Mathematical Equations are Revealing New Insights into Women’s Bodies x UNAL
By Luisa Orozco with Universidad Nacional de Colombia
When people talk about how little we know of the ocean, one figure is often repeated: barely 1% has been explored. The same cannot be said of women’s bodies, yet the comparison helps measure a long-standing void. For decades, the male body stood as the default in scientific research, while the female body remained in the background. A study from the National University of Colombia (UNAL) seeks to narrow that gap through an unconventional approach: mathematical models.
After her first period, Carolina Ramírez Mazo, now a PhD in Engineering from UNAL, was prescribed birth control pills to regulate an irregular cycle. At first, she took them without much questioning. But years later—after an undergraduate degree, a master’s, and many journeys—her perspective shifted. She encountered alternatives in Eastern medicine that seemed to understand her body differently and helped her regulate her period. That experience sparked a deeper curiosity about the menstrual cycle.
There was a time when Ramírez stepped away from engineering altogether. She studied psychology and pursued other paths until she learned of a research group modeling bodily organs through mathematics, including the uterus and ovaries: the KALMAN Research Group on Dynamic Processes, led by Dr. Lina María Gómez Echavarría at UNAL’s Medellín campus.
What began as a tentative collaboration gradually became something more. Ramírez applied to the university’s doctoral program in engineering, with Gómez as her advisor. She had a clear intention: to develop a line of research that had not yet been explored—designing mathematical models to understand how the hormonal system that links the brain to the ovaries (the hypothalamic-pituitary-ovarian axis) interacts with the endometrium, the cardiovascular system, and metabolism.
To grasp this, Gómez explains, mathematical models translate what happens in the body into equations. Instead of directly observing an organ—often difficult or impossible—researchers build formulas that describe how certain variables change over time.
“This allows us to run experiments without having to perform them on women,” she says. “Through equations, we can explore what happens when hormone levels rise or fall, and how that is reflected in the endometrium and in the cardiovascular and metabolic systems.”
The cycle where it all begins
In recent years, research—much of it led by women—has increasingly turned toward understanding the menstrual cycle. A study published in early 2026 in Nature analyzed blood samples from 2,700 women and found significant fluctuations in several components throughout the cycle. Another, from 2024, used data from more than 11,500 women wearing smartwatches to track heart rate patterns, identifying clear peaks and lows on specific days. That same year, scientists at the University of California, Santa Barbara studied the brains of 30 women who were not using hormonal contraceptives, observing changes across the menstrual cycle.
At the time, researchers pointed to a striking gap: more than half of the world’s population menstruates, yet much of what that process entails remains unknown.
The menstrual cycle is fundamental. Its four phases—menstrual, follicular, ovulatory, and luteal—shape women’s health in direct ways. Irregularities ripple outward, affecting systems as varied as the cardiovascular, metabolic, immune, and skeletal. And yet, as Ramírez notes, the cycle has been studied mostly through the lens of reproduction.
To approach it from another angle, she designed three mathematical models. The first focused on the hormonal system: in the brain, the hypothalamus sends signals to the pituitary gland, which in turn releases hormones into the bloodstream, reaching the ovaries, where estrogen and progesterone are produced. Both are essential to reproduction, but their roles differ—estrogen drives growth and activation, while progesterone stabilizes and regulates.
Ramírez linked this system to the endometrium, the uterus’s inner lining. “We used equations to simulate how these hormones cause the tissue to grow, transform, and eventually shed,” she explains. The results showed that the endometrium’s growth, maintenance, and shedding depend on a dynamic balance between estradiol and progesterone. When that balance is disrupted, the tissue may overgrow, fail to sustain itself, or shed irregularly.
“What the model shows is that the uterus responds directly to the hormonal dance of the cycle: the endometrium grows with estrogen, stabilizes with progesterone, and sheds when both decline,” she adds.
What about the heart and metabolism?
According to data published earlier this year by the American Heart Association, the percentage of women living with cardiovascular disease is expected to rise from 10.7% in 2020 to 14.4% by 2050. Reproductive health conditions, such as polycystic ovary syndrome, are also associated with higher cardiovascular risk.
Against this backdrop, Ramírez developed a second model linking hormonal cycles to cardiovascular variables, such as the behavior of blood vessels, which regulate blood flow by dilating or contracting.
The model revealed that cycle hormones influence this behavior. “Estrogen and progesterone balance each other. When that proportion is disrupted, the equilibrium between dilation and contraction shifts, and the cardiovascular system loses stability,” she explains.
A third model examined glucose and insulin metabolism—the way the body regulates blood sugar. Its findings suggest that this process is not constant throughout the month but varies with the menstrual cycle. Depending on hormonal fluctuations, the body becomes more or less efficient at managing glucose: there are moments when regulation improves, and others when it falters.
The choreography of a body
To explain how these systems work together, Ramírez turns to a simple image: a dance. There is no single protagonist, but many dancers—the uterus, blood vessels, metabolism—moving at once. At the center are two key figures, estrogen and progesterone, not taking turns but moving in tandem.
The choreography depends on timing. If one steps ahead or falls out of rhythm, the scene begins to unravel in the uterus. Meanwhile, other dancers respond: blood vessels widen or constrict, metabolism adjusts how it uses glucose. Together, these processes form a network that sustains the dance as a whole.
“One of the most important findings is that it’s not enough to look at each hormone separately. What truly matters is the balance between estrogen and progesterone, because that balance regulates effects across the entire body,” Ramírez says.
For now, both Ramírez and Gómez agree that much remains to be understood about women’s bodies. “Western medicine tends to isolate the menstrual cycle and focus on suppressing symptoms. That’s why irregular periods are so often treated with contraceptives, without asking what is actually happening in the body,” Ramírez notes. “These models could help us, in the future, think of solutions that understand the cycle as a dynamic process—one that affects other systems, and is affected by them in return.”