Direct Transcription for Dynamic Optimization: A Tutorial with a Case Study on Dual-Patient Ventilation During the COVID-19 Pandemic

TL;DR

This paper reviews numerical transcription methods for continuous-time dynamic optimization and demonstrates their application in a COVID-19 related case study on dual-patient ventilation, showing potential for efficient, individualized ventilator control.

Contribution

It provides a unified overview of transcription techniques and applies them to a novel case study, illustrating their practical use in complex biomedical problems.

Findings

Feasibility of estimating individual patient parameters with few measurements

Possibility of ventilating multiple patients with a single ventilator

Control strategies to ensure desired tidal volumes for each patient

Abstract

A variety of optimal control, estimation, system identification and design problems can be formulated as functional optimization problems with differential equality and inequality constraints. Since these problems are infinite-dimensional and often do not have a known analytical solution, one has to resort to numerical methods to compute an approximate solution. This paper uses a unifying notation to outline some of the techniques used in the transcription step of simultaneous direct methods (which discretize-then-optimize) for solving continuous-time dynamic optimization problems. We focus on collocation, integrated residual and Runge-Kutta schemes. These transcription methods are then applied to a simulation case study to answer a question that arose during the COVID-19 pandemic, namely: If there are not enough ventilators, is it possible to ventilate more than one patient on a single ventilator? The results suggest that it is possible, in principle, to estimate individual patient parameters sufficiently accurately, using a relatively small number of flow rate measurements, without needing to disconnect a patient from the system or needing more than one flow rate sensor. We also show that it is possible to ensure that two different patients can indeed receive their desired tidal volume, by modifying the resistance experienced by the air flow to each patient and controlling the ventilator pressure.