A Hill model-based phenomenological method for muscle activation was used to investigate defectiveness of the palatal muscle tone during sleep for obstructive sleep apnea (OSA) patients. Based on the stretch-stress characteristic of muscle activation when the eccentric contraction is considered, a specifically defined phenomenological strain-energy function was used, as well as the Holzapfel-type strain-energy function for the passive part. A continuum mechanical framework, including the stress tensor and elasticity tensor, was obtained, based on the defined strain-energy function. The model parameters were obtained by fitting the constitutive model to experimental test data. Three-dimensional patient-specific geometry was modeled, accounting for the muscle tissue layer and based on the quantitative histology study of the soft palate. Anatomically representative boundary conditions for the finite element calculation were also considered. Palatal muscle activation level (electromyographic data) versus the negative pressure was defined in the simulations, and the patients' activation level was set to be lower than for the healthy people. The simulation results showed that reduced in activation level for the patients causes a less negative closing pressure, and this makes the soft palate more prone to collapse. In addition, if we account for the passive-active transfer displayed as the muscle contraction corresponding to the neurogenic reflex in the soft palate, the collapse is prevented. This numerical representation of the reduced activation for the OSA patients may provide increased understanding of OSA physiology.
Keywords: 3D modeling; Numerical simulation; Obstructive sleep apnea; Palatal muscle activation; Phenomenological modeling.