Towards a numerical model of the respiratory mechanics
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When an intensive care patient is subjected to mechanical ventilation this leads to number of complications such as ventilator-induced lung injury (VILI) and ventilator-induced diaphragmatic dysfunction (VIDD). From a medical perspective, it is of interest to study and better understand the damage processes both qualitatively and more quantitatively with respect to individual patient variations. The respiratory mechanics are driven by the diaphragm, which is a thin structure with a central tendon and muscle tissue attached to the central tendon as well as to the spine, sternum, and lower ribs. Contraction of the diaphragm and the intercostal muscles is accompanied by a rotation of the ribs that expands the rib cage and thereby the lungs, leading to a pressure differential which causes air to enter the lungs. There are very few numerical models of the diaphragm and the respiratory mechanics in the literature both due to a larger focus on other organs such as the heart and brain, and due to the quite challenging geometrical and mechanical properties of the diaphragm and its non-trivial interactions with its surroundings. We are working on developing such a numerical model using meshfree radial basis function approximation methods. The meshfree nature of the methods supports dealing both with the shape and high aspect ratio of the diaphragm. In this presentation, we will discuss the reconstruction and representation of diaphragm geometries extracted from medical images as well as solving partial differential equations formulated in the geometry. We will present results for a simplified problem with linearly elastic material parameters.