# Transcranial Doppler-Based Neurofeedback to Improve Hemispheric Lateralization
## 1 Introduction  
Functional brain lateralization is a well-established principle in humans and other vertebrates [1]. It is a crucial concept for understanding how cognitive and motor activities are organized within the cerebral hemispheres. This phenomenon is particularly important for evaluating lateralized functions, such as symbolic communication, perception-action coupling, emotions, and decision-making processes [2]. Brain asymmetry displays significant implications and has been extensively studied through functional neuroimaging techniques for stroke recovery [3, 4], neurological disorders [5, 6, 7, 8], and applications in brain-computer interfaces (BCIs) and rehabilitative treatments [9, 10, 11]. Despite growing interest in lateralization in clinical and cognitive neuroscience, training its modulation through neurofeedback methodologies remains underexplored. Neurofeedback is a cognitive training technique that allows subjects to voluntarily modulate their brain activity through real-time feedback of a given indicator of mental activity. The underlying hypothesis is that this training enhances the cognitive abilities associated with the targeted brain activity by inducing neuroplastic changes in brain structures, affectingthe strength and number of synaptic connections, as well as white matter myelination and gray matter volume [12]. Although plasticity is greatest before adolescence, it persists throughout life and underlies brain development and learning [13]. Neurofeedback has found applications in the treatment of many physical and mental disorders, as well as in the field of brain-computer interfaces (BCI) [14; 15; 16]. In the latter case, it may be used to train both healthy individuals and patients to improve their control over external devices or to interact with virtual environments, making BCI technologies more responsive to the user's cognitive and emotional state [15]. Electroencephalography (EEG) stands out as the primary tool for capturing real-time electrical patterns in the brain, from which different parameters can be extracted and used as feedback signals, most commonly in visual or auditory form [17; 18]. Beside EEG, hemodynamic correlates of brain activity, such as changes in cerebral blood flow and oxygenation generated by neurovascular coupling [19], can also be detected and used for neurofeedback. Several studies have demonstrated this possibility using functional magnetic resonance imaging (fMRI) [20; 21; 22; 23] and more recently, near-infrared spectroscopy (fNIRS) [24; 25]. Compared to the weak and noisy EEG signals, hemodynamic measurements may offer a more robust detection of brain activation, although at a lower time resolution and requiring expensive equipment and complicated experimental procedures (particularly fMRI). In this respect, functional transcranial Doppler (fTCD) ultrasound, allowing for the continuous and bilateral measurement of blood velocity from the major cerebral arteries, offers an interesting alternative due to its non-invasiveness, robustness, portability, and possibility of real-time monitoring, while requiring a relatively low-cost instrumentation and simple experimental setup. Although characterized by low spatial resolution, it has often been employed to detect the lateralization of brain functions, particularly regarding language [26; 27; 28; 29; 30], and has also been recently proposed for BCI applications [31; 32]. Surprisingly, fTCD-based neurofeedback has been poorly investigated. However, it can be hypothesized that training over multiple sessions could lead the subject to increase the capacity to lateralize brain activity and cerebral blood flow to one hemisphere or the other. Moreover, self-training with neurofeedback allows the subjects to develop their own mental strategies, possibly achieving faster and larger hemodynamic changes, with implications in the fields of rehabilitation and BCIs [17].