2. Methods
2.1. General procedure
2. M ETHODS
2.1. G ENERAL PROCEDURE
To study the light spread in the cochlea of different animal species of interest using different illumination paradigms we used Monte Carlo ray tracing simulation, in the software TracePro® Standard 7.8.1 (Lambda Research Corporation).
I would like to remark that the original workflow was initially designed and implemented by Dr. Kai Bodensiek in other preliminary models, during his stay in our lab in 2015-2017. My contribution to it was 1) the inclusion of the scala vestibuli and media to correct for a possible underestimation of the interturn stimulation; 2) the implementation of the query points at the level of the dendrites in the marmoset model; 3) the design and application of the light sources of the different gerbil´s model (although he also assisted in the initial steps of the experimental position model); and 4) analysis after irradiance calculation and some modifications in the original scripts. I implemented all of it to study the light spread in the marmoset and gerbil cochlea, presented in this thesis.
2.1.1. 3D
RECONSTRUCTION OF COCHLEAR TISSUESThree different cochlear compartments were reconstructed from X-Ray tomography by Dr.
Daniel Keppeler in Avizo and imported as meshes in .stl files with less than 10000 triangles (to keep a good relation between structure resolution and computational load). This cochlear compartments were: Scala Vestibuli and Media, Scala Tympany, Rosenthal´s canal (RC) and modiolus.
In Autodesk Inventor Professional 2017 (student license) with the plugin Inventor Mesh Enabler 1.0.6, the meshes were repaired using the “Repair bodies” function and exported them as a .sat file. This files were imported to Trace Pro and scale was checked and corrected, if need it.
To account for the bone, a solid cube was created and scaled to cover the rest of the cochlear structures.
22
Figure 1. Marmoset model components. A. Solid cube to account for the bone. B. Scala vestibuli and media. C.
Scala tympani. D. Modiolus. E. Rosenthal´s canal and neuronal peripheral processes. F. Query points (enlarged for a more clear display, r = 25µm – original r = 5 µm). Green, query points at the edge of the peripheral processes. Red, query points along the centerline of the Rosenthal´s canal. G. Optical cochlear implant. Grey, flexible substrate. Blue, µled. H. Model components assembled. I. Close-up of the bottom view displaying a portion of the rays traced. Every LED´s ray is displayed with a different color.
Figure 2. Gerbil model components. A. Solid cube to account for the bone. B. Scala vestibuli and media, together with the Semicircular canals. C. Scala tympani. D. Modiolus. E. Rosenthal´s canal and neuronal peripheral processes.
F. Query points along the centerline of the Rosenthal´s canal (enlarged for a clarity, r = 25µm, original r = 5 µm). G.
Optical fiber. H. Model components assembled. I. Model displaying a portion of the rays traced.
23
2.1.2. Q
UERY POINTS2.1.2.1. ROSENTHAL´S CANAL
In order to mine the values of radiant flux, 300 query points, in the form of a 5µm diameter sphere were placed in a series of coordinates provided by Dr. Daniel Keppeler. The coordinates were obtained by fitting a spline along the centerline of the mesh corresponding to the Rosenthal´s canal in Avizo and the tonotopical organization was mapped by the use of the Greenwood´s function (Greenwood, 1961).
For the Gerbil, two different tonotopic maps were used. For the model done to study the experimental scenario and the optimal sources, published in (Wrobel et al., 2018), we fit the tonotopy-place map by using the hearing ranges described in (Müller, 1996)(ie. 32.1 - 0.25 kHz):
𝑓 = 0.255(102.1𝑥− 0.01)
For the model accounting for translational and rotational variations at three different cochlear positions, published in (Dieter et al., 2019), since it was needed to fit the full hearing range of the Gerbil as 50-0.195 kHz, the following function was used:
𝑓 = 0.39(102.1𝑥− 0.5)
For the marmoset, for a hearing range of 36.34-0.14 kHz, the following Greenwood´s function was used:
𝑓 = 0.29(102.1𝑥− 0.57) 2.1.2.2. DENDRITES
For the marmoset model, we probed the amount of light reaching the peripheral processes of the SGN. 600 query points were obtained from fitting a spline to a series of points manually registered along the edge of the peripheral processes. However, most of these initial query points provided were not embedded inside the mesh (condition needed). In order to correct the location, the following steps were taken (Figure 3):
1. An array of approximated 23.5M points, spaced in 5 µm, was created.
24 2. All those that were outside the reconstructed peripheral processes were removed
(435K points)
3. All those that were more than 100 µm away from the original query points were removed (70K points)
4. In each of the remaining ones, an sphere with 400 points in its surface was generated.
I check the percentage of these points that were inside of the mesh. All those that did not have 100% of the points inside were discarded (45K points)
5. From these remaining ones, only 1 per original query point was kept: the one that had the minimal distance to the initial query points (600 points)
Figure 3. Calculation of query points at the peripheral processes of the marmoset cochlea. A. grey, mesh corresponding to the Rosenthal´s canal and the peripheral processes query points. Black, initial query points (600).
B. Array of points spaced by 5 µm (~23.5m points). C. Array of points from b inside of mesh from a (~435k points).
D. Array of points closer to 100µm from any query points(~70k points). E. Points that can (blue, ~45.5k) or cannot (red, ~24.8k) have the center of a 5 µm sphere embedded in the mesh. F. Nearest neighbor to initial query points (600 points)
25
2.1.3. D
ATA RETRIEVALRadiant flux from every sphere was retrieved from each sphere programmatically. Then, irradiance was calculated as radiant flux/4*pi*radius2 and used for further analysis.