Accuracy and repeatability of a pressure measurement system in the patellofemoral joint

The objective of this study was to assess how accurately and repeatably the Iscan system measures force and pressure in the natural patellofemoral joint. These measurements must be made to test widely held assumptions about the relationships between mechanics, pain and cartilage degeneration. We assessed the system's accuracy by using test rigs in a materials testing machine to apply known forces and force distributions across the sensor. The root mean squared error in measuring resultant force (for five trials at each of seven load levels) was 6.5±4.4% (mean±standard deviation over all trials at all load levels), while the absolute error was −5.5±5.6%. For force distribution, the root mean squared error (for five trials at each of five force distributions) was 0.86±0.58%, while the absolute error was −0.22±1.03%. We assessed the repeatability of the system's measurements of patellofemoral contact force, pressure and force distribution in four cadaver specimens loaded in continuous and static flexion. Variability in measurement (standard deviation expressed as a percentage of the mean) was 9.1% for resultant force measurements and 3.0% for force distribution measurements for static loads, and 7.3% for resultant force and 2.2% for force distribution measurements for continuous flexion. Cementing the sensor to the cartilage lowered readings of resultant force by 31±32% (mean±standard deviation), area by 24±13% and mean pressure by 9±34% (relative to the uncemented sensor). Maximum pressure measurement, however, was 24±43% higher in the cemented sensor than in the uncemented sensor. The results suggest that the sensor measures force distribution more accurately and repeatably than absolute force. A limitation of our work, however, is that the sensor must be cemented to the patellar articular surface to make the force distribution measurements, and our results suggest that this process reduces the accuracy of force, pressure and area measurements. Our results suggest that the Iscan system's pressure measurement accuracy and repeatability are comparable to that of Fuji Prescale film, but its advantages are that it is thinner than most Fuji Prescale film, it measures contact area more accurately and that it makes continuous measurements of force, pressure and area.     

Development and validation of a subject-specific finite element model of a human clavicle

This study aimed to develop and validate a finite element (FE) model of a human clavicle which can predict the structural response and bone fractures under both axial compression and anterior–posterior three-point bending loads. Quasi-static non-injurious axial compression and three-point bending tests were first conducted on a male clavicle followed by a dynamic three-point bending test to fracture. Then, two types of FE models of the clavicle were developed using bone material properties which were set to vary with the computed tomography image density of the bone. A volumetric solid FE model comprised solely of hexahedral elements was first developed. A solid-shell FE model was then created which modelled the trabecular bone as hexahedral elements and the cortical bone as quadrilateral shell elements. Finally, simulations were carried out using these models to evaluate the influence of variations in cortical thickness, mesh density, bone material properties and modelling approach on the biomechanical responses of the clavicle, compared with experimental data. The FE results indicate that the inclusion of density-based bone material properties can provide a more accurate reproduction of the force–displacement response and bone fracture timing than a model with uniform bone material properties. Inclusion of a variable cortical thickness distribution also slightly improves the ability of the model to predict the experimental response. The methods developed in this study will be useful for creating subject-specific FE models to better understand the biomechanics and injury mechanism of the clavicle.     

Development and validation of a finite element model to simulate the opening of a medial opening wedge high tibial osteotomy

Medial opening wedge high tibial osteotomy (MOWHTO) is a surgical procedure intended to alter the coronal and sagittal plane alignment of the lower limb to primarily relieve the symptoms of osteoarthritis in the medial compartment of the knee. The purpose of this work was to develop and validate a finite element model to simulate the opening of a high tibial osteotomy and determine whether a pilot hole at the cortical hinge reduces the risk of lateral cortical fracture. Fifteen models were reconstructed from CT images of eight cadaveric specimens. The validated models indicated that the addition of the pilot hole increased the stresses and likelihood of a type-I and type-II fractures during the opening of a medial open wedge high tibial osteotomy compared to the no-hole condition.     

Development and validation of a computational model of the knee joint for the evaluation of surgical treatments for osteoarthritis

A three-dimensional (3D) knee joint computational model was developed and validated to predict knee joint contact forces and pressures for different degrees of malalignment. A 3D computational knee model was created from high-resolution radiological images to emulate passive sagittal rotation (full-extension to 65°-flexion) and weight acceptance. A cadaveric knee mounted on a six-degree-of-freedom robot was subjected to matching boundary and loading conditions. A ligament-tuning process minimised kinematic differences between the robotically loaded cadaver specimen and the finite element (FE) model. The model was validated by measured intra-articular force and pressure measurements. Percent full scale error between FE-predicted and in vitro-measured values in the medial and lateral compartments were 6.67% and 5.94%, respectively, for normalised peak pressure values, and 7.56% and 4.48%, respectively, for normalised force values. The knee model can accurately predict normalised intra-articular pressure and forces for different loading conditions and could be further developed for subject-specific surgical planning.     

Development of a statistical shape-function model of the implanted knee for real-time prediction of joint mechanics

Outcomes of total knee arthroplasty (TKA) are dependent on surgical technique, patient variability, and implant design. Non-optimal design or alignment choices may result in undesirable contact mechanics and joint kinematics, including poor joint alignment, instability, and reduced range of motion. Implant design and surgical alignment are modifiable factors with potential to improve patient outcomes, and there is a need for robust implant designs that can accommodate patient variability. Our objective was to develop a statistical shape-function model (SFM) of a posterior stabilized implanted knee to instantaneously predict joint mechanics in an efficient manner. Finite element methods were combined with Latin hypercube sampling and regression analyses to produce modeling equations relating nine implant design and six surgical alignment parameters to tibiofemoral (TF) joint mechanics outcomes during a deep knee bend. A SFM was developed and TF contact mechanics, kinematics, and soft tissue loads were instantaneously predicted from the model. Average normalized root-mean-square error predictions were between 2.79% and 9.42%, depending on the number of parameters included in the model. The statistical shape-function model generated instantaneous joint mechanics predictions using a maximum of 130 training simulations, making it ideally suited for integration into a patient-specific design and alignment optimization pipeline. Such a tool may be used to optimize kinematic function to achieve more natural motion or minimize implant wear, and may aid the engineering and clinical communities in improving patient satisfaction and surgical outcomes.     

Development and experimental validation of a finite element model of total ankle replacement

Total ankle replacement remains a less satisfactory solution compared to other joint replacements. The goal of this study was to develop and validate a finite element model of total ankle replacement, for future testing of hypotheses related to clinical issues. To validate the finite element model, an experimental setup was specifically developed and applied on 8 cadaveric tibias. A non-cemented press fit tibial component of a mobile bearing prosthesis was inserted into the tibias. Two extreme anterior and posterior positions of the mobile bearing insert were considered, as well as a centered one. An axial force of 2 kN was applied for each insert position. Strains were measured on the bone surface using digital image correlation. Tibias were CT scanned before implantation, after implantation, and after mechanical tests and removal of the prosthesis. The finite element model replicated the experimental setup. The first CT was used to build the geometry and evaluate the mechanical properties of the tibias. The second CT was used to set the implant position. The third CT was used to assess the bone-implant interface conditions. The coefficient of determination (R-squared) between the measured and predicted strains was 0.91. Predicted bone strains were maximal around the implant keel, especially at the anterior and posterior ends. The finite element model presented here is validated for future tests using more physiological loading conditions.     

Discrete element analysis is a valid method for computing joint contact stress in the hip before and after acetabular fracture

Evaluation of abnormalities in joint contact stress that develop after inaccurate reduction of an acetabular fracture may provide a potential means for predicting the risk of developing post-traumatic osteoarthritis. Discrete element analysis (DEA) is a computational technique for calculating intra-articular contact stress distributions in a fraction of the time required to obtain the same information using the more commonly employed finite element analysis technique. The goal of this work was to validate the accuracy of DEA-computed contact stress against physical measurements of contact stress made in cadaveric hips using Tekscan sensors. Four static loading tests in a variety of poses from heel-strike to toe-off were performed in two different cadaveric hip specimens with the acetabulum intact and again with an intentionally malreduced posterior wall acetabular fracture. DEA-computed contact stress was compared on a point-by-point basis to stress measured from the physical experiments. There was good agreement between computed and measured contact stress over the entire contact area (correlation coefficients ranged from 0.88 to 0.99). DEA-computed peak contact stress was within an average of 0.5 MPa (range 0.2–0.8 MPa) of the Tekscan peak stress for intact hips, and within an average of 0.6 MPa (range 0–1.6 MPa) for fractured cases. DEA-computed contact areas were within an average of 33% of the Tekscan-measured areas (range: 1.4–60%). These results indicate that the DEA methodology is a valid method for accurately estimating contact stress in both intact and fractured hips.     

A geometric approach to study the contact mechanisms in the patellofemoral joint of normal versus patellofemoral pain syndrome subjects

The biomechanics of the patellofemoral (PF) joint is complex in nature, and the aetiology of such manifestations of PF instability as patellofemoral pain syndrome (PFPS) is still unclear. At this point, the particular factors affecting PFPS have not yet been determined. This study has two objectives: (1) The first is to develop an alternative geometric method using a three-dimensional (3D) registration technique and linear mapping to investigate the PF joint contact stress using an indirect measure: the depth of virtual penetration (PD) of the patellar cartilage surface into the femoral cartilage surface. (2) The second is to develop 3D PF joint models using the finite element analysis (FEA) to quantify in vivo cartilage contact stress and to compare the peak contact stress location obtained from the FE models with the location of the maximum PD. Magnetic resonance images of healthy and PFPS subjects at knee flexion angles of 15°, 30° and 45° during isometric loading have been used to develop the geometric models. The results obtained from both approaches demonstrated that the subjects with PFPS show higher PD and contact stresses than the normal subjects. Maximum stress and PD increase with flexion angle, and occur on the lateral side in healthy and on the medial side in PFPS subjects. It has been concluded that the alternative geometric method is reliable in addition to being computationally efficient compared with FEA, and has the potential to assess the mechanics of PFPS with an accuracy similar to the FEA.     

Development and validation of a weight-bearing finite element model for total knee replacement

Total knee arthroplasty (TKA) is a successful procedure for osteoarthritis. However, some patients (19%) do have pain after surgery. A finite element model was developed based on boundary conditions of a knee rig. A 3D-model of an anatomical full leg was generated from magnetic resonance image data and a total knee prosthesis was implanted without patella resurfacing. In the finite element model, a restarting procedure was programmed in order to hold the ground reaction force constant with an adapted quadriceps muscle force during a squat from 20° to 105° of flexion. Knee rig experimental data were used to validate the numerical model in the patellofemoral and femorotibial joint. Furthermore, sensitivity analyses of Young’s modulus of the patella cartilage, posterior cruciate ligament (PCL) stiffness, and patella tendon origin were performed. Pearson’s correlations for retropatellar contact area, pressure, patella flexion, and femorotibial ap-movement were near to 1. Lowest root mean square error for retropatellar pressure, patella flexion, and femorotibial ap-movement were found for the baseline model setup with Young’s modulus of 5 MPa for patella cartilage, a downscaled PCL stiffness of 25% compared to the literature given value and an anatomical origin of the patella tendon. The results of the conducted finite element model are comparable with the experimental results. Therefore, the finite element model developed in this study can be used for further clinical investigations and will help to better understand the clinical aspects after TKA with an unresurfaced patella.     

Verification of predicted specimen-specific natural and implanted patellofemoral kinematics during simulated deep knee bend

Verified computational models represent an efficient method for studying the relationship between articular geometry, soft-tissue constraint, and patellofemoral (PF) mechanics. The current study was performed to evaluate an explicit finite element (FE) modeling approach for predicting PF kinematics in the natural and implanted knee. Experimental three-dimensional kinematic data were collected on four healthy cadaver specimens in their natural state and after total knee replacement in the Kansas knee simulator during a simulated deep knee bend activity. Specimen-specific FE models were created from medical images and CAD implant geometry, and included soft-tissue structures representing medial–lateral PF ligaments and the quadriceps tendon. Measured quadriceps loads and prescribed tibiofemoral kinematics were used to predict dynamic kinematics of an isolated PF joint between 10° and 110° femoral flexion. Model sensitivity analyses were performed to determine the effect of rigid or deformable patellar representations and perturbed PF ligament mechanical properties (pre-tension and stiffness) on model predictions and computational efficiency.Predicted PF kinematics from the deformable analyses showed average root mean square (RMS) differences for the natural and implanted states of less than 3.1° and 1.7 mm for all rotations and translations. Kinematic predictions with rigid bodies increased average RMS values slightly to 3.7° and 1.9 mm with a five-fold decrease in computational time. Two-fold increases and decreases in PF ligament initial strain and linear stiffness were found to most adversely affect kinematic predictions for flexion, internal–external tilt and inferior–superior translation in both natural and implanted states. The verified models could be used to further investigate the effects of component alignment or soft-tissue variability on natural and implant PF mechanics.     

Three-dimensional discrete element method for the prediction of protoplasmic seepage through membrane in a biological cell

This paper presents a three-dimensional and compressible biological cell model based on discrete element method using multiple interacting agent that represent cellular structures within a simulated environment. The cytoplasm and nucleoplasm fluid behavior in the cell is time dependent. When taking this approach, it is important to calibrate protoplasmic flow behaviors through simulation techniques such as compressing the cell and examining the agents representing the cell cytoplasm seeping between the ones representing the confining cell membrane. This type of modelling may motivate future work on simulating simultaneous operations and interactions of multiple cellular agents in an attempt to re-create and predict the appearance of complex phenomena such as protoplasmic seepage that is caused by the force actuations of neighboring cells. Seepage occurs when a cytoplasm agent passes between three membrane particles connected in a triangular network. Based on the force–deformation response of spheres having variable size and stiffness, semi-analytic expressions are developed for the force required to cause seepage and solved numerically to find the maximum resistance offered by the membrane against cytoplasm seepage. The equations are based on force equilibrium and the constitutive relations for particle contact and membrane stiffness. In multi-particle representations of an individual cell undergoing deformation, different modes of cytoplasm seepage through confining cell membranes can occur. This can be avoided if simple criteria are satisfied. These findings can lead to certain fundamental laws for the improvement of novel cell-to-organ simulation techniques based on discrete element method.     

Lumbar spine finite element model for healthy subjects: development and validation

Finite element (FE) method is a proven powerful and efficient tool to study the biomechanics of the human lumbar spine. However, due to the large inter-subject variability of geometries and material properties in human lumbar spines, concerns existed on the accuracy and predictive power of one single deterministic FE model with one set of spinal geometry and material properties. It was confirmed that the combined predictions (median or mean value) of several distinct FE models can be used as an improved prediction of behavior of human lumbar spine under identical loading and boundary conditions. In light of this improved prediction, five FE models (L1-L5 spinal levels) of the human lumbar spine were developed based on five healthy living subjects with identical modeling method. The five models were extensively validated through experimental and computational results in the literature. Mesh convergence and material sensitivity analysis were also conducted. We have shown that the results from the five FE models developed in this paper were consistent with the experimental data and simulation results from the existing literature. The validated modeling method introduced in this study can be used in modeling dysfunctional lumber spines such as disc degeneration and scoliosis in future work.     

Development and validation of a multi-body model of the canine stifle joint

Multi-body musculoskeletal models that can be used concurrently to predict joint contact pressures and muscle forces would be extremely valuable in studying the mechanics of joint injury. The purpose of this study was to develop an anatomically correct canine stifle joint model and validate it against experimental data. A cadaver pelvic limb from one adult dog was used in this study. The femoral head was subjected to axial motion in a mechanical tester. Kinematic and force data were used to validate the computational model. The maximum RMS error between the predicted and measured kinematics during the complete testing cycle was 11.9 mm translational motion between the tibia and the femur and 4.3° rotation between patella and femur. This model is the first step in the development of a musculoskeletal model of the hind limb with anatomically correct joints to study cartilage loading under dynamic conditions.     

Joint contact stresses calculated for acetabular dysplasia patients using discrete element analysis are significantly influenced by the applied gait pattern

Gait modifications in acetabular dysplasia patients may influence cartilage contact stress patterns within the hip joint, with serious implications for clinical outcomes and the risk of developing osteoarthritis. The objective of this study was to understand how the gait pattern used to load computational models of dysplastic hips influences computed joint mechanics. Three-dimensional pre- and post-operative hip models of thirty patients previously treated for hip dysplasia with periacetabular osteotomy (PAO) were developed for performing discrete element analysis (DEA). Using DEA, contact stress patterns were calculated for each pre- and post-operative hip model when loaded with an instrumented total hip, a dysplastic, a matched control, and a normal gait pattern. DEA models loaded with the dysplastic and matched control gait patterns had significantly higher (p = 0.012 and p < 0.001) average pre-operative maximum contact stress than models loaded with the normal gait. Models loaded with the dysplastic and matched control gait patterns had nearly significantly higher (p = 0.051) and significantly higher (p = 0.008) average pre-operative contact stress, respectively, than models loaded with the instrumented hip gait. Following PAO, the average maximum contact stress for DEA models loaded with the dysplastic and matched control patterns decreased, which was significantly different (p < 0.001) from observed increases in maximum contact stress calculated when utilizing the instrumented hip and normal gait patterns. The correlation between change in DEA-computed maximum contact stress and the change in radiographic measurements of lateral center-edge angle were greatest (R² = 0.330) when utilizing the dysplastic gait pattern. These results indicate that utilizing a dysplastic gait pattern to load DEA models may be a crucial element to capturing contact stress patterns most representative of this patient population.     

Numerical exploration of the parameter plane in a discrete predator–prey model

We propose a variant of the discrete Lotka–Volterra model for predator–prey interactions. A detailed stability and numerical analysis of the model are presented to explore the long time behaviour as each of the control parameter is varied independently. We show how the condition for survival of the predator depends on the natural death rate of predator and the efficiency of predation. The model is found to support different dynamical regimes asymptotically including predator extinction, stable fixed point and limit cycle attractors for co-existence of predator and prey and more complex dynamics involving chaotic attractors. We are able to locate exactly the domain of chaos in the parameter plane using a dimensional analysis.     

Impact orientation can significantly affect the outcome of a blunt impact to the rabbit patellofemoral joint

This laboratory has developed a subfracture, joint trauma model in rabbits. Using a dropped impact mass directed onto a slightly abducted joint, chronic softening of retropatellar cartilage and thickening of underlying subchondral bone are documented in studies to 1 year post-insult. It has been hypothesized that these tissue changes are initiated by stresses developed during impact loading. A previous analytical study by this laboratory suggests that tensile strains in retropatellar cartilage can be significantly lowered, without significantly changing the intensity of stresses in the underlying subchondral bone, by reorientation of patellar impact more centrally on the joint. In the current study comparative experiments were performed on groups of animals after either an impact directed on the slightly abducted limb or a more central impact. One-year post-trauma in animals subjected to the central-oriented impact no degradation of the shear modulus for the retropatellar cartilage was documented, but the thickness of the underlying subchondral bone was significantly increased. In contrast, alterations in cartilage and underlying bone following impact on the slightly abducted limb were consistent with previous studies. The current experimental investigation showed the sensitivity of post-trauma alterations in joint tissues to slight changes in the orientation of impact load on the joint. Interestingly, for this trauma model thickening of the underlying subchondral plate occurred without mechanical degradation of the overlying articular cartilage. This supports the current laboratory hypothesis that alterations in the subchondral bone and overlying cartilage occur independently in this animal model.     

Parametric convergence sensitivity and validation of a finite element model of the human lumbar spine

The primary objective of this study was to generate a finite element model of the human lumbar spine (L1–L5), verify mesh convergence for each tissue constituent and perform an extensive validation using both kinematic/kinetic and stress/strain data. Mesh refinement was accomplished via convergence of strain energy density (SED) predictions for each spinal tissue. The converged model was validated based on range of motion, intradiscal pressure, facet force transmission, anterolateral cortical bone strain and anterior longitudinal ligament deformation predictions. Changes in mesh resolution had the biggest impact on SED predictions under axial rotation loading. Nonlinearity of the moment-rotation curves was accurately simulated and the model predictions on the aforementioned parameters were in good agreement with experimental data. The validated and converged model will be utilised to study the effects of degeneration on the lumbar spine biomechanics, as well as to investigate the mechanical underpinning of the contemporary treatment strategies.     

Development of a statistical shape model of the patellofemoral joint for investigating relationships between shape and function

Patellofemoral (PF)-related pathologies, including joint laxity, patellar maltracking, cartilage degradation and anterior knee pain, affect nearly 25% of the population. Researchers have investigated the influence of articular geometry on kinematics and contact mechanics in order to gain insight into the etiology of these conditions. The purpose of the current study was to create a three-dimensional statistical shape model of the PF joint and to characterize relationships between PF shape and function (kinematics and contact mechanics). A statistical shape model of the patellar and femoral articular surfaces and their relative alignment was developed from magnetic resonance images. Using 15 shape parameters, the model characterized 97% of the variation in the training set. The first three shape modes primarily described variation in size, patella alta-baja and depth of the sulcus groove. A previously verified finite element model was used to predict kinematics and contact mechanics for each subject. Combining the shape and joint mechanics data, a statistical shape-function model was developed that established quantitative relations of how changes in the shape of the PF joint influence mechanics. The predictive capability of the shape-function model was evaluated by comparing statistical model and finite element predictions, resulting in kinematic root mean square errors of less than 3° and 2.5 mm. The key results of the study are dually in the implementation of a novel approach linking statistical shape and finite element models and the relationships elucidated between PF articular geometry and mechanics.     

Comparison of different analysis techniques for the determination of muscle onset in individuals with patellofemoral pain syndrome

To understand patellofemoral pain syndrome (PFPS), recent studies have focused on assessing the onset in the vastus medialis and vastus lateralis to determine whether there is a delay between these muscles’ activation. However, the results of these studies are not in agreement, as some research shows that there is a delay in the VMO, while others do not show delay. It has been suggested that this discrepancies may be due to differences in the signal processing and analysis. For this reason, this study aimed to compare the three techniques used for onset determination – automatic detection, visual inspection and cross-correlation – and to verify whether these methods are able to detect PFPS. The surface electromyography evaluation procedure was conducted in 22 pain-free control individuals and 11 with PFPS diagnoses, during a stair climbing. The standard error of measurement (SEM) showed that cross-correlation presents the lower variation (2.56/3.27, control/PFPS) in relation to visual (3.77/10.19, control/PFPS) and automatic detection (43.23/51.98, control/PFPS, respectively). But when using the cross-correlation technique, we were not able to distinguish the groups (−6.56/−9.74 ms, control/PFPS, p = 0.15). Therefore, use of muscle onset may not be the best way to distinguish individuals with PFPS.     

Intrinsic and extrinsic contributions to the passive moment at the metacarpophalangeal joint

The purpose of this investigation was to determine whether the passive range of motion at the finger joints is restricted more by intrinsic tissues (cross a single joint) or by extrinsic tissues (cross multiple joints). The passive moment at the metacarpophalangeal (MP) joint of the index finger was modeled as the sum of intrinsic and extrinsic components. The intrinsic component was modeled only as a function of MP joint angle. The extrinsic component was modeled as a function of MP joint angle and wrist angle. With the wrist fixed in seven different positions the passive moment at the MP joint of eight subjects was recorded as the finger was rotated through its range at a constant rate. The moment-angle data were fit by the model and the extrinsic and intrinsic components were calculated for a range of MP joint angles and wrist positions. With the MP joint near its extension limit, the median percent extrinsic contribution was 94% with the wrist extended 60° and 14% with the wrist flexed 60°. These percentages were 40 and 88%, respectively, with the MP joint near its flexion limit. Our findings indicate that at most wrist angles the extrinsic tissues offer greater restraint at the limits of MP joint extension and flexion than the intrinsic tissues. The intrinsic tissues predominate when the wrist is flexed or extended enough to slacken the extrinsic tissues. Additional characteristics of intrinsic and extrinsic tissues can be deduced by examining the parameter values calculated by the model.