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

The Effect of Different Degrees of Ankle Dorsiflexion Restriction on the Biomechanics of the Lower Extremity in Stop-Jumping

Purpose

The functional status of the ankle joint is critical during dynamic movements in high-intensity sports like basketball and volleyball, particularly when performing actions such as stopping jumps. Limited ankle dorsiflexion is associated with increased injury risk and biomechanical changes during stop-jump tasks. Therefore, this study aims to investigate how restricting ankle dorsiflexion affects lower extremity biomechanics during the stop-jump phase, with a focus on the adaptive changes that occur in response to this restriction. Initially, 18 participants during stop-jumping with no wedge plate (NW), 10° wedge plate (10 W), and 20° wedge plate (20 W) using dominant leg data were collected to explore the relationship between limiting ankle mobility and lower extremity biomechanics. Following this, a musculoskeletal model was developed to simulate and calculate biomechanical data. Finally, one-dimensional parametric statistical mapping (SPM1D) was utilized to evaluate between-group variation in outcome variables using a one-way repeated measures analysis of variance (ANOVA).

Results

As the ankle restriction angle increased, knee external rotation angles, knee extension angular velocities, hip extension angle, and angular velocity increased and were significantly different at different ankle restriction angles (p  < 0.001 and p=0.001), coactivation of the peripatellar muscles (BF/RF and BF/VM) increased progressively, and patellofemoral joint contact force (PTF) increased progressively during the 3%-8% phase (p=0.015). These results highlight the influence of ankle joint restriction on lower limb kinematics and patellofemoral joint loading during the stop-jump maneuver.

Conclusion

As the angle of ankle restriction increased, there was an increase in coactivation of the peripatellar muscles and an increase in PTF, possibly because a person is unable to adequately adjust their body for balance when the ankle valgus angle is restricted. The increased coactivation of the peripatellar muscles and increased patellofemoral contact force may be a compensatory response to the body's adaptation to balance adjustments.

Accuracy tradeoffs between individual bone and joint-level statistical shape models of knee morphology

Statistical shape models (SSMs) are useful tools in evaluating variation in bony anatomy to assess pathology, plan surgical interventions, and inform the design of orthopaedic implants and instrumentation. Recently, by considering multiple bones spanning a joint or the whole lower extremity, SSMs can support studies investigating articular conformity and joint mechanics. The objective of this study was to assess tradeoffs in accuracy between SSMs of the femur or tibia individually versus a combined joint-level model. Three statistical shape models were developed (femur-only, tibia-only, and joint-level) for a training set of 179 total knee arthroplasty (TKA) patients with osteoarthritis representing both genders and several ethnicities. Bone geometries were segmented from preoperative CT scans, meshed with triangular elements, and registered to a template for each SSM. Principal component analysis was performed to determine modes of variation. The statistical shape models were compared using measures of compactness, accuracy, generalization, and specificity. The generalization evaluation, assessing the ability to describe an unseen instance in a leave-one-out analysis, showed that errors were consistently smaller for the individual femur and tibia SSMs than for the joint-level model. However, when additional modes were included in the joint-level model, the errors were comparable to the individual bone results, with minimal additional computational expense. When developing more complex SSMs at the joint, lower limb, or whole-body level, the use of an error threshold to inform the number of included modes, instead of 95 % of the variation explained, can help to ensure accurate representations of anatomy.

Sex differences in patellar facet shape among healthy and osteoarthritic cohorts

OBJECTIVE

Patellofemoral osteoarthritis (OA) may be more common in females than males. Reasons for this are not fully understood, but sex differences in patellar morphology may help explain this phenomenon. We quantified differences in patellar morphology between males and females in healthy and patellofemoral OA populations.

DESIGN

A total of 97 (50F, 47M) healthy and 67 (40F, 27M) OA knees were scanned via computed tomography. OA individuals were on a waitlist for total knee replacement. Patella 3D models were segmented and 2D measurements were recorded: patellar width and height, lateral and medial facet width, and surface area. Medial and lateral facet surface topography was mapped using 81 points to describe 3D articular surface shape. Sex and group differences were assessed using Procrustes analysis of variance (ANOVA). Data were ordinated using Principal Component Analysis.

RESULTS

Differences in patellar 2D measurements between healthy and OA individuals were smaller than were differences between males and females from healthy and OA groups. Sex and healthy/OA differences were most pronounced for medial facet shape, which featured a posteriorly-curving facet and taller, narrower facet shape in males compared to females. Lateral facet shape variance was higher in OA cohorts compared to healthy groups.

CONCLUSIONS

Medial and lateral facet shapes showed different patterning of variation by sex and healthy/OA status. Lateral facet shape may be of interest in future models of OA risk in the patellofemoral joint, here showing increased magnitudes of variance associated with increased severity of disease (patellofemoral Kellgren and Lawrence score).

Three-dimensional magnetic resonance imaging-based statistical shape analysis and machine learning-based prediction of patellofemoral instability

This study performed three-dimensional (3D) magnetic resonance imaging (MRI)-based statistical shape analysis (SSA) by comparing patellofemoral instability (PFI) and normal femur models, and developed a machine learning (ML)-based prediction model. Twenty (19 patients) and 31 MRI scans (30 patients) of femurs with PFI and normal femurs, respectively, were used. Bone and cartilage segmentation of the distal femurs was performed and subsequently converted into 3D reconstructed models. The pointwise distance map showed anterior elevation of the trochlea, particularly at the central floor of the proximal trochlea, in the PFI models compared with the normal models. Principal component analysis examined shape variations in the PFI group, and several principal components exhibited shape variations in the trochlear floor and intercondylar width. Multivariate analysis showed that these shape components were significantly correlated with the PFI/non-PFI distinction after adjusting for age and sex. Our ML-based prediction model for PFI achieved a strong predictive performance with an accuracy of 0.909 ± 0.015, and an area under the curve of 0.939 ± 0.009 when using a support vector machine with a linear kernel. This study demonstrated that 3D MRI-based SSA can realistically visualize statistical results on surface models and may facilitate the understanding of complex shape features.

Statistical shape analysis and computational modeling reveal novel relationships between tibiofemoral bony geometry and knee mechanics in young, female athletes

Young female athletes participating in sports requiring rapid changes of direction are at heightened risk of suffering traumatic knee injury, especially noncontact rupture of the anterior cruciate ligament (ACL). Clinical studies have revealed that geometric features of the tibiofemoral joint are associated with increased risk of suffering noncontact ACL injury. However, the relationship between three-dimensional (3D) tibiofemoral geometry and knee mechanics in young female athletes is not well understood. We developed a statistically augmented computational modeling workflow to determine relationships between 3D geometry of the knee and tibiofemoral kinematics and ACL force in response to an applied loading sequence of compression, valgus, and anterior force, which is known to load the ACL. This workflow included 3D characterization of tibiofemoral bony geometry via principal component analysis and multibody dynamics models incorporating subject-specific knee geometries. A combination of geometric features of both the tibia and the femur that spanned all three anatomical planes was related to increased ACL force and to increased kinematic coupling (i.e., anterior, medial, and distal tibial translations and internal tibial rotation) in response to the applied loads. In contrast, a uniplanar measure of tibiofemoral geometry that is associated with ACL injury risk, sagittal plane slope of the lateral tibial plateau subchondral bone, was not related to ACL force. Thus, our workflow may aid in developing mechanics-based ACL injury screening tools for young, active females based on a unique combination of bony geometric features that are related to increased ACL loading.

Articular surface interactions distinguish dinosaurian locomotor joint poses

Our knowledge of vertebrate functional evolution depends on inferences about joint function in extinct taxa. Without rigorous criteria for evaluating joint articulation, however, such analyses risk misleading reconstructions of vertebrate animal motion. Here we propose an approach for synthesizing raycast-based measurements of 3-D articular overlap, symmetry, and congruence into a quantitative "articulation score" for any non-interpenetrating six-degree-of-freedom joint configuration. We apply our methodology to bicondylar hindlimb joints of two extant dinosaurs (guineafowl, emu) and, through comparison with in vivo kinematics, find that locomotor joint poses consistently have high articulation scores. We then exploit this relationship to constrain reconstruction of a pedal walking stride cycle for the extinct dinosaur Deinonychus antirrhopus, demonstrating the utility of our approach. As joint articulation is investigated in more living animals, the framework we establish here can be expanded to accommodate additional joints and clades, facilitating improved understanding of vertebrate animal motion and its evolution.

Finite element analysis in the optimization of posterior-stabilized total knee arthroplasty

Posterior-stabilized total knee arthroplasty (PS-TKA) is associated with high rates of satisfaction and functional recovery. This is notably attributed to implant optimization in terms of design, choice of materials, positioning and understanding of biomechanics. Finite elements analysis (FEA) is an assessment technique that contributed to this optimization by ensuring mechanical results based on numerical simulation. By close teamwork between surgeons, researchers and engineers, FEA enabled testing of certain clinical impressions. However, the methodological features of the technique led to wide variations in the presentation and interpretation of results, requiring a certain understanding of numerical and biomechanical fields by the orthopedic community. The present study provides an up-to-date review, aiming to address the following questions: what are the principles of FEA? What is the role of FEA in studying PS design in TKA? What are the key elements in the literature for understanding the role of FEA in PS-TKA? What is the contribution of FEA for understanding of tibiofemoral and patellofemoral biomechanical behavior? What are the limitations and perspectives of digital simulation and FEA in routine practice, with a particular emphasis on the "digital twin" concept? LEVEL OF EVIDENCE: V, expert opinion.

Comparative study of locking neutralization plate construct versus tension band wiring with a cannulated screw for patella fractures: experimental and finite element analysis

Transverse patella fractures, accounting for approximately 1% of Orthopedic injuries, pose intricate challenges due to their vital role in knee mechanics. This study aimed to compare the biomechanical performance of a construct, integrating cannulated screws and an anterior locking neutralization plate, with the conventional tension band wiring technique for treating these fractures. Experimental testing and Finite Element Analysis were employed to evaluate the constructs and gain profound insights into their mechanical behavior. Sixteen cadaveric knees were prepared, and transverse patella fractures were induced at the midpoints using a saw. The plate construct and tension band wire fixation were randomly assigned to the specimens. A cyclic test evaluated the implants' durability and stability, simulating knee movement during extension and flexion. Tensile testing assessed the implants' maximum failure force after cyclic testing, while Finite Element Analysis provided detailed insights into stress distribution and deformation patterns. Statistical analysis was exclusively performed for the experimental data. Results showed the plate enhanced stability with significantly lower deformation (0.09 ± 0.12 mm) compared to wire fixation (0.77 ± 0.54 mm) after 500 cycles (p = 0.004). In tensile testing, the construct also demonstrated higher failure resistance (1359 ± 21.53 N) than wire fixation (780.1 ± 22.62N) (p = 0.007). Finite Element Analysis highlighted distinct stress patterns, validating the construct's superiority. This research presents a promising treatment approach for transverse patella fractures with potential clinical impact and future research prospects. This study presents a promising advancement in addressing the intricate challenges of transverse patella fractures, with implications for refining clinical practice. The construct's improved stability and resistance to failure offer potential benefits in postoperative management and patient outcomes.

Human foot form and function: variable and versatile, yet sufficiently related to predict function from form

The human foot is a complex structure that plays an important role in our capacity for upright locomotion. Comparisons of our feet with those of our closest extinct and extant relatives have linked shape features (e.g. the longitudinal and transverse arches, heel size and toe length) to specific mechanical functions. However, foot shape varies widely across the human population, so it remains unclear if and how specific shape variants are related to locomotor mechanics. Here we constructed a statistical shape-function model (SFM) from 100 healthy participants to directly explore the relationship between the shape and function of our feet. We also examined if we could predict the joint motion and moments occurring within a person's foot during locomotion based purely on shape features. The SFM revealed that the longitudinal and transverse arches, relative foot proportions and toe shape along with their associated joint mechanics were most variable. However, each of these only accounted for small proportions of the overall variation in shape, deformation and joint mechanics, most likely owing to the high structural complexity of the foot. Nevertheless, a leave-one-out analysis showed that the SFM can accurately predict joint mechanics of a novel foot, based on its shape and deformation.

Anatomical variations of the equine femur and tibia using statistical shape modeling

The objective of this study was to provide an overarching description of the inter-subject variability of the equine femur and tibia morphology using statistical shape modeling. Fifteen femora and fourteen tibiae were used for building the femur and tibia statistical shape models, respectively. Geometric variations in each mode were explained by biometrics measured on ±3 standard deviation instances generated by the shape models. Approximately 95% of shape variations within the population were described by 6 and 3 modes in the femur and tibia shape models, respectively. In the femur shape model, the first mode of variation was scaling, followed by notable variation in the femoral mechanical-anatomical angle and femoral neck angle in mode 2. Orientation of the femoral trochlear tubercle and femoral version angle were described in mode 3 and mode 4, respectively. In the tibia shape model, the main mode of variation was also scaling. In mode 2 and mode 3, the angles of the coronal tibial plateau and the medial and lateral caudal tibial slope were described, showing the lateral caudal tibial slope angle being significantly larger than the medial. The presented femur and tibia shape models with quantified biometrics, such as femoral version angle and posterior tibial slope, could serve as a baseline for future investigations on correlation between the equine stifle morphology and joint disorders due to altered biomechanics, as well as facilitate the development of novel surgical treatment and implant design. By generating instances matching patient-specific femorotibial joint anatomy with radiographs, the shape model could assist virtual surgical planning and provide clinicians with opportunities to practice on 3D printed models.

Dynamic multi feature-class Gaussian process models

In model-based medical image analysis, three relevant features are the shape of structures of interest, their relative pose, and image intensity profiles representative of some physical properties. Often, these features are modelled separately through statistical models by decomposing the object's features into a set of basis functions through principal geodesic analysis or principal component analysis. However, analysing articulated objects in an image using independent single object models may lead to large uncertainties and impingement, especially around organ boundaries. Questions that come to mind are the feasibility of building a unique model that combines all three features of interest in the same statistical space, and what advantages can be gained for image analysis. This study presents a statistical modelling method for automatic analysis of shape, pose and intensity features in medical images which we call the Dynamic multi feature-class Gaussian process models (DMFC-GPM). The DMFC-GPM is a Gaussian process (GP)-based model with a shared latent space that encodes linear and non-linear variations. Our method is defined in a continuous domain with a principled way to represent shape, pose and intensity feature-classes in a linear space, based on deformation fields. A deformation field-based metric is adapted in the method for modelling shape and intensity variation as well as for comparing rigid transformations (pose). Moreover, DMFC-GPMs inherit properties intrinsic to GPs including marginalisation and regression. Furthermore, they allow for adding additional pose variability on top of those obtained from the image acquisition process; what we term as permutation modelling. For image analysis tasks using DMFC-GPMs, we adapt Metropolis-Hastings algorithms making the prediction of features fully probabilistic. We validate the method using controlled synthetic data and we perform experiments on bone structures from CT images of the shoulder to illustrate the efficacy of the model for pose and shape prediction. The model performance results suggest that this new modelling paradigm is robust, accurate, accessible, and has potential applications in a multitude of scenarios including the management of musculoskeletal disorders, clinical decision making and image processing.

Determining the relationship between tibiofemoral geometry and passive motion with partial least squares regression

Tibiofemoral geometry influences knee passive motion and understanding their relationship can provide insight into knee function and mechanisms of injury. However, the complexity of the geometric constraints has made characterizing the relationship challenging. The aim of this study was to determine the tibiofemoral bone geometries that explain the variation in passive motion using a partial least squares regression (PLSR) model. The PLSR model was developed for 29 healthy cadaver specimens (10 female, 19 male) with femur and tibia geometries retrieved from MRI images and six degree-of-freedom tibiofemoral kinematics determined during a flexion cycle with minimal medial pressure. The first 13 partial least squares (PLS) components explained 90% of the variation in the kinematics and accounted for 89% of the variation in geometry. The first three PLS components which shared geometric changes to particular surface congruencies of the tibial and femoral condyles explained the most amount of variation in the kinematics, primarily in anterior-posterior translation. Meanwhile, variations in femoral condyle width and the intercondylar space, tibia plateau size and conformity, and tibia eminences heights in PLS 2 and 4 explained the greatest amount of variation in internal-external rotation. PLS 4 exhibiting variation in overall size of the knee accounted for greatest amount of variation in geometry (50%) and had the greatest influence on the abduction-adduction motion and some on internal-external rotation but, overall, explained only a small proportion of the kinematics (10%). Elucidating the complex relationship between tibiofemoral bone geometry and passive kinematics may help personalize treatments for improved functional outcomes in patients.

Correlation between knee anatomy and joint laxity using principal component analysis

Knee articular geometry and surface morphology greatly affect knee joint mechanics. Intra-subject variations in bone morphology and the passive range of motion have been well documented in the literature; however, the relationship between these two characteristics is not well understood. The objective of this study was to describe the correlation between knee joint anatomical features and passive range of motion using a statistical model. A principal component model was developed using femoral and tibial articular geometry, knee joint initial stance position, and the passive laxity envelope obtained from 27 cadaveric knees. The results from the principal component analysis showed high correlation between the anatomical features and the tibiofemoral passive envelope; an increase in the average femoral condyle radii, an increase in slope of the tibial spine, and a higher tibial plateau concavity correlated with a decrease in varus-valgus and internal-external range of motion. Understanding the correlation between anatomical features and tibiofemoral laxity could aid in the development of orthopedic implant designs by quantifying the effect of perturbing specific anatomical features on knee laxity and identifying specific implant femoral and tibial articular geometry necessary to obtain a targeted passive range of motion.

A statistical shape model of soleus muscle morphology in spastic cerebral palsy

This study investigated morphological characteristics of the soleus muscle in cerebral palsy (CP) and typically developing (TD) cohorts using a statistical shape model and differentiated dominant features between the two cohorts. We generated shape models of CP and TD cohorts to characterize dominant features within each. We then generated a combined shape model of both CP and TD to assess deviations of the cohorts’ soleuses from a common mean shape, and statistically analysed differences between the cohorts. The shape models revealed similar principal components (PCs) with different variance between groups. The CP shape model yielded a distinct feature (superior–inferior shift of the broad central region) accounting for 8.1% of the model’s cumulative variance. The combined shape model presented two PCs where differences arose between CP and TD cohorts: size and aspect ratio of length–width–thickness. The distinct appearance characteristic in the CP model—described above—may implicate impaired muscle function in children with CP. Overall, children with CP had smaller muscles that also tended to be long, thin, and narrow. Shape modelling captures dominant morphological features of structures, which was used here to quantitatively describe CP muscles and further probe our understanding of the disease’s impact on the muscular system.

Magnetic Resonance Imaging-based biomechanical simulation of cartilage: A systematic review

MRI-based mathematical and computational modeling studies can contribute to a better understanding of the mechanisms governing cartilage's mechanical performance and cartilage disease. In addition, distinct modeling of cartilage is needed to optimize artificial cartilage production. These studies have opened up the prospect of further deepening our understanding of cartilage function. Furthermore, these studies reveal the initiation of an engineering-level approach to how cartilage disease affects material properties and cartilage function. Aimed at researchers in the field of MRI-based cartilage simulation, research articles pertinent to MRI-based cartilage modeling were identified, reviewed, and summarized systematically. Various MRI applications for cartilage modeling are highlighted, and the limitations of different constitutive models used are addressed. In addition, the clinical application of simulations and studied diseases are discussed. The paper's quality, based on the developed questionnaire, was assessed, and out of 79 reviewed papers, 34 papers were determined as high-quality. Due to the lack of the best constitutive models for various clinical conditions, researchers may consider the effect of constitutive material models on the cartilage disease simulation. In the future, research groups may incorporate various aspects of machine learning into constitutive models and MRI data extraction to further refine the study methodology. Moreover, researchers should strive for further reproducibility and rigorous model validation and verification, such as gait analysis.

The Genetic Epidemiology of Joint Shape and the Development of Osteoarthritis

Congruent, low-friction relative movement between the articulating elements of a synovial joint is an essential pre-requisite for sustained, efficient, function. Where disorders of joint formation or maintenance exist, mechanical overloading and osteoarthritis (OA) follow. The heritable component of OA accounts for ~ 50% of susceptible risk. Although almost 100 genetic risk loci for OA have now been identified, and the epidemiological relationship between joint development, joint shape and osteoarthritis is well established, we still have only a limited understanding of the contribution that genetic variation makes to joint shape and how this modulates OA risk. In this article, a brief overview of synovial joint development and its genetic regulation is followed by a review of current knowledge on the genetic epidemiology of established joint shape disorders and common shape variation. A summary of current genetic epidemiology of OA is also given, together with current evidence on the genetic overlap between shape variation and OA. Finally, the established genetic risk loci for both joint shape and osteoarthritis are discussed.

Patella Apex Influences Patellar Ligament Forces and Ratio

The relationship between three-dimensional shape and patellofemoral mechanics is complicated. The Wiberg patella classification is a method of distinguishing shape differences in the axial plane of the patella that can be used to connect shape differences to observed mechanics. This study uses the Wiberg patella classification to differentiate variance in a statistical shape model describing changes in patella morphology and height. We investigate how patella morphology influences force distribution within the patellofemoral joint. The Wiberg type I patella has a more symmetrical medial and lateral facet while the type III patella has a larger lateral facet compared to medial. The second principal component of the statistical shape model described shape variation that qualitatively resembled the different Wiberg patellas. We generated patellofemoral morphologies from the statistical shape model and integrated them into a musculoskeletal model with a twelve degrees-of-freedom knee. We simulated an overground walking trial with these morphologies and recorded patellofemoral mechanics and ligament forces. An increase in patellar ligament force corresponded with an increase in patella height. Wiberg type III patellas had a sharper patella apex which related to lower ratios of quadriceps tendon forces to patellar ligament forces. The change in pivot point of the patella affects the ratio of forces as well as the patellofemoral reaction force. This study provides a better understanding of how patella morphology affects fundamental patella mechanics which may help identify at-risk populations for pathology development.

[Biomechanical research on effects of pseudo-patella baja on stress of patellofemoral joint after total knee arthroplasty]

Objective

To investigate biomechanical effects of pseudo-patella baja on stress of patellofemoral joint after total knee arthroplasty (TKA) by using finite element analysis (FEA).

Methods

A series of CT and MRI of the left knee joint of two healthy volunteers and three-dimensional (3D) scanned data of TKA prosthesis were taken, and the 3D models of knee before and after TKA were established. The finite element model of pseudo-patella baja, normal patella, and alta patella after TKA were constructed by Insall-Salvafi (IS) ratio and Blackburne-Peel (BP) ratio. The load was applied along the direction of quadriceps femoris. After testing the validity of the finite element model, the high contact stress of patellofemoral joint was measured on the von Mise stress nephogram of pseudo-patella baja, normal patella, and alta patella after TKA when the knee flexion was 30°, 60°, and 90°. The average contact area was calculated according to two volunteers' data.

Results

On the finite element model of the normal patella after TKA with knee flexion 30°, 475 N pressure was applied along the direction of quadriceps femoris. The contact stress of patellofemoral joint was (1.29±0.41) MPa, which was similar to the results reported previously. The finite element model was valid. The von Mise stress nephogram showed that the stress mainly focused on the medial patellofemoral articular surface during knee flexion, and the contact point gradually moved up with the knee flexion deepened. The stress on the medial and lateral patellofemoral articular surface increased with the knee flexion deepened but decreased with the increase of patellar height. The effects of patellar height and knee flexion on the high contact stress of patellofemoral joint were similar among the finite element models after TKA based on the data of two volunteers. The high contact stress of patellofemoral joint increased with the knee flexion deepened in the same patellar height models ( P<0.05), but decreased with the increase of patellar height in the same knee flexion models ( P<0.05). The high contact stress of patellofemoral joint of pseudo-patella baja model was significantly higher than normal and alta patella models ( P<0.05). The average contact area of patellofemoral joint of pseudo-patella baja was bigger than normal and alta patella models with the knee flexion deepened.

Conclusion

The pseudo-patella baja after TKA has an important effect on the biomechanics of patellofemoral joint. Reserving the joint line and avoiding the occurrence of pseudo-patella baja can decrease the risk of anterior knee pain, patellar arthritis, and other complications caused by the increasing of contact stress of patellofemoral joint.

A comparison of Cartesian-only vs. Cartesian-spherical hybrid coordinates for statistical shape modeling in the lumbar spine

OBJECTIVE

The purpose of this study was to compare two methods for quantifying differences in geometric shapes of human lumbar vertebra using statistical shape modeling (SSM).

METHODS

A novel 3D implementation of a previously published 2D, nonlinear SSM was implemented and compared to a commonly used, Cartesian method of SSM. The nonlinear method, or Hybrid SSM, and Cartesian SSM were applied to lumbar vertebra shapes from a cohort of 18 full lumbar triangle meshes derived from CT scans. The comparison included traditional metrics for cumulative variance, generality, and specificity and results from application-based biomechanics using finite element simulation.

RESULTS

The Hybrid SSM has less compactness - likely due to the increased number of mathematical constraints in the SSM formulation. Similar results were found between methods for specificity and generality. Compared to the previously validated, manually-segmented FE model, both SSM methods produced similar and agreeable results.

CONCLUSION

Visual, statistical, and biomechanical findings did not convincingly support the superiority of the Hybrid SSM over the simpler Cartesian SSM.

SIGNIFICANCE

This work suggests that, of the two methods compared, the Cartesian SSM is adequate to capture the variations in shape of the posterior spinal structures for biomechanical modeling applications.

Regularized multi-structural shape modeling of the knee complex based on deep functional maps

The incorporation of a-priori knowledge on the shape of anatomical structures and their variation through Statistical Shape Models (SSMs) has shown to be very effective in guiding highly uncertain image segmentation problems. In this paper, we construct multiple-structure SSMs of purely geometric nature, that describe the relationship between adjacent anatomical components through Canonical Correlation Analysis. Shape inference is then conducted based on a regularization term on the shape likelihood providing more reliable structure representations. A fundamental prerequisite for performing statistical shape analysis on a set of objects is the identification of corresponding points on their associated surfaces. We address the correspondence problem using the recently proposed Functional Maps framework, which is a generalization of point-to-point correspondence to manifolds. Additionally, we show that, by incorporating techniques from the deep learning theory into this framework, we can further enhance the ability of SSMs to better capture the shape variation in a given dataset. The efficiency of our approach is illustrated through the creation of 3D models of the human knee complex in two application scenarios: incomplete or noisy shape reconstruction and missing structure estimation.

EquiSim: An Open-Source Articulatable Statistical Model of the Equine Distal Limb

Most digital models of the equine distal limb that are available in the community are static and/or subject specific; hence, they have limited applications in veterinary research. In this paper, we present an articulatable model of the entire equine distal limb based on statistical shape modeling. The model describes the inter-subject variability in bone geometry while maintaining proper jointspace distances to support model articulation toward different poses. Shape variation modes are explained in terms of common biometrics in order to ease model interpretation from a veterinary point of view. The model is publicly available through a graphical user interface (https://github.com/jvhoutte/equisim) in order to facilitate future digitalization in veterinary research, such as computer-aided designs, three-dimensional printing of bone implants, bone fracture risk assessment through finite element methods, and data registration and segmentation problems for clinical practices.

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.

Combining statistical shape modeling, CFD, and meta-modeling to approximate the patient-specific pressure-drop across the aortic valve in real-time

BACKGROUND

Advances in medical imaging, segmentation techniques, and high performance computing have stimulated the use of complex, patient-specific, three-dimensional Computational Fluid Dynamics (CFD) simulations. Patient-specific, CFD-compatible geometries of the aortic valve are readily obtained. CFD can then be used to obtain the patient-specific pressure-flow relationship of the aortic valve. However, such CFD simulations are computationally expensive, and real-time alternatives are desired.

AIM

The aim of this work is to evaluate the performance of a meta-model with respect to high-fidelity, three-dimensional CFD simulations of the aortic valve.

METHODS

Principal component analysis was used to build a statistical shape model (SSM) from a population of 74 iso-topological meshes of the aortic valve. Synthetic meshes were created with the SSM, and steady-state CFD simulations at flow-rates between 50 and 650 mL/s were performed to build a meta-model. The meta-model related the statistical shape variance, and flow-rate to the pressure-drop.

RESULTS

Even though the first three shape modes account for only 46% of shape variance, the features relevant for the pressure-drop seem to be captured. The three-mode shape-model approximates the pressure-drop with an average error of 8.8% to 10.6% for aortic valves with a geometric orifice area below 150 mm² . The proposed methodology was least accurate for aortic valve areas above 150 mm² . Further reduction to a meta-model introduces an additional 3% error.

CONCLUSIONS

Statistical shape modeling can be used to capture shape variation of the aortic valve. Meta-models trained by SSM-based CFD simulations can provide an estimate of the pressure-flow relationship in real-time.

Computational framework for population-based evaluation of TKR-implanted patellofemoral joint mechanics

Differences in patient anatomy are known to influence joint mechanics. Accordingly, intersubject anatomical variation is an important consideration when assessing the design of joint replacement implants. The objective of this study was to develop a computational workflow to perform population-based evaluations of total knee replacement implant mechanics considering variation in patient anatomy and to assess the potential for an efficient sampling strategy to support design phase screening analyses. The approach generated virtual subject anatomies using a statistical shape model of the knee and performed virtual implantation to size and align the implants. A finite-element analysis simulated a deep knee bend activity and predicted patellofemoral (PF) mechanics. The study predicted bounds of performance for kinematics and contact mechanics and investigated relationships between patient factors and outputs. For example, the patella was less flexed throughout the deep knee bend activity for patients with an alta patellar alignment. The results also showed the PF range of motions in AP and ML were generally larger with increasing femoral component size. Comparison of the 10-90% bounds between sampling strategies agreed reasonably, suggesting that Latin Hypercube sampling can be used for initial screening evaluations and followed up by more intensive Monte Carlo simulation for refined designs. The platform demonstrated a functional workflow to consider variation in joint anatomy to support robust implant design.

Musculoskeletal Multibody Simulation Analysis on the Impact of Patellar Component Design and Positioning on Joint Dynamics after Unconstrained Total Knee Arthroplasty

Patellofemoral (PF) disorders are considered a major clinical complication after total knee replacement (TKR). Malpositioning and design of the patellar component impacts knee joint dynamics, implant fixation and wear propagation. However, only a limited number of studies have addressed the biomechanical impact of the patellar component on PF dynamics and their results have been discussed controversially. To address these issues, we implemented a musculoskeletal multibody simulation (MMBS) study for the systematical analysis of the patellar component’s thickness and positioning on PF contact forces and kinematics during dynamic squat motion with virtually implanted unconstrained cruciate-retaining (CR)-TKR. The patellar button thickness clearly increased the contact forces in the PF joint (up to 27%). Similarly, the PF contact forces were affected by superior–inferior positioning (up to 16%) and mediolateral positioning (up to 8%) of the patellar button. PF kinematics was mostly affected by the mediolateral positioning and the thickness of the patellar component. A medialization of 3 mm caused a lateral patellar shift by up to 2.7 mm and lateral patellar tilt by up to 1.6°. However, deviations in the rotational positioning of the patellar button had minor effects on PF dynamics. Aiming at an optimal intraoperative patellar component alignment, the orthopedic surgeon should pay close attention to the patellar component thickness in combination with its mediolateral and superior–inferior positioning on the retropatellar surface. Our generated MMBS model provides systematic and reproducible insight into the effects of patellar component positioning and design on PF dynamics and has the potential to serve as a preoperative analysis tool.

Predicting Knee Joint Instability Using a Tibio-Femoral Statistical Shape Model

Statistical shape models (SSMs) are a well established computational technique to represent the morphological variability spread in a set of matching surfaces by means of compact descriptive quantities, traditionally called "modes of variation" (MoVs). SSMs of bony surfaces have been proposed in biomechanics and orthopedic clinics to investigate the relation between bone shape and joint biomechanics. In this work, an SSM of the tibio-femoral joint has been developed to elucidate the relation between MoVs and bone angular deformities causing knee instability. The SSM was built using 99 bony shapes (distal femur and proximal tibia surfaces obtained from segmented CT scans) of osteoarthritic patients. Hip-knee-ankle (HKA) angle, femoral varus-valgus (FVV) angle, internal-external femoral rotation (IER), tibial varus-valgus (TVV) angles, and tibial slope (TS) were available across the patient set. Discriminant analysis (DA) and logistic regression (LR) classifiers were adopted to underline specific MoVs accounting for knee instability. First, it was found that thirty-four MoVs were enough to describe 95% of the shape variability in the dataset. The most relevant MoVs were the one encoding the height of the femoral and tibial shafts (MoV #2) and the one representing variations of the axial section of the femoral shaft and its bending in the frontal plane (MoV #5). Second, using quadratic DA, the sensitivity results of the classification were very accurate, being all >0.85 (HKA: 0.96, FVV: 0.99, IER: 0.88, TVV: 1, TS: 0.87). The results of the LR classifier were mostly in agreement with DA, confirming statistical significance for MoV #2 (p = 0.02) in correspondence to IER and MoV #5 in correspondence to HKA (p = 0.0001), FVV (p = 0.001), and TS (p = 0.02). We can argue that the SSM successfully identified specific MoVs encoding ranges of alignment variability between distal femur and proximal tibia. This discloses the opportunity to use the SSM to predict potential misalignment in the knee for a new patient by processing the bone shapes, removing the need for measuring clinical landmarks as the rotation centers and mechanical axes.

Statistical shape-kinematics models of the skeletal joints: Application to the shoulder complex

Patient-specific biomechanical simulations of joints require accurate reconstruction of bony anatomy from medical image data. The articular geometries of the joints may influence their biomechanics. Statistical shape models (SSMs) have become ubiquitous in the literature and aim to capture the natural variation of biological objects. They work by learning the variation from training examples to define the space of valid biological shapes. However, the kinematic information descriptive of the anato-physiological relationship of two interacting objects is not generally encoded in the SSM. Here, we propose a framework for developing combined statistical shape and kinematics models (SSKMs) as Gaussian process morphable models to analyse the shape and kinematics relationship. We demonstrate the framework on a three-dimensional (3D) image data set consisting of ten right-handed cadaveric shoulder joints acquired using computed tomography. Additionally, we simulate specific bone motions to encode kinematics in the combined model. Our SSKM built from shoulder data (matching scapulae and humeri) correctly depicts a correlation between the shape and kinematics as hypothesized. We furthermore demonstrate the ability to marginalize from the SSKM to obtain shape-only variation and kinematics-only variation. Future work aims to use the SSKM framework to understand the relationships between kinematics and shape for various joints as well as to develop patient-specific computational models to evaluate joint biomechanics.

Evaluating risk factors involved in the alteration of biomechanics in relation to knee osteoarthritis

The knee joint is very complex in terms of degrees of mobility and for normal biomechanics it is necessary for all the anatomical structures at this level to be within physiological limits. Problems can be caused by a number of risk factors such as age, sex, weight, or local risk factors such as patellar changes represented by patela alta or patella baja, which can lead to instability of the lower limb. Risk factors that may influence the development and progression of knee osteoarthritis have been evaluated. Changes in patellar position in relation to knee osteoarthritis were also studied. A group of 377 patients hospitalized for unilateral or bilateral knee pain with instability were included in the study. 239 of the 377 starting group presented knee osteoarthritis, constituting the study group. The risk factors analyzed were age, patient sex, BMI, weight status, anatomical changes in position of the patella (patella alta and patella baja), COBB angle and spine deviation. The results indicated that obesity, anatomical changes in the position of the patella, (patella alta), COBB angle and spine deviations represent significant risk factors in the onset of knee osteoarthritis. Key words: risk factors, joint instability, knee osteoarthritis,

Fully automated patellofemoral MRI segmentation using holistically nested networks: Implications for evaluating patellofemoral osteoarthritis, pain, injury, pathology, and adolescent development

PURPOSE

Our clinical understanding of the relationship between 3D bone morphology and knee osteoarthritis, as well as our ability to investigate potential causative factors of osteoarthritis, has been hampered by the time-intensive nature of manually segmenting bone from MR images. Thus, we aim to develop and validate a fully automated deep learning framework for segmenting the patella and distal femur cortex, in both adults and actively growing adolescents.

METHODS

Data from 93 subjects, obtained from on institutional review board-approved protocol, formed the study database. 3D sagittal gradient recalled echo and gradient recalled echo with fat saturation images and manual models of the outer cortex were available for 86 femurs and 90 patellae. A deep-learning-based 2D holistically nested network (HNN) architecture was developed to automatically segment the patella and distal femur using both single (sagittal, uniplanar) and 3 cardinal plane (triplanar) methodologies. Errors in the surface-to-surface distances and the Dice coefficient were the primary measures used to quantitatively evaluate segmentation accuracy using a 9-fold cross-validation.

RESULTS

Average absolute errors for segmenting both the patella and femur were 0.33 mm. The Dice coefficients were 97% and 94% for the femur and patella. The uniplanar, relative to the triplanar, methodology produced slightly superior segmentation. Neither the presence of active growth plates nor pathology influenced segmentation accuracy.

CONCLUSION

The proposed HNN with multi-feature architecture provides a fully automatic technique capable of delineating the often indistinct interfaces between the bone and other joint structures with an accuracy better than nearly all other techniques presented previously, even when active growth plates are present.

Pair-wise vs group-wise registration in statistical shape model construction: representation of physiological and pathological variability of bony surface morphology

Statistical shape models (SSM) of bony surfaces have been widely proposed in orthopedics, especially for anatomical bone modeling, joint kinematic analysis, staging of morphological abnormality, and pre- and intra-operative shape reconstruction. In the SSM computation, reference shape selection, shape registration and point correspondence computation are fundamental aspects determining the quality (generality, specificity and compactness) of the SSM. Such procedures can be made critical by the presence of large morphological dissimilarities within the surfaces, not only because of anthropometrical variability but also mainly due to pathological abnormalities. In this work, we proposed a SW pipeline for SSM construction based on pair-wise (PW) shape registration, which requires the a-priori selection of the reference shape, and on a custom iterative point correspondence algorithm. We addressed large morphological deformations in five different bony surface sets, namely proximal femur, distal femur, patella, proximal fibula and proximal tibia, extracted from a retrospective patient dataset. The technique was compared to a method from the literature, based on group-wise (GW) shape registration. As a main finding, the proposed technique provided generalization and specificity median errors, for all the five bony regions, lower than 2 mm. The comparative analysis provided basically similar results. Particularly, for the distal femur that was the shape affected by the largest pathological deformations, the differences in generalization, specificity and compactness were lower than 0.5 mm, 0.5 mm, and 1%, respectively. We can argue the proposed pipeline, along with the robust correspondence algorithm, is able to compute high-quality SSM of bony shapes, even affected by large morphological variability.

The effect of articular geometry features identified using statistical shape modelling on knee biomechanics

Articular geometry in the knee varies widely among people which has implications for risk of injury and pathology. The goals of this work were to develop a framework to systematically vary geometry in a multibody knee model and to use this framework to investigate the effect of morphological features on dynamic knee kinematics and contact mechanics. A statistical shape model of the tibiofemoral and patellofemoral joints was created from magnetic resonance images of 14 asymptomatic knees. The shape model was then used to generate 37 unique multibody knee models based on -3 to +3 standard deviations of the scores for the first six principal components identified. Each multibody model was then incorporated into a lower extremity musculoskeletal model and the Concurrent Optimization of Muscle Activations and Kinematics (COMAK) routine was used to simulate knee mechanics for overground walking. Changes in articular geometry affected knee function, resulting in differences up to 17° in orientation, 8 mm in translation, 0.7 BW in contact force, and 2.0 MPa in mean cartilage contact pressure. Understanding the relationship between shape and function in a joint could provide insight into the mechanisms behind injury and pathology and the variability in response to treatment.

Statistical shape modeling of femur shape variability in female patients with hip dysplasia

Although increasing evidence suggests that abnormal femur geometry in developmental dysplasia of the hip (DDH) may contribute to intra-articular damage and the development of hip osteoarthritis, a comprehensive 3D description of femoral abnormalities in DDH remains incomplete. Statistical shape modeling (SSM) was used to quantify three-dimensional (3D) geometric variation among femurs in female patients with DDH and control subjects. SSM correspondence points (n = 8,192) were placed on each femur using a gradient descent energy function to derive mean DDH and control femoral shapes and principal component analysis (PCA) was then used to describe shape variation. PCA results were associated with common 2D radiographic measures of femur shape using general linear models. For patients with DDH, the first eight principal components (modes) captured 90.9% of the cumulative variance accounted for (VAF). Notably, mode 2 captured 23.6% VAF and described variation in femoral version, the neck-shaft angle, and femoral neck length, while mode 3 captured 16.4% VAF and described variation in femoral version, femoral head size, and femoral offset. SSM captured complex geometric deformities in DDH, which may not be fully described by 2D measures of the acetabulum and proximal femur alone. By determining the primary shape variations among femurs in cases of DDH, SSM may further understanding of pathologies on the femoral side of dysplastic hips, in context with more commonly recognized acetabular deformities. © 2019 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res.

The influence of compressive forces across the patellofemoral joint on patient-reported outcome after bi-cruciate stabilized total knee arthroplasty

AIMS

Patellofemoral problems are a common complication of total knee arthroplasty. A high compressive force across the patellofemoral joint may affect patient-reported outcome. However, the relationship between patient-reported outcome and the intraoperative patellofemoral contact force has not been investigated. The purpose of this study was to determine whether or not a high intraoperative patellofemoral compressive force affects patient-reported outcome.

PATIENTS AND METHODS

This prospective study included 42 patients (42 knees) with varus-type osteoarthritis who underwent a bi-cruciate stabilized total knee arthroplasty and in whom the planned alignment was confirmed on 3D CT. Of the 42 patients, 36 were women and six were men. Their mean age was 72.3 years (61 to 87) and their mean body mass index (BMI) was 24.4 kg/m ² (18.2 to 34.3). After implantation of the femoral and tibial components, the compressive force across the patellofemoral joint was measured at 10°, 30°, 60°, 90°, 120°, and 140° of flexion using a load cell (Kyowa Electronic Instruments Co., Ltd., Tokyo, Japan) manufactured in the same shape as the patellar implant. Multiple regression analyses were conducted to investigate the relationship between intraoperative patellofemoral compressive force and patient-reported outcome two years after implantation.

RESULTS

No patient had anterior knee pain after total knee arthroplasty. The compressive force across the patellofemoral joint at 140°of flexion was negatively correlated with patient satisfaction (R ² = 0.458; β = -0.706; p = 0. 041) and Forgotten Joint Score-12 (FJS-12; R ² = .378; β = -0.636; p = 0. 036). The compressive force across the patellofemoral joint at 60° of flexion was negatively correlated with the patella score (R ² = 0.417; β = -0.688; p = 0. 046).

CONCLUSION

Patient satisfaction, FJS-12, and patella score were affected by the patellofemoral compressive force at 60° and 140° of flexion. Reduction of the patellofemoral compressive forces at 60° and 140° of flexion angle during total knee arthroplasty may improve patient-reported outcome, but has no effect on anterior knee pain.

Investigating gender and ethnicity differences in proximal humeral morphology using a statistical shape model

Morphological variability in the shoulder influences the joint biomechanics and is an important consideration in arthroplasty and implant design. The objectives of this study were to quantify cortical and cancellous proximal humeral morphology and to assess whether shape variation was influenced by gender and ethnicity, with the overarching goal of informing implant design and treatment. A statistical shape model of the proximal humeral cortical and cancellous regions was developed for a training set of 84 subjects of both genders and different ethnicities. Cortical and cancellous bone geometries were reconstructed from CT scans, meshed with triangular elements, and registered to a template. Principal component analysis was applied to quantify modes of variation. Anatomical measurements were computed on the registered geometries to assess correlation with modes of variation. Parallel analysis identified six significant modes of variation, which accounted for 93% of variation in the training set and described scaling (Mode 1), inclination of the head (Modes 2 and 5), and shape of the greater tuberosity and neck region (Modes 3, 4, and 6). Size differences as described by Mode 1 were statistically significant for gender and ethnicity, where female and Asian subjects were smaller than male and Caucasian subjects, respectively; however, differences in other modes were not significant. Cortical thickness of the shaft after normalization by outer diameter was significantly larger for Asian subjects compared to Caucasian subjects. The statistical shape model quantified cortical and cancellous humeral morphology considering gender and ethnicity, providing descriptive data to support surgical planning, and implant design. © 2018 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 36:3043-3052, 2018.

Is patellofemoral pain a precursor to osteoarthritis?: Patellofemoral osteoarthritis and patellofemoral pain patients share aberrant patellar shape compared with healthy controls

Objectives

It has been hypothesized that patellofemoral pain, a common knee condition in adolescents and young adults, may be a precursor of degenerative joint changes and may ultimately lead to patellofemoral osteoarthritis. Since both conditions share several mechanical disease characteristics, such as altered contact area between the femur and patella and increased joint stress, we investigated whether these conditions share similar and different shape characteristics of the patella compared with normal controls.

Methods

This cross-sectional study compared three different study populations: 32 patellofemoral pain subjects (mean age, 32 years (22 to 45); 72% female); 56 isolated radiological patellofemoral osteoarthritis subjects (mean age, 54 years (44 to 58); 89% female); and 80 healthy control subjects (mean age, 52 years (44 to 58); 74% female). Measurements included questionnaires, and lateral and skyline radiographs of the knee. Two separate 30-point 2D statistical shape models of the patella were created from the lateral and skyline radiographs. A general linear model was used to test for differences in standardized shape modes (a specific shape variant of the patella) between patellofemoral osteoarthritis, patellofemoral pain, and controls, using Bonferroni correction and adjustment for body mass index and gender.

Results

Five shape modes showed statistically significant differences between groups: skyline modes 1 (p < 0.001), 8 (p = 0.004), and 10 (p < 0.001); and lateral modes 5 (p = 0.002) and 7 (p = 0.002). Skyline mode 8 and lateral mode 5 were similar for patellofemoral osteoarthritis and patellofemoral pain populations, while being statistically significant different from the control group.

Conclusion

Our results indicate that patellofemoral pain and patellofemoral osteoarthritis share similar shape characteristics, which are different from control subjects. These findings support the proposed continuum disease model of patellofemoral pain predisposing to the development of patellofemoral osteoarthritis.

Cite this article: J. F. A. Eijkenboom, J. H. Waarsing, E. H. G. Oei, S. M. A. Bierma-Zeinstra, M. van Middelkoop. Is patellofemoral pain a precursor to osteoarthritis? Patellofemoral osteoarthritis and patellofemoral pain patients share aberrant patellar shape compared with healthy controls. Bone Joint Res 2018;7:541–547. DOI: 10.1302/2046-3758.79.BJR-2018-0112.R1.

Stacked sparse autoencoder networks and statistical shape models for automatic staging of distal femur trochlear dysplasia

BACKGROUND

The quantitative morphological analysis of the trochlear region in the distal femur and the precise staging of the potential dysplastic condition constitute a key point for the use of personalized treatment options for the patella-femoral joint. In this paper, we integrated statistical shape models (SSM), able to represent the individual morphology of the trochlea by means of a set of parameters and stacked sparse autoencoder (SSPA) networks, which exploit the parameters to discriminate among different levels of abnormalities.

METHODS

Two datasets of distal femur reconstructions were obtained from CT scans, including pathologic and physiologic shapes. Both of them were processed to compute SSM of healthy and dysplastic trochlear regions. The parameters obtained by the 3D-3D reconstruction of a femur shape were fed into a trained SSPA classifier to automatically establish the membership to one of three clinical conditions, namely, healthy, mild dysplasia, and severe dysplasia of the trochlea. The validation was performed on a subset of the shapes not used in the construction of the SSM, by verifying the occurrence of a correct classification.

RESULTS

A major finding of the work is that SSM are able to represent anomalies of the trochlear geometry by means of specific eigenmodes of variation and to model the interplay between morphologic features related to dysplasia. Exploiting the patient-specific morphing parameters of SSM, computed by means of a 3D-3D reconstruction, SSPA is demonstrated to outperform traditional discriminant analysis in classifying healthy, mild, and severe trochlear dysplasia providing 99%, 97%, and 98% accuracy for each of the three classes, respectively (discriminant analysis accuracy: 85%, 89%, and 77%).

CONCLUSIONS

From a clinical point of view, this paper contributes to support the increasing role of SSM, integrated with deep learning techniques, in diagnostics and therapy definition as quantitative and advanced visualization tools.

Statistical modeling of the equine third metacarpal bone incorporating morphology and bone mineral density

The objective of this study was to describe the three-dimensional shape and subchondral bone mineral density (BMD) variation of the equine distal third metacarpal bone (MC3) using a statistical shape model. The association between form and function builds upon previous two-dimensional observations of MC3 epiphyseal structure. It was expected that the main source of variation would be an increase in overall MC3 bone size, correlated to an increase in subchondral BMD. Geometry and bone mineral density was obtained from CT image data of 40 healthy Thoroughbred horses. This was used to create a statistical shape model, in which the first ten components described 75% of the variation in geometry and BMD. The first principal component described an increase in overall size of the MC3 distal epiphysis, coupled with higher BMD on the disto-palmar and dorso-proximal surfaces. The second component was qualitatively described as an increased convexity of the sagittal ridge at the dorsal junction of the epiphysis and the metaphysis, coupled to increased BMD in that region. The third component showed an increase in lateral condylar surface area relative to medial condylar area. As the condyle reduced in relative surface area, the BMD at both dorsal condyles increased. The statistical shape analysis produced a compact description of 3-D shape and sub-chondral bone mineral density variation for the third metacarpal bone. This study uniquely illustrates the shape variations in a sample population of MC3 bones, and the corresponding changes in subchondral BMD.

Patellofemoral morphology is not related to pain using three-dimensional quantitative analysis in an older population: data from the Osteoarthritis Initiative

Objectives

Current structural associations of patellofemoral pain (PFP) are based on 2D imaging methodology with inherent measurement uncertainty due to positioning and rotation. This study employed novel technology to create 3D measures of commonly described patellofemoral joint imaging features and compared these features in people with and without PFP in a large cohort.

Methods

We compared two groups from the Osteoarthritis Initiative: one with localized PFP and pain on stairs, and a control group with no knee pain; both groups had no radiographic OA. MRI bone surfaces were automatically segmented and aligned using active appearance models. We applied t-tests, logistic regression and linear discriminant analysis to compare 13 imaging features (including patella position, trochlear morphology, facet area and tilt) converted into 3D equivalents, and a measure of overall 3D shape.

Results

One hundred and fifteen knees with PFP (mean age 59.7, BMI 27.5 kg/m², female 58.2%) and 438 without PFP (mean age 63.6, BMI 26.9 kg/m², female 52.9%) were included. After correction for multiple testing, no statistically significant differences were found between groups for any of the 3D imaging features or their combinations. A statistically significant discrimination was noted for overall 3D shape between genders, confirming the validity of the 3D measures.

Conclusion

Challenging current perceptions, no differences in patellofemoral morphology were found between older people with and without PFP using 3D quantitative imaging analysis. Further work is needed to see if these findings are replicated in a younger PFP population.

Sagittal plane tilting deformity of the patellofemoral joint: a new concept in patients with chondromalacia patella

PURPOSE

The aims of this study were to evaluate sagittal plane alignment in patients with chondromalacia patella via magnetic resonance imaging (MRI), analyse the relationships between the location of the patellar cartilaginous lesions and sagittal alignment and finally investigate the relationships between the sagittal plane malalignment and patellofemoral loadings using by finite element analysis.

METHODS

Fifty-one patients who were diagnosed with isolated modified Outerbridge grade 3-4 patellar chondromalacia based on MRI evaluation and 51 control subjects were evaluated. Chondromalacia patella patients were divided into three subgroups according to the chondral lesion location as superior, middle and inferior. The patella-patellar tendon angle (P-PT) was used for evaluation of sagittal alignment of patellofemoral joint. Each subgroup was compared with control group by using P-PT angle. To investigate the biomechanical effects of sagittal plane malpositioning on patellofemoral joint, bone models were created at 30°, 60° and 90° knee flexion by using mean P-PT angles, which obtained from patients with chondromalacia patellae and control subjects. The total loading and contact area values of the patellofemoral joints were investigated by finite element analysis.

RESULTS

The mean age of all participants was 52.9 ± 8.2 years. The mean P-PT angle was significantly lower in chondromalacia group (142.1° ± 3.6°) compared to control group (144.5° ± 5.3°) (p = 0.008). Chondral lesions were located in superior, middle and inferior zones in 16, 20 and 15 patients, respectively. The mean P-PT angles in patients with superior (141.8 ± 2.7) and inferior subgroups (139.2 ± 2.3) were significantly lower than the values in the control group (p < 0.05). The contact area values were detected higher in models with chondromalacia than in the control models at the same flexion degrees. There were increased loadings at 30° and 90° flexions in the sagittal patellar tilt models.

CONCLUSION

This study revealed that sagittal plain malpositioning of the patellofemoral joint might be related to chondromalacia, especially in the presence of lesions in the upper and lower part of the patella. This condition leads to supraphysiological loadings on the patellofemoral joint. Sagittal patellar tilt should be considered in the evaluation and management of patellar cartilage defects. Taking sagittal plane malalignment into consideration in patellofemoral joint evaluation will enable us to design new physical and surgical modalities.

LEVEL OF EVIDENCE

IV.

Statistical shape modeling predicts patellar bone geometry to enable stereo-radiographic kinematic tracking

Complications in the patellofemoral (PF) joint of patients with total knee replacements include patellar subluxation and dislocation, and remain a cause for revision. Kinematic measurements to assess these complications and evaluate implant designs require the accuracy of dynamic stereo-radiographic systems with 3D-2D registration techniques. While tibiofemoral kinematics are typically derived by tracking metallic implants, PF kinematic measurements are difficult as the patellar implant is radiotransparent and a representation of the resected patella bone requires either pre-surgical imaging and precise implant placement or post-surgical imaging. Statistical shape models (SSMs), used to characterize anatomic variation, provide an alternative means to obtain the representation of the resected patella for use in kinematic tracking. Using a virtual platform of a stereo-radiographic system, the objectives of this study were to evaluate the ability of an SSM to predict subject-specific 3D implanted patellar geometries from simulated 2D image profiles, and to formulate an effective data collection methodology for PF kinematics by considering accuracy for a variety of patient pose scenarios. An SSM of the patella was developed for 50 subjects and a leave-one-out approach compared SSM-predicted and actual geometries; average 3D errors were 0.45±0.07mm (mean±standard deviation), which is comparable to the accuracy of traditional segmentation. Further, initial imaging of the patella in five unique stereo radiographic perspectives yielded the most accurate representation. The ability to predict the remaining patellar geometry of the implanted PF joint with radiographic images and SSM, instead of CT, can reduce radiation exposure and streamline in vivo kinematic evaluations.

Metatarsal Shape and Foot Type: A Geometric Morphometric Analysis

Planus and cavus foot types have been associated with an increased risk of pain and disability. Improving our understanding of the geometric differences between bones in different foot types may provide insights into injury risk profiles and have implications for the design of musculoskeletal and finite-element models. In this study, we performed a geometric morphometric analysis on the geometry of metatarsal bones from 65 feet, segmented from computed tomography (CT) scans. These were categorized into four foot types: pes cavus, neutrally aligned, asymptomatic pes planus, and symptomatic pes planus. Generalized procrustes analysis (GPA) followed by permutation tests was used to determine significant shape differences associated with foot type and sex, and principal component analysis was used to find the modes of variation for each metatarsal. Significant shape differences were found between foot types for all the metatarsals (p < 0.01), most notably in the case of the second metatarsal which showed significant pairwise differences across all the foot types. Analysis of the principal components of variation showed pes cavus bones to have reduced cross-sectional areas in the sagittal and frontal planes. The first (p = 0.02) and fourth metatarsals (p = 0.003) were found to have significant sex-based differences, with first metatarsals from females shown to have reduced width, and fourth metatarsals from females shown to have reduced frontal and sagittal plane cross-sectional areas. Overall, these findings suggest that metatarsal bones have distinct morphological characteristics that are associated with foot type and sex, with implications for our understanding of anatomy and numerical modeling of the foot.

Influence of Total Knee Arthroplasty on Patellar Kinematics and Patellofemoral Pressure

BACKGROUND

Patellofemoral complications are one of the main problems after total knee arthroplasty (TKA). The design of the TKA component may affect the patellar biomechanics, which may be associated with this postoperative complication. The purpose of this study was to assess the influence of TKA and prosthesis designs on the patellar kinematics and patellofemoral pressure.

METHODS

Using fresh-frozen cadavers, we measured the patellofemoral pressure, patella offset, and patella tilt in the following 4 conditions: normal knee (patella replacement only), cruciate-retaining TKA, condylar-stabilizing TKA, and posterior-stabilized TKA.

RESULTS

The patellofemoral pressure increased significantly after the cruciate-retaining TKA and condylar-stabilizing TKA compared with the normal knee. The patella offset in the normal knee decreased with increasing knee flexion angles, while the patella offset in the TKA knees did not change significantly through the full range of motion. The amount of lateral patella tilt in the normal knee was significantly larger than the TKA knees in the full range of motion.

CONCLUSION

Although the femoral components are designed to reproduce an anatomical patellar tracking, the physiological patellar kinematics were not observed. Relatively high patellofemoral pressure and kinematic change after TKA may be associated with postoperative complications such as the anterior knee pain.

Patient-specific modeling of the trochlear morphologic anomalies by means of hyperbolic paraboloids

Diagnostic and therapeutic purposes are issuing pressing demands to improve the evaluation of the dysplasia condition of the femoral trochlea. The traditional clinical assessment of the dysplasia, based on Dejour classification, recognized 4 increasing (A, B, C, D) levels of severity. It has been extensively questioned in the literature that this classification methodology can be defective suggesting that quantitative measures can ensure more reliable criteria for the dysplasia severity assessment. This study reports on a novel technique to model the trochlear surface (TS), digitally reconstructed by 3D volumetric imaging, using three hyperbolic paraboloids (HP), one to describe the global trochlear aspect, two to represent the local aspects of the medial and lateral compartments, respectively. Results on a cohort of 43 patients, affected by aspecific anterior knee pain, demonstrate the consistency of the estimated model parameters with the morphologic aspect of the TS. The obtained small fitting error (on average lower than 0.80 mm) demonstrated that the ventral aspect of the trochlear morphology can be modeled with high accuracy by HPs. We also showed that HP modeling provides a continuous representation of morphologic variations in shape parameter space while we found that similar morphologic anomalies of the trochlear aspect are actually attributed to different severity grades in the Dejour classification. This finding is in agreement with recent works in the literature reporting that morphometric parameters can only optimistically be used to discriminate between the Grade A and the remaining three grades. In conclusion, we can assert that the proposed methodology is a further step toward modeling of anatomical surfaces that can be used to quantify deviations to normality on a patient-specific basis.

Analysis of Uncertainty and Variability in Finite Element Computational Models for Biomedical Engineering: Characterization and Propagation

Computational modeling has become a powerful tool in biomedical engineering thanks to its potential to simulate coupled systems. However, real parameters are usually not accurately known, and variability is inherent in living organisms. To cope with this, probabilistic tools, statistical analysis and stochastic approaches have been used. This article aims to review the analysis of uncertainty and variability in the context of finite element modeling in biomedical engineering. Characterization techniques and propagation methods are presented, as well as examples of their applications in biomedical finite element simulations. Uncertainty propagation methods, both non-intrusive and intrusive, are described. Finally, pros and cons of the different approaches and their use in the scientific community are presented. This leads us to identify future directions for research and methodological development of uncertainty modeling in biomedical engineering.

Constrained Statistical Modelling of Knee Flexion From Multi-Pose Magnetic Resonance Imaging

Reconstruction of the anterior cruciate ligament (ACL) through arthroscopy is one of the most common procedures in orthopaedics. It requires accurate alignment and drilling of the tibial and femoral tunnels through which the ligament graft is attached. Although commercial computer-assisted navigation systems exist to guide the placement of these tunnels, most of them are limited to a fixed pose without due consideration of dynamic factors involved in different knee flexion angles. This paper presents a new model for intraoperative guidance of arthroscopic ACL reconstruction with reduced error particularly in the ligament attachment area. The method uses 3D preoperative data at different flexion angles to build a subject-specific statistical model of knee pose. To circumvent the problem of limited training samples and ensure physically meaningful pose instantiation, homogeneous transformations between different poses and local-deformation finite element modelling are used to enlarge the training set. Subsequently, an anatomical geodesic flexion analysis is performed to extract the subject-specific flexion characteristics. The advantages of the method were also tested by detailed comparison to standard Principal Component Analysis (PCA), nonlinear PCA without training set enlargement, and other state-of-the-art articulated joint modelling methods. The method yielded sub-millimetre accuracy, demonstrating its potential clinical value.

The effects of the sagittal plane malpositioning of the patella and concomitant quadriceps hypotrophy on the patellofemoral joint: a finite element analysis

PURPOSE

Anterior knee pain is a common symptom after intramedullary nailing in tibia shaft fracture. Moreover, patellofemoral malalignment is also known to be a major reason for anterior knee pain. Patellofemoral malalignment predisposes to increased loading in patellar cartilage. In the previous study, we have demonstrated the quadriceps atrophy and patellofemoral malalignment after intramedullary nailing due to tibia shaft fracture. In this study, our aim was to clarify the effects of quadriceps atrophy and patellofemoral malalignment with the pathologic loading on the joint cartilage.

METHODS

Mesh models of patellofemoral joint were constructed with CT images and integrated with soft tissue components such as menisci and ligaments. Physiological and sagittal tilt models during extension and flexion at 15°, 30° and 60° were created generating eight models. All the models were applied with 137 N force to present the effects of normal loading and 115.7 N force for the simulation of quadriceps atrophy. Different degrees of loading were applied to evaluate the joint contact area and pressure value with the finite element analysis.

RESULTS

There was increased patellofemoral contact area in patellar tilt models with respect to normal models. The similar loading patterns were diagnosed in all models at 0° and 15° knee flexion when 137 N force was applied. Higher loading values were obtained at 30° and 60° knee flexions in sagittal tilt models. Furthermore, in the sagittal tilt models, in which the quadriceps atrophy was simulated, the loadings at 30° and 60° knee flexion were higher than in the physiological ones.

CONCLUSIONS

Sagittal malalignment of the patellofemoral joint is a new concept that results in different loading patterns in the patellofemoral joint biomechanics. This malalignment in sagittal plane leads to increased loading values on the patellofemoral joint at 30° and 60° of the knee flexions. This new concept should be kept in mind during the course of diagnosis and treatment in patients with anterior knee pain. Definition of the exact biomechanical effects of the sagittal tilting will lead to the development of new treatment modalities.

Statistical modeling to characterize relationships between knee anatomy and kinematics

The mechanics of the knee are complex and dependent on the shape of the articular surfaces and their relative alignment. Insight into how anatomy relates to kinematics can establish biomechanical norms, support the diagnosis and treatment of various pathologies (e.g., patellar maltracking) and inform implant design. Prior studies have used correlations to identify anatomical measures related to specific motions. The objective of this study was to describe relationships between knee anatomy and tibiofemoral (TF) and patellofemoral (PF) kinematics using a statistical shape and function modeling approach. A principal component (PC) analysis was performed on a 20-specimen dataset consisting of shape of the bone and cartilage for the femur, tibia and patella derived from imaging and six-degree-of-freedom TF and PF kinematics from cadaveric testing during a simulated squat. The PC modes characterized links between anatomy and kinematics; the first mode captured scaling and shape changes in the condylar radii and their influence on TF anterior-posterior translation, internal-external rotation, and the location of the femoral lowest point. Subsequent modes described relations in patella shape and alta/baja alignment impacting PF kinematics. The complex interactions described with the data-driven statistical approach provide insight into knee mechanics that is useful clinically and in implant design.