Thermal phygiology model
Description about a thermal phygiology model of ABC model
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Description about a thermal phygiology model of ABC model
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The thermal physiology model within the ABC is based on of human thermal regulation but includes several significant improvements. Our model allows unlimited body segments (compared to six in the Stolwijk model) and has 16 body segments as default. They are the head, chest, back, pelvis, right and left upper arms, right and left lower arms, right and left hands, right and left thighs, right and left lower legs, and right and left feet. Each segment is modeled as four body layers (core, muscle, fat, and skin tissues) and a clothing layer. The model calculates heat transfer within and between these segments and the environment.
Physiological mechanisms such as vasodilation, vasoconstriction, sweating, and metabolic heat production are explicitly considered. Convection, conduction (such as to a car seat or other surface in contact with any part of the body), and radiation between the body and the environment are treated independently. The model can predict human physiological responses to transient, non-uniform thermal environments.
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The ABC model is a lumped heat capacity model that assumes uniform temperature throughout an object's interior. This method is commonly used for building heat transfer, ventilation, and electricity calculations, and so on.
Calculating a person's body temperature is similar to solving the room temperature at a given time. Let's look at the very simple example below.
Given the conditions above, the indoor temperature Tin can be calculated by solving the following differential equation related to energy as equation (1). The heat flux between inside and outside can be calculated as equation (2). Here, heat transfer coefficient h is the reciprocal of the sum of the resistance values of the indoor and outdoor areas. The resistance values are generally determined by the insulation level of the building and the outdoor air.
Where:
: Heat capacity (J/K)
: Heat transfer coefficient (W/(m2・K))
: Area (m²)
: Indoor temperature (oC)
: Outdoor temperature (oC)
Below is an example of a simple indoor temperature calculation. Given the physical properties of the building and indoor heat load, we calculate the change in indoor temperature starting from 20 C, with the outside temperature fixed at 0 degrees. The result shows that the indoor temperature decreases from 20 C and reaches approximately 6 C after about 60 minutes.
In addition to heat transfer between each node, the ABC model can simulate human thermoregulation. This section explains the basics of thermoregulation and its mathematical formulation.
The human body employs sophisticated mechanisms to maintain thermal equilibrium, ensuring our core temperature is kept within a safe range. Two critical responses are triggered depending on whether we're exposed to high or low temperatures, thereby mitigating the risk of temperature-related illnesses. Through these four primary thermoregulation mechanisms - vasoconstriction and shivering when cold, and vasodilation and sweating when warm - the body skillfully maintains its thermal equilibrium, protecting against both hyperthermia and hypothermia.
Responses to high temperatures
Vasodilation: The body responds by dilating blood vessels near the skin's surface. This vasodilation increases blood flow to the skin, allowing for more efficient heat release into the surrounding environment, thus aiding in the cooling process in the body core.
Sweating: When it is difficult to maintain the core temperature only by vasodilation, our bodies begin to sweat. This process facilitates the loss of latent heat from the skin's surface, effectively cooling the skin and, subsequently, the body's core temperature.
Vasoconstriction: Vasoconstriction occurs when body temperature is low, reducing blood flow to the skin by contracting surface blood vessels. This minimizes heat loss from the skin's surface, aiding in heat preservation.
Shivering: As temperatures drop, the body initiates shivering. This muscle activity generates heat, preserving the body's core temperature.
In the model, to mathematically describe the thermoregulatory mechanisms, the difference between the set-point temperature Tset (similar to the set temperature of an air conditioner) and the actual body temperature T is treated as the error signal Error to determine the degree of thermoregulation. Set point temperature is defined as the body temperature in a thermally neutral state. Skin blood flow and sweating increase as the difference between the current temperature and the set-point temperature increases. As the difference decreases, skin blood flow decreases, and shivering thermogenesis increases.
Most thermal comfort or thermoregulatory models specify a standard man for simulation (body surface area = 1.8m2). These anthropometric parameters have a significant influence over the determination of heat exchange both within the body segments and between its surrounding environment. The ABC model allows users to customize the geometry and physiology of the human being modelled based on simple input parameters (such as weight, height, age, gender) to better account for individual differences. The table below lists physiological data modified by bodybuilder function.
Surface area
Height, weight
Dubois (1927)
[probably not implemented?] Basal metabolic heat production
Height, weight, gender, age
Harris and Benedict (1958)
Basal cardiac output
Height, weight, body fat
Gregersen (1950), Allen et al. (1956)
Thermal resistance
Body fat amount
Stolwijk (1970)
Thermal capacitance
Height, weight
Stolwijk (1970)
Countercurrent heat exchange
Height (extremity length)
Mitchell and Myers (1968)
Skin solar absorption
Skin color
Clothing solar absorption
Fabric type and color
Blum (1945)
The ABC model included extra functionalities that are either redundant or unnecessary when used with detailed CFD models:
View factor model
Solar radiation
Contact model (e.g. seat)
Custom number of body segments (clothed/nude; contact/non-contact)
The code is here. In this program, the differential equation is solved using . Implementing the forward difference method is easier than the backward difference method but is limited regarding time steps. Note that the solution diverges if you set up a higher value of time step than a certain threshold. This may be a bit geeky, but if you are more interested, you can search how to determine the time increments.
In the ABC model, the thermal network is more complex than the example above. The heat exchange within the body can be divided into four conditions based on the presence or absence of clothing and contact, as shown in the diagram below. The model calculates heat exchange with heat capacity for the core, muscles, fat, skin, and clothing. A heat balance equation is constructed for each node, and the temperatures of each node are calculated by solving simultaneous equations for the number of components. The values for thermal resistance and heat capacity of each node are based on .
As of 2024, the parameter values, formulas, and programs of the ABC model have not been publicly available, but you can refer to a similar model, , which is also based on the Stolwijk model.
Physiological data modified by body builder function (cited by )
Houdas and Ring (1982)
The original 65-node model simplified clothing into an insulation layer and assumed moisture equilibrium between the clothing layer and the air. The new clothing model was developed during Fu Ming’s time at CBE, and allows for more dynamic calculations of clothing absorption/desorption as well as the effects of air speed on heat and moisture transfer. The mathematical description of the clothing model can be found in .