arXiv subjects

Tobias K. S. Ritschel

Publications and source records attributed to Tobias K. S. Ritschel.

28 records · Page 2Linked to original sources

arXiv2022

Large-scale Virtual Clinical Trials of Closed-loop Treatments for People with Type 1 Diabetes

We propose a virtual clinical trial for assessing the safety and efficacy of closed-loop diabetes treatments prior to an actual clinical trial. Such virtual trials enable rapid and risk-free pretrial testing of algorithms, and they can be used to compare different treatment variations for large and diverse populations. The participants are represented by multiple mathematical models, consisting of stochastic differential equations, and we use Monte Carlo closed-loop simulations to compute detailed statistics of the closed-loop treatments. We implement the virtual clinical trial using high-performance software and hardware, and we present an example trial with two mathematical models of one~million participants over 52~weeks (i.e., two~million simulations), which can be completed in 2~h 9~min.

math.OC↗

arXiv2022

A whole-body multi-scale mathematical model for dynamic simulation of the metabolism in man

We propose a whole-body model of the metabolism in man as well as a generalized approach for modeling metabolic networks. Using this approach, we are able to write a large metabolic network in a systematic and compact way. We demonstrate the approach using a whole-body model of the metabolism of the three macronutrients, carbohydrates, proteins and lipids. The model contains 7 organs, 16 metabolites and 31 enzymatic reactions. All reaction rates are described by Michaelis-Menten kinetics with an addition of a hormonal regulator based on the two hormones insulin and glucagon. We incorporate ingestion of food in order to simulate metabolite concentrations during the feed-fast cycle. The model can simulate several days due to the inclusion of storage forms (glycogen, muscle protein and lipid droplets), that can be depleted if food is not ingested regularly. A physiological model incorporating complex cellular metabolism and whole-body mass dynamics can be used in virtual clinical trials. Such trials can be used to improve the development of medicine, treatment strategies such as control algorithms, and increase the likelihood of a successful clinical trial.

q-bio.QM↗

arXiv2022

High-performance Uncertainty Quantification in Large-scale Virtual Clinical Trials of Closed-loop Diabetes Treatment

In this paper, we propose a virtual clinical trial for assessing the performance and identifying risks in closed-loop diabetes treatments. Virtual clinical trials enable fast and risk-free tests of many treatment variations for large populations of fictive patients (represented by mathematical models). We use closed-loop Monte Carlo simulation, implemented in high-performance software and hardware, to quantify the uncertainty in treatment performance as well as to compare the performance in different scenarios or of different closed-loop treatments. Our software can be used for testing a wide variety of control strategies ranging from heuristical approaches to nonlinear model predictive control. We present an example of a virtual clinical trial with one million patients over 52 weeks, and we use high-performance software and hardware to conduct the virtual trial in 1 h and 22 min.

math.OC↗

arXiv2022

Nonlinear Model Predictive Control and System Identification for a Dual-hormone Artificial Pancreas

In this work, we present a switching nonlinear model predictive control (NMPC) algorithm for a dual-hormone artificial pancreas (AP), and we use maximum likelihood estimation (MLE) to identify model parameters. A dual-hormone AP consists of a continuous glucose monitor (CGM), a control algorithm, an insulin pump, and a glucagon pump. The AP is designed with a heuristic to switch between insulin and glucagon as well as state-dependent constraints. We extend an existing glucoregulatory model with glucagon and exercise for simulation, and we use a simpler model for control. We test the AP (NMPC and MLE) using in silico numerical simulations on 50 virtual people with type 1 diabetes. The system is identified for each virtual person based on data generated with the simulation model. The simulations show a mean of 89.3% time in range (3.9-10 mmol/L) and no hypoglycemic events.

math.OC↗

arXiv2022

A one-size-fits-all artificial pancreas for people with type 1 diabetes based on physiological insight and feedback control

We propose a model-free artificial pancreas (AP) for people with type 1 diabetes. The algorithmic parameters are tuned to a virtual population of 1,000,000 individuals, and the AP repeatedly estimates the basal and bolus insulin requirements necessary for maintaining normal blood glucose levels. Therefore, the AP can be used without healthcare personnel or engineers customizing the algorithm to each user. The estimates are based on bodyweight, measurements from a continuous glucose monitor (CGM), and estimates of the meal carbohydrate contents. In a virtual clinical trial with all 1,000,000 individuals (i.e., a Monte Carlo closed-loop simulation), the AP achieves a mean time in range of more than 87% and almost 89% of the participants satisfy several glycemic targets.

math.OC↗

arXiv2021

How to coordinate vaccination and social distancing to mitigate SARS-CoV-2 outbreaks

Most countries have started vaccinating people against COVID-19. However, due to limited production capacities and logistical challenges it will take months/years until herd immunity is achieved. Therefore, vaccination and social distancing have to be coordinated. In this paper, we provide some insight on this topic using optimization-based control on an age-differentiated compartmental model. For real-life decision making, we investigate the impact of the planning horizon on the optimal vaccination/social distancing strategy. We find that in order to reduce social distancing in the long run, without overburdening the healthcare system, it is essential to vaccinate the people with the highest contact rates first. That is also the case if the objective is to minimize fatalities provided that the social distancing measures are sufficiently strict. However, for short-term planning it is optimal to focus on the high-risk group.

physics.soc-ph↗

arXiv2020

How much testing and social distancing is required to control COVID-19? Some insight based on an age-differentiated compartmental model

In this paper, we provide insights on how much testing and social distancing is required to control COVID-19. To this end, we develop a compartmental model that accounts for key aspects of the disease: 1) incubation time, 2) age-dependent symptom severity, and 3) testing and hospitalization delays; the model's parameters are chosen based on medical evidence, and, for concreteness, adapted to the German situation. Then, optimal mass-testing and age-dependent social-distancing policies are determined by solving optimal control problems both in open loop and within a model predictive control framework. We aim to minimize testing and/or social distancing until herd immunity sets in under a constraint on the number of available intensive care units. We find that an early and short lockdown is inevitable but can be slowly relaxed over the following months.

math.OC↗

arXiv2020

Nonlinear model reduction of dynamical power grid models using quadratization and balanced truncation

In this work, we present a nonlinear model reduction approach for reducing two commonly used nonlinear dynamical models of power grids: the effective network (EN) model and the synchronous motor (SM) model. Such models are essential in real-time security assessments of power grids. However, as power grids are often large-scale, it is necessary to reduce the models in order to utilize them in real-time. We reformulate the nonlinear power grid models as quadratic systems and reduce them using balanced truncation based on approximations of the reachability and observability Gramians. Finally, we present examples involving numerical simulation of reduced EN and SM models of the IEEE 57 bus and IEEE 118 bus systems.

eess.SY↗

arXiv2019

Filtering and Prediction of the Blood Glucose Concentration using an Android Smart Phone and a Continuous Glucose Monitor

In this paper we numerically assess the performance of Java linear algebra libraries for the implementation of nonlinear filters in an Android smart phone (Samsung A5 2017). We implemented a linear Kalman filter (KF), an extended Kalman filter (EKF), and an unscented Kalman filter (UKF). These filters are used for state and parameter estimation, as well as fault detection and meal detection in an artificial pancreas. We present the state estimation technologies used for glucose estimation based on a continuous glucose monitor (CGM). We compared three linear algebra libraries: The Efficient Java Matrix Library (EJML), JAMA and Apache Common Math. Overall, EJML provides the best performance for linear algebra operations. We demonstrate the implementation and performance of filtering (KF, EKF and UKF) using real CGM data.

math.OC↗

arXiv2018

Dynamic Optimization of Thermodynamically Rigorous Models of Multiphase Flow in Porous Subsurface Oil Reservoirs

In this paper, we consider dynamic optimization of thermal and isothermal oil recovery processes which involve multicomponent three-phase flow in porous media. We present thermodynamically rigorous models of these processes based on 1) conservation of mass and energy, and 2) phase equilibrium. The conservation equations are partial differential equations. The phase equilibrium problems that are relevant to thermal and isothermal models are called the UV and the VT flash, and they are based on the second law of thermodynamics. We formulate these phase equilibrium problems as optimization problems and the phase equilibrium conditions as the corresponding first order optimality conditions. We demonstrate that the thermal and isothermal flow models are in a semi-explicit differential-algebraic form, and we solve the dynamic optimization problems with a previously developed gradient-based algorithm implemented in C/C++. We present numerical examples of optimized thermal and isothermal oil recovery strategies and discuss the computational performance of the dynamic optimization algorithm in these examples.

math.OC↗