Ahmet Erdemir

Dynamic Loading of the Plantar Aponeurosis in Walking

BACKGROUND The plantar aponeurosis is known to be a major contributor to arch support, but its role in transferring Achilles tendon loads to the forefoot remains poorly understood. The goal of this study was to increase our understanding of the function of the plantar aponeurosis during gait. We specifically examined the plantar aponeurosis force pattern and its relationship to Achilles tendon forces during simulations of the stance phase of gait in a cadaver model. METHODS Walking simulations were performed with seven cadaver feet. The movements of the foot and the ground reaction forces during the stance phase were reproduced by prescribing the kinematics of the proximal part of the tibia and applying forces to the tendons of extrinsic foot muscles. A fiberoptic cable was passed through the plantar aponeurosis perpendicular to its loading axis, and raw fiberoptic transducer output, tendon forces applied by the experimental setup, and ground reaction forces were simultaneously recorded during each simulation. A post-experiment calibration related fiberoptic output to plantar aponeurosis force, and linear regression analysis was used to characterize the relationship between Achilles tendon force and plantar aponeurosis tension. RESULTS Plantar aponeurosis forces gradually increased during stance and peaked in late stance. Maximum tension averaged 96% +/- 36% of body weight. There was a good correlation between plantar aponeurosis tension and Achilles tendon force (r = 0.76). CONCLUSIONS The plantar aponeurosis transmits large forces between the hindfoot and forefoot during the stance phase of gait. The varying pattern of plantar aponeurosis force and its relationship to Achilles tendon force demonstrates the importance of analyzing the function of the plantar aponeurosis throughout the stance phase of the gait cycle rather than in a static standing position. CLINICAL RELEVANCE The plantar aponeurosis plays an important role in transmitting Achilles tendon forces to the forefoot in the latter part of the stance phase of walking. Surgical procedures that require the release of this structure may disturb this mechanism and thus compromise efficient propulsion.

Considerations for reporting finite element analysis studies in biomechanics.

Simulation-based medicine and the development of complex computer models of biological structures is becoming ubiquitous for advancing biomedical engineering and clinical research. Finite element analysis (FEA) has been widely used in the last few decades to understand and predict biomechanical phenomena. Modeling and simulation approaches in biomechanics are highly interdisciplinary, involving novice and skilled developers in all areas of biomedical engineering and biology. While recent advances in model development and simulation platforms offer a wide range of tools to investigators, the decision making process during modeling and simulation has become more opaque. Hence, reliability of such models used for medical decision making and for driving multiscale analysis comes into question. Establishing guidelines for model development and dissemination is a daunting task, particularly with the complex and convoluted models used in FEA. Nonetheless, if better reporting can be established, researchers will have a better understanding of a models value and the potential for reusability through sharing will be bolstered. Thus, the goal of this document is to identify resources and considerate reporting parameters for FEA studies in biomechanics. These entail various levels of reporting parameters for model identification, model structure, simulation structure, verification, validation, and availability. While we recognize that it may not be possible to provide and detail all of the reporting considerations presented, it is possible to establish a level of confidence with selective use of these parameters. More detailed reporting, however, can establish an explicit outline of the decision-making process in simulation-based analysis for enhanced reproducibility, reusability, and sharing.

Peak Plantar Pressure and Shear Locations: Relevance to diabetic patients

Diabetic foot ulcers burden the U.S. health care system with an annual cost of approximately

Multiscale Mechanics of Articular Cartilage: Potentials and Challenges of Coupling Musculoskeletal, Joint, and Microscale Computational Models

6 billion (1). Based on the mechanical etiology of diabetic foot lesions, investigators tried to establish a relationship between ulcer occurrence and plantar pressures. Mostly, peak pressure has been chosen as an ulcer predictor. However, previous studies have yielded only moderate correlations between peak pressure and the occurrence of diabetic foot lesions (2–4). Surprisingly, in one study that examined whether plantar ulcer locations matched peak pressure sites (4), only 38% of the ulcers developed under the peak pressure area. Therefore, foot pressure was labeled as a “poor” predictor of diabetic ulcer occurrences and their location (3). Effectiveness of diabetic ulcer prediction and prevention depends on an understanding of plantar soft tissue mechanics and the complete nature of foot-ground interactions. Further investigation of plantar shear in addition to pressure is essential to minimize the neuropathic ulcer prevalence. The purpose of this study was to find whether the peak pressure and shear under the feet of diabetic patients occur at different locations. If confirmed, shear distribution may explain the deviation between peak pressure and ulcer locations and potentially help researchers design more effective interventions. Thirty volunteers were recruited, among whom 10 had diabetic neuropathy. The remaining nondiabetic subjects served as control subjects. Subjects with gross foot deformities (except minor toe clawing), prior foot surgeries, and …

Comparison of hexahedral and tetrahedral elements in finite element analysis of the foot and footwear

Articular cartilage experiences significant mechanical loads during daily activities. Healthy cartilage provides the capacity for load bearing and regulates the mechanobiological processes for tissue development, maintenance, and repair. Experimental studies at multiple scales have provided a fundamental understanding of macroscopic mechanical function, evaluation of the micromechanical environment of chondrocytes, and the foundations for mechanobiological response. In addition, computational models of cartilage have offered a concise description of experimental data at many spatial levels under healthy and diseased conditions, and have served to generate hypotheses for the mechanical and biological function. Further, modeling and simulation provides a platform for predictive risk assessment, management of dysfunction, as well as a means to relate multiple spatial scales. Simulation-based investigation of cartilage comes with many challenges including both the computational burden and often insufficient availability of data for model development and validation. This review outlines recent modeling and simulation approaches to understand cartilage function from a mechanical systems perspective, and illustrates pathways to associate mechanics with biological function. Computational representations at single scales are provided from the body down to the microstructure, along with attempts to explore multiscale mechanisms of load sharing that dictate the mechanical environment of the cartilage and chondrocytes.

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

Finite element analysis has been widely used in the field of foot and footwear biomechanics to determine plantar pressures as well as stresses and strains within soft tissue and footwear materials. When dealing with anatomical structures such as the foot, hexahedral mesh generation accounts for most of the model development time due to geometric complexities imposed by branching and embedded structures. Tetrahedral meshing, which can be more easily automated, has been the approach of choice to date in foot and footwear biomechanics. Here we use the nonlinear finite element program Abaqus (Simulia, Providence, RI) to examine the advantages and disadvantages of tetrahedral and hexahedral elements under compression and shear loading, material incompressibility, and frictional contact conditions, which are commonly seen in foot and footwear biomechanics. This study demonstrated that for a range of simulation conditions, hybrid hexahedral elements (Abaqus C3D8H) consistently performed well while hybrid linear tetrahedral elements (Abaqus C3D4H) performed poorly. On the other hand, enhanced quadratic tetrahedral elements with improved stress visualization (Abaqus C3D10I) performed as well as the hybrid hexahedral elements in terms of contact pressure and contact shear stress predictions. Although the enhanced quadratic tetrahedral element simulations were computationally expensive compared to hexahedral element simulations in both barefoot and footwear conditions, the enhanced quadratic tetrahedral element formulation seems to be very promising for foot and footwear applications as a result of decreased labor and expedited model development, all related to facilitated mesh generation.

Adaptive Surrogate Modeling for Efficient Coupling of Musculoskeletal Control and Tissue Deformation Models

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.

Finite element modeling of the first ray of the foot : A tool for the design of interventions

Finite element (FE) modeling and multibody dynamics have traditionally been applied separately to the domains of tissue mechanics and musculoskeletal movements, respectively. Simultaneous simulation of both domains is needed when interactions between tissue and movement are of interest, but this has remained largely impractical due to the high computational cost. Here we present a method for the concurrent simulation of tissue and movement, in which state of the art methods are used in each domain, and communication occurs via a surrogate modeling system based on locally weighted regression. The surrogate model only performs FE simulations when regression from previous results is not within a user-specified tolerance. For proof of concept and to illustrate feasibility, the methods were demonstrated on an optimization of jumping movement using a planar musculoskeletal model coupled to a FE model of the foot. To test the relative accuracy of the surrogate model outputs against those of the FE model, a single forward dynamics simulation was performed with FE calls at every integration step and compared with a corresponding simulation with the surrogate model included. Neural excitations obtained from the jump height optimization were used for this purpose and root mean square (RMS) difference between surrogate and FE model outputs (ankle force and moment, peak contact pressure and peak von Mises stress) were calculated. Optimization of the jump height required 1800 iterations of the movement simulation, each requiring thousands of time steps. The surrogate modeling system only used the FE model in 5% of time steps, i.e., a 95% reduction in computation time. Errors introduced by the surrogate model were less than 1 mm in jump height and RMS errors of less than 2 N in ground reaction force, 0.25 Nm in ankle moment, and 10 kPa in peak tissue stress. Adaptive surrogate modeling based on local regression allows efficient concurrent simulations of tissue mechanics and musculoskeletal movement.

The Biomechanical Relevance of Anterior Rotator Cuff Cable Tears in a Cadaveric Shoulder Model

Disorders of the first ray of the foot (defined as the hard and soft tissues of the first metatarsal, the sesamoids, and the phalanges of the great toe) are common, and therapeutic interventions to address these problems range from alterations in footwear to orthopedic surgery. Experimental verification of these procedures is often lacking, and thus, a computational modeling approach could provide a means to explore different interventional strategies. A three-dimensional finite element model of the first ray was developed for this purpose. A hexahedral mesh was constructed from magnetic resonance images of the right foot of a male subject. The soft tissue was assumed to be incompressible and hyperelastic, and the bones were modeled as rigid. Contact with friction between the foot and the floor or footwear was defined, and forces were applied to the base of the first metatarsal. Vertical force was extracted from experimental data, and a posterior force of 0.18 times the vertical force was assumed to represent loading at peak forefoot force in the late-stance phase of walking. The orientation of the model and joint configuration at that instant were obtained by minimizing the difference between model predicted and experimentally measured barefoot plantar pressures. The model were then oriented in a series of postures representative of push-off, and forces and joint moments were decreased to zero simultaneously. The pressure distribution underneath the first ray was obtained for each posture to illustrate changes under three case studies representing hallux limitus, surgical arthrodesis of the first ray, and a footwear intervention. Hallux limitus simulations showed that restriction of metatarsophalangeal joint dorsiflexion was directly related to increase and early occurrence of hallux pressures with severe immobility increasing the hallux pressures by as much as 223%. Modeling arthrodesis illustrated elevated hallux pressures when compared to barefoot and was dependent on fixation angles. One degree change in dorsiflexion and valgus fixation angles introduced approximate changes in peak hallux pressure by 95 and 22 kPa, respectively. Footwear simulations using flat insoles showed that using the given set of materials, reductions of at least 18% and 43% under metatarsal head and hallux, respectively, were possible.

Determination of elastomeric foam parameters for simulations of complex loading

BACKGROUND Anterior tears of the supraspinatus tendon are more likely to be clinically relevant than posterior tears of the supraspinatus. We hypothesized that anterior tears of the supraspinatus tendon involving the rotator cuff cable insertion are associated with greater tear gapping, decreased tendon stiffness, and increased regional tendon strain under physiologic loading conditions compared with equivalently sized tears of the rotator cuff crescent. METHODS Twelve human cadaveric shoulders were randomized to undergo simulation of equivalently sized supraspinatus tears of either the anterior rotator cuff cable (n = 6) or the adjacent rotator cuff crescent (n = 6). For each specimen, the supraspinatus tendon was cyclically loaded from 10 N to 180 N, and a custom three-dimensional optical system was used to track markers on the surface of the tendon. Tear gap distance, stiffness, and regional strains of the supraspinatus tendon were calculated. RESULTS The tear gap distance of large cable tears (median gap distance, 5.2 mm) was significantly greater than that of large crescent tears (median gap distance, 1.3 mm) (p = 0.002), the stiffness of tendons with a small (p = 0.002) or large (p = 0.002) cable tear was significantly greater than that of tendons with equivalently sized crescent tears, and regional strains across the supraspinatus were significantly increased in magnitude and altered in distribution by tears involving the anterior insertion of the rotator cuff cable. CONCLUSIONS These findings support our hypothesis that the rotator cuff cable, which is in the most anterior 8 to 12 mm of the supraspinatus tendon immediately posterior to the bicipital groove, is the primary load-bearing structure within the supraspinatus for force transmission to the proximal part of the humerus. Conversely, in the presence of an intact rotator cuff cable, the rotator cuff crescent insertion is relatively stress-shielded and plays a significantly lesser role in supraspinatus force transmission. CLINICAL RELEVANCE Clinicians should consider early repair of rotator cuff cable tears, which may need surgical intervention to address their biomechanical pathology. In contrast, surgical treatment may be more safely delayed for rotator cuff crescent tears.