Page 64 - Development of Functional Scaffolds for Bone Tissue Engineering Using 3D-Bioprinting of Cells and Biomaterials - Yasaman Zamani
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where ui is the flow velocity field, ฯ is fluid density, p is pressure, and ฮผ is dynamic viscosity. Solving the fluid flow governing equations numerically yielded the fluid velocity. From the fluid velocity information, the viscous stress tensor ๐œ๐œ๐œ๐œ was attained by using the following constitutive relation for a Newtonian fluid:
where xi and xj are the spatial coordinates (j=ฬธj).
๐œ๐œ๐œ๐œ = ๐œ‡๐œ‡๐œ‡๐œ‡(๐œ•๐œ•๐œ•๐œ•๐‘ข๐‘ข๐‘ข๐‘ข๐‘–๐‘–๐‘–๐‘– + ๐œ•๐œ•๐œ•๐œ•๐‘ข๐‘ข๐‘ข๐‘ข๐‘—๐‘—๐‘—๐‘—) (3) ๐œ•๐œ•๐œ•๐œ•๐‘ฅ๐‘ฅ๐‘ฅ๐‘ฅ๐‘—๐‘—๐‘—๐‘— ๐œ•๐œ•๐œ•๐œ•๐‘ฅ๐‘ฅ๐‘ฅ๐‘ฅ๐‘–๐‘–๐‘–๐‘–
  Statistical analysis
Data are expressed as mean ยฑ standard deviation (SD). Differences in mean values were analyzed by one-way ANOVA with Tukeyโ€™s multiple comparison test using GraphPad Prismยฎ 7.0 (GraphPad Software Inc., La Jolla, CA, USA). Differences were considered significant if p<0.05.
RESULTS
Modeling
The predicted jaw movements had similar characteristics as observed habitually [30]. Jaw opening began in the midline. The mandibular condyles moved forward as the jaw-opening muscles opened the jaw in about 50 ms and moved backwards over the articular eminence during the jaw closing. Maximum opening was followed by fast closure of the jaw.
The conventions used to express symphyseal forces and torques are illustrated in Fig. 3. During jaw opening, the symphysis underwent compression by 119.7 N along its transverse y- axis. Compression along the anteroposterior x-axis and superoinferior z-axis were negligible (Fig. 3a). When the jaw reached maximum opening, the compressive force along the transverse y-axis reached 127.5 N and then decreased during jaw closing.
The highest torque was around the z-axis (6.36 N.m) at the maximum jaw opening (Fig. 3b). Torque around the x-axis was 2.35 N.m at the maximum jaw opening. Torque around the y- axis was negligible. Summing the force along the transverse y-axis (127.5 N) with the force resulting from the torque around the anteroposterior x-axis (235 N) during a cycle of jaw opening and closing, resulted in a transverse compressive force of 362.5 N that was induced on the upper rim of the 1ร—1ร—2 cm scaffold in the symphysis (equation 4):
total transverse force in the upper rim of the scaffold = force along the y-axis + torque around the x-axis
= 127.5 + 235 = 362.5 N (compressive)
(4)
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