Mathematical model of the cerebral circulation and distribution of cerebrospinal fluid
File(s)
Author(s)
Sanchez Cazares, Karla Elena
Type
Thesis
Abstract
Shifts in cerebral fluid are known to be important in a number of diseases, and in conditions of
microgravity such as space travel. In this work we develop a fluid mechanical model from firstprinciples
incorporating key features of the flow of both blood and cerebrospinal fluid (CSF) in
the intracranial and spinal spaces.
For the cerebral blood vessels, we model the arteries and veins as symmetric bifurcating trees
with constant geometrical scaling factors between generations, assume one-dimensional flow
in each vessel and account for elastic effects via a pressure-area relationship, and we assume
the capillaries have a constant resistance. We treat the vessel walls as porous media to find
the transmural flux of plasma. We assume flow between the other compartments to be proportional
to the pressure difference; additionally, the flow to the outer-dural space is assumed to be
one-way. The set of ordinary differential equations for the evolution of the fluid pressures and
volumes of each compartment can be solved numerically. Additional features include autoregulation,
which we model by ensuring constant pressure at the microcirculation, meaning the
resulting model must be solved iteratively. Also, we can model the effect of postural changes
by including hydrostatic effects in the spinal column.
The results are in accordance with physiological measurements and indicate that the pressure
in the vasculature is highly sensitive to changes in vessel geometry, which also affects the transmural
flux, whilst ventricular and spinal subarachnoid spaces are sensitive to compliances. We
investigate transitions from supine to standing and upside down positions and also the effect
of the external pressure surrounding the outer-dural spinal compartment. The model is computationally
inexpensive and can be used as a platform for further analysis of cerebrovascular
behaviour.
microgravity such as space travel. In this work we develop a fluid mechanical model from firstprinciples
incorporating key features of the flow of both blood and cerebrospinal fluid (CSF) in
the intracranial and spinal spaces.
For the cerebral blood vessels, we model the arteries and veins as symmetric bifurcating trees
with constant geometrical scaling factors between generations, assume one-dimensional flow
in each vessel and account for elastic effects via a pressure-area relationship, and we assume
the capillaries have a constant resistance. We treat the vessel walls as porous media to find
the transmural flux of plasma. We assume flow between the other compartments to be proportional
to the pressure difference; additionally, the flow to the outer-dural space is assumed to be
one-way. The set of ordinary differential equations for the evolution of the fluid pressures and
volumes of each compartment can be solved numerically. Additional features include autoregulation,
which we model by ensuring constant pressure at the microcirculation, meaning the
resulting model must be solved iteratively. Also, we can model the effect of postural changes
by including hydrostatic effects in the spinal column.
The results are in accordance with physiological measurements and indicate that the pressure
in the vasculature is highly sensitive to changes in vessel geometry, which also affects the transmural
flux, whilst ventricular and spinal subarachnoid spaces are sensitive to compliances. We
investigate transitions from supine to standing and upside down positions and also the effect
of the external pressure surrounding the outer-dural spinal compartment. The model is computationally
inexpensive and can be used as a platform for further analysis of cerebrovascular
behaviour.
Version
Open Access
Date Issued
2018-11
Date Awarded
2019-03
Copyright Statement
Creative Commons Attribution NonCommercial Licence
License URL
Advisor
Tweedy, Jennifer H
Parker, Kim H
Publisher Department
Bioengineering
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)