MECHENG 590 Independent Studies Final Report:

Advance the Usability of Visualization Tool for Animating Simulations of

Model of Cochlear Function

Huimin JiMechanical Engineering Department

December 11, 2014

1 Abstract

Cochlea is a small shell-shaped part of the bony structure of inner ear where the mechanical en-ergy of sound vibration is changed into neural information. This project is aimed at advancing thevisualization tool for animating the simulation of model of cochlear function in order to study thefunctionality of the cochlea and cochlear mechanics, specifically in the organ of Corti (OoC). Duringthe semester, I visualized the mathematical model of cochlear motion using Abaqus to show the mo-tion of basilar membrane (BM), outer hair cell (OHC), reticular lamina (RL), hair bundles (HB) andtectorial membrane (TM) with an focus and the relative motion of hair bundles, tectorial membraneshear (TMS) motion and basilar membrane. Additionally, the responses of the model to stimulus atdifferent frequencies and sound pressure levels (SPL) are analyzed. The analyzed responses includethe deflection of hair bundles, the phase difference between hair bundles motion, tectorial membraneshear motion and basilar membrane motion, potential phase difference, as well as power injection.

2 Introduction

The cochlear resembles a coiled fluid-filled tube of decreasing diameter, with approximately 258 turns

in humans that terminates at the apex. The cross-sections of the spiral canal is divided into threeparts: scala vestibule, scala tympani, and scala media. The scala vestibule extends from the ovalwindow to the apex, where it joins the scala tympani. The scala tympani extend from the roundwindow to the apex. (Yost, 2010) Both oval window and round window are the connection of middleear and inner ear.

The main sensory structures studied in this project are in the scale media, including the basilarmembrane, the organ of Corti and the tectorial membrane as described in Section 1. The width of BMincreases along the spiral canal from the base to the apex, while the stiffness and resonant frequencyof it decreases. (Kinsler, 2000) Thus, different acoustic frequencies stimulate maximum vibrations atdifferent points on the BM. The locations where the maximum vibrations happen at the analyzedfrequencies are simulated and visualized as a compliant plate using Abaqus. There are 3-4 rows ofOHCs. The upper ends of the hair cells are hold by the reticular lamina and the base ends by Deiter’s

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cells, which form the main vertical supportive mechanism for the hair cells. The OHCs contract andexpand with excitation. The TM is a hinge-like structure that is in contact with the upper ends ofthe hair cells, namely the hair bundles. The coupling motility of TM and BM causes the deflectionof HBs.

3 Methods

3.1 Visualization of Model

Previous researchers have developed mathematical models to simulate cochlea’s response to acous-tic stimuli. Specifically, a model of the coupling of TM and BM wave as well as the correspondingmotility of OHCs and HBs to the coupling wave has been developed. Python script has been writtenrunning by Abaqus to visualize this simulation in a 3-D animation.

With the help of the previous researcher and author of Python script Jacob Schiftan, I started theproject by learning the model construction and basic operations in Abaqus. The Python script gen-erates a scaled model of the cochlea with a customizable length by adjusting the number of sections,and each section has a length of 25 microns. Due to the extended time Abaqus needed to generatelonger length of model, most animations are made using 10 sections around the best location on theBM that corresponding to the given wave frequency. In this model, both the BM and RL are modeledas compliant plane, and the OHCs are modeled as springs with upper end connected to the RL planeand lower end to the BM plane. The cilia at the upper end of the OHCs connecting the RL and BMare modeled as short lines.

After the 3-D model is constructed in Abaqus by running the python code, an animation can begenerated given the motility data of basilar membrane (BM), tectorial membrane shear (TMS), andtectorial membrane bending (TMB). The motility data generated by Nankali are decomposed intoreal parts and imaginary parts as number lists in the order that corresponds to location along thecochlea. Abaqus read numbers for the required location and simulate the motion of the constructedmodel. The animation can be viewed from different visual angles, and can also include parts of themodel to study specific motion, such as only including the motion of HBs and BM in the animation.The response of cochlea to three different frequencies (10 kHz, 14 kHz and 16 kHz) at three differentsound pressure levels (0 dB, 40 dB and 80 dB) were simulated and made into animation clips fromdifferent visual angles with different parts of the cochlear model included.

3.2 Analysis of Responses

Having the visualization model of cochlear generated by Abaqus, I took a closer look at the motilityof cochlear in the mathematical model. Given the motion data of BM, TMS and TMB, the deflectionof HBs and phase angle of electrical potential were calculated using the mathematical model byRamamoorthy. The deflection of HBs are calculated using Equation 1: (Ramamoorthy et al., 2007)

uhb(x) = ubm(x)Ψ1(b/2 − Lpc)sin(θ1 + θ2)

sin(θ2)

sin(θ1 − α)

cos(α− β)+

utms(x)

cos(α− β). (1)

The motility phase difference between the HB (uhb) and the BM (ubm) as well as the electricalpotential phase difference between the OHC (φohc) and the scala tympani (φ+st) are calculated usingthe angle function in Matlab. The phase differences are calculated in order to study the active force

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from the OHCs and the power injection. The active force from the OHCs is calculated using Equation2, and the power injection is calculated using Equation 3. The calculated results plotted and shownin Section 4.2.

F activeohc = Kohc(u

aohcj + ub+ohcj ) + ε3(φohc − φ+st)cos(ψ) (2)

Πactiveohc = Re(F active

ohc v∗BM ) (3)

4 Results and Analysis

4.1 3-D Model and Animation in Abaqus

As discussed in Section 3.1, the model is constructed by python script in Abaqus. A screenshot ofthe constructed whole model are shown in Figure 1. Figure 3 shows a screenshot of an animationthat only includes the HBs and the BM in order to take better look at the phase differences in themotion of these two parts. The wave motion of BM and deflection of HBs are obvious in Figure 3.

Figure 1: Visualized 3-D Model in Abaqus

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Figure 2: Model with HBs and BM Only

4.2 Data Analysis

The hair bundle deflection is calculated for cochlear responses at three different frequencies (10 kHz,14 kHz and 16 kHz) at 40 dB SPL. The amplitude of the calculated HB deflection is shown in Figure3. This plot shows that the location has the largest HB deflection amplitude is further from the baseof cochlea for lower frequency sound, and corresponds to the best location on basilar membrane thatresonate with the same frequency. Figure 4 shows the phase differences among the motion of HB,TMS and BM. Here the y-axis is a representation of cycles (2π). When comparing to Figure 3, itis clear that there is a phase difference of 0.75 cycle (270◦) around the best location correspondingto the sound frequency. When the phase difference plots for 10 kHz and 16 kHz show the same results.

The active force from OHCs is then calculated and plotted with the phase differences of electricalpotential difference between OHCs and scala tympani using Equation 2 (shown in Figure 5). Thelocation where the amplitude of the active force is largest corresponds to the best location on BM. Asplotted in Figure 6, the power injection of OHCs also happen at the “best location.” Since Equation3 calculates the work done by the outer hair cells. The negative power here means the influx of powerinto the hair cells. Thus, around the best location, there is first power influx into the OHC, and thenpower dissipation from the OHC.

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Figure 3: Hair Bundle Deflection at 10 kHz, 14 kHz and 16 kHz

Figure 4: Phase Difference for HB, BM and TMS Motion around Best Location at 14 kHz

Figure 5: Active Force Amplitude at 10 kHz, 14 kHz and 16 kHz

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Figure 6: Power Injection at 10 kHz, 14 kHz and 16 kHz

5 Conclusion

From this semester’s project, I have learned from the previous researcher of constructing 3-D cochleamodel in Abaqus by running python script, and visualized the mathematical model of cochlea bygenerating short movies of cochlear motion from different angles with either parts of or the wholemodel in Abaqus. From the visualized model and the data, I analyzed the cochlear response in respectto the deflection of hair bundles, the phase difference between HB, BM and TMS, as well as the activeforce and power injection of the OHC.

References

Yost, W. A. (2010). Fundamentals of Hearing: An Introduction. Fourth Edition. Academic Press.

Kinsler, L. E. (2000). Fundamentals of Acoustics. Fourth Edition. Wiley.

Ramamoorthy, S., Deo, N. V., Grosh, K. (2007). A mechano-electro-acoustical model for the cochlea:Response to acoustic stimuli. J. Acoust. Soc. Am., 121, 2758-2773.

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