|
Vol: 53(67) No: 4 / December 2008 The Use of Non-integer Order Modeling in a Tracheal Simulation Study Clara Ionescu Department of Electrical Energy, Systems and Automation, Ghent University, Faculty of Engineering, Technologiepark 913, B9052 Gent-Zwijnaarde, Belgium, phone: (00329) 264-5576, e-mail: clara@autoctrl.UGent.be Robin De Keyser Department of Electrical Energy, Systems and Automation, Ghent University, Faculty of Engineering, Technologiepark 913, B9052 Gent-Zwijnaarde, Belgium, e-mail: rdk@autoctrl.UGent.be Keywords: respiratory impedance, fractional-order model, airway geometry, modeling, simulation, mechanical properties, artificial tissue Abstract It is well-known that respiratory disease involves changes in physiological parameters of the human respiratory airways like: tube radius, tube length, thickness or percentage of the cartilage. Fractional-order parametric models can capture spatial changes in mechanical properties of tissue. Such models have not yet been used in clinical practice, but present an interesting alternative to integer-order models. A set of tests denoting changes in airway length and cross-sectional area over the trachea and the bronchi is applied on a respiratory duct simulator. The resulting observations are correlated with morphology. The fractional order model could be further used to gather necessary insight on the required mechanical properties for tracheal replacements and artificial tissue generation. References [1] B. Ziegelaar, J. Aigner, R. Staudenmaier, K. Lempart, B. Mack, T. Happ, M. Sittinger, M. Endres, A. Naumann, E. Kastenbauer, N. Rotter, “The characterisation of human respiratory epithelial cells cultured on resorbable scaffolds: first steps towards a tissue engineered tracheal replacement”, Biomaterials, 23: 1425-1438, 2002. [2] G. Maksym, J. Bates, “A distributed nonlinear model of lung tissue elasticity”, J Applied Physiology, 82(1): 32-41, 1997. [3] E. Hallers, G. Rakhorst, H. Marres, J. Jansen, T. van Kooten, H. Schutte, J. van Loon, E. van der Houwen, G. Verkerke, “Animal models for tracheal research”, Biomaterials, 25:1533-1543, 2005. [4] D. Rujan, G. Draganescu, “The use of fractal parameter for the characterization of structured surfaces”, J Optoelectronics and advanced materials 8(1), 280-284, 2006. [5] R. Segal, X. Guan, M. Shearer, T. Martonen, “Mathematical model of airflow in the lungs of children. I: effects of tumor sizes and locations”, Journal of Theoretical Medicine, 2, 199-213, 2000. [6] K. Oldham, J. Spanier, The Fractional Calculus, Academic Press, London, 1974. [7] C. Ionescu, R. De Keyser, “A Novel Parametric Model for the Human Respiratory System”, Proc. of the IASTED Int. Conf. on Modelling and Simulation, pp. 246-251, 2003. [8] C. Ionescu, R. De Keyser, “On the potential of using fractional-order systems to model the respiratory impedance”, Annals of Dunarea de Jos University of Galati, Romania, Fasc III, ISSN 1221-454X, (DOAJ), pp. 57-62, 2006. [9] C. Ionescu., R. De Keyser, “Parametric models for characterizing respiratory input impedance”, Journal of Medical Engineering & Technology, 32(4), 315-324, 2008. [10] A. Eke, P. Herman, L. Kocsis, L. Kozak, “Fractal characterization of complexity in temporal physiological signals”, Physiol. Meas., 23, R1-R38, 2002. [11] B Suki, A.L. Barabasi, K. Lutchen, “Lung tissue viscoelasticity: a mathematical framework and its molecular basis”, J Appl Physiol, 76(6): 2749-2759, 1994. [12] P. Harper, S.S. Karman, H. Pasterkamp, G.R. Wodicka, “An Acoustic Model of the Respiratory Tract”, IEEE Transactions of Biomedical Engineering, vol 48(5), pp. 543-5491, 2001. [13] G.R. Wodicka, K. N. Stevens, H.L. Golub, E.G. Cravalho, D. C. Shannon, “A model of acoustic transmission in the respiratory system”, IEEE Transactions of Biomedical Engineering, vol 36 (9), pp925-933, 1989. [14] W. M. Rohsenoro, H. Choi, “Heat, mass and momentum transfer”, Prentice-Hall INC, 1961. [15] T.F. Coleman, Y. Li, An interior trust region approach for nonlinear minimization subject to bounds, SIAM Journal on Optimization, 6, 418-445, 1996. [16] K. Adolfsson, M. Enelund, P. Olsson, “On the fractional order model of viscoelasticity”, Mechanics of Time-dependent materials, Springer, vol 9, pp. 15–34, 2005. [17] Kawaguchi et al., “Mechanical properties of artificial tracheas composed of a mesh cylinder and a spiral stent”, in Journal of Biomaterials, 3085-3090, 2001. |