System properties, feedback control and effector coordination of human temperature regulation

Abstract

The aim of human temperature regulation is to protect body processes by establishing a relative constancy of deep body temperature (regulated variable), in spite of external and internal influences on it. This is basically achieved by a distributed multi-sensor, multi-processor, multi-effector proportional feedback control system. The paper explains why proportional control implies inherent deviations of the regulated variable from the value in the thermoneutral zone. The concept of feedback of the thermal state of the body, conveniently represented by a high-weighted core temperature (T _c) and low-weighted peripheral temperatures (T _s) is equivalent to the control concept of “auxiliary feedback control”, using a main (regulated) variable (T _c), supported by an auxiliary variable (T _s). This concept implies neither regulation of T _s nor feedforward control. Steady-states result in the closed control-loop, when the open-loop properties of the (heat transfer) process are compatible with those of the thermoregulatory processors. They are called operating points or balance points and are achieved due to the inherent property of dynamical stability of the thermoregulatory feedback loop. No set-point and no comparison of signals (e.g. actual-set value) are necessary. Metabolic heat production and sweat production, though receiving the same information about the thermal state of the body, are independent effectors with different thresholds and gains. Coordination between one of these effectors and the vasomotor effector is achieved by the fact that changes in the (heat transfer) process evoked by vasomotor control are taken into account by the metabolic/sweat processor.

Appendix

Why does proportional control imply a load error?

Why does feedback control counteract a change in the heat transfer process, but follow a change in the processors?

In order to explain and to prove this and in order to have simple equations, we consider the relations in the thermoregulatory control loop for deviations Δ from a steady-state. For the heat transfer process, we may formulate the following simple equation (It is the simplest representation of the more elaborated heat balance equation derived in “System properties of temperature regulation”):

$$ \Updelta T_{\text{b}} = \, K_{\text{b}} \Updelta EM + \Updelta T_{\text{a}} $$

(12)

(T _b, body temperature, T _a, ambient temperature, EM, effector mechanisms; K _b, summarizing the properties of the heat transfer process),and for the processor with gain (g) and threshold (T ₀):

$$ \Updelta EM = - g_{EM \, } \left( {\Updelta T_{\text{b}} - \Updelta T_{0EM} } \right)\, {\text{for}}\; \Updelta T_{\text{b}} \le \Updelta T_{0EM} $$

(13)

Setting Eq. 13 into Eq. 12, which means feeding back an adequate amount of ΔEM into the heat transfer process, yields

$$ \Updelta T_{\text{b}} = \frac{1}{{1 + K_{\text{b}} g_{EM} }}\Updelta T_{\text{a}} + \frac{1}{{1 + {\frac{1}{{1 + K_{\text{b}} g_{EM} }}}}}\Updelta T_{0EM} $$

(14)

This equation shows clearly that any change of T _a (change in the heat transfer process) evokes a change of T _b, as the quotient 1/(1 + K _b g _EM ) is always greater than zero. As it is smaller than 1, it is guaranteed that the change is always smaller than without control, where ΔT _b = ΔT _a. To keep the deviation small, the effector gain has to be as great as possible, but only the theoretical value g _EM  → ∞ yields ΔT _b → 0 (no load error, independently of T _a).

Equation 14 also explains that T _b follows a change of threshold T _0EM (as evident in fever; change in the processor), but exactly only if the same purely theoretical condition g _EM  → ∞ holds, because only then the quotient preceding ΔT _0EM tends to the value “1” (ΔT _b = ΔT _0EM ).