Experimental characterization and constitutive modeling of the mechanical behavior of the human trachea
Introduction
Among the diverse tissues that form the trachea, the cartilage rings as well as the smooth muscle are the principal components responsible for the global behavior of the trachea and any change in their mechanical properties can imply a disorder in the windpipe. Trachea can be affected by several pathologies as tracheamalacia, congenital fistulae, stenosis [1], [2]. These pathologies can modify the tissues of the trachea changing the cartilage or the inner wall mechanical properties.
The function of the cartilaginous windpipe structure is to maintain the trachea open during the respiratory movements in spite of the inter-thoracic pressure. The contraction of the smooth muscle and the transmural pressure generate bending in the cartilages, collapsing them to regulate the air flow by modulating the diameter of the aerial way. The mechanical characteristics of the human trachea have not been completely determined; few studies have been made to understand the behavior of its components [3], [4], [5]. With respect to cartilage, in some of these works it is considered a non-linear material displaying higher strength in compression than in extension [5], but in most of them, the isolated tracheal cartilage was considered as a linear elastic material [6], [7]. In Rains's work [8], the stress–strain relations obtained from slices of human tracheal cartilage were considered linear for deformations up to 10% of the initial length of the samples. In fact, there was negligible hysteresis and no residual strain in specimens tested to a maximal applied strain of 10%, beyond this limit strain hysteresis and residual strain increased progressively [3]. The same consideration was used by Kempson [9] for the articular cartilage, where the response of the tissue was considered linear for deformations up to 5% of the initial length of the samples. This hypothesis was also used in some analytical models [10], [11], as well as in some finite elements simulations [12], [13].
With respect to the mechanical properties of the tracheal muscle, most of the developed works dealt with its plasticity, stiffness and extensibility. Gunst and Wu [14] treated the effects of its length on the stiffness and the extensibility at contractile time activation. Comín et al. [15] analyzed its mechanical response to oscillatory conditions and Stephens et al. [16] analyzed the influence of the temperature on force–velocity relationships. However, none of them analyzed the mechanical properties of this membrane that makes possible the collapsing of the rings and therefore the pressure balance inside the trachea.
In this study, a histological analysis was made on cartilaginous and muscular tracheal samples taken from an individual aged 46. Cartilage rings obtained from the autopsy of individuals of ages 79 and 82 without tracheal pathologies were tested using a cyclical uniaxial tensile trial confirming their linear behavior. Uniaxial quasi-static tensile tests on human tracheal smooth muscle were also made to characterize its two orthogonal families of collagen fibers and the experimental curves obtained were fitted using the Holzapfel strain-energy density function to estimate its mechanical behavior [17]. These findings allow a better understanding of the behavior of the trachea and give information to study its response under different conditions.
Section snippets
Materials and methods
First, a histological study was performed in order to relate the microstructure of the different tissues with their mechanical behavior. Then, the experimental tests were carried out for cartilage and smooth muscle samples, and finally, the experimental curves were fitted to a suitable constitutive model that could represent their particular behavior.
Results
Fig. 4 illustrates the experimental curves obtained by cyclical tests made on tracheal cartilage. It can be observed that during the loading step, the cartilage has a linear response, but when it is unloaded progressively, presents a non-linear behavior. This non-linearity can be explained by the intervention of the water which gives a viscoelastic behavior to the cartilage, especially during relaxation.
The cartilage rings mainly work in tension, so only the loading phase (Fig. 4b) until a
Discussion
As mentioned before, there are few studies that have analyzed the mechanical behavior of the trachea. The goal of this work was to analyze the mechanical response of the main constituents of the trachea under tensile conditions and to suggest a constitutive model to represent them.
Before performing any test, a histological study was made in order to analyze the structure of the different tissues involved in the trachea. The distribution of collagen fibers showed that there is not a clear
Conflict of interest
There is not any financial and personal relationship with other people or organisations that could inappropriately influence this work.
Acknowledgement
The authors gratefully acknowledge the support of the Health Institute Carlos III through the research project PI07/90023.
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