Indentation measurements on the eardrum with automated projection moiré profilometry
Introduction
The middle ear (ME) forms a mechanical impedance match between acoustic vibrations in air and the fluid vibrations in the cochlea. The system possesses an unsurpassed efficiency, and much of the details of its function are still to be revealed. Finite element modeling (FEM) and other modeling techniques are used to construct computer models of this highly sophisticated and complex mechanical system. Detailed shape models of ME morphology are an important input to improve realism of these computer models of ME mechanics. When the realism of the models gets high enough, they will allow to gain insight into the fundamental working principles of ME mechanics [1], and also to predict the outcome of surgical interventions [2], ME implantable hearing aids [3] and ME ossicle prostheses [4]. To obtain realistic results for these simulations and predictions, precise mechanic and elastic parameters of the ME components need to be incorporated in the virtual computer models [4], [5], [6].
The first main functional element in the ME chain is the eardrum or tympanic membrane (TM). The drum captures the sound vibrations present in the ear canal, and sets the malleus ossicle into motion. Apart from this, the eardrum also functions as a flexible wall, closing off the ME cavity from the environment. Because the ME cavity is closed most of the time (under normal circumstances the Eustachian tube is also closed [7], [8]), pressure differences continuously exist between the cavity and ambient, causing displacements and stretch of the eardrum. To obtain correct models of the ME function, both in the acoustic regime and under the effect of static pressure, eardrum elasticity parameters are an essential necessity [9], [10]. A way to obtain elasticity parameters is to deform the TM and measure the changes in shape.
Because the eardrum is very small (about 7 mm in diameter in human, less in many commonly used animal models such as gerbil of rabbit), it is extremely difficult to obtain samples of well-defined dimensions and measure elasticity on such samples in a classical stretch–strain pulling apparatus. A far more feasible technique is to leave the eardrum in its natural support and measure its deformation when a point load is applied. The advantage of this point indentation method is that the deformation is as simple and as straightforward as possible, but just measuring the point displacement and reaction force on the indentation needle brings, however, only limited information. Only if the deformation of the membrane is measured over a larger area, elasticity parameters can be calculated in a backward engineering process.
We therefore need an optical topographic technique, combined with a high precision point indentation setup, which allows us to measure the full-field membrane deformation evoked by a point load. Our laboratory has long experience with moiré interferometry [11], [12]: a geometrical non-contacting imaging technique for precise measurements of 3D surfaces. This optical technique is based on the geometric interference between an optical grid and its image deformed by the object surface. The moiré profilometric technique produces topograms: 2D images of the object surface covered with fringes, which, when the setup geometry is chosen well, can be interpreted as the intersection of the object with a set of parallel light and dark planes, called fringe planes. The intensity extremes of the moiré fringes in that case represent contours of equal height, which can be interpreted as altitude lines on a topographic map. Tracing of these dark and or light contours was used to extract and interpolate the height information [13]. However, far more information is embedded in the brightness variations between fringe intensity extremes, despite that brightness variations can also be caused by differences in the object reflection and illumination intensity. We extract the surface height coordinates from the recordings of several phase-shifted topograms [11], [14], [15], and after the necessary calculations, we obtain a calibrated phase map representing the object's shape.
The profilometer and indentation device together, gives us an apparatus capable of measuring accurately the 3D surface of a membrane, deformed by a precise indentation device applying a known force. The obtained data will be used by modeling specialists to obtain accurate data of eardrum elasticity parameters. In this paper we present the measurement technique and show examples of measurement results obtained on a rabbit eardrum.
Section snippets
Indentation device
The indentation apparatus consists of two main parts.
The front part carries the specimen, and consists of an assembly of X, Y and Z translation stages (Fig. 1(1,2,3)) and two orthogonally nested rotation stages (Fig. 1(4,5)). The X–Y–Z translation is needed to position the specimen exactly within the field of view of the moiré interferometer. Indentation will always be performed along the height sensitivity vector of the moiré measuring device. The orthogonal rotation stages are needed to
Measurements
For the test measurements in this paper, in which we want to demonstrate the measuring device and technique, the membrane was not preconditioned. In final experiments, where we want to obtain useful modeling data, the measurement cycle will be repeated a number of times (avoiding perforation of course), to be able to estimate repeatability of the measurements. As the subsequent indentations are performed with several seconds time lapse, hysteresis and preconditioning effects are expected to be
Discussion
The curve of displacement versus indentation force is not linear, because the eardrum is not just a flat linear elastic membrane. This indicates that simple recordings of indentation force will not suffice to calculate the elastic properties of the system. Our moiré shape measurements allow to measure displacement not only at the point of indentation, but also on the entire membrane surface. From these measurements we see that the membrane is not just locally deformed, but that the point
Conclusion
We have introduced a moiré-based optical measurement technique, which is integrated with a point indentation stimulator to perform full-field membrane shape deformations evoked by point loading. Such point indentation data are an important input to calculate membrane elasticity parameters, which contribute to middle ear biomechanics in both experimental measurement and theoretical analysis. Our apparatus allows to record indentation force to a precision better than 1 mN, and to simultaneously
Acknowledgments
This work was supported by an Aspirant fellowship of the Research Foundation-Flanders (FWO-Vlaanderen). We also thank William Deblauwe and Fred Wiese for their assistance in constructing the setup.
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