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Among the most compound elements of these models, apart from the bronchial tree structure, is the phenomenon of flow limitation in flexible bronchi, which causes them to collapse with increasing flow, thus their properties, such as resistance, compliance and inertance, are highly nonlinear and time\u2010varying. Commonly, this phenomenon is ignored, or a distributed model for the airway pressure drop is applied, simulated with a modified numerical solver of this differential equation (ODE). The disadvantages of this solution are the problems with taking into account the inherent singularity of the model and the long computation time due to iterative nature of the ODE procedure. The aim of the work was to derive an algebraic approximation of this distributed model, suitable for implementation in continuous dynamic models, to validate it by comparing the results of simulations with the respiratory system model including approximate and original (ODE solver) numerical procedures, as well as to evaluate possible acceleration of calculations. All simulations, including spontaneous breathing, mechanical ventilation with the optimal ventilatory waveform and forced expiration, proved that algebraic approximation yielded results negligibly differing from the ODE solution, and shortened the computation time by an order. The proposed approach is an attractive alternative in the case of computer implementations of pulmonary models, where simulations of flows and pressures in the complex respiratory system are of primary importance.<\/jats:p>","DOI":"10.1002\/cnm.3632","type":"journal-article","created":{"date-parts":[[2022,6,1]],"date-time":"2022-06-01T14:38:34Z","timestamp":1654094314000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Algebraic approximation of the distributed model for the pressure drop in the respiratory airways"],"prefix":"10.1002","volume":"38","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9140-1162","authenticated-orcid":false,"given":"Adam G.","family":"Polak","sequence":"first","affiliation":[{"name":"Department of Electronic and Photonic Metrology, Faculty of Electronics, Photonics and Microsystems Wroc\u0142aw University of Science and Technology Wroc\u0142aw Poland"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2022,6,12]]},"reference":[{"key":"e_1_2_7_2_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.resp.2005.03.005"},{"key":"e_1_2_7_3_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cpc.2010.11.008"},{"key":"e_1_2_7_4_1","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pone.0204191"},{"key":"e_1_2_7_5_1","doi-asserted-by":"publisher","DOI":"10.1152\/jappl.1982.52.1.44"},{"key":"e_1_2_7_6_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cmpb.2007.03.009"},{"key":"e_1_2_7_7_1","doi-asserted-by":"publisher","DOI":"10.1002\/cphy.c100025"},{"key":"e_1_2_7_8_1","doi-asserted-by":"publisher","DOI":"10.1002\/cnm.2577"},{"issue":"2","key":"e_1_2_7_9_1","first-page":"1","article-title":"Computational modeling of the obstructive lung diseases asthma and COPD","volume":"12","author":"Burrowes KS","year":"2014","journal-title":"J Transl Med"},{"key":"e_1_2_7_10_1","doi-asserted-by":"publisher","DOI":"10.1115\/1.4027485"},{"key":"e_1_2_7_11_1","doi-asserted-by":"publisher","DOI":"10.1002\/cnm.2730"},{"key":"e_1_2_7_12_1","doi-asserted-by":"publisher","DOI":"10.1002\/cnm.2812"},{"key":"e_1_2_7_13_1","doi-asserted-by":"publisher","DOI":"10.1002\/cnm.2973"},{"key":"e_1_2_7_14_1","doi-asserted-by":"publisher","DOI":"10.1002\/cnm.2898"},{"key":"e_1_2_7_15_1","doi-asserted-by":"publisher","DOI":"10.1114\/1.1588651"},{"key":"e_1_2_7_16_1","doi-asserted-by":"publisher","DOI":"10.1177\/039139880602901007"},{"key":"e_1_2_7_17_1","doi-asserted-by":"publisher","DOI":"10.1115\/1.4033475"},{"key":"e_1_2_7_18_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cmpb.2019.03.014"},{"key":"e_1_2_7_19_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10439-007-9339-1"},{"key":"e_1_2_7_20_1","doi-asserted-by":"publisher","DOI":"10.1109\/TBME.2018.2890055"},{"key":"e_1_2_7_21_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cmpb.2019.02.003"},{"key":"e_1_2_7_22_1","doi-asserted-by":"publisher","DOI":"10.1002\/cnm.3238"},{"key":"e_1_2_7_23_1","doi-asserted-by":"crossref","unstructured":"PolakAG HantosZ.Simulation of respiratory impedance variations during normal breathing using a morphometric model of the lung. 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