## 1 Introduction  
Human locomotion is controlled through a complex sensorial integration of different types of information, in particular about the relative motion between the body and the surrounding environment [1]. Visual, vestibular, proprioceptive, and auditory information is integrated by the central nervous system, allowing the generation of the perception of motion [2]. Though walking is influenced by different factors [3], the main contribution derives from visual, vestibular and proprioceptive signals. Using static cues, object-motion cues and optical flow cues, the visual system allows us to discriminate self-motion from movement of objects of the environment [4]. Vestibular cues provide motion data about changes of velocity or direction-based data about accelerations [5]. Lastly,the proprioceptive system uses joint- and muscle-related information to provide feedback about the status of the whole musculoskeletal system, which greatly contributes to the perception and control of motion during active movements [3]. Speed perception, goal-directed movements, navigation, and collision avoidance all rely on the congruency and integration of the signals provided by these different sensory systems.  
Visual information plays an important role in motion perception. In particular, optical flow information is used to estimate direction [6], egocentric speed [7], and time-to-collision [8], and it heavily contributes to heading perception [9; 10; 11]. The absolute travelled distance can also be calculated by integrating this information [12; 13]. However, when visual cues are in conflict with other sensory information about self-motion, visual information not always constitutes the \"dominant\" source of information [4; 14]. In fact, when walking at constant speed, people tend to weight the information deriving from proprioceptive cues higher than visual cues [15; 16; 17]. Nevertheless, visual input seems to have a great impact on self-motion perception while walking, and studies have shown how the manipulation of the optical flow affects visuomotor recalibration [11; 15; 17; 18; 19]. In particular, it was found that if optical flow is manipulated to create sensory conflicts when walking, the locomotor speed decreases as the optical flow speed increases [15; 20], suggesting a response to the relative weightings assigned to different sensory cues, in this case proprioceptive and visual cues [15]. Some studies have also shown that the manipulation of optical flow can significantly influence locomotor patterns [15; 17; 21; 22].  
All above-mentioned studies were performed with walking participants and, to our knowledge, the influence of optical flow on self-motion perception and on locomotor patterns has never been investigated with running individuals. Yet, locomotor patterns are modulated differently in walking and running [23; 24; 25], with automated spinal programs allowing path integration in running, while walking is more dependent on visual control [24]. For this reason, one might wonder whether the results obtained with walking individuals can be generalized to running individuals.  
Here we investigated how the presence and manipulation of a virtual optical flow influences the control of locomotion while running on a treadmill. In Experiment 1, we tested how the presence and manipulation of a virtual optical flow influences self-motion speed perception. Specifically, participants were instructed to retrieve a previously presented reference running speed while being exposed to different optical flow conditions. In Experiment 2, we investigated how the presence and manipulation of an artificial optical flow influences gait parameters while treadmill running at a self-selected constant speed with different optical flow conditions.