Mathematical aspects of apolipoprotein kinetics, with focus on metabolic diseases

Biomathematics is a branch of science that aims at describing biological processes in mathematical terms to frame and solve otherwise unsolvable research questions in the biological and medical field. Cardiovascular diseases are the number one cause of death in the world. Metabolic diseases as metabolic syndrome and diabetes increase the risk of cardiovascular diseases, due to disrupted lipid metabolism. Apolipoproteins (apo) are particles attached to the lipid-carrying proteins (lipoproteins) and give them properties. ApoC-III inhibits lipoprotein lipase, therefore lowering down the release of the triglyceride from the lipoproteins to the tissues, apoE is a ligand involved in the uptake of lipoproteins from the liver and apoA4 influences insulin secretion. Studying how fast the apolipoproteins are formed and released in the blood (secretion rate (SR)) and how fast they are removed fromtheblood(fractionalcatabolicrate(FCR))enrichesourknowledgeonlipid metabolism. Apolipoprotein kinetics studies are only possible thanks to mathematical modelling. So far the three apolipoproteins had not being measured in the same study. We analyse the time series data generated from three experiments with the nonlinear mixed effects modelling framework. The novelty consists in having validated a structural model for all the apolipoproteins across three studies and having chosen statistical error model. A covariance-variance matrix for the random effects has been designed and it has been validated in 16 out of the 18 total occasions (three apolipoproteins with 2 occasions for 3 experiments). Applications of the mathematical framework to the kinetic studies has led to advancements in the realm of lipid metabolism. In Paper I and II apoC-III kinetics is studied before and after hypercaloric fructose treatment in abdominally-obese individuals. In Paper I the modelling framework developed in this thesis is presented and further applied to apoA4 and apoE kinetics; a strong bond has been uncovered between triglyceride levels and the SR and PS of apoC-III and an association has been found between apoC-III and apoE kinetic parameters. In Paper II the results for apoC-III are combined with lipoprotein kinetics analysis. Hypercaloric fructose intake leads to an increase in triglyceride levels, but the mechanism behind this phenomenon was so far unknown; in this work, results support the hypothesis that the increase in apoC-III SR causes a rise in the apoC-III concentration with subsequentincreaseintriglyceridelevel. InPaperIIIapoC-IIIandapoEkinetics are analysed before and after a PSK9-inhibitor-based drug treatment in type-IIdiabetic individuals. ApoE FCR increases consistently and apoE diminishes as a result of the treatment. Different elements suggest that the increase in apoE FCR might be related to an increase in VLDL2 FCR

Modelling endocrine regulation of glycaemic control in animal models of diabetes

This thesis is concerned with mathematical modelling of the glucose-insulin homeostatic system, with the specific aim of mathematically modelling diabetes and diabetes-like conditions in animals. Existing models were examined and critiqued in this thesis. Additionally, structural identifiability analysis of the most widely-used model in the field, the Minimal Model, was performed using Taylor series and similarity transformation approaches. It was shown under certain assumptions that it was theoretically possible to obtain a unique set of parameters for the model from only measuring glucose. C-peptide deconvolution was performed using the WinNonLin algorithm and Maximum Entropy technique implemented in MATLAB. This was used to calculate insulin secretion, the percentage of insulin appearing in the periphery and insulin clearance rate. This was then further developed to model insulin appearance and clearance based on hepatic blood flow changes. A short-term model of the glucose-insulin and C-peptide system was initially formulated using a PID controller concept and later refined to reduce the number of model parameters. Structural identifiability analysis was performed using the Lie symmetries approach, followed by parameter estimation on rat and mice data from IVGTTs, OGTTs and hyperglycaemic clamps and sensitivity analysis. This short-term model was integrated into a long-term model to analyse Zucker and ZDF rat data to create a single model to cater for both short- and long-term dynamics. Finally, a software tool was developed to allow non-mathematical scientists to use and access the benefits of the model

Structural identifiability and indistinguishability analyses of glucose-insulin models

In this thesis, the structural identifiability analyses of established and novel glucose-insulin models was performed, to determine whether the models are globally structurally identifiable with the observations available. Structural identifiability analysis is an essential step in the modelling process and a key prerequisite to experimental design and parameter estimation. Analyses were performed assuming observations of both glucose and insulin concentrations on two versions of the well-cited Minimal Model (MM), the Original Minimal Model (OMM) and Extended Minimal Model (EMM) for the modelling of the responses to an Intravenous Glucose Tolerance Test (IVGTT); a Euglycemic Hyperinsulinemic Clamp model and two novel modified versions of the MM, a Closed-Loop Minimal Model (CLMM) and a Double-Pole in Closed-Loop Minimal Model (DPCLMM), when the models describe a complete course of glucose-insulin dynamics during an IVGTT. The CLMM proved to be unidentifiable so a reparameterisation procedure was performed on this model, yielding a globally structurally identifiable reparameterised model. Parameter estimation using these models was also performed for sets of IVGTT and glucose clamp data. The results of the parameter estimation demonstrated that global structural identifiability does not as always guarantee numerical identifiability, or vice versa. A structural indistinguishability analysis was also performed to compare the MM and the CLMM, given the same observations, where it was shown that both models are distinguishable over both pre- and post- insulin switching phases. This is the first time that all such analyses have been performed on these specific model structures. The generic and numerical results obtained demonstrate issues that may arise in practice when attempting to calculate insulin sensitivity when using such models.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Mathematical modelling of blood glucose dynamics in normal and impaired glucose tolerance

Type 2 diabetes mellitus and its preliminary stages are characterised by chronically elevated blood glucose levels, particularly after food intake. Assessing the postprandial glucose metabolism is, therefore, crucial to facilitate appropriate treatment strategies such as dietary interventions. This thesis develops mathematical models for the description of glucose profiles in response to food intake using glucose data alone. These glucose-only models thereby overcome the necessity of measuring insulin which is laborious and unreliable, thus enabling their widespread use in clinical practice. The main purpose of the developed models is the extraction of information on insulin sensitivity and meal-related glucose appearance, both of which have a significant influence on the postprandial glucose response. The extracted information is validated against the results from the established oral minimal model requiring both glucose and insulin data for identification. For both oral minimal and glucose-only models, this work proposes a novel input function for the description of the meal-related glucose appearance. This new function is fully differentiable and more suitable for modelling consecutive meal responses on the same day in comparison to the conventional but highly impractical piecewise-linear function. The models are identified from both a literature dataset and a dataset collected during an experimental study designed and conducted in the context of this work. The latter includes subjects with normal glucose tolerance, prediabetes and type 2 diabetes mellitus and features the use of continuous glucose monitoring. The model identification procedure is carried out using a variational Bayesian technique, which offers an efficient method for the probabilistic treatment of the parameter estimation task. The results demonstrate that the developed glucose-only models can be used to infer information on insulin sensitivity as they contain a parameter highly correlated to the insulin sensitivity inferred from the established oral minimal model. Furthermore, it is shown that the glucose appearance profiles inferred from the glucose only models allow the same interpretation of trends in glucose appearance with respect meal composition as the oral minimal model. Using the information on insulin sensitivity and glucose appearance, the developed models could thus support healthcare professionals in designing effective treatment strategies such as dietary interventions and monitor the disease progression from prediabetes to type 2 diabetes

STOCHASTIC SEASONAL MODELS FOR GLUCOSE PREDICTION IN TYPE 1 DIABETES

[ES] La diabetes es un importante problema de salud mundial, siendo una de las enfermedades no transmisibles más graves después de las enfermedades cardiovasculares, el cáncer y las enfermedades respiratorias crónicas. La prevalencia de la diabetes ha aumentado constantemente en las últimas décadas, especialmente en países de ingresos bajos y medios. Se estima que 425 millones de personas en todo el mundo tenían diabetes en 2017, y para 2045 este número puede aumentar a 629 millones. Alrededor del 10% de las personas con diabetes padecen diabetes tipo 1, caracterizada por una destrucción autoinmune de las células beta en el páncreas, responsables de la secreción de la hormona insulina. Sin insulina, la glucosa plasmática aumenta a niveles nocivos, provocando complicaciones vasculares a largo plazo. Hasta que se encuentre una cura, el manejo de la diabetes depende de los avances tecnológicos para terapias de reemplazo de insulina. Con la llegada de los monitores continuos de glucosa, la tecnología ha evolucionado hacia sistemas automatizados. Acuñados como "páncreas artificial", los dispositivos de control de glucosa en lazo cerrado suponen hoy en día un cambio de juego en el manejo de la diabetes. La investigación en las últimas décadas ha sido intensa, dando lugar al primer sistema comercial a fines de 2017, y muchos más están siendo desarrollados por las principales industrias de dispositivos médicos. Sin embargo, como dispositivo de primera generación, muchos problemas aún permanecen abiertos y nuevos avances tecnológicos conducirán a mejoras del sistema para obtener mejores resultados de control glucémico y reducir la carga del paciente, mejorando significativamente la calidad de vida de las personas con diabetes tipo 1. En el centro de cualquier sistema de páncreas artificial se encuentra la predicción de glucosa, tema abordado en esta tesis. La capacidad de predecir la glucosa a lo largo de un horizonte de predicción dado, y la estimación de las tendencias futuras de glucosa, es la característica más importante de cualquier sistema de páncreas artificial, para poder tomar medidas preventivas que eviten por completo el riesgo para el paciente. La predicción de glucosa puede aparecer como parte del algoritmo de control en sí, como en sistemas basados en técnicas de control predictivo basado en modelo (MPC), o como parte de un sistema de supervisión para evitar episodios de hipoglucemia. Sin embargo, predecir la glucosa es un problema muy desafiante debido a la gran variabilidad inter e intra-sujeto que sufren los pacientes, cuyas fuentes solo se entienden parcialmente. Esto limita las prestaciones predictivas de los modelos, imponiendo horizontes de predicción relativamente cortos, independientemente de la técnica de modelado utilizada (modelos fisiológicos, basados en datos o híbridos). La hipótesis de partida de esta tesis es que la complejidad de la dinámica de la glucosa requiere la capacidad de caracterizar grupos de comportamientos en los datos históricos del paciente que llevan naturalmente al concepto de modelado local. Además, la similitud de las respuestas en un grupo puede aprovecharse aún más para introducir el concepto clásico de estacionalidad en la predicción de glucosa. Como resultado, los modelos locales estacionales están en el centro de esta tesis. Se utilizan varias bases de datos clínicas que incluyen comidas mixtas y ejercicio para demostrar la viabilidad y superioridad de las prestaciones de este enfoque.[CA] La diabetisés un important problema de salut mundial, sent una de les malalties no transmissibles més greus després de les malalties cardiovasculars, el càncer i les malalties respiratòries cròniques. La prevalença de la diabetis ha augmentat constantment en les últimes dècades, especialment en països d'ingressos baixos i mitjans. S'estima que 425 milions de persones a tot el món tenien diabetis en 2017, i per 2045 aquest nombre pot augmentar a 629 milions. Al voltant del 10% de les persones amb diabetis pateixen diabetis tipus 1, caracteritzada per una destrucció autoimmune de les cèl·lules beta en el pàncrees, responsables de la secreció de l'hormona insulina. Sense insulina, la glucosa plasmàtica augmenta a nivells nocius, provocant complicacions vasculars a llarg termini. Fins que es trobi una cura, el maneig de la diabetis depén dels avenços tecnològics per a teràpies de reemplaçament d'insulina. Amb l'arribada dels monitors continus de glucosa, la tecnologia ha evolucionat cap a sistemes automatitzats. Encunyats com "pàncrees artificial", els dispositius de control de glucosa en llaç tancat suposen avui dia un canvi de joc en el maneig de la diabetis. La investigació en les últimes dècades ha estat intensa, donant lloc al primer sistema comercial a finals de 2017, i molts més estan sent desenvolupats per les principals indústries de dispositius mèdics. No obstant això, com a dispositiu de primera generació, molts problemes encara romanen oberts i nous avenços tecnològics conduiran a millores del sistema per obtenir millors resultats de control glucèmic i reduir la càrrega del pacient, millorant significativament la qualitat de vida de les persones amb diabetis tipus 1. Al centre de qualsevol sistema de pàncrees artificial es troba la predicció de glucosa, tema abordat en aquesta tesi. La capacitat de predir la glucosa al llarg d'un horitzó de predicció donat, i l'estimació de les tendències futures de glucosa, és la característica més important de qualsevol sistema de pàncrees artificial, per poder prendre mesures preventives que evitin completament el risc per el pacient. La predicció de glucosa pot aparèixer com a part de l'algoritme de control en si, com en sistemes basats en técniques de control predictiu basat en model (MPC), o com a part d'un sistema de supervisió per evitar episodis d'hipoglucèmia. No obstant això, predir la glucosa és un problema molt desafiant degut a la gran variabilitat inter i intra-subjecte que pateixen els pacients, les fonts només s'entenen parcialment. Això limita les prestacions predictives dels models, imposant horitzons de predicció relativament curts, independentment de la tècnica de modelatge utilitzada (models fisiològics, basats en dades o híbrids). La hipòtesi de partida d'aquesta tesi és que la complexitat de la dinàmica de la glucosa requereix la capacitat de caracteritzar grups de comportaments en les dades històriques del pacient que porten naturalment al concepte de modelatge local. A més, la similitud de les respostes en un grup pot aprofitar-se encara més per introduir el concepte clàssic d'estacionalitat en la predicció de glucosa. Com a resultat, els models locals estacionals estan al centre d'aquesta tesi. S'utilitzen diverses bases de dades clíniques que inclouen menjars mixtes i exercici per demostrar la viabilitat i superioritat de les prestacions d'aquest enfocament.[EN] Diabetes is a significant global health problem, one of the most serious noncommunicable diseases after cardiovascular diseases, cancer and chronic respiratory diseases. Diabetes prevalence has been steadily increasing over the past decades, especially in low- and middle-income countries. It is estimated that 425 million people worldwide had diabetes in 2017, and by 2045 this number may rise to 629 million. About 10% of people with diabetes suffer from type 1 diabetes, characterized by autoimmune destruction of the beta-cells in the pancreas, responsible for the secretion of the hormone insulin. Without insulin, plasma glucose rises to deleterious levels, provoking long-term vascular complications. Until a cure is found, the management of diabetes relies on technological developments for insulin replacement therapies. With the advent of continuous glucose monitors, technology has been evolving towards automated systems. Coined as "artificial pancreas", closed-loop glucose control devices are nowadays a game-changer in diabetes management. Research in the last decades has been intense, yielding a first commercial system in late 2017 and many more are in the pipeline of the main medical devices industry. However, as a first-generation device, many issues still remain open and new technological advancements will lead to system improvements for better glycemic control outputs and reduced patient's burden, improving significantly the quality of life of people with type 1 diabetes. At the core of any artificial pancreas system is glucose prediction, the topic addressed in this thesis. The ability to predict glucose along a given prediction horizon, and estimation of future glucose trends, is the most important feature of any artificial pancreas system, in order to be able to take preventive actions to entirely avoid risk to the patient. Glucose prediction can appear as part of the control algorithm itself, such as in systems based on model predictive control (MPC) techniques, or as part of a monitoring system to avoid hypoglycemic episodes. However, predicting glucose is a very challenging problem due to the large inter- and intra-subject variability that patients suffer, whose sources are only partially understood. These limits models forecasting performance, imposing relatively short prediction horizons, despite the modeling technique used (physiological, data-driven or hybrid approaches). The starting hypothesis of this thesis is that the complexity of glucose dynamics requires the ability to characterize clusters of behaviors in the patient's historical data naturally yielding to the concept of local modeling. Besides, the similarity of responses in a cluster can be further exploited to introduce the classical concept of seasonality into glucose prediction. As a result, seasonal local models are at the core of this thesis. Several clinical databases including mixed meals and exercise are used to demonstrate the feasibility and superiority of the performance of this approach.This work has been supported by the Spanish Ministry of Economy and Competitiveness (MINECO) under the FPI grant BES-2014-069253 and projects DPI2013-46982-C2-1-R and DPI2016-78831-C2-1-R. Moreover, with relation to this grant, a short stay was done at the end of 2017 at the Illinois Institute of Technology, Chicago, United States of America, under the supervision of Prof. Ali Cinar, for four months from 01/09/2017 to 29/12/2017.Montaser Roushdi Ali, E. (2020). STOCHASTIC SEASONAL MODELS FOR GLUCOSE PREDICTION IN TYPE 1 DIABETES [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/136574TESI

Modelling, optimisation and model predictive control of insulin delivery systems in Type 1 Diabetes Mellitus

Type 1 Diabetes Mellitus is a metabolic disease requiring lifelong treatment with exogenous insulin which significantly affects patient’s lifestyle. Therefore, it is of paramount importance to develop novel drug delivery techniques that achieve therapeutic efficacy and ensure patient safety with a minimum impact on their quality of life. Motivated by the challenge to improve the living standard of a diabetic patient, the idea of an artificial pancreas that mimics the endocrine function of a healthy pancreas has been developed in the scientific society. Towards this direction, model predictive control has been established as a very promising control strategy for blood glucose regulation in a system that is dominated by high intra- and inter-patient variability, long time delays, and presence of unknown disturbances such as diet, physical activity and stress levels. This thesis presents a framework for blood glucose regulation with optimal insulin infusion which consists of the following steps: 1. Development of a novel physiologically based compartmental model analysed up to organ level that describes glucose-insulin interactions in type 1 diabetes, 2. Derivation of an approximate model suitable for control applications, 3. Design of an appropriate control strategy and 4. In-silico validation of the closed loop control performance. The developed model’s accuracy and prediction ability is evaluated with data obtained from the literature and the UVa/Padova Simulator model, the model parameters are individually estimated and their effect on the model’s measured output, the blood glucose concentration, is identified. The model is then linearised and reduced to derive low-order linear approximations of the underlying system suitable for control applications. The proposed control design aims towards an individualised optimal insulin delivery that consists of a patient-specific model predictive controller, a state estimator, a personalised scheduling level and an open loop optimisation problem subjected to patient specific process model and constraints. This control design is modifiable to address the case of limited patient data availability resulting in an “approximation” control strategy. Both designs are validated in-silico in the presence of predefined, measured and unknown meal disturbances using both the proposed model and the UVa/Padova Simulator model as a virtual patient. The robustness of the control performance is evaluated in several conditions such as skipped meals, variability in the meal content, time and metabolic uncertainty. The simulation results of the closed loop validation studies indicate that the proposed control strategies can achieve promising glycaemic control as demonstrated by the study data. However, further prospective validation of the closed loop control strategy with real patient data is required.Open Acces

Mathematical modelling of immune condition dynamics : a clinical perspective

This thesis describes the use of mathematical modelling to analyse the treatment of patients with immune disorders; namely, Multiple Myeloma, a cancer of plasma cells that create excess monoclonal antibody; and kidney transplants, where the immune system produces polygonal antibodies against the implanted organ. Linear and nonlinear compartmental models play an important role in the analysis of biomedical systems; in this thesis several models are developed to describe the in vivo kinetics of the antibodies that are prevalent for the two disorders studied. These models are validated against patient data supplied by clinical collaborators. Through this validation process important information regarding the dynamic properties of the clinical treatment can be gathered. In order to treat patients with excess immune antibodies the clinical staff wish to reduce these high levels in the patient to near healthy concentrations. To achieve this they have two possible treatment modalities: either using artificial methods to clear the material, a process known as apheresis, or drug therapy to reduce the production of the antibody in question. Apheresis techniques differ in their ability to clear different immune complexes; the effectiveness of a range of apheresis techniques is categorised for several antibody types and antibody fragments. The models developed are then used to predict the patient response to alternative treatment methods, and schedules, to find optimal combinations. In addition, improved measurement techniques that may offer an improved diagnosis are suggested. Whilst the overall effect of drug therapy is known, through measuring the concentration of antibodies in the patient’s blood, the short-term relationship between drug application and reduction in antibody synthesis is still not well defined; therefore, methods to estimate the generation rate of the immune complex, without the need for invasive procedures, are also presented