Non-linear changes of lower extremity kinetics prior to gait transition

IntroductionThe purpose of this study was to examine the changes of lower extremity kinetics during walk-to-run (WR) transition and if the changes would follow a non-linear trend within the five strides before WR transition using a constant acceleration protocol.MethodsFourteen participants performed gait transition on the instrumented treadmill at a constant acceleration. Peak, time to peak, and movement and power of hip, knee and ankle joints were recorded and analyzed in sagittal plane for five strides before gait transition. Three Two-way MANOVA were employed to examine the differences of kinetic measures among the five strides. Univariate analysis and Post-Hoc Tukey’s test would be applied if needed. Also, Post hoc polynomial trend analyses were used to examine the trend of the kinetic measures that significantly changed during the five strides.ResultsCompared to the first four strides, significant differences were observed for peaks moments, joint powers, and time to peaks in the last stride before running at ankle, knee, and hip joints respectively. In general, the changes of kinetic variables were following a quadratic trend during the five strides before running.ConclusionJoint kinetic measures actively change in non-linear patterns during the five strides before running to prepare for the gait transition, indicating that the gait transition is an active reorganization rather than a passive reaction.     

Existence and uniqueness of a sharp travelling wave in degenerate non-linear diffusion Fisher-KPP equations

In this paper we use a dynamical systems approach to prove the existence of a unique critical value c ^* of the speed c for which the degenerate density-dependent diffusion equation u _ct = [D(u)u _x ] _x + g(u) has: 1. no travelling wave solutions for 0 < c < c ^*, 2. a travelling wave solution u(x, t) = (x - c ^* t) of sharp type satisfying (– ) = 1, () = 0 ^*; '(^*–) = – c ^*/D'(0), '(^*+) = 0 and 3. a continuum of travelling wave solutions of monotone decreasing front type for each c > c ^*. These fronts satisfy the boundary conditions (– ) = 1, '(– ) = (+ ) = '(+ ) = 0. We illustrate our analytical results with some numerical solutions.     

Linear and non-linear contrast coding in light-adapted blowfly photoreceptors

The response properties of R1–6 type photoreceptors of the blowfly (Calliphora vicina) were investigated using 1- to 600-ms light steps with contrasts from -1.00 to +1.12 at different adapting backgrounds. To prevent activation of voltage-dependent K⁺-channels, some photoreceptors were treated with ionophoretically injected tetraethylammonium. The linearity and time-course of the photoresponses depended on the adapting background and the duration of the contrast stimulus. At low backgrounds photoresponses were approximately linear regardless of the contrast step duration. However, at higher backgrounds photoreceptors produced, with long contrast steps of opposite polarities, larger and slower hyperpolarizing responses than depolarizing ones, but linear responses with equal time-courses to transient (2ms) contrast changes. The early rising phases of photoresponses were independent of the contrast signal duration, deviated to the same extent from the steady-state potential and steepened as the value of contrast was increased. The photoreceptor contrast gain increased with the background, but its value depended on the duration, the magnitude, and the polarity of the contrast step. Tetraethylammonium linearised the photoreceptor membrane, increased and delayed photoresponses probably by blocking the shunting of the outwardly rectifying potassium channels. These effects did not strongly influence on the photoreceptors' characteristic non-linear contrast dependence on light adaptation.Abbreviations LED light emitting diode - TEA tetraethylammonium ion     

Parameter identification of the calvin photosynthesis cycle

Summary This article is concerned with the determination of kinetic parameters of the Calvin photosynthesis cycle which is described by seventeen nonlinear ordinary differential equations. It is shown that the task requires dynamic data for several sets of initial conditions. The numerical technique is based upon an algorithm for non-linear optimization and Gear's numerical integration scheme for stiff systems of differential equations. The sensitivity of the parameters to noise in the data is tested with a method adapted from Rosenbrook and Storey. A preliminary set of parameters has been obtained from a preliminary set of experimental data. The numerical methods are then tested with synthetic data derived from these parameters. The mathematical model and the results obtained in the simulation are used as an aid in designing new experiments.     

Pressure Drops in a Distensible Model of End-to-side Anastomosis in Systemic-to-pulmonary Shunts

The modified Blalock-Taussig shunt is a surgical procedure used as a palliation to treat complex congenital heart defects. It consists of an interposing prosthetic tube between the innominate/subclavian artery and the right pulmonary artery. Previous experience indicates that the pressure drop across the shunt is affected by the pulmonary pressure at the distal anastomosis combined with the distensibility of the anastomosis. In this study, a computational fluid-structure interaction approach is presented to investigate the haemodynamic behaviour. Steady-state fluid dynamics and structural analyses were carried out using commercial codes based on the finite element method (FIDAP and ABAQUS) coupled by means of a purposely-developed procedure to transfer boundary conditions. Both prosthetic tube and artery walls were characterised by non-linear material properties. Three different pulmonary pressures (2, 5 and 15 mmHg) and two volume flow rates (0.4 and 0.8 l/min) were investigated. Results indicate that the effects of distensibility at the distal anastomosis on the shunt pressure drop are relevant only when the distal anastomosis on the shunt pressure drop are relevant only when the distal anastomosis is not fully distended, which occurs when the pulmonary pressure is lower than 5 mmHg.     

A mixed finite element formulation for a non-linear,transversely isotropic material model for the cardiac tissue

In this paper we present a mixed finite element method for modeling the passive properties of the myocardium. The passive properties are described by a non-linear, transversely isotropic, hyperelastic material model, and the myocardium is assumed to be almost incompressible. Single-field, pure displacement-based formulations are known to cause numerical difficulties when applied to incompressible or slightly compressible material cases. This paper presents an alternative approach in the form of a mixed formulation, where a separately interpolated pressure field is introduced as a primary unknown in addition to the displacement field. Moreover, a constraint term is included in the formulation to enforce (almost) incompressibility. Numerical results presented in the paper demonstrate the difficulties related to employing a pure displacement-based method, applying a set of physically relevant material parameter values for the cardiac tissue. The same problems are not experienced for the proposed mixed method. We show that the mixed formulation provides reasonable numerical results for compressible as well as nearly incompressible cases, also in situations of large fiber stretches. There is good agreement between the numerical results and the underlying analytical models.     

Non-linear molecular pattern classification using molecular beacons with multiple targets

In vitro pattern classification has been highlighted as an important future application of DNA computing. Previous work has demonstrated the feasibility of linear classifiers using DNA-based molecular computing. However, complex tasks require non-linear classification capability. Here we design a molecular beacon that can interact with multiple targets and experimentally shows that its fluorescent signals form a complex radial-basis function, enabling it to be used as a building block for non-linear molecular classification in vitro. The proposed method was successfully applied to solving artificial and real-world classification problems: XOR and microRNA expression patterns.     

Exploring the concept of interaction computing through the discrete algebraic analysis of the Belousov–Zhabotinsky reaction

Interaction computing (IC) aims to map the properties of integrable low-dimensional non-linear dynamical systems to the discrete domain of finite-state automata in an attempt to reproduce in software the self-organizing and dynamically stable properties of sub-cellular biochemical systems. As the work reported in this paper is still at the early stages of theory development it focuses on the analysis of a particularly simple chemical oscillator, the Belousov–Zhabotinsky (BZ) reaction. After retracing the rationale for IC developed over the past several years from the physical, biological, mathematical, and computer science points of view, the paper presents an elementary discussion of the Krohn–Rhodes decomposition of finite-state automata, including the holonomy decomposition of a simple automaton, and of its interpretation as an abstract positional number system. The method is then applied to the analysis of the algebraic properties of discrete finite-state automata derived from a simplified Petri net model of the BZ reaction. In the simplest possible and symmetrical case the corresponding automaton is, not surprisingly, found to contain exclusively cyclic groups. In a second, asymmetrical case, the decomposition is much more complex and includes five different simple non-abelian groups whose potential relevance arises from their ability to encode functionally complete algebras. The possible computational relevance of these findings is discussed and possible conclusions are drawn.     

Theoretical study of geometrical and nonlinear optical properties of pyridinum N-phenolate betaine dyes

This paper presents an ab initio quantum chemical investigation of the geometrical structures and the non-linear optical properties (NLO) of three structural isomers of pyridinium N-phenolate betaine dye. The ground state geometrical parameters and the first-order hyperpolarizabilities were calculated using the Hartree-Fock (HF) as well as the second-order perturbation Møller-Pleset (MP2) method with the 6–31G, 6–31G(d), 6–31G(d,p), 6–31+G(d), 6–31++G(d,p), 6–311+G(d), aug-cc-PVDZ and the recently developed Z3PolX basis sets. Moreover, the first-order hyperpolarizability was calculated at the coupled cluster singles and doubles (CCSD/6–31+G(d)) level of theory. The analysis of the results of calculations for the investigated isomers indicates that there are important differences in their NLO activities. Additionally, it was shown that Z3PolX basis set works reasonable well for betaine dyes.

Structural identifiability for a class of non-linear compartmental systems using linear/non-linear splitting and symbolic computation

Under certain controllability and observability restrictions, two different parameterisations for a non-linear compartmental model can only have the same input-output behaviour if they differ by a locally diffeomorphic change of basis for the state space. With further restrictions, it is possible to gain valuable information with respect to identifiability via a linear analysis. Examples are presented where non-linear identifiability analyses are substantially simplified by means of an initial linear analysis. For complex models, with four or more compartments, this linear analysis can prove lengthy to perform by hand and so symbolic computation has been employed to aid this procedure.