Cerebral autoregulation (CA) is integral to the delicate process of maintaining stable cerebral perfusion and brain tissue oxygenation against changes in arterial blood pressure. The last four decades has seen dramatic advances in understanding CA physiology, and the role that CA might play in the causation and progression of disease processes that affect the cerebral circulation such as stroke. However, the translation of these basic scientific advances into clinical practice has been limited by the maintenance of old constructs and because there are persistent gaps in our understanding of how this vital vascular mechanism should be quantified. In this review, we re-evaluate relevant studies that challenge established paradigms about how the cerebral perfusion pressure and blood flow are related. In the context of blood pressure being a major haemodynamic challenge to the cerebral circulation, we conclude that: (1) the physiological properties of CA remain inconclusive, (2) many extant methods for CA characterisation are based on simplistic assumptions that can give rise to misleading interpretations, and (3) robust evaluation of CA requires thorough consideration not only of active vasomotor function, but also the unique properties of the intracranial environment.

Blood-mediated nanoparticle delivery is a new and growing field in the development of therapeutics and diagnostics. Nanoparticle properties such as size, shape and surface chemistry can be controlled to improve their performance in biological systems. This enables modulation of immune system interactions, blood clearance profile and interaction with target cells, thereby aiding effective delivery of cargo within cells or tissues. Their ability to target and enter tissues from the blood is highly dependent on their behaviour under blood flow. Here we have produced an agent-based model of nanoparticle behaviour under blood flow in capillaries. We demonstrate that red blood cells are highly important for effective nanoparticle distribution within capillaries. Furthermore, we use this model to demonstrate how nanoparticle size can selectively target tumour tissue over normal tissue. We demonstrate that the polydispersity of nanoparticle populations is an important consideration in achieving optimal specificity and to avoid off-target effects. In future this model could be used for informing new nanoparticle design and to predict general and specific uptake properties under blood flow.


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The blood circulatory system is a dense network of blood vessels that acts to carry vital nutrients and signals to the tissues of the body, whilst simultaneously removing waste products. The circulatory system is involved in the exchange of gases, ions, macromolecules and even cells between the blood and tissue. The ability of the blood to distribute variable payloads to tissues is highly relevant to drug delivery1. Recent work has focused on utilising nanoparticle-based drug-carrier systems to aid retention and specific delivery of a multitude of potential therapeutics to hard-to-access tissues, such as tumours and the central nervous system (CNS). Nanoparticles is the general term for a diverse group of nanoscale particles designed and modified to improve desirable properties such as immune system evasion, tissue penetration, cellular uptake, cellular trafficking and cargo-delivery2,3. Their composition can vary greatly, giving different surface chemistries, shapes and sizes. A number of approaches have been taken to better understand how such properties of nanoparticles affect their applicability as a drug-delivery system. These include classic biological studies using in vitro and in vivo systems as well as in silico approaches4,5,6.

The use of in silico methodology has opened new avenues in the field of drug discovery and development, including in the design of novel chemical inhibitors by protein structural analysis7,8, drug library screening using quantitative structure-activity relationship (QSAR) methods9,10 and multi-scale modelling11. Computational fluid dynamics (CFD) is a well known in silico approach used throughout the fields of engineering, physics and increasingly biology. It aims to use computational methods to resolve the Navier-Stokes equations governing fluid flow, under set conditions and geometry. The Navier-Stokes equations refer to three coupled partial differential equations (PDEs) with the vector equation for the conservation of momentum being

Blood, as a fluid, has several properties that must be considered when utilising CFD methods for modelling. Most of these properties are a consequence of the high density of cells and cell fragments within the blood including red blood cells, white blood cells and platelets. Red blood cells (RBCs) are the most numerate blood cell, constituting 38-46% of the volume of blood, a measure referred to as the haematocrit. White blood cells and platelets constitute about 1% and

Agent-based modelling has previously proven to be a powerful tool for predictive biological modelling. Its integration with more classic CFD approaches allows great potential for testing the blood flow dependent behaviour of nanoparticles. Blood flow dynamics in capillaries are integral for distribution and subsequent uptake of blood-borne molecules. We aimed to create a simple core model that simulates blood flow with the intention of studying a variety of other processes, including but not limited to, nanoparticle distribution studies, receptor binding dynamics, the effect of ligand density and cellular trafficking, plus the effect of varying flow conditions on all of the aforementioned. A summary of this is provided in the schematic in Supplementary Figure 2.

In the microvasculature, where blood cell and capillary diameter are comparable, blood cells severely influence the fluid dynamics of blood flow. Whilst white blood cells and platelets are present in the microvasculture, the reduced number of both cells compared to red blood cells and the small size of platelets limits the influence of these cells. Therefore, we concentrate on red blood cells as the major driver of fluid dynamical changes in the microvasculature. Whilst inclusion of RBCs is important to flow modelling, direct modelling of red blood cell behaviours, such as deformation and aggregation, has been largely omitted. Previous studies have utilised several techniques, most notably immersed finite element methods, to incorporate red blood cell deformation and red blood cell interactions within flow models21,22,23. Although a similar approach could be utilised within the model described, the additional computational burden required would limit the capabilities of the model to include much of the desired additional functionality. In these theoretical studies and experimental observations, a number of red blood cell conformations have been described, including, the slipper-like, the parachute, bullet-like and disk conformations. A number of these papers also produced phase-diagrams relating the conformation to other properties of the flow, such as shear rate, confinement and flow velocity22,23. The slipper phase, according to the work of Fedosov and colleagues22,23, occurs when both shear rates and confinement are low, however the shear rates and confinement parameters of our simulations favour the parachute conformation23.

Several studies have demonstrated that both specific and non-specific interaction with proteins can affect the nanoparticle residency in the blood24,25. Protein interactions are dictated by the surface chemistry and charge. A common solution to this is to use a coating that limits protein adsorption such as polyethylene glycol (PEG) or similar26. This generally improves the systemic half-life and reduces immune cell interaction properties, thus increasing the potential therapeutic load at target tissues27,28. Therefore, in our simulations we can assume that such nanoparticles will be inert. In previous studies, it has been demonstrated that certain compositions of nanoparticles can interact with both themselves and red blood cells, with varying effects on distribution and cellular interactions29. However, these properties are likely to be individual to the nanoparticle formulation used and therefore have been omitted from our model, except for a simple rule that neither can occupy the same space. However, specific interactions are easily implementable within the model at a later stage if appropriate. A diagrammatic summary of the model built is provided in Fig. 1.

The model focuses on a single capillary (ii) taken from the capillary bed (i). The model includes the effect of laminar flow (A) on red blood cells in their native biconcave disk shape (B) causing the deformation of red blood cells into a parachute conformation (C). This subsequently affects distribution and fluid dynamics of particles in the fluid-phase of the blood, which will in turn affect interactions at the vessel wall (D). At the interface of blood and vessel wall (iii), particles proximal to the vessel wall can pass through cellular junctions between cells or fenestrations within cells and therefore freely exchange with the interstitial fluid according to the diffusion gradient (E). Particles may bind corresponding proximal receptors on the endothelial cells (F) they may then be released or internalised and subjected to various cellular trafficking systems (G).

Longitudinal cross-section (A) demonstrating velocity of blood flow along the vessel, with subsequent latitudinal cross-sections proximal to the red blood (B) cell and distal to the red blood cell (C).

In conclusion we have successfully implemented an agent-based model of nanoparticle behaviour under physiological blood flow. This model has been designed to allow the facile inclusion of cellular interactions and trafficking. This model has given us insight into the integral role of RBCs in the distribution of nanoparticles to the vessel walls. We have used this model to demonstrate that both size and polydispersity of nanoparticles must be considered together when targeting tumour tissue using the EPR effect. We predict that in future this model will be used to aid nanoparticle design to further improve tumour delivery and specific delivery to other clinically important tissues such as the CNS. 2351a5e196

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