Papadopoulos Anthony
Department of Biological Sciences, Texas Tech University, Lubbock, TX, USA.
PLoS One. 2009;4(3):e4852. doi: 10.1371/journal.pone.0004852. Epub 2009 Mar 31.
The first-degree power-law polynomial function is frequently used to describe activity metabolism for steady swimming animals. This function has been used in hydrodynamics-based metabolic studies to evaluate important parameters of energetic costs, such as the standard metabolic rate and the drag power indices. In theory, however, the power-law polynomial function of any degree greater than one can be used to describe activity metabolism for steady swimming animals. In fact, activity metabolism has been described by the conventional exponential function and the cubic polynomial function, although only the power-law polynomial function models drag power since it conforms to hydrodynamic laws. Consequently, the first-degree power-law polynomial function yields incorrect parameter values of energetic costs if activity metabolism is governed by the power-law polynomial function of any degree greater than one. This issue is important in bioenergetics because correct comparisons of energetic costs among different steady swimming animals cannot be made unless the degree of the power-law polynomial function derives from activity metabolism. In other words, a hydrodynamics-based functional form of activity metabolism is a power-law polynomial function of any degree greater than or equal to one. Therefore, the degree of the power-law polynomial function should be treated as a parameter, not as a constant. This new treatment not only conforms to hydrodynamic laws, but also ensures correct comparisons of energetic costs among different steady swimming animals. Furthermore, the exponential power-law function, which is a new hydrodynamics-based functional form of activity metabolism, is a special case of the power-law polynomial function. Hence, the link between the hydrodynamics of steady swimming and the exponential-based metabolic model is defined.
一次幂律多项式函数经常被用于描述持续游泳动物的活动代谢。该函数已被用于基于流体动力学的代谢研究中，以评估能量消耗的重要参数，如标准代谢率和阻力功率指数。然而，从理论上讲，任何大于一次的幂律多项式函数都可用于描述持续游泳动物的活动代谢。事实上，活动代谢已通过传统的指数函数和三次多项式函数来描述，尽管只有幂律多项式函数能模拟阻力功率，因为它符合流体动力学定律。因此，如果活动代谢受任何大于一次的幂律多项式函数支配，那么一次幂律多项式函数会得出能量消耗的错误参数值。这个问题在生物能量学中很重要，因为除非幂律多项式函数的次数源自活动代谢，否则无法对不同持续游泳动物的能量消耗进行正确比较。换句话说，基于流体动力学的活动代谢函数形式是任何大于或等于一次的幂律多项式函数。因此，幂律多项式函数的次数应被视为一个参数，而非一个常数。这种新的处理方式不仅符合流体动力学定律，还能确保对不同持续游泳动物的能量消耗进行正确比较。此外，指数幂律函数作为一种新的基于流体动力学的活动代谢函数形式，是幂律多项式函数的一种特殊情况。因此，定义了持续游泳的流体动力学与基于指数的代谢模型之间的联系。
