# Nonlinear Deterministic Methods for Computer Aided Diagnosis in Case of Kidney Diseases

### Andreea Udrea, Mihai Tanase, Dumitru Popescu

#### Abstract

This paper proposes a set of nonlinear deterministic methods derived from chaos theory that can serve as computed aided diagnosis tools for kidney diseases based on computer topographies (CT). These procedures target the classification of the analyzed tissue samples in normal, malign and benign affected and also enhanced visualization of the CT images. The classification methods consist in estimating the fractal dimension of the kidney tissue and, respectively, the correlation dimension of the attractor obtained from the spatial series associated to the kidney image. The enhanced visualization method associates a fractal map to the analysed image. The methods are tested on 120 CTs presenting normal and modified tissue. The degree of trustworthiness of the methods while dealing with classifications is discussed based on statistical results and samples of fractal maps associated to the images are also presented.

#### References

- Bassingthwaighte J. B., Liebovitch L. S., West B. J., 1994. Fractal Physiology. Oxford University Press
- Dobrescu R., Vasilescu C., 2004. Interdisciplinary applications of fractal and chaos theory. Romanian Academy Press, pp. 247-254, 2004
- Luzi P., Bianciardi G., Miracco C., De Santi M.M., Del Vecchio M., Alia L., Tosi P., 1999. Fractal analysis in human pathology. Ann. N.Y. Acad. Sci. 879, 255-257
- Landini G., 1998. Complexity in tumor growth patterns, Fractals in Biology and Medicine. BirkhĂ¤user Verlag, pp. 268-284
- Kantz H., Schreiber T., 2003. Nonlinear time series analysis, 2003. Cambridge University Press, 3rd edition
- Mekler A., 2008. Calculation of EEG correlation dimension: Large massifs of experimental data. Computer Methods and Programs in Biomedicine, vol. 92, pp. 154-160
- Peitgen H. O., Jurgens H., Saupe D., 1992. Chaos and Fractals - New Frontiers of Science. Springer-Verlag
- Perc M., 2005. Nonlinear time series analysis of human electrocardiogram. In European Journal of Physics, vol. 26, pp. 757-768.
- Pritchard W. S., Duke D. W., 1995. Measuring chaos in the brain: A tutorial review of EEG dimension estimation. Brain Cognition, vol. 27, pp. 353-397
- Rajendra U., Faust O., Kannathal N., Chua T., Laxminarayan S., 2005. Non-linear Analysis of EEG Signals at Various sleep stages. In Computer Methods and Programs in Biomedicine, vol. 80, pp. 37-45.
- Takens F., 1981. Detecting strange attractors in fluid turbulence. In Dynamical System andTurbulence, Rand D. A., Young, L. S. (Eds), Lecture Notes in Mathematics, Springer Verlag
- Widman G., Schreiber T., Rehberg B., Hoerof A., Elger C. E., 2000. Quantification of depth of anesthesia by nonlinear time series analysis of brain electrical activity. Physical Review E, no. 62, pp. 4898-4903

#### Paper Citation

#### in Harvard Style

Udrea A., Tanase M. and Popescu D. (2012). **Nonlinear Deterministic Methods for Computer Aided Diagnosis in Case of Kidney Diseases** . In *Proceedings of the 9th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,* ISBN 978-989-8565-21-1, pages 511-516. DOI: 10.5220/0004039405110516

#### in Bibtex Style

@conference{icinco12,

author={Andreea Udrea and Mihai Tanase and Dumitru Popescu},

title={Nonlinear Deterministic Methods for Computer Aided Diagnosis in Case of Kidney Diseases},

booktitle={Proceedings of the 9th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,},

year={2012},

pages={511-516},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0004039405110516},

isbn={978-989-8565-21-1},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 9th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,

TI - Nonlinear Deterministic Methods for Computer Aided Diagnosis in Case of Kidney Diseases

SN - 978-989-8565-21-1

AU - Udrea A.

AU - Tanase M.

AU - Popescu D.

PY - 2012

SP - 511

EP - 516

DO - 10.5220/0004039405110516