Mathematical Modeling in Systems Medicine: New Paradigms for Glucose Control in Critical Care

Stress hyperglycemia occurs frequently in critical care patients and many of the harmful repercussions may be mitigated by maintaining glucose within a ``healthy'' zone. While the exact range of the zone varies, glucose below 80 $mg/dl$ or above 130 $mg/dl$ increases risk of mortality. Zone glucose control (ZGC) is accomplished primarily using insulin administration to reduce hyperglycemia. Alternatively, we propose also allowing glucose administration to be used to raise blood glucose and avoid hypoglycemia. While there have been attempts to create improved paradigms for treatment of stress hyperglycemia, inconsistencies in glycemic control protocols as well as variation in outcomes for different ICU subpopulations has contributed to the mixed success of glucose control in critical care and subsequent disagreement regarding treatment protocols. Therefore, a more accurate, personalized treatment that is tailored to an individual may significantly improve patient outcome. The most promising method to achieve better control using a personalized strategy is through the use of a model-based decision support system (DSS), wherein a mathematical patient model is coupled with a controller and user interface that provides for semi-automatic control under the supervision of a clinician. Much of the error and subsequent failure to control blood glucose comes from the failure to resolve inter- and intrapatient variations in glucose dynamics following insulin administration. The observed variation arises from the many biologically pathways that affect insulin signaling for patients in the ICU. Mathematical modeling of the biological pathways of stress hyperglycemia can improve understanding and treatment. Trauma and infection lead to the development of systemic insulin resistance and elevated blood glucose levels associated with stress hyperglycemia. We develop mathematical models of the biological signaling pathways driving fluctuations in insulin sensitivity and resistance. Key metabolic mediators from the inflammatory response and counterregulatory response are mathematically represented acting on insulin-mediated effects causing increases or decreases in blood glucose concentration. Data from published human studies are used to calibrate a composite model of glucose and insulin dynamics augmented with biomarkers relevant to critical care. The resulting mathematical description of the underlying mechanisms of insulin resistance could be used in a model-based decision support system to estimate patient-specific metabolic status and provide more accurate insulin treatment and glucose control for critical care patients

Metaheuristic optimization of insulin infusion protocols using historical data with validation using a patient simulator

Metaheuristic search algorithms are used to develop new protocols for optimal intravenous insulin infusion rate recommendations in scenarios involving hospital in-patients with Type 1 Diabetes. Two metaheuristic search algorithms are used, namely, Particle Swarm Optimization and Covariance Matrix Adaption Evolution Strategy. The Glucose Regulation for Intensive Care Patients (GRIP) serves as the starting point of the optimization process. We base our experiments on a methodology in the literature to evaluate the favorability of insulin protocols, with a dataset of blood glucose level/insulin infusion rate time series records from 16 patients obtained from the Waikato District Health Board. New and significantly better insulin infusion strategies than GRIP are discovered from the data through metaheuristic search. The newly discovered strategies are further validated and show good performance against various competitive benchmarks using a virtual patient simulator

Machine Learning for Physiological Time Series: Representing and Controlling Blood Glucose for Diabetes Management

Type 1 diabetes is a chronic health condition affecting over one million patients in the US, where blood glucose (sugar) levels are not well regulated by the body. Researchers have sought to use physiological data (e.g., blood glucose measurements) collected from wearable devices to manage this disease, either by forecasting future blood glucose levels for predictive alarms, or by automating insulin delivery for blood glucose management. However, the application of machine learning (ML) to these data is hampered by latent context, limited supervision and complex temporal dependencies. To address these challenges, we develop and evaluate novel ML approaches in the context of i) representing physiological time series, particularly for forecasting blood glucose values and ii) decision making for when and how much insulin to deliver. When learning representations, we leverage the structure of the physiological sequence as an implicit information stream. In particular, we a) incorporate latent context when predicting adverse events by jointly modeling patterns in the data and the context those patterns occurred under, b) propose novel types of self-supervision to handle limited data and c) propose deep models that predict functions underlying trajectories to encode temporal dependencies. In the context of decision making, we use reinforcement learning (RL) for blood glucose management. Through the use of an FDA-approved simulator of the glucoregulatory system, we achieve strong performance using deep RL with and without human intervention. However, the success of RL typically depends on realistic simulators or experimental real-world deployment, neither of which are currently practical for problems in health. Thus, we propose techniques for leveraging imperfect simulators and observational data. Beyond diabetes, representing and managing physiological signals is an important problem. By adapting techniques to better leverage the structure inherent in the data we can help overcome these challenges.PHDComputer Science & EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/163134/1/ifox_1.pd

Real-world evidence for the management of blood glucose in the intensive care unit

Glycaemic control is a core aspect of patient management in the intensive care unit (ICU). Blood glucose has a well-known U-shaped relationship with mortality and morbidity in ICU patients, with both hypo- and hyper-glycaemia associated with poor patient outcomes. As a result, up to 40-90% of ICU patients receive insulin, depending on illness severity and variation in clinical practice. Generally, clinical guidelines for glycaemic control are based on a series of trials that culminated in the NICE-SUGAR study in 2009, a multicentre study demonstrating that tight glycaemic control (a target of 80-110 mg/dL) did not improve patient outcomes compared to moderate control (<180 mg/dL). However, there remain open questions around the potential for more personalised blood glucose management, which real-world evidence sources such as electronic medical records (EMRs) can play a role in answering. This thesis investigates the role that EMRs can play in glycaemic control in the ICU using open access EMR databases, covering a heterogenous 208 hospital USA based patient cohort (the eICU collaborative research database, eICU-CRD) and a large tertiary medical centre in Boston, USA (MIMIC-III and MIMIC-IV). This thesis covers: i) curation and characterisation of the eICU-CRD cohort as a data resource for real-world evidence in glycaemic control; ii) investigation of whether blood lactate modifies the relationship between blood glucose and patient outcome across different subgroups; and iii) the development and comparison of machine learning and deep learning probabilistic forecasting algorithms for blood glucose. The analysis of the eICU-CRD demonstrated that there is wide variety in clinical practice around glycaemic control in the ICU. The results enable comparison with other data resources and assessment of the suitability of the eICU-CRD for addressing specific research questions related to glycaemic control and nutrition support. Informed by this descriptive analysis, the eICU-CRD was used to examine whether blood lactate modifies the relationship between blood glucose and patient outcome across different subgroups. While adjustment for blood lactate attenuated the relationship between blood glucose and patient outcome, blood glucose remained a marker of poor prognosis. Diabetic status was found to influence this relationship, in line with increasing evidence that diabetics and non-diabetics should be considered distinct populations for the purpose of glycaemic control in the ICU. The forecasting algorithms developed using MIMIC-III and MIMIC-IV were designed to account for the intrinsic statistical difficulties present in EMRs. These include large numbers of potentially sparsely and irregularly measured input variables. The focus was on development of probabilistic approaches given the measurement error in blood glucose measures, and their potential conversion into categorical forecasts if required. Two alternative approaches were proposed. The first was to use gradient boosted tree (GBT) algorithms, along with extensive feature engineering. The second was to use continuous time recurrent neural networks (CTRNNs), which learn their own hidden features and account for irregular measurements through evolving the model hidden state using continuous time dynamics. However, several CTRNN architectures are outperformed by an autoregressive GBT model (Catboost), with only a long short-term memory (LSTM) and neural ODE based architecture (ODE-LSTM) achieving comparable performance on probabilistic forecasting metrics such as the continuous ranked probability score (ODE-LSTM: 0.118±0.001; Catboost: 0.118±0.001), ignorance score (0.152±0.008; 0.149±0.002) and interval score (175±1; 176±1). Further, the GBT method was far easier and faster to train, highlighting the importance of using appropriate non-deep learning benchmarks in the academic literature on novel statistical methodologies for analysis of EMRs. The findings highlight that EMRs are a valuable resource in medical evidence generation and characterisation of current clinical practice. Future research should aim to continue investigation of subgroup differences and utilise the forecasting algorithms as part of broader goals such as development of personalised insulin recommendation algorithms

Mathematical Models for Optimisation of Drug Administration in Intensive Care Units

Clinical status of critically ill patients is often extreme and rapidly evolving. Hence, pharmacological therapies must be tailored to patients' characteristics and adapted according to the evolution of their clinical pictures. To identify optimal personalized treatments, possible scenarios produced by different therapeutic choices must be predicted and compared. This process requires complex analyses involving the development of appropriate mathematical models. In this Thesis, I focused on two important aspects of the pharmacological treatment of critically ill patients: the administration of antimicrobial drugs and the control of their glycaemic level. Although these problems are clinically very different, the modelling of their pathophysiological mechanisms can be addressed with similar tools. I performed analyses based on retrospective clinical data collected with MargheritaTre, an electronic health record developed by GiViTI. The software to synchronize databases from hospitals to our laboratory and to preprocess data for analyses was written for the purpose of this Thesis. Starting from the study of the physiological mechanisms at the basis of vancomycin pharmacokinetics I constructed a model to describe the evolution of the plasma concentration of this drug in critically ill patients. Compartment models were fitted on a sample of 141 patients, testing about 30 patient covariates and several functional dependencies for each variable. Glucose dynamics were described through a system of delay differential equations reproducing intake, uptake and endogenous production of glucose, and organ-organ interactions mediated by hormones. Existing models, describing only the dynamics of glucose and insulin, fail to reproduce the correct evolution when glucose concentrations vary too rapidly. I improved these models, by introducing an equation describing glucagon dynamics and taking into account its effect on glucose metabolism. I investigated the dynamical properties of my model with analytical analyses, numerical simulations and fitting it to observed data

A model-based clinically-relevant chemotherapy scheduling algorithm for anticancer agents

Chemotherapy is the most commonly employed method for systemic cancer treatment of solid tumors and their metastases. The balance between cancer cell elimination and host toxicity minimization remains a challenge for clinicians when deploying chemotherapy treatments. Our approach explicitly incorporates treatment-induced toxicities into the schedule design. As a case study, we synthesize administration schedules for docetaxel, a widely used chemotherapeutic employed as a monoagent or in combination for the treatment of a variety of cancers. The primary adverse effect of docetaxel treatment is myelosuppression, characterized by neutropenia, a low plasma absolute neutrophil count (ANC). Through the use of model-based systems engineering tools, this thesis provides treatment schedules for docetaxel and its combination therapies that reduce toxic side effects and improve patient outcomes. The current algorithm employs models of tumor growth, drug pharmacokinetics, and pharmacodynamics for both anticancer effects and toxicity, as characterized by ANC. Also included is a toxicity-rescue therapy, with granulocyte colony stimulating factor (G-CSF) that serves to elevate ANC. The single-agent docetaxel chemotherapy schedule minimizes tumor volume over a multi-cycle horizon, subject to toxicity and logistical constraints imposed by clinical practice.This single-agent chemotherapy scheduling formulation is extended to combination chemotherapy using docetaxel-cisplatin or docetaxel-carboplatin drug pairs. The two platinum agents display different toxicities, with cisplatin exhibiting kidney function damage and carboplatin demonstrating the same myelosuppression effects as docetaxel. These case studies provide two different challenges to the algorithm: (i) cisplatin scheduling significantly increases the number of variables and constraints, thereby challenging the computational engine and formulation; (ii) carboplatin's overlapping toxicity tests the ability of the algorithm to schedule drugs with different mechanisms of action (they act in different phases of the cellular growth cycle) with the same toxic side effects. The simulated results demonstrate the algorithms flexibility, in scheduling both docetaxel and cisplatin or carboplatin treatments for effective tumor elimination and clinically acceptable toxicties. Overall, a clinically-relevant chemotherapy scheduling optimization algorithm is provided for designing single agent and combination chemotherapies, when toxicity and pharmacokinetic/pharmacodynamic information is available. Furthermore, the algorithm can be extended to patient-specfic treatment by updating the pharmacokinetic/pharmacodynamic models as data are collected during treatment

A Discrete-Event Simulation Approach for Modeling Human Body Glucose Metabolism

This dissertation describes CarbMetSim (Carbohydrate Metabolism Simulator), a discrete-event simulator that tracks the blood glucose level of a person in response to a timed sequence of diet and exercise activities. CarbMetSim implements broader aspects of carbohydrate metabolism in human beings with the objective of capturing the average impact of various diet/exercise activities on the blood glucose level. Key organs (stomach, intestine, portal vein, liver, kidney, muscles, adipose tissue, brain and heart) are implemented to the extent necessary to capture their impact on the production and consumption of glucose. Key metabolic pathways (glucose oxidation, glycolysis and gluconeogenesis) are accounted for by using the published values of the average flux along these pathways in the operation of different organs. CarbMetSim has the ability to model different levels of insulin resistance and insulin production ability. The impact of insulin and insulin resistance on the operation of various organs and pathways is captured in accordance with published research. The protein and lipid metabolism are implemented only to the extent that they affect carbohydrate metabolism

Annals of Intensive Care

peer reviewe