Digital holographic measurements of shape and 3D sound-induced displacements of Tympanic Membrane

Abstract

Acoustically-induced vibrations of the Tympanic Membrane (TM) play a primary role in the hearing process, in that these motions are the initial mechanical response of the ear to airborne sound. Characterization of the shape and 3D displacement patterns of the TM is a crucial step to a better understanding of the complicated mechanics of sound reception by the ear. In this paper, shape and sound-induced 3D displacements of the TM in cadaveric chinchillas are measured by a lensless Dual-Wavelength Digital Holography system (DWDHS). The DWDHS consists of Laser Delivery (LD), Optical Head (OH), and Computing Platform (CP) subsystems. Shape measurements are performed in double-exposure mode and with the use of two wavelengths of a tunable laser while nanometer-scale displacements are measured along a single sensitivity direction and with a constant wavelength. In order to extract the three principal components of displacement in full-field-of-view, and taking into consideration the anatomical dimensions of the TM, we combine principles of thin-shell theory together with both, displacement measurements along the single sensitivity vector and TM surface shape. To computationally test this approach, Finite Element Methods (FEM) are applied to the study of artificial geometries.

Keywords: Digital Holography; Middle-ear Mechanics; Shape and 3D Displacement Measurements; Sound-induced Response; Thin-shell Theory; Tympanic Membrane.

Fig.1

Algorithm used to extract 3D components of displacement by measurements of shape and one component of displacement.

Fig.2

Decomposition of the surface normal vector and resultant displacement at one point: (a) $\overrightarrow{n}$ is the surface normal vector and $\overrightarrow{n_x}$, $\overrightarrow{n_y}$ and $\overrightarrow{n_z}$ are decomposed components of $\overrightarrow{n}$ along x, y and z axes; and (b) $\overrightarrow{U}$ is the resultant displacement and $\overrightarrow{U_x}$, $\overrightarrow{U_y}$ and $\overrightarrow{U_z}$ are decomposed components of $\overrightarrow{U}$ along x, y and z axes. α, β and γ are the angles between the direction of $\overrightarrow{U}$ or $\overrightarrow{n}$ and the x, y, z axes.

Fig.3

Procedure for testing our approach by FEM simulations.

Fig.4

Computed x and y components of displacements obtained by applying our approach: (a) predicted displacement along x-axis ( $\overrightarrow{{\mathit{U}}_{\mathit{x}}}$); and (b) predicted displacement along y-axis ( $\overrightarrow{{\mathit{U}}_{\mathit{y}}}$)

Fig.5

Comparisons of x and y components of displacements between FEM solutions (U_x and U_y) and predictions obtained by our approach after data normalization.

Fig.6

Schematic views of different subsystems of our DWDHS. Laser Delivery (LD) consists of an infrared tunable laser, acousto-optic modulator (AOM), mirror, and laser to fiber coupler; Optical Head (OH) which contains a modified Michelson interferometer; and Computing Platform (CP) to control the recording parameter such as sound-excitation level and frequency, phase shifting, synchronizations for stroboscopic measurements and all the acquisition parameters. The dashed lines are analog signal lines and digital control and sense lines.

Fig.7

CAD models of the designed and implemented optical head: (a) assembled package showing characteristic dimensions; and (b) view showing its principal components. PZT: Piezoelectric Transducer, M: Mirror, P: Linear Polarizer, NDF: Neutral Density Filter, BC: Beam Splitter Cube, CCD: Digital Camera, C: Collimating lens with FC connector for optical fiber input, and O: Object.

Fig.8

Comparison of interferograms quality corresponding to different opto-mechanical configurations used during optimization of the OH by changing the incident angle of the BC. The configuration corresponding to 14 degree rotation was chosen in the final configuration.

Fig.9

Chinchilla’s TM is coated with zinc oxide to increase light reflection. The TM is shown surrounded by the bone of the middle-ear wall. The placement of the tube conducting sound to the ear and the probe microphone are also illustrated.

Fig.10

Masked and filtered wrapped optical phase of the shape of the TM, computed by lensless DWDHS (Rosowski et al. 2013).

Fig.11

Measured shape of the TM of a chinchilla: (a) 3-Dimensional shape; (b) 2-Dimensional side view of the shape; and (c) 2-Dimensional top view of the shape; the outline of the entire tympanic ring is highlighted by a circle. The black outline shows the handle of the malleus (the manubrium). The umbo of the manubrium is at the apex of the TM cone.

Fig.12

Principal components of surface normals along: (a) x-axis; (b) y-axis; and (c) z-axis (Rosowski et al. 2013). The black outline shows the handle of the malleus (the manubrium).

Fig.13

‘Out-of-plane’ or z–axis peak displacements measured at six different frequencies by DWDHS. Displacements are in the unit of μm (Rosowski et al. 2013).

Fig.14

Principal components of displacement along three orthogonal axes of the TM as obtained by application of our approach. TM was subjected to sound stimuli of 5,730 Hz, and sound pressure of 101 dB SPL: (a) 3-D view; and (b) 2D top-view. The z axis corresponds to the lateral-medial direction with medial as positive that was defined by the longitudinal axis of the illuminating and reflected laser beam. The x direction is approximate to the rostral (anterior) - caudal (posterior) axis with rostral positive. The y direction is approximate to the dorsal (superior) - ventral (inferior) direction with ventral positive. Displacements are in the unit of μm.