A three-dimensional variable geometry countercurrent model for whole limb heat transfer

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.

A Three-Dimensional Finite Element Model of the Transibial Residual Limb and Prosthetic Socket to Predict Skin Temperatures

Amputees who wear prosthetic limbs often experience discomfort from blisters and sores due to mechanical insult; these skin conditions are exacerbated by elevated skin temperatures and excessive perspiration within the prosthetic socket. The goal of this study was to create a tool for developing new prostheses that accommodate varying thermal loads arising from everyday activities. A three-dimensional thermal model of a transtibial residual limb and prosthesis was constructed using the finite element (FE) method. Transverse computerized tomography (CT) scans were used to specify the geometry of the residual limb and socket. Thermal properties from the literature were assigned to both biological tissue and prosthetic socket elements. The purpose of this work was to create a model that would aid in testing the effect of new prosthesis designs on skin temperature. To validate its output, the model was used to predict the skin temperature distribution in a common prosthetic socket system (silicone liner, wool sock, and carbon fiber socket) at rest with no mechanical loading. Skin temperatures were generally elevated near muscle and decreased anteriorly and at the distal end. Experimental temperature measurements taken at the skin-prosthesis interface of five human subjects were used to validate the model. Data extracted from the thermal model at anterior, posterior, lateral, and medial locations were typically within one standard deviation of experimental results; the mean temperatures were within 0.3 degree C for each section and were within 0.1 degree C overall.

A Three-Dimensional Finite Element Analysis of Heat Transfer in the Forearm

The finite element method was used to analyze heat transfer within a section of the forearm while exposed to different ambient conditions and with different metabolic states. The three-dimensional model accounts for the different material properties of bone, muscle and blood and incorporates a single artery-vein pair for counter-current heat exchange. The geometry of the model was developed from anatomical cross-sectional images of the forearm. The model was used to determine the effects or rest vs. exercise, free vs. forced surface convection and 0 degrees C vs. -20 degrees C external temperatures. The results of the model were compared to experimental data and the model exhibits qualitatively correct behaviour. This model can be used to study hyperthermia, burns and cryogenic freezing of tissue.

Enhancement in the effective thermal conductivity in rat spinotrapezius due to vasoregulation

This study was undertaken to gain a better understanding of the countercurrent heat exchange of thermally significant blood vessels in skeletal muscle by measuring the vascular structure and flow in an exteriorized rat spinotrapezius muscle and estimating the enhancement in the effective thermal conductivity of the muscle. Detailed anatomic measurements of the number density and length of countercurrent vessel pairs between 45 and 165 microns diameter were obtained. Moreover, diameter and blood flow in the 1A to 3A vessels were measured for muscles in which pharmacological vasoactive agents were introduced, allowing one to vary the local blood flow Peclet number from 1 to 18 in the major feeding arteries. These combined measurements have been used to estimate the range of possible enhancement in the effective thermal conductivity of the tissue. The newly derived conduction shape factor in Zhu et al. for countercurrent vessels in two-dimensional tissue preparations was used in this analysis. Our experimental data indicated that the value of this conduction shape factor was about one-third to two-thirds the value for two countercurrent vessels of the same size and spacing in an infinite medium. The experiment also revealed that the Weinbaum-Jiji expression for keff was valid for the spinotrapezius muscle when the largest vessels were less than 195 microns diameter. A fivefold increase in keff was predicted for 195 microns diameter vessels. Vasoregulation was also shown to have a dramatic effect on keff. A tissue that exhibits only small increases in keff due to countercurrent convection in its vasoconstricted state can exhibit a more than fivefold increase in keff in its vasodilated state.

A non-uniform three-dimensional perfusion model of rat tail heat transfer

Previous models of rat tail heat transfer have assumed that the tail is uniformly perfused along its length and have introduced questionable assumptions about the heat transfer role of the major axial arteries and the venous blood shunting between the superficial and deep veins. The recent experiments of Lemons and Wu have shown that (i) perfusion of the tail tip is more than tenfold higher than that in the tail base and (ii) the perfusion of the middle region of the tail increases eightfold during heat stress compared to threefold to fourfold in the base and tip. Our anatomical studies have shown that the lateral arteries are a series of radially arcading connections from the ventral artery and probably do not serve as major axial conduit vessels. These observations indicate that current views and models for the blood flow distribution and heat transfer in the major axial arteries and veins and in the rat tail cutaneous circulation need substantial revision. Based on these new experimental findings a new three-dimensional model is developed to determine the heat transfer function of the rat tail at different local and central temperatures. The predictions of the model show good agreement with the axial surface temperature distribution in the rat tail reported by Lemons and Wu. These results, when combined with our anatomical studies, indicate that there is very little shunting of blood between the superficial lateral veins and the deep ventral vein as proposed by Raman et al. Although this model is based on the rat tail anatomy, it can be modified to treat the human limb and digit.