This thesis is missing page 33 and 98. Neither of which are in the other thesis copies. -Digitization Centre / N/A / Thesis / Master of Science (MS)

This work is concerned with a better understanding of the influences that sparse long-chain branching has on the rheological and processing behavior of commercial metallocene polyethylene (mPE) resins. In order to clarify these influences, a series of six commercial polyethylenes was investigated. Four of these resins are mPE resins having varying degrees of long-chain branching and narrow molecular weight distribution. The remaining two resins are deemed controls and include a highly branched low-density polyethylene and a linear low-density polyethylene. Together, the effects of long-chain branching are considered with respect to the shear and extensional rheological properties, the melt fracture behavior, and the ability to accurately predict the flow through an abrupt 4:1 contraction geometry. The effects that sparse long-chain branching (M_branch > M_c) has on the shear and extensional rheological properties are analyzed in two separate treatments. The first focuses on the shear rheological properties of linear, sparsely branched, and highly branched PE systems. By employing a time-molecular weight superposition principle, the effects of molecular weight on the shear rheological properties are factored out. The results show that as little as 0.6 LCB/10⁴ carbons (<1 LCB/molecule) significantly increases the zero-shear viscosity, reduces the onset of shear-thinning behavior, and increases elasticity at low deformation rates when compared to linear materials of equivalent molecular weight. Conversely, a high degree of long-chain branching ultimately reduces the zero-shear viscosity. The second treatment focuses on the relationship between long-chain branching and extensional strain-hardening behavior. In this study, the McLeish-Larson molecular constitutive model is employed to relate long-chain branching to rheological behavior. The results show that extensional strain hardening arises from the presence of LCB in polyethylene resins, and that the frequency of branching in sparsely branched metallocene polyethylenes dictates the degree of strain hardening. This observation for the metallocene polyethylenes agrees well with the proposed mechanism for polymerization. The presence of long-chain branching profoundly alters the melt fracture behavior of commercial polyethylene resins. Results obtained from a sparsely branched metallocene polyethylene show that as few as one long-chain branch per two molecules was found to mitigate oscillatory slip-stick fracture often observed in linear polyethylenes. Furthermore, the presence and severity of gross melt fracture was found to increase with long-chain branching content. These indirect effects were correlated to an early onset of shear-thinning behavior and extensional strain hardening, respectively. Conversely, linear resins exhibiting a delayed onset of shear-thinning behavior and extensional strain softening were found to manifest pronounced slip-stick fracture and less severe gross melt fracture. The occurrence of surface melt fracture appeared to correlate best with the degree of shear thinning arising from both molecular weight distribution and long-chain branching. The ability to predict the flow behavior of long-chain branched and linear polyethylene resins was also investigated. Using the benchmark 4:1 planar contraction geometry, pressure profile measurements and predictions were obtained for a linear and branched polyethylene. Two sets of finite element method (FEM) predictions were obtained using a viscoelastic Phan-Thien/Tanner (PTT) model and an inelastic Generalized Newtonian Fluid (GNF) model. The results show that the predicted profiles for the linear PE resin were consistently more accurate than those of the branched PE resin, all of which were within 15% of the measured vales. Furthermore, the differences in the predictions provided by the two constitutive models was found to vary by less than 5% over the range of numerical simulations obtained. In the case of the branched PE resin, this range was very narrow due to loss of convergence. It was determined that the small differences between the PTT and GNF predictions were the result of the small contraction ratio utilized and the long relaxation behavior of the branched PE resin, which obscured the influence of extensional strain hardening on the pressure predictions. Hence, it was expected that numerical simulations of the 4:1 planar contraction flow for the mildly strain hardening metallocene polyethylenes would not be fruitful. / Ph. D.

Force regulation at the level of the actin-myosin cross-bridge (XB) can be described by a 2 state model in which the XB's cycle between a strongly bound (SB), force generating state and a weakly bound (WB), non-force generating state. This cycle can be characterized by the apparent rate constants for transition into the SB state (fapp) and returning to the WB state (gapp), Increases in XB force can be accounted for by an increase in fapp a decrease in gapp., or both. While effort towards understanding XB force regulation has focused on the notion that force production is primarily regulated by fapp the purpose of this investigation was to determine if gapp continues to force regulation at the XB and to determine whether gapp differs in,muscles with differing contractile characteristics. / Ph. D.

Few studies have investigated the neuromuscular recruitment and stabilizing control of the spine during pushing and pulling exertions. Past theoretical investigation suggest that co-contraction of the of the paraspinal muscles is necessary to stabilize the spine during pushing exertions. We hypothesized greater levels of co-contraction during pushing exertions. Co-contraction of trunk musculature was quantified during isometric pushing and pulling tasks. The mean value of co-contraction during pushing was two-fold greater (p < 0.01) than during extension. Co-contraction has been shown to increase the stiffness of the ankle but this effect has not been demonstrated in the trunk. Trunk stiffness was measured as a function of co-activation during extension exertions. Results demonstrate trunk stiffness was significantly (p < 0.01) greater with co-activation. Trunk stiffness was calculated during isometric pushing and pulling exertions. We hypothesized trunk stiffness would be greater during pushing tasks due to increased levels of co-contraction to maintain stability of the spine. Results demonstrate trunk stiffness was significantly (p < 0.05) greater during pushing compared to pulling exertions. Results suggest that trunk isometric pushing tasks require more co-contraction than pulling tasks enable to maintain spinal stability. Greater levels of co-contraction during pushing exertions caused trunk stiffness to be greater during pushing compared to pulling tasks. Results may indicate greater risk of spinal instability from motor control error during pushing tasks than pulling exertions. Future studies need to consider co-contraction and neuromuscular control of spinal stability when evaluating the biomechanical risks of pushing and pulling tasks. / Master of Science

The SH3 and cysteine rich domain 3 (Stac3) gene is expressed specifically in skeletal muscle and essential for skeletal muscle contraction and postnatal life in mice. In this dissertation project, I conducted two studies to further understand the role of STAC3 in skeletal muscle development, growth, and contraction. In the first study, I compared the contractile responses of hindlimb muscles of Stac3 knockout and control mice to electrical stimulation, high [K+]-induced membrane depolarization, and caffeine and 4-chloro-m-cresol (4-CMC) activation of ryanodine receptor (RyR). Frequent electrostimulation-, high [K+]-, 4-CMC- and caffeine-induced maximal tensions in Stac3-deleted muscles were approximately 20%, 29%, 58% and 55% of those in control muscles, respectively. 4-CMC- and caffeine-induced increases in intracellular calcium were not different between Stac3-deleted and control myotubes. Myosin-ATPase and NADH-tetrazolium reductase staining as well as gene expression analyses revealed that Stac3-deleted hindlimb muscles contained more slow type-like fibers than control muscles. These data together confirm a role of STAC3 in EC coupling but also suggest that defective EC coupling is only partially responsible for the significantly reduced contractility in Stac3-deleted hindlimb muscles. In the second study, I determined the potential role of STAC3 in postnatal skeletal muscle growth, fiber composition, and contraction by disrupting Stac3 gene expression in postnatal mice through the Flp-FRT and tamoxifen-inducible Cre-loxP systems. Postnatal Stac3 deletion inhibited body and limb muscle mass gains. Histological staining and gene expression analyses revealed that postnatal Stac3 deletion decreased the size of myofibers and increased the percentage of myofibers containing centralized nuclei without affecting the total myofiber number. Postnatal Stac3 deletion decreased limb muscle strength. Postnatal Stac3 deletion reduced electrostimulation- but not caffeine-induced maximal force output in limb muscles. Similarly, postnatal Stac3 deletion reduced electrostimulation- but not caffeine-induced calcium release from the sarcoplasmic reticulum. These results demonstrate that STAC3 is important to myofiber hypertrophy, myofiber type composition, contraction, and EC coupling in postnatal skeletal muscle. / Ph. D.

The purpose of this research was to study the relationship between muscle coordination and the performance of a simple manual tracking task. The study employed an isometric, zero order, pursuit tracking task with a laterally translating, periodic sine wave forcing function. The speed of the target was varied by altering the Frequency (3 levels) of the simple sine wave. The control/response ratio for each trial was manipulated by requiring a percentage of each subject’s flexion and extension maximum voluntary contraction effort (MVC, 5 levels) to track the target. Multiple electromyograms (EMGs) of the biceps and triceps muscle groups were taken to observe flexor and extensor activity during the tracking task. Muscle modeling techniques were used to quantify the force contributions from the biceps and triceps to the observed tracking force. It was hypothesized that significant levels of co-active muscle effort would be present during the tracking task and that this co-contraction would have a unique characteristic function about the tracking conditions which yielded optimal tracking performance. The dependent measures investigated were the absolute tracking error as a proportion of the required tracking force (proportional error, PE), the absolute antagonist muscle force (AAF), and the ratio of antagonist to agonist force (co-contraction ratio, CR). Each muscle group’s maximum muscle force (MMF) required to track each condition was also determined. The experimental design was a 3 by 5 by 2 mixed factor, repeated measures ANOVA with Gender (5 male, 5 female) as the blocking variable. The ANOVA results revealed that both target Frequency and tracking Force level had significant effects on tracking error (PE). Orthogonal polynomial contrasts showed that the Frequency effect was characteristically linear while the Force effect was quadratic in nature. A polynomial regression function was used to predict PE from the Force and Frequency conditions. This model accounted for over 96% of the variance in the PE cell means. Further analysis revealed the optimal Force level for isometric tracking to be approximately 61% MVC. Analysis of the force contributions from each muscle group revealed quadratic relationships for the actual muscle force (%MMF) of the biceps during flexion and of the triceps during extension. These results show that optimal tracking performance during flexion occurs at approximately 66% of the biceps MMF and 65% of the triceps MMF during extension. Actual MMF values were consistently larger than net force values indicating that due to the presence of co-contraction, the measured force output at the wrist underestimated the actual muscle forces involved in tracking. Neither Force nor Frequency had significant effects on absolute co-activity (AAF) showing that antagonist activity remained largely constant over the tracking conditions. However, co-activity was higher for the extension phase than for the flexion phase of the task. Both Force and Frequency had significant effects on the co-contraction ratio (CR). However, no characteristic function of co-activity was found to explain the optimal tracking performance at median levels of flexion and extension force. CR increased with increasing target speed (Frequency) while it decreased with higher tracking Force levels. Since antagonist activity (AAF) remained almost constant, these results for CR must be due to changes in the level of agonist activity needed to perform the tracking task. Higher co-contraction was also found during decreasing force production (release) than for increasing force production (exertion). Since there was no significant difference in tracking error for these parts of the task, co-activity may serve to facilitate tracking performance by controlling the rate of force release. / Master of Science

The thesis consists of two parts. The first part discusses the initial value problem of a fifth-order Korteweg-de Vries type of equation w_t + w_xxx - w_xxxxx - ⁿ&#8721;_j=1 a_jw^jw_x = 0, w(x, 0) = w₀(x) posed on a periodic domain x &#8712; [0, 2&#960;] with boundary conditions w_ix(0, t) = w_ix(2&#960;, t), i = 0, 2, 3, 4 and an L²-stabilizing feedback control law w_x(2&#960;, t) = &#945;w_x(0, t) + (1 - &#945;)w_xxx(0; t) where n is a fixed positive integer, a_j, j = 1, 2, ... n, &#945; are real constants, and |&#945;| < 1. It is shown that for w₀(x) &#8712; H¹_&#945;(0, 2&#960;) with the boundary conditions described above, the problem is locally well-posed for w &#8712; C([0, T]; H¹_&#945;(0, 2&#960;)) with a conserved volume of w, [w] = &#8747;^2&#960;₀ w(x, t)dx. Moreover, the solution with small initial condition exists globally and approaches to [w₀(x)]/(2&#960;) as t &#8594; + &#8734;. The second part concerns wave motions on water in a rectangular basin with a wave generator mounted on a side wall. The linear governing equations are used and it is assumed that the surface tension on the free surface is not zero. Two types of generators are considered, flexible and rigid. For the flexible case, it is shown that the system is exactly controllable. For the rigid case, the system is not exactly controllable in a finite-time interval. However, it is approximately controllable. The stability problem of the system with the rigid generator controlled by a static feedback is also studied and it is proved that the system is strongly stable for this case. / Ph. D.

The dissertation focuses on the nonlinear Schrodinger equation iu_t+u_{xx}+kappa|u|^2u =0, for the complex-valued function u=u(x,t) with domain t>=0, 0<=x<= L, where the parameter kappa is any non-zero real number. It is shown that the problem is locally and globally well-posed for appropriate initial data and the solution exponentially decays to zero as t goes to infinity under the boundary conditions u(0,t) = beta u(L,t) and beta u_x(0,t)-u_x(L,t) = ialpha u(0,t), where L>0, and alpha and beta are any real numbers satisfying alpha*beta<0 and beta does not equal 1 or -1. Moreover, the numerical study of controllability problem for the nonlinear Schrodinger equations is given. It is proved that the finite-difference scheme for the linear Schrodinger equation is uniformly boundary controllable and the boundary controls converge as the step sizes approach to zero. It is then shown that the discrete version of the nonlinear case is boundary null-controllable by applying the fixed point method. From the new results, some open questions are presented. / Ph. D. / The dissertation concerns the solutions of nonlinear Schrodinger (NLS) equation, which arises in many applications of physics and applied mathematics and models the propagation of light waves in fiber optics cables, surface water-waves, Langmuir waves in a hot plasma, oceanic and optical rogue waves, etc. Under certain dissipative boundary conditions, it is shown that for given initial data, the solutions of NLS equation always exist for a finite time, and for small initial data, the solutions exist for all the time and decay exponentially to zero as time goes to infinity. Moreover, by applying a boundary control at one end of the boundary, it is shown using a finite-difference approximation scheme that the linear Schrodinger equation is uniformly controllable. It is proved using fixed point method that the discrete version of the NLS equation is also boundary controllable. The results obtained may be applicable to design boundary controls to eliminate unwanted waves generated by noises as well as create the wave propagation that is important in applications.

Chez les mammifères, le muscle squelettique constitue un tissu d'importance majeure dans la régulation du transport et du métabolisme du glucose durant l'exercice physique ou en période postprandiale. La captation musculaire de glucose induite par l'insuline et la contraction musculaire s'effectue grâce à la translocation des transporteurs de glucose GLUT4 à la membrane plasmique et aux tubules transversaux à partir d'un réservoir interne. La première partie des travaux constituant cette thèse a été effectuée dans le but de clarifier si l'insuline et la contraction musculaire activent la translocation de GLUT4 à partir de réservoirs internes distincts. Par fractionnement et immunoadsorption membranaire, nous avons démontré que la contraction musculaire recrutait GLUT4 à partir de deux compartiments distincts : un compartiment associé au récepteur de la transferrine sélectivement mobilisé à la membrane plasmique et insensible à l'insuline, et un second compartiment non associé à cette protéine recruté au niveau des tubules transversaux. / Cette étude a permis de déterminer que l'insuline et la contraction musculaire recrutaient GLUT4 à partir de réservoirs distincts et que la contraction musculaire induisait la translocation de GLUT4 à la surface cellulaire à partir d'au moins deux différentes populations de vésicules GLUT4.Les deux dernières parties des travaux faisant l'objet de cette thèse ont permis de déterminer l'implication de certains médiateurs intracellulaires dans la stimulation du transport du glucose induite par la contraction musculaire ou par le AICAR, un agent mimétique de la contraction. Tout d'abord, nos travaux ont révélé que l'infusion de AICAR induit sélectivement la translocation de GLUT4 à la membrane plasmique à partir d'un compartiment enrichi en récepteur de la transferrine. De plus, nous avons démontré que la stimulation du transport du glucose par le AICAR était dépendante de l'activation de la p38 MAPK, une kinase proposée comme agent régulateur de l'activité intrinsèque de GLUT4. / D'autre part, une dernière étude nous a permis de déterminer que le AICAR active spécifiquement le transport du glucose au niveau des muscles glycolytiques isolés et que le monoxyde d'azote n'est pas impliqué dans l'effet stimulateur du AICAR sur la captation du glucose au niveau de ce type de muscle. Toutefois, l'infusion de AICAR in vivo stimule le transport de glucose dans tous les types de fibres musculaires ainsi que la production de monoxyde d'azote. De plus, l'injection de AICAR stimule la phosphorylation et l'activation de eNOS, suggérant que l'activation du transport du glucose induite par le AICAR in vivo est dépendante de l'augmentation du flot sanguin via la production de monoxyde d'azote. Globalement, ces études nous ont permis de mieux comprendre les mécanismes intracellulaires par lesquels la contraction musculaire active le transport du glucose in vitro et in vivo dans le muscle squelettique.

La dystrophie musculaire de Duchenne est une dystrophie héréditaire secondaire à l’absence de la dystrophine, ce qui induit une faiblesse et une dégénérescence des muscles. Bien que plusieurs études ont démontré que la greffe de myoblastes permet de rétablir l’expression de la dystrophine, aucune étude physiologique n’a été réalisée, jusqu’à présent, pour démontrer qu’elle peut améliorer les propriétés contractiles du muscle. Dans ce travail, j’ai étudié l’effet de la greffe de myoblastes normaux sur les propriétés contractiles du muscle de la souris mdx, un modèle animal de la maladie de Duchenne. Mes travaux ont permis de démontrer que cette greffe protège le muscle mdx durant les contractions excentriques et que cet effet n’est pas expliqué seulement par l’expression de la dystrophine. En effet, l’étude des propriétés contractiles des muscles mdx transplantés avec des myoblastes mdx, montre que les muscles greffés sont aussi moins vulnérables aux contractions excentriques que les muscles mdx non greffés. / Duchenne muscular dystrophy is a hereditary dystrophy that results from a mutation of the dystrophin gene, which induces the weakness of muscles. Although several studies have already shown that the transplantation of normal myoblasts permit to restore the expression of dystrophin, no physiological study was made to verify whether myoblast transplantation is able to improve the muscle contractile properties. In this study, I have studied the effects of normal myoblast transplantation on the contractile properties of muscles of mdx mice, a model of Duchenne Muscular Dystrophy. My studies have shown that the transplantation of normal myoblasts protects mdx muscle from damage induced by eccentric contractions, and that this effect can not be explained only by the expression of dystrophin. Indeed, the comparison of mdx muscles transplanted with mdx myoblasts with non-transplanted muscles indicated that the transplanted muscles are more resistant to eccentric contractions than the non-transplanted ones.