Table 1. Electronic search strategy.

Electronic database	Search strategy
PubMed	#1 (Self-ligated brackets “OR“ Self-ligating brackets “OR“ Self-ligating braces “OR” Self-ligated braces “OR “ Orthodontic self-ligation “OR” Orthodontic Self-ligated “OR” Orthodontic Self-ligating “OR“ SLBs) #2 (Orthodontics tooth movement “OR” Accelerate “OR” Acceleration “OR” Rate of tooth movement “OR” Rapid tooth movement “OR” Accelerated tooth movement “OR” Acceleration of tooth movement “OR” Speed tooth movement “OR” Rapid orthodontic tooth movement “OR” Orthodontic treatment time “OR” Duration of orthodontic treatment “OR” Short treatment time “OR” Reduction treatment time “OR” Rapid Orthodontics “OR” Accelerated orthodontics “OR” Accelerated orthodontic treatment “OR“ Regional accelerated phenomenon “OR” RAP) #3 (Cytokine ”OR“ vitamin D ”OR“ RANKL ”OR“ RANK ”OR“ MCSF ”OR“ PTH ”OR“ OPG ”OR“ Prostaglandins “OR” Calcium “OR” Photobiomodulation “OR” Vibrational stimulation “OR” Resonance “OR” Vibration “OR” Direct electrical current “OR” Light-Emitting Diode “OR” Surgical assisted tooth movement “OR” segmental alveolar distraction “OR” Intraseptal alveolar surgery “OR” soft lasers “OR” Double irradiation “OR” Single irradiation ”OR “ LLLT ” OR “ Low-Level Laser Therapy “OR” Light-emitting diode “OR” Micro-incisions OR Microincisions “OR” Micro-osteoperforations “OR” corticotomy “OR” alveolar decortication “OR” Selective alveolar decortication “OR” Corticision “OR“ Corticopuncture “OR” Cortico-puncture “OR” Piezoelectric surgery “OR” piezoelectric “OR” Piezosurgery “OR”piezocision “OR” Piezopuncture “OR” Piezotome-Corticision Assisted Orthodontics “OR” Piezoelectric Corticotomies “OR” Piezocision-assisted orthodontic treatment.” #4 #1 AND #2 AND #3
Scopus	#1 TITLE-ABS-KEY (Self-ligated brackets “OR“ Self-ligating brackets “OR“ Self-ligating braces “OR” Self-ligated braces “OR “ Orthodontic self-ligation “OR” Orthodontic Self-ligated “OR” Orthodontic Self-ligating “OR“ SLBs) #2 TITLE-ABS-KEY (Orthodontics tooth movement “OR” Accelerate “OR” Acceleration “OR” Rate of tooth movement “OR” Rapid tooth movement “OR” Accelerated tooth movement “OR” Acceleration of tooth movement “OR” Speed tooth movement “OR” Rapid orthodontic tooth movement “OR” Orthodontic treatment time “OR” Duration of orthodontic treatment “OR” Short treatment time “OR” Reduction treatment time “OR” Rapid Orthodontics “OR” Accelerated orthodontics “OR” Accelerated orthodontic treatment “OR“ Regional accelerated phenomenon “OR” RAP) #3 TITLE-ABS-KEY (Cytokine ”OR“ vitamin D ”OR“ RANKL ”OR“ RANK ”OR“ MCSF ”OR“ PTH ”OR“ OPG ”OR“ Prostaglandins “OR” Calcium “OR” Photobiomodulation “OR” Vibrational stimulation “OR” Resonance “OR” Vibration “OR” Direct electrical current “OR” Light-Emitting Diode “OR” Surgical assisted tooth movement “OR” segmental alveolar distraction “OR” Intraseptal alveolar surgery “OR” soft lasers “OR” Double irradiation “OR” Single irradiation ”OR “ LLLT ” OR “ Low-Level Laser Therapy “OR” Light-emitting diode “OR” Micro-incisions OR Microincisions “OR” Micro-osteoperforations “OR” corticotomy “OR” alveolar decortication “OR” Selective alveolar decortication “OR” Corticision “OR“ Corticopuncture “OR” Cortico-puncture “OR” Piezoelectric surgery “OR” piezoelectric “OR” Piezosurgery “OR”piezocision “OR” Piezopuncture “OR” Piezotome-Corticision Assisted Orthodontics “OR” Piezoelectric Corticotomies “OR” Piezocision-assisted orthodontic treatment” #4 #1 AND #2 AND #3
Embase	#1 (Self-ligated brackets “OR“ Self-ligating brackets “OR“ Self-ligating braces “OR” Self-ligated braces “OR “ Orthodontic self ligation “OR” Orthodontic Self-ligated “OR” Orthodontic Self-ligating “OR“ SLBs) #2 (Orthodontics tooth movement “OR” Accelerate “OR” Acceleration “OR” Rate of tooth movement “OR” Rapid tooth movement “OR” Accelerated tooth movement “OR” Acceleration of tooth movement “OR” Speed tooth movement “OR” Rapid orthodontic tooth movement “OR” Orthodontic treatment time “OR” Duration of orthodontic treatment “OR” Short treatment time “OR” Reduction treatment time “OR” Rapid Orthodontics “OR” Accelerated orthodontics “OR” Accelerated orthodontic treatment “OR“ Regional accelerated phenomenon “OR” RAP) #3 (Cytokine ”OR“ vitamin D ”OR“ RANKL ”OR“ RANK ”OR“ MCSF ”OR“ PTH ”OR“ OPG ”OR“ Prostaglandins “OR” Calcium “OR” Photobiomodulation “OR” Vibrational stimulation “OR” Resonance “OR” Vibration “OR” Direct electrical current “OR” Light-Emitting Diode “OR” Surgical assisted tooth movement “OR” segmental alveolar distraction “OR” Intraseptal alveolar surgery “OR” soft lasers “OR” Double irradiation “OR” Single irradiation ”OR “ LLLT ” OR “ Low-Level Laser Therapy “OR” Light-emitting diode “OR” Micro-incisions OR Microincisions “OR” Micro-osteoperforations “OR” corticotomy “OR” alveolar decortication “OR” Selective alveolar decortication “OR” Corticision “OR“ Corticopuncture “OR” Cortico-puncture “OR” Piezoelectric surgery “OR” piezoelectric “OR” Piezosurgery “OR”piezocision “OR” Piezopuncture “OR” Piezotome-Corticision Assisted Orthodontics “OR” Piezoelectric Corticotomies “OR” Piezocision-assisted orthodontic treatment.” #4 #1 AND #2 AND #3
Google Scholar	(Self-ligated brackets “OR“ Self-ligating brackets “OR“ Self-ligating braces “OR” Self-ligated braces “OR “ Orthodontic self-ligation “OR” Orthodontic Self-ligated “OR” Orthodontic Self-ligating “OR“ SLBs) AND (Orthodontics tooth movement “OR” Accelerate “OR” Acceleration “OR” Rate of tooth movement “OR” Rapid tooth movement “OR” Accelerated tooth movement “OR” Acceleration of tooth movement “OR” Speed tooth movement “OR” Rapid orthodontic tooth movement “OR” Orthodontic treatment time “OR” Duration of orthodontic treatment “OR” Short treatment time “OR” Reduction treatment time “OR” Rapid Orthodontics “OR” Accelerated orthodontics “OR” Accelerated orthodontic treatment “OR“ Regional accelerated phenomenon “OR” RAP) AND (Cytokine ”OR“ vitamin D ”OR“ RANKL ”OR“ RANK ”OR“ MCSF ”OR“ PTH ”OR“ OPG ”OR“ Prostaglandins “OR” Calcium “OR” Photobiomodulation “OR” Vibrational stimulation “OR” Resonance “OR” Vibration “OR” Direct electrical current “OR” Light-Emitting Diode “OR” Surgical assisted tooth movement “OR” segmental alveolar distraction “OR” Intraseptal alveolar surgery “OR” soft lasers “OR” Double irradiation “OR” Single irradiation ”OR “ LLLT ” OR “ Low Level-Laser Therapy “OR” Light-emitting diode “OR” Micro-incisions OR Microincisions “OR” Micro-osteoperforations “OR” corticotomy “OR” alveolar decortication “OR” Selective alveolar decortication “OR” Corticision “OR“ Corticopuncture “OR” Cortico-puncture “OR” Piezoelectric surgery “OR” piezoelectric “OR” Piezosurgery “OR”piezocision “OR” Piezopuncture “OR” Piezotome-Corticision Assisted Orthodontics “OR” Piezoelectric Corticotomies “OR” Piezocision-assisted orthodontic treatment”