Overcoming Nonlinear Partial Volume Effects in Known-Component Reconstruction of Cochlear Implants

Abstract

Nonlinear partial volume (NLPV) effects can be significant for objects with large attenuation differences and fine detail structures near the spatial resolution limits of a tomographic system. This is particularly true for small metal devices like cochlear implants. While traditional model-based approaches might alleviate these artifacts through very fine sampling of the image volume and subsampling of rays to each detector element, such solutions can be extremely burdensome in terms of memory and computational requirements. The work presented in this paper leverages the model-based approach called "known-component reconstruction" (KCR) where prior knowledge of a surgical device is integrated into the estimation. In KCR, the parameterization of the object separates the volume into an unknown background anatomy and a known component with unknown registration. Thus, one can model projections of an implant at very high spatial resolution while limiting the spatial resolution of the anatomy - in effect, modeling NLPV effects where they are most significant. We present modifications of the KCR approach that can be used to largely eliminate NLPV artifacts, and demonstrate the efficacy of the modified technique (with improved image quality and accurate implant position estimates) for the cochlear implant imaging scenario.

Figure 1

A) Surgical implantation of a cochlear implant is performed through a small opening in the cochlea. B) Projection image of a cochlear implant. While individual electrodes are near the spatial resolution limit, they are still apparent. C) In flat-panel CBCT, fine implant details and surrounding anatomy are difficult to visualize due to a number of artifacts including NLPV.

Figure 2

A) Photograph of the tip of a cochlear implant containing a series of platinum electrodes along a wire. B) An undeformed model of the metal components within a cochlear implant. C) The same model deformed using control points that define the trajectory of the center of the wire using B-splines. This model can be used within the KCR framework given a known composition to generate the implant mask (s_I), the implant attenuation (μ_I), and deformations thereof.

Figure 3

Graphical illustration of a standard forward model (top) and a forward model that approximates NLPV effects (bottom). A small portion of inner ear anatomy is shown with two cochlear implant electrodes. Whereas a standard model relates the contribution (a_ij) of each voxel to each detector element (yi), a high-fidelity forward model breaks each voxel and each native detector element into smaller elements which are integrated at the detector to accommodate the distribution of x-rays within a single detector element. Computationally, the cost of the high-resolution model increases with the cube as voxel sizes are reduced and with the square as detector elements are subsampled.

Figure 4

Simulated true volume based on high-resolution CBCT images of a temporal bone upsampled to 50 μm voxels and modified to include a simple cochlear implant model composed of a platinum wire and 20 spherical electrodes.

Figure 5

KCR approach applied to imaging of a cochlear implant. A) Penalized-likelihood reconstruction at 0.4 mm voxels exhibits substantial artifacts due to inconsistencies arising from NLPV. B) KCR image (with implant position overlaid in red) computed using the variable resolution forward model to overcome NLPV effects (0.4 mm voxels and a 0.1 mm voxel implant model) with true registration parameters known. C) The KCR result using joint estimation of the image and the registration. Both KCR images show greatly reduced NLPV artifacts with subtle residual artifacts in the joint estimation due to registration errors.

Figure 6

Illustration of the true and estimated cochlear implant positions. Surface renderings of the true and estimated implants are largely overlapping. A zoomed in version of the rendering shows a region of the implant where the position estimation error is largest; however, even in this region, the error is subvoxel (with a maximum error of about 50 μm) and much smaller than the diameter of the electrodes. One can also see the two sets of control points for the b-splines of the true and estimated implants. While mismatched in number of control points, the overall trajectory of the two splines are very close to each other.