Active System

The thermophysiological regulation is a system whose functioning is still not fully understood today. A description or a model for the thermophysiological regulation applies the relations of cause and effect that are obtained through experimental results.

Such a model cannot describe the direct functions and processes of the central nervous system.

Generally speaking, the used thermophysiological regulation model is a cascaded proportional regulation. A central controller calculates four controlled variables for the entire body based upon the temperature signals. These controlled variables are passed on to all segments where they are processed in a local controller unit. The local controller provides blood flow rates and heat fluxes that influence the thermal condition of the body. This way, the influence of different body parts on the total thermal condition can be investigated.

The skin temperatures of all body segments and the head core temperature are the input quantities of the controller. The head core temperature corresponds in the model to the temperature of the hypothalamus, the center of temperature regulation. This temperature is particularly important for the thermophysiological regulation, because the controller always uses it as a reference. From these segment temperatures, the control deviations, $θ$ , are calculated. The control deviation consists of the difference between the respective segment temperature and a target value that is called reference temperature $T_{R E F}$ . The reference temperature is known for each segment. This calculation is performed for the head core temperature and the skin temperatures.

θ_{1, 1} = T_{1, 1} - T_{{R E F}_{1, 1}}

(64 65 66 67)

θ_{4, j} = T_{4, j} - T_{{R E F}_{4, j}}

(64 65 66 67)

These control deviations are the basis for the computation of the global controlled variables. For the skin temperatures, it is distinguished whether the control deviation is a warm or a cold signal. A positive deviation corresponds to a warm signal and a negative deviation corresponds to a cold signal:

$θ_{{W A}_{4, j}} = θ_{4, j}$ for $θ_{4, j} \geq 0$

$θ_{{C O}_{4, j}} = - θ_{4, j}$ for $θ_{4, j} < 0$

The element signals are combined to a total signal. When calculating this total signal, the distribution of the thermal receptors on the skin (cold and warm spots) are taken into account. The values are obtained through multiplication of the number of cold and warm spots of a skin element with the corresponding area fraction of the entire body surface [2]. The following table gives the distribution of receptors for each skin element:


Segment	Zref (cold signal)	Xref (warm signal)
Head	6.05e-02	0.201
Torso	0.4926	0.38
Upper arm	0.01714	0.02999
Forearm	0.01714	0.01625
Hand	0.09224	0.025
Thigh	0.04514	0.08999
Lower leg	3.01e-02	0.03275
Foot	1.67e-02	0.0155

The total signals of the skin elements for warm and cold impulses are written as:

θ_{W A, T O T} = \sum_{j = 1}^{14} (θ_{{W A}_{4, j}} \cdot X_{{R E F}_{j}})

(64 65 66 67)

θ_{C O, T O T} = \sum_{j = 1}^{14} (θ_{{C O}_{4, j}} \cdot Z_{{R E F}_{j}})

(64 65 66 67)

By using these values together with the control deviation of the head core temperature, the global controlled variables during heat load (vasodilation and transpiration) and during cold load (vasoconstriction and shivering) are calculated.

After calculating the global controlled variables, these values are converted into local controlled variables for each body part. The global conversion constants are labelled G and the local conversion constants are labelled L. The global controlled variables are denoted S. To characterize the type of controlled variable, the indices $V_{d}$ for vasodilation, $V_{c}$ for vasoconstriction, $T r a n s p$ for Transpiration, and $S h i v$ for shivering are used. The local controlled variables are volumetric flow rate of blood, evaporation, and metabolic heat production.