Abstract
In this paper, a novel black-box modelling scheme applied to non-invasive temperature prediction in a homogeneous medium subjected to therapeutic ultrasound is presented. It is assumed that the temperature in a point of the medium is non-linearly related to some spectral features and one temporal feature, extracted from the collected RF-lines. The black-box models used are radial basis functions neural networks (RBFNNs), where the best-fitted models were selected from the space of model structures using a genetic multi-objective strategy. The best-fitted predictive model presents a maximum absolute error less than 0.4°C in a prediction horizon of approximately 2 h, in an unseen data sequence. This work demonstrates that this type of black-box model is well-suited for punctual and non-invasive temperature estimation, achieving, for a single point estimation, better results than the ones presented in the literature, encouraging research on multi-point non-invasive temperature estimation.



Similar content being viewed by others
References
Afantitis A, Melagraki G, Makridima K, Alexandridis A, Sarimveis H, Iglessi-Markopoulou O (2005) Prediction of high weight polymers glass transition temperature using RBF neural networks. J Mol Struc Theochem 716:193–198
Billings S, Voon W (1986) Correlation based model validity tests for non-linear models. Int J Control 44:235–244
Chinrungrueng C, Squin CH (1995) Optimal adaptive K-means algorithm with dynamic adjustment of learning rate. IEEE Trans Neural Netw 6:157–169
Ferreira PM, Faria EA, Ruano AE (2002) Neural network models in greenhouse air temperature prediction. Neurocomputing 43:51–75
Ferreira PM, Ruano AE, Fonseca CM (2003) Genetic assisted selection of RBF model structures for greenhouse inside air temperature prediction. In: Proceedings of IEEE conference on control applications, Istanbul, Turkey, vol 1, pp 576–581
Fonseca CM, Fleming PJ (1993) Genetic algorithms for multi-objective optimization: Formulation, discussion and generalization. In: Forrest S (ed) Proceedings of 5th international conference on genetic algorithms, pp 416–423
Ruano AE, Fleming PJ, Jones DI (1992) A connectionist approach to pid autotuning. IEE Proceedings, Brighton, UK, Part D, 139:279–285
Ruano AE, Crispim EM, Conceição EZE, Lúcio MMJR (2005) Prediction of building’s temperature using neural networks models. Energy Buildings (in press)
Simon C, VanBaren P, Ebbini ES (1998) Two-dimensional temperature estimation using diagnostic ultrasound. IEEE Trans Ultrason Ferroelectr Freq Control 45:1088–1099
Teixeira CA, Cortela G, Gomez H, Ruano MG, Ruano AE, Negreira C, Pereira WCA (2004) Temperature models of a homogeneous medium under therapeutic ultrasound. IFMBE News 69:52–56, URL: http://www.ifmbe-news.iee.org/ifmbe-news/nov2004/nov04s.pdf
Ter Haar G (1999) Therapeutic ultrasound. Eur J Ultrasound 9:3–9
Acknowledgements
The authors would like to thank the financial support of: Fundação para a Ciência e a Tecnologia (grant SFRH/BD/1461/2003), Portugal, and Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq/CYTED/ 490.013/03-1), Brazil. The authors would also like to acknowledge Prof. Hector Gomez and M.Sc. Guillermo Cortela for their support in the real data collection.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Teixeira, C.A., Ruano, A.E., Ruano, M.G. et al. Non-invasive temperature prediction of in vitro therapeutic ultrasound signals using neural networks. Med Bio Eng Comput 44, 111–116 (2006). https://doi.org/10.1007/s11517-005-0004-2
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11517-005-0004-2