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- Temperature models of a homogeneous medium under therapeutic ultrasoundPublication . Teixeira, C. A.; Cortela, G.; Gomez, H.; Ruano, M. Graça; Ruano, Antonio; Negreira, C.; Pereira, W. C. A.Temperature modelling of human tissue subjected to ultrasound for therapeutic use is essential for an accurate instrumental assessment and calibration. Prior studies developed on a homogeneous medium are hereby reported. Non-linear punctual temperature modelling is proposed by means of Radial Basis Functions Neural Network (RBFNN) structures. The best-performed structures are obtained using a Multiobjective Genetic Algorithm (MOGA). The best performed neural structure presents a Root Mean Square Error (RMSE) of one order magnitude less than the one presented by the best behaved linear model - the AutoRegressive with eXogenous inputs (ARX); The maximum absolute error achieved with the neural model was 0.2 ºC.
- Noninvasive black-box temperature simulation: precise spatial generalisationPublication . Teixeira, C. A.; Ruano, Antonio; Ruano, M. Graça; Pereira, W. C. A.In this paper the performance of a blackbox methodology is accessed for non-invasive timespatial temperature estimation. A gel-based phantom was heated at different intensities with therapeutic ultrasound, while temperature and RF-lines were collected. The models were trained and its structure selected to estimate the temperature in three discrete points, and at the end validated in unseen data, in the trained points and in two additional intermediate untrained points, in order to test the model s spatial generalization capacity. The best model had low complexity and a high generalization capacity, presenting in both the points and intensities a maximum absolute error inferior to 0.5 ºC, as desired in hyperthermia/diathermia.
- Linear versus non-linear non-invasive temperature predictors in a homogeneous medium subjected to physiotherapeutic ultrasoundPublication . Teixeira, C. A.; Ruano, M. Graça; Pereira, W. C. A.; Ruano, Antonio; Negreira, C.The lack of accurate time-spatial temperature estimators/predictors conditions the safe application of thermal therapies, such as hyperthermia. In this paper, a comparison between a linear and a non-linear class of models for non-invasive temperature prediction in a homogeneous medium, subjected to ultrasound at physiotherapeutic levels is presented. The linear models used were autoregressive with exogenous inputs (ARX) and the non-linear models were radial basis functions neural networks (RBFNN). In order to create and validate the models, an experiment was build to extract in vitro ultrasound RF-lines, as well as its correspondent temperature values. Then, features were extracted from the measured RF-lines and the models were trained and validated. For both the models, the best-fitted structures were selected using the multi-objective genetic algorithm (MOGA), given the enormous number of possible structures. The best RBFNN model presented a maximum absolute predictive error in the validation set five times less than the value presented by the best ARX model. In this work, the best RBFNN reached a maximum absolute error of 0.42 ºC, which is bellow the value pointed as a borderline between an appropriate and an undesired temperature estimator, which is 0.5 ºC. The average error was one order of magnitude less in the RBFNN case, and a less biased estimation was met. In addition, the best RBFNN needed less environmental information (inputs), given the capacity to non-linearly relate the information. The results obtained are encouraging, considering that coherent results should be obtained in a time-spatial modelling schema using RBFNN models.
- Neuro-genetic non-invasive temperature estimation: intensity and spatial predictionPublication . Teixeira, C. A.; Ruano, M. Graça; Ruano, Antonio; Pereira, W. C. A.Objectives: The existence of proper non-invasive temperature estimators is an essential aspect when thermal therapy applications are envisaged. These estimators must be good predictors to enable temperature estimation at different operational situations, providing better control of the therapeutic instrumentation. In this work, radial basis functions artificial neural networks were constructed to access temperature evolution on an ultrasound insonated medium. Methods: The employed models were radial basis functions neural networks with external dynamics induced by their inputs. Both the most suited set of model inputs and number of neurons in the network were found using the multi-objective genetic algorithm. The neural models were validated in two situations: the operating ones, as used in the construction of the network; and in 11 unseen situations. The new data addressed two new spatial locations and a new intensity level, assessing the intensity and space prediction capacity of the proposed model. Results: Good performance was obtained during the validation process both in terms of the spatial points considered and whenever the new intensity level was within the range of applied intensities. A maximum absolute error of 0:5 C 10% (0.5 8C is the gold-standard threshold in hyperthermia/diathermia) was attained with low computationally complex models. Conclusion: The results confirm that the proposed neuro-genetic approach enables foreseeing temperature propagation, in connection to intensity and space parameters, thus enabling the assessment of different operating situations with proper temperature resolution.
- NARX structures for non-invasive temperature estimation in non-homogeneous mediaPublication . Teixeira, C. A.; Pereira, W. C. A.; Ruano, Antonio; Ruano, M. GraçaThe safe and effective application of thermal therapies are limited by the existence of precise non-invasive temperature es-timators. Such estimators would enable a correct power deposition on the region of interest by means of a correct instrumentation control. In multi-layered media, the temperature should be estimated at each layer and especially at the interfaces, where significant temperature changes should occur during therapy. In this work, a non-linear autoregressive structure with exogenous inputs (NARX) was applied to non-invasively estimate temperature in a multi-layered (non-homogeneous) medium, while submitted to physiotherapeutic ultrasound. The NARX structure is composed by a static feed-forward radial basis functions neural network (RBFNN), with external dynamics induced by its inputs. TheNARX structure parameters were optimized by means of a multi- objective genetic algorithm. The best attained models reached a maximum absolute error inferior to 0.5 °C (proposed threshold in hyperthermia/diathermia) at both the interface and inner layer points, at four radiation intensities. These models present also a small computational complexity as desired for real-time applications. To the best of ours knowledge this is the first non-invasive estimation approach in multi-layered media using ultrasound for both heating and estimation.
- Generalization assessment of non-invasive black-box temperature estimators from therapeutic ultrasoundPublication . Teixeira, C. A.; Ruano, Antonio; Ruano, M. Graça; Pereira, W. C. A.The objective of this work is the generalisation performance assessment, in terms of intensity, of non-invasive temperature models based on radial basis functions neural networks. The models were built considering data collected at three therapeutic ultrasound intensities, (among 0.5, 1.0, 1.5 and 2.0 W/cm2) and then were validated in fresh data, which contain information from the trained intensities and form the untrained intensity. The models were built to estimate the temperature evolution (during 35 min) in a gel-based phantom, heated by physiotherapeutic ultrasound at four different intensities. It was found that the best models built without data from the intermediate intensities (0.5, 1.0 and 1.5 W/cm2) perform well in validation at all the intensities. On the other hand, the models built without data from the extrapolated intensity (2,0 W/cm2) presented unsatisfactory results in validation. This is because the models parameters were found considering a space bounded by the data used in their construction, and then the application of data outside this space resulted in poor performance. The models build without the intermediate data, for the three considered points, presented a maximum absolute error inferior to 0.5 ºC (which is accepted for therapeutic applications). The best models also presented a low computational complexity, as desired for real-time applications.
- Non-invasive tissue temperature evaluation during application of therapeutic ultrasound: precise time-spatial non-linear modellingPublication . Teixeira, C. A.; Ruano, M. Graça; Ruano, Antonio; Pereira, W. C. A.The potential of thermal therapy’s applications improve with the development of accurate non-invasive timespatial temperature models. These models should represent the non-linear tissue thermal behaviour and be capable of tracking temperature at both time-instant and spatial point. An in-vitro experiment was developed based on a gel phantom, heated by a therapeutic ultrasound (TUS) device emitting continuously. The heating process was monitored by an imaging ultrasound (IUS) transducer working in pulse-echo mode, placed perpendicularly to the TUS transducer. The IUS RF-lines and temperature values were collected 60 mm distant from the TUS transducer face. Three thermocouples were aligned along the IUS transducer axial direction and across the TUS transducer radial direction (1 cm spaced). Three different TUS intensities were applied. The non-invasive time-spatial evolutionary temperature models were created making use of radial basis functions neural networks (RBFNN). The neural network input information was: the propagation time-delay between RF-line echoes and the past temperature lags from three different medium locations and three different TUS intensities. A total of nine different operating situations were studied. The best RBFNN structures were automatically determined by a multiobjective genetic algorithm, due to the enormous number of possible structures. The RBFNN temperature models were evaluated with data never used in the models, neither at the training or structural selection phases. In order to precisely evaluate the model generalisation performance these data included the nine possible operating situations. The best model presents a maximum absolute error less than 0.5 degrees Celsius (gold-standard value for hyperthermia/diathermia applications). To be mentioned also that the best model presents low computational complexity enabling future real-time implementations. Concluding, a maximum absolute error below the gold-standard value pointed for hyperthermia/diathermia applications was attained. In addition, this methodology does not require a-priori determination of physical constants and mathematical simplifications required for analytical methodologies.