AM  Vol.5 No.12 , June 2014
Self-Similarities of Pulmonary Arterial Tree and a New Integrated Model of Pulmonary Circulation with the Name of Fractal Phasic Perfusion (FPP) Model
Author(s) Kyongyob Min*
ABSTRACT

Pulmonary arterial hypertension (PAH) has become an important topic of basic and clinical research in recent years. Morphologic researches have shown that specific PAH-lesions are located in the lobular small muscular arteries and correlate with hemodynamic measurements. However, it still remains to be shown how pathological changes of the small arteries in the lobule develop to PAH. Based on both fractal properties of pulmonary arterial tree and asynchronous phasic contractions of lobular arterial muscles under the evenness of the pulmonary capillary pressure (PCP) in the lung, the author has constructed an integrated model of pulmonary circulation which has produced a mathematical relationship between the mean pulmonary arterial pressure (MPAP) and the cardiac output (CO). By use of the expression between MPAP and CO, it has been able to explain the pathogenesis of PAH in terms of statistical changes among regional and temporal perfusions in the lung. In order to detect clinically the early stage of PAH, the author has suggested that it is important to establish the pulmonary functional imaging of regional and temporal perfusions.


Cite this paper
Min, K. (2014) Self-Similarities of Pulmonary Arterial Tree and a New Integrated Model of Pulmonary Circulation with the Name of Fractal Phasic Perfusion (FPP) Model. Applied Mathematics, 5, 1801-1809. doi: 10.4236/am.2014.512173.
References
[1]   Simonneau, G., Robbins, I.M., Beghetti, M., Channick, R.N., Delcroix, M., Denton, C.P., Elliott, C.G., Gaine, S.P., Gladwin, M.T., Jing, Z.C., et al. (2009) Updated Clinical Classification of Pulmonary Hypertension. Journal of the American College of Cardiology, 54, S43-S54.
http://dx.doi.org/10.1016/j.jacc.2009.04.012

[2]   Stacher, E., Graham, B.B., Hunt, J.M., Gandjeva, A., Groshong, S.D., McLaughlin, V., Jessup, M., Grizzle, W.E., Aldred, M.A., Cool, C.D. and Tuder, R.M. (2012) Modern Age Pathology of Pulmonary Arterial Hypertension. American Journal of Respiratory and Critical Care Medicine, 186, 263-272.
http://dx.doi.org/10.1164/rccm.201201-0164OC

[3]   Swan, H.J.C., Ganz, W., Forrester, J.S., Marcus, H., Diamond, G. and Chonette, D. (1970) Catheterization of the Heart in Man with Use of a Flow-Directed Catheter. The New England Journal of Medicine, 283, 447-451.
http://dx.doi.org/10.1056/NEJM197008272830902

[4]   Naeije, R. (2011) Pulmonary Vascular Function. In: Peacock, A.J., Naeije, R. and Rubin, L.T., Eds., Pulmonary Circulation, 3rd Edition, UK, 3-25.

[5]   Min, K., Hosoi, K., Kinoshita, Y., Hara, S., Degami, H., Takada, T. and Nakamura, T. (2012) Use of Fractal Geometry to Propose a New Mechanism of Airway-Parenchymal Interdependence. Open Journal of Molecular and Integrative Physiology, 2, 14-20.
http://dx.doi.org/10.4236/ojmip.2012.21003

[6]   Suwa, N. and Takahashi, T. (1971) Morphological and Morphometrical Analysis of Circulation in Hypertension and Ischemic Kidney. Urban & Schwarzenberg, Muenchen.

[7]   Elliott, F.M. and Reid, L. (1965) Some New Facts about the Pulmonary Artery and Its Branching Pattern. Clinical Radiology, 16, 193-198.
http://dx.doi.org/10.1016/S0009-9260(65)80042-3

[8]   Krahl, V.E. (1963) A Method of Studying the Living Lung in the Closed Thorax, and Some Preliminary Observations. Angiology, 14, 149-159.
http://dx.doi.org/10.1177/000331976301400401

[9]   Cope, D.K., Grimbert, F., Downey, J.M. and Taylor, A.E. (1992) Pulmonary Capillary Pressure: A Review. Critical Care Medicine, 20, 1043-1056.
http://dx.doi.org/10.1097/00003246-199207000-00024

[10]   Weibel, E.R. and Gomez, D.M. (1962) Architecture of the Human Lung—Use of Quantitative Methods Establishes Fundamental Relations between Size and Number of Lung Structures. Science, 137, 577-585.
http://dx.doi.org/10.1126/science.137.3530.577

[11]   Matuo, T., Okeda, R., Takahashi, M. and Funata, M. (1990) Characterization of Bifurcating Structures of Blood Vessels Using Fractal Dimensions. Forma, 5, 19-27

[12]   Kamiya, A. and Takahashi, T. (2007) Quantitative Assessments of Morphological and Functional Properties of Biological Trees Based on Their Fractal Nature. Journal of Applied Physiology, 102, 2315-2323.
http://dx.doi.org/10.1152/japplphysiol.00856.2006

[13]   Ochs, M. and Weibel, E.R. (2008) Functional Design of the Human Lung for Gas Exchange. In: Fishman, A.P., Ed., Fishman’s Pulmonary Dieases and Disorders, 4th Edition, McGraw-Hill, Boston, 23-69.

[14]   Patz, S., Hatabu, H., Butler, J.P., Washko, G., Choi, A., Rosas, I., Muradyan, I., Lisitza, N. and Dabaghyan, M. (2013) Mission of the Center for Pulmonary Functional Imaging. cpfi.spi.havard.edu

 
 
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