## 1 Introduction  
Orthodontic treatment is performed to obtain optimal occlusion in the functional harmony as well as well-balanced dental and facial esthetics in each individual [1]. When an orthodontic force is applied, alveolar bone resorption occurs at the compression side of tooth, whereas bone formation is induced in the tension side. Thus, tooth movement is observed in specific directions [2]. During orthodontic treatment, undesirable side effects are also observed, such as pain caused by chewing, loss of tooth vitality, and root resorption [3]. These side effects are induced by molecular mechanisms. For example, the first and second ones are reported to be associated with early phase reduction in alkaline phosphatase activity in dental pulp tissue [4].  
In orthodontic treatment, malocclusion with an anterior open bite is considered one of the most difficult problems to treat because it occurs due to interaction between numerous etiologic factors such as genetic, dental, skeletal, functional, soft tissue, and habit [5]. Generally, clinical features such as increased lower facial height, increasedgonal and mandibular plane angles, and increased molar dentoalveolar height have been associated with anterior open bites [6]. Among various treatment approaches, molar intrusion is recommended for anterior open-bite patients [7]. Recently, treatment with temporary anchorage devices (TADs), including miniplates and miniscrews, has been established [8], and an application of TADs to molar intrusion has improved the prognosis of treatment for anterior open bites by reducing the uncertainty of the outcome owing to patient cooperation [9; 10; 11; 12]. In addition, molar intrusion with TADs reduces a need for orthognathic surgery in borderline open-bite cases [13].  
Some studies recommended the application of miniscrews in both palatal and buccal alveolar regions of the molars, because the intrusive load can be alternated independently in each region and molar movement was controlled precisely [14; 15]. However, this method causes root proximity to the miniscrews as the intrusion progresses, and it induces failure of miniscrews [16]. Moreover, this method inevitably involves serious risks of sinus perforation and injury to tooth roots, nerves, blood vessels, etc., since the devices require drilling into the bone tissue for fixation [17; 18]; therefore, placement sites of miniscrews are restricted.  
As an effective solution to these problems, the midpalatal area is adopted as a placement site of miniscrews to perform maxillary molar intrusion. The use of midpalatal miniscrews is considered to be a useful and less invasive procedure that can ensure good stability [19]. One approach with a midpalatal miniscrew is to apply an intrusive load from a midpalatal miniscrew-attached extension arm (MMEA) (Figure 1) [19; 20]. Currently, in molar intrusion with MMEA, a transpalatal arch (TPA) is applied together because using only MMEA will cause a palatal tipping movement of the molar. However, TPA induces patient's discomfort and jeopardizes oral hygiene, thus alternative methods to TPA have to be considered. Hence, the objective of this study was to optimize the loading condition for maxillary molar intrusion avoiding tipping movement by using only MMEA through finite element (FE) analysis.