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Early auditory deprivation has serious neurodevelopmental and cognitive repercussions largely derived from impoverished and delayed language acquisition. These conditions may be associated with early changes in brain connectivity. Vibrotactile stimulation is a sensory substitution method that allows perception and discrimination of sound, and even speech. To clarify the efficacy of this approach, a vibrotactile oddball task with 700 and 900 Hz pure-tones as stimuli [counterbalanced as target (T: 20% of the total) and non-target (NT: 80%)] with simultaneous EEG recording was performed by 14 profoundly deaf and 14 normal-hearing (NH) subjects, before and after a short training period (five 1-h sessions; in 2.5–3 weeks). A small device worn on the right index finger delivered sound-wave stimuli. The training included discrimination of pure tone frequency and duration, and more complex natural sounds. A significant P300 amplitude increase and behavioral improvement was observed in both deaf and normal subjects, with no between group differences. However, a P3 with larger scalp distribution over parietal cortical areas and lateralized to the right was observed in the profoundly deaf. A graph theory analysis showed that brief training significantly increased fronto-central brain connectivity in deaf subjects, but not in NH subjects. Together, ERP tools and graph methods depicted the different functional brain dynamic in deaf and NH individuals, underlying the temporary engagement of the cognitive resources demanded by the task. Our findings showed that the index-fingertip somatosensory mechanoreceptors can discriminate sounds. Further studies are necessary to clarify brain connectivity dynamics associated with the performance of vibrotactile language-related discrimination tasks and the effect of lengthier training programs.

Children with mathematical difficulties usually have an impaired ability to process symbolic representations. Functional MRI methods have suggested that early frontoparietal connectivity can predict mathematic achievements; however, the study of brain connectivity during numerical processing remains unexplored. With the aim of evaluating this in children with different math proficiencies, we selected a sample of 40 children divided into two groups [high achievement (HA) and low achievement (LA)] according to their arithmetic scores in the Wide Range Achievement Test, 4th ed.. Participants performed a symbolic magnitude comparison task (i.e. determining which of two numbers is numerically larger), with simultaneous electrophysiological recording. Partial directed coherence and graph theory methods were used to estimate and depict frontoparietal connectivity in both groups. The behavioral measures showed that children with LA performed significantly slower and less accurately than their peers in the HA group. Significantly higher frontocentral connectivity was found in LA compared with HA; however, when the connectivity analysis was restricted to parietal locations, no relevant group differences were observed. These findings seem to support the notion that LA children require greater memory and attentional efforts to meet task demands, probably affecting early stages of symbolic comparison.

One of the fields of applied mathematics is related to model analysis. Biomedical systems are suitable candidates for this field because of their importance in life sciences including therapeutics. Here we deal with the analysis of a model recently proposed by Espinoza-Valdez et al. (2010) for the kidney vasculature developed via angiogenesis. The graph theory allows one to model quantitatively a vascular arterial tree of the kidney in sense that (1) the vertex represents a vessels bifurcation, whereas (2) each edge stands for a vessel including physiological parameters. The analytical model is based on the two processes of sprouting and splitting angiogeneses, the concentration of the vascular endothelial growth factor (VEGF), and the experimental data measurements of the rat kidneys. The fractal dimension depends on the probability of sprouting angiogenesis in the development of the arterial vascular tree of the kidney, that is, of the distribution of blood vessels in the morphology generated by the analytical model. The fractal dimension might determine whether a suitable renal vascular structure is capable of performing physiological functions under appropriate conditions. The analysis can describe the complex structures of the development vasculature in kidney.