Department of Mathematics, University of Auckland, Auckland, New Zealand.
Department of Mathematics, University of Auckland, Auckland, New Zealand.
Biophys J. 2018 Jan 23;114(2):493-501. doi: 10.1016/j.bpj.2017.11.020.
Asthma is fundamentally a disease of airway constriction. Due to a variety of experimental challenges, the dynamics of airways are poorly understood. Of specific interest is the narrowing of the airway due to forces produced by the airway smooth muscle wrapped around each airway. The interaction between the muscle and the airway wall is crucial for the airway constriction that occurs during an asthma attack. Although cross-bridge theory is a well-studied representation of complex smooth muscle dynamics, and these dynamics can be coupled to the airway wall, this comes at significant computational cost-even for isolated airways. Because many phenomena of interest in pulmonary physiology cannot be adequately understood by studying isolated airways, this presents a significant limitation. We present a distribution-moment approximation of this coupled system and study the validity of the approximation throughout the physiological range. We show that the distribution-moment approximation is valid in most conditions, and we explore the region of breakdown. These results show that in many situations, the distribution-moment approximation is a viable option that provides an orders-of-magnitude reduction in computational complexity; not only is this valuable for isolated airway studies, but it moreover offers the prospect that rich ASM dynamics might be incorporated into interacting airway models where previously this was precluded by computational cost.
哮喘从根本上说是一种气道收缩的疾病。由于各种实验挑战，气道动力学的理解还很不完善。特别感兴趣的是气道平滑肌产生的力导致气道变窄。气道平滑肌与气道壁之间的相互作用对于哮喘发作时发生的气道收缩至关重要。尽管横桥理论是平滑肌复杂动力学的一个研究充分的表示，并且这些动力学可以与气道壁耦合，但这会带来巨大的计算成本——即使对于孤立的气道也是如此。由于通过研究孤立的气道不能充分理解肺生理学中许多感兴趣的现象，这就带来了一个重大的局限性。我们提出了这个耦合系统的分布矩近似，并研究了在整个生理范围内该近似的有效性。我们表明，在大多数情况下，分布矩近似是有效的，并且我们探索了失效区域。这些结果表明，在许多情况下，分布矩近似是一种可行的选择，它可以大大降低计算复杂度；这不仅对孤立的气道研究有价值，而且还为将丰富的 ASM 动力学纳入到相互作用的气道模型中提供了前景，而此前由于计算成本的限制，这是不可能的。
