Measurement of Young's modulus of vocal folds by indentation

Abstract

Objectives: To assess the accuracy of the indentation method for stiffness measurements and to estimate the Young's modulus of the vocal fold using this technique.

Study design: Basic science.

Methods: Indentation tests were performed using a range of indenter diameters and indentation depths on single- and double-layer silicone rubber models with various cover-layer thicknesses with known geometry and Young's moduli. Measurements were repeated on intact vocal folds and isolated muscle and cover-layer samples from three cadaveric human larynges.

Results: Indentation on single-layer rubber models yielded Young's moduli with acceptable accuracy when the indentation depth was equal to or smaller than the indenter diameter, and both were smaller than the physical dimensions of the material sample. On two-layer models, the stiffness estimation was similarly influenced by indenter diameter and indentation depth, and acceptable accuracy was reached when indentation depth was much smaller than the height of the top cover layer. Measurements on midmembranous vocal fold tissue revealed location-dependent Young's moduli (in kPa) as follows: intact hemilarynx, 8.6 (range=5.3-13.1); isolated inferior medial surface cover, 7.5 (range=7-7.9); isolated medial surface cover, 4.8 (range=3.9-5.7); isolated superior surface cover, 2.9 (range=2.7-3.2); and isolated thyroarytenoid muscle, 2.0 (range=1.3-2.7).

Conclusions: Indenter diameter, indentation depth, and material thickness are important parameters in the measurement of vocal fold stiffness using the indentation technique. Measurements on human larynges showed location-dependent differences in stiffness. The stiffness of the vocal folds was also found to be higher when the vocal fold structure was still attached to the laryngeal framework compared with that when the vocal fold was separated from the framework.

Figure 1

Indentation setup shows the cylindrical indenter tip (*) attached to the force transducer in contact with vocal fold tissue (#), which is placed in saline to prevent dessication. Arrows point to the edge of the saline pool.

Figure 2

An example of the loading-unloading data over five cycles from a single layer rubber model with material thickness 25.4 mm, E = 3.14 kPa, indentation depth 5mm, and indenter diameter 5.5 mm. The slope (dF/dh) at the initial portion of the unloading cycle (red line) is calculated and used to calculate Young’s modulus (discussed in text).

Figure 3

Estimated Young’s modulus for a one-layer rubber model (cube with side lengths of 25.4 mm) as a function of indentation depth for four indenter diameters. The Young’s modulus as estimated in the stretching test was 3.14 kPa. The error bars indicate the standard deviation of the Young's modulus estimation from indentation.

Figure 4

Normalized Young’s modulus (E/E₀) as a function of the ratio of indentation depth (h) and indenter diameter (D). E = modulus measured by indentation. E₀ = modulus measured by stretching (Instron). Different symbols represent data from single-layer silicone models of different Young’s moduli.

Figure 5

Measured Young’s modulus (E) as a function of the ratio of indentation depth (h) and indenter diameter (D) for different ratios between indenter diameter and material thickness D/T. Different symbols indicate different values of the ratio D/T. Single-layer models of various thicknesses with Young’s modulus 3.14 kPa were used.

Figure 6

Estimated Young’s modulus as a function of indentation depth for three two-layer models. The depths of the cover layers were 2, 4, and 6 mm and indenter diameter was 1 mm. The Young’s modulus as estimated in the stretching test was 3.14 kPa for body and 1.1 kPa for cover layer (represented by solid horizontal lines).

Figure 7

Coronal section of ex vivo vocal fold illustrating the order of the estimated Young’s modulus from stiffest (1) to softest (4): 1 = medial inferior cover, 2 = medial cover, 3 = superior cover, 4 = TA muscle (body).