Subject-specific material properties of the heel pad: An inverse finite element analysis.

Individuals with diabetes are at a higher risk of developing foot ulcers. To better understand internal soft tissue loading and potential treatment options, subject-specific finite element (FE) foot models have been used. However, existing models typically lack subject-specific soft tissue material properties and only utilize subject-specific anatomy. Therefore, this study determined subject-specific hindfoot soft tissue material properties from one non-diabetic and one diabetic subject using inverse FE analysis. Each subject underwent cyclic MRI experiments to simulate physiological gait and to obtain compressive force and three-dimensional soft tissue imaging data at 16 phases along the loading-unloading cycles. The FE models consisted of rigid bones and nearly-incompressible first-order Ogden hyperelastic skin, fat, and muscle (resulting in six independent material parameters). Then, calcaneus and loading platen kinematics were computed from imaging data and prescribed to the FE model. Two analyses were performed for each subject. First, the skin, fat, and muscle layers were lumped into a single generic soft tissue material and optimized to the platen force. Second, the skin, fat, and muscle material properties were individually determined by simultaneously optimizing for platen force, muscle vertical displacement, and skin mediolateral bulging. Our results indicated that compared to the individual without diabetes, the individual with diabetes had stiffer generic soft tissue behavior at high strain and that the only substantially stiffer multi-material layer was fat tissue. Thus, we suggest that this protocol serves as a guideline for exploring differences in non-diabetic and diabetic soft tissue material properties in a larger population.

Regional differences in the mechanical properties of the plantar aponeurosis.

The plantar aponeurosis functions to support the foot arch during weight bearing. Accurate anatomy and material properties are critical in developing analytical and computational models of this tissue. We determined the cross-sectional areas and material properties of four regions of the plantar aponeurosis: the proximal middle and distal middle portions of the tissue and the medial (to the first ray) and lateral (to the fifth ray) regions. Bone-plantar aponeurosis-bone specimens were harvested from fifteen cadaveric feet. Cross-sectional areas were measured using molding, casting, and sectioning methods. Mechanical testing was performed using displacement control triangle waves (0.5, 1, 2, 5, and 10 Hz) loaded to physiologic tension by estimating from body weight and area ratio of the region. Five specimens were tested for each region. Regional deformations were recorded by a high-speed video camera. There were overall differences in cross-sectional areas and biomechanical behavior across regions. The stress-strain responses are non-linear and mainly elastic (energy loss 3.6% to 7.2%). Moduli at the proximal middle and distal middle regions (400 and 522 MPa) were significantly higher than the medial and lateral regions (225 and 242 MPa). The effect of frequency on biomechanical outcomes was small (e.g., 3.5% change in modulus), except for energy loss (107% increase as frequency increased from 0.5 to 10 Hz). These results indicate that the plantar aponeurosis tensile response is non-linear, nearly elastic, and frequency independent. The cross-sectional area and material properties differ by region, and we suggest that such differences be included to accurately model this structure.

A preliminary study of patient-specific mechanical properties of diabetic and healthy plantar soft tissue from gated magnetic resonance imaging.

Foot loading rate, load magnitude, and the presence of diseases such as diabetes can all affect the mechanical properties of the plantar soft tissues of the human foot. The hydraulic plantar soft tissue reducer instrument was designed to gain insight into which variables are the most significant in determining these properties. It was used with gated magnetic resonance imaging to capture three-dimensional images of feet under dynamic loading conditions. Custom electronics controlled by LabVIEW software simultaneously recorded system pressure, which was then translated to applied force values based on calibration curves. Data were collected for two subjects, one without diabetes (Subject A) and one with diabetes (Subject B). For a 0.2-Hz loading rate, and strains 0.16, 0.18, 0.20, and 0.22, Subject A's average tangential heel pad stiffness was 10 N/mm and Subject B's was 24 N/mm. Maximum test loads were approximately 200 N. Loading rate and load magnitude limitations (both were lower than physiologic values) will continue to be addressed in the next version of the instrument. However, the current hydraulic plantar soft tissue reducer did produce a data set for healthy versus diabetic tissue stiffness that agrees with previous trends. These data are also being used to improve finite element analysis models of the foot as part of a related project.

Hyperelastic compressive mechanical properties of the subcalcaneal soft tissue: An inverse finite element analysis.

Finite element (FE) foot models can provide insight into soft tissue internal stresses and allow researchers to effectively conduct parametric analyses. Accurate plantar soft tissue material properties are essential for the development of FE foot models for clinical interventions. The aim of this study was to identify the first-order and second-order Ogden hyperelastic material properties of the subcalcaneal fat using an inverse FE analysis. The cylindrical soft tissue FE model was developed based on a priori in vitro dynamic compression experiment. The model simulated a 1Hz triangle wave displacement to apply a compressive strain up to 48%. The hyperelastic properties were identified by systematically varying the material parameters to minimize the difference between the model predicted force and the target experimental data. Optimal material properties were obtained (µ1=0.0235kPa and α1=12.07 for the first-order Ogden model and µ1=-4.629×10(-6)kPa, α1=-16.829; µ2=-1.613kPa and α2=-1.043 for the second-order Ogden model). The second-order Ogden model was superior in capturing the highly nonlinear force-deformation response when compared to the first-order model (root mean square error (RMSE) 0.169N vs. 0.570N). The material sensitivity analysis indicated that the predicted force was strongly affected by the Poisson׳s ratio (12-fold increase in RMSE when reducing Poisson׳s ratio by 10% from the baseline) and the coefficient α1 (3.2-fold and 32-fold increase in RMSE for both first-order and second-order Ogden models when increasing α1 by 10% from the optimal value).

The design and validation of a magnetic resonance imaging-compatible device for obtaining mechanical properties of plantar soft tissue via gated acquisition.

Changes in the mechanical properties of the plantar soft tissue in people with diabetes may contribute to the formation of plantar ulcers. Such ulcers have been shown to be in the causal pathway for lower extremity amputation. The hydraulic plantar soft tissue reducer (HyPSTER) was designed to measure in vivo, rate-dependent plantar soft tissue compressive force and three-dimensional deformations to help understand, predict, and prevent ulcer formation. These patient-specific values can then be used in an inverse finite element analysis to determine tissue moduli, and subsequently used in a foot model to show regions of high stress under a wide variety of loading conditions. The HyPSTER uses an actuator to drive a magnetic resonance imaging-compatible hydraulic loading platform. Pressure and actuator position were synchronized with gated magnetic resonance imaging acquisition. Achievable loading rates were slower than those found in normal walking because of a water-hammer effect (pressure wave ringing) in the hydraulic system when the actuator direction was changed rapidly. The subsequent verification tests were, therefore, performed at 0.2 Hz. The unloaded displacement accuracy of the system was within 0.31%. Compliance, presumably in the system's plastic components, caused a displacement loss of 5.7 mm during a 20-mm actuator test at 1354 N. This was accounted for with a target to actual calibration curve. The positional accuracy of the HyPSTER during loaded displacement verification tests from 3 to 9 mm against a silicone backstop was 95.9% with a precision of 98.7%. The HyPSTER generated minimal artifact in the magnetic resonance imaging scanner. Careful analysis of the synchronization of the HyPSTER and the magnetic resonance imaging scanner was performed. With some limitations, the HyPSTER provided key functionality in measuring dynamic, patient-specific plantar soft tissue mechanical properties.

Evaluation of fracture resistance and failure risks of posterior partial coverage restorations.

STATEMENT OF PROBLEM: Interest in posterior partial coverage restorations has increased because these restorations provide a more conservative treatment option than traditional cohesively based restorations; however, material selection has been a controversial topic in the current literature. PURPOSE: To evaluate the fracture resistance of posterior partial coverage restorations restored with different materials, examine their stress distribution, and calculate failure risks using three-dimensional (3D) finite element analysis. METHODS: Sixty extracted third molar teeth received 2-mm occlusal reduction maintaining cusp steepness of 45 degrees relative to occlusal surface. Teeth were allocated into four groups (N = 15) and restored with different materials: feldspathic ceramic, leucite-reinforced ceramic, lithium disilicate-reinforced ceramic (EMX), or indirect resin-based composite (COM). Restorations were luted with resin cement and submitted to compressive loads (Instron Corp, Norwood, MA, USA). The data were analyzed with one-way analysis of variance, followed by Tukey's HSD tests. A 3D finite element model of posterior partial coverage restorations was developed and validated. The model was used to approximate the maximum principal stress in each of the materials under a 100-N static vertical compression at the occlusal surface of the tooth. The risk of restoration failure was quantified and compared among the four different materials. RESULTS: Group EMX had fracture resistance significantly higher than other testing groups. Group COM presented the most extensive fractures involving tooth and root structures. When compared with the other materials, group EMX exhibited higher stress concentration; however, the failure risk of the restoration was lower. CONCLUSIONS: Fracture resistance and failure risks of posterior partial coverage restorations are significantly influenced by material selection. CLINICAL SIGNIFICANCE: Many restorative materials have been advocated for partial coverage restorations. It is essential to ensure that restorative materials have sufficient strength to support occlusal forces and, in case of fracture, the remaining tooth structure is not compromised or placed at risk. This study revealed that all-ceramic materials had high incidences of fractures involving the materials themselves, whereas the predominant failure of resin-based composite involved the tooth structure in a catastrophic manner.

Finite element analysis of the foot: model validation and comparison between two common treatments of the clawed hallux deformity.

BACKGROUND: Clawed hallux is defined by first metatarsophalangeal joint extension and first interphalangeal joint flexion; it can increase plantar pressures and ulceration risk. We investigated two corrective surgical techniques, the modified Jones and flexor hallucis longus tendon transfer. METHODS: A finite element foot model was modified to generate muscle overpulls, including extensor hallucis longus, flexor hallucis longus and peroneus longus. Both corrective procedures were simulated, predicting joint angle and plantar pressure changes. FINDINGS: The clawed hallux deformity was generated by overpulling: 1) extensor hallucis longus, 2) peroneus longus + extensor hallucis longus, 3) extensor hallucis longus + flexor hallucis longus and 4) all three together. The modified Jones reduced metatarsophalangeal joint angles, but acceptable hallux pressure was found only when there was no flexor hallucis longus overpull. The flexor hallucis longus tendon transfer reduced deformity at the metatarsophalangeal and interphalangeal joints but may extended the hallux due to the unopposed extensor hallucis longus. Additionally, metatarsal head pressure increased with overpulling of the extensor hallucis longus + flexor hallucis longus, and all three muscles together. INTERPRETATION: The modified Jones was effective in correcting clawed hallux deformity involving extensor hallucis longus overpull without flexor hallucis longus overpull. The flexor hallucis longus tendon transfer was effective in correcting clawed hallux deformity resulting from the combined overpull of both extensor and flexor hallucis longus, but not with isolated extensor hallucis longus overpull. An additional procedure to reduce the metatarsal head pressure may be required concomitant to the flexor hallucis longus tendon transfer. However this procedure avoids interphalangeal joint fusion.