Boundary element method with bioheat equation for skin burn injury

Investigating the influencing factors and prediction models of skin burns for firefighters' occupational safety

Relevant studies in the fields of fire safety, occupational health and firefighter clothing were analyzed in this study to address the high injury rate among firefighters during fire rescue and the complexity of factors affecting skin burns. The findings indicate that the degree of skin burns in firefighters is primarily influenced by the heat source (heat flux, type), firefighter clothing (fabric, pattern) and the under-clothing air gap (thickness, characteristics). Since skin burns cannot be directly measured, internal skin heat transfer and burn prediction models are commonly employed to assess the impact of external factors on skin burns. These models can predict the safe working distance or time for firefighters. Investigating the influencing factors and prediction models of skin burns among firefighters holds significant value in enhancing operating procedures, optimizing firefighter clothing design and effectively preventing skin burns.

Numerical Simulation of Enhancement of Superficial Tumor Laser Hyperthermia with Silicon Nanoparticles

Biodegradable and low-toxic silicon nanoparticles (SiNPs) have potential in different biomedical applications. Previous experimental studies revealed the efficiency of some types of SiNPs in tumor hyperthermia. To analyse the feasibility of employing SiNPs produced by the laser ablation of silicon nanowire arrays in water and ethanol as agents for laser tumor hyperthermia, we numerically simulated effects of heating a millimeter-size nodal basal-cell carcinoma with embedded nanoparticles by continuous-wave laser radiation at 633 nm. Based on scanning electron microscopy data for the synthesized SiNPs size distributions, we used Mie theory to calculate their optical properties and carried out Monte Carlo simulations of light absorption inside the tumor, with and without the embedded nanoparticles, followed by an evaluation of local temperature increase based on the bioheat transfer equation. Given the same mass concentration, SiNPs obtained by the laser ablation of silicon nanowires in ethanol (eSiNPs) are characterized by smaller absorption and scattering coefficients compared to those synthesized in water (wSiNPs). In contrast, wSiNPs embedded in the tumor provide a lower overall temperature increase than eSiNPs due to the effect of shielding the laser irradiation by the highly absorbing wSiNPs-containing region at the top of the tumor. Effective tumor hyperthermia (temperature increase above 42 °C) can be performed with eSiNPs at nanoparticle mass concentrations of 3 mg/mL and higher, provided that the neighboring healthy tissues remain underheated at the applied irradiation power. The use of a laser beam with the diameter fitting the size of the tumor allows to obtain a higher temperature contrast between the tumor and surrounding normal tissues compared to the case when the beam diameter exceeds the tumor size at the comparable power.

A method to predict burn injuries of firefighters considering heterogeneous skin thickness distribution based on the instrumented manikin system

An approach was proposed to predict skin burns during heat exposure based on computational fluid dynamics and Python language. Both uniform and heterogeneous skin thickness distributions of the whole body were considered and significant differences were observed. 100% second-degree burns were reached for the uniform skin model after 4-s flash fire, and maintained during the cooling phase. Third-degree burns occurred for the heterogeneous skin model during fire exposure, and the proportion increased in the cooling phase. Results indicated that the model with uniform skin thickness probably overestimates skin burns in the early stage of fire exposure. The prediction at the latter stage of the model with heterogeneous skin thickness tended to be more serious. Ignoring blood perfusion and dynamic thermophysical parameters of the skin model was the limitation of this study. Nevertheless, this method provides the basis for further advancements in thermal protective ensembles, to enhance occupational safety of firefighters.

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.

Review of the initial treatment and avoidance of scald injuries

Scald injuries, which describe burns to living tissue from hot liquids, are a very common injury that occur across geographical, social, economic, and national boundaries. Despite their ubiquitous nature, a complete understanding of the conditions which are required to cause scald burns is not yet available. In addition, clear guidance to medical practitioners is available through various guidelines however in actual situations, the extent of the burn is not fully known and this lack of knowledge complicates care. Here, a comprehensive review is made of the available knowledge of temperatures and scald durations which lead to skin-burn injuries. The range of volumes and liquid temperatures are typical of those found in heated consumer beverages. This review can help medical practitioners design initial treatment protocols and can be used by manufacturers of hot-liquid products to avoid the most severe burns. Next, within the context of this ability to quantify burn depths, a review of current burn treatment guidelines is given. Included in this review is a visual recognition of the extent of burns into the dermal layer as well as decision guidelines for selection of patients which would benefit from referral to a dedicated burn center. It is hoped that by bringing together both the quantified burn-depth information and current treatment guidelines, this review can be used as a resource for persons in the medical, manufacturing, beverage service, and other industries to reduce the human impact of scald injuries.

Comprehensive method to predict and quantify scald burns from beverage spills

A comprehensive study was performed to quantify the risk of burns from hot beverage spills. The study was comprised of three parts. First, experiments were carried out to measure the cooling rates of beverages in a room-temperature environment by natural convection and thermal radiation. The experiments accounted for different beverage volumes, initial temperatures, cooling period between the time of service and the spill, the material which comprised the cup, the presence or absence of a cap and the presence or absence of an insulating corrugated paper sleeve. Among this list, the parameters which most influenced the temperature variation was the presence or absence of a cover or cap, the volume of the beverage and the duration of the cooling period. The second step was a series of experiments that provided temperatures at the surface of skin or skin surrogate after a spill. The experiments incorporated a single layer of cotton clothing and the exposure duration was 30 s. The outcomes of the experiments were used as input to a numerical model which calculated the temperature distribution and burn depth within tissue. Last was the implementation of the numerical model and a catalogue of burn predictions for various beverage volumes, beverage service temperatures, and durations between beverage service and spill. It is hoped that this catalogue can be used by both beverage industries and consumers to reduce the threat of burn injuries. It can also be used by treating medical professionals who can quickly estimate burn depths following a spill incident.

TEMPERATURE DISTRIBUTION AND THERMAL DAMAGE OF PERIPHERAL TISSUE IN HUMAN LIMBS DURING HEAT STRESS: A MATHEMATICAL MODEL

The physiological processes taking place in human body are disturbed by the abnormal changes in climate. The changes in environmental temperature are not effective only to compete with thermal stability of the system but also in the development of thermal injuries at the skin surfaces. Therefore, it is of great importance to estimate the temperature distribution and thermal damage in human peripherals at extreme temperatures. In this paper, the epidermis, dermis and subcutaneous tissue were modeled as uniform elements with distinct thermal properties. The bioheat equation with appropriate boundary conditions has been used to estimate the temperature profiles at the nodal points of the skin and subcutaneous tissue with variable ambient heat and metabolic activities. The model has been solved by variational finite element method and the results of the changes in temperature distribution of the body and the damage to the exposed living tissues has been interpreted graphically in relation with various atmospheric temperatures and rate of metabolic heat generation. By involving the metabolic heat generation term in bioheat equation and using the finite element approach the results obtained in this paper are more reasonable and appropriate than the results developed by Moritz and Henriques, Diller and Hayes, and Jiang et al.

A MATHEMATICAL MODEL FOR THE ESTIMATION OF THERMAL STRESS AND DEVELOPMENT OF COLD INJURIES ON THE EXPOSED ORGANS OF HUMAN BODY

The severe ambient temperature always disrupts the normal thermoregulatory system of the human body. The decrease in core temperature leads to hypothermia and the development of cold injuries takes place at the exposed shells of the human body. The intensity of the cold exposure and its duration leads to various degrees of frostbites and resulting cell damage and fluid passage from the necrotic regions. In this paper, variational finite element has been employed to estimate the thermal damage due to severe cold conditions. The formulation of the model is based on Pennes’ bioheat equation and mass diffusion equation. Moreover, the fluid passage from the cold injuries at the peripheral tissues of the human body with respect to extreme cold conditions has been analyzed in relation with other parameters.

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.

A THREE LAYER MODEL FOR THE THERMAL IMPEDANCE OF THE HUMAN SKIN: MODELING AND EXPERIMENTAL MEASUREMENTS

In this paper a dynamic three layer model for the heat transfer in the human skin is presented. The model is solved in the Laplace domain using the phasor notation. In order to compare the theoretical model with experimental results, a transient heating was carried out and the time dependent skin temperature was recorded with a thermographic camera. The transient temperature could be fitted very well to an analytical function, which could easily be transformed into the Laplace domain allowing an easy comparison between the model and the experimental results. The aim of the research is to evaluate the skin thermal parameters for all layers including the blood perfusion.

Estimating the time and temperature relationship for causation of deep-partial thickness skin burns

The objective of this study is to develop and present a simple procedure for evaluating the temperature and exposure-time conditions that lead to causation of a deep-partial thickness burn and the effect that the immediate post-burn thermal environment can have on the process. A computational model has been designed and applied to predict the time required for skin burns to reach a deep-partial thickness level of injury. The model includes multiple tissue layers including the epidermis, dermis, hypodermis, and subcutaneous tissue. Simulated exposure temperatures ranged from 62.8 to 87.8°C (145-190°F). Two scenarios were investigated. The first and worst case scenario was a direct exposure to water (characterized by a large convection coefficient) with the clothing left on the skin following the exposure. A second case consisted of a scald insult followed immediately by the skin being washed with cool water (20°C). For both cases, an Arrhenius injury model was applied whereby the extent and depth of injury were calculated and compared for the different post-burn treatments. In addition, injury values were compared with experiment data from the literature to assess verification of the numerical methodology. It was found that the clinical observations of injury extent agreed with the calculated values. Furthermore, inundation with cool water decreased skin temperatures more quickly than the clothing insulating case and led to a modest decrease in the burn extent.

Diagnosis of breast tumor using thermal tomography q-r curve

Metabolic heat, the product following the metabolism of cells, is closely related to the pathological information of living organisms, which means there are strong connections between the heat distribution and the pathological state of the living organism. The mathematical function δ is introduced in the classical Pennes bioheat transfer equation as a point heat source, and by simplifying the boundary condition, a bioheat transfer model is established. Based on the temperature distribution of the human body surface, the q−r curve of heat intensity q varying with depth r is acquired while combining the fitting method of the Lorentz curve. According to 34,977 clinical confirmed cases and the corresponding classified statistics, diagnostic criteria (for breast diseases) for judging diseases by the q−r curve are proposed. The P -value of our statistics is <0.05 , which means our classified statistics are reliable. Six typical clinical examinations are performed, and the diagnosis results are very consistent with those of B-ultrasonic images, molybdenum target x-ray, and pathological examination, which suggests that the method of diagnosing diseases with a q−r curve has very good prospects for application. It is radiation free and noninvasive to the human body.

Q-r curve of thermal tomography and its clinical application on breast tumor diagnosis

Heat is the product following the metabolism of cells, and the metabolism is closely related with the pathological information of living organism. So, there are strong ties between the heat distribution and the pathological state in living organism. In this paper, the mathematical function δ is introduced in the classical Pennes bio-heat transfer equation as the point heat source. By simplifying the boundary conditions, a novel bio-heat transfer model is established and solved in a spherical coordinate system. Based on the temperature distribution of human body surface, the information of heat source is mined layer by layer, and the corresponding q-r curve of heat intensity varying with depth is acquired combining the fitting method of Lorentz curve. According to a large number of clinical confirmed cases and statistics, the diagnostic criteria judging diseases by q-r curve are proposed. Five typical clinical practices are performed and four of the diagnosis results are very consistent with those of molybdenum target (MT) X-ray, B-ultrasonic images and pathological examination, one gives the result of early stage malignant tumor that MT X-ray and B-ultrasonic can't check out. It is a radiation-free green method with noninvasive diagnostic procedure and accurate diagnosis result.

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.

Meshless method with operator splitting technique for transient nonlinear bioheat transfer in two-dimensional skin tissues

A meshless numerical scheme combining the operator splitting method (OSM), the radial basis function (RBF) interpolation, and the method of fundamental solutions (MFS) is developed for solving transient nonlinear bioheat problems in two-dimensional (2D) skin tissues. In the numerical scheme, the nonlinearity caused by linear and exponential relationships of temperature-dependent blood perfusion rate (TDBPR) is taken into consideration. In the analysis, the OSM is used first to separate the Laplacian operator and the nonlinear source term, and then the second-order time-stepping schemes are employed for approximating two splitting operators to convert the original governing equation into a linear nonhomogeneous Helmholtz-type governing equation (NHGE) at each time step. Subsequently, the RBF interpolation and the MFS involving the fundamental solution of the Laplace equation are respectively employed to obtain approximated particular and homogeneous solutions of the nonhomogeneous Helmholtz-type governing equation. Finally, the full fields consisting of the particular and homogeneous solutions are enforced to fit the NHGE at interpolation points and the boundary conditions at boundary collocations for determining unknowns at each time step. The proposed method is verified by comparison of other methods. Furthermore, the sensitivity of the coefficients in the cases of a linear and an exponential relationship of TDBPR is investigated to reveal their bioheat effect on the skin tissue.

METHOD OF FUNDAMENTAL SOLUTIONS FOR NONLINEAR SKIN BIOHEAT MODEL

In this paper, the method of fundamental solution (MFS) coupling with the dual reciprocity method (DRM) is developed to solve nonlinear steady state bioheat transfer problems. A two-dimensional nonlinear skin model with temperature-dependent blood perfusion rate is studied. Firstly, the original bioheat transfer governing equation with nonlinear term induced by temperature-dependent blood perfusion rate is linearized with the Taylor's expansion technique. Then, the linearized governing equation with specified boundary conditions is solved using a meshless approach, in which the DRM and the MFS are employed to obtain particular and homogeneous solutions, respectively. Several numerical examples involving linear, quadratic and exponential relations between temperature and blood perfusion rate are tested to verify the efficiency and accuracy of the proposed meshless model in solving nonlinear steady state bioheat transfer problems, and also the sensitivity of coefficients in the expression of temperature-dependent blood perfusion rate is analyzed for investigating the influence of blood perfusion rate to temperature distribution in skin tissues.

NUMERICAL SIMULATION OF FRACTIONAL BIOHEAT EQUATION IN HYPERTHERMIA TREATMENT

This paper deals with the study of fractional bioheat equation for hyperthermia treatment in cancer therapy with external electromagnetic (EM) heating. Time fractional derivative is considered as Caputo fractional derivative of order α ∈ (0, 1]. Numerical solution is obtained by implicit finite difference method. The effect of anomalous diffusion in tissue has been studied. The temperature profile and thermal damage over the entire affected region are obtained for different values of α.

INFLUENCE OF INFRARED RADIATION ON THE HUMAN SKIN TEMPERATURE — EXPERIMENTAL DATA AND MODELING

The temperature rise of the hand palm has been measured with infrared thermography under the influence of an external infrared radiation source. The temperature rises could be very well fitted to exponential function, so that the experimental data could be summarized with just two parameters: amplitude and time constant. A simple mathematical model has been set up to explain the experimentally observed phenomena. It was found that the blood perfusion is essential to explain the results. From our measurements, which is essentially a noninvasive technique, several parameters could be found, the numerical values of which, agree with data found in the literature.

A FUNDAMENTAL SOLUTION-BASED FINITE ELEMENT MODEL FOR ANALYZING MULTI-LAYER SKIN BURN INJURY

To understand the physiology of tissue burns for successful clinical treatment, it is important to investigate the thermal behavior of human skin tissue subjected to heat injury. In this paper, a fundamental solution-based hybrid finite element formulation is proposed for numerically simulating steady-state temperature distribution inside a multilayer human skin tissue during burning. In the present approach, since only element boundary integrals are involved, the computational dimension is reduced by one as the fundamental solutions used analytically satisfies the bioheat governing equation. Further, in multi-layer skin modeling, the burn is applied via a heating disk at constant temperature on a part of the epidermal surface of the skin tissue. Numerical results from the proposed approach are firstly verified by comparing them with exact solutions of a simple single-layered model or the results from conventional finite element method. Thereafter, a sensitivity analysis is carried out to reveal the effect of biological and environmental parameters on temperature distribution inside the skin tissue subjected to heat injury.

Prediction and parametric analysis of thermal profiles within heated human skin using the boundary element method

In this paper, an axisymmetric model of the human skin is developed to simulate the steady-state temperature distribution during contact with a hot solid. Simulations are carried out using the boundary element method. This study seeks to investigate the feasibility of using the boundary element method in the studies of burn. A sensitivity analysis is carried out to examine the effects of various parameters on the temperature distribution inside the skin during burn. Furthermore, a statistical analysis based on the Taguchi method is performed to determine the combination of factors that produce the desired outcome (least increase in temperature). In order to validate the accuracy of the numerical scheme, results obtained using the boundary element method are compared with the solutions obtained using the more established finite-element method.