On local analysis of oscillations of a non-ideal and non-linear mechanical model

It is of major importance to consider non-ideal energy sources in engineering problems. They act on an oscillating system and at the same time experience a reciprocal action from the system. Here, a non-ideal system is studied. In this system, the interaction between source energy and motion is accomplished through a special kind of friction. Results about the stability and instability of the equilibrium point of this system are obtained. Moreover, its bifurcation curves are determined. Hopf bifurcations are found in the set of parameters of the oscillating system.

Reversible equivariant Hopf bifurcation

In this paper we study codimension-one Hopf bifurcation from symmetric equilibrium points in reversible equivariant vector fields. Such bifurcations are characterized by a doubly degenerate pair of purely imaginary eigenvalues of the linearization of the vector field at the equilibrium point. The eigenvalue movements near such a degeneracy typically follow one of three scenarios: splitting (from two pairs of imaginary eigenvalues to a quadruplet on the complex plane), passing (on the imaginary axis), or crossing (a quadruplet crossing the imaginary axis). We give a complete description of the behaviour of reversible periodic orbits in the vicinity of such a bifurcation point. For non-reversible periodic solutions. in the case of Hopf bifurcation with crossing eigenvalues. we obtain a generalization of the equivariant Hopf Theorem.

On bifurcation and symmetry of solutions of symmetric nonlinear equations with odd-harmonic forcings

In this work we study existence, bifurcation, and symmetries of small solutions of the nonlinear equation Lx = N(x, p, epsilon) + mu f, which is supposed to be equivariant under the action of a group OHm, and where f is supposed to be OHm-invariant. We assume that L is a linear operator and N(., p, epsilon) is a nonlinear operator, both defined in a Banach space X, with values in a Banach space Z, and p, mu, and epsilon are small real parameters. Under certain conditions we show the existence of symmetric solutions and under additional conditions we prove that these are the only feasible solutions. Some examples of nonlinear ordinary and partial differential equations are analyzed. (C) 1995 Academic Press, Inc.

Behavioural Analysis of a Nonlinear Mechanical System Using Transient Trajectories

This work aims at a better comprehension of the features of the solution surface of a dynamical system presenting a numerical procedure based on transient trajectories. For a given set of initial conditions an analysis is made, similar to that of a return map, looking for the new configuration of this set in the first Poincaré sections. The mentioned set of I.C. will result in a curve that can be fitted by a polynomial, i.e. an analytical expression that will be called initial function in the undamped case and transient function in the damped situation. Thus, it is possible to identify using analytical methods the main stable regions of the phase portrait without a long computational time, making easier a global comprehension of the nonlinear dynamics and the corresponding stability analysis of its solutions. This strategy allows foreseeing the dynamic behavior of the system close to the region of fundamental resonance, providing a better visualization of the structure of its phase portrait. The application chosen to present this methodology is a mechanical pendulum driven through a crankshaft that moves horizontally its suspension point.

Nonlinear dynamical analysis of an aeroelastic system with multi-segmented moment in the pitch degree-of-freedom

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Characterization of grazing bifurcation in airfoils with control surface freeplay nonlinearity

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Chaos control and sensitivity analysis of a double pendulum arm excited by an RLC circuit based nonlinear shaker

In this paper the dynamical interactions of a double pendulum arm and an electromechanical shaker is investigated. The double pendulum is a three degree of freedom system coupled to an RLC circuit based nonlinear shaker through a magnetic field, and the capacitor voltage is a nonlinear function of the instantaneous electric charge. Numerical simulations show the existence of chaotic behavior for some regions in the parameter space and this behaviour is characterized by power spectral density and Lyapunov exponents. The bifurcation diagram is constructed to explore the qualitative behaviour of the system. This kind of electromechanical system is frequently found in robotic systems, and in order to suppress the chaotic motion, the State-Dependent Riccati Equation (SDRE) control and the Nonlinear Saturation control (NSC) techniques are analyzed. The robustness of these two controllers is tested by a sensitivity analysis to parametric uncertainties.

Twelve-month clinical outcomes after coronary stenting with the Genous Bio-engineered R Stent in patients with a bifurcation lesion: from the e-HEALING (Healthy Endothelial Accelerated Lining Inhibits Neointimal Growth) registry

Background The e-Healthy Endothelial Accelerated Lining Inhibits Neointimal Growth (e-HEALING) registry was designed to capture clinical data on the use of the endothelial progenitor cell capture stent (ECS) in routine clinical practice. In this analysis, we investigated the 12-month clinical outcomes in patients treated with an ECS for a bifurcation lesion. Methods The worldwide, prospective, nonrandomized e-HEALING registry aimed to enrol 5000 patients treated for coronary artery disease with one or more ECS between October 2005 and October 2007. Clinical follow-up was obtained at 1, 6, and 12 months. The primary endpoint was target vessel failure (TVF), defined as the composite of cardiac death, myocardial infarction, and target vessel revascularization at 12 months. Results A total of 573 patients were treated for at least one bifurcation lesion and were assessed in the current analysis. Baseline characteristics showed a median age of 65 years; 21% were diabetic patients and 36% had unstable angina. A total of 63% of the bifurcation lesions were located in the left artery descending and the mean stent length was 20.7 +/- 12.6 mm. At 12 months, TVF was 12.7% and target lesion revascularization was 7.5%. Definite or probable stent thrombosis occurred in 1.7% of the patients. Moreover, one or more stents per lesion [hazard ratio (HR): 2.79, 95% confidence interval (CI): 1.60-4.86, P < 0.001], predilatation (HR: 0.39, 95% CI: 0.17-0.87, P = 0.023), and lesions located in the right coronary artery (HR: 4.56, 95% CI: 1.07-19.5, P = 0.041) were independent predictors of TVF. Conclusion In the e-HEALING registry, coronary bifurcation stenting with the ECS results in favorable clinical outcomes and low incidences of repeat revascularization and stent thrombosis. Coron Artery Dis 23:201-207 (C) 2012 Wolters Kluwer Health vertical bar Lippincott Williams & Wilkins.

An anatomical analysis of the mini-modified orbitozygomatic and supra-orbital approaches

Seven sides of cadaver heads were used to compare the surgical exposures provided by the mini-modified orbitozygomatic (MOz) and supra-orbital (SO) approaches. The Optotrak 3020 computerized tracking system (Northern Digital, Waterloo, ON, Canada) was utilized to evaluate the area of anatomical exposure defined by six points: (1) ipsilateral sphenoid ridge; (2) most distal point of the ipsilateral middle cerebral artery (MCA); (3) most distal point of the ipsilateral posterior cerebral artery (PCA); (4) most distal point of the contralateral PCA; (5) most distal point of the contralateral MCA; and (6) contralateral sphenoid ridge. Additionally, angles of approach for the ipsilateral MCA bifurcation, ipsilateral ICA bifurcation, basilar artery tip, contralateral MCA and ICA bifurcation and anterior communicating artery (AcomA) were evaluated, first for SO and then for MOz. An image guidance system was used to evaluate the limits of surgical exposure. No differences in the area of surgical exposure were noted (p > 0.05). Vertical angles were significantly wider for the ipsilateral and contralateral ICA bifurcation, AcomA, contralateral MCA and basilar tip (p < 0.05) for MOz. No differences in horizontal angles were observed between the approaches for the six targets (p > 0.05). There were no differences in the limits of exposure. MOz affords no additional surgical working space. However, our results demonstrate systematically that vertical exposure is improved. The MOz should be performed while planning an approach to these regions and a wider exposure in the vertical axis is needed. (C) 2012 Elsevier Ltd. All rights reserved.

Analysis of nonlinear dynamics of vocal folds using high-speed video observation and biomechanical modeling

Primary voice production occurs in the larynx through vibrational movements carried out by vocal folds. However, many problems can affect this complex system resulting in voice disorders. In this context, time-frequency-shape analysis based on embedding phase space plots and nonlinear dynamics methods have been used to evaluate the vocal fold dynamics during phonation. For this purpose, the present work used high-speed video to record the vocal fold movements of three subjects and extract the glottal area time series using an image segmentation algorithm. This signal is used for an optimization method which combines genetic algorithms and a quasi-Newton method to optimize the parameters of a biomechanical model of vocal folds based on lumped elements (masses, springs and dampers). After optimization, this model is capable of simulating the dynamics of recorded vocal folds and their glottal pulse. Bifurcation diagrams and phase space analysis were used to evaluate the behavior of this deterministic system in different circumstances. The results showed that this methodology can be used to extract some physiological parameters of vocal folds and reproduce some complex behaviors of these structures contributing to the scientific and clinical evaluation of voice production. (C) 2010 Elsevier Inc. All rights reserved.

Parametric Sensitivity Analysis of the Most Recent Computational Models of Rabbit Cardiac Pacemaking

The cellular basis of cardiac pacemaking activity, and specifically the quantitative contributions of particular mechanisms, is still debated. Reliable computational models of sinoatrial nodal (SAN) cells may provide mechanistic insights, but competing models are built from different data sets and with different underlying assumptions. To understand quantitative differences between alternative models, we performed thorough parameter sensitivity analyses of the SAN models of Maltsev & Lakatta (2009) and Severi et al (2012). Model parameters were randomized to generate a population of cell models with different properties, simulations performed with each set of random parameters generated 14 quantitative outputs that characterized cellular activity, and regression methods were used to analyze the population behavior. Clear differences between the two models were observed at every step of the analysis. Specifically: (1) SR Ca2+ pump activity had a greater effect on SAN cell cycle length (CL) in the Maltsev model; (2) conversely, parameters describing the funny current (If) had a greater effect on CL in the Severi model; (3) changes in rapid delayed rectifier conductance (GKr) had opposite effects on action potential amplitude in the two models; (4) within the population, a greater percentage of model cells failed to exhibit action potentials in the Maltsev model (27%) compared with the Severi model (7%), implying greater robustness in the latter; (5) confirming this initial impression, bifurcation analyses indicated that smaller relative changes in GKr or Na+-K+ pump activity led to failed action potentials in the Maltsev model. Overall, the results suggest experimental tests that can distinguish between models and alternative hypotheses, and the analysis offers strategies for developing anti-arrhythmic pharmaceuticals by predicting their effect on the pacemaking activity.

Analysis of coronary bifurcations by intravascular ultrasound and virtual histology

Background Regional differences in shear stress have been identified as reason for early plaque formation in vessel bifurcations. We aimed to investigate regional plaque morphology and composition using intravascular ultrasound (IVUS) and virtual histology (IVUS–VH) in coronary artery bifurcations. Methods We performed IVUS and IVUS–VH studies at coronary bifurcations to analyze segmental plaque burden and composition of different segments in relation to their orientation to the bifurcation. Results A total of 236 patients with a mean age of 59 ± 11 years (69% male) were analyzed. Plaque burden was higher at the contralateral vessel wall facing the bifurcation compared to the ipsilateral vessel wall and this difference was true for proximal and distal segments (proximal: 37 ± 12% and 45 ± 15% for segments at the ipsilateral and contralateral vessel wall, respectively, p < 0.001; distal: 37 ± 10% and 47 ± 15% for segments at the ipsilateral and contralateral vessel wall, respectively, p < 0.001). In addition, these segments exhibited a higher proportion of dense calcium and a lower proportion of fibrous tissue and fibro fatty tissue. Conclusions Segments on the contralateral wall of the bifurcation which have previously been identified as regions with low shear stress not only exhibited a higher plaque burden, but also a higher degree of calcification.

Clinical outcomes after zotarolimus and everolimus drug eluting stent implantation in coronary artery bifurcation lesions: insights from the RESOLUTE All Comers Trial

OBJECTIVE We investigated clinical outcomes after treatment of coronary bifurcation lesions with second generation drug eluting stents (DES). DESIGN Post hoc analysis of a randomised, multicentre, non-inferiority trial. SETTING Multicentre study. PATIENTS All comers study with minimal exclusion criteria. INTERVENTIONS Patients were treated with either zotarolimus or everolimus eluting stents. The patient population was divided according to treatment of bifurcation or non-bifurcation lesions and clinical outcomes were compared between groups. MAIN OUTCOMES MEASURES Clinical outcomes within 2-year follow-up. RESULTS A total of 2265 patients were included in the present analysis. Two-year follow-up data were available in 2223 patients: 1838 patients in the non-bifurcation group and 385 patients in the bifurcation group. At 2-year follow-up the bifurcation and the non-bifurcation lesion groups showed no significant differences in terms of cardiac death (2.3 vs 2.1, p=0.273), target lesion failure (9.7% vs 13.8%, p=0.255), major adverse cardiac events (11.5% vs 15.1%, p=0.305), target lesion revascularisation (4.7% vs 6.0%, p=0.569), and definite or probable stent thrombosis (1.6% vs 1.8%, p=0.419). CONCLUSIONS The use of second generation DES for the treatment of coronary bifurcation lesions was associated with similar long term mortality and clinical outcomes compared with non-bifurcation lesions.

Three-year outcomes of percutaneous coronary intervention with next-generation zotarolimus-eluting stents for de novo coronary bifurcation lesions.

AIMS To investigate the outcomes of percutaneous coronary intervention (PCI) in bifurcation versus non-bifurcation lesions using the next-generation Resolute zotarolimus-eluting stent (R-ZES). METHODS AND RESULTS We analyzed 3-year pooled data from the RESOLUTE All-Comers trial and the RESOLUTE International registry. The R-ZES was used in 2772 non-bifurcation lesion patients and 703 bifurcation lesion patients, of which 482 were treated with a simple-stent technique (1 stent used to treat the bifurcation lesion) and 221 with a complex bifurcation technique (2 or more stents used). The primary endpoint was 3-year target lesion failure (TLF, defined as the composite of death from cardiac causes, target vessel myocardial infarction, or clinically-indicated target lesion revascularization [TLR]), and was 13.3% in bifurcation vs 11.3% in non-bifurcation lesion patients (adjusted P=.06). Landmark analysis revealed that this difference was driven by differences in the first 30 days between bifurcation vs non-bifurcation lesions (TLF, 6.6% vs 2.7%, respectively; adjusted P<.001), which included significant differences in each component of TLF and in-stent thrombosis. Between 31 days and 3 years, TLF, its components, and stent thrombosis did not differ significantly between bifurcation lesions and non-bifurcation lesions (TLF, 7.7% vs 9.0%, respectively; adjusted P=.50). CONCLUSION The 3-year risk of TLF following PCI with R-ZES in bifurcation lesions was not significantly different from non-bifurcation lesions. However, there was an increased risk associated with bifurcation lesions during the first 30 days; beyond 30 days, bifurcation lesions and non-bifurcation lesions yielded similar 3-year outcomes.

Anatomic characteristics and clinical implications of angiographic coronary thrombus: insights from a patient-level pooled analysis of SYNTAX, RESOLUTE, and LEADERS Trials.

BACKGROUND The distribution of thrombus-containing lesions (TCLs) in an all-comer population admitted with a heterogeneous clinical presentation (stable, ustable angina, or an acute coronary syndrome) and treated with percutaneous coronary intervention is yet unclear, and the long-term prognostic implications are still disputed. This study sought to assess the distribution and prognostic implications of coronary thrombus, detected by coronary angiography, in a population recruited in all-comer percutaneous coronary intervention trials. METHODS AND RESULTS Patient-level data from 3 contemporary coronary stent trials were pooled by an independent academic research organization (Cardialysis, Rotterdam, the Netherlands). Clinical outcomes in terms of major adverse cardiac events (major adverse cardiac events, a composite of death, myocardial infarction, and repeat revascularization), death, myocardial infarction, and repeated revascularization were compared between patients with and without angiographic TCL. Preprocedural TCL was present in 257 patients (5.8%) and absent in 4193 (94.2%) patients. At 3-year follow-up, there was no difference for major adverse cardiac events (25.3 versus 25.4%; P=0.683); all-cause death (7.4 versus 6.8%; P=0.683); myocardial infarction (5.8 versus 6.0%; P=0.962), and any revascularizations (17.5 versus 17.7%; P=0.822) between patients with and without TCL. The comparison of outcomes in groups weighing the jeopardized myocardial by TCL also did not show a significant difference. TCL were seen more often in the first 2 segments of the right (43.6%) and left anterior descending (36.8%) coronary arteries. The association of TCL and bifurcation lesions was present in 40.1% of the prespecified segments. CONCLUSIONS TCL involved mainly the proximal coronary segments and did not have any effect on clinical outcomes. A more detailed thrombus burden quantification is required to investigate its prognostic implications. CLINICAL TRIAL REGISTRATION URL: http://www.clinicaltrials.gov. Unique identifiers: NCT00114972, NCT01443104, NCT00617084.