Session W08: Biological Fluid Dynamics: Physiological Microcirculation (10:00am - 10:45am CST)

Modelling cycling hypoxia by multiple equilibria of non-Newtonian blood flow through vascular networks

The presence of regions of insufficient oxygen, or hypoxia, within tumours can significantly impact patient responses to therapy. Furthermore, experimental results have shown that transient periods of cycling hypoxia can select for more therapy-resistant and invasive tumours. A useful metric for quantifying hypoxia is the haematocrit distribution in the tumour micro-circulation. We model the haematocrit distribution within a vessel network by coupling steady state equations for flow through individual vessels with phenomenological rules for haematocrit splitting at vessel bifurcations. These equations are constructed to guarantee that the volumetric flow of blood and red blood cells are conserved at vessel junctions. We hypothesis that these equations admit multiple solutions and that cycling hypoxia can be generated by stochastic fluctuations between these solutions. To facilitate the identification and enumeration of the model solutions, we propose algebraic approximations to the equations of flow and haematocrit splitting. Under these approximations, the governing equations reduce to an algebraic nonlinear system which can be analyzed using homotopic continuation, guaranteeing that all model solutions are identified. This allows for finding the solutions of larger microvascular networks that are not possible to solve directly.   

Lingering dynamics of microvascular blood flow in vivo

The microcirculation in animals and humans is directly linked to their health state. Any alterations in this blood flow may lead to pathological states, e.g. ischemia. Since typical vessel dimensions in the capillary bed are in the range of individual red blood cells, the particulate nature of blood is well pronounced. Indeed, red blood cells undergo a complex shape transition while flowing through bifurcating and merging vessels. While approaching a bifurcation apex, red blood cells can drastically reduce their velocity, and even rest at this apex. These so-called lingering events are well-known in the field of hemodynamics, however, no systematic studies concerning the effects on the subsequent bloodstream exist. We present an experimental study on living hamsters investigating the lingering events and consequences thereof. Therefore, we perform a joint method of particle tracking and integrated signal evaluation of flowing red blood cells. We show evidence that lingering events lead to a shift of median durations of cell-free areas. Further, lingering events can be linked to the redistribution of consecutive red blood cells in the bifurcating geometry as well as a spatial distancing of red blood cells.   

Quantitative experiments and mutli-scale simulations to study Red Blood Cells transmigration through inter-endothelial slits in the spleen

During their circulation through the spleen, red blood cells (RBCs) are forced to squeeze through gaps between endothelial cells that are \textasciitilde 8 times narrower than its diameter. The ensuing squeezing motion causes large RBC deformations that remove old and diseased cells from the circulation. To study the mechanics of RBC splenic filtration, we designed and characterized a family of microfluidic devices where a suspension of human RBCs flows through an array (N $=$ 50) of channels of controlled length (L), width (W) and height (H). We varied these geometrical parameters (0.75\textless W\textless 3, 4.5\textless H\textless 10 and 1\textless L\textless 5 um) and imaged the time-evolving RBC shape as single cells were passing through each channel. We also investigated this process computationally by coupling a multiscale model of the RBC membrane with a boundary integral formulation of the fluids. We find that RBC deformation and motion are strongly correlated with channel geometry upon arrival to the slit. In wider channels RBCs reorient into the direction of less constrain, cell diameter is parallel to the height of the channel. Whereas in narrower channels, cells fold into themselves (U shape) experimenting large deformations.   

Predicting vascular diameter changes to up-regulate highly unsteady blood flow in the brain vasculature by using an adjoint-based inverse model

The brain is capable of regulating cerebral blood flow in response to local changes in neural activity. However, the precise mechanisms of the underlying vasodynamics are still poorly understood. The goal of our work is to use an inverse model to calculate diameter changes that are required to achieve pre-defined flow distributions in microvascular networks. We solve the inverse problem by minimizing a cost function J, where the sensitivity of J with regard to the diameters is calculated with the adjoint method. The vasculature is represented by a flow network and the impact of red blood cells (RBCs) on flow resistance is considered by tracking the motion of RBCs through the network. Due to the stochastic behaviour of RBCs at bifurcations, the instantaneous flow characteristics are highly unsteady. Therefore, our inverse problem is solved iteratively and the adjoint equation is solved based on time averaged flow rates and pressures. We performed simulations in realistic microvascular networks and computed the diameter changes necessary to increase blood flow in specific regions of the mouse cerebral cortex. Our study revealed that fine scale regulation at the level of capillaries is necessary to achieve very localized changes in flow distributions during functional activation.   

Optimizing the distribution of nutrients with flow networks

Rivers, plants, animals, they are all using flow networks to efficiently transport their nutrients. Animals during the course of evolution developed complex circulatory systems that optimize the transport of oxygen and nutrients. These nutrients are crucial for the survival of the tissue, therefore the supplying performance of the vasculature will dictate the survival or death of the surrounding cells. Can the biological flow networks self-organize and remodel to optimally perfuse the tissue? To answer this question first we demonstrate that minimizing the energy dissipation to circulate the flows is not enough to capture the microvascular structure. The solution we propose is a local adaptation rule for the vessel radii that is able to equalize perfusion, while minimizing energy dissipation and a cost constrain. The competition between these different energy functions allows for rich complex network morphologies combining hierarchy and mesh structure. We support the validity of our model with experimental evidence from the rat mesenteric network.   

Microstrokes and capillary dilations -- investigating the effect of single capillary alterations.

Capillaries are the most frequent vessel type in the brain microvasculature. The dense and interconnected capillary bed has to ensure a robust blood supply across the cortex. Besides its relevance our knowledge of structural and functional properties of the capillary bed remains limited. We perform numerical blood flow simulations in realistic microvascular networks and alter individual capillaries in order to improve our understanding of topology and perfusion of the capillary bed. Capillary dilation has been suggested as a mechanism to up-regulate blood flow and microstrokes have been linked to diseases like dementia and Alzheimer. For both scenarios we analyze changes in blood flow rate and red blood cell (RBC) distribution with a specific focus on the impact of RBCs. This is possible thanks to our numerical model that tracks the motion of 100 thousands of RBCs through the microvasculature. Our results reveal that in response to capillary dilation the changes are strongly affected by the baseline velocity ratio at the upstream bifurcation. Moreover, we show that the severity of a microstroke is governed by the local vascular topology. Taken together, we highlight the relevance of the bi-phasic nature of blood and uncover novel topological characteristics of the capillary bed.   

Influence of Intracranial Pressure on the Cerebral Microcirculation in Pig Models with Hydrocephalus

Hydrocephalus involves abnormal accumulation of cerebral spinal fluid, resulting in elevated intracranial pressure (ICP) that often requires neurosurgical intervention. Delayed diagnosis can lead to ischemia and brain damage. There is a dire need for noninvasive techniques for assessing the ICP and brain health. This study applies contrast-enhanced ultrasound (CEUS) imaging, using a clinical system and contrast agent (Lumason, 1-3$\mu $m bubbles), to visualize the spatial distribution of cerebral microcirculation in brain sections of 5 pig models with varying ICP levels. PTV based on an optimization code involving multiple matching criteria is used for bubble tracking. The vascular maps are generated by super-positioning all the trajectories with more than 4 exposures and measuring the velocity in each vessel. To characterize the distribution of perfusion, we introduce the cerebral microcirculation (CMC) parameter by summing the velocity in all the micro vessels for each part of the brain. Results show that the CMC in the thalamus plateaus until a critical ICP, and then decreases sharply. In contrast, there is a high negative correlation between the ICP and the CMC in the cortex. Hence, the cortical CMC could potentially be used as a non-invasive quantitative indicator for the ICP.