Pioneering research analyzes the math of menstruation

Selby Frame is associate director of academic
communication at Bowdoin College. She lives
in South Portland.
(Editor's note: This article is adapted and
reprinted by permission of Bowdoin College.)

There's no easy way to
explain what happened
to mathematician Mary
Lou Zeeman though it
all began simply enough.
Nine years ago, the
Bowdoin College mathematics
professor was
chatting with a gynecologist
who mentioned
his questions about in
vitro fertilization treatment
protocols, which
included administration
of a cycle of birth control
pills to suppress ovarian
function, followed by daily
injections of hormones
to induce maturation of
follicles and eggs in the
ovaries.

He wanted to better
understand the results of
these therapies based
on factors including
a woman's age, hormonal
level and ovarian
functioning to more
accurately predict the
outcome of treatment,
tailor the treatment to
individual patients, and
reduce stressors and outright
dangers that might
interfere with pregnancy
in some women. Knowing
that Zeeman was a
mathematician, he asked
her to look at his data on
women who had received
birth control pills
and those who hadn't,
to try to see if she could
find some statistical basis
for treatment results.

Just for fun, she says,
she conscripted some of
her undergraduates at
the University of Texas at
San Antonio, where she
taught from 1991-2006.
Together, they analyzed
daily data on changes in
the women's estrogen
levels and follicle growth,
and turned up patterns
in the data that intrigued
the gynecologist. After
researching the literature
in both mathematical
and crossover math-biology
journals, Zeeman
learned something that
truly astonished her:

There was no mathematical
model for the menstrual cycle.
I was stunned, says
Zeeman. When I say
nothing, I mean that
after I searched and
searched and searched,
I found that over the last
30 years there were less
than a dozen papers
looking at the menstrual
cycle from the mathematical
point of view.

The feminist part of
me was horrified ... the
mathematical part was
thrilled.

Zeeman quickly got
to work. She steeped
herself in biology, sitting
in on college classes on
everything from Bio 101
to genetics to neurobiology.
Eventually, her
quest brought to her to
visit the University of
Michigan and earned her
a grant from the National
Science Foundation
for cross-disciplinary
research in biology at
Cornell University, where
she met up with her primary
research partner,
biologist David McCobb.
I discovered a drive
in myself I didn't know
I had, says Zeeman.
Some colleagues told
me I was destroying my
career. But I didn't have
a choice: I knew this was
what I wanted to do.

With her expertise in
geometrical dynamical
systems a mathematical
tool for studying
how things change, or
cycle Zeeman began
pioneering collaborative
work with McCobb to
begin answering some
of the basic, outstanding
questions about how the
menstrual cycle works.
The crux of the
mathematical challenge
is to gather and
plot data about the
hormonal interaction
of the hypothalamus,
pituitary and ovaries,
the biological axis of the
menstrual cycle consider
them variables. If
mathematical models
can be developed that
accurately mimic pituitary
functioning under
normal circumstances,
simulating the appropriate
parameter changes
in the same model can
then be used for understanding
interruptions in
this complex cycling for
women with a variety of
infertility problems.

Their ongoing work in
mathematical neuroendocrinolgy,
or biomathematics,
is now part of
the academic landscape
at Bowdoin, where
Zeeman is developing
a laboratory for both
the biological research
and the computational
analysis.

This work is really accessible
to undergraduates,
says Zeeman.
Because the field is so
new, there are plenty of
experiments to do that
translate between the biology
and the math. I am
hoping to interest both
biology and math majors
and get them working
together.
A Closer Look
Find a video podcast of
Mary Lou Zeeman
giving a recent talk
at www.bowdoin.
edu/podcasts .