The brain is the most complex organ of the human body. It is located in the head and is the center of the nervous system. Its largest part is the cerebral cortex, which contains tens of billions neurons. On average, each neuron is connected to other neurons through several thousand synapses, which pass electrical (or chemical) signals, to form a very intricate and extremely complex system. The brain is estimated to contain from 1 to 5× 10 synapses. The cerebral cortex is the main characteristic of the human brain (when compared to the brains of other mammals). It consists of a thick layer of neural tissue, folded in a way that maximizes the surface that can fit into the volume available (the skull, whose thick bones provide the necessary physical protection). Each side of the brain is divided into four sections, or “lobes”, called frontal lobe, parietal lobe, temporal lobe, and occipital lobe. Each of them is associated with specific functions. The so-called “executive functions”, such as attention, working memory, planning, organisation, as well as reasoning and abstract thought, are located in the more dorsolateral portions of anterior frontal lobes, while more phylogenetically “ancient” functions like emotions, risk evaluation and impulse control are situated in more medial areas belonging to the limbic system. Continuing with a rough subdivision of work: more posterior parts of the frontal lobes are in charge of voluntary movement; parietal lobes of the relationship between body and space (visuo-spatial functions); temporal lobes of memory and language (the latter lateralised to the dominant emisphere), and occipital lobes of vision. Complex association networks integrate information from the various brain regions to produce percept, thought and action. Brain structures and their functions have always fascinated scientists, philosophers and thinkers. What makes the brain special, from a wider perspective, is that its physical properties give rise to mental states and in this sense they generate what philosophers call the mind. Through more than two thousand years of Western philosophy the mind was thought to be separate from the brain. This mind-body dualism can be traced back to Plato [1] and was formulated in its modern connotation by Rene Descartes five centuries ago [2]. Despite rapid scientific progress, the mind’s connection with brain activity is not thoroughly understood and much about how the brain works remains a mystery, even nowadays. The way individual brain cells and synapses cooperate, giving rise to thought and other superior functions, has challenged biology and medicine, as well as physics and computer science. The approach to human brain damage and disease has been more successful, maybe because they are easier to define than abstract thought. The human brain is susceptible to different types of damage and disease, with different degrees of “visibility” of the pathogenetic pathway. On the one hand, there are obvious dramatic events, such as a blow to the head, a stroke, or poisoning by neurotoxins. On the other hand, there are more insidiously progressive degenerative disorders, such as Parkinson’s disease, or Alzheimer’s disease: conditions characterised by neuronal death and loss of brain volume. Finally, there are psychiatric conditions, such as schizophrenia and depression, that are also associated with brain dysfunction, although the nature of the brain abnormalities in these conditions is more subtle, and less well understood. The techniques used to study the brain can be either invasive or non-invasive. For obvious ethical reasons, the former ones are seldom performed with humans. Non-invasive techniques include neuroimaging or electroencephalography. This Focus Point of The European Physical Journal Plus contains four articles and is devoted to selected open problems in neuroscience, with the emphasis on the advanced brain signal and image processing. During the last years, the development of neuroimaging and signal processing has made the visualization and measurement of pathological brain changes in vivo possible, producing a radical change, not only in the field of scientific research, but also in the
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