The role of computational models in the search for the mechanical behavior and damage mechanisms of articular cartilage

Biomechanical evaluation of tenodesis reconstruction in ankle with deltoid ligament deficiency: a finite element analysis

PURPOSE

Isolated deltoid ligament injuries are relatively uncommon but can be a significant source of pain and disability. Several approaches to deltoid reconstruction have been reported. However, there is no previous comparative study of Wiltberger, Deland, Kitaoka and Hintermann procedures with respect to biomechanical characteristics such as kinematics, ligaments and grafts stresses using finite element analysis. The purpose of this study was to evaluate the biomechanical results of those deltoid ligament reconstructions using finite element analysis.

METHODS

A three-dimensional finite element model of the ankle including six bony structures, cartilage and nine principal ligaments surrounding the ankle joint complex was developed and validated. In addition to the intact model, superficial deltoid-deficient, deltoid-deficient, Wiltberger reconstruction, Deland reconstruction, Kitaoka reconstruction and Hintermann reconstruction models were simulated. Then, the forces in the ligaments and grafts and the kinematics of talus and calcaneus were predicted for an eversional or external torque through the range of ankle flexion.

RESULTS

No reconstructions could completely restore the values for ankle flexibility and the stresses of the lateral ligaments to normality. The Kitaoka procedure was the most effective technique in eliminating external rotation displacement. The Deland procedure restored better the talar tilt than the other three reconstructions.

CONCLUSION

This study showed that Kitaoka and Deland procedures have advantages with regard to rotational stabilities as well as ligaments stress in comparison with other methods.

Multiscale mechanics of articular cartilage: potentials and challenges of coupling musculoskeletal, joint, and microscale computational models

Articular cartilage experiences significant mechanical loads during daily activities. Healthy cartilage provides the capacity for load bearing and regulates the mechanobiological processes for tissue development, maintenance, and repair. Experimental studies at multiple scales have provided a fundamental understanding of macroscopic mechanical function, evaluation of the micromechanical environment of chondrocytes, and the foundations for mechanobiological response. In addition, computational models of cartilage have offered a concise description of experimental data at many spatial levels under healthy and diseased conditions, and have served to generate hypotheses for the mechanical and biological function. Further, modeling and simulation provides a platform for predictive risk assessment, management of dysfunction, as well as a means to relate multiple spatial scales. Simulation-based investigation of cartilage comes with many challenges including both the computational burden and often insufficient availability of data for model development and validation. This review outlines recent modeling and simulation approaches to understand cartilage function from a mechanical systems perspective, and illustrates pathways to associate mechanics with biological function. Computational representations at single scales are provided from the body down to the microstructure, along with attempts to explore multiscale mechanisms of load sharing that dictate the mechanical environment of the cartilage and chondrocytes.

Chondrocyte deformations as a function of tibiofemoral joint loading predicted by a generalized high-throughput pipeline of multi-scale simulations

Cells of the musculoskeletal system are known to respond to mechanical loading and chondrocytes within the cartilage are not an exception. However, understanding how joint level loads relate to cell level deformations, e.g. in the cartilage, is not a straightforward task. In this study, a multi-scale analysis pipeline was implemented to post-process the results of a macro-scale finite element (FE) tibiofemoral joint model to provide joint mechanics based displacement boundary conditions to micro-scale cellular FE models of the cartilage, for the purpose of characterizing chondrocyte deformations in relation to tibiofemoral joint loading. It was possible to identify the load distribution within the knee among its tissue structures and ultimately within the cartilage among its extracellular matrix, pericellular environment and resident chondrocytes. Various cellular deformation metrics (aspect ratio change, volumetric strain, cellular effective strain and maximum shear strain) were calculated. To illustrate further utility of this multi-scale modeling pipeline, two micro-scale cartilage constructs were considered: an idealized single cell at the centroid of a 100×100×100 μm block commonly used in past research studies, and an anatomically based (11 cell model of the same volume) representation of the middle zone of tibiofemoral cartilage. In both cases, chondrocytes experienced amplified deformations compared to those at the macro-scale, predicted by simulating one body weight compressive loading on the tibiofemoral joint. In the 11 cell case, all cells experienced less deformation than the single cell case, and also exhibited a larger variance in deformation compared to other cells residing in the same block. The coupling method proved to be highly scalable due to micro-scale model independence that allowed for exploitation of distributed memory computing architecture. The method's generalized nature also allows for substitution of any macro-scale and/or micro-scale model providing application for other multi-scale continuum mechanics problems.

Clustering of infrared spectra reveals histological zones in intact articular cartilage

OBJECTIVE

Articular cartilage (AC) exhibits specific zonal structure that follows the organization of collagen network and concentration of tissue constituents. The aim of this study was to investigate the potential of unsupervised clustering analysis applied to Fourier transform infrared (FTIR) microspectroscopy to detect depth-dependent structural and compositional differences in intact AC.

METHOD

Seven rabbit and eight bovine intact patellae AC samples were imaged using FTIR microspectroscopy and normalized raw spectra were clustered using the fuzzy C-means algorithm. Differences in mean spectra of clusters were investigated by quantitative estimation of collagen and proteoglycan (PG) contents, as well as by careful visual investigation of locations of spectral changes.

RESULTS

Clustering revealed the typical layered structure of AC in both species. However, more distinct clusters were found for rabbit samples, whereas bovine AC showed more complex layered structure. In both species, clustering structure corresponded with that in polarized light microscopic (PLM) images; however, some differences were also observed. Spectral differences between clusters were identified at the same spectral locations for both species. Estimated PG/collagen ratio decreased significantly from superficial to middle or deep zones, which might explain the difference in clustering results compared to PLM.

CONCLUSION

FTIR microspectroscopy in combination with cluster analysis allows detailed examination of spatial changes in AC. As far as we know, no previous single technique could reveal a layered structure of AC without any a priori information.

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.

MODELING OF KNEE ARTICULAR CARTILAGE DISSIPATION DURING GAIT ANALYSIS

Articular cartilage dissipates contact loads according to three dissipative mechanisms: frictional drag, intrinsic viscoelasticity, and surface friction. Estimation of dissipation due to these three mechanisms during gait is required to understand the dissipative properties of articular cartilage. Fourteen healthy subjects performed a gait analysis on treadmill. Tibiofemoral contact forces were estimated from inverse dynamic analysis and from a reductionist knee contact model. These contact forces and the results obtained from a preloading creep simulation were introduced into a biphasic poroviscoelastic articular cartilage model, and a one-dimensional confined compression was performed. Articular dissipation from each dissipative mechanism was estimated. Sensitivity analysis was performed to determine the effects of material parameters and length of the preloading simulation on the patterns of the dissipative mechanisms. Dissipative force patterns for all dissipative mechanisms were found to be similar to those of tibiofemoral contact forces. Frictional drag was found to be the dominant dissipative mechanism. The initial permeability and the viscoelastic spectrum parameters were found to have an important impact on the magnitude of the peaks of dissipative patterns. If appropriate material parameters are introduced, this model could be used to compare the difference between healthy and osteoarthritic human articular cartilage.

The influence of fiber orientation on the equilibrium properties of neutral and charged biphasic tissues

Constitutive models facilitate investigation into load bearing mechanisms of biological tissues and may aid attempts to engineer tissue replacements. In soft tissue models, a commonly made assumption is that collagen fibers can only bear tensile loads. Previous computational studies have demonstrated that radially aligned fibers stiffen a material in unconfined compression most by limiting lateral expansion while vertically aligned fibers buckle under the compressive loads. In this short communication, we show that in conjunction with swelling, these intuitive statements can be violated at small strains. Under such conditions, a tissue with fibers aligned parallel to the direction of load initially provides the greatest resistance to compression. The results are further put into the context of a Benninghoff architecture for articular cartilage. The predictions of this computational study demonstrate the effects of varying fiber orientations and an initial tare strain on the apparent material parameters obtained from unconfined compression tests of charged tissues.

Biomechanics of the deformity of septal L-Struts

OBJECTIVES/HYPOTHESIS

A septal L-strut is often preserved or created during septoplasty. The main intention is to provide structural stability and to straighten the nasal septum. Deformity or excessive deformation of the L-strut might cause functional or aesthetic complications. The objectives were to examine the effects of material properties, the boundary conditions, the nasal tip support, and the geometry of the L-struts on the deformity of septal L-struts.

STUDY DESIGN

Computer-aided modeling was used to create a spring-supported nasal tip and free nasal tip L strut septal cartilage models upon which simulation was performed to analyse the deformation patterns.

METHODS

A five-sided septum model was first created from the computed tomography scan of a human subject. Several models with various combinations of wider or narrower dorsal struts as well as arc of cartilage were then constructed from this septum model. The edges connected to bony supports were assumed to be fixed, and the nasal tip was assumed to be spring supported. Finite element analyses were carried out to determine the deformation and stress distribution in the septal strut for different combinations of material properties and nasal tip spring support.

RESULTS

The spring-supported nasal tip model provides a more accurate representation of the boundary conditions in the nose. In both the free and spring-supported nasal tips-the BC junction and the nasal spine are found to be the consistent points of maximum stress regardless of material properties. The preservation of an arc of cartilage and a wider dorsal strut increase the stability of the structure.

CONCLUSIONS

The introduction of a spring-supported nasal tip model provided a more accurate representation of the boundary conditions in the nose. The bony-cartilaginous junction and the nasal spine were found to be the consistent points of maximum stress, regardless of material properties. The preservation of an arc of cartilage and a wider dorsal strut increased the stability of the structure.

Baseline articular contact stress levels predict incident symptomatic knee osteoarthritis development in the MOST cohort

We studied whether contact stress estimates from knee magnetic resonance images (MRI) predict the development of incident symptomatic tibiofemoral osteoarthritis (OA) 15 months later in an at-risk cohort. This nested case-control study was conducted within a cohort of 3,026 adults, age 50 to 79 years. Thirty cases with incident symptomatic tibiofemoral OA by their 15 month follow-up visit were randomly selected and matched with 30 control subjects. Symptomatic tibiofemoral OA was defined as daily knee pain/stiffness and Kellgren-Lawrence Grade > or =2 on weight bearing, fixed-flexion radiographs. Tibiofemoral geometry was segmented on baseline knee MRI, and contact stresses were estimated using discrete element analysis. Linear mixed models for repeated measures were used to examine the association between articular contact stress and case/control status. No significant intergroup differences were found for age, sex, BMI, weight, height, or limb alignment. However, the maximum articular contact stress was 0.54 +/- 0.77 MPa (mean +/- SD) higher in incident OA cases compared to that in control knees (p = 0.0007). The interaction between case-control status and contact stress was significant above 3.20 MPa (p < 0.0001). The presence of differences in estimated contact stress 15 months prior to incidence suggests a biomechanical mechanism for symptomatic tibiofemoral OA and supports the ability to identify risk by subject-specific biomechanical modeling.

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.

Computer simulation of damage on distal femoral articular cartilage after meniscectomies

It is commonly accepted that total or partial meniscectomies cause wear of articular cartilages that leads to severe damage in a period of few years. This also produces alteration of the biomechanical environment and increases articular instability, with a progressive and degenerative arthrosic pathology. Due to these negative consequences, total meniscectomy technique has been avoided, with a clear preference for partial meniscectomies. Despite the better results obtained with this latter technique, it has been demonstrated that the knee still suffers progressive long-term wear, which alters the properties of the surface of articular cartilage. In this paper, a phenomenological isotropic damage model of articular cartilage is presented and implemented in a finite element code. We hypothesized that there is a relation between the increase of shear stress and cartilage degeneration. To confirm the hypothesis, the obtained results were compared to experimental ones. It is used to investigate the effect of meniscectomies on articular damage in the human knee joint. Two different situations were compared for the tibio-femoral joint: healthy and after meniscectomy. The distribution of damaged regions and the damage level distribution resulted qualitatively similar to experimental results, showing, for instance that, after meniscectomy, significant degeneration occurs in the lateral compartment. A noteworthy result was that patterns of damage in a total meniscectomy model give better agreement to clinical results when using relative increases in shear stress, rather than an absolute shear stress criterion. The predictions for partial meniscectomies indicated the relative severity of the procedures.

Indentation stiffness of aging human costal cartilage

Costal cartilage, connecting the ribs and sternum, serves a mechanical function in the body. It undergoes structural changes with aging but it is unclear if its material properties are affected by these changes. To investigate this question, experimental indentation load-relaxation tests were performed on human costal cartilage as a function of specimen age and sex. The experimental data were fit to spherical indentation ramp-relaxation solutions generated previously by elastic-viscoelastic correspondence [Mattice JM, Lau AG, Oyen ML and Kent RW. Spherical indentation load-relaxation of soft biological tissues. J Mater Res 2006;8:2003-10]. Numerical values of short- and long-time shear modulus and of material time-constants were examined as a function of age. Costal cartilage calcification was assessed with blinded scoring of computed tomography reconstructions of the ribcage and mechanical properties were correlated with calcification score. Overall, the costal cartilage midsubstance was slightly stiffer than articular cartilage, and did not show significant variation in stiffness with age or specimen calcification. Increased age did result in increased local variability of the indentation stiffness results. Future studies will be required to address the findings of the current study that although calcification did increase with age, the calcification was primarily found on the costal cartilage periphery, thus insignificantly affecting the midsubstance stiffness.