Experimental studies and mathematical modeling of the viscoelastic rheology of tracheobronchial mucus from respiratory healthy patients

Sandra Melina Tauwald; Johanna Michel; Marie Brandt; Veronika Vielsmeier; Christian Stemmer; Lars Krenkel

doi:10.4081/mrm.2023.923

Experimental studies and mathematical modeling of the viscoelastic rheology of tracheobronchial mucus from respiratory healthy patients

Authors

Sandra Melina Tauwald Regensburg Center of Health Sciences and Technology, Department of Biofluid Mechanics, University of Applied Sciences (OTH), Regensburg https://orcid.org/0000-0002-9332-1860
Johanna Michel Regensburg Center of Health Sciences and Technology, Department of Biofluid Mechanics, University of Applied Sciences (OTH), Regensburg https://orcid.org/0009-0008-5770-7521
Marie Brandt Department for Otorhinolaryngology, University Hospital Regensburg, Regensburg https://orcid.org/0009-0006-3332-584X
Veronika Vielsmeier Department for Otorhinolaryngology, University Hospital Regensburg, Regensburg
Christian Stemmer Chair of Aerodynamics and Fluid Mechanics, Technical University of Munich (TUM), Munich https://orcid.org/0000-0002-6904-8315
Lars Krenkel Regensburg Center of Health Sciences and Technology, Department of Biofluid Mechanics, University of Applied Sciences (OTH), Regensburg https://orcid.org/0000-0002-6275-3505

DOI: https://doi.org/10.4081/mrm.2023.923

Keywords:

Tracheobronchial mucus, rheological model, viscoelasticity

Abstract

Background: Tracheobronchial mucus plays a crucial role in pulmonary function by providing protection against inhaled pathogens. Due to its composition of water, mucins, and other biomolecules, it has a complex viscoelastic rheological behavior. This interplay of both viscous and elastic properties has not been fully described yet. In this study, we characterize the rheology of human mucus using oscillatory and transient tests. Based on the transient tests, we describe the material behavior of mucus under stress and strain loading by mathematical models.
Methods: Mucus samples were collected from clinically used endotracheal tubes. For rheological characterization, oscillatory amplitude-sweep and frequency-sweep tests, and transient creep-recovery and stress-relaxation tests were performed. The results of the transient test were approximated using the Burgers model, the Weibull distribution, and the six-element Maxwell model. The three-dimensional microstructure of the tracheobronchial mucus was visualized using scanning electron microscope imaging.
Results: Amplitude-sweep tests showed storage moduli ranging from 0.1 Pa to 10000 Pa and a median critical strain of 4 %. In frequency-sweep tests, storage and loss moduli increased with frequency, with the median of the storage modulus ranging from 10 Pa to 30 Pa, and the median of the loss modulus from 5 Pa to 14 Pa. The Burgers model approximates the viscoelastic behavior of tracheobronchial mucus during a constant load of stress appropriately (R²of 0.99), and the Weibull distribution is suitable to predict the recovery of the sample after the removal of this stress (R² of 0.99). The approximation of the stress-relaxation test data by a six-element Maxwell model shows a larger fit error (R² of 0.91).
Conclusions: This study provides a detailed description of all process steps of characterizing the rheology of tracheobronchial mucus, including sample collection, microstructure visualization, and rheological investigation. Based on this characterization, we provide mathematical models of the rheological behavior of tracheobronchial mucus. These can now be used to simulate mucus flow in the respiratory system through numerical approaches.

References

Rajendran RR, Banerjee A. Mucus transport and distribution by steady expiration in an idealized airway geometry. Med Eng Phys 2019;66:26-39.

Lillehoj ER, Kim KC. Airway mucus: its components and function. Arch Pharm Res 2002;25:770-80.

Widdicombe JG. airway surface liquid: concepts and measurements. In: D.F. Rogers, M.I. Lethem, Editors. Airway mucus: basic mechanisms and clinical perspectives. Basel: Birkhäuser; 1997. p. 1-17.

Fahy JV, Dickey BF. Airway mucus function and dysfunction. N Engl J Med 2014;23:2233-47.

Martinez-Rivera C, Crespo A, Pinedo-Sierra C, Garcia-Rivero JL, Pallares-Sanmartin A, Marina-Malanda N et al. Mucus hypersecretion in asthma is associated with rhinosinusitis, polys and exacerbations. Respir Med 2018;135:22-8.

Lafforgue O, Seyssiecq I, Poncet S, Favier J. Rheological properties of synthetic mucus for airway clearance. J Biomed Mater Res A 2018;109:386-96.

Quraishi MS, Jonas NS, Mason J. The rheology of nasal mucus: a review. Clin Otolaryngol Allied Sci 1998;5:403-13.

Ridley C, Thornton D. Mucins: the frontline defence of the lung. Biochem Soc Trans 2018;46:1099-106.

Kesimer M, Sheehan J. Mass spectrometric analysis of mucin core proteins. Methods Mol Biol 2012;842:67-79.

Lai SK, Wang Y, Wirtx D, Hanes J. Micro- and macrorheology of mucus. Adv Drug Deliv Rev 2009;61:86-100.

Boegh M, Nielsen HM. Mucus as a barrier to drug delivery – understanding and mimicking the barrier properties. Basic Clin Pharmacol Toxicol 2015;116:179-86.

Hwang SH, Litt M, Forsman WC. Rheological properties of mucus. Rheol Acta 1969;8:438-48.

Zayas G, Chiang MC, Wong E, MacDonald F, Lange C, Senthilselvan A, et al. Cough aerosol in healthy participants: fundamental knowledge to optimize droplet-spread infectious respiratory disease management. BMC Pulm Med 2021;12:11.

Silberg A. On mucociliary transport. Biorheology 1990;27:295-307.

Elizer N, Sadé J, Silberg A, Nevo AC. The role of mucus in transport by cilia. Am Rev Respir Dis 1970;102:48-52.

Hill D, Long R, Kissner W, Atieh E, Garbarine IC, Markovets M, et al. Pathological mucus and impaired mucus clearance in cystic fibrosis patients result from increased concentration, not altered pH. Eur Respir J 2018;52:1801297.

Ren S, Wang L, Shi Y, Cao M, Hao L, Luo Z et al. Numerical analysis of airway mucus clearance effectiveness using assisted coughing techniques. Sci Rep 2020;10:2030.

Ren S, Cai M, Shi Y, Luo Z, Wang T. Influence of cough airflow characteristics on respiratory mucus clearance. Phys Fluids 2022;34:41911.

Taylor C, Pearson J, Draget K, Dettmar P, Smidsrod O. Rheological characterisation of mixed gels of mucin and alginate. Carbohydr Polym 2014;59:189-95.

Hamed R, Fliegel J. Synthetic tracheal mucus with native rheological and surface tension properties. J Biomed Mater Res A 2014;102:1788-98.

App EM, Zayas JG, King M. Rheology of mucus and transepithelial potential difference: small airways versus trachea. Eur Respir J 1993;6:67-75.

Jeanneret-Grosjean A, King M, Michoud MC, Liote H, Amyot R. Sampling technique and rheology of human tracheobronchial mucus. Am Rev Respir Dis 1988;137:707-10.

Atanasova KR, Reznikov LR. Strategies for measuring airway mucus and mucins. Respir Res 2019;20:261.

Tanaka E, van Eijden T. Biomechanical behavior of the temporomandibular joint disc. Crit Rev Oral Biol Med 2003;14:138-50.

Gebrehiwot SZ, Espinosa-Leal L. Characterising the linear viscoelastic behaviour of an injection moulding grade polypropylene polymer. Mech Time-Depend Mater 2021;26:791-814.

Imane B, Kyoungtae K, Shahab RK, Sahukhal GS, Mohamed OE, Joshua UO. Creep, recovery, and stress relaxation behavior of nanostructured bioactive calcium phosphate glass-POSS/polymer composites for bone implants studied under simulated physiological conditions. J Biomed Mater Res B Appl Biomater 2019;107:2419-32.

Monticeli F, Ornaghi H, Neves R, Cioffi M. Creep/recovery and stress-relaxation tests applied in a standardized carbon fiber/epoxy composite: Design of experiment approach. J Strain Anal Eng Des 2020;55:109-17.

Chae SH, Zhao J, Edwards D, Ho PS. Characterization of the viscoelasticity of molding compounds in the time domain. J Electron Mater 2010;39:419-25.

Jory M, Bellouma K, Blanc C, Casanellas L, Petit A, Reynaud P, et al. Mucus microrheology measured on human bronchial epithelium culture. Front Phys 2019;7:19.

Wereley N, Chaudhuri A, Yoo J, John S. Bidisperse magnetorheological fluids using fe particles at nanometer and micron scale. J Intell Mater Syst Struct 2006;17:393-401.