According to the American Diabetes Association, 29.1 million Americans—approximately one out of every 11 people—are living with diabetes. Type 1 diabetes mellitus (T1DM), also known as juvenile diabetes, is a devastating disease caused by a lack of beta cells that produce insulin, a hormone secreted by the pancreas. It leaves the body unable to effectively use or store glucose for energy. This malfunction results in irregular carbohydrate metabolism and heightened glucose levels – too much sugar in the blood and urine. T1DM often coincides with life-threatening complications—such as heart disease, stroke, and kidney failure—and in some cases may result in blindness, amputation, and the development of other damaging pathologies. The risk of death in adults with diabetes is 50% higher than in those without. Additionally, diabetics tend to spend twice as much on medical expenses; the ADA estimates that the disease causes $245 billion in health care costs and lost work/wages in the United States.
To lower their chronically-high glucose levels, type 1 diabetics must take insulin daily, typically through either needles or a pump. Although multiple therapeutic regimens exist, none are without flaws. During a minisymposium at the 2017 SIAM Conference on Applications of Dynamical Systems, happening now in Snowbird, Utah, Jiaxu Li of the University of Louisville presented an integrated system—comprising multiple dynamical system models—for an artificial pancreas. The successful development of such a system could better manage insulin regulation and ultimately improve the quality of life in diabetics.
The ideal method of insulin administration involves an artificial pancreas, a closed-loop integrated system with an insulin pump, a glucose monitoring system, and closed loop control (CLC) algorithms. Jiaxu Li models one such system. Image courtesy of Jiaxu Li.
Li overviewed two traditional therapeutic regimens meant to regulate insulin and glucose levels. Conventional insulinotherapy (CIT) involves the injection of rapid and intermediate acting insulin two or three times per day. These injections should ideally coincide with meals, so as to match the anticipated peaks in insulin profiles. “For diabetics with a regular lifestyle, the regime is less intrusive than invasive therapy,” Li said. “However, the glucose level cannot be controlled very well.”
Another possible regimen is intensive insulinotherapy, also known as flexible insulin therapy (FIT). FIT allows patients to regulate the amount of insulin they take with each injection — via injection ports or pens, for example. This method offers more flexibility at mealtimes and better glycemic control than CIT, thus limiting the incidence and severity of diabetes’ complications. However, FIT also demands a substantial increase in costs and a higher education level in regard to self-care. Ultimately, the dose inaccuracies and timing discrepancies of the two aforementioned therapies can cause dangerous glucose fluctuations, including hypo- and hyperglycemia.
The ideal method of insulin administration involves an artificial pancreas, a closed-loop integrated system that includes an insulin pump, a glucose monitoring system, and closed loop control (CLC) algorithms. “It’s not 100 percent accurate, but it’s good,” Li said of the method. However, so-called “model” algorithms are needed to close the loop and complete the structure. Despite decades of study, researchers have not been able to create the required CLC algorithms, thus preventing the development of more efficient therapies. “Several companies have been working on this, but it’s still not good enough to use clinically,” Li said.
Li models his integrated system with mechanical and psychiological delays. Image courtesy of Jiaxu Li.
In an attempt to close the loop, Li presented an integrated system—tested on a virtual human—of several models that mimic the functioning of an artificial pancreas. He acknowledged some well-known impediments within this pancreas, including the need for reliable predictive models, a lack of efficient control algorithms, an unreliable glucose monitoring system, and delayed treatment effects. Li’s model diagram includes both mechanical and physiological delays, and his graduate student is currently working on how to best handle them. Getting the system just right is a challenge. “When it’s too complicated, it’s useless,” Li said. “When it’s simple, we can’t capture all of the major events.”
He then showed an impulsive model, which spontaneously injects insulin into the body, before performing rigorous analysis of an open-loop delayed differential equation (DDE) model. Next, Li compared the DDE model (from 2014) with an ordinary differential equation model from 2012. This comparison revealed surprising information about time delays, which occur when injected insulin crystals turn to insulin. Li’s model indicated that glucose peaks were actually lower with the delays, making their removal from the model unnecessary. “Time delays may help to achieve better effects to lower glucose level,” he said. “They may actually be a good thing.” Li then expanded his model with a bolus insulin injection—a quick-acting injection taken specifically at mealtimes—and compared various insulin products on the market (i.e. slow, quick, long-lasting, etc.)
Ultimately, results of the simulation of Li’s integrated system are similar to the true data. Numerical simulations indicate that the system is effective in nearly all time intervals. When integrated with an insulin pump and an institutional blood glucose monitoring system, a closed-loop artificial pancreas approach is a reliable means of controlling blood sugar in clinical applications. The success of Li’s system could finally facilitate the development and validation of operative CLC algorithms to be used in artificial pancreases. “More than 90% of simulations produce a pretty good result,” Li said. “Even though some residual cells remain, the type 1 diabetic will still have a much better life.”
|| Lina Sorg is the associate editor of SIAM News.