INTRODUCTION
Humans are poor judges of their thermal state, making it difficult for them to control their thermal comfort adequately (Billingham 1969). NASA found during the first space flight that sufficient cooling of an astronaut could not be accomplished via air convection in the suit due to ventilation, and have since been using a liquid cooling garment (LCG) to circulate water for cooling the astronaut during space walks (Chambers 1970). In the present arrangement, the astronaut controls the temperature of the water flowing through the LCG by manually adjusting the temperature control valve (TCV) located on the front of the space suit. However, manually manipulating the TCV setting can dramatically reduce the productivity of the astronaut, distracting them from the extravehicular activity (EVA) mission at hand; and since an astronaut's attention is focused on other things during EVA, there are time lags in the application of temperature control (Thor-ton et al. 2001). This can cause overheating or overcooling, placing unneeded thermal stress on the astronaut, and degrading EVA performance. Human thermal models are needed to accurately describe the transient heat transfer processes and predict the thermal response within an acceptable band of accuracy before an automatic controller can be designed. Such human thermal models are also relevant for various other applications involving fire fighters, combat pilots, hazardous waste workers, and other industries where comfort in a thermally stressful environment needs to be ensured.
The development of mathematical models for human thermoregulation started in the early 20th century (Lefevre 1911). Early models used simple representations for the human thermal system. However, in the 1960s, more detailed models were developed that incorporated our increased understanding of human thermoregulation as these complexities became known in an attempt to improve accuracy (Wissler 1964; Wydham and Atkins 1968), although many aspects of the human active thermal system are still not well understood. The passive thermal system has been computationally modeled better (Wissler 1964; Wydham and Atkins 1968; Stolwijk 1971; Gagge 1973; Fu 1995; Huizenga et al. 2001), although the parametric and model approximates do present challenges. The latter is due to unaccounted parameter variations between human subjects (inter-subject variations) and effects influencing the individual at different times (intra-subject variations). It is advantageous for a modeler to identify important parameters of the passive thermal system and quantify their effect on the model's response to gain a better understanding of modeling issues and limitations.
Numerous human thermal models have been developed and used in many practical applications for the past sixty years, starting with Pennes's (1948) development of a steady-state model to analyze heat transfer in a resting human forearm. In the 1960s and 1970s, early versions of the well-known Wissler (1964), Stolwijk (1971), and Gagge (1973) models were being developed. For the most part, all later human thermal models are probably extensions of these three mathematical models, including a more advanced model by Wissler (Mungcharoen 1989) and models used for the prediction of temperature elevation during hyperthermia (Jain 1980; Roemer and Cetas 1984). Subsequent advances in computing technology and increased experimental data on human physiology helped researchers in developing better and more sophisticated human thermal models. However, due to the natural complexity of human thermoregulation, it has been difficult to study the issue of accuracy for such models. Quantitative comparisons among models have also been difficult due to the individual characteristics of each model under particular environmental conditions (Haslam and Parsons 1989; Hwang and Konz 1977). From a user's perspective, it has not been clear which of the models would be best suited for a particular environment and application. Various research teams (Iyoho 2002; French et al. 1997; Fu 1995; Huizenga et al. 2001) have developed models in the past decade to be used in environments that range from uniformly steady-state to extremely transient and non-uniform. Models such as the Kansas State University model (Fu 1995; Hsu 1971), the Berkeley model (Huizenga et al. 2001), and the authors' model (Iyoho 2002) are in development to achieve such objectives. Even though these models incorporate more detail, they have their roots in either the Wissler (1985) or the Stolwijk (1971) model. All of these models include heat transfer within the body as well as between the body and its environment, as well as sweating, shivering, and vasomotor capabilities.
The following section presents the proposed model with additional features that serve to better predict the human thermal response at the extremities. The model includes two-dimensional conduction, finger/toe temperature predictions, arterial/venous blood flows, arteriovenous anastomoses ( AVAs), and cold-induced vasodilation.
PROPOSED TWO-DIMENSIONAL MODEL WITH EXTREMITIES
The thermal model presented in this paper, the MU man model, incorporates many aspects of past human thermal models, especially the 41-node man (Bue 1989) which is based on Stolwijk's six-segment, 25-node model (Stolwijk 1971). The 14 major cylindrical segments include the head, torso, arms, hands, fingers, legs, feet, and toes. The five fingers on each hand are represented as one cylinder, as are the five toes on each foot, neither of which are present in the 41-node man. Similar to the 41-node man, each segment contains four concentric layers, representing the four layers-the core, muscle, fat, and skin regions.
The MU man model also incorporates two-dimensional (radial and angular) heat conduction within the body as opposed to the radial-only in the 41-node man model. Each body element in the model contains six angular sectors to account for these angular temperature variations. The model utilizes the finite difference method (FDM) to solve the system of equations. The FDM approach was used as opposed to the finite element method (FEM) to achieve faster execution for simulating a variety of input conditions (Panczak et al. 1998).
The MU man model incorporates heat exchange between tissues and arteries/veins where the arterial and venous temperatures vary from element to element in contrast to a single blood pool used by the 41-node man model. In addition, the MU man model incorporates the AVAs in the digits, along with the effects of cold-induced vasodilatation (CIVD), which will be important in studies dealing with extremity discomfort.
Two-Dimensional Conduction
One-dimensional models cannot account for cases where disparate environmental conditions exist on different sides of the body. A study by Hall and Klemm (1967) showed that when the body was exposed to cold (-6.7[degrees]C [- 44.06[degrees]F]) and hot (82[degrees]C [115.6[degrees]F] and 93.3[degrees]C]) radiative temperatures on different sides of the body, skin temperature differences between the anterior and posterior sides ranged between 9[degrees]C to 10[degrees]C (-15.8[degrees]F to -14[degrees]F). These experiments by Hall and Klemm (1967) were also validated through simulations of the …
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