Laguerre Runge-Kutta-Fehlberg method for simulating laser pulse propagation in biological tissue

An efficient algorithm for solving the transient radiative transfer equation for laser pulse propagation in biological tissue is presented. A Laguerre expansion is used to represent the time dependency of the incident short pulse. The Runge–Kutta– Fehlberg method is used to solve the intensity. The discrete ordinates method is used to discretize with respect to azimuthal and zenith angles. This method offers the advantages of representing the intensity with a high accuracy using only a few Laguerre polynomials, and straightforward extension to inhomogeneous media. Also, this formulation can be easily extended for solving the 2-D and 3-D transient radiative transfer equations.

Application of radial return mapping algorithm for finite strain elastoplasticity in a hybrid finite element and particle-in-cell model

The radial return mapping algorithm within the computational context of a hybrid Finite Element and Particle-In-Cell (FE/PIC) method is constructed to allow a fluid flow FE/PIC code to be applied solid mechanic problems with large displacements and large deformations. The FE/PIC method retains the robustness of an Eulerian mesh and enables tracking of material deformation by a set of Lagrangian particles or material points. In the FE/PIC approach the particle velocities are interpolated from nodal velocities and then the particle position is updated using a suitable integration scheme, such as the 4th order Runge-Kutta scheme[1]. The strain increments are obtained from gradients of the nodal velocities at the material point positions, which are then used to evaluate the stress increment and update history variables. To obtain the stress increment from the strain increment, the nonlinear constitutive equations are solved in an incremental iterative integration scheme based on a radial return mapping algorithm[2]. A plane stress extension of a rectangular shape J2 elastoplastic material with isotropic, kinematic and combined hardening is performed as an example and for validation of the enhanced FE/PIC method. It is shown that the method is suitable for analysis of problems in crystal plasticity and metal forming. The method is specifically suitable for simulation of neighbouring microstructural phases with different constitutive equations in a multiscale material modelling framework.

Modeling of light propagation through biological tissues : a novel approach

An efficient numerical technique for modeling biological tissues using the radiative transfer equation is presented. Time dependence of the transient radiative transfer equation is approximated using Laguerre expansion. Azimuthal angle is discretized using the discrete ordinates method and the resulting set of ordinary differential equations is solved using the Runge-Kutta-Felhberg method.

An approximate numerical technique for characterizing optical pulse propagation in inhomogeneous biological tissue

An approximate numerical technique for modeling optical pulse propagation through weakly scattering biological tissue is developed by solving the photon transport equation in biological tissue that includes varying refractive index and varying scattering/absorption coefficients. The proposed technique involves first tracing the ray paths defined by the refractive index profile of the medium by solving the eikonal equation using a Runge-Kutta integration algorithm. The photon transport equation is solved only along these ray paths, minimizing the overall computational burden of the resulting algorithm. The main advantage of the current algorithm is that it enables to discretise the pulse propagation space adaptively by taking optical depth into account. Therefore, computational efficiency can be increased without compromising the accuracy of the algorithm.

Estimation of accumulated lethality under pressure-assisted thermal processing

A study was conducted to develop an integrated process lethality model for pressure-assisted thermal processing (PATP) taking into consideration the lethal contribution of both pressure and heat on spore inactivation. Assuming that the momentary inactivation rate was dependent on the survival ratio and momentary pressure-thermal history, a differential equation was formulated and numerically solved using the Runge-Kutta method. Published data on combined pressure-heat inactivation of Bacillus amyloliquefaciens spores were used to obtain model kinetic parameters that considered both pressure and thermal effects. The model was experimentally validated under several process scenarios using a pilot-scale high-pressure food processor. Using first-order kinetics in the model resulted in the overestimation of log reduction compared to the experimental values. When the n th-order kinetics was used, the computed accumulated lethality and the log reduction values were found to be in reasonable agreement with the experimental data. Within the experimental conditions studied, spatial variation in process temperature resulted up to 3.5 log variation in survivors between the top and bottom of the carrier basket. The predicted log reduction of B. amyloliquefaciens spores in deionized water and carrot purée had satisfactory accuracy (1.07-1.12) and regression coefficients (0.83-0.92). The model was also able to predict log reductions obtained during a double-pulse treatment conducted using a pilot-scale high-pressure processor. The developed model can be a useful tool to examine the effect of combined pressure-thermal treatment on bacterial spore lethality and assess PATP microbial safety. © 2013 Springer Science+Business Media New York.

Analytical thermal study on nonlinear fundamental heat transfer cases using a novel computational technique

In this paper a novel computational technique called Parameterized Perturbation Method (PPM) is used to obtain the solutions of nonlinear fundamental heat conduction equations. Three well known problems in the area of heat transfer are addressed to be solved. An analytical investigation is carried out for: (a) the temperature distribution in a fin with a temperature-dependent thermal conductivity, (b) the cooling of the lumped system with variable specific heat, and (c) the temperature distribution of a convective-radiative fin. The validity of the results of PPM solution was verified via comparison with numerical results obtained using a fourth order Runge-Kutta method. These comparisons revealed that PPM is a powerful approach for solving these problems. Also, the results showed that the main attributions of this method are very straightforward calculations and low computational burden compared to previous analytical and numerical approaches.