Basal Metabolic Rate Fourier

Thermal Energy Balance in Vertebrate Thermoregulation

The metabolic response to cold described in the text is a limited subset of the manipulations of heat flow that mammals and birds actually engage in. The complete suite of responses involves a complicated mix of variations of heat production by metabolism, adjustments of the body's thermal conductance, and heat dissipation by evaporation.

The foundation of these responses is the relationship between thermodynamic heat flux and environmental temperature expressed as Fourier's law. Where environmental temperature (Te) is less than body temperature (Tb), the thermodynamically favored flux (TFF) of heat is outward, and the physiological flux (PF) must be inward. Where Te > Tb, the PF must be outward. Of course, at Te = Tb, no PF is needed. The trouble is this: most mammals and birds cannot lower their metabolic heat production below a minimum called the basal metabolic rate (BMR). Therefore, the Fourier's law relationship between metabolic heat production and environmental temperature applies only at those temperatures where metabolic heat production (Mh) exceeds BMR. The upper limit of environmental temperature for Fourier's law is known as the lower critical temperature (LCT).

At environmental temperatures greater than the LCT, metabolic heat production is steady at the BMR (Fig. 11B.1). The animal still cannot escape the constraints of Fourier's law, however: at steady heat production and steady conductance, the temperature difference between the body and environment likewise must be steady. This difference obviously cannot persist if body temperature is to be regulated. Instead, the body's conductance is adjusted over a range of environmental temperatures, roughly between Te = LCT and Te = Tb, through variations of peripheral blood flow, postural adjustments, flattening of the fur or pelage, and so forth.

This strategy has its limitations, however, because the body's thermal conductance can be increased only by so much. Above this maximum conductance, Kmax, the minimum BMR must be offset by some active cooling of the

metabolic conductance evaporation compensation compensation compensation

Evaporative heat loss environmental temperature

Figure 11B.1 The energetics of temperature regulation in a homeothermic endothermic animal.

body, which generally involves evaporation of water from the body surface (Fig. 11B.1). Specifically, the body's net heat production, Mn, consisting of the sum of the BMR and the evaporative heat loss, Qe, must equal the TFF for heat demanded by Fourier's law:

Within a few degrees of Te = Tb, moderate increases of evaporation are sufficient to keep the body in heat balance. However, above a certain environmental temperature, called the upper critical temperature (UCL), increasing evaporation rate involves an increasing metabolic cost, because mechanisms like sweating, panting, and so forth cost energy to run. Consequently, Mh begins to rise again, requiring large increases in evaporation rate so that the net heat flux meets the demands imposed by Fourier's law. The limits on tolerable environmental temperature are set at low temperatures by the maximum metabolic rate, and at high temperatures by the maximum rate of evaporation.

sents the distinguishing mark of homeostasis—any living system, whether it be cellular, organismal, or superorganismal, that exhibits this insigne can fairly be said to be homeostatic. I will ask you now to tuck this tidbit away for a moment, while we look more deeply into the process of organismal homeostasis, again in the context of the regulation of body temperature of animals, mammals specifically.

where MPF is the metabolic work done to drive the PF. You will recognize this by now as a straightforward energy balance.

On the basis of equations 11.2, we can now state a minimum physical requirement for homeostasis: ho-meostasis requires that the thermodynamically favored flux always be matched exactly by an equal and oppositely directed physiological flux. Consequently, the rate at which physiological work is done, that is, the power requirement for homeostasis, is proportional to the magnitude of the thermodynamic potential difference between the animal and its environment (Fig. 3.3). So, for example, homeostasis of body temperature should be reflected in a rate of heat production that varies linearly with environmental temperature. We can express this relation in an equation, Fourier's law, that explicitly represents the power requirement for temperature homeostasis:

where Kh is the thermal conductance (W K-1).

The outward signs of thermal homeostasis are evident when we plot equation 11.3 as a graph of metabolic heat production versus environmental temperature (Fig. 11.1). A straightforward pattern emerges: a linear decrease of heat production with increasing environmental temperature, with a slope of -Kh, falling to a heat production of null at an environmental temperature equal to body temperature (this oversimplifies the case for vertebrate thermoregulators— see Box 11B for the rest of the story). This graph repre-

Functional Elements of Organismal Homeostasis

The process of homeostasis implies an infrastructure to make it work. Among mammals, the "machinery" for temperature homeostasis involves the entire body, but a substantial part of it resides in the anterior hypothalamus of the brain (in us, located just behind and above the backs of the eyeballs). The anterior hypothalamus receives information from temperature-sensitive cells all over the body. These encode and transmit information on the distribution of temperature throughout the body. In addition, there is a group of temperature-sensitive cells in the anterior hypothalamus itself, and these encode information on brain temperature. Some of these cells respond to elevations of hypothalamic temperature while others respond to drops in hypo-thalamic temperature. Finally, there are clusters of hypothalamic cells that are spontaneously active and whose activity does not vary with temperature.

Here we see the elements for negative feedback control of body temperature (Fig. 5.18). The sensor signals arise from the various temperature-sensitive cells throughout the body and brain. The setpoint signal arises from the temperature-insensitive cells in the anterior hypothalamus. There, the signals are processed and compared in a neural circuit that acts as a comparator. Emerging from this circuit are outputs (error signals) that activate various effectors that alter the generation of heat within the body or modulate the flow of heat between the body and environment. Together, these parts operate as a negative feedback controller for body temperature.

This feedback loop was demonstrated in elegant

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