Model for understanding thermal hysteresis during heat stress: a matter of direction

Thermal hysteresis may be used to quantify and characterize the amount of heat stress an animal experiences. Heat stress studies of farm animals suggest that above a certain threshold body temperature (Tb) is driven by ambient temperature (Ta). Patterns in the Tb-Ta phase diagram indicate the presence of hysteresis. When hysteresis is present, there are two values for Tb depending on whether Ta is increasing or decreasing. A theoretical delay-relay model is proposed to illustrate the hysteretic dynamics of the Tb-Ta relationship when Ta is cyclic. Two types of hysteresis, transitional and thermal, are identified. Thermal hysteresis becomes prominent when Ta forces Tb into an elliptical limit cycle. The area of the ellipse is an indication of the animal's heat load. Also, the resulting Tb-Ta pattern depends on the delay (or lag) between Tb and Ta. The delay suggests possible levels of heat stress. A greater delay between Tb and Ta indicates more time is needed to dissipate the heat load, implying the animal is suffering more heat stress. For a given Ta, the Tb on the decreasing (recovery) path is always higher than the Tb on the increasing (challenge) path. Essentially, the animal requires more energy to dissipate heat than to absorb it.