on the origin of cochlear spiral

it is exactly 100 years ago since Sir D‘Arcy W. Thompson in his book „On Growth and Form“ (1917) discussed the intricate and complex forms that can emerge in biology. He emphasized that the analytical mathematical approach to biological form can provide answers on the forces that acted during its (ontogenetic or phylogenetic) development.

The human cochlea is traditionally compared to the shell of the nautilus, a near perfect example of a logarithmic spiral. We were interested in the mathematical form of the human cochlea, since it would inherently involve a lot of information that can be made use of in clinical medicine: it would allow reconstructing the shape of the individual cochlea based on the limited individual information from clinical CTs by interpolating it with the cochlear analytical model (complementing the missing information from the model). The first endeavor has led to a study that quantified the variations of cochlear form (Avci et al., 2014) and allowed first consequences with respect to surgery in cochlear implantation (Avci et al., 2017).

In this endeavor we stepped into another question: what is the reason for the form of the cochlea? In the past many functional theories have been disproven. Recently, it has been suggested that the cochlear form allows to to function as a whispering gallery. If function is the driving form of the morphology, the key relations in the individual variants of the morphology should be unchanged (so as to preserve the function). High variability in this regard would disprove the function and suggest the existence of local factors that are responsible for the variations.

We tested this approach using 108 corrosion casts of the human cochlea and 30 µCTs, resulting in a unique set of 138 human cochleae analyzed at near-microscopic precision (Pietsch et al., 2017). We observed huge variability in size, but also in the genuine geometry (form) of the cochlea. This variability was inconsistent with the whispering gallery function, but showed correlations with the size of the cochlear base and the distance of facial nerve from the cochlea. This supports the alternative concept of spatial constraints being responsible for the shape of the cochlea and its individual variants.

Our analytical model failed to fit the human cochleae when a logarithmic spiral was used; instead, we had to use a more complex, polynomial spiral model. This demonstrates that the human cochlea differs in shape from the nautilus. The maximum error of the length prediction of the model was within 1 mm, the model has a validated precision of <3% (Pietsch et al., 2017). All together these data are consistent with the „efficient packing“ theories of cochlear shape and provide the first evidence-based support for this theory. The results of this study support the need of analysis of interindividual variations when testing scientific theories. In the present case the whispering gallery theory was consistent with individual examples and even the mean of the present investigation, yet the individual variance disproved the theory. This calls for caution when forming and testing theories with limited data sets, as it is common practice in e.g. anthropology and whenever dealing with extinct species.

We analyzed the variability of the modiolus - to our surprise the interindividual variability in the microanatomy was similar to the lateral wall variability (Pietsch et al., 2022). This demonstrates that a significant part of the variability is established during early development and probably is of genetic origin. Furthermore, the study documented the need for individualized cochlear implantation with modiolar-hugging electrodes.

Another recent modelling attempt allows for modelling local dips and peaks, and further provides an estimation of frequency allocation (Schurzig et al., 2021). Download it >>> here.

This work has finally culminated in the possibility for virtual cochlear implantation into the individual cochlea of the given patient (Schurzig et al., 2023, download the model >>> here). That approach allows the selection of the best fitting cochlear implant array for the individual patient, thus paves the way for personalized medicine in cochlear implants. We further studied the contribution of friction forces for cochlear implantation (Fröhlich et al., 2024).

On growth and form in biology

Reconstruction of the anatomy of the human petrous bone near the cochlea from µCT data (Avci et al., 2014). These images document that the cochlea (grey) is located in close proximity of the internal carotid, tensor tympani muscle and the facial nerve. A fourth structure, the jugular vein, was not visible in these reconstruc-tions, but is also located in proximity of the cochlea in humans (Pietsch et al., 2017).

Sea stars drawing; these creatures motivated D‘Arcy Thompson to think about the biological form and its reasons. He used the nautilus as another example, and compared the inner ear to this mollusk. Drawings by E. Haeckel.

Left: Variability observed in the corrosion casts of the human cochlea (for more details, click here. Shown is the distribution of the lateral wall length in mm (top left), angular length, wrapping (the relation of metric length and angular length) and a ratio of the B-axis of the cochlear base. The variability is high in this regard: the metric length varies from 36 to 46 mm!

Below are the vertical profiles of the cochlea organized based on the B-ratio. For those where the B-ratio documents an asymmetry along this dimension (two leftmost panels) the cochleae show the most pronounced rollercoaster vertical profile, as described in Avci et al., 2014.

Figure from Pietsch et al., 2017.

Top: Implanted cochlea in a 3D model of the inner ear, projected onto a CT image of the indivudal subject. Using our modelling work it has become possible to predict the position of the implant with an astonishing precision, as the validation on 141 patients demonstrates. From Schurzig et al. (2023).