{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:19:27Z","timestamp":1760145567436,"version":"build-2065373602"},"reference-count":28,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2024,7,31]],"date-time":"2024-07-31T00:00:00Z","timestamp":1722384000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"School of Mining, Faculty of Engineering, and the Built Environment, University of the Witwatersrand"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>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\u2013Hamiltonian 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.<\/jats:p>","DOI":"10.3390\/computation12080155","type":"journal-article","created":{"date-parts":[[2024,7,31]],"date-time":"2024-07-31T17:16:49Z","timestamp":1722446209000},"page":"155","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["A Novel Mixed Finite\/Infinite Dimensional Port\u2013Hamiltonian Model of a Mechanical Ventilator"],"prefix":"10.3390","volume":"12","author":[{"given":"Milka C. I.","family":"Madahana","sequence":"first","affiliation":[{"name":"School of Mining Engineering, University of the Witwatersrand, 2nd Floor, ARM Building, 1 Jan Smuts Avenue, Braamfontein, Johannesburg 2017, South Africa"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"John E. D.","family":"Ekoru","sequence":"additional","affiliation":[{"name":"School of Electrical and Information Engineering, University of the Witwatersrand, 2nd Floor, ARM Building, 1 Jan Smuts Avenue, Braamfontein, Johannesburg 2017, South Africa"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Otis T. C.","family":"Nyandoro","sequence":"additional","affiliation":[{"name":"School of Electrical and Information Engineering, University of the Witwatersrand, 2nd Floor, ARM Building, 1 Jan Smuts Avenue, Braamfontein, Johannesburg 2017, South Africa"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,7,31]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"e00383","DOI":"10.1016\/j.ohx.2022.e00383","article-title":"COVOX: Providing oxygen during the COVID-19 health emergency","volume":"13","author":"Rubio","year":"2023","journal-title":"HardwareX"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"194","DOI":"10.1164\/ajrccm.158.1.9708049","article-title":"The Pressure\u2013Volume Curve Is Greatly Modified by Recruitment","volume":"158","author":"Hickling","year":"1998","journal-title":"Am. J. Respir. Crit. Care Med."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Bates, J.H.T. (2009). Lung Mechanics: An Inverse Modeling Approach, Cambridge University Press.","DOI":"10.1017\/CBO9780511627156"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Maury, B. (2013). The Respiratory System in Equations, Springer. [1st ed.]. MS&A\u2014Modeling, Simulation and Applications.","DOI":"10.1007\/978-88-470-5214-7"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"731","DOI":"10.1152\/japplphysiol.01033.2004","article-title":"Anatomically based finite element models of the human pulmonary arterial and venous trees including supernumerary vessels","volume":"99","author":"Burrowes","year":"2005","journal-title":"J. Appl. Physiol."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1466","DOI":"10.1152\/japplphysiol.01289.2010","article-title":"Multi-scale lung modeling","volume":"110","author":"Tawhai","year":"2011","journal-title":"J. Appl. Physiol."},{"key":"ref_7","first-page":"A2677","article-title":"Understanding the Interdependence Between Parenchymal Deformation and Ventilation In Obstructive Lung Disease","volume":"Volume 189","author":"Berger","year":"2014","journal-title":"B30. Dynamics of Airway Narrowing in Asthma: Still Misunderstood?"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"473","DOI":"10.1016\/j.cma.2016.08.010","article-title":"Computational modelling of the respiratory system: Discussion of coupled modelling approaches and two recent extensions","volume":"314","author":"Roth","year":"2017","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"2499804","DOI":"10.1155\/2021\/2499804","article-title":"Design, Control, Modeling, and Simulation of Mechanical Ventilator for Respiratory Support","volume":"2021","author":"Tran","year":"2021","journal-title":"Math. Probl. Eng."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"111169","DOI":"10.1016\/j.chaos.2021.111169","article-title":"Design and simulation of mechanical ventilators","volume":"150","author":"Kezrane","year":"2021","journal-title":"Chaos Solitons Fractals"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"373","DOI":"10.1007\/s41403-020-00118-6","article-title":"Rapid Manufacturable Ventilator for Respiratory Emergencies of COVID-19 Disease","volume":"5","author":"Tharion","year":"2020","journal-title":"Trans. Indian Natl. Acad. Eng."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1016\/j.ifacol.2022.11.165","article-title":"Dynamic Modeling of a Low-cost Mechanical Ventilator","volume":"55","author":"Pivik","year":"2022","journal-title":"IFAC-PapersOnLine"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"707","DOI":"10.4236\/jbise.2015.810068","article-title":"Modelling and Simulation of Pressure Controlled Mechanical Ventilation System","volume":"8","year":"2015","journal-title":"J. Biomed. Sci. Eng."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"271053","DOI":"10.1155\/2014\/271053","article-title":"Modelling and Simulation of Volume Controlled Mechanical Ventilation System","volume":"2014","author":"Shi","year":"2014","journal-title":"Math. Probl. Eng."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1","DOI":"10.20428\/jst.v21i1.1017","article-title":"Simulation of Mathematical Model for Lung and Mechanical Ventilation","volume":"21","year":"2016","journal-title":"J. Sci. Technol."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"5886","DOI":"10.1016\/j.matpr.2021.04.369","article-title":"Design and simulation of AI-based low-cost mechanical ventilator: An approach","volume":"47","author":"Giri","year":"2021","journal-title":"Mater. Today Proc."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"335","DOI":"10.1055\/s-0042-1744446","article-title":"Modeling Mechanical Ventilation In Silico\u2014Potential and Pitfalls","volume":"43","author":"Hannon","year":"2022","journal-title":"Semin. Respir. Crit. Care Med."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1926711","DOI":"10.1155\/2021\/7118711","article-title":"Fuzzy PID control for respiratory systems","volume":"2021","author":"Mehedi","year":"2021","journal-title":"J. Healthc. Eng."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"395","DOI":"10.1017\/S0962492922000083","article-title":"Control of port-Hamiltonian differential-algebraic systems and applications","volume":"32","author":"Mehrmann","year":"2023","journal-title":"Acta Numer."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"393","DOI":"10.1146\/annurev-control-081219-092250","article-title":"Port-Hamiltonian Modeling for Control","volume":"3","year":"2020","journal-title":"Annu. Rev. Control Robot. Auton. Syst."},{"key":"ref_21","unstructured":"Villegas, J.A. (2007). A Port-Hamiltonian Approach to Distributed Parameter Systems. [Ph.D. Thesis, Department of Applied Mathematics, Faculty EWI, Universiteit Twente]."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1864","DOI":"10.1137\/040611677","article-title":"Dirac structures and Boundary Control Systems associated with Skew-Symmetric Differential Operators","volume":"44","author":"Zwart","year":"2005","journal-title":"SIAM J. Control Optim."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"166","DOI":"10.1016\/S0393-0440(01)00083-3","article-title":"Hamiltonian formulation of distributed-parameter systems with boundary energy flow","volume":"42","author":"Maschke","year":"2002","journal-title":"J. Geom. Phys."},{"key":"ref_24","unstructured":"Anderson, J. (1995). Computational Fluid Dynamics: The Basics with Applications, McGraw-Hill Inc.. McGraw-Hill International Editions: Mechanical Engineering."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"523","DOI":"10.1080\/13873954.2017.1280512","article-title":"A simplified lumped parameter model for pneumatic tubes","volume":"23","year":"2017","journal-title":"Math. Comput. Model. Dyn. Syst."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"H899","DOI":"10.1152\/ajpheart.00230.2014","article-title":"An integrated mathematical model of the human cardiopulmonary system: Model development","volume":"310","author":"Albanese","year":"2016","journal-title":"Am. J. Physiol.-Heart Circ. Physiol."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Bondy, J.A., and Murty, U.S.R. (1976). Graph Theory with Applications, The Macmillan Press Ltd.","DOI":"10.1007\/978-1-349-03521-2"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1016\/j.crme.2009.03.009","article-title":"Modeling and identification of a solenoid valve for PWM control applications","volume":"337","author":"Taghizadeh","year":"2009","journal-title":"Comptes Rendus M\u00e9canique"}],"container-title":["Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2079-3197\/12\/8\/155\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T15:27:26Z","timestamp":1760110046000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2079-3197\/12\/8\/155"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,7,31]]},"references-count":28,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2024,8]]}},"alternative-id":["computation12080155"],"URL":"https:\/\/doi.org\/10.3390\/computation12080155","relation":{},"ISSN":["2079-3197"],"issn-type":[{"type":"electronic","value":"2079-3197"}],"subject":[],"published":{"date-parts":[[2024,7,31]]}}}