The duration of the QT interval as a function of heart rate: a derivation based on physical principles and a comparison to measured values.
The duration of the QT interval as a function of heart rate: a derivation based on physical principles and a comparison to measured values.
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QT 间期的持续时间作为心率的函数：基于物理原理的推导以及与测量值的比较。
DOI：
10.1016/0002-8703(85)90472-7
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发表时间：
1985
影响因子：
4.8
通讯作者：
S. Kovacs
中科院分区：
文献类型：
--
作者：
S. Kovacs
回顾了电收缩持续时间（QT 间期）作为 RR 间期函数的几个定量和定性不同的公式。通过使用量纲分析对它们进行比较，从而可以纠正先前发布的代数和量纲不一致之处。除了一个例外，先前的公式发展本质上是经验性的，因此结果并不基于基本物理或生物学原理，也不一定在数学上与基本物理或生物学原理一致。为了解决歧义并确定许多提出的公式中的哪些（如果有）符合基本原理，我们从与实验结果相关的物理原理开始，并导出了 QT 间期作为 RR 间期函数的数学表达式。通过利用心脏作为泵的能量守恒方程和热力学第一定律，导出了 QT K 1′+ K 2′ RR 形式的公式。这一推导源于第一性原理并建立在实验数据的基础上，并没有定量地指定加法常数 (K 1′) 或乘法常数 (K 2′)，而是将 QT 与 RR 的函数的代数关系约束起来。该公式由两项之和组成，即 HR (RR) 独立加性常数 (K 1′) 和一项 (RR)− 1。该推导解决了所提出的公式中先前的定性差异，并在大 RR 间隔的限制中产生 QT 的有限限制。它描述了 QT 代数依赖性的本质，作为正常心脏在生理范围内运行的 RR 函数，这与基本物理原理一致，并要求舒张期持续时间（TQ 间期）作为 HR 的函数，由 TQ= RR-QT= RR-(K 1′+ K 2′ RR) 给出。
Several quantitatively and qualitatively disparate formulas for the duration of electrical systole (the QT interval) as a function of the RR interval are reviewed. These are compared by the use of dimensional analysis, which permits rectification of previously published algebraic and dimensional inconsistencies. With one exception, prior developments of formulas have been empiric in nature, with results therefore not based on or necessarily mathematically consistent with basic physical or biologic principles. In order to resolve ambiguity and determine which (if any) of the many proposed formulas is consistent with elementary priciples, we began with physical principles as they relate to the results of experiments and derived a mathematical expression for the QT interval as a function of the RR interval. By making use of equations for the conservation of energy for the heart as a pump and the first law of thermodynamics, a formula of the form QT K 1′+ K 2′ RR was derived. This derivation, stemming from first principles and founded on experimental data, does not quantitatively specify the additive (K 1′) or multiplicative constant (K 2′), but constrains the algebraic relationship of QT as a function of RR. The formula is comprised of the sum of two terms, a HR (RR) independent additive constant (K 1′) and a term (RR)− 1. The derivation resolves previous qualitative disparaties in proposed formulas and yields a finite limit for QT in the limit of large RR intervals. It delineates the nature of the algebraic dependence of QT as a function of RR for the normal heart operating in the physiologic range that is consistent with basic physical principles and requires that the duration of diastole (TQ interval) as a function of HR be given by TQ= RR-QT= RR-(K 1′+ K 2′ RR).