In clinical settings, dynamic foot function is commonly inferred from static and passive foot measurements; however, there is little evidence that static foot structure can predict dynamic foot function during walking gait. Previous research seeking to find correlations between the two have focused primarily on sagittal plane midfoot angles even though the midfoot has triplanar motion, which misses potentially important information. Additionally, the focus on kinematics alone may miss the contributions that forces play in midfoot mechanics. To address the angle limitations, a novel Signed Helical Angle (SHA) was developed to capture the triplanar motion of the midfoot from a multi-segment foot model. This was combined with foot segmental force measurements and inverse dynamics to capture dynamic midfoot stiffness. The SHA method and static-dynamic analysis were evaluated on 40 healthy subjects walking at a controlled speed. Subjects were divided into three structural groups based on static arch height (high, normal, low) and stiffness (stiff, normal, flexible). One-way ANOVA was used to evaluate differences among groups in dynamic motion and stiffness and a multiple regression was employed to evaluate relationships across the sample. Calculating the SHA resulted in a greater range of motion (ROM) compared to the sagittal Euler angle commonly used, showing that the motion in the other planes are captured in the SHA. The Finite Helical Axis (FHAx) associated with the SHA also showed that on average the population had a clear distinction between pronation and supination during the stance phase, although individual subjects exhibited substantial variability. While there were visual distinctions in the SHA and the midfoot stiffness among the three stiffness groups and the three arch height groups, the differences were not statistically significant. The only measurement achieving statistical significance was the mean of the sagittal plane midfoot Euler angles among the three AHI groups (p = 0.015); however, this is a postural measure which simply confirms that a high arch will remain high and a low arch will remain low throughout the gait cycle. The lack of any relationships between static foot structure and dynamic foot function, despite advanced modeling and measurements, further confirms that other factors play a large role in foot mechanics. Future studies should focus on evaluating the role of the intrinsic foot musculature (e.g., muscle strength, activation, and redundancy) during gait, and replacing traditional shoe and orthotic recommendations.

Due to the similar nature 3D synthetics share with in vivo cell conditions, peptide-based hydrogels pose an attractive strategy for the culturing of stem cells. One aspect of this unique cell culturing technique is the tunability of the hydrogel’s stiffness, a quality linked to stem cell differentiation. Due to this linkage, a methodology in which specific cell lineages are achieved within IIFK hydrogel cultures is proposed. This work provides an analysis for the peptide scaffold IIFK; it characterizes the effect between different peptide and PBS concentrations over the resulting hydrogel stiffness and develops a mathematical model to further elucidate this interaction. Nine different hydrogel formulations were made (with a minimum of eleven replicates each) and each of its replicate’s stiffness (storage modulus, Pa) was measured through rheological experiments. Then, two different methods of replicate selection were conducted and various models were derived, each using either of the two replicate selection methods and incorporating a specific number of replicates in their creation. Regardless of sample selection and replicate number, the generated models show extremely high significances between IIFK hydrogel stiffness and PBS concentrations over the resulting hydrogel stiffness. Data analysis shows that for IIFK, the hydrogel stiffness bears a strong behavior that can be modeled by a full quadratic equation. However, the data also shows that the dependency of the model is strongly correlated with the datasets chosen to produce it, with number of replicates and replicate values both resulting in differences in each model’s predictive reliability (e.g., 82% vs 91%). Therefore, while this thesis demonstrates the ability to model IIFK hydrogel behaviour with high predictability ratings, it also establishes the necessity of both producing more replicates as well as selecting the best values for IIFK-based hydrogel modelling.

<p> A Matrix Stiffness-Modification Technique has been proposed for the inelastic analysis of ·reinforced concrete frames subjected to short term or sustained loads. To check the applicability of the analytical method, two large scale concrete frames were tested under short-term loads and sustained-loads respectively. In addition, data for twenty-two frame tests from other sources has also been compared with the non-linear analysis. Close agreement has. been observed for all the frames considered. It was further concluded that a conventional elastic matrix method using stiffnesses based on a cracked transformed section of concrete does net yield accurate results, especially in the case of sustained loading conditions. From the method developed, comments can therefore be made on present column design practice. </p> / Thesis / Master of Engineering (MEngr)

Explicit methods are widely used in finite element analysis as efficient ways to solve differential equations. The efficiency of explicit methods relies on the economical evaluation of internal forces at each time step. The greatest efficiency can be provided by one-point quadrature. However, instability arises because of the shortcomings in the use of one-point quadrature. The instability is called hourglass mode, or spurious singular mode. An effective method to control the instability is to add “hourglass stiffness” to an element integrated by one-point quadrature. Explicit methods often require a very small time step to ensure stability. Thus, for complex problem with refined meshes, a very large number of timesteps will be required to complete the analysis. Minimizing the number of operations per time step can provide significant improvement on efficiency of the methods. Since hourglass terms typically require more computational operations than one-point quadrature terms, we are very interested in reducing the number of operations on hourglass control. In addition, considerable approximation is involved with hourglass control, and hence overall accuracy may not be seriously affected by relaxing the precision of the temporal integration of the hourglass force. Consequently, there is a possibility of trading some accuracy of the hourglass control for computational efficiency. A subcycling approach is applied to the hourglass portion of explicit methods. Namely, instead of updating hourglass forces every time step, we update hourglass forces every two steps. The proposed approach is examined with the use of mass-spring models. The applicability to more complex models is demonstrated on a 3-D model with the subcycling approach implemented into an explicit finite element code. Efficiency, stability and accuracy are discussed as important issues of the proposed approach. The mass-spring models and finite element implementation show that a beating instability can be introduced by the subcycling approach, and additional restriction is placed on the stable time step for the central difference operator. However, sufficient damping can restore the usual stability conditions. Thus, the proposed subcycling approach is seen to be highly advantageous where damping can be used, and it can cut computation time by 30% or more without significantly affecting the overall accuracy of the solution. / Thesis / Master of Applied Science (MASc)

The growing demand for compact and compliant mobility assistive devices has driven interest in low-profile actuating technologies. With the increasing mobility needs of an aging population, such devices could meet this growing market if they can provide low power capabilities, high strength, and compatibility with standard industrial fabrication processes. As a result, researchers have been investigating smart materials, such as carbon nanotube (CNT) and their higher-order structures, as potential components for soft actuator systems. However, reported works using this material within actuators have remained limited due to the material's prohibitive cost and fabrication complexity. Furthermore, presented actuator designs are difficult to compare due to custom fabrication procedures and inconsistent characterizations. The recent availability of commercial higher-order CNT products and the superior material consistency they provide present an opportunity to comprehensively analyze these materials in actuators without the challenges faced in previous work. This thesis addressed this opportunity by evaluating a stiffness-variable actuator design leveraging a commercially available CNT fibre. The evaluation focused on the effects on the mechanical and electrical properties in addition to its electrothermal and electromechanical responses when changing selected actuator design and operational parameters. The findings highlight the importance of optimal coating and embedded pre-stretch to achieve optimal contractile stress and contractile strain performance, while increased fibre diameter diminishes these properties. Furthermore, the usage of commercial CNT yarn ensured consistent mechanical and electrical properties during the fabrication and testing of actuator prototypes. This in-depth understanding of this actuator design's strengths, weaknesses, and the influence of selected operational and design parameters on performance establishes a foundation for future CNT-based actuator research within a repeatable framework.

Actin is a highly abundant protein in most eukaryotic cells. The assembly of actin monomers to double helical filaments is crucial for many cellular functions, including cell movement and cell division. Actin filament assembly in cells occurs in a crowded intracellular environment consisting of various molecules, including cations and organic osmolytes. Recent studies show that cation binding stiffens actin filaments, and a small organic osmolyte trimethylamine-N-oxide (TMAO) modulates filament assembly. However, how cations and TMAO combined affect actin filament mechanics is not understood. We hypothesize that depending on the concentrations of cations and osmolytes, there will be different effects on the stiffness and assembly of actin filaments. In this study, using TIRF we evaluate actin filament mechanics and assembly. Our findings indicate that when TMAO is present alone, it can increase the elongation rate and stiffness of actin filaments, however the inclusion of potassium levels alongside TMAO reduces the persistence length of actin filaments, suggesting a decrease in filament stiffness compared to the influence of TMAO alone. Furthermore, the elongation rate of actin filaments decreases when both TMAO and potassium ions are present. This study will help us better understand how cations and osmolytes together can affect actin filament mechanics in the living cells.

Breast cancer metastasis to the brain is one of the most lethal forms of metastases. Metastasis is regarded as a non-random process governed by several biomechanical factors including tissue stiffness. As brain tissue is ultrasoft and extremely heterogeneous compared to breast cancer primary sites; how are breast cancer cells able to colonize the vastly different microenvironment of the brain? As a key protein of the Hippo pathway, YAP is regarded as a mechanotransducer that is sensitive to changes in substrate stiffness. Its biochemical activity is intertwined with Piezo1, a mechanosensitive ion channel activated through plasma membrane deformation. To impact cellular function, YAP enters the nucleus and binds to the TEAD transcription domain triggering downstream expression of proteins involved in cell motility, wound healing, and metastasis. In this work, triple-negative breast cancers (TNBC) were shown to experience greater migration rates on stiff surfaces compared to soft PDMS substrates. Concurrently, cells showed YAP nuclear localization in a stiffness dependent manner. Then, mechanical characterization of human brain tissue was performed to characterize the stiffness heterogeneity in the brain associated with region specific metastasis. Five to six regions of the brain from two different patients showed similar patterns of stiffness heterogeneity with the anterior regions being generally stiffer than posterior regions. As Piezo1 is directly linked with detecting changes in biomechanical stimuli, it was used as a readout of surface stiffness to examine if cells in the brain could detect different regional stiffnesses. Comparisons of grey and white matter showed no significant difference in Piezo1 expression. As a drug screening framework, molecular dynamic simulations were performed to evaluate drug efficacy on well-characterized inflammatory mediators that are implicated in metastasis. These findings contribute to understanding the gap in knowledge surrounding the interplay between tissue stiffness and YAP mechanotransduction in the context of breast-to-brain metastasis. / Thesis / Master of Applied Science (MASc) / Breast cancer is the most common cause of cancer related deaths in women particularly when it spreads to the brain. The brain is composed of many different sub-locations comprised of different proteins that can change the tissue’s stiffness. Breast cancer can detect these changes and become more aggressive in its growth using a combination of proteins such as yes associated protein (YAP) and Piezo1. How these proteins interact in the context of breast to brain cancer metastasis however is poorly understood. This project examined the effects of surface stiffness, on YAP, and Piezo1 activity to understand how breast cancer and brain cells react to changes in surface stiffness. Results showed that on stiff surfaces YAP activity affects cancer cell migration. Also, human brain tissue was found to vary in stiffness depending on the region examined. Future investigations may shed light on therapies that could take advantage of learnings in this area to better target the spread of breast cancer.

The dynamic properties of the elastic coupling are not readily known; therefore testing has to be performed in order to determine these properties. This is the primary objective for this thesis. The dynamic properties in question are the stiffness and damping. An attempt to determine the dynamic properties was also be carried out through the use of finite element analysis. There are two different configurations of couplings. One configuration forms the coupling from several elastic elements, referred to as HRC elements, which are manufactured in three sizes: A, B, and C. The second configuration, referred to as the HEMD coupling, has a single elastic member in the form of a hollow rubber/fabric ring connecting the input to the output. The couplings have cords made of either polyester or nylon. These cords will affect the dynamic properties of the coupling.

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