Identification of the Problem
The potential health effects of exposure to sources of non-ionizing 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 [31]. ThermoAnalytics proposes to develop an anatomically realistic thermal computer code capable of predicting the thermal effects of known RF sources on living human and animal tissue.

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 [28]. 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 [27]. Phantom models, however, are 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 not generally 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. ThermoAnalytics proposes to modify its existing commercial thermal software to exploit the simple structure of the voxel-based description. The resulting thermal code will be compact, accurate, and able to accommodate extremely large data sets as input.

This proposal will specifically address 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 will be 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 will not be limited to RF heating, however, but will extend to a variety of environmental and therapeutic heating and cooling applications.

Background
The development of accurate, whole-body, predictive models of heat transfer in humans and primates would be an extremely important accomplishment, both scientifically and for the potential economic benefit deriving from the use of the 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 their applications are 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 are difficult to perform because experiments are invasive and boundary conditions can be difficult to quantify. Animal models are 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 is further complicated by species differences in thermal dissipation mechanisms, notably evaporative cooling. The thermoregulatory system of non-human primate species is somewhat similar to that of humans, providing better opportunities for experimental studies. Primate cooling physiology, particularly the ability to sweat, differs from that of humans however [30]. For this reason, primate studies, though very useful, have somewhat limited application [12,29].

Despite these factors, which thus far have prevented the development of accurate anatomical human models, 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 [11], 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 [6], as well as metabolic effects and the role of blood chemistry [10]. 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.

Technical Objectives
ThermoAnalytics will develop a prototype of an anatomically realistic thermal modeling tool based on its existing thermal modeling software, RadTherm. RadTherm is ThermoAnalytics' full-featured, cross-platform, thermal analysis software. RadTherm 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 RadTherm, ThermoAnalytics will develop an 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 Analysis

• automatically calculate surface view factors (Phase II)

• optionally perform steady state temperature initialization

• conduct transient thermal analysis

• convergence and solution diagnostics

Model Import and Editing
The modeling process begins by importing voxel data sets containing tissue types and SAR values. The examples in this section were derived from raw (voxel) files downloaded from the DEBL at Brooks AFB, and sar files created by running the FDTD program, downloaded from the same source (Figures 5 and 6).

The large size of voxel data sets (e.g., over 45 million voxels for a 293 x 170 x 939 voxel representation of a man) requires that we utilize compact data structures, avoid duplicate data representations, and eliminate storage by recalculating simple quantities as they are needed. Fortunately, the simple structure of the voxel description lends itself to this type of optimization. The C++ class that holds voxel data will likely consist of variables that hold the x, y, z dimensions of each voxel, the number of voxels in the x, y, z directions (nx, ny, nz), a one-dimensional array dynamically sized to hold nx o ny o nz values (typically integers or floats), and functions for accessing the voxel information at a given index or position. This storage scheme is several times smaller than if voxel data were stored using the data structures defined for solid elements. (The storage for a single solid element consists of 6 integers that hold vertex indices. There are roughly as many vertices as there are solid elements and each requires 3 floats to hold the x, y, z coordinates.) The inheritance mechanism of C++ allows us to derive the voxel data class from the same base class as our other geometric descriptions (i.e., create a variation of a data structure based on its simplest form) to optimally represent different types of geometric input (shell elements, solid elements, voxels) and use them interchangeably.

A RadTherm part (grouping of voxels with identical properties) will initially be created for each distinct tissue type in the raw file (Figure 7). The part ID for each voxel will be stored in a voxel-part ID data structure, of the form described above. Boundary conditions (metabolic heating and blood flow rate) are assigned on a part basis, so it may be desirable to have more than one part of the same tissue type. The Phase I prototype will allow voxels to be reassigned to different parts (by utilizing RadTherm's existing graphical selection mechanism) and will also allow the tissue type of a part to be changed.

The Phase I prototype will display voxel faces for editing and visualization purposes. The RadTherm display routine will be modified to scan through the voxel-part ID data structure, and for each of the six voxel faces determine whether the face is exterior, i.e., is in contact with a voxel of a different tissue type or on the edge of the model. The existing 3D graphics display routines for drawing elements (quads) will be utilized allowing the user to view the exterior voxel faces from any angle. Figure 1 is an example of a three-dimensional view of voxel data.

For two-dimensional visualization, the user will specify a viewing plane (x-y, x-z, y-z) and offset. This viewing plane could be shown on 3D point cloud of the model to help orientate the user. A cross-sectional view will be created from the voxel faces forming the specified cross section, which can be of the entire model, or of specified parts (tissue types).

Thermal Solution
The thermal solver for the phase I prototype will solve a variation of Pennes' bio-heat equation that not only includes the effects of local blood flow and metabolic heating, but also includes the heating effects of RF energy. The following equation, repeated from Section 1.1 with an added term, sar, for RF heating, is:

The results of the thermal solution will be graphically displayed using the same techniques as for model editing. Each voxel surface will be assigned a color that corresponds to the voxel temperature or SAR (Figure 8).

Figure 8

Future Investigations
We will develop plans for coupling a number of RadTherm's advanced features to thermal networks derived from voxel-based data sets. These include routines that calculate:

• Convective coefficients via classical techniques
• Convective coefficients and film temperatures via voxel-based CFD techniques
• View factors and multi-bounce radiation exchange
• Solar loading and "sky shine"
• Heat due to condensation/evaporation/mass transfer.

In addition, RadTherm's architecture supports the definition of "special" part types that add nodes to the thermal network based on the function of the part. We will define part types that could, for example, be used to model active and passive garments.

RELEVANT PUBLICATIONS

1.       Bernardi, P., Cavagnaro, M., Pisa, S., "SAR Distribution and Temperature Increase in an Anatomical Model of the Human Eye Exposed to the Field Radiated By the User Antenna in a Wireless LAN," IEEE Trans. Microwave Theory & Tech., vol.46, No. 12, December 1998.

2.       Wissler, E., "Mathematical Simulation of Human Thermal Behavior Using Whole Body Models," Heat transfer in Medicine & Biology, Vol. 1, 1985.

3.       Bligh, J., "Temperature Regulation in Mammals and Other Vertebrates," Frontiers of Biology, Vol. 30, North Holland Publishing, Amsterdam, 1973.

4.       Chato, J.C., "Heat Transfer in Bioengineering," Advanced Heat Transfer, B.T. Chao, ed. (University of Illinois Press, Urbana, 1969), p. 404-412.

5.       Giering, K., Lamplecht, I., Minet, O., "Specific Heat Capacities of Human and Animal Tissues," SPIE 2624, Sept, 1995, p. 188-197.

6.       Takemori, T., Nakajima, T., Shoji, Y., "A Fundamental Model of the Human Thermal System for Prediction of Thermal Comfort," Heat Transfer – Japanese Research, #24(2), 1995, p. 147-165.

7.       Delhomme, G., Newman, W., Roussel, B., Jouvet, M., Bowman, H., Dittmar, A., "Thermal Diffusion and Instrument System for Tissue Blood Flow Measurements: Validation in Phantoms and In Vivo Organs," IEEE Transaction on Biomedical Engineering, Vol. 41, No. 7, July, 1994.

8.       Leonard, J.B., et al, "Thermal Properties of Tissue Equivalent Phantom Materials," IEEE Transactions on Biomedical Engineering, Vol. BME-31, No. 7, July, 1984, p. 535.

9.       Eugene Stanley, H., "Physics and Biomaterials Science," MIT Press, Cambridge, MA, 1972, p. 231.

10.   Shitzer, A., Eberhart, R., "Heat Generation, Storage, and Transfer Processes," Heat Transfer in Medicine and Biology, Vol. 1, 1995, p. 137-152.

11.   Pennes, H.H., "Analysis of Tissue and Arterial Blood Temperature in the Resting Forearm," Journal of Applied Physiology, Vol. 1, p. 93-122, 1948.

12.   Spiegel, R.J., Fatmi, M.B.E., and Ward, T.R., "A Finite-Difference Electromagnetic Deposition/Thermoregulatory Model: Comparison Between Theory and Measurements," Bioelectromagnetics, 8:259-273 (1987).

13.   Chandra, A. and Mukherjee, S., 1997, Boundary Element Methods in Manufacturing, Oxford University Press, New York (ISBN: 0-19-507921-3).

14.   Curran, A.R., Editor, "User’s Manual for PRISM 3.2," ThermoAnalytics Inc., Calumet, MI, May 1997.

15.   Curran, A.R., et. al. "Automated Radiation Modeling for Vehicle Thermal Management," 1995 SAE International Congress & Exposition, Exhaust Systems & Shielding Session, Paper Number 950615, Detroit, MI, February 1995.

16.   Johnson, K.R., et. al. "A Methodology for Rapid Calculation of Computational Thermal Models," 1995 SAE Congress - Underhood Thermal Management Session, Detroit, MI, February 1995.

17.   Curran, A.R. et al, "Enhancements to the Vehicle Designer / PRISM Interface," Fifth Annual Ground Target Modeling and Validation Conference, Michigan Technological University, Houghton, Michigan, August 1994.

18.   Johnson, K.R., et. al. "Thermal Modeling in Automotive Design," Proceedings of the Fifth Annual Ground Target Modeling & Validation Conference, Houghton, MI, August 1994.

19.   Johnson, K. R., "Present State and Future of Infrared Signature Models," Proceedings of the Third Annual Ground Target Modeling and Validation Conference, MTU/KRC, August 1992.

20.   WinTherm documentation, publications, and a fully functional but node-limited demo can be downloaded from http://www.thermoanalytics.com.

21.   Nelson, D., M. Nelson, T.Walters, and P. Mason, "Thermal Effects of Millimeter Wave Irradiation of the Primate Head: Model Results" IEEE Transactions on Microwave Theory and Techniques (in press)

22.   Mason, P., W. Hurt, J. D’Andrea, T. Walters, K. Ryan, P. Gajsek, D. Nelson, K. Smith and J. Ziriax, "Effects of Frequency, Permittivity, and Voxel Size on Predicted Specific Absorption Rate Values during Electromagnetic Field Exposure," IEEE Transactions on Microwave Theory and Techniques (in press)

23.   Mason, P., W. Hurt, J. Ziriax, T. Wlaters, K. Ryan, D. Nelson and J. D'Andrea, "Models used to Determine the Bioeffects of Directed Energy Exposure" in Countering the Directed Energy Threat: Are Closed Cockpits the Ultimate Answer? NATO Research and Technology Organization report RTO-MP-30, (2000).

24.   Walters, T. J., P. A. Mason, K. L. Ryan, D. A. Nelson, and W. D. Hurt, "A Comparison of SAR Values Determined Empirically and by FD-TD Modeling" In: B.J. Klauenberg and D. Miklavic (Eds.), Radio Frequency Radiation Dosimetry, Dordrecht, The Netherlands: Kluwer Academic Publishers (1999).

25.   Nelson, D., Walters, T., Ryan, K. and Johnson, L.R., "Skin Heating Effects of Millimeter Waves: Inter-Species Variability" Advances in Heat Transfer and Mass Transfer in Biotechnology, ASME HTD-Vol. 363; BED-Vol. 44, pp. 141-4, (1999).

26.   Nelson, D. "Invited Editorial on ‘Pennes’ 1948 Paper Revisited," Journal of Applied Physiology, 85:2-3, (1998)

27.   Durney, C.H., Massoudi, H., and Iskander, M.F., (1986) RadioFrequency Radiation Dosimetry Handbook, USAF School of Aerospace Medicine Report, USAFSAM-TR-85-73, Brooks Air Force Base, TX., Fourth Edition.

28.   IEEE Standard for Safety Levels with Respect to Human Exposure to Radio Frequency Electromagnetic Fields, 3 kHz to 300 GHz: IEEE Standard C95.1, 1999 Edition. (1999).

29.  Kolka, M. A. and Elizondo, R. S., "Thermoregulation in Erythrocebus patas: a thermal balance study," J.Appl.Physiol. 55:1603-1608, (1983).

30.  Adair, ER and Adams, BW, "Adjustments in metabolic heat production by squirrel monkeys  exposed to microwaves," J. Applied Physiology, 52:1049-1058, 1982.

31.  Huiskes, R., Janssen, J.D., and Slooff, T.J., 1982, "Finite element analysis for artificial joint fixation problems in orthopaedics." Finite Elements in Biomechanics, RH Gallager, BR Simon, PC Johnson, and JF Gross, eds. (New York: J. Wiley).

32.  Nelson, D., M. Nelson, T.Walters, and P. Mason, "Thermal Effects of Millimeter Wave Irradiation of the Primate Head: Model Results" IEEE Transactions on Microwave Theory and Techniques (in press).

33.  Nelson, D., Walters, T., Ryan, K. and Johnson, L.R. "Skin Heating Effects of Millimeter Waves: Inter-Species Variability" Advances in Heat Transfer and Mass Transfer in Biotechnology 1999, ASME HTD-Vol. 363; BED-Vol. 44, pp. 141-4 (1999).