Mechanics of Undulatory Swimming in a Frictional Fluid

The sandfish lizard (Scincus scincus) swims within granular media (sand) using axial body undulations to propel itself without the use of limbs. In previous work we predicted average swimming speed by developing a numerical simulation that incorporated experimentally measured biological kinematics into a multibody sandfish model. The model was coupled to an experimentally validated soft sphere discrete element method simulation of the granular medium. In this paper, we use the simulation to study the detailed mechanics of undulatory swimming in a “granular frictional fluid” and compare the predictions to our previously developed resistive force theory (RFT) which models sand-swimming using empirically determined granular drag laws. The simulation reveals that the forward speed of the center of mass (CoM) oscillates about its average speed in antiphase with head drag. The coupling between overall body motion and body deformation results in a non-trivial pattern in the magnitude of lateral displacement of the segments along the body. The actuator torque and segment power are maximal near the center of the body and decrease to zero toward the head and the tail. Approximately 30% of the net swimming power is dissipated in head drag. The power consumption is proportional to the frequency in the biologically relevant range, which confirms that frictional forces dominate during sand-swimming by the sandfish. Comparison of the segmental forces measured in simulation with the force on a laterally oscillating rod reveals that a granular hysteresis effect causes the overestimation of the body thrust forces in the RFT. Our models provide detailed testable predictions for biological locomotion in a granular environment.     

Leatherbacks Swimming In Silico: Modeling and Verifying Their Momentum and Heat Balance Using Computational Fluid Dynamics

As global temperatures increase throughout the coming decades, species ranges will shift. New combinations of abiotic conditions will make predicting these range shifts difficult. Biophysical mechanistic niche modeling places bounds on an animal’s niche through analyzing the animal’s physical interactions with the environment. Biophysical mechanistic niche modeling is flexible enough to accommodate these new combinations of abiotic conditions. However, this approach is difficult to implement for aquatic species because of complex interactions among thrust, metabolic rate and heat transfer. We use contemporary computational fluid dynamic techniques to overcome these difficulties. We model the complex 3D motion of a swimming neonate and juvenile leatherback sea turtle to find power and heat transfer rates during the stroke. We combine the results from these simulations and a numerical model to accurately predict the core temperature of a swimming leatherback. These results are the first steps in developing a highly accurate mechanistic niche model, which can assists paleontologist in understanding biogeographic shifts as well as aid contemporary species managers about potential range shifts over the coming decades.     

Model Studies of the Dynamics of Bacterial Flagellar Motors

The bacterial flagellar motor is a rotary molecular machine that rotates the helical filaments that propel swimming bacteria. Extensive experimental and theoretical studies exist on the structure, assembly, energy input, power generation, and switching mechanism of the motor. In a previous article, we explained the general physics underneath the observed torque-speed curves with a simple two-state Fokker-Planck model. Here, we further analyze that model, showing that 1), the model predicts that the two components of the ion motive force can affect the motor dynamics differently, in agreement with latest experiments; 2), with explicit consideration of the stator spring, the model also explains the lack of dependence of the zero-load speed on stator number in the proton motor, as recently observed; and 3), the model reproduces the stepping behavior of the motor even with the existence of the stator springs and predicts the dwell-time distribution. The predicted stepping behavior of motors with two stators is discussed, and we suggest future experimental procedures for verification.     

Computational Fluid Dynamics Simulations at Micro-Scale Stenosis for Microfluidic Thrombosis Model Characterization

Platelet aggregation plays a central role in pathological thrombosis, preventing healthy physiological blood flow within the circulatory system. For decades, it was believed that platelet aggregation was primarily driven by soluble agonists such as thrombin, adenosine diphosphate and thromboxane A2. However, recent experimental findings have unveiled an intriguing but complementary biomechanical mechanism—the shear rate gradients generated from flow disturbance occurring at sites of blood vessel narrowing, otherwise known as stenosis, may rapidly trigger platelet recruitment and subsequent aggregation. In our Nature Materials 2019 paper [1], we employed microfluidic devices which incorporated micro-scale stenoses to elucidate the molecular insights underlying the prothrombotic effect of blood flow disturbance. Nevertheless, the rheological mechanisms associated with this stenotic microfluidic device are poorly characterized. To this end, we developed a computational fluid dynamics (CFD) simulation approach to systematically analyze the hemodynamic influence of bulk flow mechanics and flow medium. Grid sensitivity studies were performed to ensure accurate and reliable results. Interestingly, the peak shear rate was significantly reduced with the device thickness, suggesting that fabrication of microfluidic devices should retain thicknesses greater than 50 µm to avoid unexpected hemodynamic aberration, despite thicker devices raising the cost of materials and processing time of photolithography. Overall, as many groups in the field have designed microfluidic devices to recapitulate the effect of shear rate gradients and investigate platelet aggregation, our numerical simulation study serves as a guideline for rigorous design and fabrication of microfluidic thrombosis models.     

On-line Optimization of Biomimetic Undulatory Swimming by an Experiment-based Approach

An experiment-based approach is proposed to improve the performance of biomimetic undulatory locomotion through on-line optimization. The approach is implemented through two steps： （1） the generation of coordinated swimming gaits by artificial Central Pattern Generators （CPGs）; （2） an on-line searching of optimal parameter sets for the CPG model using Genetic Algorithm （GA）. The effectiveness of the approach is demonstrated in the optimization of swimming speed and energy effi- ciency for a biomimetic fin propulsor. To evaluate how well the input energy is converted into the kinetic energy of the pro- pulsor, an energy-efficiency index is presented and utilized as a feedback to regulate the on-line searching with a closed-loop swimming control. Experiments were conducted on propulsor prototypes with different fin segments and the optimal swimming patterns were found separately. Comparisons of results show that the optimal curvature of undulatory propulsor, which might have different shapes depending on the actual prototype design and control scheme. It is also found that the propulsor with six fin segments, is preferable because of hizher speed and lower energy efficiency.     

鞭毛细菌游动机理研究进展

鞭毛细菌是在低雷诺数条件下运动的生物体,通过旋转鞭毛而向前游动。通过概述细菌鞭毛的游动机理、在不同游动方式下鞭毛丝几何形态之间转换的物理现象、菌体反转对成束的影响以及在靠近壁时运动的墙效应机理的最新研究,提出一种与鞭毛细菌运动动力相似的宏观等效模型,该模型可以用于进一步研究鞭毛细菌的游动机理,并为仿生微型游动机器人的构造和应用提供理论研究的基础。     

Moving Domain Computational Fluid Dynamics to Interface with an Embryonic Model of Cardiac Morphogenesis

Peristaltic contraction of the embryonic heart tube produces time- and spatial-varying wall shear stress (WSS) and pressure gradients (∇P) across the atrioventricular (AV) canal. Zebrafish (Danio rerio) are a genetically tractable system to investigate cardiac morphogenesis. The use of Tg(fli1a:EGFP)^y1 transgenic embryos allowed for delineation and two-dimensional reconstruction of the endocardium. This time-varying wall motion was then prescribed in a two-dimensional moving domain computational fluid dynamics (CFD) model, providing new insights into spatial and temporal variations in WSS and ∇P during cardiac development. The CFD simulations were validated with particle image velocimetry (PIV) across the atrioventricular (AV) canal, revealing an increase in both velocities and heart rates, but a decrease in the duration of atrial systole from early to later stages. At 20-30 hours post fertilization (hpf), simulation results revealed bidirectional WSS across the AV canal in the heart tube in response to peristaltic motion of the wall. At 40-50 hpf, the tube structure undergoes cardiac looping, accompanied by a nearly 3-fold increase in WSS magnitude. At 110-120 hpf, distinct AV valve, atrium, ventricle, and bulbus arteriosus form, accompanied by incremental increases in both WSS magnitude and ∇P, but a decrease in bi-directional flow. Laminar flow develops across the AV canal at 20-30 hpf, and persists at 110-120 hpf. Reynolds numbers at the AV canal increase from 0.07±0.03 at 20-30 hpf to 0.23±0.07 at 110-120 hpf (p< 0.05, n=6), whereas Womersley numbers remain relatively unchanged from 0.11 to 0.13. Our moving domain simulations highlights hemodynamic changes in relation to cardiac morphogenesis; thereby, providing a 2-D quantitative approach to complement imaging analysis.     

A Forced Damped Oscillation Framework for Undulatory Swimming Provides New Insights into How Propulsion Arises in Active and Passive Swimming

A fundamental issue in locomotion is to understand how muscle forcing produces apparently complex deformation kinematics leading to movement of animals like undulatory swimmers. The question of whether complicated muscle forcing is required to create the observed deformation kinematics is central to the understanding of how animals control movement. In this work, a forced damped oscillation framework is applied to a chain-link model for undulatory swimming to understand how forcing leads to deformation and movement. A unified understanding of swimming, caused by muscle contractions (“active” swimming) or by forces imparted by the surrounding fluid (“passive” swimming), is obtained. We show that the forcing triggers the first few deformation modes of the body, which in turn cause the translational motion. We show that relatively simple forcing patterns can trigger seemingly complex deformation kinematics that lead to movement. For given muscle activation, the forcing frequency relative to the natural frequency of the damped oscillator is important for the emergent deformation characteristics of the body. The proposed approach also leads to a qualitative understanding of optimal deformation kinematics for fast swimming. These results, based on a chain-link model of swimming, are confirmed by fully resolved computational fluid dynamics (CFD) simulations. Prior results from the literature on the optimal value of stiffness for maximum speed are explained.     

A Mechanochemical Model of Flagellar Activity

A theory is presented which quantitatively links the physical properties of a flagellum with parameters which characterize the chemical reactions responsible for deforming the flagellum. Realistic values for the wave parameters are predicted when order-of-magnitude values for the appropriate constants are used. The model may be useful in other fields where mechanochemical coupling occurs.     

Computational Fluid Dynamics of Fish Gill Rakers During Crossflow Filtration

We study crossflow filtration mechanisms in suspension-feeding fishes using computational fluid dynamics to model fluid flow and food particle movement in the vicinity of the gill rakers. During industrial and biological crossflow filtration, particles are retained when they remain suspended in the mainstream flow traveling across the filter surface rather than traveling perpendicularly to the filter. Here we identify physical parameters and hydrodynamic processes that determine food particle movement and retention inside the fish oral cavity. We demonstrate how five variables affect flow patterns and particle trajectories: (1) flow speed inside the fish oral cavity, (2) incident angle of the flow approaching the filter, (3) dimensions of filter structures, (4) particle size, and (5) particle density. Our study indicates that empirical experiments are needed to quantify flow parameters inside the oral cavity, and morphological research is needed to quantify dimensions of the filter apparatus such as gill rakers, the gaps between rakers, and downstream barriers. Ecological studies on suspension-feeding fishes are also needed to quantify food particle size and density, as these variables can affect particle retention due to hydrodynamic processes during crossflow filtration.     

Arterial Pulsation-driven Cerebrospinal Fluid Flow in the Perivascular Space: A Computational Model

This study was conducted to determine whether local arterial pulsations are sufficient to cause cerebrospinal fluid (CSF) flow along perivascular spaces (PVS) within the spinal cord. A theoretical model of the perivascular space surrounding a "typical" small artery was analysed using computational fluid dynamics. Systolic pulsations were modelled as travelling waves on the arterial wall. The effects of wave geometry and variable pressure conditions on fluid flow were investigated. Arterial pulsations induce fluid movement in the PVS in the direction of arterial wave travel. Perivascular flow continues even in the presence of adverse pressure gradients of a few kilopascals. Flow rates are greater with increasing pulse wave velocities and arterial deformation, as both an absolute amplitude and as a proportion of the PVS. The model suggests that arterial pulsations are sufficient to cause fluid flow in the perivascular space even against modest adverse pressure gradients. Local increases in flow in this perivascular pumping mechanism or reduction in outflow may be important in the etiology of syringomyelia.     

Interstitial Fluid Flow and Drug Delivery in Vascularized Tumors: A Computational Model

Interstitial fluid is a solution that bathes and surrounds the human cells and provides them with nutrients and a way of waste removal. It is generally believed that elevated tumor interstitial fluid pressure (IFP) is partly responsible for the poor penetration and distribution of therapeutic agents in solid tumors, but the complex interplay of extravasation, permeabilities, vascular heterogeneities and diffusive and convective drug transport remains poorly understood. Here we consider–with the help of a theoretical model–the tumor IFP, interstitial fluid flow (IFF) and its impact upon drug delivery within tumor depending on biophysical determinants such as vessel network morphology, permeabilities and diffusive vs. convective transport. We developed a vascular tumor growth model, including vessel co-option, regression, and angiogenesis, that we extend here by the interstitium (represented by a porous medium obeying Darcy''s law) and sources (vessels) and sinks (lymphatics) for IFF. With it we compute the spatial variation of the IFP and IFF and determine its correlation with the vascular network morphology and physiological parameters like vessel wall permeability, tissue conductivity, distribution of lymphatics etc. We find that an increased vascular wall conductivity together with a reduction of lymph function leads to increased tumor IFP, but also that the latter does not necessarily imply a decreased extravasation rate: Generally the IF flow rate is positively correlated with the various conductivities in the system. The IFF field is then used to determine the drug distribution after an injection via a convection diffusion reaction equation for intra- and extracellular concentrations with parameters guided by experimental data for the drug Doxorubicin. We observe that the interplay of convective and diffusive drug transport can lead to quite unexpected effects in the presence of a heterogeneous, compartmentalized vasculature. Finally we discuss various strategies to increase drug exposure time of tumor cells.     

Fibrous Flagellar Hairs of Chlamydomonas reinhardtii Do Not Enhance Swimming

The flagella of Chlamydomonas reinhardtii possess fibrous ultrastructures of a nanometer-scale thickness known as mastigonemes. These structures have been widely hypothesized to enhance flagellar thrust; however, detailed hydrodynamic analysis supporting this claim is lacking. In this study, we present a comprehensive investigation into the hydrodynamic effects of mastigonemes using a genetically modified mutant lacking the fibrous structures. Through high-speed observations of freely swimming cells, we found the average and maximum swimming speeds to be unaffected by the presence of mastigonemes. In addition to swimming speeds, no significant difference was found for flagellar gait kinematics. After our observations of swimming kinematics, we present direct measurements of the hydrodynamic forces generated by flagella with and without mastigonemes. These measurements were conducted using optical tweezers, which enabled high temporal and spatial resolution of hydrodynamic forces. Through our measurements, we found no significant difference in propulsive flows due to the presence of mastigonemes. Direct comparison between measurements and fluid mechanical modeling revealed that swimming hydrodynamics were accurately captured without including mastigonemes on the modeled swimmer’s flagella. Therefore, mastigonemes do not appear to increase the flagella’s effective area while swimming, as previously thought. Our results refute the longstanding claim that mastigonemes enhance flagellar thrust in C. reinhardtii, and so, their function still remains enigmatic.     

Combining Computational Fluid Dynamics and Agent-Based Modeling: a new approach to evacuation planning

We introduce a novel hybrid of two fields-Computational Fluid Dynamics (CFD) and Agent-Based Modeling (ABM)-as a powerful new technique for urban evacuation planning. CFD is a predominant technique for modeling airborne transport of contaminants, while ABM is a powerful approach for modeling social dynamics in populations of adaptive individuals. The hybrid CFD-ABM method is capable of simulating how large, spatially-distributed populations might respond to a physically realistic contaminant plume. We demonstrate the overall feasibility of CFD-ABM evacuation design, using the case of a hypothetical aerosol release in Los Angeles to explore potential effectiveness of various policy regimes. We conclude by arguing that this new approach can be powerfully applied to arbitrary population centers, offering an unprecedented preparedness and catastrophic event response tool.     

A Comparative Study between Use of Arthroscopic Lavage and Arthrocentesis of Temporomandibular Joint Based on Computational Fluid Dynamics Analysis

Arthroscopic lavage and arthrocentesis, performed with different inner-diameter lavage needles, are the current minimally invasive techniques used in temporomandibular joint disc displacement (TMJ-DD) for pain reduction and functional improvement. In the current study, we aimed to explore the biomechanical influence and explain the diverse clinical outcomes of these two approaches with computational fluid dynamics. Data was retrospectively analyzed from 78 cases that had undergone arthroscopic lavage or arthrocentesis for TMJ-DD from 2002 to 2010. Four types of finite volume models, featuring irrigation needles of different diameters, were constructed based on computed tomography images. We investigated the flow pattern and pressure distribution of lavage fluid secondary to caliber-varying needles. Our results demonstrated that the size of outflow portal was the critical factor in determining irrigated flow rate, with a larger inflow portal and a smaller outflow portal leading to higher intra-articular pressure. This was consistent with clinical data suggesting that increasing the mouth opening and maximal contra-lateral movement led to better outcomes following arthroscopic lavage. The findings of this study could be useful for choosing the lavage apparatus according to the main complaint of pain, or limited mouth opening, and examination of joint movements.