Exploring neurodegenerative disorders using a novel integrated model of cerebral transport: Initial results

Cerebrospinal Fluid Flow

Circulation of cerebrospinal fluid and interstitial fluid around the central nervous system and through the brain transports not only those water-like fluids but also any solutes they carry, including nutrients, drugs, and metabolic wastes. Passing through brain tissue primarily during sleep, this circulation has implications for neurodegenerative disorders including Alzheimer's disease, for tissue damage during stroke and cardiac arrest, and for flow-related disorders such as hydrocephalus and syringomyelia. Recent experimental results reveal several features of this flow, but other aspects are not fully understood, including its driving mechanisms. We review the experimental evidence and theoretical modeling of cerebrospinal fluid flow, including the roles of advection and diffusion in transporting solutes. We discuss both local, detailed fluid-dynamic models of specific components of the system and global hydraulic models of the overall network of flow paths.

The glymphatic system: Current understanding and modeling

We review theoretical and numerical models of the glymphatic system, which circulates cerebrospinal fluid and interstitial fluid around the brain, facilitating solute transport. Models enable hypothesis development and predictions of transport, with clinical applications including drug delivery, stroke, cardiac arrest, and neurodegenerative disorders like Alzheimer's disease. We sort existing models into broad categories by anatomical function: Perivascular flow, transport in brain parenchyma, interfaces to perivascular spaces, efflux routes, and links to neuronal activity. Needs and opportunities for future work are highlighted wherever possible; new models, expanded models, and novel experiments to inform models could all have tremendous value for advancing the field.

Influence of interaction of cerebral fluids on ventricular deformation: A mathematical approach

This paper describes the effects of the interaction of cerebral fluids (arterial, capillary and venous blood, cerebrospinal fluid) on ventricular wall displacement and periventricular pressure using a mathematical multiphase poroelasticity model for the cerebral parenchyma. The interaction of cerebral fluids is given by a set of four numerical coefficients. A multiple linear regression with interaction is constructed that allows us to quantify the effect of these coefficients on the average ventricular wall displacement. The prevailing influence of an arterial-liquor component was observed. The sets of coefficients associated with such pathological conditions were found: normal pressure hydrocephalus, intracranial hypertension, and replacement ventriculomegaly under a prolonged hypoperfusion.

In silico trials for treatment of acute ischemic stroke: Design and implementation

An in silico trial simulates a disease and its corresponding therapies on a cohort of virtual patients to support the development and evaluation of medical devices, drugs, and treatment. In silico trials have the potential to refine, reduce cost, and partially replace current in vivo studies, namely clinical trials and animal testing. We present the design and implementation of an in silico trial for treatment of acute ischemic stroke. We propose an event-based modelling approach for the simulation of a disease and injury, where changes to the state of the system (the events) are assumed to be instantaneous. Using this approach we are able to combine a diverse set of models, spanning multiple time scales, to model acute ischemic stroke, treatment, and resulting brain tissue injury. The in silico trial is designed to be modular to aid development and reproducibility. It provides a comprehensive framework for application to any potential in silico trial. A statistical population model is used to generate cohorts of virtual patients. Patient functional outcomes are also predicted with a statistical model, using treatment and injury results and the patient's clinical parameters. We demonstrate the functionality of the event-based modelling approach and trial framework by running proof of concept in silico trials. The proof of concept trials simulate the same cohort of patients twice: once with successful treatment (successful recanalisation) and once with unsuccessful treatment (unsuccessful treatment). Ways to overcome some of the challenges and difficulties in setting up such an in silico trial are discussed, such as validation and computational limitations.

On the Sensitivity Analysis of Porous Finite Element Models for Cerebral Perfusion Estimation

Computational physiological models are promising tools to enhance the design of clinical trials and to assist in decision making. Organ-scale haemodynamic models are gaining popularity to evaluate perfusion in a virtual environment both in healthy and diseased patients. Recently, the principles of verification, validation, and uncertainty quantification of such physiological models have been laid down to ensure safe applications of engineering software in the medical device industry. The present study sets out to establish guidelines for the usage of a three-dimensional steady state porous cerebral perfusion model of the human brain following principles detailed in the verification and validation (V&V 40) standard of the American Society of Mechanical Engineers. The model relies on the finite element method and has been developed specifically to estimate how brain perfusion is altered in ischaemic stroke patients before, during, and after treatments. Simulations are compared with exact analytical solutions and a thorough sensitivity analysis is presented covering every numerical and physiological model parameter. The results suggest that such porous models can approximate blood pressure and perfusion distributions reliably even on a coarse grid with first order elements. On the other hand, higher order elements are essential to mitigate errors in volumetric blood flow rate estimation through cortical surface regions. Matching the volumetric flow rate corresponding to major cerebral arteries is identified as a validation milestone. It is found that inlet velocity boundary conditions are hard to obtain and that constant pressure inlet boundary conditions are feasible alternatives. A one-dimensional model is presented which can serve as a computationally inexpensive replacement of the three-dimensional brain model to ease parameter optimisation, sensitivity analyses and uncertainty quantification. The findings of the present study can be generalised to organ-scale porous perfusion models. The results increase the applicability of computational tools regarding treatment development for stroke and other cerebrovascular conditions.