Torque (Mknee)/N·m	p
107°	100 ± 10	150 ± 9	200 ± 11	30.4 ± 3.2	0.12
140°	120 ± 5	180 ± 6	240 ± 6	136.7 ± 3.7	0.11
179°	140 ± 8	210 ± 7	280 ± 8	98.2 ± 3.4	0.18

. The relationship between the continuous knee joint moments and knee joint angle (β) is shown in Figure 4.

As shown in Figure 4, the variation in knee joint moment during the sit-to-stand transition exhibits distinct nonlinear characteristics. During the increase in the knee joint angle from 100° to 146.8°, the knee joint moment shows a monotonically increasing trend. When the angle reaches 146.8°, the knee joint moment reaches its maximum value of 136.7 N·m. As the knee joint angle increases further from 146.8° to 175.3°, the knee joint moment begins to decrease, reaching a minimum value of approximately 92.3 N·m at 175.3°. Additionally, within the knee joint angle range of 146.8° to 175.3°, the decreasing trend in the knee joint moment is not monotonic but shows multiple oscillations. The first color in the picture represents the preparation and bending phase, the second color represents the descending phase, and the third color represents the stabilization phase. These oscillations indicate that the factors affecting the knee joint moment vary within this range, potentially including muscle strength and acceleration.

Individual biomechanical analysis revealed significant correlations between participant characteristics and knee joint loading patterns during sit-to-stand motion:

• Peak knee torque demonstrated strong positive correlation with body weight across all participants:

  -

  Lightweight participants (55–65 kg, n = 3): 118.5 ± 8.2 N·m.

  -

  Mediumweight participants (66–75 kg, n = 4): 136.7 ± 12.1 N·m.

  -

  Heavyweight participants (76–92 kg, n = 3): 152.8 ± 15.3 N·m (p < 0.01).

• Anthropometric correlations with biomechanical parameters:

  -

  Body weight was strongly correlated with peak knee torque (r = 0.89, p < 0.001).

  -

  BMI was significantly associated with joint loading duration (r = 0.72, p < 0.01).

  -

  Height showed moderate correlation with angle at peak torque (r = 0.58, p < 0.05).

• Gender-based differences were observed in movement patterns:

  -

  Male participants (n = 6) exhibited higher peak torque values (142.3 ± 16.8 N·m) compared to females (n = 4, 128.7 ± 11.2 N·m, p < 0.05).

  -

  Female participants demonstrated earlier peak torque occurrence (at 143.2° ± 3.1°) compared to males (at 147.8° ± 2.8°, p < 0.05).

• Age-group specific biomechanical characteristics:

  -

  Young adults (25–35 years) showed the most consistent torque patterns with minimal inter-individual variation.

  -

  The baseline framework derived from young adults provides a reference standard for comparison with middle-aged and elderly populations.

To avoid unnecessary time expenditure, 10 calculated moment points are first selected for finite element analysis, including the significant 146.8° maximum point, the 175.3° minimum point, and the three turning points at 145°, 147°, and 161°. Based on this, the remaining critical moment points are selected for finite element analysis using the Latin hypercube sampling method. These points are shown in

Table 3. Finite element analysis selected analysis points.

Knee Angle/°	110	120	140	145	147	149	161	165	173	180
Knee moment/(N·m)	46	107	136	125	127	111	114	117	97	98

.

A further finite element analysis of the selected key points allows for the analysis of the stress at the knee joint during the sit-to-stand motion. For example, the finite element data for when the knee joint reaches 110°, 120°, 130°, 140°, 161°, and 173° is shown in Figure 5. The results show that the stress distribution at the knee joint varies at different knee angles during the sit-to-stand motion. Furthermore, during the sit-to-stand transition, the knee joint undergoes significant stress, particularly on the meniscus and cartilage. Taking the knee joint at 110° as an example, the finite element data for the meniscus and cartilage at the knee joint is shown in Figure 6. This is because the meniscus serves as a cushion when transmitting pressure between the femur and tibia. Additionally, the stress distribution of the cartilage indicates that it plays a significant role in dispersing pressure across the joint surface.

The improved radial basis function fitting of the finite element data for knee joint flexion, based on computed values at ten discrete angles (110°, 120°, 140°, 145°, 147°, 149°, 161°, 165°, 173°, 180°), enables the continuous prediction of stress distribution patterns across the full range of knee joint motion. To validate the RBF fitting accuracy, additional finite element analyses were performed at intermediate angles not used in the original fitting process (115°, 130°, 150°, 160°, 170°). The stress distribution predictions from the RBF model showed good agreement with these validation finite element results, with an overall average error of approximately 10% for the stress distribution patterns. This demonstrates that the improved RBF effectively captures the stress distribution characteristics during knee flexion and provides a reliable approach to predicting knee joint biomechanical behavior at arbitrary angles within the physiological range.

Based on the predicted maximum knee joint stress, virtual reality and computer graphics technologies are employed to capture real-time pose information on the knee joint using a monocular camera. As the test subject performs different actions, the monocular camera estimates the body posture from the side and uploads the knee joint angle data to the host computer. The host computer then displays the biomechanical characteristics of the knee joint in a virtual character in real time. The biomechanical characteristics of the knee joint are presented in color, with the equivalent stress of the knee joint mapped to specific colors according to the predicted stress range in the script. The camera posture recognition and real-time 3D interactive software visualization are shown in Figure 7.

The test subject performs a sit–stand motion test to assess posture recognition and virtual knee joint visualization. The human posture recognition results are displayed on the left, while the virtual character and knee joint are shown on the right. Based on the equivalent stress at different knee joint angles, the knee joint is displayed in various colors. Red and blue represent the maximum and minimum values, respectively, with most of the equivalent stress values on the virtual knee joint shown in blue. The colored regions are mainly concentrated in the meniscus and cartilage, which is consistent with the results of the discontinuous finite element analysis.

4. Discussion

The proposed biomechanical framework demonstrates significant methodological advancements in knee joint analysis through the integration of experimental measurements with finite element modeling. The knee joint bears significant loads during daily activities and is the most commonly affected area in elderly individuals, making its biomechanical characteristics a key research focus. Some researchers have analyzed the mechanical properties of the knee joint for specific movements, including stair climbing, moderate-speed running, and jumping [29,30,31]. The system achieved superior accuracy compared to traditional finite element approaches that rely solely on assumed boundary conditions and simplified load models [32]. The identification of peak knee joint moments at 146.8° knee flexion (136.7 N·m) provides crucial clinical insights that align with biomechanical principles governing elderly mobility limitations during sit-to-stand transitions. This finding is particularly significant as it indicates the critical angle where elderly individuals experience the maximum joint loading, suggesting that targeted rehabilitation protocols should focus on strength training within this range while avoiding the prolonged maintenance of this position. Sit-to-stand transitions occur frequently in the daily activities of elderly individuals, representing a primary load-bearing activity for the knee joint. Building on this, researchers have used the D-H motion model and finite element analysis to study knee joint mechanics, aiming to establish effective approaches to analyzing knee joint biomechanics [33]. The D-H analysis method simplifies the human body into a linkage model, uniformly adding the masses of muscles and other tissues to the linkage, effectively capturing the motion characteristics of the knee joint. However, it is insufficient as a foundation for dynamic analysis. Using the simplified model, the principle of moment equilibrium can convert ground reaction forces into knee joint forces [34], supplementing the dynamic analysis of the knee joint and providing a foundation for finite element analysis.

The stress concentration patterns observed in the meniscus and cartilage regions corroborate clinical observations of degenerative changes in these tissues among elderly populations, validating the model’s clinical relevance. Finite element analysis is a widely used method in biomechanics, and analyzing the knee joint with FEA not only validates the theoretical analysis results but also lays the foundation for research on digital twin animation models of the knee joint. Traditional FEA methods mainly rely on assumed boundary conditions and simplified load models, simulating the target stress conditions based on theoretical assumptions and empirical data [32]. Without actual measurement data, traditional FEA cannot accurately predict the stress and strain distribution in the knee joint during different sit-to-stand movements [35]. Optical motion capture and six-dimensional force–torque measurement techniques can analyze the actual knee joint moments during sit-to-stand movements. Using these moments as a basis for FEA allows for more accurate predictions of stress and strain distribution in the knee joint during such motions. The improved radial basis function fitting yielded enhanced prediction capabilities, capturing the complexity of stress and strain distribution in the knee joint more effectively than traditional fitting methods [36]. Compared to traditional FEA methods that simulate target stress conditions based on theoretical assumptions and empirical data, the proposed approach utilizing actual knee joint moments during sit-to-stand movements allows for more accurate predictions of stress and strain distribution [32]. To evaluate the differences between these methods in predicting knee joint stress and strain, traditional FEA and FEA based on actual moments were both used to predict stress and strain distribution. The predicted results were compared with data from the existing literature, indicating that FEA based on actual moments has a smaller average error in predicting knee joint stress and strain distribution, demonstrating the validity of the proposed method and providing valuable insights for knee rehabilitation, pain assessment, and the prevention of joint diseases.

The integration of computer vision-based pose estimation with finite element modeling enables real-time biomechanical assessment, addressing a critical gap in current clinical practice where traditional finite element visualization methods are completed before analysis and cannot adapt to real-world conditions. The visualization of finite element data is an effective tool for biomechanical analysis, allowing for a clear view of the static and dynamic mechanical properties of the analysis target. However, this type of visualization is completed before the analysis and cannot adapt to real-world conditions. Building a digital twin model requires integrating the virtual model with actual conditions. Therefore, a digital model of the knee joint is constructed using 3D interactive software, with a key point recognition network implemented to monitor knee joint angles. The actual knee joint angles are then mapped in real time to the digital knee joint model, creating a complete digital twin system for the knee joint [37]. Compared with traditional finite element visualization methods, this approach easily retrieves joint forces under specific knee joint angle conditions, not only aiding in improving diagnosis, treatment, and rehabilitation but also providing researchers with a theoretical foundation.

Several methodological limitations should be acknowledged while considering future research directions that could enhance the system’s clinical utility. The participant cohort was limited to 10 healthy adults across a broad age range (25–75 years), potentially restricting generalizability to populations with existing knee pathologies such as osteoarthritis or ligament injuries. The current finite element model assumes simplified material properties and focuses exclusively on sagittal plane motion, while real-world sit-to-stand movements involve complex three-dimensional kinematics that contribute to overall joint loading. Additionally, the system primarily focuses on instantaneous knee joint moment detection and does not account for the damage caused by prolonged postures or the cumulative effects of repeated loading cycles. However, there is still value in further research. The current system primarily focuses on instantaneous knee joint moment detection and does not account for the damage caused by prolonged postures. Future studies should consider the effects of different loads and the duration of specific knee joint angles on knee joint damage to progressively improve the evaluation performance of the entire system. Integration with additional sensor technologies could enable the continuous monitoring of knee joint biomechanics during daily activities, providing unprecedented insights into real-world loading patterns and cumulative damage mechanisms. The development of intervention protocols based on real-time digital twin feedback represents a promising avenue for personalized rehabilitation, where the system could provide immediate biomechanical guidance to optimize exercise prescription and monitor treatment progress. Furthermore, expansion to include multi-planar motion analysis and validation in populations with various degrees of knee pathology would enhance the system’s clinical applicability and provide more comprehensive insights for knee rehabilitation, pain assessment, and the prevention of joint diseases.

5. Conclusions

The visualization of stress distributions represents a substantial advancement in clinical diagnostic tools, particularly valuable for elderly populations where individualized assessment is crucial for effective rehabilitation planning. The successful integration of computer vision, finite element modeling, and interactive visualization technologies demonstrates the feasibility of accessible, accurate biomechanical analysis systems for widespread clinical implementation. Future developments should focus on transformative applications that extend beyond current clinical practice limitations, particularly through integration with artificial intelligence and machine learning algorithms to enable predictive healthcare models that could anticipate joint degeneration before clinical symptoms manifest. The digital twin framework provides a foundation for developing comprehensive musculoskeletal health monitoring systems where multiple joint interactions could be analyzed simultaneously, while the combination of real-time feedback with therapeutic interventions could revolutionize rehabilitation approaches through closed-loop systems that adapt dynamically based on patient progress. The convergence of digital twin technology with emerging fields such as regenerative medicine and bioengineering presents unprecedented opportunities for developing next-generation healthcare solutions that bridge the gap between computational modeling and clinical practice, ultimately transforming how we understand, diagnose, and treat musculoskeletal disorders in aging populations.