Concurrent musculoskeletal dynamics and finite element analysis predicts altered gait patterns to reduce foot tissue loading

Current computational methods for simulating locomotion have primarily used muscle-driven multibody dynamics, in which neuromuscular control is optimized. Such simulations generally represent joints and soft tissue as simple kinematic or elastic elements for computational efficiency. These assumptions limit application in studies such as ligament injury or osteoarthritis, where local tissue loading must be predicted. Conversely, tissue can be simulated using the finite element method with assumed or measured boundary conditions, but this does not represent the effects of whole body dynamics and neuromuscular control. Coupling the two domains would overcome these limitations and allow prediction of movement strategies guided by tissue stresses. Here we demonstrate this concept in a gait simulation where a musculoskeletal model is coupled to a finite element representation of the foot. Predictive simulations incorporated peak plantar tissue deformation into the objective of the movement optimization, as well as terms to track normative gait data and minimize fatigue. Two optimizations were performed, first without the strain minimization term and second with the term. Convergence to realistic gait patterns was achieved with the second optimization realizing a 44% reduction in peak tissue strain energy density. The study demonstrated that it is possible to alter computationally predicted neuromuscular control to minimize tissue strain while including desired kinematic and muscular behavior. Future work should include experimental validation before application of the methodology to patient care.     

A multi-segment kinematic model of the foot with a novel definition of forefoot motion for use in clinical gait analysis during walking

A multi-segment kinematic model of the foot was developed for use in a gait analysis laboratory. The foot was divided into hindfoot, talus, midfoot and medial and lateral forefoot segments. Six functional joints were defined: ankle and subtalar joints, frontal and transverse plane motions of the hindfoot relative to midfoot, supination/pronation twist of the forefoot relative to midfoot and medial longitudinal arch height-to-length ratio. Twelve asymptomatic subjects were tested during barefoot walking with a six-camera optical stereometric system and auto-reflective markers organized in triads. Repeatability of the joint motions was tested using coefficients of multiple correlation. Ankle and subtalar joint motions and twisting of the forefoot were most repeatable. Hindfoot motions were least repeatable both within-subjects and between-subjects. Hindfoot and forefoot pronation in the frontal plane was found to coincide with dropping of the medial longitudinal arch between early to mid-stance, followed by supination and rising of the arch in late stance and swing phase. This multi-segment foot model addresses an unfortunate shortcoming in current gait analysis practice-the inability to measure motion within the foot. Such measurements are crucial if gait analysis is to remain relevant in the orthopaedic and rehabilitative treatment of the foot and ankle.     

A mathematical musculoskeletal shoulder model for proactive ergonomic analysis

Occupational shoulder musculoskeletal injuries and disorders are common. Generally available shoulder work analysis tools do not offer insight into specific muscle load magnitudes that may indicate increased risk, nor do they address many concerns germane to job analysis. To address these issues, a biomechanical model of the shoulder was developed to include several critical components: the systematic inclusion of kinematic and kinetic effects, population scalability, geometric realism, an empirical glenohumeral constraint, and integration with digital ergonomics analysis software tools. This unique combination of features in a single model was explored through examination of both experimental and simulated data with the developed analysis tool. The utility of the model is discussed together with a review of its specific strengths and weaknesses, and the potential for its future use in proactive ergonomic analyses and workplace simulations.     

3D finite element model of the diabetic neuropathic foot: A gait analysis driven approach

Diabetic foot is an invalidating complication of diabetes that can lead to foot ulcers. Three-dimensional (3D) finite element analysis (FEA) allows characterizing the loads developed in the different anatomical structures of the foot in dynamic conditions. The aim of this study was to develop a subject specific 3D foot FE model (FEM) of a diabetic neuropathic (DNS) and a healthy (HS) subject, whose subject specificity can be found in term of foot geometry and boundary conditions. Kinematics, kinetics and plantar pressure (PP) data were extracted from the gait analysis trials of the two subjects with this purpose. The FEM were developed segmenting bones, cartilage and skin from MRI and drawing a horizontal plate as ground support. Materials properties were adopted from previous literature. FE simulations were run with the kinematics and kinetics data of four different phases of the stance phase of gait (heel strike, loading response, midstance and push off). FEMs were then driven by group gait data of 10 neuropathic and 10 healthy subjects. Model validation focused on agreement between FEM-simulated and experimental PP.     

Biomechanical analysis of the three-dimensional foot structure during gait: a basic tool for clinical applications

A novel three-dimensional numerical model of the foot, incorporating, for the first time in the literature, realistic geometric and material properties of both skeletal and soft tissue components of the foot, was developed for biomechanical analysis of its structural behavior during gait. A system of experimental methods, integrating the optical Contact Pressure Display (CPD) method for plantar pressure measurements and a Digital Radiographic Fluoroscopy (DRF) instrument for acquisition of skeletal motion during gait, was also developed in this study and subsequently used to build the foot model and validate its predictions. Using a Finite Element solver, the stress distribution within the foot structure was obtained and regions of elevated stresses for six subphases of the stance (initial-contact, heel-strike, midstance, forefoot-contact, push-off, and toe-off) were located. For each of these subphases, the model was adapted according to the corresponding fluoroscopic data, skeletal dynamics, and active muscle force loading. Validation of the stress state was achieved by comparing model predictions of contact stress distribution with respective CPD measurements. The presently developed measurement and numerical analysis tools open new approaches for clinical applications, from simulation of the development mechanisms of common foot disorders to pre- and post-interventional evaluation of their treatment.     

A generic analytical foot rollover model for predicting translational ankle kinematics in gait simulation studies

The objective of this paper is to develop an analytical framework to representing the ankle–foot kinematics by modelling the foot as a rollover rocker, which cannot only be used as a generic tool for general gait simulation but also allows for case-specific modelling if required. Previously, the rollover models used in gait simulation have often been based on specific functions that have usually been of a simple form. In contrast, the analytical model described here is in a general form that the effective foot rollover shape can be represented by any polar function ρ=ρ(φ). Furthermore, a normalized generic foot rollover model has been established based on a normative foot rollover shape dataset of 12 normal healthy subjects. To evaluate model accuracy, the predicted ankle motions and the centre of pressure (CoP) were compared with measurement data for both subject-specific and general cases. The results demonstrated that the ankle joint motions in both vertical and horizontal directions (relative RMSE ～10%) and CoP (relative RMSE ～15% for most of the subjects) are accurately predicted over most of the stance phase (from 10% to 90% of stance). However, we found that the foot cannot be very accurately represented by a rollover model just after heel strike (HS) and just before toe off (TO), probably due to shear deformation of foot plantar tissues (ankle motion can occur without any foot rotation). The proposed foot rollover model can be used in both inverse and forward dynamics gait simulation studies and may also find applications in rehabilitation engineering.     

Reflections on clinical gait analysis

Clinical gait analysis allows the measurement and assessment of walking biomechanics, which facilitates the identification of abnormal characteristics and the recommendation of treatment alternatives. The predominant methods for this analysis currently include the tracking of external markers placed on the patient, the monitoring of patient/ground interaction (e.g. ground reaction forces), and the recording of muscle electromyographic (EMG) activity, all during gait. These data allow the computation of stride and temporal parameters, joint/segment kinematics, joint kinetics, and EMG plots that are used to gain a better understanding of a patient's walking difficulties. Gait interpretation involves a systemic evaluation of each of these types of data, noting both corroborating and conflicting information while identifying functionally significant deviations from the normal. Understanding the etiology of these abnormalities allows the formulation of a treatment plan that may involve physical therapy, bracing, and/or surgery. This process is challenging because of the complexity of the motion, neuromuscular involvement of the patient (e.g. dynamic spasticity), variability of treatment outcome, and on occasion, uncertainty about the quality of the gait data. The experience of the interpretation team with respect to gait biomechanics, a particular patient population, and the effectiveness of different treatment modalities is the principal determinant of the success of this approach. The clinical gait analysis process continues to evolve positively. It has become more comprehensive and meaningful because of an improved understanding of normal gait biomechanics and more rigorous data collection/reduction protocols that complement accumulated clinically relevant experience.     

A musculoskeletal model customized for squatting task

Most musculoskeletal models (MSKM) are designed to evaluate gait and running, which have limited range of motion (ROM). The purpose of this study was to examine the effect of wrapping surfaces (WS) at the knee and hip joints in a MSKM, on the muscle moment arms (MA) and activations during squatting. The MSKM was then customized by changing parameters of the original WS and by implementing additional WS. The WS prevent muscles from crossing into the bones, providing realistic muscle MA for large ROM. The modified MSKM is suitable for analysis up to 138° hip and 145° knee flexions.     

Kinematic analysis of a multi-segment foot model for research and clinical applications: a repeatability analysis

An unbiased understanding of foot kinematics has been difficult to achieve due to the complexity of foot structure and motion. We have developed a protocol for evaluation of foot kinematics during barefoot walking based on a multi-segment foot model. Stereophotogrammetry was used to measure retroreflective markers on three segments of the foot plus the tibia. Repeatability was evaluated between-trial, between-day and between-tester using two subjects and two testers. Subtle patterns and ranges of motion between segments of the foot were consistently detected. We found that repeatability between different days or different testers is primarily subject to variability of marker placement more than inter-tester variability or skin movement. Differences between inter-segment angle curves primarily represent a shift in the absolute value of joint angles from one set of trials to another. In the hallux, variability was greater than desired due to vibration of the marker array used. The method permits objective foot measurement in gait analysis using skin-mounted markers. Quantitative and objective characterisation of the kinematics of the foot during activity is an important area of clinical and research evaluation. With this work we hope to have provided a firm basis for a common protocol for in vivo foot study.     

Biped gait stabilization via foot placement

It is shown that stable biped gaits can be achieved by discrete foot placement based on feedback of information available at the time of foot placement. The model, developed by Townsend (1981, J. Biomechanics 14, p. 727) to evaluate the coordinations of torso motions, subsumes most of the salient body members and motions. The modeling yielded a generalized inverted pendulum with a movable support point which physically defines lateral foot placement. The principal result is that stable gaits can be defined by foot placements which are a linear function of the system center of mass position and velocity at the time of foot placement (only). Gaits may be 'smooth' or may have impulsive corrections to adjust the character of the motions and foot placement. Several general algorithms and specific simulations are presented, and calculations for non-impulsive gaits and impulsive corrections are presented. The model predictions are compared with published data. The predictions are sufficiently close to the data such that the general algorithms appear to be validated. Of particular interest are the non-sinusoidal character of the motions and the relatively simple algorithms. Indeed, the simplicity of the algorithms suggests the practical possibility of legged mobile robots. Accordingly, further investigation seems warranted for determining the parametric variation and control of gait. Some attention is also given to continuous-feedback control such as would exist during double-leg support and in specialized tasks such as rope walking or skating. Subsequent investigation will consider superposition of single and double leg support, although clearly the discrete gaits pose the more restrictive stability problem.     

A conductive rubber footswitch design for gait analysis

The performance of a footswitch which uses conductive rubber modules in foam, sandwiched between two brass shims in the form of an inner sole placed between the foot and the shoe is reported. Contact switching force decreases with module density, whilst position of the conductivity plugs in the footswitch is irrelevant. Comments on the construction of a footswich using these modules are made, in particular no modification of the conductive rubber is needed and a density throughout greater than 4 modules per square inch leads to threshold switch forces of 30 N and less which is totally acceptable for gait analysis use without fears of contact being made whilst inserting and positioned in the subject's shoe.     

A smart device inertial-sensing method for gait analysis

The purpose of this study was to establish and cross-validate a method for analyzing gait patterns determined by the center of mass (COM) through inertial sensors embedded in smart devices. The method employed an extended Kalman filter in conjunction with a quaternion rotation matrix approach to transform accelerations from the object onto the global frame. Derived by double integration, peak-to-trough changes in vertical COM position captured by a motion capture system, inertial measurement unit, and smart device were compared in terms of averaged and individual steps. The inter-rater reliability and levels of agreement for systems were discerned through intraclass correlation coefficients (ICC) and Bland–Altman plots. ICCs corresponding to inter-rater reliability were good-to-excellent for position data (ICCs,.80–.95) and acceleration data (ICCs,.54–.81). Levels of agreements were moderate for position data (LOA, 3.1–19.3%) and poor for acceleration data (LOA, 6.8%–17.8%). The Bland–Altman plots, however, revealed a small systematic error, in which peak-to-trough changes in vertical COM position were underestimated by 2.2 mm; the Kalman filter?s accuracy requires further investigation to minimize this oversight. More importantly, however, the study?s preliminary results indicate that the smart device allows for reliable COM measurements, opening up a cost-effective, user-friendly, and popular solution for remotely monitoring movement. The long-term impact of the smart device method on patient rehabilitation and therapy cannot be underestimated: not only could healthcare expenditures be curbed (smart devices being more affordable than today‘s motion sensors), but a more refined grasp of individual functioning, activity, and participation within everyday life could be attained.     

Free microvascular muscle flaps with skin graft reconstruction of extensive defects of the foot: a clinical and gait analysis study

Over the past 4 years at the Massachusetts General Hospital 18 patients have been treated for extensive defects (mean size 130 cm2) of the foot at or below the medial and lateral malleoli. These patients have been treated with free muscle flaps covered with thick split-thickness skin grafts. Full muscle flap survival has been seen in each patient, and all patients are currently ambulatory. A subgroup of nine patients are weight-bearing directly upon their skin grafts covering transferred muscle. All patients are walking without chronic breakdown over a mean follow-up of over 19 months with the exception of a single patient who has had breakdown in a region of redundant improperly tailored muscle flap. None of the skin grafted muscles has significant cutaneous sensibility. Detailed gait analysis of these patients has confirmed the weight-bearing capabilities of free muscle flaps with skin grafts and has proven to be an excellent method of foot reconstruction evaluation. It would appear from this study that cutaneous sensibility may not be necessary for successful reconstruction of the weight-bearing surface of the foot. This method of reconstruction should be considered when local tissues are not suitable for plantar foot reconstruction.     

A biomechanical model of the foot

The foot is modeled as a statically indeterminate structure supporting its load at the heads of the five metatarsals and the tuberosity of the calcaneous. The distribution of support is determined through an analysis of the deformations caused in the structure as a result of the forces at these locations. The analysis includes the effect of the plantar aponeurosis and takes into account the deformation of the metatarsals and bending of the joints. A parametric study is presented to illustrate the behavior of the solution under a broad range of conditions.     

Musculotendon parameters and musculoskeletal pathways within the human foot

In order to create a flexible model of the foot for dynamic musculoskeletal models, anthropometric data combined with geometric information describing the intrinsic musculature are needed. In this study, the left feet of two male and two female cadavers were dissected to expose the intrinsic musculotendon pathways. Three-dimensional coordinates of bony landmarks, tendon origins, insertions, and via points were digitized to submillimeter accuracy. Muscle architectural parameters were also measured, including volume, weight, and pennation angle and sarcomere, fascicle, and free tendon lengths. Optimal muscle fascicle lengths, pen-nation angles at optimal length, physiological cross-sectional areas (PCSA), and tendon slack lengths were calculated from the directly measured values. Fascicle length and pennation angle varied greatly within each subject. Average fascicle lengths normalized by optimal fascicle length varied between 0.73 and 1.25, with 75% of the formalin-preserved muscles being found in a shortened state. The muscle volume and PCSA also had a large variability within subjects but less variation between subjects. The ratio of tendon slack length to optimal fascicle length was found to vary between 1.05 and 9.56. Using this data, a deformable model of the foot can now be created. It is envisioned that deformable feet will significantly improve stability and realism in models of gait, posture, and sporting activities.     

In vivo gait analysis in a mouse femur fracture model

Although the mouse has become a preferred species for molecular studies on fracture healing, gait analysis after fracture fixation and during bone healing has not yet been performed in mice. Herein, we introduce a novel technique for gait analysis in mice and report the change of motion pattern after fracture and fixation. A standardized femur fracture was stabilized by a common pin. The non-fractured tibia was additionally marked with a pin, allowing continuous analysis of the tibio-femoral angle by digital video-radiography. Dynamic gait analysis was performed at day fourteen after surgery in a radio-opaque running wheel. Fracture fixation resulted in a significantly reduced range and maximum of the tibio-femoral angle compared to non-fractured controls. This was associated with a significantly reduced stride length. Because stride frequency was slightly increased and, thus, stride time diminished, stride velocity was not significantly reduced compared to controls. Thus, our study demonstrates distinct alterations of the gait of mice at 2 weeks after femur fracture and stabilization. Our results support the need of gait analysis in fracture healing studies to assess the animals’ well-being.     

A model to predict canine pelvic limb musculoskeletal geometry

We developed a model to predict the three-dimensional canine pelvic limb muscular geometry (i.e., all muscle moment arms during any instant in gait). Forty-one muscle origins and insertions, as well as external landmarks (to obtain anthropometric dimensions) were marked on both pelvic limbs of five dogs and digitized on biplanar radiographs. Reference frames in the pelvis, femur, and tibia established the three-dimensional coordinates of each origin, insertion, and landmark. A set of dimensionless 'scaled coordinates' was created by dividing the actual origin and insertion coordinates by selected anthropometric dimensions of each animal. Combining scaled coordinates from all ten limbs produced an averaged 'template' of scaled coordinates. To provide limited validation of the scaling procedure, we measured the anthropometric dimensions between externally palpable landmarks of two additional pelvic limbs. The anthropometric dimensions were multiplied by the averaged template coordinates to calculate two new sets of hindlimb muscle coordinates within the three bony reference frames. The two limbs then were dissected, muscle endpoints were marked, and biplanar radiographs of each of the limb segments were digitized. The actual coordinates so obtained were similar to those predicted by the template and anthropometric measures.     

An ultrasound based non-invasive method for the measurement of intrinsic foot kinematics during gait

Soft tissue artefact (STA) and marker placement variability are sources of error when measuring the intrinsic kinematics of the foot. This study aims to demonstrate a non-invasive, combined ultrasound and motion capture (US/MC) technique to directly measure foot skeletal motion. The novel approach is compared to a standard motion capture protocol. Fourteen participants underwent instrumented barefoot analysis of foot motion during gait. Markers were attached to foot allowing medial longitudinal arch angle and navicular height to be determined. For the US/MC technique, the navicular marker was replaced by an ultrasound transducer which was secured to the foot allowing the skeletal landmark to be imaged. Ultrasound cineloops showing the location of the navicular tuberosity during the walking trials were synchronised with motion capture measurements and markers mounted on the probe allowed the true position of the bony landmark to be determined throughout stance phase. Two discrete variables, minimum navicular height and maximum MLA angle, were compared between the standard and US/MC protocols. Significant differences between minimum navicular height (P=0.004, 95% CI (1.57, 6.54)) and maximum medial longitudinal arch angle (P=0.0034, 95% CI (13.8, 3.4)) were found between the measurement methods. The individual effects of STA and marker placement error were also assessed. US/MC is a non-invasive technique which may help to provide more accurate measurements of intrinsic foot kinematics.     

A closed-loop cadaveric foot and ankle loading model

Investigations of human foot and ankle biomechanics rely chiefly on cadaver experiments. The application of proper force magnitudes to the cadaver foot and ankle is essential to obtain valid biomechanical data. Data for external ground reaction forces are readily available from human motion analysis. However, determining appropriate forces for extrinsic foot and ankle muscles is more problematic. A common approach is the estimation of forces from muscle physiological cross-sectional areas and electromyographic data. We have developed a novel approach for loading the Achilles and posterior tibialis tendons that does not prescribe predetermined muscle forces. For our loading model, these muscle forces are determined experimentally using independent plantarflexion and inversion angle feedback control. The independent (input) parameters -- calcaneus plantarflexion, calcaneus inversion, ground reaction forces, and peroneus forces -- are specified. The dependent (output) parameters -- Achilles force, posterior tibialis force, joint motion, and spring ligament strain -- are functions of the independent parameters and the kinematics of the foot and ankle. We have investigated the performance of our model for a single, clinically relevant event during the gait cycle. The instantaneous external forces and foot orientation determined from human subjects in a motion analysis laboratory were simulated in vitro using closed-loop feedback control. Compared to muscle force estimates based on physiological cross-sectional area data and EMG activity at 40% of the gait cycle, the posterior tibialis force and Achilles force required when using position feedback control were greater.