Customized, Innovative New Software: 3-D Voxel-Based Bio-Heat Transfer Code
Identification of the Problem
The potential health effects of exposure to sources of nonionizing radio frequency (RF) electromagnetic energy are an area of continuing interest within the military and civilian communities. Common sources of RF exposure include mobile and cellular telephones, magnetic resonance imaging (MRI) systems, wireless local area networks, transmitting antennae, and other civilian and military communications and radar systems. One established biological effect of RF exposure is tissue heating; temperature increases as little as 4°C above normal body temperature can have potentially devastating effects on living tissue . In response, ThermoAnalytics has developed an anatomically realistic thermal computer code capable of predicting the thermal effects of known RF sources on living human and animal tissue, resulting in human thermoregulation.
The Institute of Electrical and Electronics Engineers (IEEE) recently adopted revised standards for human exposure to RF fields, specifying maximum permissible exposure (MPE) levels. The MPE level, for a given exposure frequency, is stated in terms of the specific absorption rate (SAR)—the rate of energy absorption per unit mass of tissue. The MPE depends upon the duration of exposure and whether the exposure is "controlled" to avoid physiological hazards . The rate of temperature increase in tissue is a function of the specific absorption rate. The local rate of temperature increase in a homogeneous phantom model is approximately linear with the SAR, for short-duration exposures . Phantom models, however, have been of little value in predicting tissue heating effects of RF exposure in humans or animals. The effects of metabolic heating, blood flow, and tissue heterogeneity complicate the relationship between the rate of temperature increase and the local SAR, such that a simple linear model is generally not appropriate.
The anatomical complexity and high degree of spatial resolution required to capture predicted SAR "hot spots" have led to the development of realistic anatomical data sets [1, 2]. These voxel-based descriptions are created by dividing the space occupied by the object being described (e.g., the human body) into a three-dimensional grid of small, equal-sized volume elements known as voxels. By definition, each voxel can contain only one type of tissue; a very large number of small voxels (e.g., cubes with 1mm edges) is therefore needed to capture enough detail to accurately predict SARs. The properties of the tissue in each voxel and the predicted SARs constitute the input to a thermal model, which then predicts tissue temperatures. Consequently, general-purpose, off-the-shelf thermal codes are quickly overwhelmed by the size of thermal problems that are derived from voxel-based anatomical descriptions. To address this issue, ThermoAnalytics has modified its existing commercial thermal software to exploit the simple structure of the voxel-based description. The resulting thermal code is compact, accurate, and able to accommodate extremely large data sets as input.
This customized software specifically addresses the issue of thermoregulation and bio-heat transfer modeling as it pertains to complex voxel-based anatomical descriptions with thermal loads from electromagnetic (EM) irradiation. The level and location of heat loading is derived using the finite difference time domain (FDTD) method and applied to the model as a specific absorption rate.
The applicability of the resulting computer code is not limited to RF heating, however, but extends to a variety of environmental and therapeutic heating and cooling applications.
Accomplishment and Background
ThermoAnalytics' development of accurate, whole-body, predictive models of heat transfer in humans and primates is an extremely important accomplishment, both scientifically and for the potential economic benefit derived from the use of these models. While whole-body models have been described in the literature [2, 10], the lack of anatomical detail and precision, and limited thermoregulatory mechanisms, means that their applications in the past have been limited to describing relatively gross thermal response.
Thermoregulation is an ensemble of physiological processes that differ among species, and which collectively complicate the development of predictive models. Conduction, convection, and radiation heat transfer—though well understood and consistently modeled with high levels of accuracy—are complicated by evaporation (sweating, respiration) and other phase change processes, as well as physiological responses such as vasomotor reflexes. Incomplete anatomical data sets have also prevented thermoregulatory models from providing realistic output. Furthermore, accurate model validations have been difficult to perform because experiments are invasive, and boundary conditions have been difficult to quantify. Animal models have been useful, but size and morphological differences make it extremely difficult to extrapolate from animals to humans. Extrapolation of experimental results from animal models to humans has been further complicated by species differences in thermal dissipation mechanisms, notably evaporative cooling. The thermoregulatory system of nonhuman primate species is somewhat similar to that of humans, providing better opportunities for experimental studies. Primate cooling physiology, particularly their ability to sweat, differs from that of humans, however . For this reason, primate studies, though very useful, have had somewhat limited application [12, 29].
Despite these factors, mathematical expressions have been derived which, though conceptually simple, accurately describe local temperature responses of homogeneous tissues to thermal loads. Temperature predictions are commonly based on Pennes' bio-heat transfer equation , which is the conduction heat equation with added terms to represent the metabolic heat load and convective effect of local blood flow:
The left-hand side terms of equation 1 represent, respectively, conduction through tissue with thermal conductivity kt, heat convection associated with blood flow , and metabolic heating. The right-hand side term describes the rate of energy increase of the tissue volume.
Although the theoretical basis of the Pennes' model is controversial, it has been validated in numerous species and tissues, and is widely accepted as an appropriate bio-heat transfer equation for most applications [2, 10]. It has also been shown that blood flow, vasodilatation and constriction, and other circulatory processes can be successfully modeled , as well as metabolic effects and the role of blood chemistry . Modern predictive techniques and powerful high-speed computers make application of the bio-heat equation feasible on animal and human anatomical subjects. Data sets, particularly the voxelized data available through the Visible Human Project [National Library of Medicine] and others provide an anatomical description detailed enough to apply the bio-heat equation on a scale necessary to take into account the effects of differing tissue properties, vasomotor and sudomotor responses, and the convective effects of the circulatory system.
ThermoAnalytics has developed an anatomically realistic thermal modeling tool based on its existing thermal modeling software, TAITherm. TAITherm is ThermoAnalytics' full-featured, cross-platform, thermal analysis software. TAITherm utilizes a state-of-the-art thermal solver and a user friendly Graphical User Interface (GUI) for modeling multi-mode heat transfer (radiation, conduction, and convection), phase change, and one-dimensional fluid flow. Building on the thermal computing power of TAITherm, ThermoAnalytics has successfully created this anatomical thermal modeling tool, depicted in Figures 1 and 2, capable of:
Geometry Import and Manipulation
- Import geometry in several formats, including *.raw
- Edit/fix geometry in the prototype environment
- Perform geometry diagnostics
- Thermal Model Building
- Define parts, unique tissue types, or new properties (Figures 1 & 2c)
- Apply boundary conditions, internally and externally (Figure 2a)
- If necessary, make property reassignments, automatically regenerate *.raw geometry, rerun FDTD code and reload SAR values
- Automatically calculate surface view factors (Phase II)
- Optionally perform steady-state temperature initialization
- Conduct transient thermal analysis
- Convergence and solution diagnostics
Pre and Post Processing
- Animate temperatures or IR signature (Figure 2d)
- Export results
- Plot results and export (Figure 2b)
- View SAR loading (Figure 8)