A study on thermal damage during hyperthermia treatment based on DPL model for multilayer tissues using finite element Legendre wavelet Galerkin approach

Hyperthermia is a process that uses heat from the spatial heat source to kill cancerous cells without damaging the surrounding healthy tissues. Efficacy of hyperthermia technique is related to achieve temperature at the infected cells during the treatment process. A mathematical model on heat transfer in multilayer tissues in finite domain is proposed to predict the control temperature profile at hyperthermia position. The treatment technique uses dual-phase-lag model of heat transfer in multilayer tissues with modified Gaussian distribution heat source subjected to the most generalized boundary condition and interface at the adjacent layers. The complete dual-phase-lag model of bioheat transfer is solved using finite element Legendre wavelet Galerkin approach. The present solution has been verified with exact solution in a specific case and provides a good accuracy. The effect of the variability of different parameters such as lagging times, external heat source, metabolic heat source and the most generalized boundary condition on temperature profile in multilayer tissues is analyzed and also discussed the effective approach of hyperthermia treatment. Furthermore, we studied the modified thermal damage model with regeneration of healthy tissues as well. For viewpoint of thermal damage, the least thermal damage has been observed in boundary condition of second kind. The article concludes with a discussion of better opportunities for future clinical application of hyperthermia treatment.     

A review on numerical modeling for magnetic nanoparticle hyperthermia: Progress and challenges

Recent progress in nanotechnology has advanced the development of magnetic nanoparticle (MNP) hyperthermia as a potential therapeutic platform for treating diseases. Due to the challenges in reliably predicting the spatiotemporal distribution of temperature in the living tissue during the therapy of MNP hyperthermia, critical for ensuring the safety as well as efficacy of the therapy, the development of effective and reliable numerical models is warranted. This article provides a comprehensive review on the various mathematical methods for determining specific loss power (SLP), a parameter used to quantify the heat generation capability of MNPs, as well as bio-heat models for predicting heat transfer phenomena and temperature distribution in living tissue upon the application of MNP hyperthermia. This article also discusses potential applications of the bio-heat models of MNP hyperthermia for therapeutic purposes, particularly for cancer treatment, along with their limitations that could be overcome.     

Numerical simulation of time fractional dual-phase-lag model of heat transfer within skin tissue during thermal therapy

In this paper, we investigated the thermal behavior in living biological tissues using time fractional dual-phase-lag bioheat transfer (DPLBHT) model subjected to Dirichelt boundary condition in presence of metabolic and electromagnetic heat sources during thermal therapy. We solved this bioheat transfer model using finite element Legendre wavelet Galerkin method (FELWGM) with help of block pulse function in sense of Caputo fractional order derivative. We compared the obtained results from FELWGM and exact method in a specific case, and found a high accuracy. Results are interpreted in the form of standard and anomalous cases for taking different order of time fractional DPLBHT model. The time to achieve hyperthermia position is discussed in both cases as standard and time fractional order derivative. The success of thermal therapy in the treatment of metastatic cancerous cell depends on time fractional order derivative to precise prediction and control of temperature. The effect of variability of parameters such as time fractional derivative, lagging times, blood perfusion coefficient, metabolic heat source and transmitted power on dimensionless temperature distribution in skin tissue is discussed in detail. The physiological parameters has been estimated, corresponding to the value of fractional order derivative for hyperthermia treatment therapy.     

A numerical study on dual-phase-lag model of bio-heat transfer during hyperthermia treatment

The success of hyperthermia in the treatment of cancer depends on the precise prediction and control of temperature. It was absolutely a necessity for hyperthermia treatment planning to understand the temperature distribution within living biological tissues. In this paper, dual-phase-lag model of bio-heat transfer has been studied using Gaussian distribution source term under most generalized boundary condition during hyperthermia treatment. An approximate analytical solution of the present problem has been done by Finite element wavelet Galerkin method which uses Legendre wavelet as a basis function. Multi-resolution analysis of Legendre wavelet in the present case localizes small scale variations of solution and fast switching of functional bases. The whole analysis is presented in dimensionless form. The dual-phase-lag model of bio-heat transfer has compared with Pennes and Thermal wave model of bio-heat transfer and it has been found that large differences in the temperature at the hyperthermia position and time to achieve the hyperthermia temperature exist, when we increase the value of τ_T. Particular cases when surface subjected to boundary condition of 1st, 2nd and 3rd kind are discussed in detail. The use of dual-phase-lag model of bio-heat transfer and finite element wavelet Galerkin method as a solution method helps in precise prediction of temperature. Gaussian distribution source term helps in control of temperature during hyperthermia treatment. So, it makes this study more useful for clinical applications.     

Current flow and potential in a three-dimensional syncytium

Analytical solutions are obtained describing the spread of potential in a continuous syncytium which is the three-dimensional analogue of the “cable” and “thin sheet” models. Two discrete (finite-element) models are also developed and their behaviour shown to agree with that of the continuous model. All three models are able to account for the peculiarities of passive responses to intracellular current injection in tissues such as cardiac and smooth muscle. The time course and spread of junction potentials in electrically coupled tissues is discussed.     

Two-enzyme active transport in vitro with ph induced asymmetrical functional structures.: III. Discussions based on numerical treatments of the time-dependent evolutions

Three complementary models have been considered in which pH gradients (step function. linear pH or linear H^?) impose asymmetry on a two-enzyme mixture. If the “combined pH dependences” of enzymes is pro-asymmetrical, the pH gradient induces an asymmetrical distribution of potential activities (“latent” asymmetry of functional structure). When substrate is added, “developed” asymmetry of effective activities appears which results in “substrate space wave” and pumping when the catalysed reaction couple is “inversible”. It is shown that only one steady state exists for a given boundary condition and is attained when the “combined effective activity” of enzymes is nil: the stationary flux with symmetrical boundaries or the stationary load with moving boundaries is proportional to “effective global activities” of enzymes. “Equivalent square models” could be proposed that would be able to describe “functional” or “permanent” structure pumps as well. These models belong to the thermodynamic branch and the asymmetrical “space wave” substrate concentration profiles obtained must be distinguished from dissipative structures. It appears that such primary active transport pumps are chemical equivalents of heat pumps.     

Sucrose density gradient sedimentation of E. coli ribosomes.

The behavior of E. coli ribosomes during sedimentation on sucrose gradients is predicted under a variety of conditions by computer simulations. Since numerous recent kinetic studies indicate equilibration in times short compared to the time of sedimentation, these simulations assume that the system attains local reaction equilibrium at every point in the gradient at all times. For any type of homogeneous equilibrating ribosome population, governed by a single formation constant at one atmosphere pressure for 70S couples, no more than two clearly defined zones will be resolved, although the presence of large dissociating effects due to pressure gradients in high speed experiments will spread the subunit zone. Normally the pattern will consist of a 30S zone and a so-called “70S” zone, which is in reality a mixture of 70S couples and 30S and 50S subunits in local equilibrium. The greater the dissociation into subunits, the more the “70S” zone will be slowed below the nominal rate of 70 Svedberg units. If ribosomes have been collected from the “70S” zone in several successive cycles of purification, the repeated deletion of resolved 30S subunits can result in a preparation with so large a molar excess of 50S subunits that the ensuing sucrose density gradient sedimentation pattern may exhibit a “70S” zone followed by zone of 50S subunits, insteadof a zone of 30S subunits. Our most important conclusion is that whenever a well-resolved 50S zone is present in a sucrose density gradient sedimentation experiment on E. coli ribosomes, in addition to a 30S and a “70S” zone, under conditions where ribosomes and subunits should be in reversible equilibrium, the preparation must be microheterogeneous, containing a mixture of “tight” and “loose” couples. Moreover in such cases the content of large subunits in the 50S zone must be derived entirely from “loose” couples whereas the 30S zone must contain small subunits derived from both “tight” and “loose” couples. Sedimentation patterns predicted for various mixtures of “tight” and “loose” couples display all the major characteristics of published experimental patterns for E. coli ribosomes, including the partial or complete resolution into three zones, depending on rotor velocity and level of Mg²⁺.     

Comparison of two methods for designing calorimeters using stirred tank reactors

Calorimetry is a robust method for online monitoring and controlling bioprocesses in stirred tank reactors. Up to now, reactor calorimeters have not been optimally constructed for pilot scale applications. Thus, the objective of this paper is to compare two different ways for designing reactor calorimeters and validate them. The “heat capacity” method based on the mass flow of the cooling liquid in the jacket was compared with the “heat transfer” method based on the heat transfer coefficient continuously measured in the cultivation of Escherichia coli VH33 in a 50 L stirred tank reactor. It was found that the values of the “heat transfer” method agreed very well with the calculated values from the oxygen consumption. By contrast, the curve of the “heat capacity” method deviated from that of the oxygen consumption calculated with the oxycaloric equivalent. In conclusion, the “heat transfer” method has been proven to have a higher degree of validity than the “heat capacity” method. Thus, it is a better and more robust means to measure heat generation of fermentations in stirred tank bioreactors on a pilot scale. Biotechnol. Bioeng. 2013; 110: 180–190. © 2012 Wiley Periodicals, Inc.     

Uncertainty analysis for temperature prediction of biological bodies subject to randomly spatial heating

An analytical solution to the Pennes bioheat transfer equation in three-dimensional geometry with practical hyperthermia boundary conditions and random heating was obtained in this paper. Uncertainties for the predicted temperatures of tissues due to approximate parameters were studied based on analyzing one-dimensional heat transfer in the biological bodies subject to a spatially decay heating. Contributions from each of the thermal parameters such as heat conductivity, blood perfusion rate, and metabolic rate of the tissues, the scattering coefficient and the surface power flux of the heating apparatus were compared and the uncertainty limit for temperature distribution in this case was estimated. The results are useful in a variety of clinical hyperthermia and biological thermal parameter measurement.     

Calculation of line tension in various models of lipid bilayer pore edge

The line tension of the edge of the lipid bilayer pore is calculated on the basis of the elastic theory of continuous liquid-crystal medium. Three types of deformations of the membrane were taken into account: bending, lateral stretching/compression, and tilt of the lipidic tails. Various models of structure of the pore edge are considered: models of the cylindrical shape with given radius and optimum radius, “extrapolational” model, “two-coordinate” model, and model with a hydrophobic cavity (“void”). Models can be conventionally divided into two classes. The first class includes models in which membrane monolayers are in contact with each other everywhere. Models of the second class admit appearance of a hydrophobic cavity between monolayers. Models of the first class yield value of the line tension γ, strongly differing from that known from the literature (～10 pN). For example, the value of the line tension γ obtained in the cylindrical model equals to 21 pN; in the two-coordinate model, 19 pN, and in the extrapolational model, 62 pN. At the same time, the model with cavity gives the value of γ eqal ～10 pN, provided that surface tension at the boundary of the lipid tails is close to zero. This value is in a good agreement with the literature data.     

Theory on thermal probe arrays for the distinction between the convective and the perfusive modalities of heat transfer in living tissues

Recent suggestions for an improved model of heat transfer in living tissues emphasize the existence of a convective mode due to flowing blood in addition to, or even instead of, the perfusive mode, as proposed in Pennes' "classic" bioheat equation. In view of these suggestions, it might be beneficial to develop a technique that will enable one to distinguish between these two modes of bioheat transfer. To this end, a concept that utilizes a multiprobe array of thermistors in conjunction with a revised bioheat transfer equation has been derived to distinguish between, and to quantify the perfusive and convective contribution of blood to heat transfer in living tissues. The array consists of two or more temperature sensors one of which also serves to locally insert a short pulse of heat into the tissue prior to the temperature measurements. A theoretical analysis shows that such a concept is feasible. The construction of the system involves the selection of several important design parameters, i.e., the distance between the probes, the heating power, and the pulse duration. The choice of these parameters is based on computer simulations of the actual experiment.     

A review of terms for regulated vs. forced,neurochemical-induced changes in body temperature

Deviations of the body temperature of homeothermic animals may be regulated or forced. A regulated change in core temperature is caused by a natural or synthetic compound that displaces the set-point temperature. A forced shift occurs when an excessive environmental or endogenous heat load, or heat sink, exceeds the body's capacity to thermoregulate but does not affect set-point. A fever is the paradigm of a regulated increase in body temperature, but the term fever has acquired a strict pathological definition over the past two decades. Consequently, other forms of nonpathological, regulated elevations in body temperature have generally been classified as hyperthermia; and decreases in core temperature--either forced or regulated--have generally been classified as hypothermia. Since the terms hyperthermia and hypothermia fail to distinguish a regulated vs. a forced temperature change, a confusion of terms has been created in the literature. It would appear that “resisted or unregulated hyperthermia” and “hypothermia,” respectively, are appropriate terms for describing a forced increase and decrease in core temperature. A nonpathological but regulated elevation in temperature may be defined as unresisted or regulated hyperthermia, whereas a regulated decrease in temperature may be termed unresisted or regulated hypothermia. This simple scheme appears to be the most practical means for distinguishing between forced and regulated changes in core temperature.     

Conventional and newly developed bioheat transport models in vascularized tissues: A review

Heat transfer in a biological system is a complex process and its analysis is difficult. Heterogeneous vascular architecture, blood flow in the complex network of arteries and veins, varying metabolic heat generation rates and dependence of tissue properties on its physiological condition contribute to this complexity. The understanding of heat transfer in human body is important for better insight of thermoregulatory mechanism and physiological conditions. Its understanding is also important for accurate prediction of thermal transport and temperature distribution during biomedical applications. During the last three decades, many attempts have been made by researchers to model the complex thermal behavior of the human body. These models, viz., blood perfusion, countercurrent, thermal phase-lag, porous-media, perturbation, radiation, etc. have their corresponding strengths and limitations. Along with their biomedical applications, this article reviews various contextual issues associated with these models. After brief discussion of early bioheat models, the newly developed bioheat models are discussed in detail. Dependence of these models on biological properties, viz., thermophysical and optical properties are also discussed.     

Spatial grain of adaptation is much finer than ecoregional‐scale common gardens reveal

Adaptive variation among plant populations must be known for effective conservation and restoration of imperiled species and predicting their responses to a changing climate. Common‐garden experiments, in which plants sourced from geographically distant populations are grown together such that genetic differences may be expressed, have provided much insight on adaptive variation. Common‐garden experiments also form the foundation for climate‐based seed‐transfer guidelines. However, the spatial scale at which population differentiation occurs is rarely addressed, leaving a critical information gap for parameterizing seed‐transfer guidelines and assessing species’ climate vulnerability. We asked whether adaptation was evident among populations of a foundational perennial within a single “empirical” seed‐transfer zone (based on previous common‐garden findings evaluating very distant populations) but different “provisional” seed zones (groupings of areas of similar climate and are not parameterized from common‐garden data). Seedlings from three populations originating from similar conditions within an intermediate elevation were planted into gardens nearby at the same elevation, or 250–450 m higher or lower in elevation and 0.4–25 km away. Substantial variation was observed between gardens in survival (ranging 2%–99%), foliar crown volume (7.8–22.6 dm³), and reproductive effort (0%–65%), but not among the three transplanted populations. The between garden variation was inversely related to climatic differences between the gardens and seed‐source populations, specifically the site differences in maximum–minimum annual temperatures. Results suggest that substantial site‐specificity in adaptation can occur at finer scales than is accounted for in empirical seed‐transfer guidance when the guidance is derived from broadscale common‐garden studies. Being within the same empirical seed zone, geographic unit, and even within 10 km distance may not qualify as “local” in the context of seed transfer. Moving forward, designing common‐garden experiments so that they allow for testing the scale of adaptation will help in translating the resulting seed‐transfer guidance to restoration projects.     

The role of heat shock protein 70 in the thermoresistance of prostate cancer cell line spheroids

Heat shock protein 70 (Hsp70), a protein induced in cells exposed to sublethal heat shock, is present in all living cells and has been highly conserved during evolution. The aim of the current study was to determine the role of heat shock proteins in the resistance of prostate carcinoma cell line spheroids to hyperthermia. In vitro, the expression of Hsp70 by the DU 145 cell line, when cultured as monolayer or multicellular spheroids, was studied using Western blotting and enzyme-linked immunosorbent assay methods. The level of Hsp70 in spheroid cultures for up to 26 days at 37 degrees C remained similar to monolayer cultures. However, in samples treated with hyperthermia at 43 degrees C for 120 min, the spheroid cultures expressed a higher level of Hsp70 as compared to monolayer culture. Under similar conditions of heat treatment, the spheroids showed more heat resistance than monolayer cultures as judged by the number of colonies that they formed in suspension cultures. The results suggest that cells cultured in multicellular spheroids showed more heat resistance as compared to monolayer cultures by producing higher levels of Hsp70.     

Determination of the 3D temperature distribution during ferromagnetic hyperthermia under the influence of blood flow

A numerical simulation of tissue heating during thermo-seed ferromagnetic hyperthermia was performed to determine the temperature distribution of treated tumor tissues under the influence of three large blood vessels at different locations. The effects of the blood velocity waveform, blood vessel size, Curie point of the thermo-seeds and the thermo-seed number on temperature distributions were analyzed. The results indicate that the existence of a blood vessel inside the tumor has a significant cooling effect on the temperature distribution in a treated tumor tissue, which is enhanced with an increase in blood velocity. However, the pulsatile blood flow does not have apparently different effects on the outcomes of uniformly heating target tissues in comparison with the steady blood flow during the hyperthermia process. It is also concluded that a higher Curie point temperature and an increase in the number of thermo-seeds can result in profound increases in the temperature variations of the tumor tissue. In addition, tissue-equivalent phantom experiments were conducted to confirm the cooling effects of the blood vessels, and to validate the effectiveness and accuracy of the proposed heat transfer model for the ferromagnetic hyperthermia.     

Benefit of dietary seaweed (Ascophyllum nodosum) extract in reducing heat strain and fescue toxicosis: a comparative evaluation

Much of the fescue throughout the world contains an endophytic fungus which protects the plant from heat and drought, but produces a condition known as fescue toxicosis when consumed by animals. Major symptoms include reduced feed intake and growth, and increased hyperthermia during heat stress. Seaweed extract was tested, using both rodent and bovine models, to determine potential for reduction of fescue toxicosis-induced hyperthermia. Results show that the seaweed extract reduces hyperthermia associated with fescue toxicosis.     

Heat transport mechanisms in vascular tissues: a model comparison

We have conducted a parametric comparison of three different vascular models for describing heat transport in tissue. Analytical and numerical methods were used to predict the gross temperature distribution throughout the tissue and the small-scale temperature gradients associated with thermally significant blood vessels. The models are: an array of unidirectional vessels, an array of countercurrent vessels, and a set of large vessels feeding small vessels which then drain into large vessels. We show that three continuum formulations of bioheat transfer (directed perfusion, effective conductivity, and a temperature-dependent heat sink) are limiting cases of the vascular models with respect to the thermal equilibration length of the vessels. When this length is comparable to the width of the heated region of tissue, the local temperature changes near the vessels can be comparable to the gross temperature elevation. These results are important to the use of thermal techniques used to measure the blood perfusion rate and in the treatment of cancer with local hyperthermia.