Diffusion Approximation Model Research Articles

Drying kinetics of Aristolochia cymbifera Mart. and Zucc. leaves

Drying medicinal plant materials ensures the retention of their active ingredients. The aim of this study was to fit different mathematical models to experimental data from Aristolochia cymbifera leaves to determine and evaluate the effective diffusion coefficient and to obtain the drying process activation energy under varying air conditions. The experiment was conducted at the Federal Institute of Education, Science and Technology at the Goias – Rio Verde Campus. Four drying replicates were performed in a fixed bed dryer with a controlled air speed of 1.0 m s-1 and drying temperatures of 28.8, 36.4 and 44.8°C. Increasing the drying air temperature from 28.8 to 36.4 or 44.8°C reduced the A. cymbifera leaf drying time from 58.13 to 13.10 and 5.00 h, respectively. The diffusion approximation model described the drying phenomenon the best. The effective diffusion coefficient increased with increasing air temperature and was described by the Arrhenius equation with activation energy of 107.29 kJ mol-1. Key words: Medicinal plants, jarrinha, activation energy, effective diffusion.

Cone beam x‐ray luminescence computed tomography: A feasibility study

The appearance of x-ray luminescence computed tomography (XLCT) opens new possibilities to perform molecular imaging by x ray. In the previous XLCT system, the sample was irradiated by a sequence of narrow x-ray beams and the x-ray luminescence was measured by a highly sensitive charge coupled device (CCD) camera. This resulted in a relatively long sampling time and relatively low utilization of the x-ray beam. In this paper, a novel cone beam x-ray luminescence computed tomography strategy is proposed, which can fully utilize the x-ray dose and shorten the scanning time. The imaging model and reconstruction method are described. The validity of the imaging strategy has been studied in this paper. In the cone beam XLCT system, the cone beam x ray was adopted to illuminate the sample and a highly sensitive CCD camera was utilized to acquire luminescent photons emitted from the sample. Photons scattering in biological tissues makes it an ill-posed problem to reconstruct the 3D distribution of the x-ray luminescent sample in the cone beam XLCT. In order to overcome this issue, the authors used the diffusion approximation model to describe the photon propagation in tissues, and employed the sparse regularization method for reconstruction. An incomplete variables truncated conjugate gradient method and permissible region strategy were used for reconstruction. Meanwhile, traditional x-ray CT imaging could also be performed in this system. The x-ray attenuation effect has been considered in their imaging model, which is helpful in improving the reconstruction accuracy. First, simulation experiments with cylinder phantoms were carried out to illustrate the validity of the proposed compensated method. The experimental results showed that the location error of the compensated algorithm was smaller than that of the uncompensated method. The permissible region strategy was applied and reduced the reconstruction error to less than 2 mm. The robustness and stability were then evaluated from different view numbers, different regularization parameters, different measurement noise levels, and optical parameters mismatch. The reconstruction results showed that the settings had a small effect on the reconstruction. The nonhomogeneous phantom simulation was also carried out to simulate a more complex experimental situation and evaluated their proposed method. Second, the physical cylinder phantom experiments further showed similar results in their prototype XLCT system. With the discussion of the above experiments, it was shown that the proposed method is feasible to the general case and actual experiments. Utilizing numerical simulation and physical experiments, the authors demonstrated the validity of the new cone beam XLCT method. Furthermore, compared with the previous narrow beam XLCT, the cone beam XLCT could more fully utilize the x-ray dose and the scanning time would be shortened greatly. The study of both simulation experiments and physical phantom experiments indicated that the proposed method was feasible to the general case and actual experiments.

An innovative model for congestion pricing at airports

Airport congestion is worsening worldwide, and is one of the bottlenecks constraining the development of global air transportation. Based on a comparison of the current airport congestion models, this paper improves the diffusion approximation model for airport congestion pricing developed by Milan Janic in 2005 in the following three areas: (1) redefining the processes of the congestion queue, (2) adding the threshold of congestion queue, and (3) amending the sub-model of delay costs. This new diffusion approximation model for airport congestion pricing was applied to Beijing Capital International Airport (PEK). After calculating delay times and delay costs at this airport on 21st July, 2007, the congestion tolls for various airlines at various times were calculated. This paper provides a solution for airport congestion.

Minimal cost of a Brownian risk without ruin

In this paper, we study an optimal stochastic control problem for an insurance company whose surplus process is modeled by a Brownian motion with drift (the diffusion approximation model). The company can purchase reinsurance to lower its risk and receive cash injections at discrete times to avoid ruin. Proportional reinsurance and excess-of-loss reinsurance are considered. The objective is to find an optimal reinsurance and cash injection strategy that minimizes the total cost to keep the surplus process non-negative (without ruin). Here the cost function is defined as the total discounted value of the injections. The minimal cost function is found explicitly by solving the according quasi-variational inequalities (QVIs). Its associated optimal reinsurance-injection control policy is also found.

Modeling boundary measurements of scattered light using the corrected diffusion approximation

We study the modeling and simulation of steady-state measurements of light scattered by a turbid medium taken at the boundary. In particular, we implement the recently introduced corrected diffusion approximation in two spatial dimensions to model these boundary measurements. This implementation uses expansions in plane wave solutions to compute boundary conditions and the additive boundary layer correction, and a finite element method to solve the diffusion equation. We show that this corrected diffusion approximation models boundary measurements substantially better than the standard diffusion approximation in comparison to numerical solutions of the radiative transport equation.

Sensitivity of Delta-P1 approximation model to second-order parameter

The sensitivity of the second-order parameter of the Henyey-Greenstein phase function based on the spatially-resolved diffuse reflectance within the two-point-source approximation to the Delta-P1 approximation model is studied, and the analytical expression of the sensitivity is derived. The results show that the analytic solution of the Delta-P1 approximation model for reflectance contains the second-order parameter of the scattering phase function compared with the diffusion approximation model, and the second-order parameter has significant influence (the extreme value greater than 30%) on the analytic solution for spatially-resolved diffuse reflectance with small source-detector separations ( 1.5 mm) no matter whether the absorption is weak or strong. The research has theoretical significance for obtaining the optical information abour tissue with the second-order parameter .

Vacuum Drying Characteristics of Some Vegetables

In this research the drying of four kinds of vegetables was investigated in a vacuum dryer. The effect of temperature on drying rate of samples at various temperatures (30, 35 and 45 °C) was studied. Six thin-layer drying models were fitted to drying data and suitable model was selected from them. Then effective moisture diffusivity and activation energy of samples were calculated. The Diffusion approximation model gave excellent fit for fenugreek and mint leaves and vegetative parts of leek and the page model was considered adequate to describe the thin-layer drying behavior of parsley leaves. The effective diffusivity values changed from 2.92×10 -10 to 9.81×10 -10 , 1.77×10 -10 to 5.99×10 -10 , 9.3×10 -11 to 1.7×10 -10 and 1.27×10 -9 to 3.4×10 -9 for fenugreek, mint and parsley leaves and vegetative parts of leek, respectively. An Arrhenius type of equation was used to evaluate the effect of temperature on the effective diffusivity and the activation energy values was found 66.36, 66.34, 32.27 and 51.16 kJ/ mol for fenugreek, mint and parsley leaves and vegetative parts of leek, respectively.

Periods of constant and falling-rate for infrared drying of carrot slices

The aim of this work was to study the infrared drying process of carrot slices and to determine coefficients related to the heat and mass transfer of the process. Fresh carrots were used, dried until constant weight in a dryer with infrared heating source. Different models were utilized to fit the experimental data of constant and falling drying rate periods. It was verified that the coefficients of heat and mass transfer, during the constant drying rate, significantly increased with temperature on rise. The Diffusion Approximation, Two Terms, Midili and Verna models satisfactory represented the falling period of drying rate of carrot slices. The effective diffusion coefficient increased with temperature and this relationship can be represented by the Arrhenius equation, obtaining activation energy to the drying process of 29.092 kJ mol-1.

Spectrally resolving and scattering-compensated x-ray luminescence∕fluorescence computed tomography

The nanophosphors, or other similar materials, emit near-infrared (NIR) light upon x-ray excitation. They were designed as optical probes for in vivo visualization and analysis of molecular and cellular targets, pathways, and responses. Based on the previous work on x-ray fluorescence computed tomography (XFCT) and x-ray luminescence computed tomography (XLCT), here we propose a spectrally-resolving and scattering-compensated x-ray luminescence/fluorescence computed tomography (SXLCT or SXFCT) approach to quantify a spatial distribution of nanophosphors (other similar materials or chemical elements) within a biological object. In this paper, the x-ray scattering is taken into account in the reconstruction algorithm. The NIR scattering is described in the diffusion approximation model. Then, x-ray excitations are applied with different spectra, and NIR signals are measured in a spectrally resolving fashion. Finally, a linear relationship is established between the nanophosphor distribution and measured NIR data using the finite element method and inverted using the compressive sensing technique. The numerical simulation results demonstrate the feasibility and merits of the proposed approach.

A diffusion approximation model for wireless networks based on IEEE 802.11 standard

The article presents an analytical model of wireless networks using the IEEE 802.11 protocol to access the transport medium. The model allows to determine such key factors of the quality of service as transmission delays and losses. The model is based on diffusion approximation approach which was proposed three decades ago to model wired networks. We show that it can be adapted to take into consideration the input streams with general interarrival time distributions and servers with general service time distributions. The diffusion approximation has been chosen because of fairly general assumptions of models based on it, hard to be represented in Markov models. A queueing network model can have an arbitrary topology, the intensity of transmitted flows can be represented by non-Poisson (even self-similar) streams, the service times at nodes can be defined by general distributions. These assumptions are important: because of the CSMA/CA algorithm, the overall times needed to sent a packet are far from being exponentially distributed and therefore the flows between nodes are non-Poisson. Diffusion approximation allows us also to analyse the of transient behaviour of a network when traffic intensity is changing with time.

A three-dimensional finite elements approach for the coupled radiative transfer equation and diffusion approximation modeling in fluorescence imaging

Abstract During the last few years a quite large number of fluorescence molecular imaging applications have been reported in the literature, as one of the most challenging aspects in medical imaging is to “see” a tumor embedded into tissue, which is a turbid medium, by using fluorescent probes for tumor labeling. However, the forward solvers, required for the successful convergence of the inverse problem, are still lacking accuracy and time feasibility. Moreover, initialization of these solvers may be proven even more difficult than solving the inverse problem itself. This paper describes in depth a coupled radiative transfer equation and diffusion approximation model for solving the forward problem in fluorescence imaging. The theoretical confrontation of these solvers comprises the model deployment, its Galerkin finite elements approximation and the domain discretization scheme. Finally, a new optical properties mapping algorithm, based on super-ellipsoid models, is implemented, providing a fully automated simulation target construction within feasible time.

Comparison of diffusion approximation and higher order diffusion equations for optical tomography of osteoarthritis

In this study, a simplified spherical harmonics approximated higher order diffusion model is employed for 3-D diffuse optical tomography of osteoarthritis in the finger joints. We find that the use of a higher-order diffusion model in a stand-alone framework provides significant improvement in reconstruction accuracy over the diffusion approximation model. However, we also find that this is not the case in the image-guided setting when spatial prior knowledge from x-rays is incorporated. The results show that the reconstruction error between these two models is about 15 and 4%, respectively, for stand-alone and image-guided frameworks.

Diffusion Approximation Model of Multiserver Stations with Losses

The article presents a diffusion approximation model of a G / G / N / N station – N parallel servers without queueing. Diffusion approximation allows us to include in queueing models fairly general assumptions. First of all it gives us a tool to consider in a natural way transient states of queues, which is very rare in classical queueing models. Then we may consider input streams with general interarrival time distributions and servers with general service time distributions. Single server models may be easily incorporated into a network of queues. Here, we apply the diffusion approximation formalism to study transient behaviour of G / G / N / N station and use it to construct a model of a typical call centre and to study the sliding window mechanism, a popular Call Admission Control (CAC) algorithm.

适用于强吸收的混合漫射近似及其光源近似的影响

A modified diffusion approximation model called the hybrid diffusion approximation that can be used for highly absorbing media is investigated. The analytic solution of the hybrid diffusion approximation for reflectance in two-source approximation and steady-state case with extrapolated boundary is obtained. The effects of source approximation on the analytic solution are investigated, and it is validated that two-source approximation in highly absorbing media to describe the optical properties of biological tissue is necessary. Monte Carlo simulation of recovering optical parameters from reflectant data is done with the use of this model. The errors of recovering \mu_{a} and \mu_{s} are smaller than 15% for the reduced albedo between 0.77 and 0.5 with the source-detector separation of 0.4-3 mm.

Improving image quality of diffuse optical tomography with a projection-error-based adaptive regularization method

Diffuse optical tomography (DOT) reconstructs the images of internal optical parameter distribution using noninvasive boundary measurements. The image reconstruction procedure is known to be an ill-posed problem. In order to solve such a problem, a regularization technique is needed to constrain the solution space. In this study, a projection-error-based adaptive regularization (PAR) technique is proposed to improve the reconstructed image quality. Simulations are performed using a diffusion approximation model and the simulated results demonstrate that the PAR technique can improve reconstruction precision of object more effectively. The method is demonstrated to have low sensitivity to noise at various noise levels. Moreover, with the PAR method, the detectability of an object located both at the center and near the peripheral regions has been increased largely.

TU-FF-A4-04: Comparison of Optical Diffusion Approximation and Delta P1 Approximation Models for Laser Fluence in Cancer Treatment

Purpose: Evaluation of competing optical models, the optical diffusion approximation (ODA) and delta P1 approximation for use in ablative laser cancer treatment of nanoparticles impregnated tumors.Method and Materials: Gold‐coated, silica‐core nanoshells, core diameter 180nm were placed in 1.5 wt% agar gel phantoms with nanoshell concentrations of 1.19×109 nanoshells/mL and 2.53×109 nanoshells/mL. Phantoms were cylindrical, 23 mm wide by 69 mm high and heated using laser powers of 0.64, 0.8 and 1.2Watts with 0.5cm spot size. Thermal images of heating were obtained using MRTI on a clinical 1.5 T MRI (Excite, HD, GE Healthcare Technologies, Waukesha, WI). MRTI uses a 2D fast, spoiled, gradient‐echo sequence, with field of view = 12 cm, slice thickness = 3 mm, matrix = 256 × 128 , TR/TE = 74.5 ms/15 ms, FA = 30°. MRTI utilized the complex phase difference method to calculate temperature images, one image every 5 seconds for 300 seconds. Modeling the thermal response was performed with a finite element solution of the nonhomogenous heat equation using commercial software (Comsol Multiphysics®, Comsol Inc., Burlington, MA, U.S.). Results: For the 1.19×109 nanoshells/mL phantom both ODA and delta P1 give similar results with delta P1 being better overall, root mean square (RMS) difference between experiment and the model was 3 times greater for ODA than delta P1. For the higher concentration gel (2.53×109 nanoshells/mL) the RMS difference between experiment and the model was 4 times greater in the case of ODA compared to delta P1 with ODA failing to describe the experimental data in any adequate way. The greater accuracy of the delta P1 is attributed to its treatment of scattered and unscattered components of the light as separate entities. Conclusion: ODA works for lower nanoshell concentrations, but breaks down at higher concentrations. Delta P1 works well for all concentrations tested.

Flux‐limited Diffusion Approximation Models of Giant Planet Formation by Disk Instability

Both core accretion and disk instability appear to be required as formation mechanisms in order to explain the entire range of giant planets found in extrasolar planetary systems. Disk instability is based on the formation of clumps in a marginally gravitationally unstable protoplanetary disk. These clumps can only be expected to contract and survive to become protoplanets if they are able to lose thermal energy through a combination of convection and radiative cooling. Here we present several new three-dimensional, radiative hydrodynamics models of self-gravitating protoplanetary disks, where radiative transfer is handled in the flux-limited diffusion approximation. We show that while the flux-limited models lead to higher midplane temperatures than in a diffusion approximation model without the flux limiter, the difference in temperatures does not appear to be sufficiently high to have any significant effect on the formation of self-gravitating clumps. Self-gravitating clumps form rapidly in the models both with and without the flux limiter. These models suggest that the reason for the different outcomes of numerical models of disk instability by different groups cannot be attributed solely to the handling of radiative transfer, but rather appears to be caused by a range of numerical effects and assumptions. Given the observational imperative to have disk instability form at least some extrasolar planets, these models imply that disk instability remains as a viable giant planet formation mechanism.

Modeling photon propagation in biological tissues using a generalized Delta-Eddington phase function

Photon propagation in biological tissue is commonly described by the radiative transfer equation, while the phase function in the equation represents the scattering characteristics of the medium and has significant influence on the precision of solution and the efficiency of computation. In this work, we present a generalized Delta-Eddington phase function to simplify the radiative transfer equation to an integral equation with respect to photon fluence rate. Comparing to the popular diffusion approximation model, the solution of the integral equation is highly accurate to model photon propagation in the biological tissue over a broad range of optical parameters. This methodology is validated by Monte Carlo simulation.

Bayesian decision analysis for status of Snake River spring?summer Chinook salmon Oncorhynchus tshawytscha populations at extinction risk

The viability of populations was assessed using population trend data and the Diffusion Approximation (DA) model. Various extinction risk metrics for a population are functions of the DA model parameters, and thus, estimates of the DA model parameters are key quantities. Using Bayesian methods, we showed uncertainty in those estimates, and further proceeded to a decision analysis to assess viability of populations. These methods were demonstrated using population trend data from return years since 1980 on naturally produced Snake River spring-summer Chinook salmon Oncorhynchus tshawytscha populations. Of 19 populations examined, the Catherine Creek population was assessed at serious risk, Tucannon River Spring and Grande Ronde Upper Main stem populations were assessed at minor risk, and the other populations were not at risk. This assessment helps managers to prioritize populations at risk for recovery management.

Experimental study of optical characteristics of homogeneous highly-dispersive biological medium

Specific features of the process of short laser pulse propagation through a highly-dispersive biological medium are considered. Two models are used for the theoretical description of propagation of optical radiation through a highly-dispersive medium: diffusion approximation and non-stationary axial model. Physical characteristics of the dispersive medium are determined in both models. The obtained theoretical dependences are found to be in qualitative agreement with the results of experimental study.