Collaborative Research: Computational Models of Cilia and Flagella in a Brinkman Fluid

活动纤毛和鞭毛是动态的、有弹性的、具有节律性运动的生物结构。通过协调跳动，肺部和呼吸道的纤毛有助于清除气道中潜在的有害颗粒和粘液。纤毛运动受损可导致严重的呼吸道感染。这种损害可由液体环境改变（囊性纤维化的特征）、纤毛本身缺陷（如原发性纤毛运动障碍）或其他呼吸系统疾病引起。同样，精子只有在鞭毛能够推动卵子前进的情况下才能接触到卵子并使其受精；运动能力受损导致不孕。纤毛和精子的跳动高度依赖于流体环境，其中包含纤维、蛋白质网络以及化学信号。了解弹性结构和非均质流体之间的这种关系对于开发吸入药物和药物的输送策略、新型避孕药具以及帮助治疗由于精子活力降低而导致的不孕症至关重要。该项目将专注于开发新的计算模型和数值方法，以解释这些纤维，液体中的蛋白质网络，以推断纤毛和精子的体内行为。最近的实验表明，i)浸泡在含有大型蛋白质网络和鞭毛钙浓度的液体中时，精子-鞭毛波形会发生改变；ii)以前认为的围绕气道纤毛的“水样”液体实际上含有大型蛋白质网络，或称为“刷子”。本项目将重点研究在考虑非平面弯曲和鞭毛内部生物化学的情况下，精子鞭毛和气道纤毛的涌现波形。纤毛和鞭毛将被建模成细长的、有弹性的、浸在由布林克曼方程控制的流体中的结构。正则框架和基本解将用于推导各种受限几何的新数值方法。新的数值方法将是计算效率高，并开发用于高性能计算系统。这项研究将确定调节精子向卵子前进的因素，探索纤毛和精子的各种波形，并研究纤毛周围液体中的“刷子”如何影响液体中颗粒的运输。

Motile cilia and flagella are dynamic, elastic, biological structures that exhibit rhythmic motion. Through coordinated beating, cilia in the lung and respiratory tract help to clear the airway of potentially harmful particles and mucus. Impaired cilia motion can result in serious respiratory infection. This impairment can be caused by an altered fluid environment, a characteristic of cystic fibrosis, by defects in the cilia themselves as with primary ciliary dyskinesia, or by other respiratory diseases. Similarly, a sperm is only able to reach and fertilize an egg if its flagellum can propel it forward; impaired motility results in infertility. Cilia and sperm beating is highly dependent on the fluid environment, which contains fibrous, protein networks as well as chemical signals. Understanding this relationship between elastic structure and heterogeneous fluid is vital for development of delivery strategies for inhaled drugs and medicines, new contraceptives, and aiding in infertility due to reduced sperm motility. This project will focus on the development of new computational models and numerical methods that account for these fibrous, protein networks within the fluid to infer in vivo behavior of cilia and sperm.Recent experiments have shown that i) sperm-flagella waveforms are altered when immersed in fluids containing networks of large proteins and also with flagellar calcium concentration, ii) the previously-considered `watery' fluid surrounding airway cilia actually contains a network of large proteins, or, 'brush'. This project will focus on identifying emergent waveforms of sperm flagella and airway cilia when nonplanar bending and internal flagellar biochemistry are taken into account. Cilia and flagella will be modeled as slender, elastic, structures immersed in a fluid governed by the Brinkman equation. A regularized framework and fundamental solutions will be used to derive new numerical methods for various confined geometries. The new numerical methods will be computationally-efficient and developed for use on high-performance computing systems. This research will identify factors that modulate sperm progression towards the egg, explore various waveforms of cilia and sperm, and investigate how a 'brush' in the fluid surrounding cilia might affect transport of particles within that fluid.