The Geometrical Arrangement of Knee Constraints That Makes Natural Motion Possible: Theoretical and Experimental Analysis.

The study of the knee natural motion, namely the unresisted motion that the knee exhibits in the absence of external loads, provides insights into the physiology of this articulation. The natural motion represents the baseline condition upon which deformations of its passive structures (i.e., ligaments and cartilage) take place when loads are applied. Moreover, during natural motion, the strain energy density stored within ligaments and cartilage is minimized. This reduces the chance of microdamage occurrences and the corresponding metabolic cost for tissue repairing. The study of the knee natural motion is thus fundamental in understanding the joint physiology. This paper shows that the line of action of resultant forces of all the knee constraints provided by the passive structures must intersect the instantaneous helical axis (IHA) to make the knee natural motion possible. In other words, the lines of action of all these constraints must cross the same line at each flexion angle to guarantee the natural motion of the joint. This geometrical property is first proven theoretically and then verified in four in vitro and one in vivo experiments. The geometrical characterization of the knee natural motion presented in this study provides a fundamental property that must be satisfied to allow the correct joint mobility. The knowledge of this property may thus allow the definition of better models, treatments, and devices.

A three-dimensional ankle kinetostatic model to simulate loaded and unloaded joint motion.

A kinetostatic model able to replicate both the natural unloaded motion of the tibiotalar (or ankle) joint and the joint behavior under external loads is presented. The model is developed as the second step of a sequential procedure, which allows the definition of a kinetostatic model as a generalization of a kinematic model of the joint defined at the first step. Specifically, this kinematic model taken as the starting point of the definition procedure is a parallel spatial mechanism which replicates the ankle unloaded motion. It features two rigid bodies (representing the tibia-fibula and the talus-calcaneus complexes) interconnected by five rigid binary links, that mimic three articular contacts and two nearly isometric fibers (IFs) of the tibiocalcaneal ligament (TiCaL) and calcaneofibular ligament (CaFiL). In the kinetostatic model, the five links are considered as compliant; moreover, further elastic structures are added to represent all the main ankle passive structures of the joint. Thanks to this definition procedure, the kinetostatic model still replicates the ankle unloaded motion with the same accuracy as the kinematic model. In addition, the model can replicate the behavior of the joint when external loads are applied. Finally, the structures that guide these motions are consistent with the anatomical evidence. The parameters of the model are identified for two specimens from both subject-specific and published data. Loads are then applied to the model in order to simulate two common clinical tests. The model-predicted ankle motion shows good agreement with results from the literature.

Foot kinematics as a function of ground orientation and weightbearing.

The foot is responsible for the bodyweight transfer to the ground, while adapting to different terrains and activities. Despite this fundamental role, the knowledge about the foot bone intrinsic kinematics is still limited. The aim of the study is to provide a quantitative and systematic description of the kinematics of all bones in the foot, considering the full range of dorsi/plantar flexion and pronation/supination of the foot, both in weightbearing and nonweightbearing conditions. Bone kinematics was accurately reconstructed for three specimens from a series of computed tomography scans taken in weightbearing configuration. The ground inclination was imposed through a set of wedges, varying the foot orientation both in the sagittal and coronal planes; the donor body-weight was applied or removed by a cable-rig. A total of 32 scans for each foot were acquired and segmented. Bone kinematics was expressed in terms of anatomical reference systems optimized for the foot kinematic description. Results agree with previous literature where available. However, our analysis reveals that bones such as calcaneus, navicular, intermediate cuneiform, fourth and fifth metatarsal move more during foot pronation than flexion. Weightbearing significantly increase the range of motion of almost all the bone. Cuneiform and metatarsal move more due to weightbearing than in response to ground inclination, showing their role in the load-acceptance phase. The data here reported represent a step toward a deeper understanding of the foot behavior, that may help in the definition of better treatment and medical devices, as well as new biomechanical model of the foot.

Full-field strain distribution in hierarchical electrospun nanofibrous poly-L(lactic) acid/collagen scaffolds for tendon and ligament regeneration: A multiscale study.

Regeneration of injured tendons and ligaments (T/L) is a worldwide need. In this study electrospun hierarchical scaffolds made of a poly-L (lactic) acid/collagen blend were developed reproducing all the multiscale levels of aggregation of these tissues. Scanning electron microscopy, microCT and tensile mechanical tests were carried out, including a multiscale digital volume correlation analysis to measure the full-field strain distribution of electrospun structures. The principal strains (εp1 and εp3) described the pattern of strains caused by the nanofibers rearrangement, while the deviatoric strains (εD) revealed the related internal sliding of nanofibers and bundles. The results of this study confirmed the biomimicry of such electrospun hierarchical scaffolds, paving the way to further tissue engineering and clinical applications.

Morphological and evolutionary insights into the keystone element of the human foot's medial longitudinal arch.

The evolution of the medial longitudinal arch (MLA) is one of the most impactful adaptations in the hominin foot that emerged with bipedalism. When and how it evolved in the human lineage is still unresolved. Complicating the issue, clinical definitions of flatfoot in living Homo sapiens have not reached a consensus. Here we digitally investigate the navicular morphology of H. sapiens (living, archaeological, and fossil), great apes, and fossil hominins and its correlation with the MLA. A distinctive navicular shape characterises living H. sapiens with adult acquired flexible flatfoot, while the congenital flexible flatfoot exhibits a 'normal' navicular shape. All H. sapiens groups differentiate from great apes independently from variations in the MLA, likely because of bipedalism. Most australopith, H. naledi, and H. floresiensis navicular shapes are closer to those of great apes, which is inconsistent with a human-like MLA and instead might suggest a certain degree of arboreality. Navicular shape of OH 8 and fossil H. sapiens falls within the normal living H. sapiens spectrum of variation of the MLA (including congenital flexible flatfoot and individuals with a well-developed MLA). At the same time, H. neanderthalensis seem to be characterised by a different expression of the MLA.

Prediction of Individual Knee Kinematics From an MRI Representation of the Articular Surfaces.

OBJECTIVE: The knowledge of individual joint motion may help to understand the articular physiology and to design better treatments and medical devices. Measurements of in-vivo individual motion are nowadays invasive/ionizing (fluoroscopy) or imprecise (skin markers). We propose a new approach to derive the individual knee natural motion from a three-dimensional representation of articular surfaces. METHODS: We hypothesize that tissue adaptation shapes articular surfaces to optimize load distribution. Thus, the knee natural motion is obtained as the envelope of tibiofemoral positions and orientations that minimize peak contact pressure, i.e. that maximize joint congruence. We investigated four in-vitro and one in-vivo knees. Articular surfaces were reconstructed from a reference MRI. Natural motion was computed by congruence maximization and results were validated versus experimental data, acquired through bone implanted markers, in-vitro, and single-plane fluoroscopy, in-vivo. RESULTS: In two cases, one of which in-vivo, maximum mean absolute error stays below 2.2° and 2.7 mm for rotations and translations, respectively. The remaining knees showed differences in joint internal rotation between the reference MRI and experimental motion at 0° flexion, possibly due to some laxity. The same difference is found in the model predictions, which, however, still replicate the individual knee motion. CONCLUSION: The proposed approach allows the prediction of individual joint motion based on non-ionizing MRI data. SIGNIFICANCE: This method may help to characterize healthy and, by comparison, pathological knee behavior. Moreover, it may provide an individual reference motion for the personalization of musculoskeletal models, opening the way to their clinical application.

Quantification of the errors associated with marker occlusion in stereophotogrammetric systems and implications on gait analysis.

Optoelectronic stereophotogrammetric systems (OSSs) represent the standard for gait analysis. Despite widespread, their reported accuracy in nominal working conditions shows a variability of several orders of magnitude, ranging from few microns to several millimetres. No clear explanation for this variability has been provided yet. We hypothesized that this reflects an error affecting OSS outcomes when some of the tracked markers are totally or partially occluded. The aim of this paper is to quantify this error in static and dynamic conditions, also distinguishing between total and partial marker occlusion. A Vicon system featuring 8 cameras is employed in this study. Two camera distributions, one designed to maximize OSS accuracy and another one representative of a typical gait setup, are investigated. For both the setups, static and dynamic tests are performed, evaluating the different impact of partial and total marker occlusions. Marker occlusions significantly affected the system performances. The maximum measure variation reached 1.86 mm and 7.20 mm in static and dynamic conditions, respectively, both obtained in the case of partial occlusion. This systematic source of error is likely to affect gait measures: markers placed on the patient body are often visible only by half of the cameras, with swinging arms and legs providing moving occlusions. The maximum error observed in this study can potentially affect the kinematics outcomes of conventional gait models, particularly on frontal and coronal plane, and consequently the peak muscle forces estimated with musculoskeletal models.

New anatomical reference systems for the bones of the foot and ankle complex: definitions and exploitation on clinical conditions.

BACKGROUND: A complete definition of anatomical reference systems (ARS) for all bones of the foot and ankle complex is lacking. Using a morphological approach, we propose new ARS for these bones with the aim of being highly repeatable, consistent among individuals, clinically interpretable, and also suited for a sound kinematic description. METHODS: Three specimens from healthy donors and three patients with flat feet were scanned in weight-bearing CT. The foot bones were segmented and ARS defined according to the proposed approach. To assess repeatability, intra class coefficients (ICC) were computed both intra- and inter-operator. Consistency was evaluated as the mean of the standard deviations of the ARS position and orientation, both within normal and flat feet. Clinical interpretability was evaluated by providing a quantification of the curvature variation in the medial-longitudinal and transverse arches and computing the Djiann-Annonier angle for normal and flat feet from these new ARS axes. To test the capability to also provide a sound description of the foot kinematics, the alignment between mean helical axes (MHA) and ARS axes was quantified. RESULTS: ICC was 0.99 both inter- and intra-operator. Rotational consistency was 4.7 ± 3.5 ° and 6.2 ± 4.4° for the normal and flat feet, respectively; translational consistency was 4.4 ± 4.0 mm and 5.4 ± 2.9 mm for the normal and flat feet, respectively. In both these cases, the consistency was better than what was achieved by using principal axes of inertia. Curvature variation in the arches were well described and the measurements of the Djiann-Annoier angles from both normal and flat feet matched corresponding clinical observations. The angle between tibio-talar MHA and ARS mediolateral axis in the talus was 12.3 ± 6.0, while the angle between talo-calcaneal MHA and ARS anteroposterior axis in the calcaneus was 17.2 ± 5.6, suggesting good capability to represent joint kinematics. CONCLUSIONS: The proposed ARS definitions are robust and provide a solid base for the 3-dimensional description of posture and motion of the foot and ankle complex from medical imaging.

The relationship between tibiofemoral geometry and musculoskeletal function during normal activity.

BACKGROUND: The effect of tibiofemoral geometry on musculoskeletal function is important to movement biomechanics. RESEARCH QUESTION: We hypothesised that tibiofemoral geometry determines tibiofemoral motion and musculoskeletal function. We then aimed at 1) modelling tibiofemoral motion during normal activity as a function of tibiofemoral geometry in healthy adults; and 2) quantifying the effect of tibiofemoral geometry on musculoskeletal function. METHODS: We used motion data for six activity types and CT images of the knee from 12 healthy adults. Geometrical variation of the tibia and femoral articular surfaces were measured in the CT images. The geometry-based tibiofemoral motion was calculated by fitting a parallel mechanism to geometrical variation in the cohort. Matched musculoskeletal models embedding the geometry-based tibiofemoral joint motion and a common generic tibiofemoral motion of reference were generated and used to calculate joint angles, net joint moments, muscle and joint forces for the six activities analysed. The tibiofemoral model was validated against bi-planar fluoroscopy measurements for walking for all the six planes of motion. The effect of tibiofemoral geometry on musculoskeletal function was the difference between the geometry-based model and the model of reference. RESULTS: The geometry-based tibiofemoral motion described the pattern and the variation during walking for all six motion components, except the pattern of anterior tibial translation. Tibiofemoral geometry had moderate effect on cohort-averages of musculoskeletal function (R2 = 0.60-1), although its effect was high in specific instances of the model, outputs and activities analysed, reaching 2.94 BW for the ankle reaction force during stair descent. In conclusion, tibiofemoral geometry is a major determinant of tibiofemoral motion during walking. SIGNIFICANCE: Geometrical variations of the tibiofemoral joint are important for studying musculoskeletal function during normal activity in specific individuals but not for studying cohort averages of musculoskeletal function. This finding expands current knowledge of movement biomechanics.

Relationship of Knee Forces to Subjective Function Pre- and Post-ACL Reconstruction.

PURPOSE: Although basic objective measures (e.g., knee laxity, strength, and hop tests) have been related to subjective measures of function, associations between knee-specific objective and subjective measures have yet to be completed. The objective was to determine if knee joint contact and ligament forces differ between pre- and post-anterior cruciate ligament (ACL) reconstructed states and if these forces relate to their patient's respective subjective functional ability scores. METHODS: Twelve patients performed a hopping task before and after reconstruction. Magnetic resonance images and OpenSim were used to develop patient-specific models in static optimization and joint reaction analyses. Questionnaires concerning each patient's subjective functional ability were also collected and correlated with knee joint contact and ligament forces. RESULTS: No significant differences were observed between deficient and reconstructed groups with respect to knee joint contact or ligament forces. Nevertheless, there were several significant (P < 0.05) moderate to strong correlations between subjective and objective measures including Tegner activity level to contact force in both states (r = 0.67-0.76) and International Knee Documentation Committee to compressive and anterior shear forces (r = 0.64-0.66). CONCLUSION: Knee-specific objective measures of a patient's functional capacity can represent their subjective ability, which explains this relationship to a greater extent than past anatomical and gross objective measures of function. This consolidation is imperative for improving the current rehabilitation schema as it allows for external validation of objective and subjective functional measures. With poor validation of subjective function against objective measures of function, the reinjury rate is unlikely to diminish, continuing the heavy financial burden on health care systems.

Effect of implementing magnetic resonance imaging for patient-specific OpenSim models on lower-body kinematics and knee ligament lengths.

BACKGROUND: OpenSim models are typically based on cadaver findings that are generalized to represent a wide range of populations, which curbs their validity. Patient-specific modelling through incorporating magnetic resonance imaging (MRI) improves the model's biofidelity with respect to joint alignment and articulations, muscle wrapping, and ligament insertions. The purpose of this study was to determine if the inclusion of an MRI-based knee model would elicit differences in lower limb kinematics and resulting knee ligament lengths during a side cut task. METHODS: Eleven participants were analyzed with the popular Rajagopal OpenSim model, two variations of the same model to include three and six degrees of freedom knee (DOF), and a fourth version featuring a four DOF MRI-based knee model. These four models were used in an inverse kinematics analysis of a side cut task and the resulting lower limb kinematics and knee ligament lengths were analyzed. RESULTS: The MRI-based model was more responsive to the movement task than the original Rajagopal model while less susceptible to soft tissue artifact than the unconstrained six DOF model. Ligament isometry was greatest in the original Rajagopal model and smallest in the six DOF model. CONCLUSIONS: When using musculoskeletal modelling software, one must acutely consider the model choice as the resulting kinematics and ligament lengths are dependent on this decision. The MRI-based knee model is responsive to the kinematics and ligament lengths of highly dynamic tasks and may prove to be the most valid option for continuing with late-stage modelling operations such as static optimization.

Development and validation of subject-specific pediatric multibody knee kinematic models with ligamentous constraints.

Computational knee models that replicate the joint motion are important tools to discern difficult-to-measure functional joint biomechanics. Numerous knee kinematic models of different complexity, with either generic or subject-specific anatomy, have been presented and used to predict three-dimensional tibiofemoral (TFJ) and patellofemoral (PFJ) joint kinematics of cadavers or healthy adults, but not pediatric populations. The aims of this study were: (i) to develop subject-specific TFJ and PFJ kinematic models, with TFJ models having either rigid or extensible ligament constraints, for eight healthy pediatric participants and (ii) to validate the estimated joint and ligament kinematics against in vivo kinematics measured from magnetic resonance imaging (MRI) at four TFJ flexion angles. Three different TFJ models were created from MRIs and used to solve the TFJ kinematics: (i) 5-rigid-link parallel mechanism with rigid surface contact and isometric anterior cruciate (ACL), posterior cruciate (PCL) and medial collateral (MCL) ligaments (ΔLnull), (ii) 6-link parallel mechanism with minimized ACL, PCL, MCL and lateral collateral ligament (LCL) length changes (ΔLmin) and (iii) 6-link parallel mechanism with prescribed ACL, PCL, MCL and LCL length variations (ΔLmatch). Each model's geometrical parameters were optimized using a Multiple Objective Particle Swarm algorithm. When compared to MRI-measured data, ΔLnull and ΔLmatch performed the best, with average root mean square errors below 6.93° and 4.23 mm for TFJ and PFJ angles and displacements, respectively, and below 2.01 mm for ligament lengths (<4.32% ligament strain). Therefore, within these error ranges, ΔLnull and ΔLmatch can be used to estimate three-dimensional pediatric TFJ, PFJ and ligament kinematics and can be incorporated into lower-limb models to estimate joint kinematics and kinetics during dynamic tasks.

Kinematic models of lower limb joints for musculo-skeletal modelling and optimization in gait analysis.

Kinematic models of lower limb joints have several potential applications in musculoskeletal modelling of the locomotion apparatus, including the reproduction of the natural joint motion. These models have recently revealed their value also for in vivo motion analysis experiments, where the soft-tissue artefact is a critical known problem. This arises at the interface between the skin markers and the underlying bone, and can be reduced by defining multibody kinematic models of the lower limb and by running optimization processes aimed at obtaining estimates of position and orientation of relevant bones. With respect to standard methods based on the separate optimization of each single body segment, this technique makes it also possible to respect joint kinematic constraints. Whereas the hip joint is traditionally assumed as a 3 degrees of freedom ball and socket articulation, many previous studies have proposed a number of different kinematic models for the knee and ankle joints. Some of these are rigid, while others have compliant elements. Some models have clear anatomical correspondences and include real joint constraints; other models are more kinematically oriented, these being mainly aimed at reproducing joint kinematics. This paper provides a critical review of the kinematic models reported in literature for the major lower limb joints and used for the reduction of soft-tissue artefact. Advantages and disadvantages of these models are discussed, considering their anatomical significance, accuracy of predictions, computational costs, feasibility of personalization, and other features. Their use in the optimization process is also addressed, both in normal and pathological subjects.

Feasibility of using MRIs to create subject-specific parallel-mechanism joint models.

Musculoskeletal models typically use generic 2D models for the tibiofemoral (TFJ) and patellofemoral (PFJ) joints, with a hinge talocrural joint (TCJ), which are scaled to each subject׳s bone dimensions. Alternatively joints' measured kinematics in cadavers are well-predicted using 3D cadaver-specific models. These employ mechanisms constrained by the articulations of geometric objects fitted to the joint׳s surfaces. In this study, we developed TFJ, PFJ and TCJ mechanism-based models off MRIs for fourteen participants and compared the estimated kinematics with those from published studies modified to be consistent with mechanisms models and subject-specific anatomical landmarks. The models' parameters were estimated by fitting spheres to segmented articular cartilage surfaces, while ligament attachment points were selected from their bony attachment regions. Each participant׳s kinematics were estimated by ensuring no length changes in ligaments and constant distances between spheres' centres. Two parameters' optimizations were performed; both avoid singularities and one best matches the kinematic patterns off published studies. Sensitivity analysis determined which parameters the models were sensitive to. With both optimization methods, kinematics did not present singularities but correlation values were higher, exceeding 0.6, when matching the published studies. However, ranges of motion (ROM) were different between estimated and published studies. Across participants, models presented large parameter variation. Small variations were found between estimated- and optimized-parameters, and in the estimated-rotations and translations' means and ROM. Model results were sensitive to changes in distal tibia, talus and patella spheres' centres. These models can be implemented in subject-specific rigid-body musculoskeletal models to estimate joint moments and loads.

Validation of a multi-body optimization with knee kinematic models including ligament constraints.

Motion analysis aims at evaluating the joint kinematics but the relative movement between the bones and the skin markers, known as soft tissue artifact (STA), introduces large errors. Multi-body optimization (MBO) methods were proposed to compensate for the STA. However, the validation of the MBO methods using no or simple kinematic constraints (e.g., spherical joint) demonstrated inaccurate in vivo kinematics. Anatomical constraints were introduced in MBO methods and various ligament constraints were proposed in the literature. The validation of these methods has not been performed yet. The objective of this study was to validate, against in vivo knee joint kinematics measured by intra-cortical pins on three subjects, the model-based kinematics obtained by MBO methods using three different types of ligament constraints. The MBO method introducing minimized or prescribed ligament length variations showed some improvements in the estimation of knee kinematics when compared to no kinematic constraints, to degree-of-freedom (DoF) coupling curves, and to null ligament length variations. However, the improvements were marginal when compared to spherical constraints. The errors obtained by minimized and prescribed ligament length variations were below 2.5° and 4.1mm for the joint angles and displacements while the errors obtained with spherical joint constraints were below 2.2° and 3.1mm. These errors are generally lower than the errors previously reported in the literature. As a conclusion, this study presented encouraging results for the compensation of the STA by MBO and for the introduction of anatomical constraints in MBO. Personalization of the geometry should be considered for further improvements.

One-degree-of-freedom spherical model for the passive motion of the human ankle joint.

Mathematical modelling of mobility at the human ankle joint is essential for prosthetics and orthotic design. The scope of this study is to show that the ankle joint passive motion can be represented by a one-degree-of-freedom spherical motion. Moreover, this motion is modelled by a one-degree-of-freedom spherical parallel mechanism model, and the optimal pivot-point position is determined. Passive motion and anatomical data were taken from in vitro experiments in nine lower limb specimens. For each of these, a spherical mechanism, including the tibiofibular and talocalcaneal segments connected by a spherical pair and by the calcaneofibular and tibiocalcaneal ligament links, was defined from the corresponding experimental kinematics and geometry. An iterative procedure was used to optimize the geometry of the model, able to predict original experimental motion. The results of the simulations showed a good replication of the original natural motion, despite the numerous model assumptions and simplifications, with mean differences between experiments and predictions smaller than 1.3 mm (average 0.33 mm) for the three joint position components and smaller than 0.7° (average 0.32°) for the two out-of-sagittal plane rotations, once plotted versus the full flexion arc. The relevant pivot-point position after model optimization was found within the tibial mortise, but not exactly in a central location. The present combined experimental and modelling analysis of passive motion at the human ankle joint shows that a one degree-of-freedom spherical mechanism predicts well what is observed in real joints, although its computational complexity is comparable to the standard hinge joint model.

Strip-driven devices for the spatial motion guidance of human joints.

Orthoses and exoskeletons need devices that can replicate the natural spatial motion of human joints. These devices should be simple and should have a high accuracy, in order not to constrain and load the joints unnaturally. In this study, strip-driven devices are proposed to guide the spatial joint motion. Classic planar devices are generalized to obtain rolling without slipping between two ruled surfaces. The special case of spherical motion is presented and analysed in details. The influence of several design parameters on the kinematic and static behaviour of these devices is also presented.