Keywords
diagnosis
ejection fraction
fractal dimension
How to Cite
Abstract
Introduction: Cardiac irregularity is adequately described by means of fractal geometry, which was the basis for the development of a diagnosis of the left ventriculogram. Methods: All possible permutations of similarity degrees from fractal dimensions were simulated for the ventricle in systole, diastole and the totality. Permutations were defined between the previously established minimum and maximum values of similarity degrees for moderate and severe abnormality. Results: The total number of ventricular prototypes between moderate and severe abnormality was established. The total number of possible ventricular structure prototypes is 1614: 794 ventricles with moderate abnormality and 820 with severe abnormality. Previous measurements of ventricles with a diagnosis of moderate and severe abnormality were found within the generalization. Conclusions: An objective geometric methodology was developed, which is of diagnostic aid in the clinical practice. It determined all possible left ventricular structures with moderate and severe abnormality, independently of clinical classifications.
Tacchi H. Disfunción sistólica ventricular izquierda asintomática. Insuf Card. 2007;2(1):32-6.
Wang T, Evans JC, Benjamin EJ, et al. Natural history of asymptomatic left ventricular systolic dysfunction in the community. Circulation 2003;108:977-82.
Flores J, Moya P, Calvo JC, et al. Manual de enfermería en cardiología intervencionista y hemodinámica. En: Flores J, Moya P, Calvo JC et al., editores. Procedimientos diagnósticos [internet]. Sevilla: Asociación Española de Enfermería en Cardiología [Cited Jan 1 2013]. Avalaible in: http://www.enfermeriaencardiologia.com/publicaciones/manuales/hemo/hemo_16.pdf.
Lang RM, Bierig M, Devereux RB, et al. Recommendations for chamber quantification: A report from de American Society of Echocardiography Guidelines and Standards committee and the Chamber Quantification Writing Group, developed in conjunction with the European Association of Echocardiography. J Am Soc Echocardiogr. 2005;12:1440-63.
Salazar G, Pedraza J, Cuenca G, et al. Guías colombianas sobre recomendaciones para realizar el informe del ecocardiograma transtorácico. Rev Col Cardiol. 2007;14(1):1-10.
Mandelbrot B. The fractal geometry of nature. San Francisco: Freeman; 1972.
Mandelbrot B. How long is the coast of Britain?: Statistical self-similarity and fractional dimension. Science. 1967;156(3775).
Falconer K. Box counting dimensions. En: Falconer K, editor. Fractal geometry. Chichester: John Wiley & Sons; 1990. p. 38-44.
Peitgen H, Jürgens H, Saupe D. Length, area and dimension: Measuring complexity and scalling properties. En: Peitgen H, Jürgens H, Saupe D, editors. Chaos and fractals: New frontiers of science. New York: Springer-Verlag; 1992. p. 183-228.
Vasiljevic J, Reljin B, Sopta J, et al. Application of multifractal analysis on microscopic images in the classification of metastatic bone disease. Biomed Microdevices. 2012;14:541-8.
Stehlík M, Mrkvička T, Filus J, et al. Recent developments on testing in cancer risk: A fractal and stochastic geometry. J Reliab Stat Stud. 2012;5:83-95.
Landini G, Rippin JW. Fractal dimensions of epithelial-connective tissue interfaces in premalignant and malignant epithelial lesions of the floor of mouth. Anal Quant Cytol Histol. 1993;15:144-9.
Gazit Y, Baish JW, Safabaksh N. Fractal characteristics of tumor vascular architecture during tumor growth and regression. Microcirculation. 1997;4(4):395-402.
Rodríguez J, Prieto S, Correa C, et al. Theoretical generalization of normal and sick coronary arteries with fractal dimensions and the arterial intrinsic mathematical harmony. BMC Medical Physics. 2010;10:1.
Rodríguez J, Prieto S, Ortiz L, Correa C, Álvarez L, Bernal P, et
al. Variabilidad de la dimensión fractal de la ramificación coronaria izquierda en ausencia y presencia de EAO moderada y severa. Rev Colomb Cardiol. 2007;14(3):173-80.
Rodríguez J, Prieto S, Correa C, et al. Diagnóstico fractal del ventriculograma cardiaco izquierdo: geometría fractal del ventriculograma durante la dinámica cardiaca. Rev Colomb Cardiol. 2012;19(1):18-24.
Ministerio de Salud de Colombia. Resolución 8430, por la cual se establecen las normas científicas, técnicas y administrativas para la investigación en salud; 1993.
Kappenberger L. Arrhythmia: a therapeutic dilemma. En: Virag N, Blanc O, Kappenberger L, editors. Computer simulation and experimental assessment of cardiac electrophysiology. Lausanne: Futura Publishing Company; 2001. p. 185-8.
Brogan WC, Glamann B, Lange RA, et al. Comparison of single and biplane ventriculogram for determination of left ventricular volume and ejection fraction. Am J Cardiol 1992;69:1079-82.
Migliore R, Darú V. ¿La fracción de eyección sigue teniendo vigencia cuando podemos evaluar la función ventricular con nuevos índices de deformación? Rev Argent Cardiol. 2011;79(5):429-34.
Rodríguez J, Prieto S, Ortiz L, et al. Diagnóstico matemático de ecocardiografías pediátricas con medidas de dimensión fractal evaluadas con armonía matemática intrínseca. Rev Colomb Cardiol. 2010;17:79-86.
Rodríguez J, Prieto S, Correa C, et al. Generalización fractal de células preneoplásicas y cancerígenas del epitelio escamoso cervical. una nueva metodología de aplicación clínica. Rev Fac Med. 2010;18(2):173-81.
Rodríguez J, Correa C, Melo M, et al. Chaotic cardiac law: Developing predictions of clinical application. J Med Med Sci. 2013;4(2):79-84.
Crutchfield J, Farmer D, Packard N, et al. Caos. En: Crutchfield J, Farmer D, Packard N et al., editores. Orden y caos. Barcelona: Prensa Científica; 1990. p. 78-90.
Feynman R, Leighton RB, Sands M. Comportamiento cuántico. En: Feynman R. Leighton RB, Sands M, editores. Física. Vol. 1. Wilmington: Addison-Wesley Iberoamericana; 1987. p. 37-1-37-16.
Feynman R, Leighton RB, Sands M. Principios de la mecánica estadística. En: Feynman RP, Leighton RB, Sands M, editores. Física. Vol. 1. Wilmington: Addison-Wesley Iberoamericana; 1987.
Rodríguez J, Prieto S, Domínguez D, et al. Mathematical-physical prediction of cardiac dynamics using the proportional entropy of dynamic systems. J Med Med Sci. 2013;4(8):370-81.
Rodríguez J, Prieto S, Correa C, et al. Predictions of CD4 lymphocytes’ count in HIV patients from complete blood count. BMC Medical Physics. 2013;13:3.
Rodríguez J, Bernal P, Correa C, et al. Predicción de unión de péptidos de MSA-2 y AMA-1de Plasmodium falciparum al HLA clase II. Inmunología. 2009;28(3):115-24.
Rodríguez J, Bernal P, Prieto S, et al. Teoría de péptidos de alta unión de malaria al glóbulo rojo: predicciones teóricas de nuevos péptidos de unión y mutaciones teóricas predictivas de aminoácidos críticos. Inmunología. 2010;29(1):7-19.
Correa C, Rodríguez J, Prieto S, et al. Geometric diagnosis of erythrocyte morphophysiology. J Med Med Sci. 2012;3(11):715-20.
Rodríguez J. Método para la predicción de la dinámica temporal de la malaria en los municipios de Colombia. Rev Panam Salud Pública. 2010;27(3):211-8.
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