Friday
October
25,
2013
9:30
-
10:30
am,
E5
6111
"Heart
Wall
Myofibers
are
Arranged
in
Minimal
Surfaces"
Dr.
Kaleem
Siddiqi
Professor
and
William
Dawson
Scholar
in
the
School
of
Computer
Science
McGill
University
Abstract:
Heart
wall
myofibers
wind
as
helices
around
the
ventricles,
strengthening
them
in
a
manner
analogous
to
the
reinforcement
of
concrete
cylindrical
columns
by
spiral
steel
cables.
A
multitude
of
such
fibers,
arranged
smoothly
and
regularly,
contract
and
relax
as
an
integrated
functional
unit
as
the
heart
beats.
To
orchestrate
this,
fiber
tangling
must
be
avoided
while
pumping
should
be
efficient.
Current
models
of
myofiber
orientation
across
the
heart
wall
suggest
groupings
into
sheets
or
bands,
but
the
precise
geometry
of
bundles
of
myofibers
is
unknown.
Here
we
show
that
this
arrangement
takes
the
form
of
a
special
minimal
surface,
the
generalized
helicoid,
closing
the
gap
between
individual
myofibers
and
their
collective
wall
structure.
The
model
holds
across
species,
with
a
smooth
variation
in
its
three
curvature
parameters
within
the
myocardial
wall
providing
tight
fits
to
diffusion
magnetic
resonance
images
from
the
rat,
the
dog
and
the
human.
Mathematically
it
explains
how
myofibers
are
bundled
in
the
heart
wall
while
economizing
fiber
length
and
optimizing
ventricular
ejection
volume
as
they
contract.
The
generalized
helicoid
provides
a
novel
foundation
for
analyzing
the
fibrous
composite
of
the
heart
wall
and
should
therefore
find
applications
in
heart
tissue
engineering
and
in
the
study
of
heart
muscle
diseases.
Please
contact
David
Clausi
if
you
are
interested
in
meeting
with
Dr.
Siddiqi.