Modeling the lung: Integer-order viscoelastic models – Part 2

Victor Perez, Jamille Pasco

Abstract

The mechanical behavior of lung tissue, especially under pathological conditions such as acute respiratory distress syndrome (ARDS), cannot be fully described by simple elastic or viscous models. Instead, the lung exhibits viscoelastic properties that depend on both the rate and duration of deformation. Integer-order viscoelastic models, including the Maxwell, Kelvin-Voigt, Zener, Anti-Zener, and Burgers models, have historically provided a conceptual framework for understanding lung mechanics by representing tissue as combinations of springs and dashpots governed by first- or second-order differential equations. These models are valuable for educational purposes and initial clinical interpretation, allowing quantification of phenomena such as stress relaxation and creep. However, their main limitation lies in their inability to capture the continuous distribution of relaxation times and the power-law response observed in biological tissues, particularly in heterogeneous and injured lungs as seen in ARDS. More complex models, such as the generalized Maxwell model, offer improved accuracy but at the cost of increased mathematical complexity and parameterization, restricting their routine clinical use. Recent evidence suggests that fractional-order models may provide a more physiologically accurate and parsimonious description of lung viscoelasticity, capturing frequency dependence and long-term responses with fewer parameters. The development of advanced models is essential for optimizing protective ventilation strategies and understanding the mechanisms underlying ventilator-induced lung injury.

Keywords: lung viscoelasticity, integer-order models, Maxwell model, Kelvin-Voigt model, Zener model, Anti-Zener model, Burgers model, ventilator-induced lung injury.

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