A framework for parametric modeling of ankle ligaments to determine the in situ response under gross foot motion

Ligament sprains account for a majority of injuries to the foot and ankle complex, but ligament properties have not been understood well due to the difficulties in replicating the complex geometry, in situ stress state, and non-uniformity of the strain. For a full investigation of the injury mechanism, it is essential to build up a foot and ankle model validated at the level of bony kinematics and ligament properties. This study developed a framework to parameterize the ligament response for determining the in situ stress state and heterogeneous force–elongation characteristics using a finite element ankle model. Nine major ankle ligaments and the interosseous membrane were modeled as discrete elements corresponding functionally to the ligamentous microstructure of collagen fibers and having parameterized toe region and stiffness at the fiber level. The range of the design variables in the ligament model was determined from existing experimental data. Sensitivity of the bony kinematics to each variable was investigated by design of experiment. The results highlighted the critical role of the length of the toe region of the ligamentous fibers on the bony kinematics with the cumulative influence of more than 95%, while the fiber stiffness was statistically insignificant with an influence of less than 1% under the given variable range and loading conditions. With the flexibility of variable adjustment and high computational efficiency, the presented ankle model was generic in nature so as to maximize its applicability to capture the individual ligament behaviors in future studies.     

Searching for the “sweet spot”: the foot rotation and parallel engagement of ankle ligaments in maximizing injury tolerance

Ligament sprains, defined as tearing of bands of fibrous tissues within ligaments, account for a majority of injuries to the foot and ankle complex in field-based sports. External rotation of the foot is considered the primary injury mechanism of syndesmotic ankle sprains with concomitant flexion and inversion/eversion associated with particular patterns of ligament trauma. However, the influence of the magnitude and direction of loading vectors to the ankle on the in situ stress state of the ligaments has not been quantified in the literature. The objective of the present study was to search for the maximum injury tolerance of a human foot with an acceptable subfailure distribution of individual ligaments. We used a previously developed and comprehensively validated foot and ankle model to reproduce a range of combined foot rotation experienced during high-risk sports activities. Biomechanical computational investigation was performed on initial foot rotation from \(20{^{\circ }}\) of plantar flexion to \(15{^{\circ }}\) of dorsiflexion, and from \(15{^{\circ }}\) of inversion to \(15{^{\circ }}\) of eversion prior to external rotation. Change in initial foot rotation shifted injury initiation among different ligaments and resulted in a wide range of injury tolerances at the structural level (e.g., 36–125 Nm of rotational moment). The observed trend was in agreement with a parallel experimental study that initial plantar flexion decreased the incidence of syndesmotic injury compared to a neutral foot. A mechanism of distributing even loads across ligaments subjected to combined foot rotations was identified. This mechanism is potential to obtain the maximum load-bearing capability of a foot and ankle while minimizing the injury severity of ligaments. Such improved understanding of ligament injuries in athletes is necessary to facilitate injury management by clinicians and countermeasure development by biomechanists.     

A real-time computational model for estimating kinematics of ankle ligaments

Background: An accurate assessment of ankle ligament kinematics is crucial in understanding the injury mechanisms and can help to improve the treatment of an injured ankle, especially when used in conjunction with robot-assisted therapy. A number of computational models have been developed and validated for assessing the kinematics of ankle ligaments. However, few of them can do real-time assessment to allow for an input into robotic rehabilitation programs. Method: An ankle computational model was proposed and validated to quantify the kinematics of ankle ligaments as the foot moves in real-time. This model consists of three bone segments with three rotational degrees of freedom (DOFs) and 12 ankle ligaments. This model uses inputs for three position variables that can be measured from sensors in many ankle robotic devices that detect postures within the foot–ankle environment and outputs the kinematics of ankle ligaments. Validation of this model in terms of ligament length and strain was conducted by comparing it with published data on cadaver anatomy and magnetic resonance imaging. Results: The model based on ligament lengths and strains is in concurrence with those from the published studies but is sensitive to ligament attachment positions. Conclusions: This ankle computational model has the potential to be used in robot-assisted therapy for real-time assessment of ligament kinematics. The results provide information regarding the quantification of kinematics associated with ankle ligaments related to the disability level and can be used for optimizing the robotic training trajectory.     

New parameters describing how knee ligaments carry force in situ predict interspecimen variations in laxity during simulated clinical exams

Knee laxity, defined as the net translation or rotation of the tibia relative to the femur in a given direction in response to an applied load, is highly variable from person to person. High levels of knee laxity as assessed during routine clinical exams are associated with first-time ligament injury and graft reinjury following reconstruction. During laxity exams, ligaments carry force to resist the applied load; however, relationships between intersubject variations in knee laxity and variations in how ligaments carry force as the knee moves through its passive envelope of motion, which we refer to as ligament engagement, are not well established. Thus, the objectives of this study were, first, to define parameters describing ligament engagement and, then, to link variations in ligament engagement and variations in laxity across a group of knees. We used a robotic manipulator in a cadaveric knee model (n = 20) to quantify how important knee stabilizers, namely the anterior and posterior cruciate ligaments (ACL and PCL, respectively), as well as the medial collateral ligament (MCL) engage during respective tests of anterior, posterior, and valgus laxity. Ligament engagement was quantified using three parameters: (1) in situ slack, defined as the relative tibiofemoral motion from the neutral position of the joint to the position where the ligament began to carry force; (2) in situ stiffness, defined as the slope of the linear portion of the ligament force–tibial motion response; and (3) ligament force at the peak applied load. Knee laxity was related to parameters of ligament engagement using univariate and multivariate regression models. Variations in the in situ slack of the ACL and PCL predicted anterior and posterior laxity, while variations in both in situ slack and in situ stiffness of the MCL predicted valgus laxity. Parameters of ligament engagement may be useful to further characterize the in situ biomechanical function of ligaments and ligament grafts.     

The effect of damage to the lateral collateral ligaments on the mechanical characteristics of the ankle joint--an in-vitro study

Injuries to the lateral collateral ligaments of the ankle joint are among the most frequently occurring injuries at the lower limb. The present study was conducted for the purpose of establishing the basis for the development of a quantitative diagnostic procedure for such injuries. To achieve this goal, the effect of four types of ligament injuries on the three-dimensional mechanical characteristics of the ankle were investigated. These types of injuries consisted of: 1) isolated tear of the anterior talofibular ligament; 2) isolated tear of the calcaneofibular ligament; 3) isolated tear of the posterior talofibular ligament; and 4) combined tear of both the anterior talofibular ligament and the calcaneofibular ligament. The experiments were conducted on 31 amputated lower limbs and consisted of comparing the three-dimensional load-displacement and flexibility characteristics of the ankle joint prior to and following sectioning of selected ligaments. The experimental and analytical procedures used to derive these characteristics was developed previously by the authors. From the results of this study it was concluded that the three-dimensional flexibility characteristics of the ankle joint are strongly influenced by damage to the lateral collateral ligaments. Furthermore, it was found that each type of ligament injury produced unique and identifiably changes in the flexibility characteristics of the ankle. These unique changes, which are described in detail in this paper, can be used to discriminate between the different types of ligament injuries. Consequently, it was concluded that it is feasible to develop a quantitative diagnostic procedure for ankle ligament injuries based on the effect of the injury on the flexibility characteristics of the ankle.     

Computational modeling to predict mechanical function of joints: application to the lower leg with simulation of two cadaver studies

Computational models of musculoskeletal joints and limbs can provide useful information about joint mechanics. Validated models can be used as predictive devices for understanding joint function and serve as clinical tools for predicting the outcome of surgical procedures. A new computational modeling approach was developed for simulating joint kinematics that are dictated by bone/joint anatomy, ligamentous constraints, and applied loading. Three-dimensional computational models of the lower leg were created to illustrate the application of this new approach. Model development began with generating three-dimensional surfaces of each bone from CT images and then importing into the three-dimensional solid modeling software SOLIDWORKS and motion simulation package COSMOSMOTION. Through SOLIDWORKS and COSMOSMOTION, each bone surface file was filled to create a solid object and positioned necessary components added, and simulations executed. Three-dimensional contacts were added to inhibit intersection of the bones during motion. Ligaments were represented as linear springs. Model predictions were then validated by comparison to two different cadaver studies, syndesmotic injury and repair and ankle inversion following ligament transection. The syndesmotic injury model was able to predict tibial rotation, fibular rotation, and anterior/posterior displacement. In the inversion simulation, calcaneofibular ligament extension and angles of inversion compared well. Some experimental data proved harder to simulate accurately, due to certain software limitations and lack of complete experimental data. Other parameters that could not be easily obtained experimentally can be predicted and analyzed by the computational simulations. In the syndesmotic injury study, the force generated in the tibionavicular and calcaneofibular ligaments reduced with the insertion of the staple, indicating how this repair technique changes joint function. After transection of the calcaneofibular ligament in the inversion stability study, a major increase in force was seen in several of the ligaments on the lateral aspect of the foot and ankle, indicating the recruitment of other structures to permit function after injury. Overall, the computational models were able to predict joint kinematics of the lower leg with particular focus on the ankle complex. This same approach can be taken to create models of other limb segments such as the elbow and wrist. Additional parameters can be calculated in the models that are not easily obtained experimentally such as ligament forces, force transmission across joints, and three-dimensional movement of all bones. Muscle activation can be incorporated in the model through the action of applied forces within the software for future studies.     

A mechanistic damage model for ligaments

PurposeThe accuracy of biomechanical models is predicated on the realism by which they represent their biomechanical tissues. Unfortunately, most models use phenomenological ligament models that neglect the behaviour in the failure region. Therefore, the purpose of this investigation was to test whether a mechanistic model of ligamentous tissue portrays behaviour representative of actual ligament failure tests.ModelThe model tracks the time-evolution of a population of collagen fibres in a theoretical ligament. Each collagen fibre is treated as an independent linear cables with constant stiffness. Model equations were derived by assuming these fibres act as a continuum and applying a conservation law akin to Huxley’s muscle model. A breaking function models the rate of collagen fibre breakage at a given displacement, and was chosen to be a linear function for this preliminary analysis.MethodsThe model was fitted to experimental average curves for the cervical anterior longitudinal ligament. In addition, the model was cyclically loaded to test whether the tissue model behaves similarly.ResultsThe model agreed very well with experiment with an RMS error of 14.23 N and an R² of 0.995. Cyclic loading exhibited a reduction in force similar to experimental data.Discussion and conclusionThe proposed model showcases behaviour reminiscent of actual ligaments being strained to failure and undergoing cyclic load. Future work could incorporate viscous effects, or validate the model further by testing it in various loading conditions. Characterizing the breaking function more accurately would also lead to better results.     

Determination of dynamic ankle ligament strains from a computational model driven by motion analysis based kinematic data

External rotation of the foot has been implicated in high ankle sprains. Recent studies by this laboratory, and others, have suggested that torsional traction characteristics of the shoe-surface interface may play a role in ankle injury. While ankle injuries most often involve damage to ligaments due to excessive strains, the studies conducted by this laboratory and others have largely used surrogate models of the lower extremity to determine shoe-surface interface characteristics based on torque measures alone. The objective of this study was to develop a methodology that would integrate a motion analysis-based kinematic foot model with a computational model of the ankle to determine dynamic ankle ligament strains during external foot rotation. Six subjects performed single-legged, internal rotation of the body with a planted foot while a marker-based motion analysis was conducted to track the hindfoot motion relative to the tibia. These kinematic data were used to drive an established computational ankle model. Ankle ligament strains, as a function of time, were determined. The anterior tibiofibular ligament (ATiFL) experienced the highest strain at 9.2±1.1%, followed by the anterior deltoid ligament (ADL) at 7.8±0.7%, averaged over the six subjects. The peak ATiFL strain occurred prior to peak strain in the ADL in all subjects. This novel methodology may provide new insights into mechanisms of high ankle sprains and offer a basis for future evaluations of shoe-surface interface characteristics using human subjects rather than mechanical surrogate devices.     

Effect of simulated joint instability and bracing on ankle and subtalar joint flexibility

It is clinically challenging to distinguish between ankle and subtalar joints instability in vivo. Understanding the changes in load-displacement at the ankle and subtalar joints after ligament injuries may detect specific changes in joint characteristics that cannot be detected by investigating changes in range of motion alone. The effect of restricting joints end range of motion with ankle braces was already established, but little is known about the effect of an ankle brace on the flexibility of the injured ankle and subtalar joints. Therefore, the purposes of this study were to (1) understand how flexibility is affected at the ankle and subtalar joints after sectioning lateral and intrinsic ligaments during combined sagittal foot position and inversion and during internal rotation and (2) investigate the effect of a semi-rigid ankle brace on the ankle and subtalar joint flexibility. Kinematics and kinetics were collected from nine cadaver feet during inversion through the range of ankle flexion and during internal rotation. Motion was applied with and without a brace on an intact foot and after sequentially sectioning the calcaneofibular ligament (CFL) and the intrinsic ligaments. Segmental flexibility was defined as the slope of the angle-moment curve for each 1 Nm interval. Early flexibility significantly increased at the ankle and subtalar joint after CFL sectioning during inversion. The semi-rigid ankle brace significantly decreased early flexibility at the subtalar joint during inversion and internal rotation for all ligament conditions and at the ankle joint after all ligaments were cut.     

Investigation of whiplash injuries in the upper cervical spine using a detailed neck model

Whiplash injuries continue to have significant societal cost; however, the mechanism and location of whiplash injury is still under investigation. Recently, the upper cervical spine ligaments, particularly the alar ligament, have been identified as a potential whiplash injury location. In this study, a detailed and validated explicit finite element model of a 50th percentile male cervical spine in a seated posture was used to investigate upper cervical spine response and the potential for whiplash injury resulting from vehicle crash scenarios. This model was previously validated at the segment and whole spine levels for both kinematics and soft tissue strains in frontal and rear impact scenarios. The model predicted increasing upper cervical spine ligament strain with increasing impact severity. Considering all upper cervical spine ligaments, the distractions in the apical and alar ligaments were the largest relative to their failure strains, in agreement with the clinical findings. The model predicted the potential for injury to the apical ligament for 15.2 g frontal or 11.7 g rear impacts, and to the alar ligament for a 20.7 g frontal or 14.4 g rear impact based on the ligament distractions. Future studies should consider the effect of initial occupant position on ligament distraction.     

Structural features associated with movement and ‘catch’ of sea-urchin spines

Spine catch ligaments of a sea urchin Arbacia punctulata were extended under constant load. Ligaments from an undisturbed animal may show any extension rate from zero (catch state) to rapid extension to failure. Replacing the preparation bath with Ca²⁺- and Mg²⁺-free sea water reversibly abolishes the catch state. The fine structure of the outer muscle layer and inner ligament cone associated with the spine base is described. The unstriated paramyosin muscles bear thin flanges and form compact interlocking rows. Subsurface cisternae are associated with the plasma membrane. The muscles are innervated by glia-free axons ending in bulbous terminals containing lucent synaptic vesicles. The ligament comprises cylindrical bundles of collagen fibrils: one or more minute muscle fibers (paramyosin) lie parallel with and closely adjoining each bundle. The mean diameter of these muscles is 0.3 μg and they occupy 2–3 % of the ligament's cross-sectional area. Axons containing electronopaque secretory droplets accompany the muscles between the collagen bundles: the cell bodies of these neurones generally lie on the outer surface of the ligament. When an urchin points a spine, the ligament on the side of the contracting spine muscle shortens but does not buckle. A function of the intraligamental muscles is to effect this non-buckled shortening. The catch mechanism (which resides entirely within the ligament) may be due either to the intraligamental muscles and/or to a locked polymer mechanism in which matrix molecules between collagen fibrils are reversibly crosslinked by divalent cations.     

Deformation and stress distribution of the human foot after plantar ligaments release: A cadaveric study and finite element analysis

The majority of foot deformities are related to arch collapse or instability, especially the longitudinal arch. Although the relationship between the plantar fascia and arch height has been previously investigated, the stress distribution remains unclear. The aim of this study was to explore the role of the plantar ligaments in foot arch biomechanics. We constructed a geometrical detailed three-dimensional (3-D) finite element (FE) model of the human foot and ankle from computer tomography images. The model comprised the majority of joints in the foot as well as bone segments, major ligaments, and plantar soft tissue. Release of the plantar fascia and other ligaments was simulated to evaluate the corresponding biomechanical effects on load distribution of the bony and ligamentous structures. These intrinsic ligaments of the foot arch were sectioned to simulate different pathologic situations of injury to the plantar ligaments, and to explore bone segment displacement and stress distribution. The validity of the 3-D FE model was verified by comparing results with experimentally measured data via the displacement and von Mise stress of each bone segment. Plantar fascia release decreased arch height, but did not cause total collapse of the foot arch. The longitudinal foot arch was lost when all the four major plantar ligaments were sectioned simultaneously. Plantar fascia release was compromised by increased strain applied to the plantar ligaments and intensified stress in the midfoot and metatarsal bones. Load redistribution among the centralized metatarsal bones and focal stress relief at the calcaneal insertion were predicted. The 3-D FE model indicated that plantar fascia release may provide relief of focal stress and associated heel pain. However, these operative procedures may pose a risk to arch stability and clinically may produce dorsolateral midfoot pain. The initial strategy for treating plantar fasciitis should be non-operative.     

A failure model for ligaments

We propose a failure model for ligament which assumes that sequential uncrimping and stretching of collagen fibers is responsible for the mechanical response of ligament. We further assume that the fibers rupture sequentially and in a brittle, strain-limited manner. The model was fit to stress strain curves obtained from medial collateral ligaments of New Zealand White rabbits from two age groups (4 and 7 months). The model indicated that collagen modulus values ranged from 300 to 680 MPa and that fiber failure strains ranged from 6 to 22%. The model provides a convenient means of describing the elastic and failure response of ligament using four structurally based parameters.     

Immunohistochemical analysis of connective tissue in patients with pelvic organ prolapse

The uterosacral ligaments are an important part of the pelvic support system. The objective of this study was to compare the expression of collagen type I and collagen type III in the uterosacral ligament biopsies from women with and without pelvic organ prolapse (POP). The uterosacral ligament biopsies were obtained from women with POP (n = 29) and non-POP subjects (n = 35). Immunohistochemistry for collagen type I and collagen type III was performed on formalin-fixed and paraffin-embedded sections. The two groups were matched for age, body mass index, parity and postmenopausal status. The expression of collagen type I (p < 0.001) and collagen type III (p < 0.0001) differed between women with POP and non-POP subjects. There was decreased expression of collagen type I and increased expression of collagen type III in uterosacral ligaments of women with POP compared with non-POP subjects. This difference indicates a possible relationship between POP and the immunohistochemical expression of collagen type I and collagen type III in uterosacral ligaments.     

Avian-like tibiotarsi of pterodactyloids (Reptilia: Pterosauria) from the Upper Jurassic of East Africa

Tibiotarsi ofDsungaripterus?brancai (Reck) (Upper Jurassic, East Africa),D. weii Young (Lower Cretaceous, China) andPuntanipterus globosus Bonaparte & Sanchez (Lower Cretaceous, South America) have a bird-like distal end with attachment areas for a transverse ligament anteriorly, lateral and medial ligamentous prominences, and an anteroposteriorly, expanded pulley-like articular surface. The M. extensor digitorum longus flexed the ankle and probably also extended the digits as in living birds and mammals. A separate tendinous slip for digit I probably passed from the M. flexor digitorum longus in a groove posteroventral to the medial ligamentous prominence.     

Biomechanical study using fuzzy systems to quantify collagen fiber recruitment and predict creep of the rabbit medial collateral ligament

In normal daily activities, ligaments are subjected to repeated loads, and respond to this environment with creep and fatigue. While progressive recruitment of the collagen fibers is responsible for the toe region of the ligament stress-strain curve, recruitment also represents an elegant feature to help ligaments resist creep. The use of artificial intelligence techniques in computational modeling allows a large number of parameters and their interactions to be incorporated beyond the capacity of classical mathematical models. The objective of the work described here is to demonstrate a tool for modeling creep of the rabbit medial collateral ligament that can incorporate the different parameters while quantifying the effect of collagen fiber recruitment during creep. An intelligent algorithm was developed to predict ligament creep. The modeling is performed in two steps: first, the ill-defined fiber recruitment is quantified using the fuzzy logic. Second, this fiber recruitment is incorporated along with creep stress and creep time to model creep using an adaptive neurofuzzy inference system. The model was trained and tested using an experimental database including creep tests and crimp image analysis. The model confirms that quantification of fiber recruitment is important for accurate prediction of ligament creep behavior at physiological loads.     

带线锚钉修复三角韧带损伤的效果及对患者踝关节功能的影响

目的:研究带线锚钉修复三角韧带损伤在踝关节骨折内固定治疗中的作用及对踝关节功能的影响。方法:回顾性分析2012年9月至2016年8月本院收治的72例裸关节骨折并三角韧带损伤患者并且行切开复位钢板置入内固定,及采取带线锚钉内固定方式修复三角韧带损伤视为观察组;另选取同期在本院进行踝关节骨折内固定治疗但不修复三角韧带的72例患者视为对照组。分析患者治疗前、治疗后1个月、3个月、6个月踝关节功能恢复情况,观察患侧内踝间隙和不良反应。结果:观察组在治疗后1个月、3个月、6个月的AOFAS评分显著高于对照组(P0.05)。观察组在治疗后6个月后的患侧内踝间隙显著小于对照组(P0.05)。结论:带线锚钉修复三角韧带损伤在踝关节骨折内固定治疗中,可明显降低患侧内踝间隙距离,可促进患者踝关节功能恢复,无严重不良反应,值得进一步广泛推广使用。     

Structure-function relationship of human spinal ligaments

A combination of light, scanning and transmission electron microscopy was used to investigate the morphology and ultrastructure of normal human spinal ligaments sampled from adult surgical specimens. The ligamenta flava consist mostly of dense elastic fibers, whereas the supraspinous and interspinous ligaments are preponderantly collagenous. In all ligaments, the collagen fascicles are characterized by a regular crimp structure. The inner collagen fibers of interspinous ligaments tend to be oriented parallel to the spinous processes while those of the peripheral layers run in postero-cranial direction. The presence of proteoglycan filaments is clearly demonstrated in all of the ligaments examined. They are mainly located at the d band of the collagen fibrils. These findings are discussed in relation to the function of the posterior ligamentous system. It is suggested that the interspinous ligaments are able to transmit tension from the thoracolumbar fascia to the spine. Finally, the spinal ligaments are thought to be involved in the control mechanism of the spine.