Session L02: Focus Session: Transport Phenomena in Active Biological Networks

Optimization of nutrient transport in active and adaptive networks

Animal and plant vasculature is characterized by a rich hierarchical structure that is though to minimize dissipation, and when loops exist, provide robustness to damage and fluctuating load. The qualitative features of these networks can be reproduced by simple "use-it or lose-it" rules, which use local mechanical information, such as the shear stress of the vessel wall, to modify the lumen diameter of the vessels. However, these models ignore the importance of solutes: the flow carries oxygen and other nutrients that need to be distributed to the tissue according to the metabolic demands. In this talk we propose a local adaptation rule that accounts for homogeneous perfusion, in addition to energy dissipation and material cost. The competition between these terms produces rich network morphologies. We show that our local rule is consistent with the vascular architecture seen in the rat mesentery network.   

Artificial intelligence velocimetry reveals in vivo pressure gradients in brain cerebrospinal fluid

Cerebrospinal fluid (CSF) circulates around and through brain tissue, sweeping away metabolic wastes that correlate with diseases including Alzheimer's, contributing to damaging swelling during stroke and cardiac arrest, and offering a potential pathway for drug delivery. Brain CSF flow is difficult to quantify in vivo at all, and quantifying the pressure gradients associated with flow has been altogether impossible up to now. We reveal pressure gradients for the first time by combining in vivo particle tracking with artificial intelligence velocimetry (AIV). In AIV, neural networks are trained to infer pressure and velocity fields by simultaneously minimizing mismatch with experimental measurements, minimizing error in the momentum and mass equations, and minimizing error in the boundary conditions. The pressure fields we infer extend throughout the three-dimensional perivascular spaces where CSF flows. We quantify typical pressure gradients and compare to prior estimates from theory. We show that the inertial term in the momentum equation is negligible, enabling lower-cost simulation in the future. With fluid-structure interaction in mind, we compare pressure fluctuations to the stiffness of bounding tissue. Finally, we characterize the magnitude and spatiotemporal variation of pressure gradients to gain insight into the fluid dynamical mechanisms driving CSF flow in the brain.   

Dynamics of hydraulic and contractile wave-mediated fluid transport during Drosophila oogenesis

From insects to mice, oocytes develop within cysts alongside nurse-like sister germ cells. Prior to fertilization, the nurse cells’ cytoplasm is transported into the oocyte, which grows as its sister cells regress and die. Although critical for fertility, the biology and physics underlying this process are poorly understood. Here, we combined live imaging of germline cysts, genetic perturbations, and mathematical modeling to investigate the dynamics and mechanisms that enable cytoplasmic transport in Drosophila melanogaster egg chambers. We discovered that during “nurse cell (NC) dumping” most cytoplasm is transported into the oocyte independently of changes in myosin-II contractility, with dynamics instead explained by an effective Young–Laplace law, suggesting hydraulic transport induced by cell surface tension. A minimal flow-network model correctly predicts the directionality, intercellular pattern, and time scale of transport. Long thought to trigger transport through “squeezing,” changes in actomyosin contractility only play a role in the later stages of dumping. Our work thus demonstrates how biological and physical mechanisms cooperate during a critical developmental process that, until now, was thought to be mainly biochemically regulated.

    

A brain-wide model of glymphatic solute transport

Metabolic waste removal through fluid systems, such as the lymphatic system, is indispensable for maintaining homeostasis. The brain contains no lymph vessels, prompting research into alternative waste clearance methods. One hypothesis is of the glymphatic system, in which waste is cleared via cerebrospinal fluid (CSF) flowing through the perivascular spaces that surround blood vessels. CSF trickles through the outer wall of the perivascular space to clear waste from the brain. While several models and in vivo studies have explored CSF flow, there has been little investigation into the motion of waste within that fluid, particularly on the brain-wide scale. Many solutes are created and removed through cellular activity, creating sources and sinks in the fluid network. We build on an existing hydraulic resistance model of CSF flow through periarterial spaces and the parenchyma [1]. Using flow rates from the model, we solve two different 1D, steady-state advection-diffusion equations. In one equation, which is appropriate for the delivery of nutrients or drugs, the source term describing solute gain and loss depends on the concentration within the perivascular space. In the other, which is appropriate for wastes produced in the brain, the source term is independent of concentration. Some model parameters such as porosities and solute production rates are not well defined, so we perform a sensitivity analysis to determine in which areas of the model further in vivo investigation is needed to ensure accuracy.

[1] Tithof, Jeffrey, et al. "A network model of glymphatic flow under different experimentally-motivated parametric scenarios." Iscience 25.5 (2022): 104258.   

Fluid flow in an artificial model of a collecting lymphatic

Fluid flows in vascular networks are among the most effective way to transport matter and information for life. One striking example of swift and versatile transport is the lymphatic system in which lymph is transported across the whole body of mammals against intricate changes of pressures. In the collecting lymphatics, lymph is transported via vessel contractions combined with valve leaflets that ensure unidirectional transport. The nature of the active contractions, the multi-scale and multi-physics of the system make it challenging to model. Numerical simulations have brought many answers to these limitations. Yet, questions on the propagation of the vessel contractions along the lymphatic network remain difficult to answer.

Here, we study experimentally fluid transport in an upscaled model of a collecting lymphatic. We finely control the amplitude, the wavelength and the speed of the contraction wave, and the structure of the collecting lymphatic. Our results suggest that the presence of valve leaflets not only increases the flow rate, but also enables efficient transport for low speeds and for a limited number of actuation points. Overall, our work opens the way to systematic experimental studies of fluid transport in actuated channels.   

Probing contraction of blood clots under flow

Blood clots are active material involved in physiologic and pathologic processes. Clotting disorders prevent body's natural ability to achieve hemostasis and lead to bleeding, stroke, or heart attack. Upon injury, platelets aggregate to form blood clots that undergo contraction to stem blood flow from a vessel. The contraction is driven by collective behavior of platelets extending filopodia to impose contractile forces on the fibrin scaffold, leading to drastic changes in clot volume and elastic modulus. Clot contraction happens inside blood vessel and it has been shown that RBCs and flow have substantial influence on the mechanical properties and contraction process of blood clots. Understanding the biophysical mechanism of clot contraction within blood flow is critical for the development of new diagnoses and treatments for bleeding disorders and thrombotic disorders. We integrate RBCs and flow with our validated mesoscale platelet-fibrin clot contraction model. We evaluate the effects of RBC concentration, flow velocity, and how fibrin clot is bounded by vessel on the macroscale biomaterial properties and contraction dynamics of blood clots. We probe the effect of clot contraction on RBC shape and ability to remain within clot and the effect of clot contraction on flow.   

Sizes and Shapes of Fluid Channels in Brain Cortex

The flow of the cerebrospinal fluid (CSF) through perivascular spaces (PVSs) that surround vessels in the brain is a crucial part of the glymphatic system, which clears metabolic waste and might someday be used for drug delivery. The failure or abnormal functioning of the glymphatic system has been linked to neurodegenerative diseases like Alzheimer’s. The size and shape of the PVSs strongly affect the velocity and pressure of CSF, since hydraulic resistance scales inversely with PVS width to the fourth power. Existing descriptions of PVS shape use highly idealized geometries based on only a few in vivo observations. We characterized surface vessels and PVSs by quantitatively describing their sizes and shapes at 26 locations, in 15 different mice, from thousands of three-dimensional, in vivo images. We present a new idealized geometry for surface PVSs and validate the idealized geometry by comparing the PVS-vessel area ratio and hydraulic resistance for the idealized geometry and the original shape of the perivascular space obtained directly from the imaging data.

    

A valve mechanism for artery motion to drive cerebrospinal fluid into brain tissue

Metabolic waste is cleared from the brain in part by the flow of cerebrospinal fluid (CSF) fluid through perivascular spaces (PVSs) that surround blood vessels. Experiments show that global oscillations in vessel diameter increase CSF inflow. How those oscillations cause net flow into -- not out of -- brain tissue is not well understood, however. A valve mechanism is needed, but no valves are found inside the PVS space. We hypothesize that the gaps in the outer PVS boundary change size as pressure varies, altering tissue permeability and functioning like valves. Simulating flow driven by vessel wall motion in the presence of pressure-dependent permeability, we found that inflow can be promoted over outflow. We will discuss the range of parameters that allow valve-like action and their relevance to the real brain.   

Lumped Parameter Simulations of Lymphatic Vessels Reveal Dynamics of Cerebrospinal Fluid Efflux from the Skull

Experiments from the last decade have revealed that lymphatic vessels exist in the meninges (the tissue surrounding the brain) and play an important role in removing metabolic waste from the brain. Cerebrospinal fluid (CSF) circulates through the brain (known as the glymphatic system) carrying the wastes then drains through these meningeal lymphatic vessels (MLVs) in many different locations, eventually reaching the larger cervical lymphatic vessels (CLVs) located in the neck. The details of these different parallel outflow routes are still debated, but recent studies in mice suggest that the majority of CSF leaves across the cribriform plate, which is in the vicinity of the nasal sinuses. Our research aims to simulate this efflux pathway to gain insight into the driving mechanisms of efflux and variability in physiological and pathological conditions. We adapt prior lumped numerical modeling to simulate CLVs, which we connect to a network of channels representing MLVs that drain fluid from a variable-pressure compartment representing the subarachnoid space inside the skull. We investigate how the intrinsic pumping (i.e., contractions) of CLVs and oscillations of intracranial pressure affect the net flow. Our preliminary results provide insight into brain metabolic waste removal via CSF efflux and point to mechanisms of disrupted clearance in pathological conditions, increasing the risk of developing neurodegenerative diseases. 

    

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