Three-Dimensional Finite Element Modeling of Blast Wave Transmission From the External Ear to a Spiral Cochlea

Hearing loss and tinnitus persist as the top disabilities treated by Veteran Affairs despite the impact hearing conservation programs have begun to make [1,2]. Service members are at an increased risk for hearing loss from blast-related ear injuries due to being deployed to environments where blast overpressures (BOP) are frequent [1,3]. BOP exposure induces observable damages to the middle ear, but the mechanisms of inner ear blast-related injuries, such as cochlear synaptopathy and hair cell loss, are neither well understood nor observed noninvasively.

Various studies have experimentally shown that the tympanic membrane (TM) and stapes experience extreme displacements and the cochlea and basilar membrane (BM) exhibit high pressures during blast and intense noise exposure [4–6]. Dual laser Doppler vibrometry techniques were used to monitor the motion of the TM and stapes footplate (SFP) during blast exposure measuring displacements much higher than that during typical sound exposure [5–7]. The intracochlear pressure during BOP exposure has only recently been measured experimentally to reveal pressures within the cochlea that would undoubtedly cause damage to the tissue within the cochlea [4]. Recent advancements in experimental studies have provided an early insight into the transmitted energy into the cochlea; however, the BM’s motion during blast exposure has not been empirically measured during the harsh blast environment.

With the difficulty of observing BM motion experimentally, researchers have adapted computational models of the ear to simulate blast transmission in the ear [8–10]. A recently published study [8] modeled blast transmission from the external ear canal to a straight, 2-chamber cochlea in a three-dimensional (3D) finite element (FE) model of the human ear which augmented a previous experimentally validated, blast model [11]. Brown et al.’s [8] model predicted the large displacements of the BM and the high intracochlear pressures comparable to published measurements of cochlear pressure during blast exposure [4]. Other computational models, like the auditory hazard assessment algorithm for humans model [10], have been developed to predict the potential harm from high-pressure inputs to the inner ear [9]. While current advancements make progress in understanding cochlear mechanics during BOP, these models considered the BM in the widely used straight cochlear configuration and do not consider the effect the cochlea’s spiral geometry has on the pressure transmission and BM displacement during BOP exposure [8–10]. While the shape does not significantly alter the BM frequency tuning at normal sound pressure levels [12], significant discrepancies between the two types of models may occur when the cochlea experiences high pressures during blast exposure.

In the present article, we report the development of a 3D FE model of the entire human ear to simulate the transmission of BOP waves from the ear canal through the middle ear and into a spiral cochlea to determine the effect from the cochlea’s spiral structure during blast exposure. The FE model’s middle ear section was validated with the experimental data obtained in human temporal bones (TBs) where the experimentally measured blast pressure was applied at the ear canal entrance in the model. The displacements of the middle ear ossicles (e.g., SFP) and cochlea BM and the intracochlear pressures were derived from the model, and the BM displacements were compared to displacements simulated in a straight cochlea model. In this study, we aim to provide a more anatomically accurate computational tool for the prediction of blast wave transmission from the ear canal to the cochlea for future applications for assisting the prevention, diagnosis, and treatment of blast-induced hearing loss.

The FE model of the entire human ear was created based on the model reported by Brown et al. [8] and used the spiral cochlea structure from Gan et al. [13]. The outer and middle ear was constructed from histological cross-sectional images of a human TB (left ear, 55-year-old, male) [14], and the spiral cochlea with two and a half turns was also from histological cross-sectional images in a different male human TB (left ear, 52-year-old) [13]. For this model, the straight, two-chamber cochlea from Brown et al. [8] was replaced with a two-chamber, spiral cochlea and connected to the SFP and round window membrane. The cochlea was remeshed in Hypermesh 2019 (Altair Engineering, Inc., Troy, MI) with pyramid and tetrahedral elements to improve performance in transient, high deformation analyses.

The developed ear model consisting of the meshed ear canal, middle ear, and cochlea can be seen in Fig. 1(a). The middle ear consisted of the ossicles and their suspensory ligaments and tendons, pars flaccida and pars tensa of the TM, TM annulus, manubrium, incudomallear and incudostapedial joints (IMJ and ISJ, respectively), stapedial annular ligament, and middle ear cavity. The spiral cochlea had two chambers, scala vestibuli (SV) and scala tympani (ST) above and below the BM, respectively, with a vestibule volume between the SV and SFP (Figs. 1(a) and 1(c)). The BM separated the SV and ST fluid chambers with two supporting structures (spiral lamina and spiral ligament) (Fig. 1(b)). The BM was 32 mm in length and separated into 124 portions with varying material properties. The resulting meshes for the ear canal, middle ear, and cochlea contained 19,522, 48,376, and 139,542 elements, respectively.

Figure 2(a) illustrates the location of P0 where the model’s input was applied. Various locations throughout the model were monitored for pressure to track blast wave transmission in the ear (Figs. 2(a) and 2(b)): near the TM in the ear canal (P1), behind the TM in the middle ear cavity (P2), and five points in both the SV and ST along the BM from the base to the apex (P_SV1 – P_SV5 and P_ST1 – P_ST5, respectively). Additional model-derived results include the displacements of the SFP and BM.

For brevity, specific details that were similar to the model reported by Brown et al. [8] can be found in the Supplemental Materials on the ASME Digital Collection or the previously reported model, and this includes: material and fluid properties, boundary conditions, FE analysis, blast experiments, and data analysis.

The use of a spiral cochlea did not significantly change middle ear pressures when compared to that in previous models that utilized a cochlear load mass or a two-chamber straight cochlea [8,11]. The middle ear blast wave transmission remained validated with the P1 peak pressures of 64.0 and 58.6 kPa and P1:P0 ratios of 2.08 and 1.91 for the model and experimental results, respectively (9.2% error). Other specific data values and figures showing the pressure monitored at P1 and P2 are in the Supplemental Materials.

Figure 3 shows the cochlear pressures at various locations in the SV (P_SV1 – P_SV5) and ST (P_ST1 – P_ST5) from the base to the apex (shown in Fig. 2(b)): 2.5 (a), 13 (b), 18 (c), 23.25 (d), and 28.25 (e) mm from the base of the BM. Maximum peak pressures in the SV (solid lines) and the ST (dashed lines) at P_SV1 – P_SV5 and P_ST1 – P_ST5, respectively, are summarized in Table 1. As illustrated by Fig. 3, the maximum pressure within the SV of the cochlea decreases from the base to the apex with the inverse true for the ST. A trend in the model was observed where the pressure waveforms decreased in magnitude difference as closer to the apex with the greatest pressure difference between the SV and ST being 174.0 kPa near the base (2.5 mm; Fig. 3(a)) and decreasing to 17.8 kPa near the apex (28.25 mm; Fig. 3(e)), which was also observed in a previous straight cochlea model [8]. The greatest positive and negative pressures of 175.2 kPa at 0.175 ms and −100.9 kPa at 1.122 ms, respectively, were observed in the SV at 2.5 mm from the base (P_SV1; Fig. 3(a)).

The motion of the SFP can be seen in Fig. 4 where the displacement of the SFP plane is plotted in three directions (piston, anterior, and superior) over a 2 ms time duration. The piston direction is the direction normal to the SFP plane where the negative direction would be into the cochlea. The anterior and superior directional movements are the rocking motions of the SFP plane in the anterior-posterior and superior-inferior directions, respectively. The greatest displacement magnitude was 28.5 μm into the cochlea (negative) at 0.25 ms with the largest positive displacement of 27.4 μm at the second maximum peak at 0.79 ms (Fig. 4(a)). The first two peak-to-peak displacements (49.5 and 38.8 μm for the first and second, respectively) seem to have the greatest impact on the cochlear pressure since the cochlear pressure in the base quickly diminishes after 1 ms (Fig. 3(a)). Figure 4(b) plots the superior and anterior directional movements of the SFP at a smaller range due to the magnitude of their displacements being much smaller than the piston direction displacements. The maximum displacements for the superior and anterior directions were 4.0 μm at 0.56 ms and 6.9 μm at 0.18 ms, respectively, which were more than four times less than the maximum magnitude in the piston direction. Even though these displacements were small when compared to the piston direction, all of the displacements were much larger than the SFP displacements during low-frequency sound stimuli at 90 dB sound pressure level (< 0.1 μm) [7].

Figure 5 shows the displacement of the model’s BM over 2 ms at 2.5, 13, 18, 23.25, and 28.25 mm from the base of the cochlea, and the maximum normal displacements at these points are summarized in Table 1 with a negative value indicating displacement downward toward the ST normal to the plane of the BM. The maximum upward displacements were 6.5, 15.9, 14.4, 2.6, and 0.0 μm, respectively, over the 2 ms time duration. The results show the BM motion near the base was closely tied to the cochlear pressure generated by the SFP (Fig. 3(a)), and the motion of the BM was more centered around the origin than the motion of the BM further away from the base. While the cyclic wave response can be seen in the BM away from the base, a negative broad peak formed in the BM and grew with increasing distance from the base of the BM. This reflected a passive, low frequency traveling wave often discussed with BM inner ear mechanics [15], and interestingly, such a prominent traveling wave effect was not observed in a previous blast model [8].

To illustrate the effect a spiral cochlea has on the BM response, Fig. 6 plots the transverse displacement of the BM from the spiral cochlea model and compares it to that from the straight cochlea model reported by Brown et al. [8]. The BM transverse motion is the direction perpendicular to the length of the BM element with the positive motion being toward the center of the cochlea’s spiral. The maximum displacements for each position along the length of the BM (2.5, 13, 18, 23.25, and 28.25 mm) are shown in Table 1. The trend of the transverse motion in the BM mirrored the BM’s normal motion shown in Fig. 5 except for at 28.25 mm where most of the motion was away from the center of the cochlea; however, the transverse displacement of the BM was about two magnitudes less than the normal displacement of the BM. While the transverse displacement was far less than the normal displacement, it was much greater than the transverse displacement simulated by the straight two-chamber cochlea model reported by Brown et al. [8] which the max displacement was 0.59 nm and the typical displacement was less than 300 pm. Such a small displacement would be essentially no motion for a model of this scale. In addition, the transverse motion of the BM was greater than normal directions displacements measured during acoustic simulation (<10 nm at 120 dB) [16].

The pressure distribution within the SV and ST of the spiral cochlea (pressure contour plot) is shown in Figs. 7(a)–7(c)) at three different positions along the BM at the base (2.5 mm), middle (18 mm), and apex (28.25 mm) turns. The time point for each pressure contour is the time at which the first maximum peak pressure occurred at the respective position. It is important to note that the pressure contours for the basal (Fig. 7(a)) and middle (Fig. 7(b)) turns have separate pressure scales due to the large difference in pressure ranges in the SV and ST chambers. The right side of the contour plots is toward the center of the spiral cochlea. As seen in Fig. 7, the increase in pressure distribution asymmetry is apparent from the base to the apex of the cochlea. The base of the cochlea shows minimal symmetry across the width of the cochlea with a pressure variation of less than 3 kPa between the left (outer) and right (inner) sides of the SV (Fig. 7(a)). When the first pressure peak occurs at the apex (Fig. 7(c)), the pressure distribution was completely asymmetric across the width of the spiral cochlea with the higher pressure skewing to the outer curve of the cochlea. The increase in asymmetry across the BM in Fig. 7(c) correlates to the increased transverse displacement of the BM beyond the base of the cochlea (Fig. 6). The pressure difference between the outer (left) and inner (right) curve of the cochlea was less than 3, 4, and 2.1 kPa for the basal, middle, and apex turns of the SV, respectively, and 0.24, 1.2, and 2.4 kPa for the basal, middle, and apex turns of the ST, respectively.

Blast models of the human body aim to predict and assess the damage sustained during blast exposure as a final goal, and models of the auditory system attempt to predict the long-term hearing loss caused by BOPs [8–10]. The auditory hazard assessment algorithm for humans model was such a model that has been incrementally improved since the early 1990s to predict the possible long-term hearing loss with a simple output [10]. Mathematical models like the above were created from data obtained from animal experiments and then are converted to a human model through patient data [10]. These models do continue to improve as more data becomes available; however, these models are intrinsically unable to model the complex fluid dynamics within the cochlea during blast exposure. Studies have shown that, even under normal sound stimuli, the spiral shape of the cochlea has an effect on the fluid dynamics and pressure distribution within the cochlea when compared to a straight cochlear model [12,17] and would undoubtedly have an effect during BOP exposure. Advancing blast models of the peripheral auditory system to include the spiral shape of the cochlea is a necessary step to accurately represent the cochlear response during blast [18].

The blast model by Brown et al. [8] is the most relevant study for comparing the cochlear response between straight and spiral cochlea models. By utilizing the same experimental BOP as input for P0 (see Fig. S1 in available in the Supplemental Materials on the ASME Digital Collection), and it was found that there were no significant changes in the pressures of the middle ear and displacement of the TM. The spiral cochlea did change the resulting displacement of the SFP when compare to the straight cochlea. The overall trend of the SFP piston motion and initial displacement into the cochlea were very similar (−28.5 and −27.5 μm for the spiral and straight cochlea, respectively); however, the following maximum peaks after the initial minimum were less than half the magnitude of the maximum SFP displacement reported by Brown et al. [8]. Furthermore, the initial anterior directional movement was greater for the spiral cochlea model, but overall displacement magnitudes were similar. When compared to Jiang et al.’s SFP measurements during blast exposure [6], the frequency trend of the SFP motion was similar between the model and experimental results in that the stapes sharply displaced between the positive and negative peaks; however, the magnitude displaced was greater for the experimentally measured SFP despite the same BOP waveform (TB sample 18-1 L in Ref. [6]) being used for P0 in the model.

As previously mentioned, the BM of the spiral cochlea exhibited a broad negative peak that grew as the pressure transmitted from the base to the apex. This was not observed to this degree in the BM reported by Brown et al. [8]. The BM displacement of the straight cochlea model was smaller in magnitude and the cyclic motion centered around the origin throughout most of the cochlea. In addition, the BM fluctuations that originated at the base persisted and grew in magnitude until near the apex where most of the waves combined [8]. The greater BM displacement seen in the spiral cochlea model may be due to the greater intracochlear pressure when compared to the straight cochlea (49.9 and 175.2 kPa for the straight and spiral cochleae, respectively). This was likely due to the smaller cross-sectional area and volume of the spiral cochlea, which would increase the resulting pressure from the same amount of input energy from the stapes. Moreover, the pressure distribution differed across the cross section of the spiral cochlea (Fig. 7) where straight cochlea models have shown to have a symmetrical pressure distribution across the cochlea [12]. Similar results were observed by Ren et al. [12] where straight and spiral cochlear models were directly compared in an acoustic simulation, and the pressure distribution skewed toward the outer curve of the spiral cochlea while the straight cochlea model exhibited a symmetric pressure distribution. Ren et al. [12] did not find any significant changes in neither the normal nor transverse displacements of the BM; however, the intracochlear pressure was far less than this study, and the boundary constraints of the BM elements did not allow for transverse motion. In the current study, the asymmetric pressure distribution and pressure difference between the SV and ST caused the BM to deform in the transverse direction where the symmetry of the straight cochlea did not allow for much transverse motion (Fig. 6).

The lack of experimental intracochlear pressure measurements during blast is a limitation for validation of the cochlea in blast models, as very few studies have measured cochlear pressure during blast exposure. Greene et al. [4] measured the intracochlear pressure in cadaveric heads in blast conditions, and while this was an important advancement for the field, intracochlear pressure measurements exhibited large variances within the results showing the need for further research. An animal model that relates intracochlear pressure during BOP exposure and the resulting inner ear damage would be needed to determine if the pressure distribution difference between the spiral and straight cochlear models is significant. Furthermore, injury data relating to the experienced intracochlear pressure would support our model for the prediction of inner ear injury during blast. To date, the intracochlear pressure has not been experimentally measured in an animal model.

Currently, a few studies compare the results between straight and spiral cochlea models to determine the significant effects between the model geometries [12], but a spiral cochlea model has not been used to model blast exposure. Understanding how the spiral shape of the cochlea affects BM motion and BOP pressure transmission throughout the cochlea will help with future developments of a more comprehensive ear blast model. Future work includes developing a three-chambered, spiral cochlea with an exact anatomic structure for simulation of blast pressures from the ear canal entrance to the cochlea. A model with this capability would give insight into how the Reissner’s membrane and three chambers affect pressure transmission through the cochlea. In addition, it is unclear if the Reissner’s membrane protects the organ of Corti from the initial high-pressure increase of the BOP or if it passively transmits pressure to the scala media.

A human ear FE model with a two-chamber spiral cochlea was developed and simulated BOP transmission throughout the outer, middle, and inner ear. The BOP input with a peak pressure of 30.7 kPa resulted in large displacements of the stapes, which caused high intracochlear pressures and significant BM displacements. The abnormally high SFP displacement had a maximum magnitude of 28.5 μm resulting in intracochlear pressures as high as 175.2 kPa and BM displacements up to 43.2 μm. The spiral shape of the cochlea caused an asymmetric pressure distribution across the width of the cochlea or the SV and ST chambers and allowed for significant transverse motion of the BM. The spiral cochlea model developed in this study provides a necessary advancement from the commonly utilized straight cochlea model to increase understanding of the cochlear mechanics during blast exposure, and in doing so, progresses toward a model able to predict the potential hearing loss sustained during BOP exposure.

We would like to acknowledge Paige Welch for her early work in the development of the spiral cochlea FE model.

• Department of Defense (DOD) (Grant No. W81XWH-14-1-0228; Funder ID: 10.13039/100000005).