Fractal dynamics of time series fluctuations for estimating the efficiency of dolphin-assisted therapies on children with trisomy 21

In particular, certain types of disabilities such as trisomy 21 or Down Syndrome have both physical and alternative therapies. Among the alternative therapies are dolphin-assisted ones, which is a technique that consists in the interaction of the human being with dolphins (usually of the bottlenose species), where a therapist also intervenes; through which we try to improve the quality of life of both children and adults who suffer serious health problems, especially chronic diseases and psychological. In the present study, the Electroencephalogram (EEG) signal recorded during a session of Dolphin Therapy in children with Down Syndrome is evaluated. From the EEG of children diagnosed were built time series fluctuations, specifically of standard deviation ν (t, τ). The self-affinity of the time series ν (t, τ) (treated as interfaces in motion) is characterized by the scaling behavior of the structure functions $\sigma \propto \left( {\delta _t^H} \right)$, with H as the roughness exponent. It was found that the behavior of children with trisomy 21 is similar to the modeled by the Family-Vicsek scaling dynamic for a kinetic roughening of moving interface. Therefore it would possible to characterize and model the studied time series ν (t, τ) by using the tools from the theory of kinetic roughening such as the Langeving type $\frac{{\partial V}}{{{\partial _\tau }}} = \Phi \left( {\frac{{\partial V}}{{{\partial _\tau }}}} \right) + \eta \left( {t,\tau } \right) + F$ where F is the external force, η (t, τ) the noise, and Φ is the real form of the function.