Comparaison de deux modèles hybrides simulant la propagation de la lumière dans les tissus biologiques

In this paper, two numerical hybrid methods to model photon transport phenomena in biological tissues are compared. The coupled radiative transfer–diffusion model is based on the finite element solution of the radiative transfer equation and its approximation. The hybrid Monte-Carlo–diffusion consists in modeling the propagation of laser light in turbid media with the pure statistical Monte-Carlo method in the vicinity of the source and the boundaries and the diffusion approximation elsewhere in the domain. We apply these codes to calculate the spatially resolved reflectance amplitude and phase resulting from an intensity modulated laser beam. The results show that the hybrid methods can be used to simulate light propagation with good accuracy and speed.     

Some exact solutions of a generalized Fisher equation related to the problem of biological invasion

The problem of biological invasion in a model single-species community is considered, the spatiotemporal dynamics of the system being described by a modified Fisher equation. For a special case, we obtain an exact solution describing self-similar growth of the initially inhabited domain. By comparison with numerical solutions, we show that this exact solution may be applicable to describe an early stage of a biological invasion preceding the propagation of the stationary travelling wave. Also, the exact solution is applied to the problem of critical aggregation to derive sufficient conditions of population extinction. Finally, we show that the solution we obtain is in agreement with some data from field observations.     

The effect of shear stress on solitary waves in arteries

In the present work, we study the propagation of solitary waves in a prestressed thick walled elastic tube filled with an incompressible inviscid fluid. In order to include the geometric dispersion in the analysis the wall inertia and shear deformation effects are taken into account for the inner pressure-cross-sectional area relation. Using the reductive perturbation technique, the propagation of weakly non-linear waves in the long-wave approximation is examined. It is shown that, contrary to thin tube theories, the present approach makes it possible to have solitary waves even for a Mooney-Rivlin (M-R) material. Due to dependence of the coefficients of the governing Korteweg-deVries equation on initial deformation, the solution profile changes with inner pressure and the axial stretch. The variation of wave profiles for a class of elastic materals are depicted in graphical forms. As might be seen from these illustrations, with increasing thickness ratio, the profile of solitary wave is steepened for a M-R material but it is broadened for biological tissues.     

Earthquakes site effects modeling by hybrid MS-BIEM: the case study of Sofia, Bulgaria

The study solves 2D elastodynamic model for seismic in-plane wave propagation in laterally inhomogeneous geological profiles situated in a vertically inhomogeneous half-space with a seismic source. For the aim, an efficient hybrid Modal Summation-Boundary Integral Equation Method (MSM-BIEM) is applied. The MSM is used as a tool for the simulation of wave propagation from the source position to the local multilayered laterally inhomogeneous geological profile, where the BIEM is applied. The BIEM is based on the frequency-dependent fundamental solution of the governing equation in elastodynamics and the hybrid method works in the frequency domain. The inverse FFT solution is applied to obtain time histories. The hybrid tool is applied to several models for the investigation of local site effects due to: (a) the impedance contrasts between soil layers, (b) surface topography and lateral inhomogeneity, (c) the seismic source properties and (d) the existence of water saturation in soils. The application of the modeling tool is a contribution to the seismic risk analysis of Sofia city.     

实验探索非靶组织光学参数对超声调制光的影响

生物组织是一种复杂的多层高散射介质,探索光在超声作用下的生物组织中的传播规律是超声调制光学成像术必须解决的一个基本问题,关系到最终进行图像处理与重建。通过实验探索超声调制光信号在双层和三层组织中的传播规律。实验结果表明非靶组织的光学属性（吸收系数和散射系数）和组织结构（单层或多层）都不影响超声调制光信号的调制深度。调制深度只与超声焦区介质（即靶组织）的声光属性有关,具有较佳的抗干扰性,适合用于图像重构。     

Effect of plant interaction on wind-induced crop motion

Plant motion due to wind affects plant growth, a phenomenon called thigmomorphogenesis. Despite intensive studies of the turbulence over plant canopies, the study of plant motion induced by wind has often been limited to individual trees or cereal plants. Few models of global canopy motions are available. Moreover the numerical analysis of models that are based on individual stems becomes time consuming when dealing with crops. A model of motion within the canopies is proposed here using a wave propagation equation within a homogenized continuous medium, and a forcing function representing turbulent gusts advected over the canopy. This model is derived from a discrete model of a set of plant shoots represented as individual oscillators, including elastic contacts between shoots. Such contacts induce nonlinearities into the wave equation. A new experimental method to measure stem dynamical properties and elastic collision properties is presented with an illustration on alfalfa stems. Results obtained modeling plant motions in an alfalfa crop are presented.     

Ion-acoustic solitons in Bi-Ion dusty plasma

The propagation of ion-acoustic solitons in a warm dusty plasma containing two ion species is investigated theoretically. Using an approach based on the Korteveg de Vries equation, it is shown that the critical value of the negative ion density that separates the domains of existence of compression and rarefaction solitons depends continuously on the dust density. A modified Korteveg de Vries equation for the critical density is derived in the higher order of the expansion in the small parameter. It is found that the nonlinear coefficient of this equation is positive for any values of the dust density and the masses of positive and negative ions. For the case where the negative ion density is close to its critical value, a soliton solution is found that takes into account both the quadratic and cubic nonlinearities. The propagation of a solitary wave of arbitrary amplitude is investigated by the quasi-potential method. It is shown that the range of dust densities around the critical value within which solitary waves with positive and negative potentials can exist simultaneously is relatively wide.     

Ultrasound propagation in anisotropic soft tissues: the application of linear elastic theory

Linear elastic theory has served well in modeling the mechanical properties of numerous materials. In modeling ultrasonic wave propagation in biological soft tissues, an isotropic model has usually been employed. Many tissues, however, possess a lower order of symmetry, and the speed of sound in muscle is known to vary with the direction of propagation. In this study, by applying linear regression to acoustic microscopic data from seven frog sartorius specimens, four observable elastic constants associated with a transversely isotropic model were obtained. The average values of these constants were c11 = 2.64, c13 = 3.39 and c33 = 4.40 Nm-2 for resting muscles and c11 = 2.65, c13 = 3.43 and c33 = 4.57 Nm-2 for muscles undergoing tetanic contraction, where '1' and '3' represent the transverse and longitudinal axes, respectively. In all cases, c44 was 0, indicating a minimal contribution from longitudinal shear. For all seven specimens, the model of transverse isotropy provided a better fit of the data than that of isotropy.     

Filling of partially collapsed compliant tubes

Filling of a thin-walled, highly compliant tube in a partially collapsed condition is studied. The theory, based on one-dimensional flow, takes account of friction, longitudinal tension, and the highly nonlinear pressure-area law for the tube. Various aspects of filling behavior are revealed by alternative calculations using: (i) the method of characteristics; (ii) numerical integration of the continuity, momentum, and tube-law equations; and (iii) a crude but simple lumped-element capacitance-inertance-resistance model. Varied phenomena appear. At high Reynolds number, these include dispersive wave trains associated with circumferential bending stiffness and longitudinal tension, nonlinear changes of wave form, development of highly asymmetrical wave reflections, and sloshing. At low Reynolds number, the area changes with time in a diffusivelike manner. The experiments exhibited the dispersive phenomena predicted by the theory.     

Efficient Higher Order Full-Wave Numerical Analysis of 3-D Cloaking Structures

Highly efficient and versatile computational electromagnetic analysis of 3-D transformation-based metamaterial cloaking structures based on a hybridization of a higher order finite element method for discretization of the cloaking region and a higher order method of moments for numerical termination of the computational domain is proposed and demonstrated. The technique allows for an effective modeling of the continuously inhomogeneous anisotropic cloaking region, for cloaks based on both linear and nonlinear coordinate transformations, using a very small number of large curved finite elements with continuous spatial variations of permittivity and permeability tensors and high-order p-refined field approximations throughout their volumes, with a very small total number of unknowns. In analysis, there is no need for a discretization of the permittivity and permeability profiles of the cloak, namely for piecewise homogeneous (layered) approximate models, with material tensors replaced by appropriate piecewise constant approximations. Numerical results show a very significant reduction (three to five orders of magnitude for the simplest possible 6-element model and five to seven orders of magnitude for an h-refined 24-element model) in the scattering cross section of a perfectly conducting sphere with a metamaterial cloak, in a broad range of wavelengths. Given the introduced explicit approximations in modeling of the spherical geometry and continuous material tensor profiles (both by fourth-order Lagrange interpolating functions), and inherent numerical approximations involved in the finite element and moment method techniques and codes, the cloaking effects are shown to be predicted rather accurately by the full-wave numerical analysis method.     

Beyond the chemical master equation: Stochastic chemical kinetics coupled with auxiliary processes

The chemical master equation and its continuum approximations are indispensable tools in the modeling of chemical reaction networks. These are routinely used to capture complex nonlinear phenomena such as multimodality as well as transient events such as first-passage times, that accurately characterise a plethora of biological and chemical processes. However, some mechanisms, such as heterogeneous cellular growth or phenotypic selection at the population level, cannot be represented by the master equation and thus have been tackled separately. In this work, we propose a unifying framework that augments the chemical master equation to capture such auxiliary dynamics, and we develop and analyse a numerical solver that accurately simulates the system dynamics. We showcase these contributions by casting a diverse array of examples from the literature within this framework and applying the solver to both match and extend previous studies. Analytical calculations performed for each example validate our numerical results and benchmark the solver implementation.     

Fusion modes of an axially symmetrical mirror trap with the high power injection of fast particles

We analyzed the energy balance of a fusion system based on an axially symmetrical open trap. In the considered system, the injection of high-energy (fast) particles is the main source of plasma external heating. Simulation of physical kinetics of the injected particles is based on the numerical solution of the Fokker-Planck equation taking into account scattering into the domain of losses and participation in the fusion reactions. Despite the considerable energy losses of the injected particles when leaving the trap due to the angular scattering, the considered system is sufficiently effective to be used as a source of neutrals for the hybrid (fusion-fission) reactor. The principle possibility of achieving a power amplification of Q _pl ≈ 1 in plasma was demonstrated in operation modes with high neutron yield.     

Numerical modeling and dosimetry of the 35 mm Petri dish under 46 GHz millimeter wave exposure

Experimental studies on effects of millimeter wave (MMW) exposure on cells cultured in Petri dishes have attracted interest in recent decades. To improve the quantification of the biological responses toward the MMW energy, an accurate and precise MMW dosimetry is to be provided. By using the finite difference time domain (FDTD) method, the numerical dosimetry is performed for a typical 35 mm Petri dish under 46 GHz continuous MMW exposure from an irradiator of a specified power pattern. With the aim of building a precise model, the meniscus at the interface between the culture solution and the Petri dish sidewall is taken into account, followed by the modeling of smooth edges of the Petri dish. The trilinear interpolation is introduced to assist the FDTD method to obtain a more precise dosimetric assessment. The specific absorption rate (SAR) distributions in the cornea cells covered by culture solution in the Petri dish are calculated and compared to display the effects of using Petri dish models of various precision and the trilinear interpolation on dosimetry results. In addition, the SAR distribution in the cells is analyzed to study its homogeneity. The results indicate that the precise Petri dish model and the application of the trilinear interpolation are helpful in improving the precision of numerical dosimetry. It is also revealed that the inhomogeneity of the SAR distribution is well beyond neglect, which deserves cautious consideration in experiments investigating MMW effects on cells in vitro.     

Theoretical analysis on relationship between the neural activity and the EEG

Firstly, a collective oscillation mode of the neural activity is derived from the neural network system by using the multicompartment equation and the projection operator technique. This technique takes into account higher order interactions among neurons. The solution of the equation gives a chain structure with an infinite number of circuit loops in which each of them is only composed of four neurons. The obtained eigenvalues are quite similar to the spectrum of frequencies of the EEG. Secondly, the time-dependent behavior of the observed EEG is simulated by starting from the elementary process of action potential trains of neurons, which includes the effect of the collective oscillation mode mentioned above. This gives a comprehensive derivation of the EEG from the neural activity of action potentials. The simulation assumes that information of the action potential trains can be transmitted to the EEG through the intermediate states of the postsynaptic potential trains and the slow waves. The paper reports that a slightly modulated activity of a relatively small amount of neurons can cause a strong influence on the shape of the global EEG and that the calculated results reproduce the characteristic features of the EEG in a rat such as the theta rhythm, the spindle wave and the arousal wave.     

Characterization of absorption and scattering properties for various yeast strains by time-resolved spectroscopy

An understanding of the optical properties of biological media and cells is essential to the development of noninvasive optical studies of tissues. Unicellular organisms offer a unique opportunity to investigate the factors affecting light propagation, since they can be manipulated in ways impossible for more complex biological samples. In this study, we examined optical absorption and scattering properties of strongly multiple scattering yeast suspensions by means of near-infrared (NIR) time-resolved spectroscopy (TRS) and a sample substitution method. We determined the critical parameters for photon migration by varying the cell organelle content, the cell ploidy, the cell size, and the concentration of suspended cells. The results indicate that the photon absorption is insensitive to cell differentiation and that the cell volume is the primary factor determining light-scattering property.     

Electro-mechanical behavior of wet bone--Part II: Wave propagation

In this study, a general mixture model, which was developed for wet bone, has been used to analyze the flexural wave propagation in long bones. The electrical conduction is taken into account as well as the piezo-electric properties of bone tissue. The general formulation is simplified and certain assumptions made to yield a particular set of equations. The solution of the magnetic induction vector outside the bone due to the mechanical wave propagation is obtained. The results are compared with a similar problem using dry bone. The results indicate that the electro-mechanical properties of bone tissue could be used for monitoring the rate of fracture healing in long bones.     

Hydrodynamic interaction of two unsteady model microorganisms

The study of pair-wise interactions between swimming microorganisms is fundamental to the understanding of the rheological and transport properties of semi-dilute suspensions. In this paper, the hydrodynamic interaction of two ciliated microorganisms is investigated numerically using a boundary-element method, and the microorganisms are modeled as spherical squirmers that swim by time-dependent surface deformations. The results show that the inclusion of the unsteady terms in the ciliary propulsion model has a large impact on the trajectories of the interacting cells, and causes a significant change in scattering angles with potential important consequences on the diffusion properties of semi-dilute suspensions. Furthermore, the analysis of the shear stress acting on the surface of the microorganisms revealed that the duration and the intensity of the near-field interaction are significantly modified by the presence of unsteadiness. This observation may account for the hydrodynamic nature of randomness in some biological reactions, and supersedes the distinction between intrinsic randomness and hydrodynamic interactions, adding a further element to the understanding and modeling of interacting microorganisms.     

Mechanical pulse wave propagation in gel, normal and oedematous tissues.

The velocity, attenuation and frequency content of the mechanical pulse wave propagation in gels of various water contents, in normal tissues from various sites and in oedematous tissues from different patients were investigated. The properties of the propagated pulse wave depend on the water content of the gel and the viscoelastic properties of the tissues. From the dependence of the pulse wave propagation velocity on elasticity, viscosity and density, information may be obtained concerning the effects of oedema on the mechanical properties of tissue.     

Mathematical analysis of an integral equation arising from population dynamics

In this paper, we establish the existence of travelling wave solution to an intrinsically non-linear differential–integral equation formed as a result of mathematical modelling of the evolution of an asexual population in a changing environment. This equation is first converted to a non-linear integral equation. The discretization and manipulation of the corresponding eigenvalue problem allows us to use the theory of positive matrices to get some very useful estimates and then to confirm the existence of solution. We also exhibit numerical simulation results and explain the biological meaning of the results.