Numerical simulation for heat transfer in tissues during thermal therapy

In this paper, a mathematical model describing the process of heat transfer in biological tissues for different coordinate system during thermal therapy by electromagnetic radiation is studied. The boundary value problem governing this process has been solved using Galerkin’s method taking B-polynomial as basis function. The system of ordinary differential equation in unknown time variable, thus obtained, is solved by homotopy perturbation method. The effect of thermal conductivity, antenna power constant, surface temperature, and blood perfusion rate on temperature for different coordinates are discussed. It has been observed that the process is faster in spherical symmetric coordinates in comparison to axisymmetric coordinate and faster in axisymmetric in comparison to Cartesian coordinate.     

Numerical simulation of thermal bone necrosis during cementation of femoral prostheses

The implant of a femoral prosthesis is a critical process because of the relatively high temperature values reached at the bone/cement interface during the cementation of the infibulum. In fact, the cement is actually a polymer that polymerizes in situ generating heat. Moreover, the conversion of monomer into polymer is never 100%; this is dangerous because of the toxicity of the monomer. In this paper, we present a 3-D axisymmetric mathematical model capable of taking into account both the geometry of the implant and the chemical/physical properties of the cement. This model, together with its numerical simulation, thus represents a useful tool to set up the optimal conditions for the new materials developed in this orthopaedic field. The real complex geometry is assumed to be a bone/cement/metallic system having cylindrical symmetry, thus allowing the model to be reduced to two space variables. The cementation process is described by the Fourier heat equation coupled with a suitable polymerization kinetics. The numerical approximation is accomplished by semi-implicit finite differences in time and finite elements in space with numerical quadrature. The full discrete scheme amounts to solve linear positive definite symmetric systems preceded by an elementwise algebraic computation. We present various numerical simulations which confirm some critical aspects of this orthopaedic fixing technique such as thermal bone necrosis and the presence of unreacted residual monomer.This work was partially supported by MURST (Fondi per la Ricerca Scientifica 40%) and CNR (IAN, Contract 880032601, and Progetto Finalizzato Sistemi Informatici e Calcolo Parallelo, Sottoprogetto Calcolo Scientifico per Grandi Sistemi) of Italy     

Numerical simulation of bubble transport in a bifurcating microchannel: a preliminary study

In this paper, we present the computational fluid dynamics (CFD) simulations of bubble transport in a first generation bifurcating microchannel. In the present study, the human arteriole is modeled as a two-dimensional (2D) rectangular bifurcating microchannel. The microchannel is filled with blood and a single perfluorocarbon (PFC) bubble is introduced in the parent channel. The simulations are carried out to identify the lodging and dislodging pressures for two nondimensional bubble sizes, L(d) (ratio of the dimensional bubble length to the parent tube diameter), that is for L(d)?=?1 and L(d)?=?2. Subsequently, the bubble transport and splitting behavior due to the presence of symmetry and asymmetry in the daughter channels of the microchannel is studied for these bubble sizes. The splitting behavior of the bubble under the effect of gravity is also assessed and reported here. For the symmetric bifurcation model, the splitting ratio (SR) (ratio of bubble volume in bottom daughter channel to bubble volume in top daughter channel), of the bubble was found to be 1. For the asymmetric model, the splitting ratio was found to be less than 1. The loss in the bubble volume in the asymmetric model was attributed to surface tension effects and the resistance offered by the flow, which led to the bubble sticking and sliding along the walls of the channel. With the increase in roll angle, Φ (angle which the plane makes with the horizontal to study the effects of gravity), there was a decline in the splitting ratio.     

Numerical study of size-structured population models: a case of Gambussia affinis

We study, from a numerical point of view, some properties of a model which describes the evolution of a population of Gambussia affinis. Our model includes sufficiently smooth vital functions. First we select, among four numerical methods of second order, the most appropriate in terms of adaptation to the problem. The most efficient method also reveals new properties of the model for long times, such as the tendency to periodicity, obtained with different initial conditions. We also discuss some advantages and deficiencies of the model.     

Numerical simulation of a surface barrier discharge in air

The development of a surface barrier discharge in air at atmospheric pressure under the action of a constant voltage of different polarity is simulated numerically. When the polarity of the high-voltage electrode is negative, the discharge develops as an ionization wave that moves along the dielectric surface. When the polarity is positive, the discharge develops as a streamer that first moves above the dielectric surface and then comes into contact with and continues to develop along it. In the case of a high-voltage electrode of positive polarity, the discharge zone above the dielectric surface is approximately five times thicker than that in the case of negative polarity. The characteristic aspects of numerical simulation of the streamer phase of a surface barrier discharge are discussed. The numerical results on the density of the charge stored at the dielectric surface and on the length of the discharge zone agree with the experimental data.     

Numerical simulation of circulation in a Caribbean-type backreef lagoon

A numerical model based on the vertically intergrated equations of motion and continuity was used to simulate circulation in a shallow, well-mixed, Caribbean-type backreef lagoon. As the focus of previous research, Great Pond Bay, St. Croix, provided a suitable study site. Tides, wind, and the effect of waves impinging on the reef were incorporated within the model. Direction of simulated flow under various wind and wave regimes agrees well with patterns found during current meter and drogue tracking experiments. When momentum transfer over the reef due to wave breaking and set-up is added, the magnitude of flow within the lagoon, ranging 5–30 cm/s, also compares favorably to in situ measurements. Model results indicate a relatively rapid and realistic flushing period of less than one day. Results of this study indicate that numerical modeling techniques potentially offer an accurate and cost-effective means to predict the pattern of water movement within coral-reef lagoons.     

Numerical simulation of cross-country skiing

A program for numerical simulation of a whole ski race, from start to finish, is developed in MATLAB. The track is modelled by a set of cubical splines in two dimensions and can be used to simulate a track in a closed loop or with the start and finish at different locations. The forces considered in the simulations are gravitational force, normal force between snow and skis, drag force from the wind, frictional force between snow and ski and driving force from the skier. The differential equations of motion are solved from start to finish with the Runge-Kutta method. Different wind situations during the race can be modelled, as well as different glide conditions on different parts of the track. It is also possible to vary the available power during the race. The simulation program's output is the total time of the race, together with the forces and speed during different parts of the race and intermediate times at selected points. Some preliminary simulations are also presented.     

Numerical simulation of a single cell passing through a narrow slit

The narrow slit between endothelial cells that line the microvessel wall is the principal pathway for tumor cell extravasation to the surrounding tissue. To understand this crucial step for tumor hematogenous metastasis, we used dissipative particle dynamics method to investigate an individual cell passing through a narrow slit numerically. The cell membrane was simulated by a spring-based network model which can separate the internal cytoplasm and surrounding fluid. The effects of the cell elasticity, cell shape, nucleus and slit size on the cell transmigration through the slit were investigated. Under a fixed driving force, the cell with higher elasticity can be elongated more and pass faster through the slit. When the slit width decreases to 2/3 of the cell diameter, the spherical cell becomes jammed despite reducing its elasticity modulus by 10 times. However, transforming the cell from a spherical to ellipsoidal shape and increasing the cell surface area by merely 9.3 % can enable the cell to pass through the narrow slit. Therefore, the cell shape and surface area increase play a more important role than the cell elasticity in cell passing through the narrow slit. In addition, the simulation results indicate that the cell migration velocity decreases during entrance but increases during exit of the slit, which is qualitatively in agreement with the experimental observation.     

Numerical simulation of selective freezing of target biological tissues following injection of solutions with specific thermal properties

Recently, we proposed a method for controlling the extent of freezing during cryosurgery by percutaneously injecting some solutions with particular thermal properties into the target tissues. In order to better understand the mechanism of the enhancement of freezing by these injections, a new numerical algorithm was developed to simulate the corresponding heat transfer process that is involved. The three-dimensional phase change processes in biological tissues subjected to cryoprobe freezing, with or without injection, were compared numerically. Two specific cases were investigated to illustrate the selective freezing method: the injection of solutions with high thermal conductivity; the injection of solutions with low latent heat. It was found that the localized injection of such solutions could significantly enhance the freezing effect and decrease the lowest temperature in the target tissues. The result also suggests that the injection of these solutions may be a feasible and flexible way to control the size of the ice ball and its direction of growth during cryosurgery, which will help to optimize the treatment process.     

A comparative analysis of photosynthetic recovery from thermal stress: a desert plant case study

Our understanding of the effects of heat stress on plant photosynthesis has progressed rapidly in recent years through the use of chlorophyll a fluorescence techniques. These methods frequently involve the treatment of leaves for several hours in dark conditions to estimate declines in maximum quantum yield of photsystem II (F _V/F _M), rarely accounting for the recovery of effective quantum yield (ΔF/F _M′) after thermally induced damage occurs. Exposure to high temperature extremes, however, can occur over minutes, rather than hours, and recent studies suggest that light influences damage recovery. Also, the current focus on agriculturally important crops may lead to assumptions about average stress responses and a poor understanding about the variation among species’ thermal tolerance. We present a chlorophyll a fluorescence protocol incorporating subsaturating light to address whether species’ thermal tolerance thresholds (T ₅₀) are related to the ability to recover from short-term heat stress in 41 Australian desert species. We found that damage incurred by 15-min thermal stress events was most strongly negatively correlated with the capacity of species to recover after a stress event of 50 °C in summer. Phylogenetically independent contrast analyses revealed that basal divergences partially explain this relationship. Although T ₅₀ and recovery capacity were positively correlated, the relationship was weaker for species with high T ₅₀ values (>51 °C). Results highlight that, even within a single desert biome, species vary widely in their physiological response to high temperature stress and recovery metrics provide more comprehensive information than damage metrics alone.     

Testing the thermal limits of Eccritotarsus catarinensis: a case of thermal plasticity

Water hyacinth is considered the most damaging aquatic weed in South Africa. The success of biocontrol initiatives against the weed varies nation-wide, but control remains generally unattainable in higher altitude, temperate regions. Eccritotarsus catarinensis (Hemiptera: Miridae) is a biocontrol agent of water hyacinth that was first released in South Africa in 1996. By 2011, it was established at over 30 sites across the country. These include the Kubusi River, a site with a temperate climate where agent establishment and persistence was unexpected. This study compared the critical thermal limits of the Kubusi River insect population with a laboratory-reared culture to determine whether any physiological plasticity was evident that could account for its unexpected establishment. There were no significant differences in critical thermal maxima (CT_max) or minima (CT_min) between sexes, while the effect of rate of temperature change on the thermal parameters in the experiments had a significant impact in some trials. Both CT_max and CT_min differed significantly between the two populations, with the field individuals tolerating significantly lower temperatures (CT_min: ?0.3°C?±?0.063 [SE], CT_max: 42.8°C?±?0.155 [SE]) than those maintained in the laboratory (CT_min: 1.1°C?±?0.054 [SE], CT_max: 44.9°C?±?0.196 [SE]). Acclimation of each population to the environmental conditions typical of the other for a five-day period illustrated that short-term acclimation accounted for some, but not all of the variation between their lower thermal limits. This study provides evidence for the first cold-adapted strain of E. catarinensis in the field, with potential value for introduction into other colder regions where water hyacinth control is currently unattainable.     

Language as a community of interacting belief systems: A case study involving conduct toward self and others

Words such as selfish and altruistic that describe conduct toward self and others are notoriously ambiguous in everyday language. I argue that the ambiguity is caused, in part, by the coexistence of multiple belief systems that use the same words in different ways. Each belief system is a relatively coherent linguistic entity that provides a guide for human behavior. It is therefore a functional entity with design features that dictate specific word meaning. Since different belief systems guide human behavior in different directions, specific word meanings cannot be maintained across belief systems. Other sources of linguistic ambiguity include i) functional ambiguity that increases the effectiveness of a belief system, ii) ambiguity between belief systems that are functionally identical but historically distinct, and iii) active interference between belief systems. I illustrate these points with a natural history study of the word selfish and related words in everyday language. In general, language and the thought that it represents should be studied in the same way that ecologists study multi-species communities.     

The utility of nuclear introns for investigating hybridization and genetic introgression: a case study involving Brachyramphus murrelets

Interspecific hybridization can have importantconsequences for conservation, but can bedifficult to detect using morphologicalmarkers. To test the utility of nuclear intronsfor investigating hybridization and geneticintrogression, we analyzed variation in fivenuclear introns and the mitochondrialcytochrome b gene in two species ofseabirds that are declining and may behybridizing: marbled murrelets(Brachyramphus marmoratus) and Kittlitz'smurrelets (B. brevirostris). No alleleswere shared between samples of the two species,and intron alleles formed reciprocallymonophyletic groups in gene trees. Our resultssuggest that few murrelets in Alaska areF ₁, F ₂or back-cross hybrids,and that gene pools of these species have beenindependent for 1.8 to 5.7 million years. Weconclude that introns are a potentially richsource of markers for analyzing hybridizationand introgression in endangered or decliningspecies.     

Numerical simulation of the urine flow in a stented ureter

When a stent is implanted in a blocked ureter, the urine passing from the kidney to the bladder must traverse a very complicated flow path. That path consists of two parallel passages, one of which is the bore of the stent and the other is the annular space between the external surface of the stent and the inner wall of the ureter. The flow path is further complicated by the presence of numerous pass-through holes that are deployed along the length of the stent. These holes allow urine to pass between the annulus and the bore. Further complexity in the pattern of the urine flow occurs because the coiled "pig tails," which hold the stent in place, contain multiple ports for fluid ingress and egress. The fluid flow in a stented ureter has been quantitatively analyzed here for the first time using numerical simulation. The numerical solutions obtained here fully reveal the details of the urine flow throughout the entire stented ureter. It was found that in the absence of blockages, most of the pass-through holes are inactive. Furthermore, only the port in each coiled pig tail that is nearest the stent proper is actively involved in the urine flow. Only in the presence of blockages, which may occur due to encrustation or biofouling, are the numerous pass-through holes activated. The numerical simulations are able to track the urine flow through the pass-through holes as well as adjacent to the blockages. The simulations are also able to provide highly accurate results for the kidney-to-bladder urine flow rate. The simulation method presented here constitutes a powerful new tool for rational design of ureteral stents in the future.     

Quantum-classical simulation methods for hydrogen transfer in enzymes: a case study of dihydrofolate reductase

A variety of theoretical approaches have been used to investigate hydrogen transfer in enzymatic reactions. The free energy barriers for hydrogen transfer in enzymes have been calculated using classical molecular dynamics simulations in conjunction with quantum mechanical/molecular mechanical and empirical valence bond potentials. Nuclear quantum effects have been included with several different approaches. Applications of these approaches to hydride transfer in dihydrofolate reductase are consistent with experimental measurements and provide significant insight into the protein conformational changes that facilitate the hydride transfer reaction.     

Numerical simulation of a stroke: computational problems and methodology

We discuss the difficulties of the numerical simulation of a stroke, and we describe the numerical methods which we have developed and used to obtain some realistic results. Nowadays, the computations are performed in two-dimensional slices of a brain, but the strategies to obtain full three-dimensional simulations are explored. This paper is written so as to be understandable by non-mathematicians.     

Numerical simulation of aldolase tetramer stability

A theoretical study of aldolase tetramer stability, conducted by finite difference Poisson-Boltzmann (FDPB) and modified Tanford-Kirkwood (MTK) techniques using the atomic coordinates of human aldolase, is described. A method for calculating the interaction energy between subunits is proposed. An analysis of the contribution of different energy terms to the stability and oligomeric equilibria (monomer ⇔ dimer ⇔ tetramer) of aldolase is made. It is shown that the loss of solvation energy and electrostatic interactions at very high and low pH-s destabilise the oligomers. These energy terms are compensated over a wide pH range by the stabilization energy due to hydrophobic interactions. It is shown that the aldolase tetramer is energetically more preferable than other oligomers in the pH range from 5 to 11. Subunit-subunit interactions within the tetramer suggest one dimeric form to be the most stable of the possible sub-parts. For this reason the tetramer can be thought of as a “dimer of dimers”. A comparison between our theoretical results and available experimental data shows that the dissociation of the aldolase tetramer below pH 3–4 cooperatively leads to acid denaturation. A second dissociation is predicted to occur at high pH (>12) in addition to the well known acidic dissociation. The analysis suggests that a mutation of His20 or Arg257 to a neutral residue could decrease the pH of the acidic dissociation by approximately 1 pH unit. Received: 16 February 1998 / Revised version: 8 April 1998 / Accepted: 19 April 1998     

Numerical simulation of the cardiovascular system

In this article, we aim at giving a non-technical overview of some mathematical models currently used in the numerical simulation of the cardiovascular system. A hierarchy of models for blood flows in large arteries is briefly described as well as an electromechanical model for the heart. We discuss some possible applications of the numerical simulations of such models, for example the optimization of prostheses. We also address the issue of the data assimilation for the calibration of the models.     

A simulation study of the feedback of phytoplankton on thermal structure via light extinction

1. A simulation study of the feedback of phytoplankton biomass on temperature stratification in the large, monomictic Lake Constance was undertaken. Phytoplankton biomass affects the light extinction coefficient (LEC) of the water and, in turn, the vertical distribution of short‐wave radiation, which shapes the temperature stratification in the lake. 2. A sensitivity study of the variation in LEC using the hydrodynamic model DYRESM showed that a high LEC is associated with stronger stratification, shallower thermoclines, higher surface temperatures and reduced heat content during the heating phase of the lake. During the cooling phase, a shallower thermocline at high LEC leads to a faster decrease in water temperature so that during autumn, a high LEC is associated with lower surface temperatures. Thermal structure was particularly sensitive to changes in LEC when its value was below 0.5 m^?1. 3. When LEC is simulated dynamically with the coupled hydrodynamic–ecological model DYRESM‐CAEDYM, its value is a function of phytoplankton dynamics that change vertically and temporally. Comparing simulations with and without dynamic LEC (i.e. with and without phytoplankton dynamics) produced a complex picture: during the vegetation period, we often found a warmer surface layer and colder water beneath in the simulations with dynamic LEC, as expected from the higher LEC when phytoplankton is abundant. However, since phytoplankton biomass (as LEC) fluctuates and because of occasional cooling phases, the patterns were comparatively weak and not consistent over the whole growing season. 4. The most obvious patterns emerged by comparing simulations of oligotrophic and eutrophic conditions. In the eutrophic state, with its higher LEC, stratification was stronger and characterized by higher surface water temperatures, a shallower thermocline and colder water temperatures between 5 and 10 m depth. 5. Statistical analysis of long‐term data of water temperatures in Lake Constance, corrected for external forcing by air temperature, revealed a significant tendency towards warmer temperatures at 7.5 and 10 m depths with decreasing LECs over the course of reoligotrophication. This finding is consistent with our model results.