A numerically validated probabilistic model of a simplified total hip replacement construct

Computational models of bone fracture healing and applications: a review

Fracture healing is a very complex physiological process involving multiple events at different temporal and spatial scales, such as cell migration and tissue differentiation, in which mechanical stimuli and biochemical factors assume key roles. With the continuous improvement of computer technology in recent years, computer models have provided excellent solutions for studying the complex process of bone healing. These models not only provide profound insights into the mechanisms of fracture healing, but also have important implications for clinical treatment strategies. In this review, we first provide an overview of research in the field of computational models of fracture healing based on CiteSpace software, followed by a summary of recent advances, and a discussion of the limitations of these models and future directions for improvement. Finally, we provide a systematic summary of the application of computational models of fracture healing in three areas: bone tissue engineering, fixator optimization and clinical treatment strategies. The application of computational models of bone healing in clinical treatment is immature, but an inevitable trend, and as these models become more refined, their role in guiding clinical treatment will become more prominent.

A probabilistic approach for assessing the mechanical performance of intertrochanteric fracture stabilized with proximal femoral nail antirotation

Maintaining post-operative mechanical stability is crucial for successfully healing intertrochanteric fractures treated with the Proximal Femoral Nail Antirotation (PFNA) system. This stability is primarily dependent on the bone mineral density (BMD) and strain on the fracture. Current PFNA failure analyses often overlook the uncertainties related to BMD and body weight (BW). Therefore, this study aimed to develop a probabilistic model using finite element modeling and engineering reliability analysis to assess the post-operative performance of PFNA under various physiological loading conditions. The model predictions were validated through a series of experimental test. The results revealed a negative nonlinear relationship between the BMD and compressive strain. Conversely, the BW was positively and linearly correlated with the compressive strain. Importantly, the compressive strain was more sensitive to BW than to BMD when the BMD exceeded 0.6 g/cm3. Potential trabecular bone compression failure is also indicated if BMD is equal to or below 0.15 g/cm3 and BW increases to approximately 2.5 times the normal or higher. This study emphasizes that variations in the BMD significantly affect the probability of failure of a PFNA system. Thus, careful planning of post-operative physical therapy is essential. For patients aged > 50 years restrictions on high-intensity activities are advised, while limiting strenuous movements is recommended for those aged > 65 years.

A probabilistic approach for modelling bone fracture healing under Ilizarov circular fixator

Bone fracture treatments using Ilizarov circular fixator (ICF) involve dealing with uncertainties about a range of critical factors that control the mechanical microenvironment of the fracture site such as ICF configuration, fracture gap size, physiological loading etc. To date, the effects of the uncertainties about these critical factors on the mechanical microenvironment of the fracture site have not been fully understood. The purpose of this study is to tackle this challenge by using computational modelling in conjunction with engineering reliability analysis. Particularly, the effects of uncertainties in fracture gap size (GS), level of weight-bearing (P), ICF wire pretension (T) and wire diameter (WD) on the fracture site mechanical microenvironment at the beginning of the reparative phase of healing was investigated in this study. The results show that the mechanical microenvironment of fracture site stabilised with ICF is very sensitive to the uncertainties in P and GS. For example, an increase in the coefficient of variation of P (COV_P ) from 0.1 to 0.9 (i.e., an increase in the uncertainty in P) could reduce the probability of achieving a favourable mechanical microenvironment within the fracture site (i.e., Probability of Success, PoS) by more than 50%, while an increase in the coefficient of variation of GS (COV_GS ) from 0.1 to 0.9 could decrease PoS by around 30%. In contrast, an increase in the uncertainties in T and WD (COV increase from 0.1 to 0.9) has little influence on the fracture site mechanical microenvironment (PoS changes <5%).

A probabilistic-based approach for computational simulation of bone fracture healing

BACKGROUND AND OBJECTIVE

It is widely known that bone fracture healing is affected by mechanical factors such as fracture geometry, fixation configuration and post-operative weight bearing loading. However, there are several uncertainties associated with the magnitude of the mechanical factors affecting bone healing as it is challenging to adjust and control them in clinical practice. The current bone fracture healing investigations mainly adopt a deterministic approach for identifying the optimal mechanical conditions for a favourable bone healing outcome. However, a probabilistic approach should be used in the analysis to incorporate such uncertainties for prediction of bone healing.

METHODS

In this study we developed a probabilistic-based computational model to predict the probability of delayed healing or non-union under different fracture treatment mechanical conditions for fractures stabilised by locking plates.

RESULTS

The results show that there is a strong positive linear correlation between the mechanical stimulations (S) in the fracture gap and the magnitude of weight bearing, the bone-plate distance (BPD) and the plate working length (WL), whereas the fracture gap size has a highly negative and nonlinear correlation with S. While the results show that fracture mechanical microenvironment is more sensitive to the uncertainties in WL compared to BPD, the uncertainty associated with the magnitude of WL is very low and can be resulted from implant manufacturing tolerance. However, there is a high uncertainty associated with the magnitude of BPD as it cannot be accurately adjusted during the surgery. The results show that the tissue differentiation at the far cortex of fracture gap is more sensitive to the variation of BPD compared with that at the near cortex. The probability of delayed healing (fibrous tissue formation) at far cortex is increased from 0% to 40% when coefficient of variation (COV) of BPD rises from 0.1 to 0.9 (for average BPD = 2 mm, WL = 65 mm, fracture gap size = 3 mm and Weight bearing = 150 N). Further, both near and far cortex of fracture site are sensitive to the variation in weight bearing loading.

CONCLUSIONS

The developed probabilistic model may lead to useful guidelines that could help orthopaedic surgeons identify how reliable a specific fracture treatment strategy is.

Intubation biomechanics: validation of a finite element model of cervical spine motion during endotracheal intubation in intact and injured conditions

OBJECTIVE

Because of limitations inherent to cadaver models of endotracheal intubation, the authors’ group developed a finite element (FE) model of the human cervical spine and spinal cord. Their aims were to 1) compare FE model predictions of intervertebral motion during intubation with intervertebral motion measured in patients with intact cervical spines and in cadavers with spine injuries at C-2 and C3–4 and 2) estimate spinal cord strains during intubation under these conditions.

METHODS

The FE model was designed to replicate the properties of an intact (stable) spine in patients, C-2 injury (Type II odontoid fracture), and a severe C3–4 distractive-flexion injury from prior cadaver studies. The authors recorded the laryngoscope force values from 2 different laryngoscopes (Macintosh, high intubation force; Airtraq, low intubation force) used during the patient and cadaver intubation studies. FE-modeled motion was compared with experimentally measured motion, and corresponding cord strain values were calculated.

RESULTS

FE model predictions of intact intervertebral motions were comparable to motions measured in patients and in cadavers at occiput–C2. In intact subaxial segments, the FE model more closely predicted patient intervertebral motions than did cadavers. With C-2 injury, FE-predicted motions did not differ from cadaver measurements. With C3–4 injury, however, the FE model predicted greater motions than were measured in cadavers. FE model cord strains during intubation were greater for the Macintosh laryngoscope than the Airtraq laryngoscope but were comparable among the 3 conditions (intact, C-2 injury, and C3–4 injury).

CONCLUSIONS

The FE model is comparable to patients and cadaver models in estimating occiput–C2 motion during intubation in both intact and injured conditions. The FE model may be superior to cadavers in predicting motions of subaxial segments in intact and injured conditions.

Analysis of Uncertainty and Variability in Finite Element Computational Models for Biomedical Engineering: Characterization and Propagation

Computational modeling has become a powerful tool in biomedical engineering thanks to its potential to simulate coupled systems. However, real parameters are usually not accurately known, and variability is inherent in living organisms. To cope with this, probabilistic tools, statistical analysis and stochastic approaches have been used. This article aims to review the analysis of uncertainty and variability in the context of finite element modeling in biomedical engineering. Characterization techniques and propagation methods are presented, as well as examples of their applications in biomedical finite element simulations. Uncertainty propagation methods, both non-intrusive and intrusive, are described. Finally, pros and cons of the different approaches and their use in the scientific community are presented. This leads us to identify future directions for research and methodological development of uncertainty modeling in biomedical engineering.

Uncertainty quantification for personalized analyses of human proximal femurs

Computational models for the personalized analysis of human femurs contain uncertainties in bone material properties and loads, which affect the simulation results. To quantify the influence we developed a probabilistic framework based on polynomial chaos (PC) that propagates stochastic input variables through any computational model. We considered a stochastic E-ρ relationship and a stochastic hip contact force, representing realistic variability of experimental data. Their influence on the prediction of principal strains (ϵ1 and ϵ3) was quantified for one human proximal femur, including sensitivity and reliability analysis. Large variabilities in the principal strain predictions were found in the cortical shell of the femoral neck, with coefficients of variation of ≈40%. Between 60 and 80% of the variance in ϵ1 and ϵ3 are attributable to the uncertainty in the E-ρ relationship, while ≈10% are caused by the load magnitude and 5-30% by the load direction. Principal strain directions were unaffected by material and loading uncertainties. The antero-superior and medial inferior sides of the neck exhibited the largest probabilities for tensile and compression failure, however all were very small (pf<0.001). In summary, uncertainty quantification with PC has been demonstrated to efficiently and accurately describe the influence of very different stochastic inputs, which increases the credibility and explanatory power of personalized analyses of human proximal femurs.