Effects of Condylar Elastic Properties to Temporomandibular Joint Stress

Table 1

Ultrasound velocity and elastic property of the condyle (mean ± SD, 𝑛=6).

Ultrasound velocity		Elastic coefficients		Technical constants (GPa)
(×10^3 m/s)		(GPa)		Young’s modulus		Shear modulus		Poisson’s ratio
𝑣11	1.73±0.04	𝑐11	4.19±0.12	𝐸1	3.05±0.16	𝐺12	0.88±0.03	𝜈21	0.42±0.03
𝑣22	1.79±0.08	𝑐22	4.60±0.21	𝐸2	3.58±0.19	𝐺23	0.95±0.05	𝜈12	0.36±0.01
𝑣33	1.53±0.01	𝑐33	3.25±0.18	𝐸3	2.73±0.19	𝐺13	0.68±0.04	𝜈31	0.28±0.02
𝑣12/12	0.90±0.02	𝑐44	0.95±0.05					𝜈13	0.31±0.02
𝑣23/23	0.93±0.01	𝑐55	0.68±0.04					𝜈23	0.17±0.03
𝑣13/13	0.97±0.03	𝑐66	0.86±0.03					𝜈32	0.13±0.02
𝑣12	0.79±0.01	𝑐12	1.99±0.05
𝑣23	0.83±0.02	𝑐23	1.39±0.02
𝑣13	0.70±0.03	𝑐13	1.12±0.05

𝑣: ultrasound velocities that were measured directly by ultrasonic method; 𝑣₁₁, 𝑣₂₂, 𝑣₃₃, 𝑣_12/12, 𝑣_23/2𝑋, 𝑣_13/13 were longitudinal wave speed measured with the generation and sensing transducer in line, and 𝑣₁₂, 𝑣₂₃, 𝑣₁₃ were the transverse wave speed measured with the generation and sensing transducer at a right angle. 𝑐: elastic coefficients that were calculated from 𝑣. 𝐸 (Young’s modulus), 𝐺 (Shear modulus), and 𝜈 (Poisson’s ratio) were calculated from 𝑐 and would be further applied into the finite element analysis for material definition of the condyle. For subscript numbers of 𝑣, 𝐸, 𝐺, and 𝜈. 1 was in the antero-posterior direction, 2 was in the vertical direction, and 3 was in the mesio-lateral direction, while the subscript numbers of 𝑐 did not the indicate directions, which were just the calculation results from 𝑣𝑖𝑗 and further for calculating the technical constants.