## 1 Introduction
Through cell-cell interactions, these precursors recognize RANK-L expressed by osteoblasts and, in the presence of macrophage colony-stimulating factor (M-CSF), undergo differentiation into osteoclasts. This binding facilitates the rapid differentiation of hematopoietic osteoclast precursors into mature osteoclasts. Mature osteoclasts, in turn, express both RANK and RANK-L, promoting their survival and stimulating bone-resorbing activity. On the other hand, osteoprotegerin (OPG), a soluble RANK-L decoy receptor predominantly produced by osteoblasts, acts to prevent osteoclast formation and boneresorption by inhibiting the interaction between RANK and RANK-L [12; 13]. OPG exerts biological effects on bone cells, including the inhibition of osteocl differentiation, the suppression of activation of matrix osteoclasts, and the induction of apoptosis. The process of bone remodeling during orthodontic tooth movement is regulated by maintaining a balance between the binding of RANK to RANK-L and the production of OPG [12; 13; 14]. Mature osteoclasts release exosomes expressing RANK on their surface, establishing a binding interaction with RANK-L in osteoblasts and triggering reverse signaling. This, in turn, activates the PI3K-Akt pathway, increasing osteoblast activity. At the same time, OPG produced by osteoblasts acts as a regulator, preventing bone resorption by binding to RANK-L expressed by osteoblasts. This interaction maintains the balance between bone resorption and formation in the dynamic process of bone remodeling [15]. Some researchers have established that between 80 and 95% of patients may present some grade of pain during orthodontic procedures. The experience of pain significantly contributes to interruptions or premature discontinuations in treatment [16]. This sensory and emotional experience, often underestimated by orthodontists, not only makes orthodontic treatment difficult but it also has detrimental effects on physical and mental health [17]. In orthodontic treatment, both modeling and bone remodeling are determinants for the rate of OTM. Bone modeling during OTM is an inflammatory process, and the rate-limiting factor of dental movement is bone resorption at the bone-periodontal ligament interface [18]. Both the vascular changes generated by OTM and the release of inflammatory mediators, such as histamine, prostaglandandins, leukotrienes, and cytokines, cause pain during treatment [19]. Several methods have been proposed to control pain caused by orthodontic treatment, such as administration of analgesics, vibratory stimulation, local anesthesia, chewing a \"bite wafer\" or gum, and, more recently, the use of low-level lasers for oral therapy [17; 20]. Treatment with nonsteroidal anti-inflammatory analgesics (NSAIDs), such as ketorolac, ibuprofen, naproxen, and COX3 inhibitors such as acetaminophen, are the most commonly used analgesics to control pain caused by orthodontic dental movement [17; 21]. Regarding drugs to inhibit or relieve pain during orthodontic treatment, such as acetaminophen and ketorolac, it is known that they can inhibit the expression of RANK-L, which can affect OTM and thus inhibit bone remodeling [22]. Currently, several studies have evaluated the effect of different analgesics such as ibuprofen, acetaminophen, and celecoxib on OTM [22; 23; 24]. However, the effect of ketorolac on RANK-L has not been evaluated, so further clinical studies are essential to determine the effect of this drug on bone resorption and, consequently, on OTM, so that the orthodontist can choose and recommend the best analgesic. Therefore, the present study aimed to compare the effects of ketorolac and acetaminophen on RANK-L during OTM.