New thermal wave aspects on burn evaluation of skin subjected to instantaneous heating

Photothermal effects of terahertz-band and optical electromagnetic radiation on human tissues

The field of wireless communication has witnessed tremendous advancements in the past few decades, leading to more pervasive and ubiquitous networks. Human bodies are continually exposed to electromagnetic radiation, but typically this does not impact the body as the radiation is non-ionizing and the waves carry low power. However, with progress in the sixth generation (6G) of wireless networks and the adoption of the spectrum above 100 GHz in the next few years, higher power radiation is needed to cover larger areas, exposing humans to stronger and more prolonged radiation. Also, water has a high absorption coefficient at these frequencies and could lead to thermal effects on the skin. Hence, there is a need to study the radiation effects on human tissues, specifically the photothermal effects. In this paper, we present a custom-built, multi-physics model to investigate electromagnetic wave propagation in human tissue and study its subsequent photothermal effects. The proposed finite-element model consists of two segments-the first one estimates the intensity distribution along the beam path, while the second calculates the increase in temperature due to the wave distribution inside the tissue. We determine the intensity variation in the tissue using the radiative transfer equation and compare the results with Monte Carlo analysis and existing analytical models. The intensity information is then utilized to predict the rise in temperature with a bio-heat transfer module, powered by Pennes' bioheat equation. The model is parametric, and we perform a systematic photothermal analysis to recognize the crucial variables responsible for the temperature growth inside the tissue, particularly for terahertz and near-infrared optical frequencies. Our numerical model can serve as a benchmark for studying the high-frequency radiation effects on complex heterogeneous media such as human tissue.

Computational study on 2D three-phase lag bioheat model during cryosurgery using RBF meshfree method

Biological tissue has a multidimensional and non-homogeneous inner structure by nature. The temperature distribution and freezing front locations in biological tissue are crucial to optimizing the damage to tissue during cryosurgery. There is a need for a good mathematical model and effective simulation techniques to predict the effectiveness of the therapy. The present study concerns the numerical study of phase change phenomena during cryosurgery using the three-phase lag (TPL) bioheat model in arbitrary soft tissue domains, i.e., circular (Γ₁), ameba-like (Γ₂), and multiconnected (Γ₃). We employ the effective heat capacity formulation to solve the nonlinear governing equation. The Gaussian radial basis function and Crank-Nicolson finite difference approximation are applied for spatial and time derivatives, respectively. Using the present algorithm, we study the impact of phase lag (τ_v) due to thermal displacement involved in the TPL model on phase change interface position and thermal distribution in all three domains. The obtained results may be beneficial in the field of oncology.

Bio-thermal response and thermal damage in biological tissues with non-equilibrium effect and temperature-dependent properties induced by pulse-laser irradiation

Comprehension of thermal behavior underlying the living biological tissues helps successful applications of current heat therapies. The present work is to explore the heat transport properties of irradiated tissue during tis thermal treatment, in which the local thermal non-equilibrium effect as well as temperature-dependent properties arose from complicated anatomical structure, is considered. Based on the generalized dual-phase lag (GDPL) model, a non-linear governing equation of tissue temperature with variable thermal physical properties is proposed. The effective procedure constructed on an explicit finite difference scheme is then developed to predict numerically the thermal response and thermal damage irradiated by a pulse laser as a therapeutic heat source. The parametric study on variable thermal physical parameters including the phase lag times, heat conductivity, specific heat capacity and blood perfusion rate has been performed to evaluate their influence on temperature distribution in time and space. On this basis, the thermal damage with different laser variables such as laser intensity and exposure time are further analyzed.

Photothermal conversion and transfer in photothermal therapy: From macroscale to nanoscale

Photothermal therapy (PTT) is a promising alternative therapy for benign or even malignant tumors. To improve the selective heating of tumor cells, target-specific photothermal conversion agents are often included, especially nanoparticles. Meanwhile, some indirect methods by manipulating the radiation and heat delivery are also adopted. Therefore, to gain a clear understanding of the mechanism, and to improve the controllability of PTT, a few issues need to be clarified, including bioheat and radiation transfer, localized and collective heating of nanoparticles, etc. In this review, we provide an introduction to the typical bioheat transfer and radiation transfer models along with the dynamic thermophysical properties of biological tissue. On this basis, we reviewed the most recent advances in the temperature control methods in PTT from macroscale to nanoscale. Most importantly, a comprehensive introduction of the localized and collective heating effects of nanoparticle clusters is provided to give a clear insight into the mechanism for PPT from the microscale and nanoscale point of view.

Calculation of Effective Thermal Conductivity for Human Skin Using the Fractal Monte Carlo Method

In this work, an effective thermal conductivity (ETC) for living tissues, which directly affects the energy transport process, is determined. The fractal scaling and Monte Carlo methods are used to describe the tissue as a porous medium, and blood is considered a Newtonian and non-Newtonian fluid for comparative and analytical purposes. The effect of the principal variables-such as fractal dimensions DT and Df, porosity, and the power-law index, n-on the temperature profiles as a function of time and tissue depth, for one- and three-layer tissues, besides temperature distribution, are presented. ETC was improved by considering high tissue porosity, low tortuosity, and shear-thinning fluids. In three-layer tissues with different porosities, perfusion with a non-Newtonian fluid contributes to the understanding of the heat transfer process in some parts of the human body.

The effect of heat flux distribution and internal heat generation on the thermal damage in multilayer tissue in thermotherapy

Proper analysis of the temperature distribution during heat therapy in the target tissue and around it will prevent damage to other adjacent healthy cells. In this study, the exact solution of steady and unsteady of the hyperbolic bioheat equations is performed for multilayer skin with tumor at different heat fluxes on its surface and the generation of internal heat in the tumor. By determining the temperature distribution in three modes of constant heat flux, parabolic heat flux and internal heat generation in tumor tissue, the amount of burn in all three modes is evaluated. The results indicated that the Fourier or non-Fourier behavior of tissue has no role in the rate of burns in thermotherapy processes. At equal powers applied to the tissue, the internal heat generation in the tumor, constant flux and parabolic flux on the skin surface have the most uniform and most non-uniform temperature distribution, respectively and cause the least and the most thermal damage in the tissue.

A Non-Fourier Bioheat Transfer Model for Cryosurgery of Tumor Tissue with Minimum Collateral Damage

BACKGROUND AND OBJECTIVES

Incorporation of non-Fourier heat conduction while studying heat transfer phenomena in biological materials has emerged has an important approach as it predicts better and more realistic results than Fourier based models. In this article we have proposed a non-Fourier computational model and applied the same to simulate cryosurgery of lung tumor and attempted minimization of freezing damage of healthy lung tissue using pulsed laser irradiation.

METHODS

A non-Fourier bioheat transfer model for phase change in biological tissues is solved via a Fourier heat conduction based solution approach. A unified model is proposed combining all variants of bioheat models: Fourier's heat conduction based Pennes' bioheat model, hyperbolic heat conduction model and dual phase lag model. The proposed model takes into account the different thermophysical properties of frozen and unfrozen regions. In order to mimic the actual biotransport process, the blood perfusion and metabolic heat generation are switched off in the frozen region. Implicit source based enthalpy method is used to model phase change process. A new iterative enthalpy update equation is developed for capturing evolution of freezing front implicitly. Finite Volume based numerical discretization technique is used to discretize the governing PDE. The resulting discrete algebraic equation set is solved implicitly by Tri-diagonal Matrix Algorithm. The proposed model is verified with existing results from the literature.

RESULTS

For Fourier heat conduction, freezing time of 99.99% of tumor is 1247s, which increases to 1267s for τ_q= 5s (τ_T= 0s) and again reduces to 1255s for τ_q= 5s and τ_T= 3s. τ_q and τ_T are phase lag parameters for non-Fourier heat conduction. For τ_q= 5s and τ_T= 0.05s, the freezing damage of healthy tissue decreases by 23.76% when pulsed laser irradiation (I_o = 10⁶ W/m²) is used to warm the neighboring healthy tissue.

CONCLUSIONS

So non-Fourier bioheat transport models are better and more accurate in predicting temperature history, freezing time and freezing front propagation as compared to Fourier based models. Pulsed laser irradiation can prove to be a very efficient technique in minimizing collateral damage during cryosurgery.

Residence time distribution (RTD) revisited

Residence Time Distribution (RTD) theory is revisited and tracer technology discussed. The background of RTD following Danckwerts ideas is presented by introducing "distribution" functions for residence time, internal age and intensity function and how to experimentally obtain them with tracer techniques (curves C and F of Danckwerts). Compartment models to describe fluid flow in real reactors are reviewed and progressive modeling of chromatographic processes discussed in some detail. The shortcomings of Standard Dispersion Model (SDM) are addressed, the Taylor-Aris model discussed and the Wave Model of Westerterp's group introduced. The contribution of Computational Fluid Dynamics (CFD) is highlighted to calculate RTD from momentum and mass transport equations and to access spatial age distribution and degree of mixing. Finally smart RTD and future challenges are discussed.

A space-fractional Pennes bioheat conduction model for skin tissue

This study attempts to develop a modified Pennes bioheat conduction model for skin tissue, by using space-fractional derivative. The developed fractional model is applied to capture the thermal behaviour of the skin tissue subjected to heating and cooling procedures. It is found that with the increase of the fractional order, the predicted temperature of the skin tissue at the heating stage increases, while it decreases at the cooling stage. Irrespective of the value of the fractional order, the simulated temperature along the skin tissue at both heating and cooling stages became stable after several seconds thermal conduction. The fractional model reduces to the original Pennes model when the fractional order equals to two.

Characterization of Thermal Damage Due to Two-Temperature High-Order Thermal Lagging in a Three-Dimensional Biological Tissue Subjected to a Rectangular Laser Pulse

The use of lasers and thermal transfers on the skin is fundamental in medical and clinical treatments. In this paper, we constructed and applied bioheat transfer equations in the context of a two-temperature heat conduction model in order to discuss the three-dimensional variation in the temperature of laser-irradiated biological tissue. The amount of thermal damage in the tissue was calculated using the Arrhenius integral. Mathematical difficulties were encountered in applying the equations. As a result, the Laplace and Fourier transform technique was employed, and solutions for the conductive temperature and dynamical temperature were obtained in the Fourier transform domain.

Modeling of One-Dimensional Thermoelastic Dual-Phase-Lag Skin Tissue Subjected to Different Types of Thermal Loading

This work introduces a mathematical model of thermoelastic skin tissue in the context of the dual-phase-lag heat conduction law. One-dimensional skin tissue has been considered with a small thickness and its outer surface traction free. The bounding plane of the skin tissue is subjected to three different types of thermal loading; thermal shock, ramp type heating, and harmonic heating. The inner surface has no temperature increment and traction free. Laplace transform techniques have been used, and its inversions have been calculated by using the Tzuo method. The numerical results have been represented in figures. The thermal shock time parameter, the ramp-type heat parameter, and the angular thermal parameter have significant effects on the temperature increment, the strain, the displacement, and the stress distributions, and they play vital roles in the speed propagation of the thermomechanical waves through the skin tissue.

Numerical simulation of fractional non-Fourier heat conduction in skin tissue

In this paper, a fractional non-Fourier heat conduction model is employed to simulate the heat diffusion through the skin tissue, as a biological system, upon immediate contact with a heat source. In order to study skin models and different boundary aspects, two problems: the three-layer skin tissue in contact with a hot water source and a single-layer skin tissue exposed suddenly to a heat source generated by a laser are investigated. In both cases, the super-diffusion fractional non-Fourier model is used to simulate the heat transfer diffused through the skin tissue. In the first case, the governing equation is solved using an implicit method, and in the second problem, its governing equation is solved using a finite volume method. In the fractional non-Fourier model, the effect of the model's essential parameters (αand τ) on the prediction of temperature distribution in skin tissue is studied as well as the effect of other parameters such as the blood rate is studied. In addition, grid study has been investigated and the most efficient and appropriate gird is obtained. The results are validated against the DPL (Dual-Phase Lag) model's results. The fractional single-phase-lag model's results indicate that this model is highly precise and encompasses all the results of the dual-phase-lag model. The results also show the high precision of the model, taking into account both the microstructure interactions and the lags.

Two-dimensional closed-form model for temperature in living tissues for hyperthermia treatments

This research article determines an exact analytical expression for 2-D thermal field in single layer living tissues under a therapeutic condition by means of Fourier and non-Fourier heat transfer approaches. An actual spatially dependent initial condition has been adopted to analyze the heat propagation in tissues. The exact analytical determination for this actual initial condition for temperature may be difficult. However, in this study, an approximate analytical method has newly been established for an appropriate initial condition. With this initial expression, an exact temperature distribution for 2-D heat conduction in plane co-ordinates has been investigated for the predefined therapeutic boundary condition to have knowledge for practical aspects of the thermal therapy. Laplace Transform Method (LTM) in conjunction with the Inversion Theorem is used for the analytical solution treatment. We have utilized both Pennes' bioheat equation (PBHE) and thermal wave model of bioheat equation (TWMBHE) for the analysis. The influence of thermo-biological behavior on 2-D heat conduction in tissues has been studied with the variation of several dependable parameters in relation to the Hyperthermia treatment protocol in a moderate temperature range (42-45°C). The result in the present study has been evidenced for the biological heat transfer for the enforcement of different circumstances and also has been validated with the published value where the maximum temperature deviation of 2.6% has been recorded. We conclude that the temperature curve for TWMBHE model shows a higher waveform nature for low thermal relaxation time and this wavy nature gradually diminishes with an increase in relaxation time. The maximum peak temperature attains 46.3°C for the relaxation time = 2s and with the increase in the relaxation time the peak temperature gradually falls. The impact of blood perfusion rate on the relaxation time has also been established in this paper.

Thermal injury of skin and subcutaneous tissues: A review of experimental approaches and numerical models

Thermal injury to skin and subcutaneous tissue is common in both civilian and combat scenarios. Understanding the change in tissue morphologies and properties and the underlying mechanisms of thermal injury are of vital importance to clinical determination of the degree of burn and treatment approach. This review aims at summarizing the research involving experimental and numerical studies of skin and subcutaneous tissue subjected to thermal injury. The review consists of two parts. The first part deals with experimental studies including burn protocols and prevailing imaging approaches. The second part deals with existing numerical models for burns of tissue and related computational simulations. Based on this review, we conclude that though there is literature contributing to the knowledge of the pathology and pathogenesis of tissue burn, there is scant quantitative information regarding changes in tissue properties including mechanical, thermal, electrical and optical properties as a result of burns that are linked to altered tissue morphology.

A review of the evidence for threshold of burn injury

INTRODUCTION

Burn injury is common and depth is one measure of severity. Although the depth of burn injury is determined by many factors, the relationship between the temperature of the injurious agent and exposure duration, known as the time-temperature relationship, is widely accepted as one of the cornerstones of burn research. Moritz and Henriques first proposed this relationship in 1947 and their seminal work has been cited extensively. However, over the years, readers have misinterpreted their findings and incorporated misleading information about the time-temperature relationship into a wide range of industrial standards, burn prevention literature and medicolegal opinion.

AIM

The purpose of this paper is to present a critical review of the evidence that relates temperature and time to cell death and the depth of burn injury. These concepts are used by researchers, burn prevention strategists, burn care teams and child protection professionals involved in ascertaining how the mechanism of burning relates to the injury pattern and whether the injury is consistent with the history.

REVIEW METHODS

This review explores the robustness of the currently available evidence. The paper summarises the research from burn damage experimental work as well as bioheat transfer models and discusses the merits and limitations of these approaches.

REVIEW FINDINGS

There is broad agreement between in vitro and in vivo studies for superficial burns. There is clear evidence that the perception of pain in adult human skin occurs just above 43°C. When the basal layer of the epidermis reaches 44°C, burn injury occurs. For superficial dermal burns, the rate of tissue damage increases logarithmically with a linear increase in temperature. Beyond 70°C, rate of damage is so rapid that interpretation can be difficult. Depth of injury is also influenced by skin thickness, blood flow and cooling after injury. There is less clinical evidence for a time-temperature relationship for deep or subdermal burns. Bioheat transfer models are useful in research and becoming increasingly sophisticated but currently have limited practical use. Time-temperature relationships have not been established for burns in children's skin, although standards for domestic hot water suggest that the maximum temperature should be revised downward by 3-4°C to provide adequate burn protection for children.

CONCLUSION

Time-temperature relationships established for pain and superficial dermal burns in adult human skin have an extensive experimental modeling basis and reasonable clinical validation. However, time-temperature relationships for subdermal burns, full thickness burns and burn injury in children have limited clinical validation, being extrapolated from other data, and should be used with caution, particularly if presented during expert evidence.

Influence of Initial Moisture Content on Heat and Moisture Transfer in Firefighters' Protective Clothing

This paper presents a model for heat and moisture transfer through firefighters' protective clothing (FPC) during radiation exposure. The model, which accounts for air gaps in the FPC as well as heat transfer through human skin, investigates the effect of different initial moisture contents on the thermal insulation performance of FPC. Temperature, water vapor density, and the volume fraction of liquid water profiles were monitored during the simulation, and the heat quantity absorbed by water evaporation was calculated. Then the maximum durations of heat before the wearer acquires first- and second-degree burns were calculated based on the bioheat transfer equation and the Henriques equation. The results show that both the moisture weight in each layer and the total moisture weight increase linearly within a given environmental humidity level. The initial moisture content in FPC samples significantly influenced the maximum water vapor density. The first- and second-degree burn injury time increase 16 sec and 18 sec when the RH increases from 0% to 90%. The total quantity of heat accounted for by water evaporation was about 10% when the relative humidity (RH) is 80%. Finally, a linear relationship was identified between initial moisture content and the human skin burn injury time before suffering first- and second-degree burn injuries.

Thermography-based blood flow imaging in human skin of the hands and feet: a spectral filtering approach

The determination of the relationship between skin blood flow and skin temperature dynamics is the main problem in thermography-based blood flow imaging. Oscillations in skin blood flow are the source of thermal waves propagating from micro-vessels toward the skin's surface, as assumed in this study. This hypothesis allows us to use equations for the attenuation and dispersion of thermal waves for converting the temperature signal into the blood flow signal, and vice versa. We developed a spectral filtering approach (SFA), which is a new technique for thermography-based blood flow imaging. In contrast to other processing techniques, the SFA implies calculations in the spectral domain rather than in the time domain. Therefore, it eliminates the need to solve differential equations. The developed technique was verified within 0.005-0.1 Hz, including the endothelial, neurogenic and myogenic frequency bands of blood flow oscillations. The algorithm for an inverse conversion of the blood flow signal into the skin temperature signal is addressed. The examples of blood flow imaging of hands during cuff occlusion and feet during heating of the back are illustrated. The processing of infrared (IR) thermograms using the SFA allowed us to restore the blood flow signals and achieve correlations of about 0.8 with a waveform of a photoplethysmographic signal. The prospective applications of the thermography-based blood flow imaging technique include non-contact monitoring of the blood supply during engraftment of skin flaps and burns healing, as well the use of contact temperature sensors to monitor low-frequency oscillations of peripheral blood flow.

DEVELOPING ANALYTICAL MODELS OF PREDICTING SKIN TEMPERATURE AND DAMAGE EXTENT FROM SINGLE-LAYER INTO MULTI-LAYER ONES

As a starting point for developing analytical models of predicting skin temperature and damage extent into multi-layer ones, a double-layer model consisting of two distinguished and attached layers is considered: a tissue layer containing blood vessels and a tissue layer containing no blood vessels. The Pennes model is applied for the tissue containing blood vessels. Applying the Laplace transform, then the inversion theorem for Laplace transforms and the Cauchy residue theorem, the desired skin temperature function is obtained. Applying the temperature function in a damage model, the severity and degree of damage can be determined. Validating this model against previous analytical, numerical and experimental data, the error rate is determined.

NUMERICAL ANALYSIS OF TRIPLE LAYER SKIN TISSUE FREEZING USING NON-FOURIER HEAT CONDUCTION

The classical Fourier’s law assumes that the propagation speed of thermal disturbance is infinite, which is contradictory to physical reality. The living tissues are highly non-homogeneous and need a relaxation time to accumulate enough energy to transfer to the nearest element. This study proposes hyperbolic bio-heat model to study the freezing process in triple layer skin tissue with non-ideal property of skin tissue, metabolism and blood perfusion. The enthalpy formulation and finite difference method are used to solve the hyperbolic bio-heat model for triple layer skin tissue freezing. The effects of relaxation time for heat flux on temperature profile, liquidus and solidus interfaces are studied during the freezing of skin tissue. It is observed that the different values of relaxation time for heat flux have significant effect on temperature distribution, liquidus and solidus interfaces within the skin tissue.

Tissue responses to fractional transient heating with sinusoidal heat flux condition on skin surface

A fractional model of Bioheat equation for describing quantitatively the thermal responses of skin tissue under sinusoidal heat flux conditions on skin surface is given. Laplace transform technique is used to obtain the solution in a closed form. The resulting formulation is applied to one-dimensional application to investigate the temperature distribution in skin with instantaneous surface heating for different cases. According to the numerical results and its graphs, conclusion about the fractional bioheat transfer equation has been constructed. Sensitivity analysis is performed to explore the thermal effects of various control parameters on tissue temperature. The comparisons are made with the results obtained in the case of the absence of time-fractional order. © 2016 Japanese Society of Animal Science.

Comprehensive analytical model for CW laser induced heat in turbid media

In this work, we present a new analytical approach to model continuous wave laser induced temperature in highly homogeneous turbid media. First, the diffusion equation is used to model light transport and a comprehensive solution is derived analytically by obtaining a special Greens' function. Next, the time-dependent bio-heat equation is used to describe the induced heat increase and propagation within the medium. The bio-heat equation is solved analytically utilizing the separation of variables technique. Our theoretical model is successfully validated using numerical simulations and experimental studies with agarose phantoms and ex-vivo chicken breast samples. The encouraging results show that our method can be implemented as a simulation tool to determine important laser parameters that govern the magnitude of temperature rise within homogenous biological tissue or organs.

Heat treatment modelling using strongly continuous semigroups

In this paper, mathematical simulation of bioheat transfer phenomenon within the living tissue is studied using the thermal wave model. Three different sources that have therapeutic applications in laser surgery, cornea laser heating and cancer hyperthermia are used. Spatial and transient heating source, on the skin surface and inside biological body, are considered by using step heating, sinusoidal and constant heating. Mathematical simulations describe a non-Fourier process. Exact solution for the corresponding non-Fourier bioheat transfer model that has time lag in its heat flux is proposed using strongly continuous semigroup theory in conjunction with variational methods. The abstract differential equation, infinitesimal generator and corresponding strongly continuous semigroup are proposed. It is proved that related semigroup is a contraction semigroup and is exponentially stable. Mathematical simulations are done for skin burning and thermal therapy in 10 different models and the related solutions are depicted. Unlike numerical solutions, which suffer from uncertain physical results, proposed analytical solutions do not have unwanted numerical oscillations.

Prediction methods of skin burn for performance evaluation of thermal protective clothing

Most test methods use skin burn prediction to evaluate the thermal protective performance of clothing. In this paper, we reviewed different burn prediction methods used in clothing evaluation. The empirical criterion and the mathematical model were analyzed in detail as well as their relationship and limitations. Using an empirical criterion, the onset of skin burn is determined by the accumulated skin surface energy in certain periods. On the other hand, the mathematical model, which indicates denatured collagen, is more complex, which involves a heat transfer model and a burn model. Further studies should be conducted to examine the situations where the prediction methods are derived. New technologies may be used in the future to explore precise or suitable prediction methods for both flash fire tests and increasingly lower-intensity tests.

Fourier, hyperbolic and relativistic heat transfer equations: a comparative analytical study

Parabolic heat equation based on Fourier's theory (FHE), and hyperbolic heat equation (HHE), has been used to mathematically model the temperature distributions of biological tissue during thermal ablation. However, both equations have certain theoretical limitations. The FHE assumes an infinite thermal energy propagation speed, whereas the HHE might possibly be in breach of the second law of thermodynamics. The relativistic heat equation (RHE) is a hyperbolic-like equation, whose theoretical model is based on the theory of relativity and which was designed to overcome these theoretical impediments. In this study, the three heat equations for modelling of thermal ablation of biological tissues (FHE, HHE and RHE) were solved analytically and the temperature distributions compared. We found that RHE temperature values were always lower than those of the FHE, while the HHE values were higher than the FHE, except for the early stages of heating and at points away from the electrode. Although both HHE and RHE are mathematically hyperbolic, peaks were only found in the HHE temperature profiles. The three solutions converged for infinite time or infinite distance from the electrode. The percentage differences between the FHE and the other equations were larger for higher values of thermal relaxation time in HHE.

Determination of the amplitude and phase relationships between oscillations in skin temperature and photoplethysmography-measured blood flow in fingertips

It is well established that skin temperature oscillations in fingertips coexist with blood flow oscillations and there is a certain correlation between them. At the same time, the reasons for differences in waveform and the delay between the blood flow and temperature oscillations are far from being fully understood. In this study we determine the relationships between spectral components of the blood flow and temperature oscillations in fingertips, and we ascertain the frequency dependences of amplitude attenuation and delay time for the temperature oscillations. The blood flow oscillations were considered as a source of thermal waves propagating from micro-vessels towards the skin surface and manifesting as temperature oscillations. The finger temperature was measured by infrared thermography and blood flow was assessed by photoplethysmography for ten healthy subjects. The time-frequency analysis of oscillations was based on the Morlet wavelet transform. The frequency dependences of delay time and amplitude attenuation in temperature compared with blood flow oscillations have been determined in endothelial (0.005-0.02 Hz) and neurogenic (0.02-0.05 Hz) frequency bands using the wavelet spectra. We approximated the experimental frequency dependences by equations describing thermal wave propagation through the medium and taking into account the thermal properties and thickness of a tissue. Results of analysis show that with the increase of frequency f the delay time of temperature oscillations decreases inversely proportional to f(1/2), and the attenuation of the amplitude increases directly proportional to exp f(1/2). Using these relationships allows us to increase correlation between the processed temperature oscillations and blood flow oscillations from 0.2 to 0.7 within the frequency interval 0.005-0.05 Hz. The established experimental and theoretical relationships clarify an understanding of interrelation between the dynamics of blood flow and skin temperature, and define possibilities and limitations of temperature measurements as a method of blood flow assessment in extremities.

Thermal effect of endoscopic thermal vapour ablation on the lung surface in human ex vivo tissue

PURPOSE

An investigation of the thermal effect and the potential for injury at the lung surface following thermal vapour ablation (InterVapor), an energy-based method of achieving endoscopic lung volume reduction.

METHODS

Heated water vapour was delivered to fifteen ex vivo human lungs using standard clinical procedure, and the thermal effect at the visceral pleura was monitored with an infrared camera. The time-temperature response was analysed mathematically to determine a cumulative injury quotient, which was compared to published thresholds.

RESULTS

The cumulative injury quotients for all 71 treatments of ex vivo tissue were found to be below the threshold for first degree burn and no other markers of tissue injury at the lung surface were observed.

CONCLUSION

The safety profile for thermal vapour ablation is further supported by the demonstration that the thermal effect in a worst-case model is not expected to cause injury at the lung surface.

Fuzzy approach for reducing subjectivity in estimating occupational accident severity

Quantifying or, more generally, estimating the severity of the possible consequences of occupational accidents is a decisive step in any occupational risk assessment process. Because of the lack of historic information (accident data collection and recording are incipient and insufficient, particularly in construction) and the lack of practical tools in the construction industry, the estimation/quantification of occupational accident severity is a notably arbitrary process rather than a systematic and rigorous assessment. This work proposes several severity functions (based on a safety risk assessment) to represent biomechanical knowledge with the aim of determining the severity level of occupational accidents in the construction industry and, consequently, improving occupational risk assessment quality. We follow a fuzzy approach because it makes it possible to capture and represent imprecise knowledge in a simple and understandable way for users and specialists.

Temperature and burn injury prediction of human skin exposed to microwaves: a model analysis

A one-dimensional multi-layer model is presented to characterize skin temperature rises and burn processes resulting from skin exposure to microwaves. Temperature variations and damage function analyses in the skin tissue exposed to microwaves were predicted depending on blood perfusion rate, thermal conductivity, power density, and exposure time. Thermal wave model was applied and the bio-heat transfer equation was solved using the finite difference time domain method. The thermal wave model of bio-heat transfer predicts a lower temperature rise than a model that uses Pennes' equation. When approaching steady state, the solutions overlaps with that obtained using the Pennes' equation. The results obtained may help to analyze the consequences of short-time high-power MW exposures in biological tissues.

Analytical validation of COMSOL Multiphysics for theoretical models of Radiofrequency ablation including the Hyperbolic Bioheat transfer equation

In this paper we outline our main findings about the differences between the use of the Bioheat Equation and the Hyperbolic Bioheat Equation in theoretical models for Radiofrequency (RF) ablation. At the moment, we have been working on the analytical approach to solve both equations, but more recently, we have considered numerical models based on the Finite Element Method (FEM). As a first step to use FEM, we conducted a comparative study between the temperature profiles obtained from the analytical solutions and those obtained from FEM. Regarding the differences between both methods, we obtain agreement in less than 5% of relative differences. Then FEM is a good alternative to model heating of biological tissues using BE and HBE in, for example, more complex and realistic geometries.

Assessment of hyperbolic heat transfer equation in theoretical modeling for radiofrequency heating techniques

Theoretical modeling is a technique widely used to study the electrical-thermal performance of different surgical procedures based on tissue heating by use of radiofrequency (RF) currents. Most models employ a parabolic heat transfer equation (PHTE) based on Fourier's theory, which assumes an infinite propagation speed of thermal energy. We recently proposed a one-dimensional model in which the electrical-thermal coupled problem was analytically solved by using a hyperbolic heat transfer equation (HHTE), i.e. by considering a non zero thermal relaxation time. In this study, we particularized this solution to three typical examples of RF heating of biological tissues: heating of the cornea for refractive surgery, cardiac ablation for eliminating arrhythmias, and hepatic ablation for destroying tumors. A comparison was made of the PHTE and HHTE solutions. The differences between their temperature profiles were found to be higher for lower times and shorter distances from the electrode surface. Our results therefore suggest that HHTE should be considered for RF heating of the cornea (which requires very small electrodes and a heating time of 0.6 s), and for rapid ablations in cardiac tissue (less than 30 s).

Effect of the thermal wave in radiofrequency ablation modeling: an analytical study

To date, all radiofrequency heating (RFH) theoretical models have employed Fourier's heat transfer equation (FHTE), which assumes infinite thermal energy propagation speed. Although this equation is probably suitable for modeling most RFH techniques, it may not be so for surgical procedures in which very short heating times are employed. In such cases, a non-Fourier model should be considered by using the hyperbolic heat transfer equation (HHTE). Our aim was to compare the temperature profiles obtained from the FHTE and HHTE for RFH modeling. We built a one-dimensional theoretical model based on a spherical electrode totally embedded and in close contact with biological tissue of infinite dimensions. We solved the electrical-thermal coupled problem analytically by including the power source in both equations. A comparison of the analytical solutions from the HHTE and FHTE showed that (1) for short times and locations close to the electrode surface, the HHTE produced temperatures higher than the FHTE, however, this trend became negligible for longer times, when both equations produced similar temperature profiles (HHTE always being higher than FHTE); (2) for points distant from the electrode surface and for very short times, the HHTE temperature was lower than the FHTE, however, after a delay time, this tendency inverted and the HHTE temperature increased to the maximum; (3) from a mathematical point of view, the HHTE solution showed cuspidal-type singularities, which were materialized as a temperature peak traveling through the medium at a finite speed. This peak rose at the electrode surface, and clearly reflected the wave nature of the thermal problem; (4) the differences between the FHTE and HHTE temperature profiles were smaller for the lower values of thermal relaxation time and locations further from the electrode surface.

Heat analysis of biological tissue exposed to microwave by using thermal wave model of bio-heat transfer (TWMBT)

Thermal analyses of biological tissues exposed to microwaves were studied by using thermal wave model of bio-heat transfer (TWMBT). As a model, skin stratified as three layers with various thermal physical properties were simulated and thermal wave model of bio-heat transfer equations were solved by using finite difference method. Finally, the thermal variations were simulated in the cross section of the model. Comparative studies on the traditional Pennes' equations and thermal wave model of bio-heat transfer were performed and evaluated. Furthermore, temperature variations in the skin exposed to microwave were predicted depending on blood perfusion rate, thermal conductivity, frequency and power density of microwave, and exposure time. Thermal wave model of bio-heat transfer gives lower heat rise predictions than that of Pennes' equation, initially. When it approaches to steady state, it overlaps with the Pennes' equation.

Finite element analysis and experimental verification of multilayered tissue characterization using the thermal technique

The objective of this research is to develop noninvasive techniques to determine thermal properties of layered biologic structures based on measurements from the surface. The self-heated thermistor technique is evaluated both numerically and experimentally. The finite element analyses, which confirm the experimental results, are used to study the temperature profiles occurring in the thermistor-tissue system. An in vitro tissue model was constructed by placing Teflon of varying thickness between the biologic tissue and the self-heated thermistor. The experiments were performed using two different-sized thermistors on six tissue samples. A self-heated thermistor was used to determine the thermal conductivity of tissue covered by a thin layer Teflon. The results from experimental data clearly indicate that this technique can penetrate below the thin layers of Teflon and thus is sensitive to the thermal properties of the underlying tissue. The factors which may introduce error in the experimental data are (i) poor thermal/physical contact between the thermistor probe and tissue sample, and (ii) water loss from tissue during the course of experimentation. The finite element analysis was used to simulate the experimental conditions and to calculate transient temperature profile generated by the thermistor bead. The results of finite element analysis are in accordance with the experimental data.