This paper proposes a new biologically-inspired phenomenological model of insulin release that can be used to continuously monitor a person with diabetes and therefore recommend insulin dose and predict events. Given all the parameters and conditions that have to be met in order to achieve stability, the proposed insulin-release system will be considered as highly non-linear and dynamical. The resulting model will study the mechanisms that keep the system from reaching a chaotic state (diabetes), based on the property of self-organised criticality. This property was selected since it has been previously identified and studied in other dynamical biological systems. The proposed model will then be used as part of a model-based reasoning system that aims to support patients with diabetes

Aldea, Arantza

Munoz-Balbontin, Mireya

olde Scheper, Tjeerd V.

Oxford Brookes University: RADAR

Developing a Dynamic Bio-inspired IntelligentSystem to Support Diabetic PatientsMireya Munoz-Balbontin, Tjeerd V. olde Scheper, and Arantza AldeaDepartment of Computing and Communication Technologies - Oxford Brookes UniversityWheatley Campus, Oxford, OX33 1HX - United KingdomAbstract.This paper proposes a new biologically-inspired phenomenological modelof insulin release that can be used to continuously monitor a person withdiabetes and therefore recommend insulin dose and predict events. Givenall the parameters and conditions that have to be met in order to achievestability, the proposed insulin-release system will be considered as highlynon-linear and dynamical. The resulting model will study the mechanismsthat keep the system from reaching a chaotic state (diabetes), based onthe property of self-organised criticality. This property was selected sinceit has been previously identified and studied in other dynamical biologicalsystems. The proposed model will then be used as part of a model-basedreasoning system that aims to support patients with diabetes.1 IntroductionRegulation of insulin and glucose in the human body is part of a complex dy-namical system, whose understanding and study is highly relevant for the man-agement of diabetes. This system is in turn influenced by factors such as mealintake, heart rate, exercise, sleep, and other factors. Research and developmenton the insulin release system, also known as the artificial pancreas, can be tracedback at least 50 years [1]. The models, signals, and control algorithms involvedin the design of the insulin-release clinical system are the three most relevantareas of study. This research has facilitated the advancement of continuous glu-cose monitoring technologies, and the development of medical devices that assisttype 1 diabetic patients in self-management of their condition.Significant improvements have been made in continuous glucose monitoringtechnologies, and several control techniques have been tested and implementedon medical devices. However, in the context of modelling, it was found that asignificant discrepancy exists between the physiological understanding and thelow-level mechanisms that permit the physiological state [2]. This finding is themain motivation for the development of the model proposed in this paper. Themodelling approach will be improved by studying the phenomenological aspectsof insulin release using mathematical properties.This paper summarizes the preliminary research that was conducted, as wellas the modelling approaches that will be considered in order to construct theresearch proposal. The model will then be used to identify how individual dia-betes patients are influenced by di↵erent factors such as carbohydrate intakes,hormones, physical exercise and so on, and therefore support them in their re-quired insulin doses.2 Preliminary research on Bio-Inspired ModelsTo better understand the features of the model proposed in this research, physi-ological and mathematical models were studied. Among the physiological mod-els analysed, minimal and maximal models were identified as the main modelsconsidered for CGM technology development. For the purpose of this researchproject, further studying of the phenomenological aspects of insulin-release us-ing mathematical properties will be conducted. This was decided given a fewmisrepresentations found in physiological models, which are briefly also detailedin this section.2.1 Physiological modelsA physiological model is defined as the qualitative or quantitative representa-tion of an actual physiological system. Quantitative physiological modelling ispreferred, and considered to be more useful, as it provides a mathematical rep-resentation characterized by di↵erential equations [5]. The most commonly usedapproach for the artificial pancreas system is compartmental modelling [4], a spe-cial case of physiological modelling where the movement of a substance betweencompartments is described. Furthermore, there are two classes of physiologically-based models for the artificial pancreas system, both described in this section:maximal models and minimal models.Minimal models focus on explaining the key components of the system andmeasuring essential processes involved in healthy state and diabetes. One of theearliest models documented is the one developed by Bergman and colleagues backin the 70s [1]. The aforementioned model has undergone several modificationsto include additional compartments and incorporate the e↵ects of disturbancessuch as meal or exercise. Other examples of minimal models include the com-partmental approaches proposed by Insel, et. al. and Cobelli et. al. in [2] whichattempt to measure and understand glucose metabolism and its regulation byinsulin.Maximal models attempt to simulate the glucose insulin system using allavailable knowledge of functionality, thus allowing the researcher to carry outexperiments in particular scenarios [3]. Useful information on the general func-tions of the system has been collected. One of the most representative examplesis that of the GIM (Glucose Insulin Model) simulation software, which was de-signed based on the model proposed by Chiara Dalla Man, Robert A. Rizza, andClaudio Cobelli [4], consisting of 12 di↵erential equations and 35 parameters.This software has been useful to simulate healthy state subjects, type 2 diabeticsubjects, and impaired glucose-tolerant subjects in two main scenarios: mealand daily life. The model developed by Grodzky, Jonkers and Henquin [9], wasable to demonstrate the number of active cells is a sigmoidal function of glucoseconcentration, and suggest that insulin release is subject to di↵erent thresholds .Minimal models are commonly used to analyse the data obtained from glu-cose tolerance tests. Although the results obtained prove useful, they tend tomisrepresent the actual dynamics of the glucose-insulin system given that theyare modelled in steady state. Some misrepresentation is also observed in maxi-mal models, given that several of the parameters used in the system are derivedfrom steady-state conditions.Several other studies have been conducted in an attempt to understand theinsulin release phenomenon in the human pancreas, these include glucose toler-ance tests and in vitro studies (see [2] and [9]).After revising the state-of-the-art in physiological modelling for the artificialpancreas, it was concluded that these models alone would not be su cient forthe development of this research project. The studied models have been ableto provide useful information about the phenomenon of insulin release in thepancreas, and they provide solid evidence of progress in the field. However,it is considered that the models do not accurately represent the physiologicalstate as they provide a generalized mathematically reduced approach, ratherthan a detailed representation on the phenomenon of insulin-release. It was thusdecided to explore a di↵erent set of methods to further develop the researchproject. These are presented in the subsequent section of this article.2.2 Computational models and propertiesThis section introduces the property of self-organized criticality, Turing mech-anisms, and two reaction-di↵usion systems that will be considered as the foun-dation for the development of the model. These properties and systems havebeen chosen since they have been previously studied and identified in biologicalsystems. While physiological models focus on representing the physical inter-actions of the system, the following systems and properties focus on describingcomplex mathematical scenarios, such as chemical reactions and/or the interac-tion between an activator and an inhibitor.The property of self-organized criticality is particular to dynamical systemsthat are attracted to a critical point; for the past decade it has been identifiedand studied in biological systems. It has proven useful in defining and under-standing neuronal communication, the functionality of protein families, patternformation in biological systems, among others [11].Turing mechanisms have been useful in research related to pattern formation,particularly in biological patterns such as the scales of fish, the formation of afoetus and, at a more molecular level, pattern formation in cellular slime mouldand calcium activity [7]. The model which can assist in studying these mecha-nisms is the two-variable Lengyel-Epstein model; a model for the photosensitivechlorine dioxide-iodine-malonic acid reaction (CDIMA). It has proven useful forinvestigating the continuous e↵ect of external influence on Turing pattern for-mation. (see [7] and [8])Reaction-di↵usion systems and models are also used to describe pattern for-mation phenomena (including Turing patterns), particularly in systems that in-volve the interaction of many components. The model of interest for the purposeof this project is the Gray-Scott model, given the wide range of spatio-temporaldynamics it supports [10]. This model describes auto-catalytic chemical reac-tions of type: A + 2B ! 3B ; B ! C, where the first equation represents anauto-catalytic process. It is possible to observe a wide range of dynamics whenthe input to the reactor is a continuous uniform flow of species A. The systemcan have up to three homogeneous steady-states: one trivial, and two non-trivial.Another system of interest is the Brusselator. This system represents theinteraction between a reactor and an inhibitor, and is nowadays considered oneof the simplest reaction-di↵usion systems capable of generating complex spatialpatterns [13]. The proposed activator-inhibitor interaction is a well-known prin-ciple to explain pattern formation in chemical, ecological, physical, and biologicalsystems.3 Criticality analysis of the insulin-release systemThree possible approaches to improve the modelling methodology were identifiedduring the preliminary research stage. The approaches were identified based onfindings from physiological models that indicate the presence of criticality in thesystem. The approaches are described in the following subsections and will haveto be analysed and simulated in order to fulfil the aim of the research project.3.1 Finding 1: Non linearity and dynamical requirementsIn mathematical terms, the insulin release system has to be considered as highlynon-linear and dynamical. Given all of the parameters involved and the condi-tions needed to reach stability, it qualifies as one of the dynamical systems thatis attracted to a critical point, this critical point being a normal glucose level.The low- level mechanisms of insulin release which control the system so that itdoes not become chaotic (diabetes), have to be studied to gather a wider knowl-edge on the e↵ect they have over the global state of stability [12]. This will beachieved by studying the property of criticality observed in the insulin-releasesystem.3.2 Finding 2: Identification of critical patternsA recent study has found that local feedback has a direct e↵ect on the orien-tation of the Turing pattern in a system, and can change the global or localdynamics in it [7]. These findings can assist in understanding and defining thecommunication mechanisms followed by beta cells which lead to the release ofinsulin. This will be achieved by adding constraints to the insulin-release sys-tem, such as thresholds and external stimuli (e.g. meal and exercise). By addingthese disturbances to the system, it will be possible to observe the e↵ect on theinsulin-release pattern, and whether or not it converges to a critical point.3.3 Finding 3: Insulin delivery as a wave functionIn the study by Jonkers and Henquin [9] it was demonstrated how beta cellsare recruited in accordance with the sensed concentration of glucose, given thatthey have di↵erent threshold sensitivities to it. The study also shows how thebehaviour of a single cell can be extrapolated to the behaviour of the islet (clus-ter) it is associated with. This property can indicate that the propagation ofinsulin secretion behaves as a wave function. The control of such a system hasbeen studied by Y. N. Kyrychko et. al [10]. Where an activator/inhibitor controlwas applied on a Gray-Scott model based system, convergence to stability wasachieved regardless of the chaotic nature of the system.In the following stage of development, the low level mechanisms of insulinrelease will be simulated to observe their influence on stability at a global level.This will be achieved using coupled oscillators to represent the interaction ofpancreatic  -cells, which represents the foundation for the development of theproposed model.4 Bio-Inspired Model-Based ReasoningIn model based reasoning, an explicit model of the behaviour of the system isused to predict its reaction given a set of initial conditions and constraints. Thepredicted behaviour is then compared with the actual system and if discrep-ancies are found and assuming that the model is accurate then the reasoningmechanism can adapt the model to detect and identify the discrepancies. Ac-cording to Herrero et al, [6] model-based reasoning has been proposed in di↵erentareas related to diabetes: Safety of monitoring devices, artificial pancreas, andprediction of hypoglycaemia.In this research we propose to use a dynamic bio-inspired mathematical modelto better model patient assimilation of glucose. The model will then be part ofa MBR system that will be used to monitor a patient, detect when insulin isneeded and identify the doses required.The simulation and validation of the model will be performed using realpatient data, which will be facilitated given the collaboration with Pepper projectEU (http://www.pepper.eu.com/)5 ConclusionThis paper proposes the development of a bio-inspired mathematical model of in-sulin release. Three approaches to assist in studying the property of criticality inthe insulin-release system have been identified, and will be considered to developthe model. There is no evidence suggesting that the mathematical propertiesand models listed in this document have been used to model the phenomeno-logical aspects of insulin release in the pancreas. A major advantage of usingthem is their capability of explaining complex dynamical systems using a simplermathematical approach. Implementing this novel methodology could help fill insome gaps in physiological modelling, such as the inclusion of disturbances andnon-linearities present in the system.6 AcknowledgementsM.M.B. acknowledges financial support from Oxford Brookes University, andCONACyT. The authors also acknowledge the close collaboration with H2020Pepper Project (http://www.pepper.eu.com/), and its partners. This work hasreceived funding from the EU Horizon 2020 research and innovation programmeunder grant agreement No 689810.References[1] Cobelli C, Renard E and Kovatchev B. Artificial pancreas: Past, present, future. Diabetes60(11):2672-2682, 2011.[2] Cobelli C, Man CD, Sparacino G, Magni L, Nicolao G De and Kovatchev BP, Diabetes:Models , Signals , and Control, 2:54-96, 2009.[3] Dalla Man C, Raimondo DM, Rizza RA and Cobelli C, GIM, Simulation Software of MealGlucose-Insulin Model. Journal of diabetes science and technology (Online) 1(3):323-30,2007.[4] Dalla Man C, R. A. Rizza, and C. Cobelli, Meal simulation model of the glucose-insulinsystem, IEEE Trans. on Biomedical Eng., vol. 54, no. 10, pp. 1740-1749, 2007.[5] Enderle J, and Bronzino J. Introduction To Biomedical Engineering . 3rd ed. London:Academic Press, 2011. pp. 127-131.[6] Herrero P, Lopez B, and Martin C, PEPPER: Patient Empowerment Through PredictivePersonalised Decision Support. Proceedings of the 1st ECAI Workshop on Artificial intel-ligence for Diabetes, 22nd European Conference on Artificial Intelligence (ECAI 2016),pages 8-9.[7] Ji L and Li QS, E↵ect of local feedback on Turing pattern formation, Chemical PhysicsLetters 391(1-3): 176-180, 2004.[8] Ji L and Li QS, Turing pattern formation in coupled reaction-di↵usion systems: E↵ectsof sub-environment and external influence. Chemical Physics Letters 424(4-6):432-436,2006.[9] Jonkers FC and Henquin JC, Measurements of cytoplasmic Ca2+ in islet cell clusters showthat glucose rapidly recruits  -cells and gradually increases the individual cell response,Diabetes 50(3): 540-550, 2001.[10] Kyrychko YN, Blyuss KB, Hogan SJ and Scho¨ll E, Control of spatiotemporal patterns inthe Gray-Scott model. Chaos 19(4):1-7, 2009.[11] Mora T and Bialek W, Are Biological Systems Poised at Criticality? Journal of StatisticalPhysics 144(2):268-302, 2011.[12] olde Scheper T, Why metabolic systems are rarely chaotic. BioSystems 94(1-2):145-152,2008.[13] Wang K, Steyn-Ross M, Steyn-Ross D, Wilson M, Sleigh J, and Shiraishi Y, ”Simula-tions of pattern dynamics for reaction-di↵usion systems via SIMULINK.” BMC SystemsBiology, vol. 8, no. 1, p. 45, 2014.

Developing a dynamic bio-inspired intelligent system to support diabetic patients

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Developing a dynamic bio-inspired intelligent system to support diabetic patients

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