During landing, lower-body bones experience large mechanical loads and are deformed. It is essential to measure bone deformation to better understand the mechanisms of bone stress injuries associated with impacts. A novel approach integrating subject-specific musculoskeletal modeling and finite element analysis is used to measure tibial strain during dynamic movements.
Bone stress injuries are common in sports and military trainings. Repetitive large ground impact forces during training could be the cause. It is essential to determine the effect of high ground impact forces on lower-body bone deformation to better understand the mechanisms of bone stress injuries. Conventional strain gauge measurement has been used to study in vivo tibia deformation. This method is associated with limitations including invasiveness of the procedure, involvement of few human subjects, and limited strain data from small bone surface areas. The current study intends to introduce a novel approach to study tibia bone strain under high impact loading conditions. A subject-specific musculoskeletal model was created to represent a healthy male (19 years, 80 kg, 1,800 mm). A flexible finite element tibia model was created based on a computed tomography (CT) scan of the subject's right tibia. Laboratory motion capture was performed to obtain kinematics and ground reaction forces of drop-landings from different heights (26, 39, 52 cm). Multibody dynamic computer simulations combined with a modal analysis of the flexible tibia were performed to quantify tibia strain during drop-landings. Calculated tibia strain data were in good agreement with previous in vivo studies. It is evident that this non-invasive approach can be applied to study tibia bone strain during high impact activities for a large cohort, which will lead to a better understanding of injury mechanism of tibia stress fractures.
Bone stress injuries, such as stress fractures, are severe overuse injuries requiring long periods of recovery and incurring significant medical cost1,2. Stress fractures are common both in athletic and military populations. Among all sports related injuries, stress fractures account for 10% of the total3. In particular, track athletes face a higher injury rate at 20%4. Soldiers also experience a high rate of stress fractures. For instance, a 6% injury rate was reported for the US Army1 and a 31% injury rate was reported in the Israeli Army5. Among all reported stress fractures, tibia stress fracture is the most common one6,7,8.
Sports and physical trainings with a higher risk of tibia stress fracture are normally associated with high ground impacts (e.g., jumping, landing, and cutting). During locomotion, a ground impact force is applied to the body when the foot contacts the ground. This impact force is dissipated by the musculoskeletal system and footwear. The skeletal system serves as a series of levers allowing muscles to apply forces to absorb the ground impact9. When the leg muscles cannot adequately reduce the ground impact, lower-body bones must absorb the residual force. Bone structure will experience deformation during this process. Repetitive absorption of residual impact force may result in microdamages in the bone, which will accumulate and become stress fractures. To date, information related to bone reaction to external ground impact forces is limited. It is important to study how the tibia bone responds to the mechanical load introduced by high impact forces during dynamic motions. Examining tibia bone deformation during high impact activities could lead to a better understanding of the mechanism of tibia stress fracture.
Conventional techniques used to measure bone deformation in vivo rely on instrumented strain gauges10,11,12,13,14,15. Surgical procedures are needed to implant strain gauges on bone surface. Due to the invasive nature, in vivo studies are limited by a small sample of volunteers. In addition, the strain gauge can only monitor a small region of the bone surface. Recently, a non-invasive method utilizing computer simulation to analyze bone strain was introduced16,17. This methodology allows for the ability to combine musculoskeletal modeling and computational simulations to study bone strain during human movement.
A musculoskeletal model is represented by a skeleton and skeletal muscles. The skeleton consists of bone segments, which are rigid or non-deformable bodies. Skeletal muscles are modeled as controllers using the progressive-integral-derivative (PID) algorithm. The three-term PID control uses errors in estimation to improve the output accuracy18. In essence, PID controllers representing muscles try to duplicate body movements by developing necessary forces to produce length changes of the muscles over time. The PID controller uses the error in the length/time curve to modify the force for reproducing the movement. This simulation process creates a feasible solution to coordinate all muscles to work together to move the skeleton and produce the body movement.
One or more segments in the skeleton of the musculoskeletal model can be modeled as flexible bodies to allow measurement of deformation. For instance, the tibia bone can be broken down into a finite number of elements, which consists of thousands of elements and nodes. The effect of mechanical loading on the flexible tibia can be examined through finite element (FE) analysis. The FE analysis calculates the loading response of individual elements over time. As the number of bone elements and nodes increase, the computation time of the FE analysis will significantly increase.
To reduce computational cost with accurate evaluation of flexible bodies' deformation, modal FE analysis has been developed and used within the automotive and aerospace industry19,20. Instead of analyzing individual FE elements' responses to mechanical load in the time domain, this procedure assesses an object's mechanical responses based on different vibrational frequencies in the frequency domain. This method results in a significant reduction in computation time while providing accurate measurement of deformation20. Although modal FE analysis has been widely used to study mechanical fatigue in automotive and aerospace areas, the application of this method has been very limited in human movement science. Al Nazer et al., used a modal FE analysis to examine tibial deformation during human gait and reported encouraging results16,17. However, their method was greatly affected by only using limited kinematic data from an experiment to drive the computer simulations; There were no real ground impact forces used to assist the simulations. This approach may be reasonable for studying low impact slow motions such as walking, but it is not a feasible solution to study high ground impact movements. Thus, in order to examine lower-body bone reactions during dynamic high impact activities, it is essential to develop an innovative approach to address the limitations associated with the previously reported method. Specifically, a method utilizing accurate experimental kinematic data and real ground impact forces must be developed. Therefore, the goal of this study was to develop a subject-specific musculoskeletal model to perform multibody dynamic simulations with modal FE analysis to examine tibial strain during high impact activities. A dynamic high impact movement represented by drop-landings from different heights was selected to test the method.
The experiment was conducted under the Helsinki Declaration. Prior to data collection, the subject reviewed and signed the consent form approved by the University Institutional Review Board before participating in the study.
1. CT Imaging Protocol
2. Anthropometric Measurement Protocol
3. Motion Capture Protocol
NOTE: See Table of Materials for all software and tools used.
4. Subject Specific Modeling Procedure
5. Multi-body Dynamics Simulations
6. Creating a Flexible Tibia Model
7. Strain Data Analyses
A healthy Caucasian male (19 years, height 1,800 mm, mass 80 kg) volunteered for the study. Prior to data collection, the subject reviewed and signed the consent form approved by the University Institutional Review Board before participating in the study. The experiment was conducted under the Helsinki Declaration. The experiment was performed based on the following protocol.
In order to verify the accuracy of the forward dynamic simulation, lower-body joint angles from the simulation were compared to the corresponding joint angles measured from the motion capture data processed by a biomechanics analysis program. A statistical analysis software was used to calculate cross-correlation coefficients of the comparisons. The cross-correlation calculation allowed 10 lags in both positive and negative directions. Each lag corresponded to a one time step in the forward dynamic simulation (0.01 s). The maximum cross-correlation coefficients were identified.
Visual inspection of Figure 2, Figure 3,and Figure 4 demonstrates the similarities between the joint angles produced with the experimental data and with the simulation data. Strong cross-correlation coefficients were found between the experimental and simulation joint angles at zero lag (Table 1).
The peak strains at the antero-medial region of the mid-tibial shaft during landing from three different heights are presented in Table 2. Among the three landing heights, the 52 cm landing condition demonstrated the largest peak maximum principal, peak minimum principal, and peak maximum shear strains. In addition, it was observed that, as the drop height increased, the peak maximum principal strains increased.
Figure 1: Subject-specific musculoskeletal model created in the present study. This lower body musculoskeletal model includes six rigid segments (pelvis, left and right femurs, left tibia, and left and right feet) and one flexible tibia (right tibia). 90 leg muscles are attached to the model. For visualization purpose, each muscle is represented by a coral color line. Joint centers are represented by light blue balls for right lower body and purple balls for left lower body. Please click here to view a larger version of this figure.
Figure 2: Joint angle comparisons (in degrees) between experimental motion capture data and simulation data for drop-landing from 26 cm height. Solid lines represent joint angles computed with experimental motion capture data. Dotted lines represent joint angles produced by multibody dynamic simulation data. Vertical lines represent moments of impact. Please click here to view a larger version of this figure.
Figure 3: Joint angle comparisons (in degrees) between experimental motion capture data and simulation data for drop-landing from 39 cm height. Solid lines represent joint angles computed with experimental motion capture data. Dotted lines represent joint angles produced by multibody dynamic simulation data. Vertical lines represent moments of impact. Please click here to view a larger version of this figure.
Figure 4: Joint angle comparisons (in degrees) between experimental motion capture data and simulation data for drop-landing from 52 cm height. Solid lines represent joint angles computed with experimental motion capture data. Dotted lines represent joint angles produced by multibody dynamic simulation data. Vertical lines represent moments of impact. Please click here to view a larger version of this figure.
Droplanding Heights | ||||||
26 cm | 39 cm | 52 cm | ||||
Lower-body Joints | Cross-correlation Coefficient | Lag | Cross-correlation Coefficient | Lag | Cross-correlation Coefficient | Lag |
Ankle | 0.998 | 0 | 0.998 | 0 | 0.999 | 0 |
Knee | 1 | 0 | 1 | 0 | 1 | 0 |
Hip | 0.999 | 0 | 1 | 0 | 1 | 0 |
Table 1: Cross-correlation coefficients and lags from comparisons between joint angles produced based on motion capture data and joint angles produced from simulation data. One trial at each height was used for the comparisons. Zero lag indicates no difference in time when joint angles were produced between the two approaches.
Droplanding Heights | |||
Bone Strain (µstrain) | 26 cm | 39 cm | 52 cm |
Maximum Principal | 1160 | 1270 | 1410 |
Minimum Principal | -659 | -598 | -867 |
Maximum Shear | 893 | 870 | 1140 |
Table 2: Tibia bone strains at the antero-medial aspect of the mid-tibial shaft during drop-landing from three different heights. Maximum principal, minimum principal, and maximum shear strains are presented.
The purpose of this study was to develop a non-invasive method to determine tibia deformation during high impact activities. Quantifying tibia strain due to impact loading will lead to a better understanding of tibia stress fracture. In this study, a subject-specific musculoskeletal model was developed, and computer simulations were run to duplicate the drop-landing movements performed in a laboratory setting. The effect of drop-landing height on tibial strain was examined. In this study, we observed that as the drop-landing height increased, so did the peak maximum principal strains. Also, among the three landing conditions, the 52-cm condition resulted in the highest peak maximum principal, minimum principal, and maximum shear strains.
Limited in vivo data are available in the literature with regard to the effect of drop-landing on tibia strain. Milgrom et al., reported the maximum principal strain ranging from 896-1,007 µstrain during landings from three different heights (26, 39, 52 cm)14. Ekenman et al. reported an average strain of 2,128 µstrain during landing from a 45 cm height13. The maximum principal strain from the computer simulations were between 1,160-1,410 µstrain during landing from three different heights (26, 39, 52 cm), which were higher than those reported by Milgrom et al. but were lower than that reported by Ekenman et al.13,14
The following reasons may contribute to the difference in strain between the current and previous studies. First, demographic differences exist between the subjects in this and previous studies. We used a physically active male subject. Ekenman's study involved a female subject13. Milgrom's study included both males and females and reported the average strains14. Second, footwear may play a role in differences in bone strain.Lanyon et al. studied the effect of footwear on tibial strains, they found that walking and running barefoot resulted in greater strains compared to wearing shoes12. The current study used a barefoot landing protocol, the strain values calculated were greater than those by Milgrom et al. study, which used a landing protocol with standard athletic shoes14. Third, alterations in landing strategy may also influence the tibial strain. In the present study, it was possible that the subject might choose a strategy such as increasing trunk flexion to help reduce the impact when the drop-landing height increased. This strategy could help protect the tibia from large strains. Milgrom et al. also suggested a possible protective strategy used by his subjects14. Fourth, there could be a slight difference in locations where tibial strain was monitored. Our study examined the bone strain at the antero-medial aspect of the mid-tibial shaft. In Milgrom et al., strains were recorded from the medial region of the mid-tibial shaft14. The sagittal plane bending moment on the tibia during landing may result in high maximum principal strain in places near the anterior regions of the tibial shaft. Nonetheless, our strain results appear to be comparable to results from previous studies and fall in the strain range (400-2,200 µstrain) reported by those in vivo studies10,13,14.
The tibial strain values obtained from this non-invasive approach are influenced by the accuracy of the musculoskeletal model. Cross-correlations were performed to examine the experimental joint angle data and computer simulation data during drop-landings. Strong correlation coefficients were found between the experimentally measured data and computer simulation data. This indicates that the subject-specific model developed in this study can reasonably replicate the drop-landing movements. In addition, the tibial strains reported in this study were well below 3,000 µstrain, which confirms the assumption derived from other studies that the tibia bone deformation is linear during drop-landings14,15. Thus, with the calculated strain data being in the linear range and excellent replications of landing movement patterns, we concluded that the strain data obtained from this non-invasive approach were reasonably accurate. Furthermore, the current study only recruited one subject to examine bone strain during drop-landings. Future studies could examine whether there is a dose response relationship between drop-landing heights and tibia bone strains by using a large sample size.
The significance of this study is to introduce an innovative non-invasive method of measuring bone deformation. This non-invasive approach addresses the limitations associated with the conventional in vivo strain gauge measurement, which could not be applied to a large sample of human subjects. In addition, the current proposed method addresses limitations associated with a previously reported non-invasive method16,17, which was impacted by using limited kinematic data to drive the simulations and was only suitable for studying low ground impact movements such as walking. As tibia stress fractures remain high in the athletic and military populations, it is critical to study the effect of high impact physical activities (e.g., running, jumping, and cutting) on tibial bone responses. The current innovative non-invasive approach appears to be a feasible solution for conducting these studies. This will shed light on developing adequate physical training protocols for athletes and military recruits to reduce tibia stress injuries. Furthermore, this innovative non-invasive method presents an opportunity to evaluate bone strains in other bones inaccessible with implemented gauges such as the femur and navicular.
Important issues related to this non-invasive bone strain measurement must be addressed here. Firstly, a generic lower-body musculoskeletal model is created based on the individual's age, gender, body mass, and body height by using the GeBOD database27. Experimentally measured spatial locations of lower-body joint centers are used to refine the musculoskeletal model. Compared to the generic model, this subject-specific modeling approach presents a better musculoskeletal model of the individual's physical structure. Future studies could consider developing a full body musculoskeletal model for upper body movement during multibody dynamic simulations.
Secondly, there are 45 muscles assigned to each leg in the model. Origins and insertions of the muscles are anatomically determined27. A simple closed-loop algorithm is used to manage individual muscle's force production. Specifically, the change of muscle length history during dynamic motion such as landing is recorded via the inverse kinematic simulation. When the forward dynamic simulation is run, a PID controller was assigned to each muscle and used to regulate the necessary muscle force for duplicating the muscle length history recorded earlier. This simple closed-loop algorithm produces excellent results in replicating joint kinematics. However, this approach does not account for neural coordination among muscles with similar functions and could not account for co-contractions from antagonists. Future works may consider using a Hill-based muscle model, which consists of an active contractile element (CE) and a passive elastic element (PE). The Hill-based model integrates the muscle's force-velocity and force-length relationships to produce tension. The calculated muscle force can then be compared to EMG data for validation.
Thirdly, a subject-specific tibia model is created from CT images to represent the true geometry of the tibia bone under investigation. While CT imaging is the primary method to obtain the true geometry of the tibia bone, other imaging techniques such as magnetic resonance imaging (MRI) can also be used to produce the subject-specific tibia model. Also, the current modeling protocol assumes the material property of the tibia to be isotropic. A generic density value of 1.9E-6 kg/cm3 and a single Young's modulus of 17 GPa are assigned to all tibial FE elements. Future studies may consider obtaining density values from all regions in the tibia. This can be done by introducing a calibrated phantom during the CT scan. Bone density can then be calculated based on CT's Hounsfield units. Young's modulus of the bone tissue can be further calculated based on density data. Assigning subject-specific material properties to the tibial FE model will yield more realistic bone strain results through simulations.
Fourthly, a modal FE analysis is used to compute bone strains. During this modal analysis, frequency responses are computed to match mechanical loadings (linear and angular forces) imposed to the knee and ankle joints. A flexible tibia represented by an MNF file is generated from the modal FE analysis. This flexible tibia is introduced to the subject-specific musculoskeletal model to replace the corresponding rigid tibia. During the subsequent forward dynamic simulation, deformation of the flexible tibia at each time step is quantified. Compared to the traditional FE analysis, which computes the mechanical responses of an FE object consisting of thousands of degrees of freedom (thousands of elements and nodes) at each time step of motion, this modal analysis approach deals with far less numbers of degrees of freedom within the frequency domain (e.g., 12 loading conditions from the knee and ankle joints). With the modal analysis approach, computation time is significantly reduced from multiple hours/days to less than 1 h for a typical simulation. Besides the benefit of consuming less computer time, modal analysis approach is ideal for computing small deformation (< 10%) experienced by stiff structures such as bone tissue.
Finally, the advantages of the current non-invasive approach over a previously reported method16,17 must be addressed here. A) Our musculoskeletal model is refined to possess more accurate lower-body joint centers, which are produced through the functional joint assessment22. However, the previous method defines joint centers for the model based on the Plug-in Gait procedure21 with the help of using a limited number of visual markers. B) This model incorporates 45 muscles to each leg compared to only 12 muscles used in the previous model. Increasing the number of leg muscles in the musculoskeletal model would improve the quality of the simulation. C) During the inverse kinematic simulation, the musculoskeletal model is driven by a set of 34 visual markers placed on the lower body, which allows better duplication of the actual movement. In contrast, the previous approach only uses 16 markers to drive the same simulation, and this may introduce numerical errors to the simulation. D) During the forward dynamic simulation, the real ground impact forces are applied to this musculoskeletal model to simulate the movement. However, the previous method is not able to incorporate ground impact forces in the simulation. Without using real ground impact forces during forward dynamic simulations, the previous method is limited to study low impact activities. The above steps we take to improve the fidelity of the subject-specific musculoskeletal model appear to be successful for examining tibial deformation during human movements. The addition of incorporating true ground impact forces in simulations proves to be necessary to study bone strain during high ground impact activities.
In conclusion, in vivo tibia bone deformation is normally measured by the conventional stain gauge method. This approach is associated with limitations such as an invasive nature, fewer volunteers, small bone surface areas being analyzed, etc. A novel approach employed multibody dynamic simulations with modal FE analysis was proposed in this study to quantify tibia deformation during drop-landings. It is evident that this approach can address the limitations inherited from the conventional strain gauge measurement. In addition, as this approach benefits from using real experimental kinematic and kinetic data, as well as a subject-specific musculoskeletal model and flexible tibia to perform dynamic simulation and modal FE analysis, it represents a huge improvement in the research protocol over a previously reported method. Thus, this non-invasive approach utilizing subject-specific data for multibody dynamic simulations combined with modal FE analysis could become a promising tool to study tibial deformation during dynamic motion. Future research could employ this method to study bone strains during high impact activities for a large cohort to study injury mechanisms of bone stress fractures.
The authors have nothing to disclose.
Department of the Army #W81XWH-08-1-0587, #W81XWH-15-1-0006; Ball State University 2010 ASPiRE grant.
CT Scanner | GE Medical System | N/A | Light Speed VCT. For performing tibia CT scan. |
Motion Capture System | Vicon Inc | N/A | Vicon FX40 high speed cameras. For performing 3D motion capture. |
Force plates | AMTI Inc | N/A | Collecting 3D ground reaction forces |
Vicon Nexus | Vicon Inc | N/A | Motion capture software program. For processing visual marker trajectory data. |
Visual 3D | C-Motion Inc | N/A | Biomechanics analysis software. For computing 3D kinematics and kinetics of human movements. |
MATLAB | Mathworks Inc | N/A | Computer programming software. For performing raw data filtering, data conversion, and data processing. |
ADAMS 2012 | MSC Software Inc | N/A | Multibody dynamic computer simulation program. |
LifeMOD | Lifemodeler Inc | N/A | A software Plug-in in ADAMS. For building human body musculo-skeletal models. |
MIMICS 13 | Materialise Inc | N/A | Image processing program. A 3D modeling tool to process imaging data. For creating 3D tibia model from CT scans. |
MARC 2012 | MSC Software Inc | N/A | Finite element analysis software. For performing volumn meshing, generating tibia FE model, and running modal FE analysis. |
SPSS 19 | IBM Inc | N/A | Statistical analysis software. |