An anatomically based patient-specific finite element model of patella articulation: towards a diagnostic tool

An innovative anti-rotation tension band wiring for treating transverse patellar fractures: finite element analysis and mechanical testing

BACKGROUND

The displacement and rotation of the Kirschner wire (K-wire) in the traditional tension band wiring (TBW) led to a high rate of postoperative complications. The anti-rotation tension band wiring (ARTBW) could address these issues and achieve satisfactory clinical outcomes. This study aimed to investigate the biomechanical performance of the ARTBW in treating transverse patellar fracture compared to traditional TBW using finite element analysis (FEA) and mechanical testing.

METHODS

We conducted a FEA to evaluate the biomechanical performance of traditional TBW and ARTBW at knee flexion angles of 20°, 45°, and 90°. Furthermore, we compared the mechanical properties under a 45° knee flexion through static tensile tests and dynamic fatigue testing. The K-wire pull-out test was also conducted to evaluate the bonding strength between K-wires and cancellous bone of two surgical approaches.

RESULTS

The outcome of FEA demonstrated the compression force on the articular surface of ARTBW was 28.11%, 27.32%, and 52.86% higher than traditional TBW at knee flexion angles of 20°, 45°, and 90°, respectively. In mechanical testing, the mechanical properties of ARTBW were similar to the traditional TBW. In the K-wire pull-out test, the pull-out strength of ARTBW was significantly greater than the traditional TBW (111.58 ± 2.38 N vs. 64.71 ± 4.22 N, P < 0.001).

CONCLUSIONS

The ARTBW retained the advantages of traditional TBW, and achieved greater compression force of articular surface, and greater pull-out strength of K-wires. Moreover, ARTBW effectively avoided the rotation of the K-wires. Therefore, ARTBW demonstrates potential as a promising technique for treating patellar fractures.

Determining a musculoskeletal system's pre-stretched state using continuum-mechanical forward modelling and joint range optimization

The subject-specific range of motion (RoM) of a musculoskeletal joint system is balanced by pre-tension levels of individual muscles, which affects their contraction capability. Such an inherent pre-tension or pre-stretch of muscles is not measureable with in vivo experiments. Using a 3D continuum mechanical forward simulation approach for motion analysis of the musculoskeletal system of the forearm with 3 flexor and 2 extensor muscles, we developed an optimization process to determine the muscle fibre pre-stretches for an initial arm position, which is given human dataset. We used RoM values of a healthy person to balance the motion in extension and flexion. The performed sensitivity study shows that the fibre pre-stretches of the m. brachialis, m. biceps brachii and m. triceps brachii with 91 % dominate the objective flexion ratio, while m. brachiradialis and m. anconeus amount 7.8 % and 1.2 % . Within the multi-dimensional space of the surrogate model, 3D sub-spaces of primary variables, namely the dominant muscles and the global objective, flexion ratio, exhibit a path of optimal solutions. Within this optimal path, the muscle fibre pre-stretch of two flexors demonstrate a negative correlation, while, in contrast, the primary extensor, m. triceps brachii correlates positively to each of the flexors. Comparing the global optimum with four other designs along the optimal path, we saw large deviations, e.g., up to 15∘ in motion and up to 40% in muscle force. This underlines the importance of accurate determination of fibre pre-stretch in muscles, especially, their role in pathological muscular disorders and surgical applications such as free muscle or tendon transfer.

Exploring the muscle architecture effect on the mechanical behaviour of mouse rotator cuff muscles

Incorporating detailed muscle architecture aspects into computational models can enable researchers to gain deeper insights into the complexity of muscle function, movement, and performance. In this study, we employed histological, multiphoton image processing, and finite element method techniques to characterise the mechanical dependency on the architectural behaviour of supraspinatus and infraspinatus mouse muscles. While mechanical tests revealed a stiffer passive behaviour in the supraspinatus muscle, the collagen content was found to be two times higher in the infraspinatus. This effect was unveiled by analysing the alignment of fibres during muscle stretch with the 3D models and the parameters obtained in the fitting. Therefore, a strong dependence of muscle behaviour, both active and passive, was found on fibre orientation rather than collagen content.

Modeling of active skeletal muscles: a 3D continuum approach incorporating multiple muscle interactions

Skeletal muscles have a highly organized hierarchical structure, whose main function is to generate forces for movement and stability. To understand the complex heterogeneous behaviors of muscles, computational modeling has advanced as a non-invasive approach to evaluate relevant mechanical quantities. Aiming to improve musculoskeletal predictions, this paper presents a framework for modeling 3D deformable muscles that includes continuum constitutive representation, parametric determination, model validation, fiber distribution estimation, and integration of multiple muscles into a system level for joint motion simulation. The passive and active muscle properties were modeled based on the strain energy approach with Hill-type hyperelastic constitutive laws. A parametric study was conducted to validate the model using experimental datasets of passive and active rabbit leg muscles. The active muscle model with calibrated material parameters was then implemented to simulate knee bending during a squat with multiple quadriceps muscles. A computational fluid dynamics (CFD) fiber simulation approach was utilized to estimate the fiber arrangements for each muscle, and a cohesive contact approach was applied to simulate the interactions among muscles. The single muscle simulation results showed that both passive and active muscle elongation responses matched the range of the testing data. The dynamic simulation of knee flexion and extension showed the predictive capability of the model for estimating the active quadriceps responses, which indicates that the presented modeling pipeline is effective and stable for simulating multiple muscle configurations. This work provided an effective framework of a 3D continuum muscle model for complex muscle behavior simulation, which will facilitate additional computational and experimental studies of skeletal muscle mechanics. This study will offer valuable insight into the future development of multiscale neuromuscular models and applications of these models to a wide variety of relevant areas such as biomechanics and clinical research.

Future Directions in Patellofemoral Imaging and 3D Modeling

PURPOSE OF REVIEW

Patellofemoral instability involves complex, three-dimensional pathological anatomy. However, current clinical evaluation and diagnosis relies on attempting to capture the pathology through numerous two-dimensional measurements. This current review focuses on recent advancements in patellofemoral imaging and three-dimensional modeling.

RECENT FINDINGS

Several studies have demonstrated the utility of dynamic imaging modalities. Specifically, radiographic patellar tracking correlates with symptomatic instability, and quadriceps activation and weightbearing alter patellar kinematics. Further advancements include the study of three-dimensional models. Automation of commonly utilized measurements such as tibial tubercle-trochlear groove (TT-TG) distance has the potential to resolve issues with inter-rater reliability and fluctuation with knee flexion or tibial rotation. Future directions include development of robust computational models (e.g., finite element analysis) capable of incorporating patient-specific data for surgical planning purposes. While several studies have utilized novel dynamic imaging and modeling techniques to enhance our understanding of patellofemoral joint mechanics, these methods have yet to find a definitive clinical utility. Further investigation is required to develop practical implementation into clinical workflow.

Combining advanced computational and imaging techniques as a quantitative tool to estimate patellofemoral joint stress during downhill gait: A feasibility study

BACKGROUND

The onset and progression of patellofemoral osteoarthritis (OA) has been linked to alterations in cartilage stress-a potential precursor to pain and subsequent cartilage degradation. A lack in quantitative tools for objectively evaluating patellofemoral joint contact stress limits our understanding of pathomechanics associated with OA.

RESEARCH QUESTION

Could computational modeling and biplane fluoroscopy techniques be used to discriminate in-vivo, subject-specific patellofemoral stress profiles in individuals with and without patellofemoral OA?

METHODS

The current study employed a discrete element modeling framework driven by in-vivo, subject-specific kinematics during downhill gait to discriminate unique patellofemoral stress profiles in individuals with patellofemoral OA (n = 5) as compared to older individuals without OA (n = 6). All participants underwent biplane fluoroscopy kinematic tracking while walking on a declined instrumented treadmill. Subject-specific kinematics were combined with high resolution geometrical models to estimate patellofemoral joint contact stress during 0%, 25 %, 50 %, 75 % and 100 % of the loading response phase of downhill gait.

RESULTS

Individuals with patellofemoral OA demonstrated earlier increases in patellofemoral stress in the lateral patellofemoral compartment during loading response as compared to OA-free controls (P = 0.021). Overall, both groups exhibited increased patellofemoral contact stress early in the loading response phase of gait as compared to the end of loading response. Results from this study show increased stress profiles in individuals with patellofemoral OA, indicating increasing joint loading in early phases of gait.

SIGNIFICANCE

This modeling framework-combining arthrokinematics with discrete element models-can objectively estimate changes in patellofemoral joint stress, with potential applications to evaluate outcomes from various treatment programs, including surgical and non-surgical rehabilitation treatments.

Biomechanical analysis of canine medial patellar luxation with femoral varus deformity using a computer model

Background

Femoral varus deformities complicating the realignment of the quadriceps muscles are frequently associated with medial patellar luxation (MPL) in dogs. Therefore, distal femoral osteotomy (DFO) is recommended in dogs affected with severe MPL and a distal femoral varus deformity. The presence of an anatomic lateral distal femoral angle (aLDFA) of ≥ 102° has been anecdotally recommended as an indication for performing corrective DFO in large-breed dogs. However, the effect of a femoral varus deformity on MPL has not been scientifically evaluated. We aimed to evaluate the influence of a femoral varus deformity on MPL using a finite element method based computer model.

Three-dimensionally reconstructed computed tomographic images of a normal femur from a Beagle dog were deformed using meshing software to create distal varus deformities. A total of thirteen aLDFAs, including 95°, 98° and 100°–110°, were simulated. The patellar positions and reaction force between the patella and trochlear grooves were calculated for all finite element models under constant rectus femoris muscle activation.

Results

The patella was displaced medially from the trochlear groove at an aLDFA of ≥103°. With an aLDFA of 103° to 110°, the reaction force was equal to zero and then decreased to negative values during the simulation, while other models with aLDFAs of 95°, 98°, and 100°-102° had positive reaction force values. The patella began to luxate at 24.90 seconds (sec) with an aLDFA of 103°, 19.80 sec with an aLDFA of 104°, 21.40 sec with an aLDFA of 105°, 20.10 sec with an aLDFA of 106°, 18.60 sec with an aLDFA of 107°, 15.30 sec with an aLDFA of 108°, 16.60 sec with an aLDFA of 109°, and 11.90 sec with an aLDFA of 110°.

Conclusion

Severe distal femoral varus with an aLDFA of ≥103° caused MPL when other anatomical factors were controlled. Thissimplified computer model provides complementary information to anecdotal cutoffs for DFO, hence it should be applied to clinical patients with caution.

Influence of femoral external shape on internal architecture and fracture risk

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

Multiscale modeling of the neuromuscular system: Coupling neurophysiology and skeletal muscle mechanics

Mathematical models and computer simulations have the great potential to substantially increase our understanding of the biophysical behavior of the neuromuscular system. This, however, requires detailed multiscale, and multiphysics models. Once validated, such models allow systematic in silico investigations that are not necessarily feasible within experiments and, therefore, have the ability to provide valuable insights into the complex interrelations within the healthy system and for pathological conditions. Most of the existing models focus on individual parts of the neuromuscular system and do not consider the neuromuscular system as an integrated physiological system. Hence, the aim of this advanced review is to facilitate the prospective development of detailed biophysical models of the entire neuromuscular system. For this purpose, this review is subdivided into three parts. The first part introduces the key anatomical and physiological aspects of the healthy neuromuscular system necessary for modeling the neuromuscular system. The second part provides an overview on state-of-the-art modeling approaches representing all major components of the neuromuscular system on different time and length scales. Within the last part, a specific multiscale neuromuscular system model is introduced. The integrated system model combines existing models of the motor neuron pool, of the sensory system and of a multiscale model describing the mechanical behavior of skeletal muscles. Since many sub-models are based on strictly biophysical modeling approaches, it closely represents the underlying physiological system and thus could be employed as starting point for further improvements and future developments. This article is categorized under: Physiology > Mammalian Physiology in Health and Disease Analytical and Computational Methods > Computational Methods Models of Systems Properties and Processes > Organ, Tissue, and Physiological Models.

Development and validation of a kinematically-driven discrete element model of the patellofemoral joint

Quantifying the complex loads at the patellofemoral joint (PFJ) is vital to understanding the development of PFJ pain and osteoarthritis. Discrete element analysis (DEA) is a computationally efficient method to estimate cartilage contact stresses with potential application at the PFJ to better understand PFJ mechanics. The current study validated a DEA modeling framework driven by PFJ kinematics to predict experimentally-measured PFJ contact stress distributions. Two cadaveric knee specimens underwent quadriceps muscle [215 N] and joint compression [350 N] forces at ten discrete knee positions representing PFJ positions during early gait while measured PFJ kinematics were used to drive specimen-specific DEA models. DEA-computed contact stress and area were compared to experimentally-measured data. There was good agreement between computed and measured mean and peak stress across the specimens and positions (r = 0.63-0.85). DEA-computed mean stress was within an average of 12% (range: 1-47%) of the experimentally-measured mean stress while DEA-computed peak stress was within an average of 22% (range: 1-40%). Stress magnitudes were within the ranges measured (0.17-1.26 MPa computationally vs 0.12-1.13 MPa experimentally). DEA-computed areas overestimated measured areas (average error = 60%; range: 4-117%) with magnitudes ranging from 139 to 307 mm² computationally vs 74-194 mm² experimentally. DEA estimates of the ratio of lateral to medial patellofemoral stress distribution predicted the experimental data well (mean error = 15%) with minimal measurement bias. These results indicate that kinematically-driven DEA models can provide good estimates of relative changes in PFJ contact stress.

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.

Gradient-based optimization with B-splines on sparse grids for solving forward-dynamics simulations of three-dimensional, continuum-mechanical musculoskeletal system models

Investigating the interplay between muscular activity and motion is the basis to improve our understanding of healthy or diseased musculoskeletal systems. To be able to analyze the musculoskeletal systems, computational models are used. Albeit some severe modeling assumptions, almost all existing musculoskeletal system simulations appeal to multibody simulation frameworks. Although continuum-mechanical musculoskeletal system models can compensate for some of these limitations, they are essentially not considered because of their computational complexity and cost. The proposed framework is the first activation-driven musculoskeletal system model, in which the exerted skeletal muscle forces are computed using 3-dimensional, continuum-mechanical skeletal muscle models and in which muscle activations are determined based on a constraint optimization problem. Numerical feasibility is achieved by computing sparse grid surrogates with hierarchical B-splines, and adaptive sparse grid refinement further reduces the computational effort. The choice of B-splines allows the use of all existing gradient-based optimization techniques without further numerical approximation. This paper demonstrates that the resulting surrogates have low relative errors (less than 0.76%) and can be used within forward simulations that are subject to constraint optimization. To demonstrate this, we set up several different test scenarios in which an upper limb model consisting of the elbow joint, the biceps and triceps brachii, and an external load is subjected to different optimization criteria. Even though this novel method has only been demonstrated for a 2-muscle system, it can easily be extended to musculoskeletal systems with 3 or more muscles.

[A finite element analysis of petal-shaped poly-axial locking plate fixation in treatment of Y-shaped patellar fracture]

Objective

To establish the finite element model of Y-shaped patellar fracture fixed with titanium-alloy petal-shaped poly-axial locking plate and to implement the finite element mechanical analysis.

Methods

The three-dimensional model was created by software Mimics 19.0, Rhino 5.0, and 3-Matic 11.0. The finite element analysis was implemented by ANSYS Workbench 16.0 to calculate the Von-Mises stress and displacement. Before calculated, the upper and lower poles of the patella were constrained. The 2.0, 3.5, and 4.4 MPa compressive stresses were applied to the 1/3 patellofemoral joint surface of the lower, middle, and upper part of the patella respectively, and to simulated the force upon patella when knee flexion of 20, 45, and 90°.

Results

The number of nodes and elements of the finite element model obtained was 456 839 and 245 449, respectively. The max value of Von-Mises stress of all the three conditions simulated was 151.48 MPa under condition simulating the knee flexion of 90°, which was lower than the yield strength value of the titanium-alloy and patella. The max total displacement value was 0.092 8 mm under condition simulating knee flexion of 45°, which was acceptable according to clinical criterion. The stress concentrated around the non-vertical fracture line and near the area where the screws were sparse.

Conclusion

The titanium-alloy petal-shaped poly-axial locking plate have enough biomechanical stiffness to fix the Y-shaped patellar fracture, but the result need to be proved in future.

A diffusion-weighted imaging informed continuum model of the rabbit triceps surae complex

The NZ white rabbit is the animal of choice for much experimental work due to its muscular frame and similar response to human diseases, and is one of the few mammals that have had their genome sequenced. However, continuum-level computational models of rabbit muscle detailing fibre architecture are limited in the literature, especially the triceps surae complex (gastrocnemius, plantaris and soleus), which has similar biomechanics and translatable findings to the human. This study presents a geometrical model of the rabbit triceps surae informed with diffusion-weighted imaging (DWI)-based fibres. Passive rabbit-specific material properties are estimated using known muscle deformation inferred from magnetic resonance imaging data and dorsiflexion force measured with a custom-built rabbit rig and transducer. Muscle shape prediction is evaluated against a second rabbit. This study revealed that the triceps surae steady-state force post-rigor is close to post-mortem for small deformations but increases by a fixed ratio as the deformation increases and can be used to evaluate the passive behaviour of muscle. DWI fibre orientation significantly influences shape and mechanics during simulated computational muscle contraction. The presented triceps surae force and material properties may be used to inform the constitutive behaviour of continuum rabbit muscle models used to investigate pathology and musculotendon treatments that may be translated to the human condition.

Predicting Knee Osteoarthritis

Treatment options for osteoarthritis (OA) beyond pain relief or total knee replacement are very limited. Because of this, attention has shifted to identifying which factors increase the risk of OA in vulnerable populations in order to be able to give recommendations to delay disease onset or to slow disease progression. The gold standard is then to use principles of risk management, first to provide subject-specific estimates of risk and then to find ways of reducing that risk. Population studies of OA risk based on statistical associations do not provide such individually tailored information. Here we argue that mechanistic models of cartilage tissue maintenance and damage coupled to statistical models incorporating model uncertainty, united within the framework of structural reliability analysis, provide an avenue for bridging the disciplines of epidemiology, cell biology, genetics and biomechanics. Such models promise subject-specific OA risk assessment and personalized strategies for mitigating or even avoiding OA. We illustrate the proposed approach with a simple model of cartilage extracellular matrix synthesis and loss regulated by daily physical activity.

Relationship between the shape and density distribution of the femur and its natural frequencies of vibration

It has been recently suggested that mechanical loads applied at frequencies close to the natural frequencies of bone could enhance bone apposition due to the resonance phenomenon. Other applications of bone modal analysis are also suggested. For the above-mentioned applications, it is important to understand how patient-specific bone shape and density distribution influence the natural frequencies of bones. We used finite element models to study the effects of bone shape and density distribution on the natural frequencies of the femur in free boundary conditions. A statistical shape and appearance model that describes shape and density distribution independently was created, based on a training set of 27 femora. The natural frequencies were then calculated for different shape modes varied around the mean shape while keeping the mean density distribution, for different appearance modes around the mean density distribution while keeping the mean bone shape, and for the 27 training femora. Single shape or appearance modes could cause up to 15% variations in the natural frequencies with certain modes having the greatest impact. For the actual femora, shape and density distribution changed the natural frequencies by up to 38%. First appearance mode that describes the general cortical bone thickness and trabecular bone density had one of the strongest impacts. The first appearance mode could therefore provide a sensitive measure of general bone health and disease progression. Since shape and density could cause large variations in the calculated natural frequencies, patient-specific FE models are needed for accurate estimation of bone natural frequencies.

Squatting-related tibiofemoral shear reaction forces and a biomechanical rationale for femoral component loosening

Previous gait studies on squatting have described a rapid reversal in the direction of the tibiofemoral joint shear reaction force when going into a full weight-bearing deep knee flexion squat. The effects of such a shear reversal have not been considered with regard to the loading demand on knee implants in patients whose activities of daily living require frequent squatting. In this paper, the shear reversal effect is discussed and simulated in a finite element knee implant-bone model, to evaluate the possible biomechanical significance of this effect on femoral component loosening of high flexion implants as reported in the literature. The analysis shows that one of the effects of the shear reversal was a switch between large compressive and large tensile principal strains, from knee extension to flexion, respectively, in the region of the anterior flange of the femoral component. Together with the known material limits of cement and bone, this large mismatch in strains as a function of knee position provides new insight into how and why knee implants may fail in patients who perform frequent squatting.

Finite element analysis to characterize how varying patellar loading influences pressure applied to cartilage: model evaluation

A finite element analysis (FEA) modeling technique has been developed to characterize how varying the orientation of the patellar tendon influences the patellofemoral pressure distribution. To evaluate the accuracy of the technique, models were created from MRI images to represent five knees that were previously tested in vitro to determine the influence of hamstrings loading on patellofemoral contact pressures. Hamstrings loading increased the lateral and posterior orientation of the patellar tendon. Each model was loaded at 40°, 60°, and 80° of flexion with quadriceps force vectors representing the experimental loading conditions. The orientation of the patellar tendon was represented for the loaded and unloaded hamstrings conditions based on experimental measures of tibiofemoral alignment. Similar to the experimental data, simulated loading of the hamstrings within the FEA models shifted the center of pressure laterally and increased the maximum lateral pressure. Significant (p < 0.05) differences were identified for the center of pressure and maximum lateral pressure from paired t-tests carried out at the individual flexion angles. The ability to replicate experimental trends indicates that the FEA models can be used for future studies focused on determining how variations in the orientation of the patellar tendon related to anatomical or loading variations or surgical procedures influence the patellofemoral pressure distribution.

Bone remodelling in the natural acetabulum is influenced by muscle force-induced bone stress

A modelling framework using the international Physiome Project is presented for evaluating the role of muscles on acetabular stress patterns in the natural hip. The novel developments include the following: (i) an efficient method for model generation with validation; (ii) the inclusion of electromyography-estimated muscle forces from gait; and (iii) the role that muscles play in the hip stress pattern. The 3D finite element hip model includes anatomically based muscle area attachments, material properties derived from Hounsfield units and validation against an Instron compression test. The primary outcome from this study is that hip loading applied as anatomically accurate muscle forces redistributes the stress pattern and reduces peak stress throughout the pelvis and within the acetabulum compared with applying the same net hip force without muscles through the femur. Muscle forces also increased stress where large muscles have small insertion sites. This has implications for the hip where bone stress and strain are key excitation variables used to initiate bone remodelling based on the strain-based bone remodelling theory. Inclusion of muscle forces reduces the predicted sites and degree of remodelling. The secondary outcome is that the key muscles that influenced remodelling in the acetabulum were the rectus femoris, adductor magnus and iliacus.

Integrating degenerative mechanisms in bone and cartilage: a multiscale approach

At the whole organ level, degenerative mechanisms in bone and cartilage are primarily attributed to modifications in loading pattern. Either a change in magnitude or location can initiate a degenerative path. At the micro scale we often see changes in structure such as porosity increase in bone and fibrillation in cartilage. These changes contribute to a reduced structural integrity that weakens the bulk strength of tissue. Finally, at the cell level we have modeling and remodeling pathways that may be disrupted through disease, drugs and altered stimulus from the micro and macro scales. In order to understand this entire process and the roles each level plays a multiscale modeling framework is necessary. This framework can take whole body loadings and pass information through finer spatial scales in order to understand how everyday dynamic movements influence micro and cellular response. In a similar manner, cellular and microstructural processes regulate whole bulk properties and modify whole organ strength. In this study we highlight the multiscale links developed as part of the open-source ontologies for the Physiome Project using the lower limb as an example. We consider the influence of remodeling in (i) anabolic treatments in cortical bone; and (ii) subchondral bone and cartilage degeneration.

Finite element analysis of resurfacing depth and obliquity on patella stress and stability in TKA

Patella resurfacing in total knee arthroplasty (TKA) reduces postoperative complications and revisions; however, the optimal cutting depth and angle that minimize patellar strain and fracture remain unclear. We performed three-dimensional finite element analysis (FEA) of resurfacing cutting depth and obliquity to assess the stresses in each component of the knee joint, and fatigue testing to determine cyclic loading conditions over the expected life span of the implant. Maximum stress on the patella increased as cutting depth increased up to 8mm; peak stresses on the idealized button further increased at 10-mm depth. Medial superior obliquities below 3° showed the lowest stress on the patella and button and the highest fatigue life. An oblique cut of 3° with respect to the inferior end increased patellar stress and reduced fatigue life, making this the least successful approach. Taken together, our FEA supports the use of minimal cutting depths at -3° with respect to the superior end for patellar resurfacing in TKA in order to minimize stresses in the structure and improve TKA durability. Future studies will assess the effect of patella button placement to account for real-world practice variations.

Investigation of the role of crimps in collagen fibers in tendon with a microstructually based finite element model

Tendon has a hierarchical structure that links tendon, fascicle, fibre and fibrils. In particular tendon fibres are made up of fibrils that have distinctive wavy forms called crimps. Experimental and imaging studies have shown that this crimp pattern plays an important role in mechanical properties of tendon but its exact influence has not been identified. We have developed a micro finite element model of tendon that contains accurate crimp patterns embedded in the model. This model utilizes a unique material coordinate system that is aligned in the direction of fibres. The crimp was implemented by performing fibre fitting procedure, which aligns the material coordinate system according to the crimp angle. FE analysis study was performed to identify the influence of crimp morphology on stress distribution pattern in tendon. Introduction of crimp angle to the model produced heterogeneous deformation and stress transfer patterns whereas the one without any crimp patterns predicted a uniform stress pattern. Future works include parametric studies on the influence of crimp pattern and morphology on stress distribution pattern in the tissue.

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.

Patient-specific finite element modeling of bones

Finite element modeling is an engineering tool for structural analysis that has been used for many years to assess the relationship between load transfer and bone morphology and to optimize the design and fixation of orthopedic implants. Due to recent developments in finite element model generation, for example, improved computed tomography imaging quality, improved segmentation algorithms, and faster computers, the accuracy of finite element modeling has increased vastly and finite element models simulating the anatomy and properties of an individual patient can be constructed. Such so-called patient-specific finite element models are potentially valuable tools for orthopedic surgeons in fracture risk assessment or pre- and intraoperative planning of implant placement. The aim of this article is to provide a critical overview of current themes in patient-specific finite element modeling of bones. In addition, the state-of-the-art in patient-specific modeling of bones is compared with the requirements for a clinically applicable patient-specific finite element method, and judgment is passed on the feasibility of application of patient-specific finite element modeling as a part of clinical orthopedic routine. It is concluded that further development in certain aspects of patient-specific finite element modeling are needed before finite element modeling can be used as a routine clinical tool.

Physical modeling with orthotropic material based on harmonic fields

Although it is well known that human bone tissues have obvious orthotropic material properties, most works in the physical modeling field adopted oversimplified isotropic or approximated transversely isotropic elasticity due to the simplicity. This paper presents a convenient methodology based on harmonic fields, to construct volumetric finite element mesh integrated with complete orthotropic material. The basic idea is taking advantage of the fact that the longitudinal axis direction indicated by the shape configuration of most bone tissues is compatible with the trajectory of the maximum material stiffness. First, surface harmonic fields of the longitudinal axis direction for individual bone models were generated, whose scalar distribution pattern tends to conform very well to the object shape. The scalar iso-contours were extracted and sampled adaptively to construct volumetric meshes of high quality. Following, the surface harmonic fields were expanded over the whole volumetric domain to create longitudinal and radial volumetric harmonic fields, from which the gradient vector fields were calculated and employed as the orthotropic principal axes vector fields. Contrastive finite element analyses demonstrated that elastic orthotropy has significant effect on simulating stresses and strains, including the value as well as distribution pattern, which underlines the relevance of our orthotropic modeling scheme.

Mechanics of the foot Part 1: a continuum framework for evaluating soft tissue stiffening in the pathologic foot

Soft tissue stiffening is a common mechanical observation reported in foot pathologies including diabetes mellitus and gout. These material changes influence the spatial distribution of stress and affect blood flow, which is essential to nutrient entry and waste removal. An anatomically-based subject-specific foot model was developed to explore the influence of tissue stiffening on plantar pressure and internal von Mises stress at heel-strike, midstance and toe-off. This work draws on the model database developed for the Physiome project consisting of muscles, bones, soft tissue and other structures such as sensory nerves. The anisotropic structure of soft tissue was embedded in a single continuum as an efficient model for finite soft tissue deformation, and customisation methods were used to capture the unique foot profile. The model was informed by kinetics from an instrumented treadmill and kinematics from motion capture, synchronised together. Foot sole pressure predictions were evaluated against a commercial pressure platform. Key outcomes showed that internal stress can be up to 1.6 times the surface pressure with implications for internal soft tissue damage not observed at the surface. The main nerve branch stimulated during gait was the lateral plantar nerve. This subject-specific modelling framework can play an integral part in therapeutic treatments by informing assistive strategies such as mechanical noise stimulation and orthotics.

PATELLA TRACKING WITH PERIPATELLAR SOFT TISSUE STABILIZERS AS A FUNCTION OF DYNAMIC SUBJECT-SPECIFIC KNEE FLEXION

Musculoskeletal modeling has found wide application in joint biomechanics investigations. This technique has been improved by incorporating subject-specific skeletal elements and passive patellofemoral stabilizers in a dynamic analysis. After trochlear engagement, the volunteers' patellae displaced laterally, whereas tilt was subject specific. Comparison of the tilt and mediolateral position values to in vivo MRI values at 30° knee flexion showed a mean accuracy of 84.4% and 96.9%, respectively. Medial patellofemoral ligament tension decreased with knee flexion, while the patellar tendon–quadriceps tendon ratio ranged from 0.4 to 1.2. The patellofemoral contact load–quadriceps tendon load ratio ranged from 0.7 to 1.3, whereas the mediolateral load component–resultant load ratio ranged from 0 to 0.4. Three validated subject-specific musculoskeletal models facilitated the analysis of patellofemoral biomechanics: Subject-specific patella tracking and passive stabilizer response was analyzed as a function of dynamic knee flexion.

A data-driven surrogate model to connect scales between multi-domain biomechanics simulations

A data driven surrogate was developed to bridge the gap between finite element and multibody modeling and to expand the information available from a rigid multibody cartilage simulation. An indentation experiment performed on canine stifle cartilage was modeled in both paradigms with acceptable accuracy and the data were used to create the surrogate. Neural networks were found to adequately approximate the von Mises stress calculated by the finite element model based on force values provided from the multibody model with a correlation coefficient over 0.96.

Computational modeling of airway and pulmonary vascular structure and function: development of a "lung physiome"

Computational models of lung structure and function necessarily span multiple spatial and temporal scales, i.e., dynamic molecular interactions give rise to whole organ function, and the link between these scales cannot be fully understood if only molecular or organ-level function is considered. Here, we review progress in constructing multiscale finite element models of lung structure and function that are aimed at providing a computational framework for bridging the spatial scales from molecular to whole organ. These include structural models of the intact lung, embedded models of the pulmonary airways that couple to model lung tissue, and models of the pulmonary vasculature that account for distinct structural differences at the extra- and intra-acinar levels. Biophysically based functional models for tissue deformation, pulmonary blood flow, and airway bronchoconstriction are also described. The development of these advanced multiscale models has led to a better understanding of complex physiological mechanisms that govern regional lung perfusion and emergent heterogeneity during bronchoconstriction.

A multiscale framework based on the physiome markup languages for exploring the initiation of osteoarthritis at the bone-cartilage interface

The initiation of osteoarthritis (OA) has been linked to the onset and progression of pathologic mechanisms at the cartilage-bone interface. Most importantly, this degenerative disease involves cross-talk between the cartilage and subchondral bone environments, so an informative model should contain the complete complex. In order to evaluate this process, we have developed a multiscale model using the open-source ontologies developed for the Physiome Project with cartilage and bone descriptions at the cellular, micro, and macro levels. In this way, we can effectively model the influence of whole body loadings at the macro level and the influence of bone organization and architecture at the micro level, and have cell level processes that determine bone and cartilage remodeling. Cell information is then passed up the spatial scales to modify micro architecture and provide a macro spatial characterization of cartilage inflammation. We evaluate the framework by linking a common knee injury (anterior cruciate ligament deficiency) to proinflammatory mediators as a possible pathway to initiate OA. This framework provides a "virtual bone-cartilage" tool for evaluating hypotheses, treatment effects, and disease onset to inform and strengthen clinical studies.

Model predictions of increased knee joint loading in regions of thinner articular cartilage after patellar tendon adhesion

Patellar tendon adhesion is a complication from anterior cruciate ligament (ACL) reconstruction that may affect patellofemoral and tibiofemoral biomechanics. A computational model was used to investigate the changes in knee joint mechanics due to patellar tendon adhesion under normal physiological loading during gait. The calculations showed that patellar tendon adhesion up to the level of the anterior tibial plateau led to patellar infera, increased patellar flexion, and increased anterior tibial translation. These kinematic changes were associated with increased patellar contact force, a distal shift in peak patellar contact pressure, a posterior shift in peak tibial contact pressure, and increased peak tangential contact sliding distance over one gait cycle (i.e., contact slip). Postadhesion, patellar and tibial contact locations corresponded to regions of thinner cartilage. The predicted distal shift in patellar contact was in contrast to other patellar infera studies. Average patellar and tibial cartilage pressure did not change significantly following patellar tendon adhesion; however, peak medial tibial pressure increased. These results suggest that changes in peak tibial cartilage pressure, contact slip, and the migration of contact to regions of thinner cartilage are associated with patellar tendon adhesion and may be responsible for initiating patellofemoral pain and knee joint structural damage observed following ACL reconstruction.

The effect of connective tissue material uncertainties on knee joint mechanics under isolated loading conditions

Although variability in connective tissue parameters is widely reported and recognized, systematic examination of the effect of such parametric uncertainties on predictions derived from a full anatomical joint model is lacking. As such, a sensitivity analysis was performed to consider the behavior of a three-dimensional, non-linear, finite element knee model with connective tissue material parameters that varied within a given interval. The model included the coupled mechanics of the tibio-femoral and patello-femoral degrees of freedom. Seven primary connective tissues modeled as non-linear continua, articular cartilages described by a linear elastic model, and menisci modeled as transverse isotropic elastic materials were included. In this study, a multi-factorial global sensitivity analysis is proposed, which can detect the contribution of influential material parameters while maintaining the potential effect of parametric interactions. To illustrate the effect of material uncertainties on model predictions, exemplar loading conditions reported in a number of isolated experimental paradigms were used. Our findings illustrated that the inclusion of material uncertainties in a coupled tibio-femoral and patello-femoral model reveals biomechanical interactions that otherwise would remain unknown. For example, our analysis revealed that the effect of anterior cruciate ligament parameter variations on the patello-femoral kinematic and kinetic response sensitivities was significantly larger, over a range of flexion angles, when compared to variations associated with material parameters of tissues intrinsic to the patello-femoral joint. We argue that the systematic sensitivity framework presented herein will help identify key material uncertainties that merit further research and provide insight on those uncertainties that may not be as relative to a given response.

Validation of computational models in biomechanics

The topics of verification and validation have increasingly been discussed in the field of computational biomechanics, and many recent articles have applied these concepts in an attempt to build credibility for models of complex biological systems. Verification and validation are evolving techniques that, if used improperly, can lead to false conclusions about a system under study. In basic science, these erroneous conclusions may lead to failure of a subsequent hypothesis, but they can have more profound effects if the model is designed to predict patient outcomes. While several authors have reviewed verification and validation as they pertain to traditional solid and fluid mechanics, it is the intent of this paper to present them in the context of computational biomechanics. Specifically, the task of model validation will be discussed, with a focus on current techniques. It is hoped that this review will encourage investigators to engage and adopt the verification and validation process in an effort to increase peer acceptance of computational biomechanics models.

Effect of an UHMWPE patellar component on stress fields in the patella: a finite element analysis

An increased stress in the patella due to the implantation of a patellar button may also be another potential source of pain in total knee arthroplasty patients. This study assessed the location inside the patella having largest stress change after implantation of an ultra high molecular polyethylene patella button. Finite elements models of the patellae before and after implantation of patellar button were created. Experimentally determined spring constants of muscles and ligaments, and patellofemoral contacting loads were applied to the models at 30 degrees , 60 degrees , and 90 degrees of knee flexion. The Von Mises stress of the intact patella decreased with increased knee flexion, while that of implanted patella increased. Also, the stress range in the implanted patella was 3-9 times higher than in the intact one. The highly stressed region of the intact patella moved proximally with higher knee flexion angles, while that of the implanted model stayed near the central anterior patella. At 90 degrees of knee flexion, the stress in the anterodistal patella increased considerably after implantation of a patella button so that the anterodistal patella may be susceptible to be painful source after the total knee replacement.

Computational modeling for bedside application

Advances in computer power, novel diagnostic and therapeutic medical technologies, and an increasing knowledge of pathophysiology from gene to organ systems make it increasingly feasible to apply multiscale patient-specific modeling based on proven disease mechanisms. Such models may guide and predict the response to therapy in many areas of medicine. This is an exciting and relatively new approach, for which efficient methods and computational tools are of the utmost importance. Investigators have designed patient-specific models in almost all areas of human physiology. Not only will these models be useful in clinical settings to predict and optimize the outcome from surgery and non-interventional therapy, but they will also provide pathophysiologic insights from the cellular level to the organ system level. Models, therefore, will provide insight as to why specific interventions succeed or fail.

Development and Validation of Patient-Specific Finite Element Models of the Hemipelvis Generated From a Sparse CT Data Set

To produce a patient-specific finite element (FE) model of a bone such as the pelvis, a complete computer tomographic (CT) or magnetic resonance imaging (MRI) geometric data set is desirable. However, most patient data are limited to a specific region of interest such as the acetabulum. We have overcome this problem by providing a hybrid method that is capable of generating accurate FE models from sparse patient data sets. In this paper, we have validated our technique with mechanical experiments. Three cadaveric embalmed pelves were strain gauged and used in mechanical experiments. FE models were generated from the CT scans of the pelves. Material properties for cancellous bone were obtained from the CT scans and assigned to the FE mesh using a spatially varying field embedded inside the mesh while other materials used in the model were obtained from the literature. Although our FE meshes have large elements, the spatially varying field allowed them to have location dependent inhomogeneous material properties. For each pelvis, five different FE meshes with a varying number of patient CT slices (8–12) were generated to determine how many patient CT slices are needed for good accuracy. All five mesh types showed good agreement between the model and experimental strains. Meshes generated with incomplete data sets showed very similar stress distributions to those obtained from the FE mesh generated with complete data sets. Our modeling approach provides an important step in advancing the application of FE models from the research environment to the clinical setting.

Influence of meniscectomy and meniscus replacement on the stress distribution in human knee joint

Studying the mechanics of the knee joint has direct implications in understanding the state of human health and disease and can aid in treatment of injuries. In this work, we developed an axisymmetric model of the human knee joint using finite element method, which consisted of separate parts representing tibia, meniscus and femoral, and tibial articular cartilages. The articular cartilages were modeled as three separate layers with different material characteristics: top superficial layer, middle layer, and calcified layer. The biphasic characteristic of both meniscus and cartilage layers were included in the computational model. The developed model was employed to investigate several aspects of mechanical response of the knee joint under external loading associated with the standing posture. Specifically, we studied the role of the material characteristic of the articular cartilage and meniscus on the distribution of the shear stresses in the healthy knee joint and the knee joint after meniscectomy. We further employed the proposed computational model to study the mechanics of the knee joint with an artificial meniscus. Our calculations suggested an optimal elastic modulus of about 110 MPa for the artificial meniscus which was modeled as a linear isotropic material. The suggested optimum stiffness of the artificial meniscus corresponds to the stiffness of the physiological meniscus in the circumferential direction.

Experimental measurement and quantification of frictional contact between biological surfaces experiencing large deformation and slip

Interactions between contacting biological surfaces may play significant roles in physiological and pathological processes. Theoretical models have described some special cases of contact, using one or more simplifying assumptions. Experimental quantification of contact could help to validate theoretical analyses. The objective of this study was to develop a general mathematical approach describing the dynamics of deformation and relative surface motion between contacting bodies and to implement this approach to describe the contact between two experimentally tracked tissue surfaces. A theoretical formulation (in 2-D and 3-D) of contact using the movement of discrete tissue markers is described. The method was validated using theoretically generated 3-D datasets, with <1% error for a wide range of parameters. The method was applied to the contact loading of opposing articular cartilage tissues, where displacements of cell nuclei were tracked optically and used to quantify the movements and deformations of the surfaces. Compared to tissues with matched material properties, tissues with mismatched material properties exhibited increased disparities in lateral expansion and relative motion (sliding) between the contacting surfaces.

Frictional contact mechanics methods for soft materials: Application to tracking breast cancers

Mammography is currently the most widely used screening and diagnostic tool for breast cancer. Because X-ray images are 2D projections of a 3D object, it is not trivial to localise features identified in mammogram pairs within the breast volume. Furthermore, mammograms represent highly deformed configurations of the breast under compression, thus the tumour localisation process relies on the clinician's experience. Biomechanical models of the breast undergoing mammographic compressions have been developed to overcome this limitation. In this study, we present the development of a modelling framework that implements Coulomb's frictional law with a finite element analysis using a C(1)-continuous Hermite mesh. We compared two methods of this contact mechanics implementation: the penalty method, and the augmented Lagrangian method, the latter of which is more accurate but computationally more expensive compared to the former. Simulation results were compared with experimental data from a soft silicon gel phantom in order to evaluate the modelling accuracy of each method. Both methods resulted in surface-deformation root-mean-square errors of less than 2mm, whilst the maximum internal marker prediction error was less than 3mm when simulating two mammographic-like compressions. Simulation results were confirmed using the augmented Lagrangian method, which provided similar accuracy. We conclude that contact mechanics on soft elastic materials using the penalty method with an appropriate choice of the penalty parameters provides sufficient accuracy (with contact constraints suitably enforced), and may thus be useful for tracking breast tumours between clinical images.

Recognizing knee pathologies by classifying instantaneous screws of the six degrees-of-freedom knee motion

We address the problem of knee pathology assessment by using screw theory to describe the knee motion and by using the screw representation of the motion as an input to a machine learning classifier. The flexions of knees with different pathologies are tracked using an optical tracking system. The instantaneous screw parameters which describe the transformation of the tibia with respect to the femur in each two successive observation is represented as the instantaneous screw axis of the motion given in its Plücker line coordinates along with its corresponding pitch. The set of instantaneous screw parameters associated with a particular knee with a given pathology is then identified and clustered in R(6) to form a "signature" of the motion for the given pathology. Sawbones model and two cadaver knees with different pathologies were tracked, and the resulting screws were used to train a classifier system. The system was then tested successfully with new, never-trained-before data. The classifier demonstrated a very high success rate in identifying the knee pathology.