A Novel Mixed Finite/Infinite Dimensional Port–Hamiltonian Model of a Mechanical Ventilator
Authors
Milka C. I. Madahana, John E. D. Ekoru, Otis T. C. Nyandoro
Abstract
Mechanical ventilation is a life-saving treatment for critically ill patients who are struggling to breathe independently due to injury or disease. Globally, per year, there has always been a large number of individuals who have required mechanical ventilation. The COVID-19 pandemic brought to light the significance of mechanical ventilation, which played a significant role in sustaining COVID-19-infected critically ill patients who could not breathe on their own. The pandemic drew the attention of the world to the shortage of ventilators globally. Some of the challenges to providing an adequate number of ventilators include: increased demand for ventilators, supply chain disruptions, manufacturing constraints, distribution inequalities, financial constraints, maintenance and logistics difficulties, training and expertise shortages, and the lack of design and development of affordable mechanical ventilators that satisfy the stipulated requirements. This research work presents the formulation of a detailed Port–Hamiltonian model of a mechanical ventilator integrated with the human respiratory system. The interconnection and coupling conditions for the various subsystems within the mechanical ventilator and the coupling between the mechanical ventilator and the human respiratory system are also presented. Structure-preserving discretization is provided alongside numerical simulations and results. The obtained results are found to be comparable to results presented in the literature. Future work will include the design of suitable controllers for the system.
Citation
- Journal: Computation
- Year: 2024
- Volume: 12
- Issue: 8
- Pages: 155
- Publisher: MDPI AG
- DOI: 10.3390/computation12080155
BibTeX
@article{Madahana_2024,
title={{A Novel Mixed Finite/Infinite Dimensional Port–Hamiltonian Model of a Mechanical Ventilator}},
volume={12},
ISSN={2079-3197},
DOI={10.3390/computation12080155},
number={8},
journal={Computation},
publisher={MDPI AG},
author={Madahana, Milka C. I. and Ekoru, John E. D. and Nyandoro, Otis T. C.},
year={2024},
pages={155}
}
References
- Rubio, J. et al. COVOX: Providing oxygen during the COVID-19 health emergency. HardwareX vol. 13 e00383 (2023) – 10.1016/j.ohx.2022.e00383
- HICKLING, K. G. The Pressure–Volume Curve Is Greatly Modified by Recruitment. American Journal of Respiratory and Critical Care Medicine vol. 158 194–202 (1998) – 10.1164/ajrccm.158.1.9708049
- Bates, J. H. T. Lung Mechanics. (2009) doi:10.1017/cbo9780511627156 – 10.1017/cbo9780511627156
- Maury, B. The Respiratory System in Equations. (Springer Milan, 2013). doi:10.1007/978-88-470-5214-7 – 10.1007/978-88-470-5214-7
- Burrowes, K. S., Hunter, P. J. & Tawhai, M. H. Anatomically based finite element models of the human pulmonary arterial and venous trees including supernumerary vessels. Journal of Applied Physiology vol. 99 731–738 (2005) – 10.1152/japplphysiol.01033.2004
- Tawhai, M. H. & Bates, J. H. T. Multi-scale lung modeling. Journal of Applied Physiology vol. 110 1466–1472 (2011) – 10.1152/japplphysiol.01289.2010
- Berger, Understanding the Interdependence Between Parenchymal Deformation and Ventilation In Obstructive Lung Disease. B30. Dynamics of Airway Narrowing in Asthma: Still Misunderstood? (2014)
- Roth, C. J., Yoshihara, L., Ismail, M. & Wall, W. A. Computational modelling of the respiratory system: Discussion of coupled modelling approaches and two recent extensions. Computer Methods in Applied Mechanics and Engineering vol. 314 473–493 (2017) – 10.1016/j.cma.2016.08.010
- Tran, A. S., Thinh Ngo, H. Q., Dong, V. K. & Vo, A. H. Design, Control, Modeling, and Simulation of Mechanical Ventilator for Respiratory Support. Mathematical Problems in Engineering vol. 2021 1–15 (2021) – 10.1155/2021/2499804
- El-Hadj, A. et al. Design and simulation of mechanical ventilators. Chaos, Solitons & Fractals vol. 150 111169 (2021) – 10.1016/j.chaos.2021.111169
- Tharion, J., Kapil, S., Muthu, N., Tharion, J. G. & Kanagaraj, S. Rapid Manufacturable Ventilator for Respiratory Emergencies of COVID-19 Disease. Transactions of the Indian National Academy of Engineering vol. 5 373–378 (2020) – 10.1007/s41403-020-00118-6
- Pivik, W. J., Clayton, G. M., Jones, G. F. & Nataraj, C. Dynamic Modeling of a Low-cost Mechanical Ventilator. IFAC-PapersOnLine vol. 55 81–85 (2022) – 10.1016/j.ifacol.2022.11.165
- Al-Naggar, N. Q. Modelling and Simulation of Pressure Controlled Mechanical Ventilation System. Journal of Biomedical Science and Engineering vol. 08 707–716 (2015) – 10.4236/jbise.2015.810068
- Shi, Y., Ren, S., Cai, M. & Xu, W. Modelling and Simulation of Volume Controlled Mechanical Ventilation System. Mathematical Problems in Engineering vol. 2014 (2014) – 10.1155/2014/271053
- Al-Naggar, N. Q., Al-Hetari, H. Y. & Al-Akwaa, F. M. Simulation of Mathematical Model for Lung and Mechanical Ventilation. Journal of Science and Technology vol. 21 1–9 (2016) – 10.20428/jst.v21i1.1017
- Giri, J., Kshirsagar, N. & Wanjari, A. Design and simulation of AI-based low-cost mechanical ventilator: An approach. Materials Today: Proceedings vol. 47 5886–5891 (2021) – 10.1016/j.matpr.2021.04.369
- Hannon, D. M. et al. Modeling Mechanical Ventilation In Silico—Potential and Pitfalls. Seminars in Respiratory and Critical Care Medicine vol. 43 335–345 (2022) – 10.1055/s-0042-1744446
- Mehedi, I. M., Shah, H. S. M., Al-Saggaf, U. M., Mansouri, R. & Bettayeb, M. Fuzzy PID Control for Respiratory Systems. Journal of Healthcare Engineering vol. 2021 1–6 (2021) – 10.1155/2021/7118711
- Mehrmann, V. & Unger, B. Control of port-Hamiltonian differential-algebraic systems and applications. Acta Numerica vol. 32 395–515 (2023) – 10.1017/s0962492922000083
- van der Schaft, A. Port-Hamiltonian Modeling for Control. Annual Review of Control, Robotics, and Autonomous Systems vol. 3 393–416 (2020) – 10.1146/annurev-control-081219-092250
- Le Gorrec, Y., Zwart, H. & Maschke, B. Dirac structures and Boundary Control Systems associated with Skew-Symmetric Differential Operators. SIAM Journal on Control and Optimization vol. 44 1864–1892 (2005) – 10.1137/040611677
- van der Schaft, A. J. & Maschke, B. M. Hamiltonian formulation of distributed-parameter systems with boundary energy flow. Journal of Geometry and Physics vol. 42 166–194 (2002) – 10.1016/s0393-0440(01)00083-3
- Kamiński, Z. A simplified lumped parameter model for pneumatic tubes. Mathematical and Computer Modelling of Dynamical Systems vol. 23 523–535 (2017) – 10.1080/13873954.2017.1280512
- Albanese, A., Cheng, L., Ursino, M. & Chbat, N. W. An integrated mathematical model of the human cardiopulmonary system: model development. American Journal of Physiology-Heart and Circulatory Physiology vol. 310 H899–H921 (2016) – 10.1152/ajpheart.00230.2014
- Bondy, J. A. & Murty, U. S. R. Graph Theory with Applications. (Macmillan Education UK, 1976). doi:10.1007/978-1-349-03521-2 – 10.1007/978-1-349-03521-2
- Taghizadeh, M., Ghaffari, A. & Najafi, F. Modeling and identification of a solenoid valve for PWM control applications. Comptes Rendus. Mécanique vol. 337 131–140 (2009) – 10.1016/j.crme.2009.03.009