Building the 2nd Model -- Add Shivering to the Model

Riggs' model includes the physiological responses of sweating when it's hot and shivering when it's cold. Shivering is the key to his model's homeostatic properties with cold conditions. (Shivering is an involuntary contraction of the muscles to release chemical energy into the core.) The next step is to incorporate Riggs' assumptions on shivering, as shown in Figure 4.

Figure 4. Flow Diagram for the Second Model.

Figure 4 shows a new heat flow from shivering to increase the energy in the core. Shivering heat production is the product of a standard amount of heat from shivering and two multiplicative factors used to replicate Riggs' approach. Riggs assumes that the standard heat from shivering is 252 kcal/hr. This large value reveals the potential for shivering to counteract the heat losses seen in the previous model. In Figure 1, for example, skin heat loss from radiation is over 80 kcal/hr. If the skin temperature gradient were to double due to a drop in ambient temperature, we would see an immediate increase of 80 kcal/hr of heat loss from radiation. If the "multiplicative factors" shown in Figure 4 were to call on 32% of the 252 kcal/hr of standard shivering, shivering would completely counter the extra 80 kcal/hr of heat loss.

The first of the two "multiplicative factors" in Figure 4 is the shivering initiation multiplier from cooler core. Figure 5 shows the shape of this multiplier. Notice that the multiplier is zero if the core temperature is 37 degrees or higher. In other words, there is no shivering unless the core temperature falls below 37 degrees. If this happens, the multiplier climbs rather quickly to 1.0 "turning on" the full power of the 252 kcal/hour of shivering. The nonlinear shape in Figure 5 matches Riggs' equation 11.E. Riggs specified this equation to match the empirical results by Benzinger(1963).

Figure 5. The shivering initiation multiplier from cooler core as a function of the core temperature.

The second factor is the shivering multiplier from normalized temperature difference. The "normalization" depends on a normalizing factor, K, which depends on the core temperature as shown in Figure 6 below. This chart shows a linear growth in the normalization factor as the core temperature falls below 37 degrees. If the core were at 35 degrees, for example, the normalization factor would be at 25 degrees C.

Figure 6. The normalizing factor (K) as a function of the core temperature.

This factor is then used to normalize (i.e. reduce) the value of the skin temperature difference. A graph function (~) is used to represent the shape in Figure 6, but the final entry in the graph is set to 1 (rather than 0) to avoid division by zero. Riggs' normalized difference is based on a critical skin temperature for extra shivering of 21 degrees. The calculation of the normalized difference is best illustrated with an example. Suppose the core temperature were 35 degrees, and the skin temperature were 11 degrees. With such a cold core, the first multiplier would "turn on" 100% of the standard shivering. The second multiplier calls on "extra shivering" if the skin temperature falls below the critical skin temperature of 21 degrees. In this example, the skin temperature is a full 10 degrees below the critical value for extra shivering. Riggs normalizes this 10 degree difference by dividing by K, the normalizing factor shown in Figure 5. With a core temperature of 35 degrees, K would be 25, and the normalized skin temperature difference would be a negative 10/25 or -0.4.

The normalized difference is then used in Figure 7 to find the second of the two shivering multipliers. For this example, the second multiplier would be at 2.0. Since the first multiplier is at 1.0, the total heat production from shivering is twice the standard value of 252 kcal/hr. The graph in Figure 7 was selected to match Riggs' equation 10.E. This equation was designed to match the empirical work by Benzinger (1963).

Figure 7. The shivering multiplier from normalized temperature difference as a function of the normalized temperature difference.

New Feedback Loops from Shivering

Three additional feedback loops in the expanded model are shown in Figure 8. Each of these loops may be connected to Rigg's qualitative description of shivering. The negative loop at the top of the diagram involves the shivering multiplier from a cooler core. It will be active whenever the core temperature falls below 37 degrees. This is probably the loop that Riggs has in mind when he talks about "core modulated shivering."

A positive feedback loop appears in the middle of the diagram. It reveals a vicious circle that can lead the system to break down if the core temperature should fall too low. This loop is probably responsible for Riggs' finding that the "regulatory mechanisms must fail at very low ambient temperatures. The third loop in Figure 8 is a negative loop at the bottom of the diagram. It involves the skin temperature,and is active when the skin temperature falls below the critical value of 21 degrees C. This loop is probably what Riggs has in mind when he refers to "skin-modulated shivering."

Figure 8. New Loops Introduced by the Addition of Shivering.