




Biofluid Dynamics & Medical Science / Dynamique des
biofluides et sciences médicales (Siv Sivaloganathan, Organizer)
 JAMES DRAKE, University of Toronto, Hospital for Sick Children, 555 University
Avenue, Toronto, Ontario M5G 1X8
Requirement for new mathematical models of the brain for hydrocephalus
treatment

Hydrocephalus is a common condition in which spinal fluid (essentially
water) builds up inside the brain, compressing the brain tissue and
producing neurological dysfunction. Hydrocephalus is usually treated
with an indwelling valved tube called a shunt. Most shunts over drain
the brain, leading to collapse of the fluid cavities. The average
patient develops a shunt complication within 2 years, often related to
collapse of the fluid cavities (brain ventricles) around the shunt
drainage holes. Patients often endure many repeat surgeries for
complications.
A number of mathematical models of the brain and shunt systems have
been developed to reduce shunt complication rates. Shunt valves with
more sophisticated fluid flow characteristics, based on simplified
pressurevolume models of the brain, have been developed to reduce this
over draining tendency. Unfortunately they have had no effect on the
size of the ventricles, or the complication rate. Neurosurgeons would
prefer to place the shunt in what will ultimately be a slightly dilated
portion of the ventricle but currently have no strategy for doing so.
More sophisticated models of the brain, which span a longer time frame,
and address the shape changes in the hydrocephalic brain, are needed to
develop improved shunt designs, and placement strategies.
 CORINA DRAPACA, Waterloo
Transient ventricular wall dynamics in shunted hydrocephalus

Hydrocephalus is still an endemic condition in the pediatric population
with a prevalence of 11.5%. Within limits, the dilatation of the
ventricles can be reversed by shunting procedures. Unfortunately, the
rate of shunt failure is unacceptably high and an important risk factor
in this regard is the positioning of the catheter's tip. Finding an
optimal solution to this problem requires the creation of a good
mathematical model capable of predicting the evolution of the
ventricular walls configuration in shunted hydrocephalus. In this
paper we report on some progress recently made in the mathematical
description of the shorttime ventricular wall dynamics in a simplified
(cylindrical) geometry. In particular, we shall focus on the free
boundary value problem resulting from an application of the theory of
consolidation in porous media.
 TONY HEENAN, Department of Mechanical Engineering, Queen's University,
Kingston, Ontario K7L 3N6
Visualization of the flow through the human oropharynx

The overall structure and dynamics of breathing flow through the human
oropharynx (OP) is poorly understood. This is due to a lack of good
quality data on the flow regimes. The complex and variable geometry of
the OP makes traditional pointbased measurements impractical, while
the combination of complex geometry and sufficiently high Reynolds
number makes accurate numerical simulation expensive.
This paper presents preliminary, qualitative results from an
experimental, fieldmeasurement (PIV) based study of OP fluid
dynamics. A series of highspeed digital video recordings were made of
the flow in an idealized model of the OP, and these are presented. The
flow was marked using the smokewire technique, and illuminated with an
Argon Ion laser. Visualizations for constant flow rates of 30L/min and
90L/min are presented. The features and behaviour revealed in the
recordings are discussed.
(joint work with A. Pollard and W. Finlay)
 E. KRAUSE, Aerodynamisches Institut, Wuellnerstr., 52062 Aachen, Germany
Flowmodeling for the human circulatory system

The blood flow in the human circulatory system is modeled with
simplified fluid mechanical relations. The system is decomposed into
four active elements, which are used to simulate the filling and the
emptying of the left and right atrium and ventricle. The contraction and
relaxation of the heart muscle is described with Hill's model extended
to the right ventricle. The opening and closing of the four heart valves
are simulated with timedependent resistance coefficients, approaching
infinity when the valves close. Each of the other eleven passive
elements is assumed to consist out of a reservoir with elastic walls and
a rigid tube with variable crosssection, connecting the element to its
neighbor. The simplified momentum and continuity equation are used to
describe the timedependent onedimensional flow in the elements, with
the viscous forces represented by resistance coefficients. The model
results in 32 nonlinear ordinary differential equations of first order,
which are solved with the RungeKutta method. Blood pressures and
volumes in the atria, the ventricles and in the aorta, simulated so far,
agree well with measured physiological data. Longtime simulations were
carried out, also for physiologically high and varying heart rates, as
well as for pathological changes, as for example valvular abnormalities.
 KATRIN ROHLF, Department of Applied Mathematics, University of Waterloo, Waterloo
Ontario N2L 3G1
Stochastic theory of blood flow in small vessels

It is wellknown that blood is a suspension of cells in plasma. Since
the red blood cells (RBCs for short) are the largest of these, and by
far the most in number, they are believed to be the main contributors
to the many peculiarities of flowing blood.
One of the key attributes of RBCs is that in the absence of shear, they
begin to stick togethera process called aggregationand form
chainlike aggregates called rouleaux. In fact, if the shear rates are
not too large, aggregation still occurs even in flowing blood. Thus,
if one is interested in a detailed mathematical description of blood
flow in small vessels (e.g. arterioles and large capillaries where the
shear forces are known to be small), one cannot ignore the effects of
the aggregates, which in general, surface through nonNewtonian
properties of the fluid.
In this talk, a stochastic description of an aggregation process will
be presented. Multiparticle collisions will be taken into account, as
well as the formation and breakup of the aggregates, which occur if
shear forces are taken into account. The results will be discussed
with specific application to RBC aggregation and their resulting
connection to the macroscopic nonNewtonian flow properties of blood.
 MAREK STASTNA, University of Waterloo, Waterloo, Ontario N2L 3G1
Some Problems in the application of consolidation theory to
hydrocephalus

This talk will outline several problems in the application of
consolidation theory to the clinical condition of hydrocephalus. One
set of problems relates to the fact that the equations of consolidation
theory have several odd properties from a computational standpoint.
Another relates to the phenomenological nature of the applications of
consolidation theory in brain biomechanics (as well as other fields in
which nonintrusive experimental data is difficult to obtain). This
second set of problems relates to issues such as space dependent
material parameters, deformation dependent permeability, and free
boundaries. The talk will contain a mixture of analytic and numerical
work. All material will be presented at an elementary level.
 JOHN STOCKIE, Simon Fraser University, Burnaby, British Columbia V5A 1S6
Simulating flexible fibres immersed in fluid

The motion of flexible, elastic fibres immersed in a surrounding fluid
arises in many applications, including polymer
composite materials, swimming microorganisms, and wood pulp processing.
We develop a model of a single fibre using the ``immersed boundary''
framework, which has proven effective in modeling elastic boundaries
such as the heart wall. The primary advantage in using the immersed
boundary method is its ability capture the complex, hydrodynamic
interaction between fibre and fluid that is typically neglected in other
models of fibre motion. We perform a series of 2D and 3D numerical
simulations of a single fibre subjected to planar shear, and draw
comparisons with experimental observations. Our results reproduce the
observed orbital motions of actual fibres, and exhibit behaviour not
captured by other models.

