Finite element-based probabilistic analysis tool for orthopaedic applications

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.

Designing and in vitro testing of a novel patient-specific total knee prosthesis using the probabilistic approach

In order to prevent failure as well as ensure comfort, patient-specific modelling for prostheses has been gaining interest. However, deterministic analyses have been widely used in the design process without considering any variation/uncertainties related to the design parameters of such prostheses. Therefore, this study aims to compare the performance of patient-specific anatomic Total Knee Arthroplasty (TKA) with off-the-shelf TKA. In the patient-specific model, the femoral condyle curves were considered in the femoral component's inner and outer surface design. The tibial component was designed to completely cover the tibia cutting surface. In vitro experiments were conducted to compare these two models in terms of loosening of the components. A probabilistic approach based on the finite element method was also used to compute the probability of failure of both models. According to the deterministic analysis results, 103.10 and 21.67 MPa von Mises stress values were obtained for the femoral component and cement in the anatomical model, while these values were 175.86 and 25.76 MPa, respectively, for the conventional model. In order to predict loosening damage due to local osteolysis or stress shield, it was determined that the deformation values in the examined cement structures were 15% lower in the anatomical model. According to probabilistic analysis results, it was observed that the probability of encountering an extreme value for the anatomical model is far less than that of the conventional model. This indicates that the anatomical model is safer than the conventional model, considering the failure scenarios in this study.

Sensitivity of a Subject-specific Ankle Sprain Simulation to Extrinsic Versus Intrinsic Biomechanical Factors

Ankle sprains are the most common musculoskeletal injury in sport and military activity, despite existing prophylactic strategies. The purpose of this report was to develop a probabilistic simulation of lateral ankle sprains during single-limb drop landing, towards accelerating innovation in ankle sprain prevention. A deterministic, subject-specific musculoskeletal model was extended with automation and probabilistic distributions on sprain-related biomechanical factors. Probabilistic simulations were generated using traditional Monte Carlo techniques and the advanced mean value method, a more computationally-efficient approach. Predicted distributions of peak ankle joint rotations, velocities, and moments borne by supporting passive structures agreed favorably with the deterministic model and with reports of real sprain biomechanics. Parameter sensitivities identified that predictions were most strongly influenced by drop height, subtalar joint posture at contact, invertor/evertor co-activation, and passive ankle stiffness. The advanced mean value method predicted confidence bounds comparable to a 1000-trial Monte Carlo simulation, and required only 14 model evaluations and 4-min processing time. The extended probabilistic simulation may be useful to virtually test new prophylactic strategies for ankle sprains, and is made available for open-source use (https://simtk.org/projects/sprain-sim).

Intubation Biomechanics: Clinical Implications of Computational Modeling of Intervertebral Motion and Spinal Cord Strain during Tracheal Intubation in an Intact Cervical Spine

BACKGROUND

In a closed claims study, most patients experiencing cervical spinal cord injury had stable cervical spines. This raises two questions. First, in the presence of an intact (stable) cervical spine, are there tracheal intubation conditions in which cervical intervertebral motions exceed physiologically normal maximum values? Second, with an intact spine, are there tracheal intubation conditions in which potentially injurious cervical cord strains can occur?

METHODS

This study utilized a computational model of the cervical spine and cord to predict intervertebral motions (rotation, translation) and cord strains (stretch, compression). Routine (Macintosh) intubation force conditions were defined by a specific application location (mid-C3 vertebral body), magnitude (48.8 N), and direction (70 degrees). A total of 48 intubation conditions were modeled: all combinations of 4 force locations (cephalad and caudad of routine), 4 magnitudes (50 to 200% of routine), and 3 directions (50, 70, and 90 degrees). Modeled maximum intervertebral motions were compared to motions reported in previous clinical studies of the range of voluntary cervical motion. Modeled peak cord strains were compared to potential strain injury thresholds.

RESULTS

Modeled maximum intervertebral motions occurred with maximum force magnitude (97.6 N) and did not differ from physiologically normal maximum motion values. Peak tensile cord strains (stretch) did not exceed the potential injury threshold (0.14) in any of the 48 force conditions. Peak compressive strains exceeded the potential injury threshold (-0.20) in 3 of 48 conditions, all with maximum force magnitude applied in a nonroutine location.

CONCLUSIONS

With an intact cervical spine, even with application of twice the routine value of force magnitude, intervertebral motions during intubation did not exceed physiologically normal maximum values. However, under nonroutine high-force conditions, compressive strains exceeded potentially injurious values. In patients whose cords have less than normal tolerance to acute strain, compressive strains occurring with routine intubation forces may reach potentially injurious values.

EDITOR’S PERSPECTIVE

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.

Uncertainty quantification implementations in human hemodynamic flows

BACKGROUND AND OBJECTIVE

Human hemodynamic modeling is usually influenced by uncertainties occurring from a considerable unavailability of information linked to the boundary conditions and the physical properties used in the numerical models. Calculating the effect of these uncertainties on the numerical findings along the cardiovascular system is a demanding process due to the complexity of the morphology of the body and the area dynamics. To cope with all these difficulties, Uncertainty Quantification (UQ) methods seem to be an ideal tool.

RESULTS

This study focuses on analyzing and summarizing some of the recent research efforts and directions of implementing UQ in human hemodynamic flows by analyzing 139 research papers. Initially, the suitability of applying this approach is analyzed and demonstrated. Then, an overview of the most significant research work in various fields of biomedical hemodynamic engineering is presented. Finally, it is attempted to identify any possible forthcoming directions for research and methodological progress of UQ in biomedical sciences.

CONCLUSION

This review concludes that by finding the best statistical methods and parameters to represent the propagated uncertainties, while achieving a good interpretation of the interaction between input-output, is crucial for implementing UQ in biomedical sciences.

Establishing the Biofidelity of a Multiphysics Finite Element Model of the Human Heart

PURPOSE

Accelerating development of new therapeutic cardiac devices remains a clinical and technical priority. High-performance computing and the emergence of functional and complex in silico models of human anatomy can be an engine to accelerate the commercialization of innovative, safe, and effective devices.

METHODS

An existing three-dimensional, nonlinear model of a human heart with flow boundary conditions was evaluated. Its muscular tissues were exercised using electrophysiological boundary conditions, creating a dynamic, electro-mechanical simulation of the kinetics of the human heart. Anatomic metrics were selected to characterize the functional biofidelity of the model based on their significance to the design of cardiac devices. The model output was queried through the cardiac cycle and compared to in vivo literature values.

RESULTS

For the kinematics of mitral and aortic valves and curvature of coronary vessels, the model's performance was at or above the 95th percentile range of the in vivo data from large patient cohorts. One exception was the kinematics of the tricuspid valve. The model's mechanical use environment would subject devices to generally conservative use conditions.

CONCLUSIONS

This conservative simulated use environment for heart-based medical devices, and its judicious application in the evaluation of medical devices is justified, but careful interpretation of the results is encouraged.

Finite Element Analysis of a Controlled Dynamization Device for External Circular Fixation

Objective  To virtually prototype a device for external circular fixation of long bone fractures with controlled dynamization made of two different materials and predict their mechanical behavior by using the finite element analysis (FEA) method. Method  A software was used for 3D modeling two metal parts closely attached by a sliding dovetail joint and a high-density silicone damper. Distinctive FEAs were simulated by considering two different materials (stainless steel or titanium), modes (locked or dynamized) and loading conditions (static/point or dynamic/0.5 sec) with uniform 150 kg axial load on top of the device. Results  The finite elements (FEs) model presented 81,872 nodes and 45,922 elements. Considering stainless steel, the maximum stress peak (140.98 MPa) was reached with the device locked under static loading, while the greatest displacement (2.415 × 10 ^-3 mm) was observed with the device locked and under dynamic loading. Regarding titanium, the device presented the maximum stress peak (141.45 MPa) under static loading and with the device locked, while the greatest displacement (3.975 × 10 ^-3 mm) was found with the device locked and under dynamic loading. Conclusion  The prototyped device played the role of stress support with acceptable deformation in both locked and dynamized modes and may be fabricated with both stainless steel and titanium.

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.

A lower extremity model for muscle-driven simulation of activity using explicit finite element modeling

A key strength of computational modeling is that it can provide estimates of muscle, ligament, and joint loads, stresses, and strains through non-invasive means. However, simulations that can predict the forces in the muscles during activity while maintaining sufficient complexity to realistically represent the muscles and joint structures can be computationally challenging. For this reason, the current state of the art is to apply separate rigid-body dynamic and finite-element (FE) analyses in series. However, the use of two or more disconnected models often fails to capture key interactions between the joint-level and whole-body scales. Single framework MSFE models have the potential to overcome the limitations associated with disconnected models in series. The objectives of the current study were to create a multi-scale FE model of the human lower extremity that combines optimization, dynamic muscle modeling, and structural FE analysis in a single framework and to apply this framework to evaluate the mechanics of healthy knee specimens during two activities. Two subject-specific FE models (Model 1, Model 2) of the lower extremity were developed in ABAQUS/Explicit including detailed representations of the muscles. Muscle forces, knee joint loading, and articular contact were calculated for two activities using an inverse dynamics approach and static optimization. Quadriceps muscle forces peaked at the onset of chair rise (2174 N, 1962 N) and in early stance phase (510 N, 525 N), while gait saw peak forces in the hamstrings (851 N, 868 N) in midstance. Joint forces were similar in magnitude to available telemetric patient data. This study demonstrates the feasibility of detailed quasi-static, muscle-driven simulations in an FE framework.

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.

Evaluating the Effects of Ankle-Foot Orthosis Mechanical Property Assumptions on Gait Simulation Muscle Force Results

Musculoskeletal modeling and simulation techniques have been used to gain insights into movement disabilities for many populations, such as ambulatory children with cerebral palsy (CP). The individuals who can benefit from these techniques are often limited to those who can walk without assistive devices, due to challenges in accurately modeling these devices. Specifically, many children with CP require the use of ankle-foot orthoses (AFOs) to improve their walking ability, and modeling these devices is important to understand their role in walking mechanics. The purpose of this study was to quantify the effects of AFO mechanical property assumptions, including rotational stiffness, damping, and equilibrium angle of the ankle and subtalar joints, on the estimation of lower-limb muscle forces during stance for children with CP. We analyzed two walking gait cycles for two children with CP while they were wearing their own prescribed AFOs. We generated 1000-trial Monte Carlo simulations for each of the walking gait cycles, resulting in a total of 4000 walking simulations. We found that AFO mechanical property assumptions influenced the force estimates for all the muscles in the model, with the ankle muscles having the largest resulting variability. Muscle forces were most sensitive to assumptions of AFO ankle and subtalar stiffness, which should therefore be measured when possible. Muscle force estimates were less sensitive to estimates of damping and equilibrium angle. When stiffness measurements are not available, limitations on the accuracy of muscle force estimates for all the muscles in the model, especially the ankle muscles, should be acknowledged.

Using a Bayesian Network to Predict L5/S1 Spinal Compression Force from Posture, Hand Load, Anthropometry, and Disc Injury Status

Stochastic biomechanical modeling has become a useful tool most commonly implemented using Monte Carlo simulation, advanced mean value theorem, or Markov chain modeling. Bayesian networks are a novel method for probabilistic modeling in artificial intelligence, risk modeling, and machine learning. The purpose of this study was to evaluate the suitability of Bayesian networks for biomechanical modeling using a static biomechanical model of spinal forces during lifting. A 20-node Bayesian network model was used to implement a well-established static two-dimensional biomechanical model for predicting L5/S1 compression and shear forces. The model was also implemented as a Monte Carlo simulation in MATLAB. Mean L5/S1 spinal compression force estimates differed by 0.8%, and shear force estimates were the same. The model was extended to incorporate evidence about disc injury, which can modify the prior probability estimates to provide posterior probability estimates of spinal compression force. An example showed that changing disc injury status from false to true increased the estimate of mean L5/S1 compression force by 14.7%. This work shows that Bayesian networks can be used to implement a whole-body biomechanical model used in occupational biomechanics and incorporate disc injury.

Effect of rotational prosthetic alignment variation on tibiofemoral contact pressure distribution and joint kinematics in total knee replacement

In total knee replacement surgery, implant alignment is one of the most important criteria for successful long-term clinical outcome. During total knee replacement implantation, femoral and tibial alignment are determined through appropriate bone resections, which could vary based on patient anatomy, implant design and surgical technique and further influence loading conditions and clinical outcomes. The current research focused on three critical alignment parameters for total knee replacement insertion: femoral component internal/external (I/E) rotation, varus-valgus tibiofemoral angulation and posterior tibial slope. A computational finite element model of total knee replacement implant was developed and validated comparing with kinematic outputs generated from experimentally simulated knee joint motion. The FE model was then used to assess 12 different alignment scenarios based on previous case reports. Postoperative knee kinematics and joint contact pressure during simulated gait motion were assessed. According to the parametric study, FE model cases with femoral rotation revealed extra tibial I/E rotation in the predefined direction but negligible change in tibial anterior-posterior translation; cases with increased tibial slope showed notably increased tibial external rotation and anterior translation; cases with varus tibiofemoral angle presented slightly more tibial external rotation, whereas cases with valgus angle presented an observable increase in tibial internal rotation at the middle phase of the gait cycle. Finally, the response surface obtained from the postprocessing study demonstrated good statistical correlation with existing case study results, providing reliable estimation of peak tibiofemoral contact pressure affected by combinations of alignment parameters. The observations indicate that femoral external alignment should be favored clinically for enhanced patellar tracking and reduced contact pressure concentration for better long-term performance. Posterior tibial slope enables deep knee flexion. Extra femoral internal rotation as well as tibiofemoral varus-valgus alignment could be avoided in surgery due to deficiency in patellar tracking and high pressure concentration.

A New Model to Study Fatigue in Dental Implants Based on Probabilistic Finite Elements and Cumulative Damage Model

The aim of this study was to predict the fatigue life of two different connections of a dental implant as in load transfer to bone. Two three-dimensional models were created and assembled. All models were subjected to a natural masticatory force of 118 N in the angle of 75° to the occlusal plane. All degrees of freedom in the inferior border of the cortical bone were restrained, and the mesial and distal borders of the end of the bone section were constrained. Fatigue material data and loads were assumed as random variables. Maximum principal stresses on bone were evaluated. Then, the probability of failure was obtained by the probabilistic approach. The maximum principal stress distribution predicted in the cortical and trabecular bone is 32 MPa for external connection and 39 MPa for internal connection. A mean life of 103 and 210 million cycles were obtained for external and internal connection, respectively. Probability cumulative function was also evaluated for both connection types. This stochastic model employs a cumulative damage model and probabilistic finite element method. This methodology allows the possibility of measured uncertainties and has a good precision on the results.

Computational model-based probabilistic analysis of in vivo material properties for ligament stiffness using the laxity test and computed tomography

The objective of this paper was to evaluate in vivo material properties in order to address technical aspects of computational modeling of ligaments in the tibiofemoral joint using a probabilistic method. The laxity test was applied to the anterior-posterior drawer under 30° and 90° of flexion with a series of stress radiographs, a Telos device, and computed tomography. Ligament stiffness was investigated using sensitivity analysis based on the Monte-Carlo method with a subject-specific finite element model generated from in vivo computed tomography and magnetic resonance imaging data, subjected to laxity test conditions. The material properties of ligament stiffness and initial ligament strain in a subject-specific finite element model were optimized to minimize the differences between the movements of the tibia and femur in the finite element model and the computed tomography images in the laxity test. The posterior cruciate ligament was the most significant factor in flexion and posterior drawer, while the anterior cruciate ligament primarily was the most significant factor for the anterior drawer. The optimized material properties model predictions in simulation and the laxity test were more accurate than predictions based on the initial material properties in subject-specific computed tomography measurement. Thus, this study establishes a standard for future designs in allograft, xenograft, and artificial ligaments for anterior cruciate ligament and posterior cruciate ligament injuries.

LIFETIME MODEL OF KNEE WITH DAMAGED CARTILAGE USING BEARING LIFE THEORY

The articular cartilage in the human knee plays an important role to ensure a lifetime knee function for an individual. Due to damage of the cartilage in the knee, the coefficient of friction (COF) increases even after treatments for the cartilage, due to the poor self-healing ability of the cartilage, resulting in decreased knee life. As the mechanism of the function of the knee joint is similar to a bearing, a model based on the regression model of cylindrical bearing life has been developed. The model is used to evaluate the effect of the COF on the lifetime of the knee. The results show the correlation between the life of the knee and the COF of the knee cartilage. The knee lifetime depends on the ratio of the COF of the healthy cartilage to the damaged cartilage. The results demonstrate the effect of the COF on the knee lifetime, which is an exponential decrease in the life of the knee for both males and females.

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.

Contribution of geometric design parameters to knee implant performance: Conflicting impact of conformity on kinematics and contact mechanics

BACKGROUND

Articular geometry of knee implant has a competing impact on kinematics and contact mechanics of total knee arthroplasty (TKA) such that geometry with lower contact pressure will impose more constraints on knee kinematics. The geometric parameters that may cause this competing effect have not been well understood. This study aimed to quantify the underlying relationships between implant geometry as input and its performance metrics as output.

METHODS

Parametric dimensions of a fixed-bearing cruciate retaining implant were randomized to generate a number of perturbed implant geometries. Performance metrics (i.e., maximum contact pressure, anterior-posterior range of motion [A-P ROM] and internal-external range of motion [I-E ROM]) of each randomized design were calculated using finite element analysis. The relative contributions of individual geometric variables to the performance metrics were then determined in terms of sensitivity indices (SI).

RESULTS

The femoral and tibial distal or posterior radii and femoral frontal radius are the key parameters. In the sagittal plane, distal curvature of the femoral and tibial influenced both contact pressure, i.e., SI=0.57; SI=0.65, and A-P ROM, i.e., SI=0.58; SI=0.6, respectively. However, posterior curvature of the femoral and tibial implants had a smaller impact on the contact pressure, i.e., SI=0.31; SI=0.23 and a higher impact on the I-E ROM, i.e., SI=0.72; SI=0.58. It is noteworthy that in the frontal plane, frontal radius of the femoral implant impacted both contact pressure (SI=0.38) and I-E ROM (SI=0.35).

CONCLUSION

Findings of this study highlighted how changes in the conformity of the femoral and tibial can impact the performance metrics.

Probabilistic sensitivity analysis of in-vehicle reach tasks for digital human models considering anthropometric measurement uncertainty

For design using digital human models, human anthropometry data are required as input and are extracted from measurements. There is inherent error associated with these measurements which impacts the output of the simulation. Current techniques in digital human modeling applications primarily employ deterministic methods which are not well suited for handling variability in anthropometric measurement. An alternative to deterministic methods is probabilistic/sensitivity analysis. This study presents a probabilistic sensitivity approach to gain insights into how uncertainty in anthropometric measurements can affect the results of a digital human model with the specific application of vehicle-related reach tasks. Sensitivity levels are found to determine the importance of variability in each joint angle and link length to the final reach. A55-degree of freedom (DOF) digital human model is introduced to demonstrate the sensitivity approach for reach tasks. Seven right-hand reach target points and two left-hand reach target points (creating a total of 14 reach tasks) within a vehicle are used to compare the sensitivities in the joint angles and link lengths resulting from measurement uncertainty. The results show that the importance of each joint angle or link length is dependent on the characteristics of the reach task and sensitivities for joint angles, and link lengths are different for each reach task.

Posterior stabilized versus cruciate retaining total knee arthroplasty designs: conformity affects the performance reliability of the design over the patient population

Commercially available fixed bearing knee prostheses are mainly divided into two groups: posterior stabilized (PS) versus cruciate retaining (CR). Despite the widespread comparative studies, the debate continues regarding the superiority of one type over the other. This study used a combined finite element (FE) simulation and principal component analysis (PCA) to evaluate "reliability" and "sensitivity" of two PS designs versus two CR designs over a patient population. Four fixed bearing implants were chosen: PFC (DePuy), PFC Sigma (DePuy), NexGen (Zimmer) and Genesis II (Smith & Nephew). Using PCA, a large probabilistic knee joint motion and loading database was generated based on the available experimental data from literature. The probabilistic knee joint data were applied to each implant in a FE simulation to calculate the potential envelopes of kinematics (i.e. anterior-posterior [AP] displacement and internal-external [IE] rotation) and contact mechanics. The performance envelopes were considered as an indicator of performance reliability. For each implant, PCA was used to highlight how much the implant performance was influenced by changes in each input parameter (sensitivity). Results showed that (1) conformity directly affected the reliability of the knee implant over a patient population such that lesser conformity designs (PS or CR), had higher kinematic variability and were more influenced by AP force and IE torque, (2) contact reliability did not differ noticeably among different designs and (3) CR or PS designs affected the relative rank of critical factors that influenced the reliability of each design. Such investigations enlighten the underlying biomechanics of various implant designs and can be utilized to estimate the potential performance of an implant design over a patient population.

Three-dimensional finite element analysis of occipitocervical fixation using an anterior occiput-to-axis locking plate system: a pilot study

BACKGROUND CONTEXT

Although there are many techniques for occipitocervical fixation, there have been no reports regarding occipitocervical fixation via the use of an anterior anatomical locking plate system.

PURPOSE

The biomechanics of this new system were analyzed by a three-dimensional finite element to provide a theoretical basis for clinical application.

STUDY DESIGN

This was a modeling study.

PATIENT SAMPLE

We studied a 27-year-old healthy male volunteer in whom cervical disease was excluded via X-ray examination.

OUTCOME MEASURES

The states of stress and strain of these two internal fixation devices were analyzed.

METHODS

A three-dimensional finite element model of normal occiput-C2 was established based on the anatomical data from a Chinese population. An unstable model of occipital-cervical region was established by subtracting several unit structures from the normal model. An anterior occiput-to-axis locking titanium plate system was then applied and an anterior occiput-to-axis screw fixation was performed on the unstable model. Limitation of motion was performed on the surface of the fixed model, and physiological loads were imposed on the surface of the skull base.

RESULTS

Under various loads from different directions, the peak values of displacement of the anterior occiput-to-axis locking titanium plate system decreased 15.5%, 12.5%, 14.4%, and 23.7%, respectively, under the loads of flexion, extension, lateral bending, and axial rotation. Compared with the anterior occiput-to-axis screw fixation, the peak values of stress of the anterior occiput-to-axis locking titanium plate system also decreased 3.9%, 2.9%, 9.7%, and 7.2%, respectively, under the loads of flexion, extension, lateral bending, and axial rotation.

CONCLUSION

The anterior occiput-to-axis locking titanium plate system proved superior to the anterior occiput-to-axis screw system both in the stress distribution and fixation stability based on finite element analysis. It provides a new clinical option for anterior occipitocervical fixation.

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.

Effects of densitometry, material mapping and load estimation uncertainties on the accuracy of patient-specific finite-element models of the scapula

Patient-specific biomechanical models including patient-specific finite-element (FE) models are considered potentially important tools for providing personalized healthcare to patients with musculoskeletal diseases. A multi-step procedure is often needed to generate a patient-specific FE model. As all involved steps are associated with certain levels of uncertainty, it is important to study how the uncertainties of individual components propagate to final simulation results. In this study, we considered a specific case of this problem where the uncertainties of the involved steps were known and the aim was to determine the uncertainty of the predicted strain distribution. The effects of uncertainties of three important components of patient-specific models, including bone density, musculoskeletal loads and the parameters of the material mapping relationship on the predicted strain distributions, were studied. It was found that the number of uncertain components and the level of their uncertainty determine the uncertainty of simulation results. The 'average' uncertainty values were found to be relatively small even for high levels of uncertainty in the components of the model. The 'maximum' uncertainty values were, however, quite high and occurred in the areas of the scapula that are of the greatest clinical relevance. In addition, the uncertainty of the simulation result was found to be dependent on the type of movement analysed, with abduction movements presenting consistently lower uncertainty values than flexion movements.

External fixator configurations in tibia fractures: 1D optimization and 3D analysis comparison

The use of external fixation devices in orthopedic surgery is very common in open tibial fractures. A properly applied fixator may improve the healing process while one improperly applied might delay the healing process. The several external fixator systems used in clinical today, can be categorized into uniplanar-unilateral, uniplanar-bilateral, biplanar and multiplanar. The stability on the fracture focus and, therefore, the fracture healing process, is related with the type of external fixator configuration that is selected. The aim of this study is to discuss the principles for the successful application of unilateral-uniplanar external fixation, the assembly of its components, for the case of a transverse fractures using computational models. In this context, the fixation stiffness characteristics are evaluated using a simplified 1D finite element model for the tibia and external fixator. The beams are modeled with realistic cross-sectional geometry and material properties instead of a simplified model. The VABS (the Variational Asymptotic Beam Section analysis) methodology is used to compute the cross-sectional model for the generalized Timoshenko model, which was embedded in the finite element solver FEAP. The use of Timoshenko beam theory allows accounting for several kinds of loads, including torsion moments. Optimal design is performed with respect to the assembly of fixator components using a genetic algorithm. The optimization procedure is based on the evaluation of an objective function, which is dependent on the displacement at the fracture focus. The initial and optimal results are compared by performing a 3D analysis, for which different three-dimensional finite element models are created. The geometrical model of a tibia is created on the basis of data acquired by CAT scan, made for a healthy tibia of a 22 year old male. The 3D comparison of the 1D optimal results show a clear improvement on the objective function for the several load cases and, therefore, it is shown that appropriate selection of the external fixator geometrical features can lead to an improvement on the stability of the external fixator. The results obtained show that the optimal position of the side beam and the first pin should be as close as possible to the bone interface and as close as possible to the fracture focus, respectively. Concerning the second pin, it should be placed away from the first pin in case of flexion loads, to axial and torsion loads the second pin should be placed near the first pin.

Subject-specific analysis of joint contact mechanics: application to the study of osteoarthritis and surgical planning

Advances in computational mechanics, constitutive modeling, and techniques for subject-specific modeling have opened the door to patient-specific simulation of the relationships between joint mechanics and osteoarthritis (OA), as well as patient-specific preoperative planning. This article reviews the application of computational biomechanics to the simulation of joint contact mechanics as relevant to the study of OA. This review begins with background regarding OA and the mechanical causes of OA in the context of simulations of joint mechanics. The broad range of technical considerations in creating validated subject-specific whole joint models is discussed. The types of computational models available for the study of joint mechanics are reviewed. The types of constitutive models that are available for articular cartilage are reviewed, with special attention to choosing an appropriate constitutive model for the application at hand. Issues related to model generation are discussed, including acquisition of model geometry from volumetric image data and specific considerations for acquisition of computed tomography and magnetic resonance imaging data. Approaches to model validation are reviewed. The areas of parametric analysis, factorial design, and probabilistic analysis are reviewed in the context of simulations of joint contact mechanics. Following the review of technical considerations, the article details insights that have been obtained from computational models of joint mechanics for normal joints; patient populations; the study of specific aspects of joint mechanics relevant to OA, such as congruency and instability; and preoperative planning. Finally, future directions for research and application are summarized.

Life prediction of different commercial dental implants as influence by uncertainties in their fatigue material properties and loading conditions

Probabilistic analyses allow the effect of uncertainty in system parameters to be determined. In the literature, many researchers have investigated static loading effects on dental implants. However, the intrinsic variability and uncertainty of most of the main problem parameters are not accounted for. The objective of this research was to apply a probabilistic computational approach to predict the fatigue life of three different commercial dental implants considering the variability and uncertainty in their fatigue material properties and loading conditions. For one of the commercial dental implants, the influence of its diameter in the fatigue life performance was also studied. This stochastic technique was based on the combination of a probabilistic finite element method (PFEM) and a cumulative damage approach known as B-model. After 6 million of loading cycles, local failure probabilities of 0.3, 0.4 and 0.91 were predicted for the Lifecore, Avinent and GMI implants, respectively (diameter of 3.75mm). The influence of the diameter for the GMI implant was studied and the results predicted a local failure probability of 0.91 and 0.1 for the 3.75mm and 5mm, respectively. In all cases the highest failure probability was located at the upper screw-threads. Therefore, the probabilistic methodology proposed herein may be a useful tool for performing a qualitative comparison between different commercial dental implants.

A probabilistic modelling scheme for analysis of long-term failure of cemented femoral joint replacements

Reliable prediction of long-term medical device performance using computer simulation requires consideration of variability in surgical procedure, as well as patient-specific factors. However, even deterministic simulation of long-term failure processes for such devices is time and resource consuming so that including variability can lead to excessive time to achieve useful predictions. This study investigates the use of an accelerated probabilistic framework for predicting the likely performance envelope of a device and applies it to femoral prosthesis loosening in cemented hip arthroplasty.

A creep and fatigue damage failure model for bone cement, in conjunction with an interfacial fatigue model for the implant–cement interface, was used to simulate loosening of a prosthesis within a cement mantle. A deterministic set of trial simulations was used to account for variability of a set of surgical and patient factors, and a response surface method was used to perform and accelerate a Monte Carlo simulation to achieve an estimate of the likely range of prosthesis loosening. The proposed framework was used to conceptually investigate the influence of prosthesis selection and surgical placement on prosthesis migration.

Results demonstrate that the response surface method is capable of dramatically reducing the time to achieve convergence in mean and variance of predicted response variables. A critical requirement for realistic predictions is the size and quality of the initial training dataset used to generate the response surface and further work is required to determine the recommendations for a minimum number of initial trials. Results of this conceptual application predicted that loosening was sensitive to the implant size and femoral width. Furthermore, different rankings of implant performance were predicted when only individual simulations (e.g. an average condition) were used to rank implants, compared with when stochastic simulations were used. In conclusion, the proposed framework provides a viable approach to predicting realistic ranges of loosening behaviour for orthopaedic implants in reduced timeframes compared with conventional Monte Carlo simulations.

Identifying alignment parameters affecting implanted patellofemoral mechanics

Complications of the patellofemoral (PF) joint remain a common cause for revision of total knee replacements. PF complications, such as patellar maltracking, subluxation, and implant failure, have been linked to femoral and patellar component alignment. In this study, a dynamic finite element model of an implanted PF joint was applied in conjunction with a probabilistic simulation to establish relationships between alignment parameters and PF kinematics, contact mechanics, and internal stresses. Both traditional sensitivity analysis and a coupled probabilistic and principal component analysis approach were applied to characterize relationships between implant alignment and resulting joint mechanics. Critical alignment parameters, and combinations of parameters, affecting PF mechanics were identified for three patellar designs (dome, modified dome, and anatomic). Femoral internal-external (I-E) alignment was identified as a critical alignment factor for all component designs, influencing medial-lateral contact force and anterior-posterior translation. The anatomic design was sensitive to patellar flexion-extension (F-E) alignment, while the dome, as expected, was less influenced by rotational alignment, and more by translational position. The modified dome was sensitive to a combination of superior-inferior, F-E, and I-E alignments. Understanding the relationships and design-specific dependencies between alignment parameters can aid preoperative planning, and help focus instrumentation design on those alignment parameters of primary concern.

Computationally efficient finite element evaluation of natural patellofemoral mechanics

Finite element methods have been applied to evaluate in vivo joint behavior, new devices, and surgical techniques but have typically been applied to a small or single subject cohort. Anatomic variability necessitates the use of many subject-specific models or probabilistic methods in order to adequately evaluate a device or procedure for a population. However, a fully deformable finite element model can be computationally expensive, prohibiting large multisubject or probabilistic analyses. The aim of this study was to develop a group of subject-specific models of the patellofemoral joint and evaluate trade-offs in analysis time and accuracy with fully deformable and rigid body articular cartilage representations. Finite element models of eight subjects were used to tune a pressure-overclosure relationship during a simulated deep flexion cycle. Patellofemoral kinematics and contact mechanics were evaluated and compared between a fully deformable and a rigid body analysis. Additional eight subjects were used to determine the validity of the rigid body pressure-overclosure relationship as a subject-independent parameter. There was good agreement in predicted kinematics and contact mechanics between deformable and rigid analyses for both the tuned and test groups. Root mean square differences in kinematics were less than 0.5 deg and 0.2 mm for both groups throughout flexion. Differences in contact area and peak and average contact pressures averaged 5.4%, 9.6%, and 3.8%, respectively, for the tuned group and 6.9%, 13.1%, and 6.4%, respectively, for the test group, with no significant differences between the two groups. There was a 95% reduction in computational time with the rigid body analysis as compared with the deformable analysis. The tuned pressure-overclosure relationship derived from the patellofemoral analysis was also applied to tibiofemoral (TF) articular cartilage in a group of eight subjects. Differences in contact area and peak and average contact pressures averaged 8.3%, 11.2%, and 5.7% between rigid and deformable analyses in the tibiofemoral joint. As statistical, probabilistic, and optimization techniques can require hundreds to thousands of analyses, a viable platform is crucial to component evaluation or clinical applications. The computationally efficient rigid body platform described in this study may be integrated with statistical and probabilistic methods and has potential clinical application in understanding in vivo joint mechanics on a subject-specific or population basis.

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.

Probabilistic finite element analysis of the uncemented hip replacement--effect of femur characteristics and implant design geometry

In the present study, a probabilistic finite element tool was assessed using an uncemented total hip replacement model. Fully bonded and frictional interfaces were investigated for combinations of three proximal femurs and two implant designs, the Proxima short stem and the IPS hip stem prostheses. The Monte Carlo method was used with two performance indicators: the percentage of bone volume that exceeded specified strain limits and the maximum nodal micromotion. The six degrees of freedom of bone-implant relative position, magnitude of the hip contact force (L), and spatial direction of L were the random variables. The distal portion of the proximal femurs was completely constrained and some of the main muscle forces acting in the hip were applied. The coefficients of the linear approximation between the random variables and the output were used as the sensitivity values. In all cases, bone-implant position related parameters were the most sensitive parameters. The results varied depending on the femur, the implant design and the interface conditions. Values of maximum nodal micromotion agreed with results from previous studies, confirming the robustness of the implemented computational tool. It was demonstrated that results from a single model study should not be generalised to the entire population of femurs and that bone variability is an important factor that should be investigated in such analyses.

Effect of geometrical uncertainty on cemented hip implant structural integrity

A large number of parameters such as material properties, geometry, and structural strength are involved in the design and analysis of cemented hip implants. Uncertainties in these parameters have a potential to compromise the structural performance and lifetime of implants. Statistical analyses are well suited to investigating this type of problem as they can estimate the influence of these uncertainties on the incidence of failure. Recent investigations have focused on the effect of uncertainty in cement properties and loading condition on the integrity of the construct. The present study hypothesizes that geometrical uncertainties will play a role in cement mantle failure. Finite element input parameters were simulated as random variables and different modes of failure were investigated using a response surface method (RSM). The magnitude of random von Mises stresses varied up to 8 MPa, compared with a maximum nominal value of 2.38 MPa. Results obtained using RSM are shown to match well with a benchmark direct Monte Carlo simulation method. The resulting probability that the maximum cement stress will exceed the nominal stress is 62%. The load and the bone and prosthesis geometries were found to be the parameters most likely to influence the magnitude of the cement stresses and therefore to contribute most to the probability of failure.