Application of Fractional Calculus in the Dynamical Analysis and Control of Mechanical Manipulators

Mathematics Subject Classification: 26A33, 93C83, 93C85, 68T40

Fluid dynamics and platelet deposition in a model arterial stenosis

The objective of this study was to gain further understanding and elucidation of the fluid dynamic factors and flow-induced mechanisms of the thrombogenic process of platelet deposition onto, and possible subsequent embolization from, the walls of an arterial stenosis. This has been accomplished by measurement of the axial dependence of platelet deposition within a modeled arterial stenosis for a transitional flow and a completely laminar flow field. The stenotic region of the model was collagen-coated to simulate a damaged endothelial lining of an artery. Fluid dynamics within a stenosis was studied using qualitative flow visualization, and was further compared to the in vitro platelet deposition studies. Normalized platelet density (NPD) measurements indicate decreased levels of NPD in the high shear throat region of the stenosis for a Reynolds number of 300 and a drastic increase in NPD at the throat for a Reynolds number of 175. This study provides further understanding of the flow dynamic effects on thrombus development within a stenosis. ^

Dynamics of the Disk-Pendulum Coupled System With Vertical Excitation

This paper investigates the static and dynamic characteristics of the semi-elliptical rocking disk on which a pendulum pinned. This coupled system’s response is also analyzed analytically and numerically when a vertical harmonic excitation is applied to the bottom of the rocking disk. Lagrange’s Equation is used to derive the motion equations of the disk-pendulum coupled system. The second derivative test for the system’s potential energy shows how the location of the pendulum’s pivotal point affects the number and stability of equilibria, and the change of location presents different bifurcation diagrams for different geometries of the rocking disk. For both vertically excited and unforced cases, the coupled system shows chaos easily, but the proper chosen parameters can still help the system reach and keep the steady state. For the steady state of the vertically excited rocking disk without a pendulum, the variation of the excitation’s amplitude and frequency result in the hysteresis for the amplitude of the response. When a pendulum is pinned on the rocking disk, three major categories of steady states are presently in the numerical way.

Role of Vinculin in Regulating Force-Sensitive Dynamics of Adherens Junctions During Collective Cell Migration

Dynamic processes such as morphogenesis and tissue patterning require the precise control of many cellular processes, especially cell migration. Historically, these processes are thought to be mediated by genetic and biochemical signaling pathways. However, recent advances have unraveled a previously unappreciated role of mechanical forces in regulating these homeostatic processes in of multicellular systems. In multicellular systems cells adhere to both deformable extracellular matrix (ECM) and other cells, which are sources of applied forces and means of mechanical support. Cells detect and respond to these mechanical signals through a poorly understood process called mechanotransduction, which can have profound effects on processes such as cell migration. These effects are largely mediated by the sub cellular structures that link cells to the ECM, called focal adhesions (FAs), or cells to other cells, termed adherens junctions (AJs).

Overall this thesis is comprised of my work on identifying a novel force dependent function of vinculin, a protein which resides in both FAs and AJs - in dynamic process of collective migration. Using a collective migration assay as a model for collective cell behavior and a fluorescence resonance energy transfer (FRET) based molecular tension sensor for vinculin I demonstrated a spatial gradient of tension across vinculin in the direction of migration. To define this novel force-dependent role of vinculin in collective migration I took advantage of previously established shRNA based vinculin knock down Marin-Darby Canine Kidney (MDCK) epithelial cells.

The first part of my thesis comprises of my work demonstrating the mechanosensitive role of vinculin at AJ’s in collectively migrating cells. Using vinculin knockdown cells and vinculin mutants, which specifically disrupt vinculin’s ability to bind actin (VinI997A) or disrupt its ability to localize to AJs without affecting its localization at FAs (VinY822F), I establish a role of force across vinculin in E-cadherin internalization and clipping. Furthermore by measuring E-cadherin dynamics using fluorescence recovery after bleaching (FRAP) analysis I show that vinculin inhibition affects the turnover of E-cadherin at AJs. Together these data reveal a novel mechanosensitive role of vinculin in E-cadherin internalization and turnover in a migrating cell layer, which is contrary to the previously identified role of vinculin in potentiating E-cadherin junctions in a static monolayer.

For the last part of my thesis I designed a novel tension sensor to probe tension across N-cadherin (NTS). N-cadherin plays a critical role in cardiomyocytes, vascular smooth muscle cells, neurons and neural crest cells. Similar to E-cadherin, N-cadherin is also believed to bear tension and play a role in mechanotransduction pathways. To identify the role of tension across N-cadherin I designed a novel FRET-based molecular tension sensor for N-cadherin. I tested the ability of NTS to sense molecular tension in vascular smooth muscle cells, cardiomyocytes and cancer cells. Finally in collaboration with the Horwitz lab we have been able to show a role of tension across N-cadherin in synaptogenesis of neurons.

A predictive computational fluid dynamics study of carotid artery

Abstract not available

Apicomplexans pulling the strings: manipulation of the host cell cytoskeleton dynamics

Invasive stages of apicomplexan parasites require a host cell to survive, proliferate and advance to the next life cycle stage. Once invasion is achieved, apicomplexans interact closely with the host cell cytoskeleton, but in many cases the different species have evolved distinct mechanisms and pathways to modulate the structural organization of cytoskeletal filaments. The host cell cytoskeleton is a complex network, largely, but not exclusively, composed of microtubules, actin microfilaments and intermediate filaments, all of which are modulated by associated proteins, and it is involved in diverse functions including maintenance of cell morphology and mechanical support, migration, signal transduction, nutrient uptake, membrane and organelle trafficking and cell division. The ability of apicomplexans to modulate the cytoskeleton to their own advantage is clearly beneficial. We here review different aspects of the interactions of apicomplexans with the three main cytoskeletal filament types, provide information on the currently known parasite effector proteins and respective host cell targets involved, and how these interactions modulate the host cell physiology. Some of these findings could provide novel targets that could be exploited for the development of preventive and/or therapeutic strategies.

Effects of Drive Speed Modulation on Dynamics of Slender Rotating Structures

Slender rotating structures are used in many mechanical systems. These structures can suffer from undesired vibrations that can affect the components and safety of a system. Furthermore, since some these structures can operate in a harsh environment, installation and operation of sensors that are needed for closed-loop and collocated control schemes may not be feasible. Hence, the need for an open-loop non-collocated scheme for control of the dynamics of these structures. In this work, the effects of drive speed modulation on the dynamics of slender rotating structures are studied. Slender rotating structures are a type of mechanical rotating structures, whose length to diameter ratio is large. For these structures, the torsion mode natural frequencies can be low. In particular, for isotropic structures, the first few torsion mode frequencies can be of the same order as the first few bending mode frequencies. These situations can be conducive for energy transfer amongst bending and torsion modes. Scenarios with torsional vibrations experienced by rotating structures with continuous rotor-stator contact occur in many rotating mechanical systems. Drill strings used in the oil and gas industry are an example of rotating structures whose torsional vibrations can be deleterious to the components of the drilling system. As a novel approach to mitigate undesired vibrations, the effects of adding a sinusoidal excitation to the rotation speed of a drill string are studied. A portion of the drill string located within a borewell is considered and this rotating structure has been modeled as an extended Jeffcott rotor and a sinusoidal excitation has been added to the drive speed of the rotor. After constructing a three-degree-of-freedom model to capture lateral and torsional motions, the equations of motions are reduced to a single differential equation governing torsional vibrations during continuous stator contact. An approximate solution has been obtained by making use of the Method of Direct Partition of Motions with the governing torsional equation of motion. The results showed that for a rotor undergoing forward or backward whirling, the addition of sinusoidal excitation to the drive speed can cause an increase in the equivalent torsional stiffness, smooth the discontinuous friction force at contact, and reduce the regions of negative slope in the friction coefficient variation with respect to speed. Experiments with a scaled drill string apparatus have also been conducted and the experimental results show good agreement with the numerical results obtained from the developed models. These findings suggest that the extended Jeffcott rotordynamics model can be useful for studies of rotor dynamics in situations with continuous rotor-stator contact. Furthermore, the results obtained suggest that the drive speed modulation scheme can have value for attenuating drill-string vibrations.

Vortex Shedding Dynamics in Long Aspect-Ratio Aerodynamics Bodies

The focus of the current dissertation is to study qualitatively the underlying physics of vortex-shedding and wake dynamics in long aspect-ratio aerodynamics in incompressible viscous flow through the use of the KLE method. We carried out a long series of numerical experiments in the cases of flow around the cylinder at low Reynolds numbers. The study of flow at low Reynolds numbers provides an insight in the fluid physics and also plays a critical role when applying to stalled turbine rotors. Many of the conclusions about the qualitative nature of the physical mechanisms characterizing vortex formation, shedding and further interaction analyzed here at low Re could be extended to other Re regimes and help to understand the separation of the boundary layers in airfoils and other aerodynamic surfaces. In the long run, it aims to provide a better understanding of the complex multi-physics problems involving fluid-structure-control interaction through improved mathematical computational models of the multi-physics process. Besides the scientific conclusions produced, the research work on streamlined and bluff-body condition will also serve as a valuable guide for the future design of blade aerodynamics and the placement of wind turbines and hydrakinetic turbines, increasing the efficiency in the use of expensive workforce, supplies, and infrastructure. After the introductory section describing the main fields of application of wind power and hydrokinetic turbines, we describe the main features and theoretical background of the numerical method used here. Then, we present the analysis of the numerical experimentation results for the oscillatory regime right before the onset of vortex shedding for circular cylinders. We verified the wake length of the closed near-wake behind the cylinder and analysed the decay of the wake at the wake formation region, and then studied the St-Re relationship at the Reynolds numbers before the wake sheds compared to the experimental data. We found a theoretical model that describes the time evolution of the amplitude of fluctuations in the vorticity field on the twin vortex wake, which accurately matches the numerical results in terms of the frequency of the oscillation and rate of decay. We also proposed a model based on an analog circuit that is able to interpret the concerning flow by reducing the number of degrees of freedom. It follows the idea of the non-linear oscillator and resembles the dynamics mechanism of the closed near-wake with a common configured sine wave oscillator. This low-dimensional circuital model may also help to understand the underlying physical mechanisms, related to vorticity transport, that give origin to those oscillations.

The Crosslinking Degree Controls The Mechanical, Rheological, And Swelling Properties Of Hyaluronic Acid Microparticles.

Viscosupplements, used for treating joint and cartilage diseases, restore the rheological properties of synovial fluid, regulate joint homeostasis and act as scaffolds for cell growth and tissue regeneration. Most viscosupplements are hydrogels composed of hyaluronic acid (HA) microparticles suspended in fluid HA. These microparticles are crosslinked with chemicals to assure their stability against enzyme degradation and to prolong the action of the viscosupplement. However, the crosslinking also modifies the mechanical, swelling and rheological properties of the HA microparticle hydrogels, with consequences on the effectiveness of the application. The aim of this study is to correlate the crosslinking degree (CD) with these properties to achieve modulation of HA/DVS microparticles through CD control. Because divinyl sulfone (DVS) is the usual crosslinker of HA in viscosupplements, we examined the effects of CD by preparing HA microparticles at 1:1, 2:1, 3:1, and 5:1 HA/DVS mass ratios. The CD was calculated from inductively coupled plasma spectrometry data. HA microparticles were previously sized to a mean diameter of 87.5 µm. Higher CD increased the viscoelasticity and the extrusion force and reduced the swelling of the HA microparticle hydrogels, which also showed Newtonian pseudoplastic behavior and were classified as covalent weak. The hydrogels were not cytotoxic to fibroblasts according to an MTT (3-[4,5-dimethylthiazol-2-yl]-2,5-diphenyltetrazolium bromide) assay. © 2014 Wiley Periodicals, Inc. J Biomed Mater Res Part A, 2014.

Assessment Of The Fixation Of Mandibular Symphysis Fractures Using Conical Cannulated Screws: Mechanical And Photoelastic Tests.

The aim of this study was to use mechanical and photoelastic tests to compare the performance of cannulated screws with other fixation methods in mandibular symphysis fractures. Ten polyurethane mandibles were allocated to each group and fixed as follows: group PRP, 2 perpendicular miniplates; group PLL, 1 miniplate and 1 plate, parallel; and group CS, 2 cannulated screws. Vertical linear loading tests were performed. The differences between mean values were analyzed with the Tukey test. The photoelastic test was carried out using a polariscope. The results revealed differences between the CS and PRP groups at 1, 3, 5, and 10 millimeters of displacement. The photoelastic test confirmed higher stress concentration in all groups close to the mandibular base, whereas the CS group showed it throughout the region assessed. Conical cannulated screws performed well in mechanical and photoelastic tests.

Peripheral P2x7 Receptor-induced Mechanical Hyperalgesia Is Mediated By Bradykinin.

P2X7 receptors play an important role in inflammatory hyperalgesia, but the mechanisms involved in their hyperalgesic role are not completely understood. In this study, we hypothesized that P2X7 receptor activation induces mechanical hyperalgesia via the inflammatory mediators bradykinin, sympathomimetic amines, prostaglandin E2 (PGE2), and pro-inflammatory cytokines and via neutrophil migration in rats. We found that 2'(3')-O-(4-benzoylbenzoyl)adenosine 5'-triphosphate triethylammonium salt (BzATP), the most potent P2X7 receptor agonist available, induced a dose-dependent mechanical hyperalgesia that was blocked by the P2X7 receptor-selective antagonist A-438079 but unaffected by the P2X1,3,2/3 receptor antagonist TNP-ATP. These findings confirm that, although BzATP also acts at both P2X1 and P2X3 receptors, BzATP-induced hyperalgesia was mediated only by P2X7 receptor activation. Co-administration of selective antagonists of bradykinin B1 (Des-Arg(8)-Leu(9)-BK (DALBK)) or B2 receptors (bradyzide), β1 (atenolol) or β2 adrenoceptors (ICI 118,551), or local pre-treatment with the cyclooxygenase inhibitor indomethacin or the nonspecific selectin inhibitor fucoidan each significantly reduced BzATP-induced mechanical hyperalgesia in the rat hind paw. BzATP also induced the release of the pro-inflammatory cytokines tumor necrosis factor α (TNF-α), interleukin (IL)-1β, IL-6 and cytokine-induced neutrophil chemoattractant-1 (CINC-1), an effect that was significantly reduced by A-438079. Co-administration of DALBK or bradyzide with BzATP significantly reduced BzATP-induced IL-1β and CINC-1 release. These results indicate that peripheral P2X7 receptor activation induces mechanical hyperalgesia via inflammatory mediators, especially bradykinin, which may contribute to pro-inflammatory cytokine release. These pro-inflammatory cytokines in turn may mediate the contributions of PGE2, sympathomimetic amines and neutrophil migration to the mechanical hyperalgesia induced by local P2X7 receptor activation.

Influence Of Fluorescent Dye On Physical-mechanical Properties Of Luting Cements For Confocal Microscopy Analysis.

To evaluate the influence of a fluorescent dye (rhodamine B) on the physical and mechanical properties of three different luting cements: a conventional adhesive luting cement (RelyX ARC, 3M/ESPE), a self-adhesive luting cement (RelyX U-200, 3M/ESPE), and a self-etching and self-adhesive luting cement (SeT PP, SDI). The cements were mixed with 0.03 wt% rhodamine B, formed into bar-shaped specimens (n = 10), and light cured using an LED curing unit (Radii, SDI) with a radiant exposure of 32 J/cm(2) . The Knoop hardness (KHN), flexural strength (FS), and Young's modulus (YM) analyses were evaluated after storage for 24 h. Outcomes were subjected to two-way ANOVA and Tukey's test (P = 0.05) for multiple comparisons. No significant differences in FS or YM were observed among the tested groups (P ≥ 0.05); the addition of rhodamine B increased the hardness of the luting cements tested. The addition of a fluorescent agent at 0.03 wt% concentration does not negatively affect the physical-mechanical properties of the luting cement polymerization behavior.

Interplay Between Cell Growth And Cell Cycle In Plants.

The growth of organs and whole plants depends on both cell growth and cell-cycle progression, but the interaction between both processes is poorly understood. In plants, the balance between growth and cell-cycle progression requires coordinated regulation of four different processes: macromolecular synthesis (cytoplasmic growth), turgor-driven cell-wall extension, mitotic cycle, and endocycle. Potential feedbacks between these processes include a cell-size checkpoint operating before DNA synthesis and a link between DNA contents and maximum cell size. In addition, key intercellular signals and growth regulatory genes appear to target at the same time cell-cycle and cell-growth functions. For example, auxin, gibberellin, and brassinosteroid all have parallel links to cell-cycle progression (through S-phase Cyclin D-CDK and the anaphase-promoting complex) and cell-wall functions (through cell-wall extensibility or microtubule dynamics). Another intercellular signal mediated by microtubule dynamics is the mechanical stress caused by growth of interconnected cells. Superimposed on developmental controls, sugar signalling through the TOR pathway has recently emerged as a central control point linking cytoplasmic growth, cell-cycle and cell-wall functions. Recent progress in quantitative imaging and computational modelling will facilitate analysis of the multiple interconnections between plant cell growth and cell cycle and ultimately will be required for the predictive manipulation of plant growth.

Obesity Versus Osteoarthritis: Beyond The Mechanical Overload.

Obesity is currently considered a major public health problem in the world, already reaching epidemic characteristics, according to the World Health Organization. Excess weight is the major risk factor associated with various diseases, such as type 2 diabetes mellitus, hypertension, dyslipidemia and osteometabolic diseases, including osteoporosis and osteoarthritis. Osteoarthritis is the most prevalent rheumatic disease and the leading cause of physical disability and reduced quality of life of the population over 65 years. It mainly involves the joints that bear weight - knees and hips. However, along with the cases of obesity, its prevalence is increasing, and even in other joints, such as hands. Thus, it is assumed that the influence of obesity on the development of OA is beyond mechanical overload. The purpose of this review was to correlate the possible mechanisms underlying the genesis and development of these two diseases. Increased fat mass is directly proportional to excessive consumption of saturated fatty acids, responsible for systemic low-grade inflammation condition and insulin and leptin resistance. At high levels, leptin assumes inflammatory characteristics and acts in the articular cartilage, triggering the inflammatory process and changing homeostasis this tissue with consequent degeneration. We conclude that obesity is a risk factor for osteoarthritis and that physical activity and changes in diet composition can reverse the inflammatory and leptin resistance, reducing progression or preventing the onset of osteoarthritis.

Site Specific Spin Dynamics In Bafe2as2: Tuning The Ground State By Orbital Differentiation.

The role of orbital differentiation on the emergence of superconductivity in the Fe-based superconductors remains an open question to the scientific community. In this investigation, we employ a suitable microscopic spin probe technique, namely Electron Spin Resonance (ESR), to investigate this issue on selected chemically substituted BaFe2As2 single crystals. As the spin-density wave (SDW) phase is suppressed, we observe a clear increase of the Fe 3d bands anisotropy along with their localization at the FeAs plane. Such an increase of the planar orbital content is interestingly independent of the chemical substitution responsible for suppressing the SDW phase. As a consequence, the magnetic fluctuations in combination with this particular symmetry of the Fe 3d bands are propitious ingredients for the emergence of superconductivity in this class of materials.