## 1 Introduction  
Understanding the quantifiable effects of peripheral somatosensory stimulation in the brain is crucial, particularly in rehabilitative and therapeutic interventions designed to mitigate movement disorders that are associated with cerebrovascular stroke, traumatic brain injury, and progressive neuromotor brain diseases, which degrade locomotion, digital manipulation, speech, gesture, and deglutition [1, 2, 3]. Numerous clinical studies have shown beneficial effects of somatosensory stimulation in the treatment of movement disorders in subacute and chronic stroke patients [4, 5, 6, 7]; however, the results are far from conclusive [8, 9, 10], as the improvements can be rather subjective or extremely difficult to quantify. Another approach gaining traction in animal models involves the use of sensorimotor interventions to promote blood circulation to the infarcted areas of the brain [11, 12]. The limitations or lack of neurotechnological tools and brain imaging techniques is an impeding factor in the advancement of neurotherapeutics for sensorimotor impairments. Noninvasiveness, ease of use, portability, accessibility, affordability, personalization of care, and robust data analytics are all important factors when any potential imaging or therapeutic technique is being considered. Near-Infrared Spectroscopy (NIRS) is an emerging example of a simple yet powerful tool that can be used both as a neuroimaging modality for indirect monitoring of cortical blood oxygenation, or as a therapeutic tool when employed in brain-computer interfaces or neurofeedback applications [13; 14; 15; 16]. Since the early 1990s [17; 18], functional near-infrared spectroscopy (fNIRS) has become an increasingly appealing neuroimaging tool that is used by researchers to study the functional activation of the human brain [19; 20], particularly the cortical hemodynamic response (HR). The signals of interest in human fNIRS are derived from the photon absorption rates of two Hemoglobin (Hb) chromophores in the bloodstream, i.e., oxygenated-Hb (HbO) and deoxygenated-Hb (HbR). fNIRS is particularly suitable for studying superficial layers (2-3 cm deep) of cortex in human adults, e.g., in somatosensory and motor research, due to theoretical and practical constraints in imaging deeper layers of the adult brain imposed by the photon path, scattering and absorption [21; 22; 23; 24]. The human tactile somatosensory network is localized to the parietal and frontal cerebral cortices and it shares reciprocal connectivity with tactile-velocity representations in the cerebellum and thalamus [25]. Recent fMRI studies have demonstrated a best-velocity sensitivity to saltatory preumotactile stimuli traversing the hand [26] and face [27] ranging from 5 to 65 cm/s. Thus, reproducible and quantitative stimulus delivery is crucial in sensorimotor rehabilitation, training, and research. Additionally, noninvasiveness, versatility, and multimodal compatibility of the applicable techniques are especially important. The pneumatic tactile stimulation array used in this study [26; 28] is compatible with all imaging modalities and it enables us to systematically deliver programmable tactile stimuli in distinct patterns and salient velocities [29; 30; 31]. Methodological differences in the analysis of fNIRS data [32; 33] can potentially lead to inconsistent interpretations. Machine learning algorithms are being increasingly utilized for fNIRS analysis in order to minimize such disparities and improve reproducibility [34; 35; 36]. The initial objective of this paper is to validate the existence of any form of encoding of stimulus velocity in HR, and to ultimately design stimulus protocols, e.g., for post-stroke sensorimotor rehabilitation of upper extremities, which would maximally evoke HR in S1 and M1.