Medical Significance
Diabetes Mellitus (DM) is an autoimmune disease that is characterized by the lack of production of insulin from the pancreas. Insulin is the hormone responsible for transporting the primary energy source, glucose, from the blood stream to the muscles [1]. The build up of this glucose in the blood is defined as hyperglycemia, which is one of the main side effects of DM. Prolonged hyperglycemia can cause the body to break down fat storages to use for energy, which causes ketones to build up in the blood. A ketone is a byproduct from the breakdown of fat that occurs when blood sugar is high. The body needs energy due to the lack of insulin transporting glucose from the blood to other tissues. Ketones alter the pH of the blood, which make them particularly dangerous for diabetics, as changes in blood pH can be fatal. A combination of hyperglycemia and ketones can result in diabetic ketoacidosis (DKA), which can result in death if left untreated [2].
Of the 30.3 million individuals diagnosed with DM in the U.S., the goal of each of them should be proper glycemic control to avoid DKA [2]. Due to the self-monitoring aspects of diabetes and many other factors, it is the seventh cause of death in the U.S., taking the lives of almost 253,000 people in 2015. There are many complications that arise with uncontrolled diabetes, some of which are: neuropathy, retinopathy, blindness, and amputation of limbs [2,3]. These are mainly caused from prolonged hyperglycemia. With the annual spending of diabetes being $245 billion, it surpasses the cost of cancer, which is $170 billion [2,4]. This makes diabetes an ideal disease to invest money and time in, along with the hopes of making the lives of diabetics slightly easier.
Diabetes mellitus is further divided into two categories: type 1 and type 2 diabetes. While the concept of diabetes is held true for both divisions – that insulin is not properly transporting sugar from the blood – to the tissues. The root cause of type 1 diabetes (T1D) is either from genetics or an autoimmune attack of the cells in the pancreas. In T1D, the pancreas stops producing insulin, while in type 2 diabetes the pancreas is still producing insulin, but not at a fast enough rate. Type 2 diabetes is caused from poor diet and a lack of exercise, along with other risk factors that increase ones chance to be diagnosed [5]. In this proposal T1D will be the default focus, although this proposal could be related to either type 1 or type 2 diabetes.
Mathematical Model
The method used to model glucose and insulin absorption is credited to Dr. Roman Hovorka and his team, who designed a system with two inputs and one output. The two inputs are glucose and insulin consumption with the output being the glycemic level. The model is set up with 4 subsystems consisting of, “Glucose absorption, Insulin absorption, Insulin action, and Glucose subsystem” [6]. When either insulin or glucose is injected into the blood stream, it must be absorbed in order to be effective. This absorption by cells and tissues is simply membrane transport, which can be modeled by differential equations. By using discrete blood sugar values obtained from a continuous glucose monitor (CGM) and the ability to model this activity at a molecular level, predictions of future blood sugar values can be obtained. If one was to look at a graph of blood sugar vs. time, there will be multiple spikes that resemble parabolas opening down. By also knowing the characteristics of these graphs and the graphical analysis that comes with it, it is possible to predict blood sugar trends. Finding the slope and locating the maximum value between select blood sugar values is necessary and can easily be done. The slope at any time in the plot of blood sugar vs. time is synonymous with the trend of blood sugar at that time. Being able to model the trend in blood sugar can be useful for diabetics, as it will provide more information about whether blood sugar is rising or dropping at a given rate.
Competing Methods
The focus of this project is to increase glycemic awareness and control, which can be achieved in many different ways – not only by mathematical modeling – but also effective management strategies. One must focus on the basis of glycemic control and the ways that it can be controlled.
Dexcom Continuous Glucose Monitor (CGM)
The Dexcom CGM consists of a sensor that is inserted subcutaneously and held onto the skin by an adhesive. A Bluetooth transmitter is also inserted in a slot that is held in by the adhesive and receives input from the sensor. This transmitter sends this data to a receiver, which is a device with an LCD screen that displays the trend of blood sugar values. The sensor needs to be changed every seven days to avoid infection [7]. This method is a highly specialized and industrial approach to managing glycemic control, which makes it expensive. This method is also particularly convenient and can outweigh the high cost for some patients.
Traditional Finger Prick
Diabetics must check their blood sugar before meals and if they are feeling any symptoms of low or high blood sugar at any given time. A finger prick is necessary for testing blood sugar; one must take a sample of blood using a lancing tool and apply the blood to the meter. Unlike the CGM, a trend cannot be determined from one finger prick, which makes this method less effective with improving glycemic control.
Proper Diet and Exercise
There are multiple studies that prove that consistent exercise can increase glycemic control and decrease the occurrence of hyperglycemia in diabetics. Exercising sessions can lead to an improvement of glycemic homeostasis for about 2-3 days after exercise, which is one of the main reasons it is strongly recommended for diabetics [8]. Although for some individuals, exercise can be inconvenient and bothersome. Consuming foods that are high in carbohydrates is not recommended for diabetics, as hyperglycemia can be a result of this. Keeping a proper diet that favors low-glycemic food is ideal, such as non-starchy vegetables and fruits [9].
References
[1] Diabetes Mellitus. Funk & Wagnalls New World Encyclopedia. 2017:1p. 1. https://ezproxy.gl.iit.edu/login?url=http://search.ebscohost.com/login.aspx?direct=true&db=funk&AN=DI049400&site=ehost-live. Accessed October 5, 2018.
[2] “DKA (Ketoacidosis) & Ketones”.diabetes.org. American Diabetes Association. n.d. Web. (October 5, 2018).
[2] Centers for Disease Control and Prevention. National Diabetes Statistics Report, 2017. Atlanta, GA: Centers for Disease Control and Prevention, U.S. Dept of Health and Human Services; 2017.
[3] Mohan, V., Mapari, J. A., Karnad, P. D., Mann, J. S., & Maheshwari, V. K. (2018). Reduced Diabetes Mellitus-related Comorbidities by Regular Self-monitoring of Blood Glucose: Economic and Quality of Life Implications. Indian Journal of Endocrinology & Metabolism, 22(4), 461–465. https://doi-org.ezproxy.gl.iit.edu/10.4103/ijem.IJEMpass:[_]216_17
[4]Cancer Prevalence and Cost of Care Projections. (2011). Retrieved from https://costprojections.cancer.gov/
[5] "Type 2." diabetes.org. American Diabetes Association. n.d. Web. (October 5, 2018).
[6] Rebro, M., & Tarnik, M. (2015). Adaptive Glycemic Control: Implementation in Matlab(Publication). Retrieved October 5, 2018, from Slovak University of Technology, Faculty of Electrical Engineering and Information Technology website: https://www2.humusoft.cz/www/papers/tcp2015/052_rebro.pdf
[7] “Continuous Glucose Monitoring.” National Institute of Diabetes and Digestive and Kidney Diseases. (2017, June 01). Retrieved from https://www.niddk.nih.gov/health-information/diabetes/overview/managing-diabetes/continuous-glucose-monitoring
[8] Dijk, J. V., & Loon, L. J. (2015). Exercise Strategies to Optimize Glycemic Control in Type 2 Diabetes: A Continuing Glucose Monitoring Perspective. Diabetes Spectrum, 28(1), 24-31. doi:10.2337/diaspect.28.1.24
[9] Diabetes Diet, Eating, & Physical Activity. (2016, November 01). Retrieved from https://www.niddk.nih.gov/health-information/diabetes/overview/diet-eating-physical-activity
[10] Hoadley, David, and Arvind Ananthan. Using Modeling and Simulation in the Design of Closed-Loop Insulin Delivery System. Mathworks, Inc., 2013, Using Modeling and Simulation in the Design of Closed-Loop Insulin Delivery System, www.mathworks.com/content/dam/mathworks/tag-team/Objects/u/DMD2013_Closed-Loop_Insulin-Delivery.pdf.
[11] Owren, Marit. “Automatic Blood Glucose Control in Diabetes.” Norwegian University of Science and Technology, June 2009, daim.idi.ntnu.no/masteroppgaver/004/4503/masteroppgave.pdf.
[12] Hovorka, Roman, et al. “Nonlinear Model Predictive Control of Glucose Concentration in Subjects with Type 1 Diabetes.” Physiological Measurement, vol. 25, no. 4, 2004, pp. 905–920., doi:10.1088/0967-3334/25/4/010.