## 1 Introduction
Finally, a randomized controlled trial concluded that using a palatal appliance does not result in any permanent growth change or tissue gain [21]. Various surgical techniques have also been applied in an attempt to mitigate the problems of tissue deficiency. These techniques varied between surgeons, and there is still no consensus on which is the best protocol for treating CLP patients. Seventeen different surgical sequences for repairing unilateral complete clefts were identified in a survey of over 201 European cleft centers [22]. Three main surgical principles to mitigate the tissue deficiency in CLP have evolved [23]. The first principle limits the closure only to either the oral or the nasal mucosa layer by applying a so called single-layer closure [24; 25; 26; 27]. This procedure involves turning over the mucosa from either the oral or the nasal cavity like a book page while leaving an open wound on the back side of the turned-over mucosa. The second principle involves detaching the oral tissue and shifting it over the cleft area while creating an open wound that heals outside the cleft area from where the tissue has been detached [28; 29; 30]. In the third principle, tissue from outside the palatal area is used to cover the open wound areas that result from the first or second technique [31; 32; 33; 34]. While all of these surgical techniques are able to close the cleft gap using the available tissue, none of them result in the generation of new mucoperiosteal tissue. Adjuvant therapies or strategies such as tissue expansion [35] and distraction osteogenesis (DO) [36] have been attempted to increase the volume of tissue in the areas of tissue deficiency in clefts. The principles of DO require a bone cut through the palatal shelf ridges. However, in infants this would damage the dental follicles that are embedded in the palatal shelf ridges. Most tissue engineering studies have focused on the application of biomaterials purely for bone generation [37]. However, the palatal cleft comprises bone and two mucosal layers, which makes it a difficult target for biomaterial or tissue-engineering techniques. Animal experiments suggest that periosteal distraction osteogenesis (PDO) is an appealing option for utilizing the principles of DO [38; 39; 40] for combined bone and soft tissue generation without the need for a bone cut. PDO is performed by gradual lift-up on the mucoperiosteum from the underlying bone by applying mechanical loading. The physical tissue strain and biological tissue stimulus to bone and periosteum lead to new tissue formation. We therefore address PDO as a potential treatment strategy to target the tissue deficiency in orofacial clefts while using magnetic forces to exert the necessary tissue strain. Magnetic forces have been used in orthodontics to generate tooth movement and to promote tissue reactions [41]. Finite element (FE) analysis is a numerical tool to compute the stress and strain fields in the bone structure under external loading. It thereby reveals the distribution of the internal loads and deformations. Computational FE analysis has provided crucial basic data for understanding mechanical interactions between the magnets and mucoperiosteal tissue for tissue expansion [42]. The loading distribution depends on the shape and size of individual anatomical structures and malformation. Previously, this method has been used to assess the maxillary load transfer during conventional DO in patients with cleft lip and palate [43]. In our previous study we have examined the feasibility of dental magnets as distraction devices in newborns with UCLP [44]. Unilateral clefts form 76% of all CLP cases worldwide which still leaves the BCLP, accounting for one fourth (24%) of all CLP unaddressed [45]. As the anatomy of BCLP is different from UCLP, it is the aim of this study to compare the load transfer of magnetic forces used for PDO in both UCLP and BCLP in silico models.