Alexandra K. Diem

This package implements the 1D blood flow equations (Olufsen et al., 2000) using the finite element framework FEniCS (Alnaes et al., 2015). The package provides tools for modelling blood flow through a network of arteries by solving a 1D approximation of the cross-sectional area and flow rate of each artery.

The mechanisms behind the clearance of soluble waste from deep within the parenchyma of the brain remain unclear. Experimental evidence reveals that one pathway for clearance of waste, termed intra-mural peri-arterial drainage (IPAD), is the rapid drainage of interstitial fluid along basement membranes (BM) of the smooth muscle cells of cerebral arteries; failure of IPAD is closely associated with the pathology of Alzheimer’s disease (AD), but its driving mechanism remains unclear. We have previously shown that arterial pulsations generated by the heart beat are not strong enough to drive IPAD. Here we present computational evidence for a mechanism for clearance of waste from the brain that is driven by functional hyperaemia, that is, the dilatation of cerebral arterioles as a consequence of increased nutrient demand from neurons. This mechanism is based on our model for the flow of fluid through the vascular BM. It accounts for clearance rates observed in mouse experiments, and aligns with pathological observations and recommendations to lower the individual risk of AD, such as mental and physical activity. Thus, our neurovascular hypothesis should act as the new working hypothesis for the driving force behind IPAD.

Computer science offers a large set of tools for prototyping, writing, running, testing, validating, sharing and reproducing results, however computational science lags behind. In the best case, authors may provide their source code as a compressed archive and they may feel confident their research is reproducible. But this is not exactly true. James Buckheit and David Donoho proposed more than two decades ago that an article about computational results is advertising, not scholarship. The actual scholarship is the full software environment, code, and data that produced the result. This implies new workflows, in particular in peer-reviews. Existing journals have been slow to adapt: source codes are rarely requested, hardly ever actually executed to check that they produce the results advertised in the article. ReScience is a peer-reviewed journal that targets computational research and encourages the explicit replication of already published research, promoting new and open-source implementations in order to ensure that the original research can be replicated from its description. To achieve this goal, the whole publishing chain is radically different from other traditional scientific journals. ReScience resides on GitHub where each new implementation of a computational study is made available together with comments, explanations, and software tests.

The mechanisms behind waste clearance from deep within the parenchyma of the brain remain unclear to this date. Experimental evidence has shown that one pathway for waste clearance, termed intramural periarterial drainage (IPAD), is the rapid drainage of interstitial fluid (ISF) via basement membranes (BM) of the smooth muscle cells (SMC) of cerebral arteries and its failure is closely associated with the pathology of Alzheimer's disease (AD). We have previously shown that arterial pulsations from the heart beat are not strong enough to drive waste clearance. Here we demonstrate computational evidence for a mechanism for cerebral waste clearance that is driven by functional hyperaemia, that is, the dilation of cerebral arteries as a consequence of increased neuronal demand. This mechanism is based on our model for fluid flow through the vascular basement membrane. It accounts for waste clearance rates observed in mouse experiments and aligns with pathological observations as well as recommendations to lower the individual risk of AD, such as keeping mentally and physically active.

Alzheimer's Disease (AD) is the most common form of dementia and to date there is no cure or efficient prophylaxis. The cognitive decline correlates with the accumulation of amyloid-β (Aβ) in the walls of capillaries and arteries. Our group has demonstrated that interstitial fluid and Aβ are eliminated from the brain along the basement membranes of capillaries and arteries, the intramural periarterial drainage (IPAD) pathway. With advancing age and arteriosclerosis, the stiffness of arterial walls, this pathway fails in its function and Aβ accumulates in the walls of arteries. In this study we tested the hypothesis that arterial pulsations drive IPAD and that a valve mechanism ensures the net drainage in a direction opposite to that of the blood flow. This hypothesis was tested using a mathematical model of the drainage mechanism. We demonstrate firstly that arterial pulsations are not strong enough to produce drainage velocities comparable to experimental observations. Secondly, we demonstrate that a valve mechanism such as directional permeability of the IPAD pathway is necessary to achieve a net reverse flow. The mathematical simulation results are confirmed by assessing the pattern of IPAD in mice using pulse modulators, showing no significant alteration of IPAD. Our results indicate that forces other than the cardiac pulsations are responsible for efficient IPAD.

Finite-differences methods such as the Lax-Wendroff method (LW) are commonly used to solve 1D models of blood flow. These models solve for blood flow and lumen area and are useful in disease research, such as hypertension and atherosclerosis, where flow and pressure are good indicators for the presence of disease. Despite the popularity of the LW method to solve the blood flow equations, no implementation of a LW solver for these equations has been published and made publicly available. This leads to the reimplementation of the same methods within different research groups and makes verification of results more difficult. The Vascular Modelling in Python (VaMpy) toolkit is a Python package that aims to fill this gap. It implements Richtmyer’s two-step Lax-Wendroff scheme to solve 1D model equations of blood flow in arterial trees and aims at facilitating the solution of blood flow problems for various medical applications. Funding statement: The development of this software was supported by an EPSRC Doctoral Training Centre grant (EP/G03690X/1)

The accumulation of soluble and insoluble amyloid-beta (A-beta) in the brain indicates failure of elimination of A-beta from the brain with age and Alzheimer's disease. There is a variety of mechanisms for elimination of A-beta from the brain. They include the action of microglia and enzymes together with receptor-mediated absorption of A-beta into the blood and periarterial lymphatic drainage of A-beta. Although the brain possesses no conventional lymphatics, experimental studies have shown that fluid and solutes, such as A-beta, are eliminated from the brain along 100 nm wide basement membranes in the walls of cerebral capillaries and arteries. This lymphatic drainage pathway is reflected in the deposition of A-beta in the walls of human arteries with age and Alzheimer's disease as cerebral amyloid angiopathy (CAA). Initially, A-beta diffuses through the extracellular spaces of grey matter in the brain and then enters basement membranes in capillaries and arteries to flow out of the brain. Although diffusion through the extracellular spaces of the brain has been well characterised, the exact mechanism whereby perivascular elimination of A-beta occurs has not been resolved. Here we use a computational model to describe the process of periarterial drainage in the context of diffusion in the brain, demonstrating that periarterial drainage along basement membranes is very rapid compared with diffusion. Our results are a validation of experimental data and are significant in the context of failure of periarterial drainage as a mechanism underlying the pathogenesis of AD as well as complications associated with its immunotherapy.

Alzheimer’s disease is characterized by accumulation of amyloid-β (Aβ) in the brain and in the walls of cerebral arteries. The focus of this work is on clearance of Aβ along artery walls, the failure of which may explain the accumulation of Aβ in Alzheimer’s disease. Periarterial basement membranes form continuous channels from cerebral capillaries to major arteries on the surface of the brain. Arterial pressure pulses drive peristaltic flow in the basement membranes in the same direction as blood flow. Here we forward the hypothesis that flexible structures within the basement membrane, if oriented such they present greater resistance to forward than retrograde flow, may cause net reverse flow, advecting Aβ along with it. A solution was obtained for peristaltic flow with low Reynolds number, long wavelength compared to channel height and small channel height compared to vessel radius in a Darcy–Brinkman medium representing a square array of cylinders. Results show that retrograde flow is promoted by high cylinder volume fraction and low peristaltic amplitude. A decrease in cylinder concentration and/or an increase in amplitude, both of which may occur during ageing, can reduce retrograde flow or even cause a transition from retrograde to forward flow. Such changes may explain the accumulation of Aβ in the brain and in artery walls in Alzheimer’s disease.