Visual peripersonal space (i.e., the space immediately surrounding the body) is represented by multimodal neurons integrating tactile stimuli applied on a body part with visual stimuli delivered near the same body part, e.g., the hand. Tool use may modify the boundaries of the peri-hand area, where vision and touch are integrated. The neural mechanisms underlying such plasticity have not been yet identified. To this aim, neural network modelling may be integrated with experimental research. In the present work, we pursued two main objectives: (i) using an artificial neural network to postulate some physiological mechanisms for peri-hand space plasticity in order to account for in-vivo data; (ii) validating model predictions with an ad-hoc behavioural experiment on an extinction patient. The model assumes that the modification of peri-hand space arises from a Hebbian growing of visual synapses converging into the multimodal area, which extends the visual receptive field (RF) of the peripersonal bimodal neurons. Under this hypothesis, the model is able to interpret and explain controversial results in the current literature, showing how different tool-use tasks during the learning phase result in different re-sizing effects of the peri-hand space. Importantly, the model also implies that, after tool-use, a far visual stimulus acts as a near one, independently of whether the tool is present or absent in the subject's hand. This prediction has been validated by an in-vivo experiment on a right brain-damaged patient suffering from visual-tactile extinction. This study demonstrates how neural network modelling may integrate with experimental studies, by generating new predictions and suggesting novel experiments to investigate cognitive processes. (Contains 3 tables and 12 figures.)