Stress concentration around an atelectatic region: A finite element model

Abstract

Lung parenchyma surrounding an atelectatic region is thought to be subjected to increased stress compared with the rest of the lung. Using 37 hexagonal cells made of linear springs, Mead et al. (1970) measured a stress concentration greater than 30% in the springs surrounding a stiffer central cell. We re-examine the problem using a 2D finite element model of 500 cells made of thin filaments with a non-linear stress-strain relationship. We study the consequences of increasing the central stiff region from one to nine contiguous cells in regular hexagonal honeycombs and random Voronoi honeycombs. The honeycomb structures were uniformly expanded with strains of 15%, 30%, 45% and 55% above their resting, non-deformed geometry. The curve of biaxial stress vs. fractional area change has a similar shape to that of the pressure-volume curve of the lung, showing an initial regime with relatively flat slope and a final regime with decreasing slope, tending toward an asymptote. Regular honeycombs had little variability in the maximum stress in radially oriented filaments adjacent to the central stiff region. In contrast, some filaments in random Voronoi honeycombs were subjected to stress concentration approximately 16 times the average stress concentration in the radially oriented filaments adjacent to the stiff region. These results may have implications in selecting the appropriate strategy for mechanical ventilation in ARDS and defining a "safe" level of alveolar pressure for ventilating atelectatic lungs.

The micromechanics of lung alveoli: structure and function of surfactant and tissue components

“…This model was further developed and applied to simulate the time course and lung mechanical impairment of pulmonary fibrosis as well as pulmonary emphysema including response to lung volume reduction surgery (Bates et al 2007; Mishima et al 1999; Mondoñedo and Suki 2017). In addition, spring models were used to understand aspects of alveolar and alveolar-airway interdependence (Ma and Bates 2012, 2014; Ma et al 2013a, b, 2015; Mead et al 1970; Makiyama et al 2014; Bates et al 2007). It has long been understood that alveolar interdependence plays an important role in the determining strain at the level of individual septa (Mead et al 1970; Perlman et al 2011).…”

“…Heterogeneous ventilation occurs in the context of surfactant dysfunction, alveolar collapse, intra-alveolar edema formation, lung inflammation or focal fibrotic remodeling. These pathologies have been assigned the roles of stress concentrators which might impose potential harmful stresses and strains on surrounding tissue during respiration (Mead et al 1970; Makiyama et al 2014). The spring model proposed by Mead et al (1970) was based on the interdependence of hexagonally shaped alveoli which share inter-alveolar septal walls.…”

“…As long as ventilation is homogenous the intra-pulmonary stresses are balanced, protecting lung units (= alveoli) from end-expiratory collapse and inspiratory overdistension. Inhomogeneity in ventilation of alveoli is linked to severe abnormalities in alveolar micromechanics due to end-expiratory collapse combined with enormous stress and intra-tidal deformation (= strain) of neighbouring alveoli including inter-alveolar septa (Mead et al 1970; Wilson and Bachofen 1982; Makiyama et al 2014). These predictions implicate that within an injured lung alveolar micromechanics can be locally severely altered and might become an independent trigger of lung injury progression.…”

Should Early Prone Positioning Be a Standard of Care in ARDS With Refractory Hypoxemia?

“…The consistently quoted response rate is approximately 70%. 38 The more even distribution of trans-alveolar pressure accomplished by the prone-modified chest wall may reduce the impact of stress focusing at the junctions of closed and open alveoli, 39 reduce the tendency for airway opening and closure, allow the use of less PEEP, improve afterload to the right ventricle, 40,41 and permit reduction of potentially toxic concentrations of inspired oxygen. To achieve a survival benefit, it would appear from published data that the patient should be positioned prone for the majority of the day for at least several days.…”

Strain heterogeneity in the injured lung: cause or consequence?

“…Another possible explanation for the synergy between low PEEP and high Vt in VILI pathogenesis is that alveolarscale heterogeneity and interdependence cause localized tissue distension and injury greater than would be predicted simply from regional or whole lung volume changes (2,10). It is also possible that VILI is due predominantly to atelectrauma; low PEEP is necessary to allow decruitment, whereas high inspiratory pressures are required to cyclically reopen collapsed units (4).…”