An open-source musculoskeletal model of the lumbar spine and lower limbs: a validation for movements of the lumbar spine.

Musculoskeletal models of the lumbar spine have been developed with varying levels of detail for a wide range of clinical applications. Providing consistency is ensured throughout the modelling approach, these models can be combined with other computational models and be used in predictive modelling studies to investigate bone health deterioration and the associated fracture risk. To provide precise physiological loading conditions for such predictive modelling studies, a new full-body musculoskeletal model including a detailed and consistent representation of the lower limbs and the lumbar spine was developed. The model was assessed against in vivo measurements from the literature for a range of spine movements representative of daily living activities. Comparison between model estimations and electromyography recordings was also made for a range of lifting tasks. This new musculoskeletal model will provide a comprehensive physiological mechanical environment for future predictive finite element modelling studies on bone structural adaptation. It is freely available on https://simtk.org/projects/llsm/.

Reliability and minimal detectable change of the 'Imperial Spine' marker set for the evaluation of spinal and lower limb kinematics in adults.

OBJECTIVES: As a step towards the comprehensive evaluation of movement in patients with low back pain, the aim of this study is to design a marker set (three rigid segment spine, pelvic and lower limb model) and evaluate the reliability and minimal detectable change (MDC) of this marker set in healthy adults during gait and sit to stand (STS) tasks using three dimensional motion capture. RESULTS: The 'Imperial Spine' marker set was used to assess relative peak angles during gait and STS tasks using the minimum recommended sample size (n = 10) for reliability studies with minimum Intraclass Correlation Coefficient (ICC) of 0.70, optimum ICC 0.90 and 9 trials replicated per subject per task. Intra- and inter-tester reliability between an experienced and inexperienced user was examined. ICC, mean, standard error (SEM), Bland Altman 95% limits of agreement (LOA) and MDC were computed. ICC values demonstrated excellent intra- and inter-tester reliability in both tasks, particularly in the sagittal plane (majority ICCs > 0.80). SEM measurements were lower in gait (0.8-5.5°) than STS tasks (1°-12.6°) as were MDC values. LOA demonstrated good agreement. The 'Imperial Spine' marker set is reliable for use in healthy adults during functional tasks. Future evaluation in patients is required.

Influence of femoral external shape on internal architecture and fracture risk.

The internal architecture of the femur and its fracture behaviour vary greatly between subjects. Femoral architecture and subsequent fracture risk are strongly influenced by load distribution during physical activities of daily living. The objective of this work is to evaluate the impact of outer cortical surface shape as a key affector of load distribution driving femoral structure and fracture behaviour. Different femur cortical shapes are generated using a statistical shape model. Their mesoscale internal architecture is predicted for the same activity regime using a structural optimisation approach previously reported by the authors and fracture under longitudinal compression is simulated. The resulting total volume of bone is similar in all geometries although substantial differences are observed in distribution between trabecular and cortical tissue. Greater neck-shaft and anteversion angles show a protective effect in longitudinal compression while a thinner shaft increases fracture risk.

Rate and age-dependent damage elasticity formulation for efficient hip fracture simulations.

Prediction of bone failure is beneficial in a range of clinical situations from screening of osteoporotic patients with high fracture risk to assessment of protective equipment against trauma. Computational efficiency is an important feature to consider when developing failure models for iterative applications, such as patient-specific diagnosis or design of orthopaedic devices. The authors previously developed a methodology to generate efficient mesoscale structural full bone models. The aim of this study was to implement a damage elasticity formulation representative of an elasto-plastic material model with age and strain rate dependencies compatible with these structural models. This material model was assessed in the prediction of femoral fractures in longitudinal compression and side fall scenarios. The simulations predicted failure loads and fracture patterns in good agreement with reported results from experimental studies. The observed influence of strain rate on failure load was consistent with literature. The superiority of a simplified elasto-plastic formulation over an elasto-brittle bone material model was assessed. This computationally efficient damage elasticity formulation was capable of capturing fracture development after onset.

Microscale poroelastic metamodel for efficient mesoscale bone remodelling simulations.

Bone functional tissue adaptation is a multiaspect physiological process driven by interrelated mechanical and biological stimuli which requires the combined activity of osteoclasts and osteoblasts. In previous work, the authors developed a phenomenological mesoscale structural modelling approach capable of predicting internal structure of the femur based on daily activity loading, which relied on the iterative update of the cross-sectional areas of truss and shell elements representative of trabecular and cortical bones, respectively. The objective of this study was to introduce trabecular reorientation in the phenomenological model at limited computational cost. To this aim, a metamodel derived from poroelastic microscale continuum simulations was used to predict the functional adaptation of a simplified proximal structural femur model. Clear smooth trabecular tracts are predicted to form in the regions corresponding to the main trabecular groups identified in literature, at minimal computational cost.

Application of a falsification strategy to a musculoskeletal model of the lower limb and accuracy of the predicted hip contact force vector.

In the literature, lower limb musculoskeletal models validated against in vivo measured hip contact forces (HCFs) exhibit a tendency to overestimate the HCFs magnitude and predict inaccurate components of the HCF vector in the transverse plane. In order to investigate this issue, a musculoskeletal model was forced to produce HCFs identical to those measured and the resulting joint equilibrium equations were studied through both a general approach and a static optimization framework. In the former case, the existence of solutions to the equilibrium equations was investigated and the effect of varying the intersegmental moments and the muscle tetanic stress assessed: for a value of 100 N/cm(2) and moments calculated from an inverse dynamics analysis on average only 62% of analyzed frames were solvable for level walking and 70% for stair climbing. In the static optimization study, the model could reproduce the experimental HCFs but the recruited muscles were unable to simultaneously equilibrate the hip intersegmental moments without the contribution of reserve moment actuators. Without constraints imposed on the HCFs, the predicted HCF vectors presented maximum angle deviations up to 22° for level walking and 33° for stair climbing during the gait stance phase. The influence of the medio-lateral HCF component on the solvability of the equilibrium equations and the muscle recruitment alteration when the model was forced to produce the experimental HCFs suggest that a more accurate geometrical representation of the gluteal muscles is mandatory to improve predictions of the HCF vector yielded by the static optimization technique.

Evaluating a suitable level of model complexity for finite element analysis of the intact acetabulum.

To enable large-scale multi-factorial finite element (FE) studies, the FE models used must be as computationally efficient as is feasible, while maintaining a suitable level of definition. The present study seeks to find an optimum level of model complexity for use in such large-scale studies by investigating which model attributes are most influential over the chosen model outputs of principal stress and strain in the intact acetabulum. A multi-factorial sensitivity study was carried out using 128 FE models, representing combinations of the following variables: bone stiffness distribution, imposed muscle loading, boundary condition location, hip joint contact conditions and patient's bone anatomy. The relative sensitivity of each input factor was analysed, and it was concluded that the optimum level of model definition must include CT-dependent trabecular bone properties and a sliding interface at the hip joint. It was found that it was not essential to describe the ligamentous sacroiliac and pubic symphysis joints; these could be rigidly fixed in space; and for the normal walking load case, muscle forces may be neglected. It was also concluded that a variety of bone anatomies should be included in a multi-factorial analysis if results are to be inferred for a wider population.

A hierarchy of computationally derived surgical and patient influences on metal on metal press-fit acetabular cup failure.

The impact of anatomical variation and surgical error on excessive wear and loosening of the acetabular component of large diameter metal-on-metal hip arthroplasties was measured using a multi-factorial analysis through 112 different simulations. Each surgical scenario was subject to eight different daily loading activities using finite element analysis. Excessive wear appears to be predominantly dependent on cup orientation, with inclination error having a higher influence than version error, according to the study findings. Acetabular cup loosening, as inferred from initial implant stability, appears to depend predominantly on factors concerning the area of cup-bone contact, specifically the level of cup seating achieved and the individual patient's anatomy. The extent of press fit obtained at time of surgery did not appear to influence either mechanism of failure in this study.

Validation of FE micromotions and strains around a press-fit cup: introducing a new micromotion measuring technique.

Finite element (FE) analysis provides an useful tool with which to analyze the potential performance of implantations in a variety of surgical, patient and design scenarios. To enable the use of FE analysis in the investigation of such implants, models must be experimentally validated. Validation of a pelvic model with an implanted press-fit cup in terms of micromotion and strain is presented here. A new method of micromotion has been introduced to better describe the overall movement of the cup within the pelvis. The method uses a digitizing arm to monitor the relative movement between markers on the cup and the surrounding acetabulum. FE analysis was used to replicate an experimental set up using a synthetic hemi-pelvis with a press-fitted all-metal cup, subject to the maximum loading observed during normal walking. The work presented here has confirmed the ability of FE models to accurately describe the mechanical performance of the press-fitted acetabulum and surrounding bone under typical loading conditions in terms of micromotion and strain distribution, but has demonstrated limitations in its ability to predict numerical micromotion values. A promising digitizing technique for measuring acetabular micromotions has also been introduced.

An open source lower limb model: Hip joint validation.

Musculoskeletal lower limb models have been shown to be able to predict hip contact forces (HCFs) that are comparable to in vivo measurements obtained from instrumented prostheses. However, the muscle recruitment predicted by these models does not necessarily compare well to measured electromyographic (EMG) signals. In order to verify if it is possible to accurately estimate HCFs from muscle force patterns consistent with EMG measurements, a lower limb model based on a published anatomical dataset (Klein Horsman et al., 2007. Clinical Biomechanics. 22, 239-247) has been implemented in the open source software OpenSim. A cycle-to-cycle hip joint validation was conducted against HCFs recorded during gait and stair climbing trials of four arthroplasty patients (Bergmann et al., 2001. Journal of Biomechanics. 34, 859-871). Hip joint muscle tensions were estimated by minimizing a polynomial function of the muscle forces. The resulting muscle activation patterns obtained by assessing multiple powers of the objective function were compared against EMG profiles from the literature. Calculated HCFs denoted a tendency to monotonically increase their magnitude when raising the power of the objective function; the best estimation obtained from muscle forces consistent with experimental EMG profiles was found when a quadratic objective function was minimized (average overestimation at experimental peak frame: 10.1% for walking, 7.8% for stair climbing). The lower limb model can produce appropriate balanced sets of muscle forces and joint contact forces that can be used in a range of applications requiring accurate quantification of both. The developed model is available at the website https://simtk.org/home/low_limb_london.

The femur as a musculo-skeletal construct: a free boundary condition modelling approach.

Previous finite element studies of the femur have made simplifications to varying extents with regard to the boundary conditions used during analysis. Fixed boundary conditions are generally applied to the distal femur when examining the proximal behaviour at the hip joint, while the same can be said for the proximal femur when examining the distal behaviour at the knee joint. While fixed boundary condition analyses have been validated against in vitro experiments it remains a matter of debate as to whether the numerical and experimental models are indicative of the in vivo situation. This study presents a finite element model in which the femur is treated as a complete musculo-skeletal construct, spanning between the hip and knee joints. Linear and non-linear implementations of a free boundary condition modelling approach are applied to the bone through the explicit inclusion of muscles and ligaments spanning both the hip joint and the knee joint. A non-linear force regulated, muscle strain based activation strategy was found to result in lower observed principal strains in the cortex of the femur, compared to a linear activation strategy. The non-linear implementation of the model in particular, was found to produce hip and knee joint reaction forces consistent with in vivo data from instrumented implants.

Finite element modelling of the pelvis: inclusion of muscular and ligamentous boundary conditions.

Previous finite element studies of the pelvis, including subject-specific studies have made extensive simplifications with regards to the boundary conditions used during analysis. Fixed boundary conditions are generally utilised at the pubis and superior part of the ilium. While it can be demonstrated that these models provide a close match for certain in vitro experiments that use similar boundary conditions, the resulting stress-strain fields in the cortex in particular are unlikely to be those found in vivo. This study presents a finite element analysis in which the pelvis is supported by muscular and ligamentous boundary conditions, applied using spring elements distributed over realistic attachment sites. The analysis is compared to an analysis in which the pelvis is restrained by fixed boundary conditions applied at the sacro-iliac joints. Striking differences in the stress-strain fields observed in cortical bone in particular, are found between the two analyses. The inclusion of muscular and ligamentous boundary conditions is found to lower the occurrence of stress concentrations within the cortex.

3D non-linear analysis of the acetabular construct following impaction grafting.

The study investigates the short-term behaviour of the acetabular construct following revision hip arthroplasty, carried out using the Slooff-Ling impaction grafting technique; using 3D finite element analyses. An elasto-plastic material model is used to describe the constitutive behaviour of morsellised cortico-cancellous bone (MCB) graft, since it has been shown that MCB undergoes significant plastic deformation under normal physiological loads. Based on previous experimental studies carried out by the authors and others, MCB is modelled using non-linear elasticity and Drucker Prager Cap (DPC) plasticity. Loading associated with walking, sitting down, and standing up is applied to the acetabular cup through a femoral head using smooth sliding surfaces. The analyses yield distinctive patterns of migration and rotation due to different activities. These are found to be similar to those observed in the clinical setting.

The elastic properties of morsellised cortico-cancellous bone graft are dependent on its prior loading.

Confined compression experiments were carried out on cortico-cancellous bone taken from bovine femoral condyles to assess the effect of prior loading on the elastic confined modulus, E(c) of morsellised cortico-cancellous bone (MCB). Measurements were taken to find the values of E(c) for MCB subjected to cyclic loading resulting in axial stresses in the range of 0.5-3.0 N mm(2). Two values of E(c) were considered: E(ic), the instantaneous modulus, and E(dc), the delayed modulus allowing for stress relaxation effects. It was found that the values of E(c) increased with increasing maximum axial stress. It was also found that for each stress level the values of E(c) increased as the number of load cycles increased. The dependence of E(c) on the maximum axial stress and the number of load cycles is seen to explain the wide range of values for the apparent modulus of MCB found in previous studies. Tests examining the stress relaxation behaviour of MCB are also discussed. The results indicate that a minimum of 10 compaction episodes are required for MCB to achieve around 90% of its predicted maximum stiffness for a given compaction force.

The effect of acetabular cup size on the short-term stability of revision hip arthroplasty: a finite element investigation.

The study uses idealized two-dimensional finite element models to examine the behaviour of the acetabular construct following revision hip arthroplasty, carried out using the Slooff-Ling impaction grafting technique. The behaviour of bone graft was considered in detail, with non-linear elasticity and non-associated plasticity being adopted. Load was applied to the acetabular construct through a femoral head using smooth sliding surfaces. In particular, four models were subjected to two idealized cyclic load cases to investigate the effect of acetabular cup size on the short-term stability of the acetabular construct. The study suggests that benefits may be gained by using the largest practical size of acetabular cup.