Measurements of three-dimensional shape and sound-induced motion of the chinchilla tympanic membrane

Abstract

Opto-electronic computer holographic measurements were made of the tympanic membrane (TM) in cadaveric chinchillas. Measurements with two laser wavelengths were used to compute the 3D-shape of the TM. Single laser wavelength measurements locked to eight distinct phases of a tonal stimulus were used to determine the magnitude and the relative phase of the surface displacements. These measurements were made at over 250,000 points on the TM surface. The measured motions contained spatial phase variations consistent with relatively low-order (large spatial frequency) modal motions and smaller magnitude higher-order (smaller spatial frequency) motions that appear to travel, but may also be explained by losses within the membrane. The measurement of shape and thin shell theory allowed us to separate the measured motions into those components orthogonal to the plane of the tympanic ring, and those components within the plane of the tympanic ring based on the 3D-shape. The predicted in-plane motion components are generally smaller than the out-of-plane perpendicular component of motion. Since the derivation of in-plane and out-of plane depended primarily on the membrane shape, the relative sizes of the predicted motion components did not vary with frequency.

Summary: A new method for simultaneously measuring the shape and sound-induced motion of the tympanic membrane is utilized to estimate the 3D motion on the membrane surface. This article is part of a special issue entitled "MEMRO 2012".

Figure 1

The tunable laser, strobe switch, optical path length shifter, CCD camera, stimulus and timing generator, earphone, microphone and the measurement control computer. The dashed lines are analog and digital stimulus and sensing lines.

Figure 2

Masked and filtered wrapped phase image, ϕ(x,y), computed from a two-laser shape measurement. The gray scale of each pixel is coded with a value between +/− π. The three fringe lines (the transitions between black and white that are labeled with white numbers) suggest the total phase change between the outer rim and the apex of the cone (marked by a ‘+’) is just over 6π, and equivalent to a rim to a cone height of (6π/4π)*1.521 or 2.28 mm (Eqn. 3).

Figure 3

A reconstruction of the shape of a chinchilla TM. 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 corresponds roughly to the rostral (anterior) - caudal (posterior) axis with rostral positive. The y direction corresponds roughly to the dorsal (superior) – ventral (inferior) direction with ventral positive. The black outline shows the connection of the TM to the manubrium of the malleus. The umbo of the manubrium is at the apex of the TM cone, which is colored deep red. The ventral (inferior) edge of the TM is hidden from view by a significant remnant of the boney ear canal. The inset in the upper left corner shows a 2-dimensional view of the TM looking along the x-axis.

Figure 4

A lateral surface view of the three Cartesian components of the unit vector normal to the TM surface. A). A schematic illustrating the normal vector n at a point on the TM surface, and its decomposition into three Cartesian vectors with signed magnitudes of n_x, n_y, and n_z and corresponding unit vectors based on a z axis defined by the direction of the illuminating and reflected laser light. The α, β and γ describe the angles between the normal vector and the Cartesian vectors. B & C). Color rendering of n_x(x,y) and n_y(x,y). Note that x and y components of the normal vector are negative for positions where the gradient of the TM surface in x and y is negative. The outline of the manubrium is included in the figure for orientation. D). A color rendering of n_z(x,y). Due to the conical shape of the TM and the similarity of n_z(x,y) to the normal vector, n_z(x,y) is always positive. The components of the normal unit vector are unitless.

Figure 5

Color renderings of the fundamental Fourier magnitude and angle of the sound-induced motion of the TM surface along the z axis made at 5 combinations of stimulus frequency and level. The leftmost data column contains the computed magnitudes of motion. The center column contains the computed angles. The rightmost column shows the square of the correlation coefficient between the measured time waveform at each point and the waveform predicted by the Fourier magnitude and angle. Each figure in the data table shows the location of the manubrium, with the umbo at its central tip. The magnitude color bars are coded in micrometers. The phase colorbars are in radians. The correlation colorbar show variations in R² between 0 and 1.

Figure 6

Illumination-observation geometry of an interferometric optical setup: (a) overall geometry; and (b) detail showing motions, U, at a single point on the object. Points of illumination and observation are P₁, P₂, and vectors of illumination and observation are K₁, K₂. Geometry relates motions with sample shape as well as with optical phase measurements via Equation 4.

Figure 7

The relationship between the displacement normal to the TM surface U and the signed magnitudes of the three Cartesian components that describe the normal displacement U_X, U_Y, and U_Z.

Figure 8

The components of the normal displacement U. (A & B) The x and y components of the normal displacement calculated as describe above. The color bar in between (which scale both positive and negative values in μm) applies to both columns. Because U_X and U_Y are the product of the normal displacement magnitude and the x and y components of the normal unit vector, the scales include both negative and positive values. (C & D) The magnitude of the z component of the normal displacement U_Z and the computed normal displacement U. The color bars in between these two columns only scale positive values.