For many students, math’s honeymoon ends at differential equations—calculus mainstays that describe how dynamic systems change over time.
Math-oriented students may face a hundred differential equations during their college education.
But likely not thousands, or a million, or a trillion.
Leave that to a supercomputer and AI.
As part of his research into medical digital twins, Esteban Hernandez-Vargas, University of Idaho associate professor of mathematics, and his colleagues use AI to solve the truckloads of complex differential equations necessary to make a digital model of the human heart.
“There are about 3 billion cells in a human heart,” Hernandez-Vargas said. “To model 3 billion, you need to simulate a trillion differential equations because we model each cell to learn how it communicates and interacts with other cells.”
Digital twins are computer-based versions of something that exists in the real world. In healthcare, a medical digital twin can represent a specific patient and their health condition, or they can be digital replicas of body systems, such as the respiratory system.
They can also be organs.
Hernandez-Vargas of the College of Science and fellow researchers at the Uniformed Services University in Washington D.C. are building a computer model of the human heart to learn how best to prevent a patient from dying of trauma created by a battlefield injury. The study is funded by the Department of Defense, which wants to learn how to increase the survival rates of soldiers who have sustained battlefield injuries and are suffering from traumatic hemorrhagic shock.
The model will simulate what happens during and after severe blood loss, including problems with blood flow, electrical activity and the mitochondria that power heart cells.
With help from the U of I’s high-performance computing resources, also known as the Lemhi supercomputer, shared through a partnership with the Idaho National Laboratory, and because of U of I’s machine-learning expertise, Hernandez-Vargas and his colleagues aim to run realistic simulations. They want to identify the key factors that cause heart failure and deadly abnormal rhythms after hemorrhagic shock.
Scientists have struggled to understand why in traumatic hemorrhagic shock, although severe bleeding has been stopped and blood volume has been restored, many patients still develop heart problems. Some die from heart failure or dangerous heart rhythms, Hernandez-Vargas said.
We model each cell to learn how it communicates with other cells.
Esteban Hernandez-Vargas
Associate professor of mathematics
“It’s a very complicated system that we’re just beginning to understand,” he said.
Hernandez-Vargas was one of 47 researchers to attend a seminar in Paris that laid out the need to use AI in the medical field to replicate human organs and their precise function and reaction to disease, trauma and medicine as well as human organ systems such as the respiratory and circulatory system.
“Medical digital twins — virtual models of individual patients that mirror an individual patient’s health status — have the potential to transform how infectious diseases are monitored and treated,” Hernandez-Vargas said.
What emerged from the conference was an agreement among medical researchers across the globe to collaborate to create “immune digital twins” that combine medical, immunology and computer science knowledge to improve treatment and drug development. The goals were outlined in the journal article, “Immune digital twins for complex human pathologies: applications, limitations, and challenges.”
“We were scientists from medicine, immunology and computer science agreeing to work together to develop immune digital twins,” he said. “We also discussed the challenges scientists must solve before immune digital twins can be used regularly in hospitals.”
Among them is the understanding that a digital twin based on a person’s medical history from the past may not be an accurate model down the road because of the ever-changing human body.
“Updating computer models is an important part of creating digital twins, but it is often overlooked,” Hernandez-Vargas said. “Digital twins need to use new information about a patient over time so they can stay accurate and up to date.”
To make predictions about a person’s future health, scientists can use special computer methods called adaptive estimators to keep updating these models.
“These methods can estimate things that cannot be directly measured and adjust the model as the patient’s health changes,” he said.