Medical Informatics

Diabetes mellitus, commonly referred to as diabetes, is a heterogeneous group of metabolic diseases, which are characterized by elavated boold glucose level. Elevated blood glucose level chronically damages internal organs, such as eyes, kidneys, nerves or blood vessels, and eventually may lead to death. Diabetes is the 8th most common cause of death. 50% of people with diabetes die of cardiovascular disease (primarily heart disease and stroke), and 10-20% of people with diabetes die of kidney failure. Prevalence of diabetes in the Europe is about 10.3% of men and 9.6% of women aged 25 years and over, and this is gradually increasing among all ages, mostly due to increases in overweight and obesity, unhealthy diet and physical inactivity.

We distinguish two types of diabetes. While diabetes type 1 is an autoimmune disease, very often diagnosed around 15th year of life, diabetes type 2 is a metabolic disorder caused by insulin resistance and relative lack of insulin, often diagnosed in adult patients. Treatment of diabetes involves lowering blood glucose and the levels of other known risk factors that damage blood vessels. People with type 1 diabetes require insulin; people with type 2 diabetes can be treated with oral medication, but may also require insulin. Each insulin dosage must correspond with the current blood glucose level, otherwise, it could kill the patient (as a result of hypoglycemia, i.e., the state when blood sugar decreases to below normal levels). However, checking blood glucose levels presents a significant discomfort to a patient since it involves piercing the skin to draw blood. A motivated patient is, therefore, reluctant to perform the check more than five times per day; a common patient does so only twice or thrice per day. It might be insufficient because some dangerous changes of glucose concentration might elude the detection. The solution to this problem lies in getting the needed information in a less invasive way.

For more information, see: http://www.euro.who.int/en/health-topics/noncommunicable-diseases/diabetes/data-and-statistics

Existing Approaches

Continuous glucose monitoring system (CGMS), which is also a part of insulin pumps used to dose insulin fully automatically, measures interstitial fluid glucose level in subcutaneous tissue. This minimally invasive technique provides a value each five minutes. However, glucose level of subcutaneous tissue is not necessarily the same as blood glucose level. A number of important changes of blood glucose level cannot be intuitively deduced from the continuously monitored glucose level of subcutaneous tissue. A sophisticated model of blood glucose dynamics has to be used.

Among these models, the one developed by Steil and Rebrin [Ste05] has achieved a prominent position, mainly due to its low complexity. The Steil-Rebrin model is a two-compartment model assuming that interstitial fluid glucose levels are a convolution of blood glucose levels and the impulse response of the system with only one unknown parameter. It states that blood glucose level is proportional to interstitial fluid glucose level and its change – a first order derivative. According to our experiments [Kou14], the Steil-Rebrin model achieves average relative error of 18.1% due to its over simplification of glucose dynamics.

Our Approach

Figure 1: Block schema of blood glucose level calculation. The b(t) and i(t) symbols denote the respective blood and interstitial fluid glucose levels at time t.

Our diffusion model [Kou14] is a physiological model that calculates the blood glucose level from CGMS-measured levels and reference samples of the blood glucose level. The model relates the present blood and interstitial fluid glucose levels to the future interstitial fluid glucose level. Glucose may appear in the blood, e.g., due to consumed carbohydrates, the breakdown of liver glycogen or an infusion. From the blood, glucose is transported across the capillary membrane into the interstitial fluid. The rate of such a transport is limited by the capillary membrane surface, permeability and concentration gradient between the blood and interstitial fluid glucose levels. In the interstitial fluid, the glucose is either utilized or leaves the interstitial fluid. Depending on the blood glucose level, part of the interstitial fluid glucose can be transported back into the blood, with the same limits applied to the transport in the opposite direction. In addition, a part of the interstitial fluid glucose may leave through an accessory exit route such as lymphatic system, eventually appearing in the blood. Both the blood and interstitial fluid glucose levels affect each other. In addition, they are both controlled by a number of hormones, neural signals and substrate effects [Lon11]. This is a complex system whose modelling would lead to a complex model with a considerable number of parameters. Such a model may be prone to overfitting. In such a case, the model would describe the error noise instead of capturing the relationship between the individual compartments of the system. In addition, too many parameters may make it impossible to determine if we do not have enough input levels to capture the dynamics of the glucose system.

Instead of designing a complex model, we approach the problem in the manner of federative co-simulation. In co-simulation, the entire system is decoupled into smaller parts, each of which is modelled with its own simulator. These simulators communicate with each other, while treating each other as a black box. In federative co-simulations such as high-level architecture, a simulator can be used together with a live device to increase the overall precision of entire simulation [Chen12]. Our model describes the correlation between the blood and interstitial fluid glucose levels across the capillary membrane. The blood and interstitial fluid represent interfaces that connect our model (simulator) to other compartments (devices) in the system. As a result, we do not need to calculate, e.g., using the insulin level that moderates the glucose uptake by cells. Instead of such a calculation, the biological system itself carries out the necessary actions and applies the results to the blood and interstitial fluid glucose levels, which we read subsequently – thus having the effects of insulin already and precisely processed. As a result, the model requires no inputs such as the insulin dosage or the volume of consumed carbohydrates. The model requires only the continuous measuring of the interstitial fluid glucose level and several samples of the blood glucose level to estimate the model parameters.

Let us imagine the model to run in parallel with the real transport of glucose across the capillary membrane. The model states that the system changes the interstitial fluid glucose level in such a manner so that the interstitial fluid glucose level at three different times infers the blood glucose level at one of those times. Initially, we use the blood glucose level to determine the parameters of the model – i.e., quantifying the effects that exert an influence over the glucose transport across the capillary membrane. Then, we continuously measure the interstitial fluid glucose level to calculate a continuous curve of the blood glucose level. We compare the calculated blood glucose level to the measured blood glucose level to estimate the calculation error.

Figure 2: An example of blood glucose level reconstruction.

Figure 2 depicts a sample blood glucose level reconstruction. Blue curve represents CGMS-measured interstitial fluid glucose level in subcutaneous tissue. Red squares represent self-monitored blood glucose levels (SBGM). Brown curve represents the calculated continuous curve of blood glucose level, which fit the measured blood glucose levels. In addition, Figure 2 illustrates as the patient does no SBGM measuring in the night hours. The blood and interstitial fluid glucose levels are not necessarily the same, and patient has no blood glucose levels for his physician to improve evaluation of patient’s night condition.

When compared with the Steil–Rebrin model, our diffusion model outperformed theirs while introducing no additional require ments for glucose sample collection. We implementated both models in C++ and conclude that our model is a bit slower to compute than its counterpart but its optimisations are still in progress.

Figure 3. A Clarke Error Grid comparing the Steil–Rebrin model (cross-marks) with our diffusion model (circle-marks).

Portal

In order to get our model from academy to physicians and diabetics, we have developped a web portal that calculates a continuous curve of blood glucose level from glucose levels of subcutaneous tissue. To our best knowledge, we are running the very first portal that offers this. The portal is open to physicians and patients, both of which can upload data exported from CGMS. At present the portal is being used by the clinicians of University Hospital in Pilsen, Czech Republic, who finds it valuable, and by a couple of individual registered users. Using the portal, the diabetes community can test and provide feedback about the implemented model. Any physician can use the portal to educate the patient about the importance of continuous glucose monitoring. With the introduced web portal, our method can reach any doctor's office thanks to the Internet. The portal is available at https://diabetes.zcu.cz.

Screenshots and Videos

References

[Chen12] Chen D, Wang L, Chen J. Large-Scale Simulation: Models, Algorithms, and Applications. CRC Press, 2012.

[Kou14] Koutný T. Blood glucose level reconstruction as a function of transcapillary glucose transport. Computers in Biology and Medicine 2014, 53: 171–178.

[Lon11] Longo D, Fauci A, Kasper D, Hauser S, Jameson J, Loscalzo J. Harrison's Principles of Internal Medicine. NewYork, McGraw-Hill, 2011

[Ste05] Steil GM, Rebrin K, Hariri F, et al. Interstitial fluid glucose dynamics during insulin-induced hypoglycaemia. Diabetologia 2005, 48(9): 1833-1840.