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Blood in Motion
Applied mathematician George Karniadakis models
how diseases alter the body’s circulation.
P
recisely describing how blood flows through the smallest vessels is no simple
matter. Fluid dynamics comes into play, but so does particle dynamics at
the level of atoms and molecules. Including every atom and molecule in
a numerical model of blood circulation is not feasible, even using today’s fastest
computers. So applied mathematician George Karniadakis of Brown University and
his colleagues have simplified. They begin on a slightly larger scale—bundling atoms and molecules into groups of 10 or more—and model blood circulation. Their
technique, aided by scientists at Argonne National Laboratory, is producing new insight into the ways that diseases disrupt normal blood flow. Karniadakis spoke with
American Scientist contributing editor Catherine Clabby about the work.
What are a few of the biggest challenges to modeling blood flow
through vessels?
Blood is a really complex fluid with
many yet-unexplored properties. Any
modeling errors greatly affect simulation results. For capillaries and vessels such as arterioles and venules,
which connect capillaries to arteries
and veins, the difficulty is how to scale
up the molecular-based modeling. So
we have developed a multiscale approach to capture the effects of both
the flow and the particle dynamics
and to quantify their interactions. The
geometric complexity of the human arterial tree is another big challenge. For
large arteries, MRI scans can be used
to extract and reconstruct patientspecific arterial geometries, but this is
not possible at the small scale. Finally,
the viscous and elastic properties of
blood cells and arterial walls introduce
big uncertainties.
What is your multiscale technique, and
how could it be medically useful?
We need to span a range of spatial and
temporal scales so that we can numerically portray many components accurately. That includes proteins such as
spectrin, which is part of the cytoskeleton of red blood cells, and fibrinogen,
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which is involved in blood coagulation.
At the same time we need to reach up
to the vessel scale, and we need to model how those two scales influence one
another. There are no standard ways of
doing that. But there have been some
recent advances in coarse-graining molecular dynamics methods: ways to represent systems with less than all-atom
resolution. These methods do a good
job of modeling blood cells, plasma,
proteins, and arterial walls while simplifying the computational complexity. The coarser-grain approach still
requires supercomputers to carry out
realistic simulations, but it makes the
problem more manageable. We have
used these models to explore what
specific changes to blood flow occur in
vessels affected by sickle cell disease,
malaria, and brain aneurysms.
What have your new simulations revealed about how diseases disrupt
blood flow?
One recent example is new insight into
what causes painful episodes in people with sickle cell disease. Healthy
red blood cells are round and flexible, and easily change shape to move
through even the smallest blood vessels. Among people with sickle cell
disease, blood cells can be hard, sticky,
Healthy red
blood cells (orange)
are more adept than malariainfected cells (blue) at squeezing
through tight spaces in a simulated
capillary. Horizontal lines denote
flow patterns; the dots are plasma
particles. (Image courtesy of
Argonne National Laboratory.)
and abnormally shaped. They resemble sickles. The common wisdom has
been that this distorted shape causes
blood cells to get stuck in tiny vessels and block the flow of oxygenated
blood. The blockages lead to severe
pain, tissue damage, and sometimes
fatal organ damage.
With our modeling we could explore how qualities of multiple blood
cells changed by sickle cell disease
affect these blockages. We concluded
that a subset of red blood cells plays
an important role. They do not become
rigid but do become stickier because of
sickle cell disease. Receptors on surfaces of these cells cause them to stick to
capillary walls, narrowing the diameter of some vessels. Sickle-shaped cells
then stack up behind them, creating
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blockages. The two work in tandem,
but the sticky cells start the blockage.
What about infectious diseases—can
they affect blood flow as well?
We have also quantified some of the
biophysical characteristics of blood
cells altered by the parasite that causes
malaria. We have observed that red
blood cells infected by Plasmodium falciparum are as much as 50–100 times
stiffer than healthy ones. With the
loss of elasticity, these cells cannot
pass through capillaries, so they block
them. We also are making progress in
understanding how blood platelets
collect on the surfaces of blood vessels
in the carotid arteries and in the brain
during the development of cerebral
aneurysms, a risk factor for strokes.
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Has it been challenging to create visualizations that capture the complexity
of this research?
There are no existing tools for the kind
of multiscale visualizations needed to
capture simultaneously details of protein dynamics and also cell or vessel
dynamics. Joseph Insley, primary software development specialist, and Michael Papka, director of the Argonne
Leadership Computing Facility, our
collaborators at Argonne National
Laboratory, are pioneering multiscale
visualizations. Their work helps us
observe interactions between protein,
cell, and vessel dynamics that we cannot extract using standard software.
Such visualizations have helped us
devise new numerical methods to capture variation in blood flow.
What are your wider goals for this
kind of biological modeling?
Our goal is twofold. We want to fully
understand, at the molecular and arterial level, all the biophysical aspects of
blood flow that are affected by the diseases we currently study. And we want
to develop a general computational
framework that, together with laboratory microfluidic measurements, can be
used to better understand effects from
other diseases. Those effects include
microcirculation changes associated
with the human immunodeficiency
virus (HIV), diabetes, and even metastatic cancer. Our ultimate objective is
to develop a patient-specific, multiscale
computational framework that will aid
researchers and clinicians in the prognosis of hematologic disorders.
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Clockwise from above: Malaria-infected red
blood cells tumble in turbulent flow; blood
platelets aggregate on the wall of an aneurysm;
and sickle cells clump together, blocking proper
circulation, in these modeled images. (Images
courtesy of Argonne National Laboratory.)
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