Modeling the lung: Fractional viscoelastic models – Part 3

Victor Perez, Jamille Pasco

Abstract

Lung viscoelasticity is governed by the intricate interplay of alveolar-interstitial architecture, including the elastin-collagen network, alveolar microgeometry, and surfactant dynamics. Traditional integer-order mechanical models have provided foundational frameworks for describing lung tissue mechanics but are limited by their inability to capture the empirically observed power-law responses and the broad distribution of relaxation times inherent to heterogeneous biological tissues, particularly in pathological states like acute respiratory distress syndrome (ARDS). Fractional viscoelastic models, grounded in fractional calculus, overcome these limitations by employing non-integer order derivatives and the spring-pot element, enabling a parsimonious and robust description of viscoelastic phenomena such as stress relaxation, creep, and hysteresis across wide temporal and spectral domains. These models encapsulate the memory effect and fractal architecture of lung parenchyma, offering a unified and physically interpretable parameterization of viscoelasticity. Composite fractional models demonstrate superior accuracy in fitting experimental data and predicting the dynamic response of the respiratory system. Their clinical application holds promise for optimizing protective ventilation strategies, individualizing PEEP titration, and reducing ventilator-induced lung injury (VILI) by enabling real-time assessment of tissue mechanics. The adoption of fractional viscoelastic models represents a paradigm shift in respiratory biomechanics, providing advanced tools for both research and clinical practice.

Keywords: fractional calculus, lung viscoelasticity, spring-pot, power-law, ARDS, respiratory mechanics.

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