Table 1.

Ranges of objective functions (F₀, SPL, subglottal pressure) and decision variable (μ₁) used for optimized simulation. Other parameters were kept constant. Three surgeries were simulated (see Figure 1). The subscripts denote the layer specified: layer 1: normal SLLP or scar; layer 2: ligament; layer 3: muscle; layer 4: implant. The material in the FEM was considered as a fiber-gel compound, fiber-like along the vocal fold longitudinally, but gel-like in the coronal plane, i.e. transversally isotropic. The longitudinal shear moduli of SLLP, ligament, and muscle were designated as ${\mu }_1^{\prime },{\mu }_2^{\prime }$, and ${\mu }_3^{\prime }$, respectively. The transverse shear moduli of SLLP, ligament, and muscle were designated as μ₁, μ₂, and μ₃, respectively, and reflect the gel properties. Viscosity is designated by η₁, η₂, and η₃. For the scar layer, ${\mu }_1^{\prime }$ would increase with greater deposition of organized collagen in the longitudinal orientation. Since collagen fibers are randomly organized in scar⁴⁵, ${\mu }_1^{\prime }$ was not altered. The lower boundary of μ₁ was increased 3-fold to account for the higher collagen fiber content in scar. This was based on the observation that scarred vocal fold tissue demonstrates a smaller range for μ with an increased lower limit.⁴⁶

	Normal vocal fold	Subepithelial	Transligamental	Subligamental
F0 (Hz)	120 (90–150)	120 (90–150)	120 (90–150)	120 (90–150)
SPL (dB)	70 (60–80)	70 (60–80)	70 (60–80)	70 (60–80)
Subglottal pressure (kPa)	0.01 to 2	0.01 to 2	0.01 to 2	0.01 to 2
μ′1 (dyn/cm2)	5000	5000	5000	5000
μ′2 (dyn/cm2)	20000	20000	20000	n/a
μ′3 (dyn/cm2)	15000	15000	15000	15000
μ′4 (dyn/cm2)	n/a	500000	500000	500000
μ1 (dyn/cm2)	5000–50000	15000–50000	15000–50000	15000–50000
μ2 (dyn/cm2)	5000	5000	5000	n/a
μ3 (dyn/cm2)	5000	5000	5000	5000
μ4 (dyn/cm2)	n/a	500000	500000	500000
η1 (poise)	2	2	2	2
η2 (poise)	2	2	2	n/a
η3 (poise)	2	2	2	2
η4 (poise)	n/a	50	50	50
Case 1 - Rectangular
VF convergence (cm)	x01 = 0.03	x01 = 0.03	x01 = 0.03	x01 = 0.03
	x02 = 0.03	x02 = 0.03	x02 = 0.03	x02 = 0.03
VF bulging (cm)	0	0	0	0
Case 2 - 1X convergent
VF convergence (cm)	x01 = 0.06	x01 = 0.06	x01 = 0.06	x01 = 0.06
	x02 = 0.03	x02 = 0.03	x02 = 0.03	x02 = 0.03
VF bulging (cm)	0	0	0	0
Case 3 - 2X convergent
VF convergence (cm)	x01 = 0.12	x01 = 0.12	x01 = 0.12	x01 = 0.12
	x02 = 0.03	x02 = 0.03	x02 = 0.03	x02 = 0.03
VF bulging (cm)	0	0	0	0
Case 4 - 1X convergent with bulging
VF convergence (cm)	x01 = 0.06	x01 = 0.06	x01 = 0.06	x01 = 0.06
	x02 = 0.03	x02 = 0.03	x02 = 0.03	x02 = 0.03
VF bulging (cm)	0.03	0.03	0.03	0.03
Case 5 – 2X convergent with bulging
VF convergence (cm)	x01 = 0.12	x01 = 0.12	x01 = 0.12	x01 = 0.12
	x02 = 0.03	x02 = 0.03	x02 = 0.03	x02 = 0.03
VF bulging (cm)	0.07	0.07	0.07	0.07