A computational tool for the probabilistic finite element analysis of an uncemented total hip replacement considering variability in bone–implant version angle

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.

Mandibular reconstruction system reliability analysis using probabilistic finite element method

The aim of this study was to design for mandibular reconstruction of large lateral defect with minimum target reliability with designated confidence interval under bite force range of 300 ± 102 N. The performance of the models has been evaluated by numerical analysis considering the uncertainty of input parameters. Computer-Aided design was used to develop the models of three designs according to the patient's anatomy and to achieve to near symmetry of the mandible. Stress-strength modeling was utilized for the probabilistic physics of failure analysis under assumption of a quasi-static load. Monte-Carlo simulation was also applied for probabilistic finite element analysis and reliability assessment. The sensitivity analysis of the models was developed to reflect the significance of the variables in the models. The deterministic stress analysis shows that the highest stress and the second maximum stress are 110 MPa and 85 MPa for cortical bone around the screws, respectively. Also, it is determined that the maximum plate stress of the titanium conventional plate model is 580 MPa. The reconstruction system success rate was improved in all models by observing the anatomy of the patient's mandible in the plate designs by computer-aided design and additive manufacturing techniques. Based on the results, the reliability of plate strength and pull-out screws strength are 99.99% and 96.71% for the fibula free flap model, respectively, and 99.99% and 94.17%, respectively, for the customized prosthesis model. Probability sensitivity factors showed that uncertainty in the elastic modulus of the cortical bone has the greatest effect on the probability of screws loosening.

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%).

Influence of different anteversion alignments of a cementless hip stem on primary stability and strain distribution

BACKGROUND

Stem anteversion in total hip arthroplasty is well known to have a high impact on dislocation, but empirical data regarding the clinical and biomechanical influence is lacking. Therefore, we evaluated the impact of different anteversion alignments on the primary stability and strain distribution of a cementless stem.

METHODS

The cementless CLS Spotorno stem was implanted in 3 different groups (each group n = 6, total n = 21) with different anteversion alignments: reference anteversion (8°), +15° torsion in anteversion (+23°), -15° torsion in retroversion (-7°) using composite femurs (Sawbones). Primary stability was determined by 3-dimensional micromotions using a dynamic loading procedure simulating walking on level ground. Additionally, surface strains were registered before and after stem insertion in the 3 different groups, using one composite femur for each group (total n = 3).

FINDINGS

The micromotion measurements did not show a significant difference between the 3 evaluated alignments. Moreover, determination of the strain distribution did also not reveal an obvious difference.

INTERPRETATION

This biomechanical study simulating walking on level ground indicates that there is no considerable influence of stem ante-/retroversion variation (±15°) on the initial stability and strain distribution when evaluating the cementless CLS Spotorno in composite femora.

Influence of population variability in ligament material properties on the mechanical behavior of ankle: a computational investigation

Biomechanical behavior of ankle ligaments varies among individuals, with the underlying mechanism at multiple scales remaining unquantified. The present probabilistic study investigated how population variability in ligament material properties would influence the joint mechanics. A previously developed finite element ankle model with parametric ligament properties was used. Taking the typical external rotation as example loading scenario, joint stability of the investigated population was consistently shared by specific ligaments within a narrow tolerance range, i.e. 62.8 ± 8.2 Nm under 36.1 ± 5.7° foot rotation. In parallel, the inherent material variability significantly alters the consequent injury patterns. Three most vulnerable ligaments and the consequent rupture sequences were identified, with the structural weak spot and the following progressive stability loss dominated by the relative stiffness among ligaments. This study demonstrated the feasibility of biofidelic models in investigating individual difference at the material level, and emphasized the importance of probabilistic description of individual difference when identifying the injury mechanism of a broad spectrum.

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.

Virtual trial to evaluate the robustness of cementless femoral stems to patient and surgical variation

Primary stability is essential for the success of cementless femoral stems. In this study, patient specific finite element (FE) models were used to assess changes in primary stability due to variability in patient anatomy, bone properties and stem alignment for two commonly used cementless femoral stems, Corail® and Summit® (DePuy Synthes, Warsaw, USA). Computed-tomography images of the femur were obtained for 8 males and 8 females. An automated algorithm was used to determine the stem position and size which minimized the endo-cortical space, and then span the plausible surgical envelope of implant positions constrained by the endo-cortical boundary. A total of 1952 models were generated and ran, each with a unique alignment scenario. Peak hip contact and muscle forces for stair climbing were scaled to the donor's body weight and applied to the model. The primary stability was assessed by comparing the implant micromotion and peri-prosthetic strains to thresholds (150 μm and 7000 µε, respectively) above which fibrous tissue differentiation and bone damage are expected to prevail. Despite the wide range of implant positions included, FE prediction were mostly below the thresholds (medians: Corail®: 20-74 µm and 1150-2884 µε, Summit®: 25-111 µm and 860-3010 µε), but sensitivity of micromotion and interfacial strains varied across femora, with the majority being sensitive (p < 0.0029) to average bone mineral density, cranio-caudal angle, post-implantation anteversion angle and lateral offset of the femur. The results confirm the relationship between implant position and primary stability was highly dependent on the patient and the stem design used.

Biomechanical Robustness of a Contemporary Cementless Stem to Surgical Variation in Stem Size and Position

Successful designs of total hip replacement (THR) need to be robust to surgical variation in sizing and positioning of the femoral stem. This study presents an automated method for comprehensive evaluation of the potential impact of surgical variability in sizing and positioning on the primary stability of a contemporary cementless femoral stem (Corail®, DePuy Synthes). A patient-specific finite element (FE) model of a femur was generated from computed tomography (CT) images from a female donor. An automated algorithm was developed to span the plausible surgical envelope of implant positions constrained by the inner cortical boundary. The analysis was performed on four stem sizes: oversized, ideal (nominal) sized, and undersized by up to two stem sizes. For each size, Latin hypercube sampling was used to generate models for 100 unique alignment scenarios. For each scenario, peak hip contact and muscle forces published for stair climbing were scaled to the donor's body weight and applied to the model. The risk of implant loosening was assessed by comparing the bone–implant micromotion/strains to thresholds (150 μm and 7000 με) above which fibrous tissue is expected to prevail and the periprosthetic bone to yield, respectively. The risk of long-term loosening due to adverse bone resorption was assessed using bone adaptation theory. The range of implant positions generated effectively spanned the available intracortical space. The Corail stem was found stable and robust to changes in size and position, with the majority of the bone–implant interface undergoing micromotion and interfacial strains that are well below 150 μm and 7000 με, respectively. Nevertheless, the range of implant positions generated caused an increase of up to 50% in peak micromotion and up to 25% in interfacial strains, particularly for retroverted stems placed in a medial position.

Influence of collars on the primary stability of cementless femoral stems: A finite element study using a diverse patient cohort

For cementless femoral stems, there is debate as to whether a collar enhances primary stability and load transfer compared to collarless designs. Finite Element (FE) analysis has the potential to compare stem designs within the same cohort, allowing for subtle performance differences to be identified, if present. Subject-specific FE models of intact and implanted femora were run for a diverse cohort (21 males, 20 females; BMI 16.4-41.2 kg/m² , age 50-80 yrs). Collared and collarless versions of Corail^® (DePuy Synthes, Warsaw, IN) were sized and positioned using an automated algorithm that aligns the femoral/stem axes, preserves the head-center location, and maximizes metaphyseal fit. Joint contact and muscle forces simulating peak forces in level gait and stair climbing and were scaled to the body mass and applied to each subject. Three failure scenarios were assessed: Potential for peri-prosthetic fibrous tissue formation (stem micromotion), potential for peri-prosthetic bone damage (equivalent strains), and calcar bone remodeling (changes in strain-energy density). Comparisons were performed using paired t-tests. Only subtle differences were found (mean 90th percentile micromotion: Collared = 86 µm, collarless = 92.5 µm, mean 90th percentile interface strains: Collared = 733 µϵ, collarless = 767 µϵ, and similar remodeling stimuli were predicted). The slight differences observed were small in comparison with the inter-patient variability. Statement of clinical significance: Our results suggest that the presence/absence of a collar is unlikely to substantially alter the bone-implant biomechanics nor the initial mechanical environment. Hence, a collar is likely to have minimal clinical impact. Analysis using different femoral stem designs is recommended before generalising these findings. © 2017 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 36:1185-1195, 2018.

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.

Failure analysis of the cement mantle in total hip arthroplasty with an efficient probabilistic method

Accurate prediction of long-term behaviour of cemented hip implants is very important not only for patient comfort but also for elimination of any revision operation due to failure of implants. Therefore, a more realistic computer model was generated and then used for both deterministic and probabilistic analyses of the hip implant in this study. The deterministic failure analysis was carried out for the most common failure states of the cement mantle. On the other hand, most of the design parameters of the cemented hip are inherently uncertain quantities. Therefore, the probabilistic failure analysis was also carried out considering the fatigue failure of the cement mantle since it is the most critical failure state. However, the probabilistic analysis generally requires large amount of time; thus, a response surface method proposed in this study was used to reduce the computation time for the analysis of the cemented hip implant. The results demonstrate that using an efficient probabilistic approach can significantly reduce the computation time for the failure probability of the cement from several hours to minutes. The results also show that even the deterministic failure analyses do not indicate any failure of the cement mantle with high safety factors, the probabilistic analysis predicts the failure probability of the cement mantle as 8%, which must be considered during the evaluation of the success of the cemented hip implants.

A review of probabilistic analysis in orthopaedic biomechanics

Probabilistic analysis methods are being increasingly applied in the orthopaedics and biomechanics literature to account for uncertainty and variability in subject geometries, properties of various structures, kinematics and joint loading, as well as uncertainty in implant alignment. As a complement to experiments, finite element modelling, and statistical analysis, probabilistic analysis provides a method of characterizing the potential impact of variability in parameters on performance. This paper presents an overview of probabilistic analysis and a review of biomechanics literature utilizing probabilistic methods in structural reliability, kinematics, joint mechanics, musculoskeletal modelling, and patient-specific representations. The aim of this review paper is to demonstrate the wide range of applications of probabilistic methods and to aid researchers and clinicians in better understanding probabilistic analyses.

Ninety-degree chevron osteotomy for correction of hallux valgus deformity: clinical data and finite element analysis

Hallux valgus is a very common foot disorder, with its prevalence estimated at 33% in adult shoe-wearing populations. Conservative management is the initial treatment of choice for this condition, but surgery is sometimes needed. The 60(0) angle Chevron osteotomy is an accepted method for correction of mild to moderate hallux valgus in adults less than 60 years old. A modified 90(0) angle Chevron osteotomy has also been described; this modified technique can confer some advantages compared to the 60(0) angle method, and reported results are good. In the current work we present clinical data from a cohort of fifty-one female patients who had surgery for sixty-two hallux valgus deformities. In addition, in order to get a better physical insight and study the mechanical stresses along the two osteotomies, Finite Element Analysis (FEA) was also conducted. FEA indicated enhanced mechanical bonding with the modified 90(0) Chevron osteotomy, because the compressive stresses that keep the two bone parts together are stronger, and the shearing stresses that tend to slide the two bone parts apart are weaker, compared to the typical 60(0) technique. Follow-up data on our patient cohort show good or excellent long-term clinical results with the modified 90(0) angle technique. These results are consistent with the FEA-based hypothesis that a 90(0) Chevron osteotomy confers certain mechanical advantages compared to the typical 60(0) procedure.