Session M17: Biological fluid dynamics: Brains and Spines

Mathematical Modeling of Nanoparticle Transport across Blood-Brain Barrier (BBB)

Drug delivery to brain is a major challenge for the treatment of neurodegenerative disorders due to the presence of BBB, a highly selective barricade formed by microvascular endothelial cells. In recent years, different types of nanoparticles have been tested as potential drug carriers through BBB with varying degrees of success. In this study, we have developed a theoretical model to quantify the transport of nanoparticles through BBB endothelial cells based on mass action laws, where an artificial neural network (ANN) model is used to estimate the kinetic rate parameters from experimental data. Experimental data are obtained from a transwell (in-vitro) BBB model constructed with mouse endothelial cells. Results of mass action model with estimated parameters show that it can successfully predict the transient behavior of nanoparticle transport across BBB. Model results also indicate that the endocytosis of nanoparticles through apical membrane is much faster process than the exocytosis of nanoparticles via basolateral membrane. The results of this study can help in designing new drug carriers for effective and noninvasive cure of brain diseases.   

Platelet simulations to enhance computational fluid modeling of intracranial aneurysm coil embolization

Intracranial aneurysms can rupture causing a devastating hemorrhagic stroke. An increasingly preferable treatment to prevent rupture is minimally-invasive endovascular coil embolization, which utilizes metallic coils to fill the aneurysm dome, occlude blood flow inside the dome, and promote the formation of a stable thrombus.  Eulerian computational fluid dynamics has allowed for greater understanding of aneurysm hemodynamics, but these methods don’t fully characterize the platelet microenvironment and platelet activation that is critical for progressive thrombosis and subsequent aneurysm healing. Platelet activation is known to be associated with shear stress and particularly with platelet accumulation in areas of prolonged residence time. We apply novel Langrangian computational modeling to patient-specific aneurysmal vasculature before and after treatment with embolic coils to characterize both hemodynamic and platelet microenvironment variables, resulting in significantly more accurate prediction of treatment outcomes. Establishing clinically-useful metrics to quantify the increased proportion of platelets having a thrombogenic residence time will inform future treatment approaches, thus mitigating the risk of hemorrhagic stroke.    

In vivo measurements reveal cerebrospinal fluid flow reduction in hypertension

High blood pressure promotes deposition of amyloid-β and is a known risk factor for Alzheimer’s disease. The mechanisms underlying this interaction are not well understood. Removal of amyloid-β from the brain’s interstitial fluid is facilitated by the flow of cerebrospinal fluid (CSF) through perivascular spaces (PVSs) which surround the cerebral vasculature. However, limitations in imaging techniques have impeded the measurement of such flows. Recently, our interdisciplinary collaboration has developed a novel in vivo imaging approach combining two photon microscopy and particle tracking velocimetry which has enabled the first ever quantitative measurements of CSF flow in the PVSs of mouse brains. Our measurements support the hypothesis that such flows are driven primarily by motion of the adjacent arterial wall, a peristalsis-like effect previously referred to as perivascular pumping. By increasing blood pressure, we alter the dynamics of the arterial wall motion and observe a concurrent decrease in the net CSF flow speed. Our results offer a potential causal mechanism by which hypertension reduces perivascular pumping of CSF leading to increased risk for neurodegenerative disorders, including Alzheimer's disease.   

Flow and transport in the spinal canal. Part 1: Eulerian velocity field

We have investigated the flow of cerebrospinal fluid in the subarachnoid space of the spinal canal. A major feature of spinal fluid flow is its oscillation, which is driven mainly by the intracranial pressure fluctuations that occur with each heart beat, resulting in an oscillatory velocity component with angular frequency ω, equal to that of the cardiac cycle. Because of the limited compliance of the subarachnoid space, the tidal volume is a a small fraction ε « 1 of the total CSF volume in the spinal canal. An asymptotic analysis in the limit ε « 1 accounting for the slenderness of the flow is employed to describe the Eulerian velocity field. The oscillatory motion is seen to be determined in the first approximation by a linear unsteady lubrication problem, which can be solved to give a closed-form solution, with the nonlinear terms associated with the convective acceleration and the deformation of the canal producing a small velocity correction with a steady-streaming component. The resulting magnitude of this steady velocity is a factor ε smaller than that of the pulsating flow, yielding associated residence times of order ε^-2  ω^-1 »  ω^-1, consistent with previous experimental observations of the bulk flow in the spinal canal.   

Flow and transport in the spinal canal. Part 3: Effects of canal geometry and dura-membrane compliance

A reduced transport description is used to investigate the dispersion rate of a drug carried by the cerebrospinal fluid, with attention given to effects of the spinal canal geometry and variations of compliance of the outer dura membrane. First, a simplified geometric model is used to show that tapering, i.e. a gradual narrowing of the cross-sectional area of the subarachnoid space (SAS) from top to bottom, as well as an increasing canal compliance towards the lumbar end, enhance the upward transport rate of a drug injected in the lumbar region. Next, a realistic spinal canal geometry based on MRI measurements (taken from Sass et al., Fluids Barriers CNS, 2017) is employed to show the detailed drug transport in the SAS. Additionally, our work addresses effects associated with micro-anatomical features. The presence of nerve roots protruding from the spinal cord is investigated by considering the oscillatory motion around a cylindrical post confined between two parallel plates. For large values of the relevant Strouhal number we find at leading order a harmonic Stokes flow, whereas steady-streaming effects enter in the first-order corrections, which are computed for realistic values of the Womersley number and of the cylinder height-to-radius ratio.