Department of Statistics, University of Nebraska-Lincoln, 349C Hardin NW, Lincoln, NE 68583-0963, USA.
Int J Biometeorol. 2010 Nov;54(6):637-45. doi: 10.1007/s00484-009-0299-z. Epub 2010 Feb 6.
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.
热滞环可用于量化和描述动物所经历的热应激程度。农场动物的热应激研究表明，在一定的体温阈值（Tb）以上，体温是由环境温度（Ta）驱动的。Tb-Ta 相图中的模式表明存在滞后现象。当滞后存在时，Tb 有两个值，具体取决于 Ta 是增加还是减少。本文提出了一个理论延迟继电器模型，以说明 Ta 为周期性时 Tb-Ta 关系的滞后动力学。确定了两种类型的滞后，即过渡滞后和热滞后。当 Ta 将 Tb 推到椭圆形极限环时，热滞后变得明显。椭圆的面积是动物热负荷的一个指标。此外，Tb-Ta 模式的结果取决于 Tb 和 Ta 之间的延迟（或滞后）。延迟表明可能存在的热应激水平。Tb 和 Ta 之间的延迟越大，意味着需要更多的时间来散发热量负荷，这表明动物正在承受更多的热应激。对于给定的 Ta，Tb 在下降（恢复）路径上总是高于在上升（挑战）路径上的 Tb。从本质上讲，动物消耗的能量来散发热量比吸收热量要多。
