INTRODUCTION: Coupling in the distal foot may be due, at least in part, to the foot's windlass mechanism. This mechanism has been demonstrated passively, but its role in dynamic movement is still unclear. A systematic manipulation of metatarsophalangeal (MTP) mechanics may help determine to what extent distal foot coupling during dynamic and active movement is due to the windlass mechanism versus active muscle contractions or springlike ligaments. Furthermore, exploring the windlass mechanism in feet with varying foot structure may aid our understanding of the relationship between foot structure and foot function. PURPOSE: The overall purpose of this study is to investigate the kinematic and kinetic coupling between the MTP and midtarsal joints through a systematic manipulation of the windlass mechanism (achieved through methodical changes to MTP motion). Additionally, we aimed to explore the relationship between foot structure and the efficacy of the windlass mechanism during passive, active, and dynamic movement. METHODS: First, arch height and flexibility were measured using the Arch Height Index Measurement System. Next, participants performed four order-randomized conditions where MTP extension was isolated: 1) Seated Passive MTP Extension, 2) Seated Active MTP Extension, 3) Standing Passive MTP Extension, and 4) Standing Active MTP Extension. Lastly, participants performed three heel raise conditions that manipulated the starting position of the MTP joint: 1) Neutral: normal heel raise, 2) ToeExt: heel raise with the toes placed on an inclined surface of 30 degrees to put the MTP joint into extension, and 3) ToeFlex: heel raise with the toes placed on a declined surface of 30 degrees to put the MTP joint into flexion. All conditions were performed to a metronome of 40 beats per minute to control angular velocity. A kinetic multisegment foot model was created in Visual 3D software and used to calculate ankle, midtarsal, and MTP joint angles, moments, powers, and work. RESULTS: Kinematic coupling was approximately six times greater in the heel raise conditions compared to the isolated MTP extension conditions and suggests that the windlass mechanism only plays a small role in dynamic tasks. This is likely due to the greater involvement of active muscle contractions during heel raises. As the starting position of the MTP joint became increasingly extended, the amount of negative work at the MTP joint increased concomitantly with increased positive work done at the midtarsal joint, while net distal-to-hindfoot work remained unchanged. Our combined results suggest that there is substantial coupling within the distal foot, but this coupling is likely attributed to more than simple passive energy transfer from the windlass mechanism. Future investigations into the intrinsic foot muscle activation and biarticular muscle effects are likely needed to determine the source of this coupling. Lastly, the relationship between foot structure and function is still unclear and our results suggest that arch height or arch flexibility alone may not be adequate predictors of dynamic foot function.

The contribution of the midfoot in landing mechanics is understudied. Therefore, the main purpose of this study was to quantify midtarsal joint kinematics and kinetics during a barefoot single-leg landing task. A secondary aim of this study was to explore the relationship between static foot posture and dynamic midfoot function. In a cross-sectional study design, 48 females (age = 20.4 ± 1.8 yr, height = 1.6 ± 0.06 m, weight = 57.3 ± 5.5 kg, BMI = 21.6 ± 1.7 kg·m-1) performed drop landings from a height of 0.4 m onto split force platforms. Subjects hung from wooden rings and landed on their dominant leg. Midtarsal joint kinematic and kinetic data were recorded using a motion capture software system in conjunction with a custom multisegment foot model marker set. Arch height index (AHI) for both seated and standing conditions was measured using the Arch Height Index Measurement System (AHIMS). Kinematic data revealed an average sagittal plane midtarsal range of motion (ROM) of 27 degrees through the landing phase. Kinetic data showed that between 7% and 22% of the total power absorption during the landing was performed by the midtarsal joint. Standing AHI was correlated negatively with sagittal plane midtarsal ROM (p = 0.0264) and positively with midtarsal work (p = 0.0212). Standing midfoot angle (MA) was correlated positively with sagittal plane midtarsal ROM (p = 0.0005) and negatively with midtarsal work (p = 0.0250). The midfoot contributes substantially to landing mechanics during a barefoot single-leg landing task. Static foot posture may be a valuable measurement in predicting midfoot kinematics and kinetics.

This Ph.D. dissertation focuses on a comprehensive study of seismic waveform similarity aiming at two themes: (1) reliable identification of repeating earthquakes (repeaters) and (2) investigation of the detailed source process of induced seismicity through the three-dimensional spatiotemporal evolution of mainly neighbouring earthquakes. Theme 1: Reliable identification of repeaters. Repeaters, occurring repeatedly on the same fault patch with nearly identical waveforms, are usually identified with the match-filtering (MF) method which essentially measures the degree of waveform similarity between an earthquake pair through the corresponding cross-correlation coefficient (CC). However, the performance of the MF method can be severely affected by the length of the cross‐correlation window, the frequency band of the applied digital filter, and the presence of a large‐amplitude wave train. To optimize the performance of MF, I first examine the effects of different operational parameters and determine generic rules for selecting the window length and the optimal frequency passband. To minimize the impact of a large‐amplitude wave train, I then develop a new method, named the match-filtering with multisegment cross-correlation (MFMC) method. By equally incorporating the contributions from various segments of the waveforms, the new method is much more effective in capturing the minor waveform discrepancy between an event pair due to location difference and hence is more reliable in detecting potential repeaters and discriminating non-repeaters with large inter-event separation. With both synthetic and borehole array waveform data, I further reveal that waveform similarity is controlled by not only the inter-event separation but also many other factors, including station azimuth, epicentral distance, velocity structure, etc. Therefore, in contrast to the traditional view, the results indicate that waveform similarity alone is insufficient to unambiguously identify true repeaters. For reliable repeater identification, we should rely on a physics-based approach considering both the overlapped source area and magnitude difference. Specifically, I define an event pair to be true repeaters if their inter-event separation is smaller than the rupture radius of the larger event and their magnitude difference is no more than 1. For the precise estimation of inter-event distance in cases of limited data, I develop the differential traveltime double-difference (DTDD) method which relies on the relative S-P differential traveltime. The findings of this study imply that previously identified repeaters and their interpretations/hypotheses potentially can be biased and hence may need a systematic reexamination. Theme 2: Investigation of the detailed source process of induced seismicity. Earthquakes induced by hydraulic fracturing (HF), especially those with large magnitudes, are often observed to have occurred near/after well completion. The delayed triggering of induced seismicity with respect to injection commencement poses serious challenges for risk mitigation and hazard assessment. By performing waveform cross-correlation and hierarchical clustering analysis, I reveal a high-resolution three-dimensional source migration process with mainshock delayed triggering that is probably controlled by local hydrogeological conditions. The results suggest that poroelastic effects might contribute to induced seismicity but are likely insufficient to activate a non-critically stressed fault of sufficient size. My analysis shows that the rapid pore-pressure build-up from HF can be very localized and capable of producing large, felt earthquakes on non-critically stressed fault segments. I further infer that the number of critically stressed, large intraplate faults should be very limited, and that reactivation of such faults may require sufficient pore-pressure accumulation. The findings of this study may also explain why so few fluid injections are seismogenic. / Graduate

In this study, anisotropic shells of revolution subject to symmetric and unsymmetrical static loads are analysed. In derivation of governing equations to be used in the solution, first order transverse shear effects are included in the formulation. The governing equations can be listed as kinematic equations, constitutive equations, and equations of motion. The equations of motion are derived from Hamilton&rsquo / s principle, the constitutive equations are developed under the assumptions of the classical lamination theory and the kinematic equations are based on the Reissner-Naghdi linear shell theory. In the solution method, these governing equations are manipulated and written as a set called fundamental set of equations. In order to handle anisotropy and first order transverse shear deformations, the fundamental set of equations is transformed into 20 first order ordinary differential equations using finite exponential Fourier decomposition and then solved with multisegment method of integration, after reduction of the two-point boundary value problem to a series of initial value problems. The results are compared with finite element analysis results for a number of sample cases and good agreement is found. Case studies are performed for circular cylindrical shell and truncated spherical shell geometries. While reviewing the results, effects of temperature and pressure loads, both constant and variable throughout the shell, are discussed. Some drawbacks of the first order transverse shear deformation theory are exhibited.