A 3D discrete model of the diaphragm and human trunk

arXiv:0808.0339v1 [physics.med-ph] 3 Aug 2008 ESAIM: PROCEEDINGS, Vol. ?, 2018, 1-10 Editors: Will be set by the publisher A 3D DISCRETE MODEL OF THE DIAPHRAGM AND HUMAN TRUNK ∗ Emmanuel Promayon1 and Pierre Baconnier1, 2 Abstract. In this paper, a 3D discrete model is presented to model the movements of the trunk during breathing. In this model, objects are represented by physical particles on their contours. A simple notion of force generated by a linear actuator allows the model to create forces on each particle by way of a geometrical attractor. Tissue elasticity and contractility are modeled by local shape memory and muscular fibers attractors. A specific dynamic MRI study was used to build a simple trunk model comprised of by three compartments: lungs, diaphragm and abdomen. This model was registered on the real geometry. Simulation results were compared qualitatively as well as quantitatively to the experimental data, in terms of volume and geometry. A good correlation was obtained between the model and the real data. Thanks to this model, pathology such as hemidiaphragm paralysis can also be simulated. R´esum´e. Dans cet article nous pr´esentons un mod`ele discret 3D permettant de mod´eliser les mou- vements du tronc pendant la respiration. Les objets du mod`ele sont repr´esent´es par des particules physiques sur leurs contours. Une notion simple de force induite par des actuateurs lin´eaires permet de g´enerer des forces au niveau des particules en utilisant un attracteur g´eom´etrique. Les propri´et´es ´elastiques et contractiles d’un tissu sont ainsi mod´elis´ees par des attracteurs de m´emoire de forme locale et de fibre musculaire. `A partir d’une ´etude sp´ecifique en IRM dynamique, nous avons construit un mod`ele de tronc simplifi´e comprenant trois compartiments : les poumons, le diaphragme et l’abdomen. Ce mod`ele est recal´e sur la g´eom´etrie r´eelle. Nous confrontons les simulations obtenues aussi bien qualitativement que quantitativement, en terme de variation de volume et de g´eom´etrie. Une bonne correlation est obtenue entre le mod`ele et les donn´ees r´eelles. Grˆace `a ce mod`ele nous montrons enfin que l’on peut simuler la paralysie h´emidiaphragmatique. Introduction The diaphragm has two main roles: anatomically it separates the thoracic compartment from the abdominal compartment and physiologically it is the main respiratory muscle. The action of this muscle is complex and depends mainly on its size, its shape, and its attachments and links to surrounding organs and skeleton. The human adult diaphragm is shaped like a dome: a central tendon originates the muscular fibers. Laterally the fibers are inserted on the 7th to the 12th ribs (see Fig. 1, left). During inspiration, the diaphragm contracts and the abdominal content plays the role of a lever resulting in an enlargement of the thoracic cavity. This enlargement generates a negative pressure inside the rib cage, drawing air into the lungs. When the diaphragm relaxes, the air is expelled, helped also by the elasticity of the lung and the tissues lining the thoracic cavity. The ∗This project was partly funded by CNRS ACINIM LePoumonVousDisJe and CNRS Inter-EPST program Bio-Informatique. 1 TIMC-IMAG, CNRS UMR 5525, Universit´e Joseph Fourier, Grenoble, Institut d’Ing´enierie de l’Information de Sant´e, Domaine de la Merci, F-38706 La Tronche Cedex, France. e-mail: Emmanuel.Promayon@imag.fr Pierre.Baconnier@imag.fr 2 CHU Grenoble, Hopital Michallon, F-38700 La Tronche, France c⃝EDP Sciences, SMAI 2018 2 ESAIM: PROCEEDINGS Figure 1. Human trunk. The diaphragm and its skeleton attachment (left). Reconstructed diaphragm surface (right). abdominal compartment can be considered as incompressible during a given period of time (several minutes). Indeed, apart from a small gastric gas content, the abdominal cavity is filled with organs of quasi constant volume (blood volume variations are neglected) as all human tissues except lung. The stomach is commonly isolated from the remaining digestive tract by two closed sphincters, its gas content is then constant and considered incompressible in the range of observed gastric pressures. A model of the diaphragm and its surrounding structures can be used in two simulation fields: physiology and computer assisted surgery. It has to be geometric and kinematic as well as dynamic. If the simulated movements are produced by the model at a sufficiently fast rate, it can be used to predict the diaphragm and abdominal organ positions during respiration thus being able to drive an imaging device or a conformative radiotherapy. It is also important to be able to model specific diaphragm pathologies, such as hemidiaphragm paralysis, as they can highly alter the abdominal organ movements. Physiological studies of the respiratory system classically include volume and pressure variations. But as the diaphragm is not visible nor easily accessible from outside the body, studying the diaphragm deformation requires to use th

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