2.2. Patient-Specific EAM

For each patient, pre- and postimplantation CT images were automatically segmented using previously published techniques^4–6 to localize the position of the electrodes and the anatomical structures that we used to create EAMs, including ST, SV, and MO. As previously mentioned, our segmentation algorithm prevents us from segmenting SM and RM. While RM is an important structure for natural hearing, its width is finer than the resolution of the μCT images, so ignoring it does not affect the electrical simulations achieved by our model; thus, segmentation of the RM was not considered critical in this study. The 3-D meshes of the anatomical structures are surfaces composed of a set of points, and they were created using an active-shape model approach.¹⁹ High-resolution EAMs were created using μCT images of nine cochlea specimens as previously described.¹⁷ In brief, for each specimen, a uniform 3-D grid of nodes with spacing of 0.072 mm was defined over the field of view of the μCT image. Each node was assigned to a tissue class, including air, bone, soft tissue, neural tissue, and electrolytic fluid. Nodes that were enclosed by either ST or SV were assigned to the electrolytic fluid tissue class, and nodes enclosed by MO were classified as neural tissue. For the remaining nodes, a simple thresholding of the μCT was applied to decide among air, bone, and soft tissue. The tissue classes correspond to different electrical resistivity values. The default values for these tissue classes are: ∞Ωcm for air, 5000Ωcm for bone, 300Ωcm for soft tissue, 600Ωcm for neural tissue, and 50Ωcm for electrolytic fluid.²⁰

We warped each individual μCT to match the shape of the patient cochlea and combined the tissue segmentations using a voting scheme. To do this, the patient CT image was nonlinearly registered to each of the high-resolution μCTs using thin-plate splines (TPS).²¹ The TPS formulation presented in Eq. (1) is limited to 2-D, but extension to the 3-D formulation we used in this work is straightforward. TPS define a nonrigid transformation that minimizes the bending energy, which is given by

The surface points of the segmented ST, SV, and MO were used as landmarks in the patient CT image. For a one-to-one point correspondence to exist between these surfaces and the manual segmentations of the ST, SV, and MO in the μCT images, the active shape model was registered to each of the μCT images. This was done in a semiautomated fashion where, first, the active shape model was fit to the image, then visible errors between the active shape model and the manual segmentations were manually corrected using software designed for this purpose, and finally the closest points on the manual segmentation surfaces were found. These points were used as the landmarks in the μCT images for the TPS transformation. The TPS registration between the low-resolution patient CT image and high-resolution μCTs allowed us to create a high-resolution resistivity map for each patient. The TPS mapping between two different spaces defined by two corresponding landmark point sets (xi,yi) and (xi′,yi′) has the form

where U(r)=r2logr is the radial basis function, a0,a1, and a2 are the affine coefficients, and wi is the weight vector. The coefficients and the weight vector are determined such that total bending energy, e.g., total curvature, is minimized while providing an exact transformation between the two sets of landmark points.

The patient resistivity map was created in the region around the patient’s cochlea and with the same resolution as the grids defined on the μCTs. The TPS registrations provided the nonlinear mapping between the patient space and μCT spaces and were used to label each node in a new high-resolution patient resistivity map. For each node x in the patient resistivity map, the corresponding point y in a μCT can be found using the TPS registration. The tissue class of y was then stored as a candidate assignment for the tissue class of x. This procedure was followed for each μCT image, resulting in nine different tissue candidates zi i=[1,2,…,9], for each node. A final resistivity map was achieved using a majority voting scheme among all of the nine tissue candidates

where Z is the final tissue class. Once the resistivity map was created, we used the position of the electrode array and electrodes found using postimplantation CT images to determine the location of the 16 stimulating electrodes and the silicone electrode array in the high-resolution resistivity maps. This was achieved by first rigidly registering the postoperative CT image to the preoperative CT image of the same patient, and then using this registration to transform the electrodes and the electrode array from postoperative CT image space to the preoperative CT image space. In Fig. 2, the silicone electrode array, the stimulating electrodes, and the MO are shown in gray, black, and red, respectively. The silicone electrode array was modeled as a perfectly resistive material. The electrodes on the other hand were modeled as 2-D plates located on the surface of the electrode array facing the neural stimulating sites. In CIs, the ground electrode is located near the surface of the skull adjacent to the ear to which the electrode array is implanted. Thus, the ground electrode is located relatively far from the stimulating electrodes and the SG nerve cells. Since our model only includes 5 mm of space around the cochlea, to simulate a distant ground, we defined the entire border of the model to be ground. Then, one of the stimulating electrodes was chosen as a current source whose current sinks to ground. We then defined the system of linear equations defined by Poisson’s equation for electrical current at each node

where ϕ is the voltage and f is a constant. Solving this system of equations using the biconjugate gradient method,²² the final output of the model is the voltage map V, which contains the voltage at each of the nodes. This follows the approach proposed by Whiten.¹¹

The 3-D meshes of the MO, the silicone array, and the stimulating electrodes, in red, gray, and black, respectively.

The second step of the approach we propose to create patient-specific EAMs includes optimizing the resistivity values of different tissue classes to match the patient-specific values. Given that in vivo measurements of the resistivity values of different tissue classes are not possible, a different approach was taken to try to adjust these parameters. This approach is as follows: intracochlear potentials were calculated for a given patient with default tissue resistivity values for each of the 16 electrodes injecting 32μA of current into the system. The simulated voltage distribution was then compared to the actual measured voltage distribution acquired from the patient, and new tissue resistivity values were selected to try to improve the agreement between the two. We designed a heuristic search approach that leverages our knowledge of how changes in the resistivity values of different tissue types affect the simulated voltage distribution. We found that a change in the electrolytic fluid resistivity has negligible effects, whereas a change in the resistivity values of soft tissue and neural tissue have different effects as shown in Fig. 3. The principal effect when changing the soft tissue resistivity value is a change in the average value of the voltage distribution across electrodes while the shape of the voltage distribution maintains the same slope. Changing neural tissue resistivity value on the other hand sharpens or flattens the curve, i.e., a decrease in the neural tissue resistivity value will result in a flattening of the curve and vice versa.

The effect of the change in the different tissue resistivity values.

Using this knowledge, we developed an automatic heuristic search as shown in Algorithm 1. In this algorithm, the resistivity values of the soft and neural tissues are adjusted based on average error, which is the average normalized mean difference between simulation results and the acquired patient data computed as shown in the pseudocode. The algorithm first calculates the error, the normalized mean difference between the simulation voltage distribution vector and the voltage distribution vector acquired from the patient for a stimulating electrode, for each of the 16 electrodes. It then checks whether those values have all the same sign, i.e., whether simulation results are either bigger or smaller than the acquired patient data for all of the 16 active electrodes. If they all have the same sign, then it adjusts the soft tissue resistivity value by multiplying it by 1 plus the average error. If the signs are different, then it calculates the slope of each curve and adjusts the neural tissue resistivity value by multiplying it by the ratio of the two slopes. The heuristic search runs until the change in the absolute value of the average error is less than a threshold value or a maximum number of iterations are completed. This heuristic search, rather than a generic search scheme, was adopted because the heuristic search uses a priori knowledge of the effect of the two parameters to converge more quickly than a generic search could, which is important due to the high computation time required for each iteration in the search.

Optimizing tissue resistivity values.