Optimal bang-bang ventilation under mechanical cycle closure: a reduced lung gas-exchange model
Abstract
Many reduced and control-oriented respiratory models prescribe a ventilatory waveform. Here we ask a narrower inverse question: once cycle duration and mechanical closure are fixed, what ventilation pattern maximizes a reduced oxygen-transfer criterion? We study a minimal 0D model coupling global lung deformation to alveolar oxygen concentration. Under explicit quantitative and nondegeneracy assumptions, every optimal control is bang-bang with exactly two switchings, producing one inflation phase followed by one deflation phase. Thus optimality selects the internal two phase inspiration-expiration organization. The concentration of oxygen is not impose at the beginning and the end of a cycle. We prove that repetition of a fixed mechanical cycle induces a unique stable periodic concentration regime, where the concentration at the beginning and the end remains the same. Numerical simulations recover the two-switch structure for the nominal parameter set and indicate its persistence in a linear viscoelastic extension.
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BibTeX
@misc{jaba2026optimal,
title = {{Optimal bang-bang ventilation under mechanical cycle closure: a reduced lung gas-exchange model}},
author = {Mabrouk Ben Jaba and Yannick Privat and Jean-François Scheid and Zakaria Belhachmi and Benjamin Mauroy},
howpublished = {HAL},
year = {2026},
month = sep,
url = {https://hal.science/hal-05768458v1},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Optimal bang-bang ventilation under mechanical cycle closure: a reduced lung gas-exchange model
AU - Mabrouk Ben Jaba
AU - Yannick Privat
AU - Jean-François Scheid
AU - Zakaria Belhachmi
AU - Benjamin Mauroy
PY - 2026
DA - 2026/09/29
PB - HAL
UR - https://hal.science/hal-05768458v1
AB - Many reduced and control-oriented respiratory models prescribe a ventilatory waveform. Here we ask a narrower inverse question: once cycle duration and mechanical closure are fixed, what ventilation pattern maximizes a reduced oxygen-transfer criterion? We study a minimal 0D model coupling global lung deformation to alveolar oxygen concentration. Under explicit quantitative and nondegeneracy assumptions, every optimal control is bang-bang with exactly two switchings, producing one inflation phase followed by one deflation phase. Thus optimality selects the internal two phase inspiration-expiration organization. The concentration of oxygen is not impose at the beginning and the end of a cycle. We prove that repetition of a fixed mechanical cycle induces a unique stable periodic concentration regime, where the concentration at the beginning and the end remains the same. Numerical simulations recover the two-switch structure for the nominal parameter set and indicate its persistence in a linear viscoelastic extension.
ER -