In modern surgery, a multitude of minimally intrusive operational techniques are used which are based on the punctual heating of target zones of human tissue via laser or radio-frequency currents. Traditionally, these processes are modeled by the bio
heat equation introduced by Pennes, who considers Fouriers theory of heat conduction. We present an alternative and more realistic model established by the hyperbolic equation of heat transfer. To demonstrate some features and advantages of our proposed method, we apply the obtained results to different types of tissue heating with high energy fluxes, in particular radiofrequency heating and pulsed laser treatment of the cornea to correct refractive errors. Hopefully, the results of our approach help to refine surgical interventions in this novel field of medical treatment.
We discuss the direct use of cubic-matrix splines to obtain continuous approximations to the unique solution of matrix models of the type $Y(x) = f(x,Y(x))$. For numerical illustration, an estimation of the approximation error, an algorithm for its implementation, and an example are given.
State estimation is necessary in diagnosing anomalies in Water Demand Systems (WDS). In this paper we present a neural network performing such a task. State estimation is performed by using optimization, which tries to reconcile all the available inf
ormation. Quantification of the uncertainty of the input data (telemetry measures and demand predictions) can be achieved by means of robust estate estimation. Using a mathematical model of the network, fuzzy estimated states for anomalous states of the network can be obtained. They are used to train a neural network capable of assessing WDS anomalies associated with particular sets of measurements.
