Medical Biophysics 3970Z Six Week Project Determining the Mechanical Properties of the Eardrum through Modelling

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1 1 Medical Biophysics 3970Z Six Week Project Determining the Mechanical Properties of the Eardrum through Modelling INTRODUCTION The mechanism of hearing involves a series of coordinated transfers, which all must occur flawlessly to prevent distortion or cancellation of the sound wave before it can be interpreted by the brain. The eardrum, also known as the tympanic membrane, is an essential structure in this series of transfers. It is a very thin, delicate tissue which separates the outer ear, where the sound wave is funnelled, and the middle ear where three very small bones, known as the ossicles, transfer the energy from the wave energy to mechanical energy in the cochlea. This occurs because the sound waves cause the eardrum to vibrate. The eardrum is directly connected in series to the ossicle bones, which will also vibrate. The last bone of the ossicles is directly connected to the oval window, which transmits the energy to the cochlea (Johnson, 2003). Therefore, it is very important that the eardrum maintain the correct biomechanical properties. If it is too stiff or too flexible, the sound wave will not travel into the middle or inner ear correctly. One study has shown that inflammation of the ear, or otitis media can cause a loss of stiffness in the eardrum and can also lead to problems such as retraction pockets and cholesteatoma, which can lead to hearing loss and even death (von Unge and Dircks, 2009). It is important to be able to recognize normal mechanical properties of the eardrum, so that when cases of the abnormal present themselves they can be adequately diagnosed and treated. However, testing the mechanical properties of the eardrum present problems, due to the extreme difficulty in extracting the eardrum while maintaining its structural integrity. The objective of this report is to determine the mechanical properties of the eardrum through a comparison method utilizing experimental data to create a realistic model. THEORY The tympanic membrane resides in the tympanic bulla, which a very thin, bony capsule. There are three major areas of the tympanic membrane. The pars tensa is the largest region. The manubrium is a thin strip found in the middle of the membrane, which is where the eardrum connects to the first bone of the ossicles, the malleus. The pars flaccid is a small region just above where the manubrium would intersect with the bulla, and is more compliant than the pars tensa. The area of interest for this report is the pars tensa, as it is the main mechanical area of the eardrum (Samani, 2010). In order to determine the mechanical properties of the eardrum, a numerical optimization algorithm was used to compare experimentally determined data to a finite element model (FEM) created using Abaqus software. An FEM is a technique of solving partial differential equations. It works by dividing a material into many triangular or quadrilateral elements, which have nodes at the vertices (Samani, 2010). Analyzing how each node/element responds to a stimulus can tell us how the material as a whole is responding to the stimulus. The FEM allows the user to construct a simulation of a material and apply particular boundary conditions and mechanical properties, and then observe how the material will deform under particular applied loads. However, in the case of this experiment, three values were selected to be variable. A numerical optimization algorithm then worked in conjunction with experimentally determined data to match the FEM to the experimental data. When the FEM was found

2 2 to match the data, the optimization algorithm tells the user which values for the three variable parameters were used to create that particular model. All other parameters were held constant by the algorithm. Most notably, the Poisson s ratio was held constant at 0.3. Poisson s ratio is an intrinsic property that all materials have their own value for. It is a measure of how much the material will shrink in one direction when a stress is applied in a perpendicular direction (Samani, 2010). For the purposes of the eardrum, it was determined by previous studies that changing the value of the Poisson s ratio does not have a significant effect on the outcome of the numerical optimization algorithm (Funnell, 1975). Young s modulus is a measure of the relationship of the strain that results from the input of a stress. In other words, it is how much the material deforms when a particular force is applied to a certain area of a material. Young s modulus mathematically can be described as: Shear modulus is a similar numerical quantity, expect it regards the force that is being applied tangentially to an area and the given displacement that results tangentially (Samani, 2010). It can be described mathematically as: The three values chosen to be variable in this experiment are the Young s modulus in the longitudinal direction, the Young s modulus in the transverse direction, and the in-plane shear modulus. Images of the ear drum were taken using a Mini Moiré sensor. This machine uses a laser coupled with a charge-coupled device (CCD) to take very high resolution images of the ear. These images were used both to create the FEM and for the purposes of the pressurization technique. However, the ear drum is not a very reflective surface, so a coating must be applied in the form of either white Chinese ink, or magnesium oxide dust which allows the laser to be reflected back and the image to be taken (Dirckx and Decraemer, 1997). METHOD A Rat was chosen for this report to simulate human data as the ear of a rat is found to be structurally similar to that of a human. There are some structural differences, such as the pars flaccid occupies a larger area in the ear tympanic membrane in a rat than in a human (Hellstrom et al, 1982). However, overall the rat ear drum is a good approximation of the human ear drum and is more easily accessible. Only one rat subject was used in this experiment due to time constraints. The middle ear was removed from the rat using a surgical scalpel, microblade, scissors and tweezers. Once the bulla was extracted, a microscope and pneumatic surgical drill were used to carefully remove the top of the bulla above where the eardrum is located so that it is visible and able to be photographed using the previously mentioned Mini Moiré sensor. Due to the extreme delicacy and small size of the eardrum, it is essential that this step be performed with the utmost of patience in order to keep the ear drum intact and not compromise any of the structural integrity. Once the eardrum was exposed it was placed in a holder and photographed using the Mini Moiré sensor. Images originally look like Figure 1.

3 3 Figure 1 Image of the bulla and eardrum from a rat. The circle in the middle is where the eardrum is located and is therefore the location of interest in this photo. This image was manipulated in order for it to be utilized to create the FEM. First, it was imported into Geomagic software, where everything but the eardrum area was removed. The data was then smoothed and holes were filled. Holes occur because there are data points missing from the original image. The Mini Moiré sensor is not able to image the entire eardrum due to the bulla covering some areas and the way that the tissue lays. While in the Geomagic software program, the image is as seen in Figure 2.

4 4 Figure 2 Shows an image of what the eardrum data looks like while it is being manipulated in the Geomagic software. This data must then be imported into Matlab as a cloud of points. Matlab is a computer programming software that can perform many mathematical functions. The cloud of points is then imported into Abaqus and the FEM is created from it. Boundary conditions were set such that the eardrum model was clamped on its edge, as it would be in the eardrum. The FEM is visible in Figure 3. Figure 3 Image of the FEM of the eardrum in Abaqus software. The blue area represents the pars tensa, the green represents the pars flaccid and the red represents the manubrium. There are two methods used for experimentation. It should be noted that these two techniques are not in any way depend on each other, and they can be performed independently without the other. The two methods are used simply as a method of verifying each other. The first is called the indentation method. It requires the use of an indentation apparatus, of which there is a picture in Figure 4.

5 5 Figure 4 Image of the indentation apparatus. The gold point descends onto the ear drum which is situated on the yellow block. There is a force sensor located below the apparatus which measures the force applied and another sensor in the indentor which measures the displacement that the indentor has travelled. The ossicle bones were immobilized so that they cannot move when this method of experimentation occurs. The bulla with the ear drum inside was placed on the yellow block seen in Figure 4. The gold rod with a very fine tip slowly descends into the tissue. There is a pressure sensor underneath the apparatus, which measures the force that was being applied to the eardrum as the indenter presses into it. The indenter apparatus also measured how much it displaced from its resting position. Using this data, a force displacement curve was constructed. The second method of experimentation is the pressurization technique. This involves some extra preparation of the bulla. The ossicle bones were again immobilized so that the results acquired are only as a result of changes to the ear drum. Then a small hole was created on the opposite side the bulla, and a syringe was inserted into it. The bulla was then wrapped in paper towel and this paper towel was covered in wax, to create an air tight environment within the bulla. The hole where the eardrum is visible for pictures was not covered. Then, using increments of 0.5kPa, the pressure on the opposite side of the eardrum was changed from 0kPa to 4kPa. This was done by using the syringe to inject air into the bulla. At each pressure, the ear drum was photographed using the same method as previously mentioned to create the FEM, and again all the same steps were taken until it was imported into Abaqus. After the experimentation is complete, the same experiments were simulated in the FEM. Estimates for the three variable values were input. For the indentation technique, a force displacement curve was created based on how the FEM reacted to a simulated applied indentation. Unfortunately,

6 6 due to time constraints, in this report only the indentation technique was performed. After the experimental data was captured and simulated model was runm the two force displacement curves were compared. Then the numerical optimization algorithm was run to determine which values could be input into the FEM to obtain a force-displacement curve that is most similar to the experimental data. RESULTS A force vs. displacement graph for the original simulated data and the experimental data was constructed, and is seen in Figure 5. Force vs. Displacement Curve for Indentation Method before Numerical Optimization Figure 5 Graph of Force vs. Indentation Displacement for the Indentation method before numerical optimization has been applied. The experimental data is in red, and the simulated data is in red. It is clearly visible that the two lines do not match, indicating that the incorrect values have been input into the FEM. The experimental data (in red) and the simulated data (blue) do not match. This results because the incorrect values for the three parameters of interest, the longitudinal Young s modulus, the transverse Young s modulus and the in-plane shear modulus, are incorrect. If they were the correct values then the simulated model would act exactly as the experimental data. Once the numerical optimization has been run, a force-displacement curve is seen in Figure 6.

7 7 Force vs. Displacement Curve for Indentation Method after Numerical Optimization Figure 6 - Graph of Force vs. Indentation Displacement for the Indentation method after numerical optimization has been applied. The experimental data is in red, and the simulated data is in red. In this graph it is visible that the two plots line up very closely. This indicates that the correct, or very close to the correct values have been input into the FEM. This time, the experimental and the simulated data match very closely. This results because the correct, or very close to the correct values have been input for the three variable values. The numerical optimization algorithm finished its iterations with values of 20MPa for the transversal Young s modulus, 34MPa for the longitudinal Young s modulus, and 12MPa for the in-plane shear modulus. DISCUSSION The use of the FEM to model the eardrum has been used for many years now. It was originally first constructed in a 1978 study which created a simple model that was only valid at low frequencies (Funnell and Laszlo, 1978). This initial FEM made many assumptions due to lack of information, such as uniform thickness of the ear and collagen/elastin fibre orientations. Studies since then have worked to correct these values in order to create the most realistic FEM of the eardrum possible. For example, one study measured the thickness of the eardrum at various locations on the eardrum. This was to eliminate the previous assumption of uniform thickness, and replace it with the correct values (Kuypers et al., 2006). Another study performed very recently (in 2010) found that the average value of the Young s modulus is 21.7MPa, which is only 8.5% different than the value for the transversal Young s modulus value found within this report (Samani and Ladak, 2010).

8 8 There are many sources of error to be considered when regarding the accuracy of the results presented. The value of the Poisson s ratio was chosen to be 0.3. The value of Poisson s ratio was found in previous studies not to have too large of an impact on the final results; however it is still unknown what the correct value for the Poisson s ratio is, so a small effect could be observed. If the correct value for the Poisson s ratio was determined, this source of error would be eliminated. Another source of error comes with regards to the method. When images were taken using the Mini Moiré sensor, the images were first imported into Geomagic software. Because the data had many holes and irregularities, Geomagic software tools were used to smooth out the data and reduce some of the noise. The holes were also filled. Whenever collected data is altered to reduce noise, an element of error is added. Reducing noise does not make the data any more accurate, it simply makes it easier to work with. When it comes to filling holes, there is added error because data points are being created where they previously did not exist. The program works to interpolate the data to select the values that it believe are most likely to fit between data points, however there is no way of knowing how accurate these new points actually are. Since this report was simply meant as a six-week project, lack of time presents more errors that could be adjusted if more time had been allotted. Only one eardrum was used for testing. If the results are to be confirmed at all more samples must be taken and compared with averages. Statisically speaking, there is no way of knowing where this one patient would fall on a normal distribution curve. There is no way of knowing whether or not these results are representative of the population or if they are simply an outlier. Also, due to time constraints only the indentation method was able to be performed. Had there been more time, the pressurization technique could also have been used to verify the results of the indentation test. As it was, timing was insufficient. CONCLUSION The use of comparing experimental data to a life-like model can be extremely useful in order to determine biomechanical properties of a material. With regards to the ear drum, comparing experimentally determined force vs. displacement graphs (generated by the indentation technique) to the same curve generated from a FEM can teach us how to adjust the FEM to make it as realistic as possible. The numerical optimization algorithm is a very useful tool to save the user the time of individually trying different values and seeing which results give the best data. The values that the numerical optimization algorithm gave for the variables chosen in this report are the following: transverse Young s modulus = 20MPa, longitudinal Young s modulus = 34MPa and in-place shear modulus = 12MPa. In order to verify the results of this report, more time is required to perform the indentation test on more patients, and also to perform and analyze the results of the pressurization technique on more patients. REFERENCES Dirckx, J.J.J. and Decraemer, W.F. (1997). Coating techniques in optical interferometric metrology. Applied Optics. 36(13):

9 9 Funnell, W.R.J. and Laszlo, C.A. (1975). Modelling the eardrum as a doubly curved shell using the finite-element method. J. Acoust. Soc. Am. 57(S1): S72-S72. Funnell, W.R.J. and Laszlo, C.A. (1978). Modelling of the cat eardrum as a thin shell using the finiteelement method. J Accoust Soc Am. 63(5): Hellstrom, S., Salen, B. and Stenfors, L. (1982). Anatomy of the rat middle ear. A study under the dissection microscope. Acta Anat (Basel). 112(4): Johnson, L.R. (2003). Essential Medical Physiology (Third Edition). Amsterdam: Elsevier Academic Press. Kuypers, L.C., Decraemer, W.F., and Dirckx, J.J.J. (2006). Thickness distribution of fresh and preserved human eardrums measured with confocal microscopy. 27(2): Samani, A. (2010). Elasticity and the Biology of Elastic Materials. London Ontario: UWO Department of Medical Biophysics. Samani, A. (2010). Introduction to Finite Element Method (FEM). London Ontario: UWO Department of Medical Biophysics. Samani, A. and Lakad, H.M. (2010). Modelling the Mechanical Behaviour of the Eardrum. London Ontario: UWO Department of Medical Biophysics. Samani, A. and Lakad, H.M. (2010). Measuring the quasi-static Young s modulus of the eardrum using an indentation technique. Hearing Research. 263(1-2): von Unge, M. and Dircks, J.J. (2009). Functional effects of repeated pressure loads upon the tympanic membrane: mechanical stiffness measurements after simulated habitual sniffing. Eur Arch Otorhinolaryngol. 266(8):