Development of the mandibular curve of spee and maxillary compensating curve: A finite element model

The curved planes of the human dentition seen in the sagittal view, the mandibular curve of Spee and the maxillary compensating curve, have clinical importance to modern dentistry and potential relevance to the craniofacial evolution of hominins. However, the mechanism providing the formation of these curved planes is poorly understood. To explore this further, we use a simplified finite element model, consisting of maxillary and mandibular “blocks”, developed to simulate tooth eruption, and forces opposing eruption, during simplified masticatory function. We test our hypothesis that curved occlusal planes develop from interplay between tooth eruption, occlusal load, and mandibular movement. Our results indicate that our simulation of rhythmic chewing movement, tooth eruption, and tooth eruption inhibition, applied concurrently, results in a transformation of the contacting maxillary and mandibular block surfaces from flat to curved. The depth of the curvature appears to be dependent on the radius length of the rotating (chewing) movement of the mandibular block. Our results suggest mandibular function and maxillo-mandibular spatial relationship may contribute to the development of human occlusal curvature.

矢状面（sagittal view）下观察到的人类牙列（human dentition）所呈现的曲面形态，即下颌斯匹氏曲线（mandibular curve of Spee）与上颌补偿曲线（maxillary compensating curve），在现代牙科学中具有重要临床价值，且与人亚科类群（hominins）的颅面演化（craniofacial evolution）存在潜在关联。然而，目前对这些曲面形态形成的机制仍知之甚少。为进一步探究该机制，我们构建了由上颌与下颌“块体”组成的简化有限元模型（finite element model），用于在简化的咀嚼功能（masticatory function）过程中模拟牙齿萌出（tooth eruption）以及对抗萌出的作用力。我们验证了如下假说：曲面咬合平面（occlusal planes）是由牙齿萌出、咬合载荷（occlusal load）与下颌运动（mandibular movement）之间的相互作用形成的。研究结果表明，同时施加节律性咀嚼运动（rhythmic chewing movement）、牙齿萌出与牙齿萌出抑制的模拟操作后，上颌与下颌块体的接触表面会从平坦形态转变为曲面形态。曲面的深度似乎取决于下颌块体旋转（咀嚼）运动的半径长度。本研究结果提示，下颌功能与上下颌空间关系或可助力人类咬合曲面的形成。