Page 78 - Development of Functional Scaffolds for Bone Tissue Engineering Using 3D-Bioprinting of Cells and Biomaterials - Yasaman Zamani

SUPPLEMENTARY INFORMATION
Details of the model
The mandible and the skull are considered as three-dimensional rigid bodies. They make contact at both temporomandibular joints and at bite points, which is located at the dental arc. A Cartesian coordinate system is fixed to the skull. The origin is defined between the joints in the midsagittal plane. The positive x-axis is pointing forward and the positive y-axis to the right, both parallel to the Frankfort Horizontal plane (FH). The positive z-axis is pointing upward, perpendicular to the FH. Mutual independent muscle elements are exerting forces between mandible and skull. Each muscle element is assumed to contract statically, and to develop a single force along a straight line. The muscle forces (Fi) are balanced by the reaction forces, elicited at the temporomandibular joints (Fj), and the bite points (Fb). During contraction of the masticatory muscles, the mandible is assumed to be in static equilibrium. When the system is not in static equilibrium, the mandible may accelerate (both linearly and rotational):
𝑁𝑁𝑁𝑁 2 𝑣𝑣𝑣𝑣𝑡𝑡𝑡𝑡𝑣𝑣𝑣𝑣 ∑𝐹𝐹𝐹𝐹𝑖𝑖𝑖𝑖+∑𝐹𝐹𝐹𝐹𝑗𝑗𝑗𝑗+𝐹𝐹𝐹𝐹𝑏𝑏𝑏𝑏=𝑚𝑚𝑚𝑚 𝑡𝑡𝑡𝑡 (1)
𝑖𝑖𝑖𝑖=1 𝑗𝑗𝑗𝑗=1 𝑁𝑁𝑁𝑁2
∑ 𝑀𝑀𝑀𝑀𝑖𝑖𝑖𝑖 + ∑ 𝑀𝑀𝑀𝑀𝑗𝑗𝑗𝑗 + 𝑀𝑀𝑀𝑀𝑏𝑏𝑏𝑏 = 𝑚𝑚𝑚𝑚 (2) 𝑖𝑖𝑖𝑖=1 𝑗𝑗𝑗𝑗=1
where moments are taken about the axes of the coordinate system.
The inputs are the activation patterns of the muscles. The constant input parameters (attachments, maximum force, fiber length, sarcomere length) had been obtained from eight human cadavers. The force a muscle exerted in interval i (Fi) was equal to:
Fi=Fmax.(FLi.FVi.FQi+FPi) (3)
where Fmax is maximal tetanic force (30 N.cm-2 of cross-section); FL is force/length factor, dependent on the length of the sarcomere; FV is force/velocity factor, dependent on the velocity of the sarcomere; FQ is activation factor, dependent on EMG level; FP is force scaling factor for the parallel elastic element. FLi and FVi depended on the average length and length change of the sarcomere in interval i, respectively. The FQi depended on iEMG levels in interval i and previous intervals, as there was a delay between the electrical and mechanical activation of the
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