On the possibility of non-invasive multilayer temperature estimation using soft-computing methods

This work reports original results on the possibility of non-invasive temperature estimation (NITE) in a multilayered phantom by applying soft-computing methods. The existence of reliable non-invasive temperature estimator models would improve the security and efficacy of thermal therapies. These points would lead to a broader acceptance of this kind of therapies. Several approaches based on medical imaging technologies were proposed, magnetic resonance imaging (MRI) being appointed as the only one to achieve the acceptable temperature resolutions for hyperthermia purposes. However, MRI intrinsic characteristics (e.g., high instrumentation cost) lead us to use backscattered ultrasound (BSU). Among the different BSU features, temporal echo-shifts have received a major attention. These shifts are due to changes of speed-of-sound and expansion of the medium.

The originality of this work involves two aspects: the estimator model itself is original (based on soft-computing methods) and the application to temperature estimation in a three-layer phantom is also not reported in literature.

In this work a three-layer (non-homogeneous) phantom was developed. The two external layers were composed of (in % of weight): 86.5% degassed water, 11% glycerin and 2.5% agar-agar. The intermediate layer was obtained by adding graphite powder in the amount of 2% of the water weight to the above composition. The phantom was developed to have attenuation and speed-of-sound similar to in vivo muscle, according to the literature. BSU signals were collected and cumulative temporal echo-shifts computed. These shifts and the past temperature values were then considered as possible estimators inputs. A soft-computing methodology was applied to look for appropriate multilayered temperature estimators. The methodology involves radial-basis functions neural networks (RBFNN) with structure optimized by the multi-objective genetic algorithm (MOGA). In this work 40 operating conditions were considered, i.e. five 5-mm spaced spatial points and eight therapeutic intensities (I(SATA)): 0.3, 0.5, 0.7, 1.0, 1.3, 1.5, 1.7 and 2.0W/cm(2). Models were trained and selected to estimate temperature at only four intensities, then during the validation phase, the best-fitted models were analyzed in data collected at the eight intensities. This procedure leads to a more realistic evaluation of the generalisation level of the best-obtained structures.

At the end of the identification phase, 82 (preferable) estimator models were achieved. The majority of them present an average maximum absolute error (MAE) inferior to 0.5 degrees C. The best-fitted estimator presents a MAE of only 0.4 degrees C for both the 40 operating conditions. This means that the gold-standard maximum error (0.5 degrees C) pointed for hyperthermia was fulfilled independently of the intensity and spatial position considered, showing the improved generalisation capacity of the identified estimator models. As the majority of the preferable estimator models, the best one presents 6 inputs and 11 neurons. In addition to the appropriate error performance, the estimator models present also a reduced computational complexity and then the possibility to be applied in real-time.

A non-invasive temperature estimation model, based on soft-computing technique, was proposed for a three-layered phantom. The best-achieved estimator models presented an appropriate error performance regardless of the spatial point considered (inside or at the interface of the layers) and of the intensity applied. Other methodologies published so far, estimate temperature only in homogeneous media. The main drawback of the proposed methodology is the necessity of a-priory knowledge of the temperature behavior. Data used for training and optimisation should be representative, i.e., they should cover all possible physical situations of the estimation environment.