ESM-CT: a precise method for localization of DBS electrodes in CT images

Abstract

Background:

Deep brain stimulation (DBS) of the subthalamic nucleus produces variable effects in Parkinson disease. Variation may result from different electrode positions relative to target. Thus, precise electrode localization is crucial when investigating DBS effects.

New method:

We developed a semi-automated method, Electrode Shaft Modeling in CT images (ESM- CT) to reconstruct DBS lead trajectories and contact locations. We evaluated methodological sensitivity to operator-dependent steps, robustness to image resampling, and test-retest replicability. ESM-CT was applied in 56 patients to study electrode position change (and relation to time between scans, postoperative subdural air volume, and head tilt during acquisition) between images acquired immediately post-implantation (DBS-CT) and months later (DEL-CT).

Results:

Electrode tip localization was robust to image resampling and replicable to within ~0.2mm on test-retest comparisons. Systematic electrode displacement occurred rostral-ventral-lateral between DBS-CT and DEL-CT scans. Head angle was a major explanatory factor (p<0.001,Pearson’s r=0.46, both sides) and volume of subdural air weakly predicted electrode displacement (p=0.02,r=0.29:p=0.1,r=0.25 for left:right). Modeled shaft curvature was slightly greater in DEL-CT. Magnitude of displacement and degree of curvature were independent of elapsed time between scans.

Comparison with Existing Methods:

Comparison of ESM-CT against two existing methods revealed systematic differences in one coordinate (1±0.3mm,p <0.001) for one method and in three coordinates for another method (x:0.1±0.1mm, y:0.4±0.2mm, z:0.4±0.2mm, p<10⁻¹⁰). Within-method coordinate variability across participants is similar.

Conclusion:

We describe a robust and precise method for CT DBS contact localization. Application revealed that acquisition head angle significantly impacts electrode position. DBS localization schemes should account for head angle.

1. Introduction

Deep brain stimulation (DBS) for symptomatic treatment of Parkinson disease typically targets the sub-thalamic nucleus (STN) (Benabid et al., 1994; Deuschl et al., 2006; Limousin et al., 1995). It is well documented that the motor, psychiatric and cognitive effects of STN DBS are variable (Campbell et al., 2012; Campbell et al., 2008; Garcia-Garcia et al., 2016; Hershey et al., 2010; Houeto et al., 2003; Mandat et al., 2006; Perriol et al., 2006; Wodarg et al., 2012). This variability is thought to reflect differences in DBS electrode position relative to the STN (Cooper et al., 2011; Greenhouse et al., 2011; Hershey et al., 2010; Hilliard et al., 2011; Parent and Hazrati, 1995; Wodarg et al., 2012; York et al., 2009), surrounding areas (Lanotte et al., 2002; Plaha et al., 2006; Voges et al., 2002), and/or stimulated neuronal elements (Chaturvedi et al., 2010; Howell and McIntyre, 2017). Most research efforts along these lines correlate DBS electrode location with various behavioral outcomes or patient-specific computational models across stimulation paradigms (Butson et al., 2007; McIntyre et al., 2007). However, substantial errors from image co-registration (Klein et al., 2009) and imprecise electrode localization on post-operative CT (Hemm et al., 2009) limit interpretation of such research efforts. Thus, precise and accurate DBS electrode localization methods are critical for ongoing computational and in vivo studies relying on advanced neuroimaging methods such as tractography, functional connectivity, and improved contrast in anatomical imaging. DBS contact localization is particularly relevant to ongoing research efforts in a growing application of directional DBS electrodes (Butson and McIntyre, 2015; Pourfar et al., 2015).

Behavioral and computational studies addressing the efficacy of DBS require accurate contact localization at the time of study (Guehl et al., 2007; McClelland et al., 2005). As many areas of the brain targeted for DBS exhibit poor contrast on conventional clinical MRI, DBS localization frequently relies on image registration fusing a patient-specific image with a specified atlas. This approach allows determination of contact location relative to anatomical structures such as the STN and is common to many research protocols localizing DBS electrodes. DBS contacts may be localized in vivo using either computed X-ray tomography (CT) or magnetic resonance imaging (MRI) (Garcia-Garcia et al., 2016;Horn and Kuhn, 2015; Pollo et al., 2007). Although both modalities have limitations (refer to Discussion), many institutions use CT for this purpose. Several methods have been developed for CT-based contact localization. Some groups reconstruct implant geometry from two-dimensional CT slices (Horn and Kuhn, 2015; Motevakel and Medvedev, 2014); others explicitly compute centroids of CT signals corresponding to contact arrays (Husch et al., 2018; Lauro et al., 2016); yet others register geometric electrode array models to CT images in three dimensions (D’Albis et al., 2015; Hebb and Miller, 2010; Lauro et al., 2016). Most of these methods model implants as a straight line. There currently is no gold standard. Moreover, the precision of some methods relative to targeted structures has not been evaluated (Butson and McIntyre, 2015).

Precise measurement of DBS electrode position is imperative for longitudinal studies of the effects of contact position on behavioral or neurophysiological outcomes. Since post-implantation electrode movement may influence contact position (Elias et al., 2007; Miyagi et al., 2007; Morishita et al., 2017; Saleh et al., 2016; Sillay et al., 2013; van den Munckhof et al., 2010), it is important to isolate factors contributing to this movement and consequent impact on function (Choi et al., 2017). The volume of post-operative subdural air (Elias et al., 2007; Miyagi et al., 2007; van den Munckhof et al., 2010) and technical factors at the time of implantation (Morishita et al., 2017) are known to influence electrode position. However, additional factors may also contribute and these cannot be studied without taking into account the precision of contact localization.

The primary objective of the current work is to develop a reliable technique to localize DBS electrodes in CT images. To this end, we present here a novel semi-automated electrode localization algorithm: ESM-CT (Electrode Shaft Modeling in CT images). Our method constructs a three- dimensional representation of the implant and iteratively optimizes the shaft trajectory and electrode tip location. The shaft is modeled by a low degree polynomial curve, so ESM-CT can also assess changes in implant (including the electrode array) curvature. Using actual clinical images, we assessed methodological sensitivity of ESM-CT to operator-dependent steps, robustness to image resampling, and test-retest replicability; we also compared ESM-CT to two previously published methods (Husch et al., 2018; Videen et al., 2008). The source code is made freely available for the scientific community. Our approach offers precise semi-automated electrode localization with minimal user input, minimizes assumptions regarding electrode geometry and image preprocessing, is robust to resampling, and demonstrates good reproducibility on repeat testing over a wide range of acquisition angles. Thus, as a secondary goal, we investigated factors that may relate to systematic electrode movement over time. Using ESM-CT, we analyzed electrode movement in the months following surgery in a cohort of DBS study participants and isolated explanatory factors using multivariable statistical regression.

2. Materials and Methods

2.1. Participants and imaging

Starting with a clinical database of over 680 patients with clinically defined Parkinson disease (Hughes et al., 1992), we identified 69 individuals with prior bilateral STN DBS surgery (Tabbal et al., 2007) who consented to DBS outcomes research at our institution and had all of the following images: (i) pre-operative T2-weighted structural MRI (referred to as MRI in the rest of this text), (ii) immediate post- operative CT scan (DBS-CT), and (iii) delayed CT scan (DEL-CT). Thirteen patients were excluded because of motion artifacts in DBS-CT or surgical revision of DBS electrodes prior to DEL-CT. Thus, images in 56 participants (36 male, age at surgery 62±9 years) were used to evaluate the ESM-CT algorithm and determine factors contributing to post-DBS implantation electrode migration.

MRI was acquired on 3T Siemens 3T MAGNETOM Trio scanner at 0.9mm isotropic voxel resolution (3D SPACE, TR=3.2s, TE=461ms, flip angle=120°). Although T1-weighted images were available, T2-weighted images were used for atlas registration in order to better visualize the STN. We have recently published a T2-weighted atlas specifically designed for STN localization (Milchenko et al., 2018). DBS-CT was acquired at a Siemens Somatom Definition scanner (variable in-plane resolution 0.5±0.05mm, slice thickness 1mm) while the patient was perfectly supine. The DEL-CT (in-plane resolution 0.4±0.03mm, slice thickness 1mm) was acquired within 4 to 82 months (median of 10 months) following DBS-CT. Importantly, the participant’s neck was flexed (head placed on a pillow and rolled towel) to reduce ocular radiation (Figure 1).

Figure 1.

Top row: (A) sagittal slice from a typical DBS-CT; (B) sagittal slice from a typical DEL-CT; bottom row: schematic relative head position during scan for slice above. Vertical white lines depict scanning plane. Note the difference in acquisition angle α between DBS-CT and DEL-CT.

All aspects of this study related to human subjects were conducted in accordance with The Code of Ethics of the World Medical Association and were approved by the Human Research Protection Office at Washington University; all participants provided written informed consent.

2.2. Surgical technique

Two neurosurgeons at Washington University performed all DBS electrode implantations. Surgical technique, STN targeting, DBS electrode placement, microelectrode recording, and macrostimulation procedures have been previously described (Tabbal et al., 2007). All participants had bilateral implantation of the Medtronic model 3389 DBS electrode, the distal geometry of which comprises four cylindrical metallic contacts, 1.27-mm in diameter and 1.5-mm in length, spaced 0.5-mm apart (Figure 2). DBS-CT images of the head were obtained immediately after removal of the stereotactic frame on the day of surgery to exclude intracranial hemorrhage. For our electrode localization and migration analyses, we used the center of the second most distal contact (contact 1 as labeled in Figure 2) since we clinically target this region (Tabbal et al., 2007). Additionally, this strategy allows for potential future application to different electrode designs that incorporate the distal contact as the electrode tip versus the model here that incorporates a non-metallic tip.

Figure 2.

Configuration of model 3389 electrode array. Red dot indicates the location used for electrode migration analysis.

2.3. Contact localization method

2.3.1. DBS Electrode localization strategy in ESM-CT.

The ESM-CT procedure (Electrode Shaft Modeling in CT images) takes the post-implantation CT image as input. An operator views the CT image in FslView (Jenkinson et al., 2012) and saves a mask containing four voxels encoding the coordinates of the proximal and distal ends (P_p and P_d ) of the left and right electrode shafts (Figure 3). P_d can be placed anywhere within 5 mm of the electrode tip, and P_p anywhere within 5 mm of the visible shaft, within 10–15 mm from the inner table of the skull (see Supplementary video 1). The manual step takes under 1 minute and requires minimal operator training; the rest of the algorithm is fully automatic. Following endpoint initialization, ESM-CT assigns 80 points on this initial straight line approximation of the electrode shaft, S = [P_p; P_d], with denser sampling at the distal end (Figure 3). Implant trajectory and electrode tip location are then optimized in the following two steps repeated over two iterations.

Figure 3.

Implant trajectory at Step 1 of ESM-CT procedure. Segment S=[P_d; P_p] initializes the trajectory. The curve represents trajectory interpolation found at the end of Step 1.

Step 1 models bowing (curvature) of the shaft. At each P_i, a narrow (FWHM=0.5 mm), circular Gaussian distribution is defined in the plane perpendicular to the shaft $\left(S_{\perp }^i\right)$, centered on P_i (Figure 3). The coordinates of P_i then are adjusted within $S_{\perp }^i$ to maximize the integrated overlap of the shaft model with the CT image. Thus, at each point, the maximized quantity is

$${\displaystyle \int g\left({\text{P}}_i-x\right)I\left(x\right)dV,}$$ (1)

where x is the image coordinate, g(∙) is a two-dimensional Gaussian kernel in plane $S_{\perp }^i,I\left(x\right)$ is the CT image intensity, and dV is the volume element restricted to a narrow (5 mm radius) disk centered on P_i. In practice, the integral is evaluated on a 3D grid at 0.1 mm intervals using trilinear interpolation of I(x). The coordinates of P_i are optimized by two-dimensional simplex algorithm (Press et al., 2007).

Once the shaft trajectory centers {P_i, i = 1,…, 80} are adjusted for bowing, ESM-CT fits to them a three-dimensional quadratic curve, T(𝑡), parameterized by 𝑡, 0 ≤ t ≤ 1:

$$\text{T}\left(t\right)=\left[\begin{array}{l}x\left(t\right)\\ y\left(t\right)\\ z\left(t\right)\end{array}\right]=A\left[\begin{array}{l}{t}^2\\ t\\ 1\end{array}\right],$$ (2)

where A is a 3 × 3 coefficient matrix found by solving a system of 9 linear equations defined by a least squares formulation of the interpolation problem. The curve parameterization is chosen so that T(0) = P_p and T(1) = P_d.

In Step 2, ESM-CT uses an analytic representation of a cylinder, C_e, matching the dimensions of the implanted contact array (7.5×1.27×1.27mm in case of Model 3389 (Figure 2)). The shaft trajectory length is adjusted to maximize overlap of C_ewith the CT image. The optimized quantity is

$${{\displaystyle \int \text{C}}}_e\left(x\right)I\left(x\right)w\left(x\right)dV,$$ (3)

where w(x) is a Gaussian weighting function centered on the shaft axis that, empirically, improves robustness to metal artifacts. The parameterized trajectory is adjusted such that the endpoints of the C_e axis lie on T with the distal endpoint P_d at T(1). As before, ESM-CT evaluates the integral on a 0.1 mm grid. Optimization is done using one-dimensional gradient descent.

Steps 1 and 2 are repeated starting with the revised coordinates of P_d determined in the first iteration. ESM-CT then reports the coordinates of all contacts, shaft trajectory, and its mean curvature. The average intensity profile along the shaft trajectory (Figure 4) can be viewed to verify the results.

Figure 4.

Verification of ESM-CT outcome. Moving average of intensity in a CT image sampled along different DBS implant trajectory estimates: initial straight line estimate (orange), straight line found by ESM-CT (blue), final curve found by ESM-CT (green). X axis represents fractional position along the implant, with x = 0 at proximal end and x = 1 at the distal end. Dotted vertical lines indicate the detected boundaries of the contact array.

2.3.2. Calculating electrode location in standard atlas space.

To represent contact coordinates in a standard atlas space, we rigidly coregister the CT image to a preoperative T2-weighted (T2w) MRI using the conjugate metric gradient (cmg) objective function (Rowland et al., 2005). This objective function maximizes the alignment of image gradients without regard to sign, i.e., tissue type boundaries. This strategy is useful in cross-modal registration. In registering CT to T2-weighted MRI, the boundary between skull and CSF is a well-defined contour in both images (but of opposite sign) and is a major driver in the registration. The T2w is, in turn, nonlinearly registered, via the bm-cmg (block matching with cmg objective function) algorithm to an average T2-weighted, Parkinson disease (PD) population representative template in MNI152 space (Milchenko et al., 2018). Example coregistered CT and MR images are shown in Figure 5. Upon completion of all registration steps, both the CT (with associated analytic models of the implant) and T2w images are mutually coregistered in MNI152 space.

Figure 5.

Spatially coregistered MRI (A), DBS-CT (B) and DEL-CT (C) in MNI152 space. Left to right: sagittal, coronal and axial views. Red edge contours were computed from MRI and superimposed over DBS-CT and DEL-CT.

2.4. Evaluation of electrode migration factors

2.4.1. Estimation of post-surgical intracranial air volume.

To quantify post-implantation pneumocephalus, the DBS-CT image was automatically segmented to identify all contiguous 3D regions having volume greater than 50 mm³ with signal intensity between 0 to 400 Hounsfield units (HU). An operator with neuroanatomy training reviewed the segmentation results using a tri-planar viewer (Jenkinson et al., 2012) to ensure that the identified segments represented intracranial air (Figure 6).

Figure 6.

Clusters of intracranial air on a DBS-CT image identified by an operator. Left to right: sagittal, coronal and axial views. In this case one cluster (brown) was identified on the right and one (blue) on the left side.

2.4.2. Analysis of electrode movement.

After obtaining contact locations for DBS-CT in MNI space (see Calculating electrode location in standard atlas space above), we coregistered DEL-CT to DBS-CT using the cross-modal (cmg) voxel similarity measure. Following that, we composed transforms (DEL-CT → DBS-CT ᵒ DBS-CT → MNI atlas) to obtain contact locations for DEL-CT in MNI space (Figure 7). To measure the change in electrode position across the DBS-CT and DEL-CT images, we compared the coordinates of contact1 in MNI152 space for both the right and left implants. These are the contacts targeted at posterior-lateral STN during DBS surgery. We then computed multivariable linear regression models for the difference in each coordinate (Δx, Δy, Δz) and total Euclidean distance $E=\sqrt{\Delta x^2+\Delta y^2+\Delta z^2}$, with covariates being (i) time interval between scans (ΔT, months), (ii) post- implantation air volume (A, mm³) (iii) change in head-tilt angle (Δα, degrees; Figure 1) and (iv) change in implant trajectory curvature (ΔK, m^-1). Regression analyses were conducted using the fitlm procedure in MATLAB R2015a statistics toolbox and independently replicated in SPSS (v.25).

Figure 7.

Obtaining contact locations in MNI152 space. Arrows indicate information flow.

3. Results

3.1. Evaluation of ESM-CT

3.1.1. Implementation and performance.

ESM-CT was implemented in C++, using the newmat library (Eddelbüttel, 1996) for matrix algebra. An optional QC snapshot can be generated in MATLAB. The online repository with the source code for Linux (gcc, gnu-make) and Windows (Visual C++) platforms is available to the scientific community at https://github.com/mmilch01/esm-ct. The only runtime dependency for localizing contacts in CT is the FSL package (Jenkinson et al., 2012). ESM-CT outputs voxel coordinates marking the beginning and end of the contact array in original CT image space. Typical time for manual initialization of ESM-CT step was <1 min, with automatic procedure run time of 5–10 seconds per electrode on a 64-bit Linux node.

3.1.2. Sensitivity to variability in manual selection of endpoints.

Two operators independently initialized the proximal and distal shaft endpoints in the first 50 images from the DBS-CT cohort. We ran ESM-CT using each of these initializations and computed the change in contact1 coordinates attributable to variable operator initialization. The median coordinate change over 50 images, expressed as Euclidean distance, was 0.13 mm.

3.1.3. Sensitivity to image resampling errors.

To estimate sensitivity to image resampling we created ten rotation transforms, each comprising a product of rotations about x, y and z axes. Rotation angle about each axis was assigned a random value from a uniform distribution between −30 and 30 degrees. We then applied these transforms to each of the 56 DBS-CT images, thus creating 10 copies of each; trilinear interpolation was used for resampling. The operator-selected initialization endpoints were correspondingly rotated. ESM-CT was run and the resulting centers of contact1 on both sides were transformed back to the original space and compared to the results obtained by analysis of the original DBS-CT image. Discrepancy in contact coordinates was expressed as Euclidean distance in mm. This control analysis revealed an average discrepancy of 0.23±0.1mm on both sides. Average discrepancy across all images and electrodes for each rotation angle separately shown on Figure 8. Importantly, only the absolute angle of rotation about the x axis significantly correlated with the increased error (Pearson’s r=0.93); this is revealed an average discrepancy of 0.23±0.1mm on both sides. Average discrepancy across all images and electrodes for each rotation angle separately shown on Figure 8. Importantly, only the absolute angle of rotation about the x axis significantly correlated with the increased error (Pearson’s r=0.93); this is likely due to lower resolution of DBS-CT acquisitions in the z direction that resulted in a decrease in fit for both electrodes across axial slices after rotating about the x axis. This subsequently resulted in a loss of implant image resolution and higher localization error compared to rotations about the y and z axes. Overall the test indicates that ESM-CT should be robust to positioning of the head in the scanner bore.

Figure 8.

Mean and standard deviation of discrepancy in distal contact location computed by ESM-CT in original and rotated images. The discrepancy was averaged over nine tested images, each rotated in 1° increments between −30° and +30° about the x (sagittal direction in image space), y (coronal direction in image space), and z axis (axial direction in image space).

3.1.4. Rescan precision in clinical images.

To estimate the test-retest (TRT) precision, we evaluated ESM-CT in a set of clinical CTs acquired within 21 days of DBS-CT. We identified five study participants with such repeated CTs (REP-CT). One participant had five REP-CTs (4 images with 3 mm and one with 1 mm slice thickness — to evaluate high clinical suspicion of a right pontomedullary acute infarct; no infarct or mass effect was present in any image); two had 2 REP-CTs (1 mm slice thickness- one to evaluate potential intracranial infection in the setting of a superficial wound infection; the other required imaging in the context of right DBS lead revision), and the remaining two had one REP-CT (1 mm slice thickness) each (obtained in one participant for post-operative delirium and the other prior to explanation of an infected left lead). In-plane pixel dimensions for all scans were 0.5±0.02mm. Each REP-CT was rigid body coregistered (cmg objective function) to the DBS-CT of the same participant, yielding 11 image pairs (DBS-CT vs. REP-CT) in total.

ESM-CT was run on all CT pairs and difference in contact1 coordinates was evaluated in both hemispheres, yielding a total of 22 comparisons. The coordinate discrepancy between DBS-CT and REP-CT was expressed in mm and percentage of slice thickness. In three cases, the contact array was poorly defined owing to a narrow angle between the CT acquisition plane and implant trajectory; these localizations were discarded. Of the 19 useable REP-CTs, 10 were in images with 3 mm slices; the average TRT discrepancy in these cases was 0.95±0.63 mm, or 32%±21% of slice thickness. In the 9 cases with 1mm slices, the mean TRT discrepancy was 0.53±0.29 mm. Importantly, there was no correlation between time between the first and repeated scan, and the magnitude of discrepancy.

3.1.5. Comparison of ESM-CT to a previously published manual method.

We applied a previously published, manual contact localization method (Videen et al., 2008) (method 1) in a separate set of 84 participants with DBS-CT and DBS-MR images that had been processed previously by this method. ESM-CT was run in these cases and both sets of contact1 coordinates were transformed to MNI152 space using each participant’s T2w image (see above, Calculating electrode location in standard space). Contact1 localization differences were individually evaluated in x, y, and z coordinates. In paired two- tailed t-test for population means, significant differences were found only for the z coordinate (p<0.001), which showed a mean difference of 1±0.3 mm on both sides. However, within-method coordinate variability across participants was not significantly different across the two methods (p=0.4 in F-test for equal variances). The current method requires substantially less manual processing, and is therefore preferred.

3.1.6. Comparison of ESM-CT to a previously published automated method.

We also compared ESM-CT to another recently published automated contact localization method known as PaCER (Husch et al., 2018) (method 2) available via the LEAD-DBS MATLAB package, which is widely used (Horn and Kuhn, 2015). PaCER also models the electrode shaft as a curve as in our implementation. We ran PaCER electrode localization on all 56 clinical DBS-CT images. Manual assignment of hemisphere was required as PaCER randomly ordered the analyzed electrodes (sides were swapped in 26 cases). Contact1 coordinates obtained by ESM-CT and PaCER were transformed to MNI152 space and compared. The average difference in coordinates (method dependent bias), for right/left sides respectively, was 0.14±0.1/0.12±0.1 mm for x, 0.37±0.18/0.38±0.14 mm for y, and 0.36±0.18/0.33±0.12 mm for z axes. Average Euclidean difference thus was 0.52 mm on both sides. For a paired two-tailed t-test for population means, all these differences were significant at p<10^-10. As with method 1, within-method coordinate variability across participants was not significantly different (p=0.5 for all coordinates in F-test for equal variances).

3.2. Systematic movement of DBS implants

3.2.1. Apparent longitudinal change in implant position.

A secondary objective of this investigation was to assess longitudinal stability of implant position utilizing ESM-CT. To this end, we ran ESM-CT on the DBS-CT and DEL-CT images in the 56 primary study participants, thereby obtaining measures of interval change in contact1 coordinates and shaft curvature in 112 DBS electrodes (Table 1). Apparent contact1 movement was significant along the anterior-posterior axis (Δy=0.5±0.5 mm on both sides, left: t(55)=−6.59, p<0.001; right: t(55)=−6.38,p<0.001) and the superior-inferior axis (Δz=−0.9±0.6 mm on both sides, left: t(55)=8.93, p<0.001; right: t(55)=12.83, p<0.001) , but not in the left-right axis (Δx, −0.1±0.5 mm). Shaft curvature significantlyincreased from DBS-CT to DEL-CT (ΔK=0.18 m⁻¹ left, t(55) =−4.1, p<0.001; 0.14 m⁻¹ right, t(55)=−3.0, p<0.01). Average change in electrode position is illustrated in Figure 9.

Table 1.

Mean change in contact #1 location and shaft curvature between DBS-CT to DEL-CT. t is the value of t statistic with 55 degrees of freedom; p value is two-tailed. Δx, Δy, Δz = change in the respective Cartesian coordinate (MNI152 space), and ΔK= change in implant trajectory curvature

	Δx, mm		Δy, mm		Δz, mm		ΔK, m−1
	change	t(p)	change	t(p)	change	t(p)	change	t(p)
Left	−0.1±0.5	1.73(0.09)	0.5±0.5	−6.59(< 0.001)	−0.9±0.6	8.93(< 0.001	0.18	−4.1(0.001)
Right	0.0±0.5	− 1.95(0.06)	0.5±0.5	−6.38(< 0.001)	−0.9±0.6	12.8(< 0.001)	0.14	−3.0(0.01)

Figure 9.

3D rendering of a skull based on the average template of 56 CT-DBS images, co-aligned in common space. Red: average of DBS implants in CT-DBS images. Implants were co-aligned separately for each side using rigid body transform, and averaged across 56 study participants. Green: Average of DBS implants in corresponding 56 CT-DEL images, resampled to the CT-DBS average template space using computed 6-DOF rigid body CT-DBS↔CT-DEL transform. Note the diffence in average CT-DBS and CT-DEL implant trajectories.

3.2.2. Evaluation of explanatory factors.

Results obtained by multivariable linear regression of change in implant geometry (ΔK, Δx, Δy, Δz, E) on predictor covariates (post implantation air volume [A], acquisition angle difference [Δα], inter-scan interval [ΔT]) are listed in Table 2. The same table also reports Pearson correlation coefficients between predictor and dependent variables.

Table 2.

Pearson correlation coefficients (r) between dependent measures (columns) and predictor variables (rows). The R2 statistic reports the total correlation between dependent measure and predictor variables from the regression model. Significant linear models (bottom row, p-value) and predictor variables are marked with one (0.01<p<0.05) or two stars (p<0.001). Alpha (p) values are not corrected for multiple comparisons. A = volume of immediate post-operative subdural air (mm3), Δα = difference in acquisition head angle between scans, ΔT = time between CT acquisitions, ΔK= change in implant trajectory curvature. E = total Euclidean distance, (√(〖Δx〗^2+〖Δy〗^2+〖Δz〗^2 )), Δx,Δy, Δz represent change in the respective Cartesian coordinate (MNI152 space). All predictor variables are displayed for both the left (L) and right (R) brain

dependent	predictor	ΔK, L	ΔK, R	E, L	E, R	Δx, L	Δx, R	Δy, L	Δy, R	Δz, L	Δz, R
A (air)		0.01	−0.2	0.29*	0.25*	0.06	0.07	0.05	0.19	−0.05	−0.1
Δα (angle)		−0.41**	−0.48**	−0.29*	−0.21	0.05	0.22	0.04	0.05	0.46**	0.46**
ΔT (delay)		−0.11	−0.11	0.01	−0.05	0.02	0.2	−0.2	−0.12	0.08	0.21
R2		0.23	0.22	0.17	0.11	0.007	0.07	0.07	0.0	0.22	0.24
Regression Model P value		0.003*	0.005*	0.02	0.1	0.9	0.3	0.3	0.2	0.005*	0.002*

Table 2 demonstrates that head tilt (Δα), more than any other explanatory factor, accounted for change in measured electrode geometry. Δα significantly predicted both change in implant curvature and apparent ventral movement (negative Δz) on both sides. Linear model fits for curvature change and ventral contact movement are shown in Figure 10. Intracranial air (A) significantly predicted total change in contact1 coordinates (E) on both sides. However, it should be noted that the distribution of A was very non-normal: the median value of A was 3.9 cm³ whereas 3 participants had over 20 cm3 intracranial air volume. This circumstance may account for the asymmetric significance results obtained for the influence of A on E (p = 0.02 vs. p = 0.1 on the left vs. right).

10.

Linear models for (A, B) implant curvature change (ΔK), and (C, D) for z displacement (Δz) in MNI152 space. All models were computed for 56 PD study participants, with volume of subdural air A in DBS-CT and change in acquisition angle Δα as covariates. Actual value (x axis) vs linear model prediction (y axis) is plotted.

4. Discussion

Here, we describe ESM-CT, a semi-automated method for localizing DBS electrodes on the basis of CT images. ESM-CT is robust to operator initialization and image resampling and is reliable on direct repeat scan testing. The self-contained source code of ESM-CT is freely available for research purposes. Application of ESM-CT demonstrated systematic differences in implant geometry in comparisons of immediate post-operative vs. delayed CT images (median 9 months after surgery, range 4–82 months). c). Our observations indicate that DBS research requiring electrode localization should account for head-tilt, utilizing precise methods such as ESM-CT.

4.1. Novelty of ESM-CT

ESM-CT improves upon prior DBS electrode localization strategies (D’Albis et al., 2015; Hebb and Miller, 2010; Horn and Kuhn, 2015; Lauro et al., 2016; Motevakel and Medvedev, 2014). Unlike many previous methods, ESM-CT models the electrode shaft by a low degree polynomial (our implementation supports arbitrary degree, but we found that quadratic polynomials were most robust), and reports implant curvature along the locations of all contacts. Most published methods involve substantial pre-processing of input images and use features derived from the CT image such as number of voxels in connected regions and principal directions, or centroids to detect electrodes. Each combination of features depends on implicit assumptions about the underlying electrode geometry. Breach of any of these assumptions owing to low resolution, low contrast to noise, presence of other metal objects, or other artifacts, may lead to decreased precision. In addition, applicability of an electrode localization method to other implant models with different statistical properties, or different geometries would also depend on selected features. Using a different CT scanner model or acquisition mode may also affect statistical properties of implant images. ESM-CT, on the other hand, operates only on the general assumption that the CT signal from metal is on average the brightest compared to surrounding tissue. Manual initialization of ESM-CT is fast, requires only minimal operator training, is robust to variability in operator initialization, and excludes algorithmic electrode misclassification. In addition, ESM-CT avoids the common approach of tracking 2D slices to reconstruct the full electrode. In our experience, such tracking is both prone to local artifacts and is sensitive to the angle between the implant and the CT acquisition plane. As we demonstrate above, our fully three-dimensional model of both the shaft and contact array allows precise localization over a wide range of acquisition angles is robust to resampling, and shows good repeatability on repeat testing. This combination of robustness and minimal assumptions makes our strategy potentially applicable to other electrode models and/or configurations.

4.2. Comparison to other contact localization methods

We compared ESM-CT to two previously published methods, one based on manual identification of DBS contacts (Videen et al., 2008) (method 1) and PaCER, a recent automated open source method (Husch et al., 2018) (method 2). All contact location comparisons were done in standard MNI152 space. These comparisons revealed a significant mean difference (Δz) of 1 mm for method 1. This method determines the last ‘visible’ contact array slice and determines ‘depth of penetration’ in the last slice (Videen et al., 2008). However, since electrodes are imaged under some (variable) angle to the z plane, the value of ‘depth of penetration’ may not fully describe the z coordinate of the electrode tip. If electrodes are imaged at a large angle to the z plane, as is the case in our data, this might explain the observed systematic difference in z coordinate. This hypothesis is also in part supported by much smaller difference in z coordinate (Δz = 0.3 mm) with method 2.

Variance in computed contact location over participants was comparable across methods. This result most likely indicates that the true variability in contact locations in our dataset exceeded method- dependent imprecision. ESM-CT and method 2 showed better agreement (Δx = 0.1 mm, Δy = 0.4 mm, Δz = 0.3 mm, total Euclidean difference of 0.5 mm), which may be due to less dependency on manual steps compared to method 1. However, remaining small systematic differences indicate that a common calibration strategy (e.g., based on DBS phantom imaging) may be required to directly compare the results produced by different localization methods.

4.3. Post-operative electrode displacement

Using ESM-CT, we observed displacement of both DBS electrodes in the months following DBS (median 10 months after surgery, range 4–82 months). Prior studies reported electrode movement in a lateral, rostral and dorsal (i.e., +Δz) direction from the time of surgery to repeat scans (Choi et al., 2017; Morishita et al., 2017; van den Munckhof et al., 2010). In contrast, we find electrode movement in the`lateral, rostral and ventral (i.e., -Δz) direction (MNI152 space). Methodological differences across studies likely account for these discrepant findings. Specifically, our analysis compared immediate post-operative CT images (DBS-CT) obtained in a strictly supine position to DEL-CT images obtained with head tilt (rotation about the left-right axis component). In fact, our data demonstrate that head angle during acquisition predicted both change in shaft curvature and ventral movement. We suggest that the pull of gravity may account for the axial (z) component of electrode movement in our study. The plausibility of this explanation is supported by a prior study that demonstrated brain displacement of 1–2 mm in the subthalamic region from linear acceleration (Feng et al., 2010). Although future studies may be necessary to confirm our findings, we clearly show that head angle during image acquisition influences apparent electrode location.

Immediate post-operative subdural air volume also predicted apparent electrode movement. Similar findings, attributed to subdural air or CSF loss, have been previously reported (Halpern et al., 2008; Khan et al., 2008; Miyagi et al., 2007; van den Munckhof et al., 2010). The present post-operative intracranial air volumes were small in comparison to those in previous reports, likely because the surgical technique (Sadeghi et al., 2015; Tabbal et al., 2007) was specifically designed to minimize pneumocephalus. Surgical techniques for minimizing intraoperative and post-operative electrode displacement continue to be developed (Coenen et al., 2011; Sharim et al., 2015; Steel and Basu, 2017).

4.4. Significance of postoperative electrode displacement

Small differences in active contact location are known to influence the efficacy of STN DBS (Cooper et al., 2011; Hershey et al., 2010; Hill et al., 2013; Wodarg et al., 2012). Such findings are plausible, as the radius of neural excitation resulting from 2.5-volt monopolar stimulation has been estimated as 2-mm (Mikos et al., 2011). Thus, an electrode shift of only a few millimeters may greatly affect research outcomes correlating behavior, local physiology, or computational models reliant on precise DBS electrode location. This is particularly relevant in research geared toward effects of current steering and adaptive control in DBS (Butson and McIntyre, 2008; Dembek et al., 2017; Fernandez-Garcia et al., 2017; Hoang et al., 2017; Tinkhauser et al., 2018). Our method localizes contacts with a precision well under 1 mm, hence, may also be useful in the development of more precise clinical applications such as DBS implantation operative technique, field models of DBS stimulation programming (Butson and McIntyre, 2015), and evaluation of other potential influences on electrode movement such as time following surgery, target location, and, to a lesser extent, pathology, sex, and disease duration (Lalys et al., 2014). However, clinical relevance of sub-millimeter shifts in DBS electrode position relies on ongoing research efforts to correlate precise DBS localization to studies of outcome and mechanism.

4.5. Limitations

ESM-CT measures electrode position with respect to bone rather than brain structures. Determining contact location with respect to brain structures depends upon co-registration of the CT with a pre-operative MRI. This limitation is common to all existing CT-based DBS localization methods.

4.6. Conclusions

Precise determination of DBS electrode position is necessary for studying the effects of DBS. We developed a fast, precise (sub-millimeter precision), semi-automated method for determining DBS electrode position on the basis of CT scans. Using this method, we demonstrate that post-operative DBS electrode position is influenced by head angle with respect to gravity at the time of image acquisition. These results require follow-up studies to investigate the relationship of DBS electrode shift to anatomical structures (e.g., the STN).

Highlights:

• Precise DBS electrode position is critical to study structure-function relationship

• We developed a precise method for determining DBS electrode position using CT scans

• Our semi-automated method (ESM-CT) is robust to resampling with good reproducibility

• Head angle at time of image acquisition affects calculated DBS electrode position