Growth and development of the maxillofacial complex is of tremendous interest to scientists, clinicians, and even the general public. Most craniofacial anomalies and dentofacial deformities result from inherited mutations and aberrant environmental modulation of multiple genes. Mechanical forces readily modulate the bone and cartilage growth [10]. An exogenous force must possess certain characteristics before it qualifies as a mechanical stimulus, defined as a mechanical signal capable of eliciting anabolic or catabolic growth response. The three-dimensional finite element analysis applied in the mechanical analysis of stresses and strain in the field of engineering makes it possible to elucidate the biomechanical state variables such as displacement, strain and stress induced in living structures by various external forces.

Patients with clefts of the lip and palate present with an abnormal skeletal structure and facial morphology as a result of intrinsic, functional and iatrogenic causes [10]. In patients with a unilateral cleft lip and palate, asymmetric development of the facial skeleton in all three planes (transverse, sagittal and coronal) has been documented in literature [11]. A multitude of variables can influence the outcome leading to such asymmetry, such as the geometry of the cleft itself and the resulting differences in the transfer of occlusal loading forces that can influence subsequent upper facial skeletal development and remodeling [1]. The complete unilateral cleft lip and palate introduces an asymmetry in the facial skeleton and the extent to which it contributes to the skeletal deformity remains to be elucidated.

The finite element methods previously had been used to model the load transfers within the skull and the maxilla [12]. However, none of these studies addressed the clinically relevant situation in which the facial skeleton is disrupted by a cleft. As the first step toward developing a clinically relevant, patient-specific FEM, the present study focused solely on the biomechanical response to the occlusal forces in the maxillary complex of a unilateral cleft lip and palate. During masticatory function such as incising, masticating and chewing, the functional loads are transmitted through the dentition to the maxilla and upper mid-facial skeleton. In an unaffected maxilla, the transmission of occlusal loads would be expected to result in symmetrical stress and strain distribution within the mid-facial skeleton to the extent of the symmetry of the facial skeleton [1].

The current FEM model revealed stress concentration zones at the medial nasomaxillary buttresses on both the non-cleft and cleft sides, with a higher stress concentration observed on the non-cleft side as well as at the lateral zygomatic-maxillary buttresses. These locations clinically correspond to the structural buttresses where the bone is thicker anatomically [1]. A wider area of stress distribution was also observed on the non-cleft side of the maxillary complex when compared to the cleft side. The presence of a unilateral cleft lip and palate breaches the structural integrity of the skeleton and alters the transmission pattern of the functional loads within the maxilla, which is transmitted primarily through the non-cleft side rather than the cleft side. Correspondingly, the stress and strain distribution on the maxillary complex with a complete unilateral cleft lip and palate is both non-uniform and asymmetric with regard to the mid-sagittal plane, i.e., the stresses and strain intensified on the non-cleft side and decreased on the cleft side. These predictions confirm our first hypothesis that the complete unilateral cleft lip and palate leads to a non-uniform and asymmetric stress and strain distribution pattern in the maxillary complex of such an individual. Such an asymmetric stress and strain distribution would suggest an asymmetrical skeletal development on the non-cleft side when compared to the cleft side.

The fact that a certain level of stress and strain, corresponding to the threshold strain, is required to trigger the strain-induced bone modeling [13], the skeletal segments with higher stress and strain levels, such as the non-cleft side, would be expected to have a greater potential to develop and grow in response. In contrast, the segment with lower stress and strain levels, such as the cleft side, is less likely to further develop and grow. This may provide a possible explanation, from a biomechanical point of view, as to why the individual with a unilateral cleft lip and palate develops a differential between the two maxillary segments both in volumetric size and in spatial dimensions [3]. However, our study does not exclude the effect of other extrinsic, intrinsic and iatrogenic factors that may contribute to the mid-facial skeletal asymmetry.

As a preliminary study on a patient-specific cleft lip and palate, certain assumptions were necessary to simplify the model and to emphasize the stresses in the maxillary complex. The application of a linear elastic material model to the maxilla neglected the nonlinear dynamic responses of the bony materials. The homogeneous and isotropic assumption simplified the structure of the maxillary bone and especially the unique load-bearing feature of the dentition and the surrounding soft tissues such as the periodontal ligament. Additionally, assumptions about material properties of the dentition and periodontal tissues, together with the simulated occlusal loading forces at the dentition, would lead to a less accurate prediction within the immediate dental region. Whereas the material model was more accurate with regard to the maxillary complex as a whole, the loading effect, according to St. Venant’s principle, would be less likely to significantly influence the predictions in the region of interest that are away from where the loads were applied. Therefore, the stress and strain pattern on the maxillary complex, away from the dentition, would be expected to be more accurate.

Previous studies on the facial skeletal development revealed that individuals with unilateral cleft lip and palate present with a significant degree of facial asymmetry as seen on frontal cephalometric radiographs at the level of the nasomaxillary complex [13], as well as of the lower facial skeleton [14]. When the stress patterns were evaluated, the results of this study were similar to the studies of Zhao et al., who also concluded that the stresses were intensified on the non-cleft side [1]. The stress distributions in these studies were accepted as uneven and asymmetric with regard to the midline plane. In the said study, a clefting pattern was introduced to a normal maxilla in a FE model to study the stress and strain distribution. However, material properties to separate cancellous, cortical bone and teeth were not included. The action of the masseter muscle during occlusal loading was also not taken into consideration. The fact that individuals with unilateral cleft lip and palate display a unilateral malformation allowed us to utilize the measurements of the contralateral non-cleft side of the individual as internal control. However, the fact that normal and ‘clefting’ occur in the same individual should be taken into consideration when interpreting the results, since it is possible that the development of the cleft side could influence the control side within the same individual [15].

Biomechanical models of the human maxillary complex and the masticatory system are not perfect, while they are based on a number of assumptions and simplifications. The adequacy of the FE computational model to the real system depends on the correctness of representation of the geometry and material properties of the modeled object, the type and number of elements and the boundary conditions imposed on the model. The point of application, magnitude, and direction of forces may easily be varied to simulate the clinical situation. Thus, FEM would be an effective approach in the investigation of the biomechanical behavior of the maxillofacial skeleton in all three planes. It should also be noted that the structure and spatial relationships of various craniofacial components vary among individuals with cleft lip and palate. These factors may contribute to varied responses of the maxillary complex on simulated occlusal loading. Though the results of the study are valid only for a patient-specific maxillary complex, the displacement can be a baseline for a larger population. Determination of strains and stresses in the maxillary complex of a unilateral cleft lip and palate patient under simulated occlusal loading has an important impact in different clinical situations. From a biological view, it is known that strains determine to a great extent the functional behavior of bone cells. Therefore, knowledge of this parameter may permit assessment of the regenerative capacity of bone turnover in various states (fracture healing, callus stabilization or transplant healing).

Concerning the biomechanics of bones, stress evaluation in various anatomical zones can be used to investigate potential fracture sites under simulated loading. Additionally, new prostheses design for the rehabilitation of cleft palate patients can be improved, through the help of combined assessment of stresses and strains. Hence, it may be possible to minimize facial disfiguration in affected patients by addressing the mid-facial asymmetries in the growing cleft patients at early developmental stages. The maxillofacial surgeon can make use of stress distribution for better treatment for correcting jaw anomalies. The study also helps to estimate patient-specific tooth load distribution in a complete unilateral cleft lip and palate patient. This could provide reference data for studies on the biomechanics of prosthetic devices used in the rehabilitation of cleft patients.