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

运动纤毛和鞭毛是动态的，弹性的，生物结构，表现出有节奏的运动。通过协调跳动，肺和呼吸道中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。这种损害可由改变的液体环境（囊性纤维化的特征）、纤毛本身的缺陷（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它前进的情况下才能到达卵子并使其受精;运动能力受损会导致不育。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。了解弹性结构和异质流体之间的这种关系对于开发吸入药物和药物、新避孕药的递送策略以及帮助由于精子活力降低而导致的不孕症至关重要。 本项目将致力于开发新的计算模型和数值方法，以解释流体中这些纤维状蛋白质网络，从而推断纤毛和精子的体内行为。最近的实验表明，i）精子鞭毛波形在浸入含有大蛋白质网络的流体中时会发生改变，并且鞭毛钙浓度也会发生变化，ii）先前认为的围绕气道纤毛的"水样"流体实际上包含大蛋白质的网络，或"刷子"。本计画将著重于辨识精子鞭毛与呼吸道纤毛在非平面弯曲与鞭毛内生化作用下的波形。纤毛和鞭毛将被建模为细长的，弹性的，结构沉浸在流体由布林克曼方程。一个正规化的框架和基本解决方案将被用来获得新的数值方法，为各种限制的几何形状。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进展的因素，探索纤毛和精子的各种波形，并研究纤毛周围流体中的“刷子”如何影响流体中颗粒的运输。

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.