# The Influence of Loading Program on the Stimulated Callus Mineralization
## 1 Introduction  
The mandible (lower jaw) is the only load-bearing, moveable bone in the skull. Fractures in the mandible may happen as a result of infection, car accident, falling, sudden hit, or after a resection for pathology, e.g., cancer, treatment. As the only moveable bone of the cranium (skull), the mandible is subject to stresses and because of its shape, location, and function, the loads are unique to it [1]. This work focuses on the mandible fractures and healing process of the callus tissue after trauma. Such processes are known and thoroughly described for long bones, but in literature, there are no such works about mandible where complex states of stress and strain occur. The callus is a tissue formed between two bone parts after bone trauma. This process consists of three phases: reactive, reparative, and the remodeling phase during which different cells take part. In the first hours after the trauma, fibroblasts replicate and form a loose aggregate of cells, known as granulation tissue. Then, the fibroblasts within the granulation tissue develop into chondroblasts and this process culminates in a new mass of heterogeneous tissue, which is known as a fracture callus. The mineralized matrix is penetrated by osteoblasts, which form new lamellar bone in the form of the trabecular bone [2]. During the healing process, the properties of the callus tissue change make it mechanically stronger. The Young's (elasticity) modulus of the callus, which increases in this process of mineralization, is used as an indicator of material mechanical properties. The soft callus tissue transforms into bone tissue [2]. There is a need for the formulation of mechanical models for biomaterial transformation,which enables computational analysis, eventually reducing animal studies or clinical trials, and helps to plan healing processes. There are many ways to reconstruct the mandible. The most popular one involves plates and screws. It is noted that after the bone trauma the biomechanics of mandible changes [3]. It is not possible to load it with physiological values of the biting forces since they must be significantly reduced. During the first days after surgery, the patient may only eat slurry food using a straw. The most serious cases include very radical means when the braces and rails are used to immobilize the broken region of the mandible. In such cases, there are almost no stresses in the callus and, therefore, the tissue is not stimulated. It is noted that eating tough food too soon may lead to tissue resorption and it is important to keep the patient's mandible immobilized [4; 5]. Also, when micro-cracks occur under high tissue loading, bone resorption is induced [6; 7]. According to [PERSON]'s law [8], tissue is able to change its internal material properties (i.e., density, Young's modulus) to adjust to external loads placed upon it. This biological process is called remodeling. During this process, regulated by bone cells (osteoblasts and osteoclasts), both bone loss (resorption) and formation (apposition) may occur. Based on the [PERSON] [9] mechanostat theory, bone tissue resorbs when the stimulus value drops below a certain threshold value, but formation occurs when the stimulus exceeds the upper threshold value. If a value of the mechanical stimulus remains in a lazy zone, i.e., between the lower and the upper values, remodeling does not take place. Since the applied load results in a specific strain-stress condition in the tissue material, it is accepted that the mineralization process is mechanically stimulated. It is observed that the speed of the mineralization process is not constant and changes continuously with the stimulus value. For a stimulus value beyond the lazy zone, the speed increases, reaches its maximum, and then decreases down to negative values; this is what denotes overload resorption process [3; 10; 11; 12]. Indeed, overload resorption occurs when the mechanical stimulus increases too excessively.