March/April 2021 19Fractals
are found
throughout the
natural world—
from ammonite
fossils to
snowflakes.
Specifically,
Leonardo da
Vinci studied the
fractal nature
of trees, noting
“all the branches
of a tree at
every stage of
its height whenput together
are equal in
thickness to
the trunk.”
This growth
pattern, in which
the size and
thickness of a
tree’s branches
correlate to
the size and
thickness of
its trunk, has
become known
as Leonardo’s
“rule” of trees.A 2011 paper
published by
scientists at
Aix-Marseille
University
in France
investigated
Leonardo’s rule
and found that
many trees
grow this way in
order to avoid
the damaging
effects of
violent wind-
storms.procedures in order to make their data available
to researchers around the world.
The study of trabeculae might date back
centuries, and scientists have looked at the
recurring, weblike, and unusual pattern of mus-
cle fibers for almost 450 years. But that hasn’t
been enough to understand why the muscle is
there, what it’s doing, or how it develops.
“You can see these structures on all scans
of the heart and take for granted what they’re
for,” O’Regan says. “We needed machine learn-
ing to take the data and analyze it, coupled with
access to really large populations that have imag-
ing as well as genetic information.” Through this
recent research, the team was able to identify
common features across different patient imag-
ery, cross-check that with patient records, and
begin to draw conclusions about the biological
purpose behind structural trabeculae.
Before this study, the trabeculae were pri-
marily considered in an embryonic context. “We
knew they were important in developing hearts,
but their role in adults hadn’t been recognized at
all,” O’Regan says. “Our research suggests that
they have an important effect on the performance
of the heart by improving how much blood can be
pumped during each heartbeat.”
O’Regan and his team discovered that people
whose hearts had a smoother inner surface—
meaning they had fewer trabecular fibers—were
at greater risk of heart failure. That could mean
the heart pumps blood less efficiently in these peo-
ple, he says. They also found that having too many
muscle fibers could actually slow blood f low in
the heart and increase the likelihood that a per-
son will develop blood clots. In future research,
the team plans to develop computer simulations
to explore how f luids like blood may interact with
deformable surfaces like trabeculae.
The team used mathematics and comput-
ing power to study how trabeculae develop their
characteristic lace-like structure. “We used this
principle called fractal analysis [on] this pattern
of muscles in the heart and began to understand
how that muscle develops at a molecular scale,”
O’Regan says. “Leonardo was really interested
in fractals as well—he was interested in branch-
ing patterns of trees and came up with the rule
that determined how they branch, bringing those
two domains together.”
Fractal analysis appears in everything from
mapmaking to telecoms. Every time you zoom in
on Google Maps, a major “trunk” branches into
smaller and smaller areas. And covering Earth
with high-speed internet involves branching from
telecommunication lines—thick “trunks” that
cross the continent—to regional and local net-
works that reach into your home. In the case of the
heart, the trabeculae likewise branch into smaller
and smaller threads.
By studying the human genome as well as the
trabeculae of their subjects, O’Regan began to
pinpoint genes that affect how trabeculae form
and function. These discoveries could have impli-
cations for how other body cells form and behave,
including nerves and the brain. “There might be a
really important mechanism in nature that deter-
mines how structures in the body branch and form
that treelike pattern,” O’Regan explains.
Humans aren’t the only animals to have trabec-
ulae. The structures are found in all vertebrates,
so O’Regan’s team speculated “there was a strong
likelihood they were doing something import-
ant.” Da Vinci, centuries ahead of our time, did,
too (see sidebar). O’Regan and his colleagues have
built upon the 15th century polymath’s work to
develop the tools that can finally unravel the mys-
tery behind these tangled structures.LEONARDO BRANCHES OUT