EFFECT OF DATA NORMALIZATION ON THE CREATION OF NEURO PROBABILISTIC ATLASES

Abstract

In the past fifteen years, rapid improvements in imaging technology and methodology have had a tremendous impact on how we study the human brain. During deep brain stimulation (DBS) surgeries, detailed anatomical images can be combined with physiological data obtained by micro-electrode recordings (MER) and stimulations to address questions relating to the location of specific motor or sensorial functions. The main advantage of techniques such as MER and micro-stimulation over brain imaging is their ability to localize patient physiological activity with a high degree of spatial resolution. Aggregating data acquired from large populations permits to build what are commonly referred to as statistical atlases. Data points from statistical atlases can be combined to produce probabilistic maps. A crucial step in this process is the inter-subject spatial normalization that is required to relate a position in one subject’s brain to a position in another subject’s brain. In this paper, we study the impact of spatial normalization techniques on building statistical atlases. We show that the Talairach or AC-PC coordinate system commonly used in the medical literature produces atlases that are more dispersed than those obtained with normalization methods that rely on non-linear volumetric image registration. We also show that the maps produced using non-linear techniques correlate with their expected anatomic positions.

Introduction

Brain mapping is a set of neuroscience techniques predicated on the mapping of biological quantities or properties onto spatial representations of the brain. In deep brain stimulation (DBS) neurosurgeries, brain mapping is based on intra-operative electrophysiological recordings made to identify optimal locations for the implantation of electrodes. Since the pioneering days of DBS, data has been collected, spatially normalized, analyzed, and interpreted to study the location of motor and sensorial brain functions. One approach is to build probabilistic maps that associate with every voxel in the brain image an index that represents the likelihood of observing a particular response to the experiment of interest [1-4]. When populating these maps, the estimation of the location of functional areas in the brain is affected by two main sources of errors: (1) the error in the actual anatomical location of the measurement in a particular subject, and (2) the error made when normalizing data sets across subjects.

The first error is dependent on a number of factors. In DBS procedures, recording and stimulating electrodes are most often tracked with respect to a pre-operative scan by using a stereotactic frame affixed to the patient’s skull. We have reported that localization errors for the stereotactic frame used at our institution are negligible and comparable to commonly used stereotactic frames [5,6]. Another factor is that the brain is subject to several forces that can make it shift during the procedure [7,8]. In 2009, we reported that brain shift occurs in DBS surgeries with evidence of tissue displacement around the target of as much as 4.06 mm and studied its impact on the creation of probabilistic maps [9]. Techniques to track this shift are being developed but have not yet been proven to be accurate enough for DBS surgeries that require sub-millimetric precision [10]. Our surgical team minimizes this error by making small burr holes, and using gel foam and fiber sealants.

To address the second source of error, in this study, we quantify the effect of spatial normalization methods. Spatial normalization is a key element related to statistical analysis as it affects the spatial resolution of a study that involves a direct comparison across subjects. One purpose of spatial normalization is to bring homologous areas into their closest possible alignment, but this can be difficult to assess because of the lack of a gold standard against which to compare. The stereotaxic or Talairach coordinate system [11] has found the most widespread acceptance in the clinical community to normalize DBS-related observations for localization and communication of three-dimensional positions in the brain. It uses the anterior (AC) and posterior (PC) commissures as internal landmarks to define a right-handed coordinate system. Their mid-point typically defines the origin even though either the AC or PC is sometimes used instead. A point in 3D space is then defined as being anterior-posterior, medial-lateral and dorsal-ventral to this origin. We have shown in the past that there is substantial inter-surgeon variability in the selection of these commissures which define the Talairach reference system and that non-linear image registration or normalization can be used to reduce this variability [12,13]. Non-linear or non-rigid normalization methods use a mathematical measure of overall image mismatch and a minimization algorithm that iteratively changes the transformations in order to find the best set of parameters to match the image to the reference volume. Usually, they begin by optimizing linear parameters: translations, rotations, scaling, and often shears as well. They then proceed to find the best set of non-linear (warping) parameters to further match the morphological details of the reference brain. Pluim et al. [14] provide a detailed survey of mutual-information-based methods [15-17] for medical image registration. Chakravarty et al. [18] survey various atlas warping techniques used for DBS and suggest that template-based atlas-to-patient warping techniques such as the methods above that use MRI imaging for atlas creation work best for customizing the atlas to patient data.

In this study, we compare the effect of using the Talairach coordinates versus those obtained by non-linear normalization on the creation of statistical atlases and demonstrate that the normalization scheme has a substantial effect on their quality.

Materials and Methods

For the purpose of this study, we intra-operatively collected 1099 stimulation response data points from 108 DBS VIM implantations in 100 patients who underwent VIM DBS surgery between February 2004 and June 2010. Of these, only those that recorded at least 50% efficacy (measured subjectively by a neurologist during surgery) were chosen to represent successful tremor relief. This resulted in 620 data points from 86 implantations. The surgeries were performed at Vanderbilt University Medical Center by two neurosurgeons; co-authors PEK and JSN.

The following types of spatial normalization schemes were compared: 1) the use of the stereotaxic or Talairach coordinates of each data point, and 2) a 3D volumetric non-linear image registration algorithm called the Adaptive Bases Algorithm (ABA) [19] that automatically registers a subject’s brain MRI to the MRI of the reference volume called the atlas. ABA combines an affine registration (9 DOF: translation, rotation and anisotropic scaling) followed by a non-rigid registration. The non-rigid registration algorithm computes a deformation field that is modeled as a linear combination of radial basis functions with finite support. This results in a transformation with several thousands of degrees of freedom. Two transformations (one from the atlas to the subject and the other from the subject to the atlas) that are constrained to be inverses of each other are computed simultaneously. ABA reduces the computational complexity and improves the convergence properties of related splines-based approaches [20-23] by identifying regions of mis-registration and adapting the compliance of the transformation locally. The algorithm arrives at the final deformation iteratively across scales and resolutions, starting with large scale transformations computed on down sampled images and progressing to local transformation computed a maximum resolution. Once normalized, each data point is used to create functional atlases of stimulation response data.

We demonstrate the effect of the spatial normalization by showing the differences in the localization and shape of probabilistic maps of symptom relief in essential tremor patients. The probabilistic maps are created by using the method described in [24]. Briefly, this consists of centering a spherical shell model at each data point, with a radius proportional to the level of stimulation that triggered the control of the symptoms. The probabilistic models are then summed over the whole reference volume and normalized to produce a map ranging between 0 and 1. It has been extensively reported that the optimal location for symptom relief in essential tremor patients using DBS is in the ventral intermediate (Vim) nucleus [25]. Because of lack of gold standard, we use an anatomical atlas to show the position of the maps relatively to the anatomy. Not yet as popular as the Schaltenbrand-Wahren Atlas [26], the Paris atlas [27] overcomes a number of its limitation by providing the user with an accurate 3D histological atlas associated with an MRI T1 scan of reference. Using our non-rigid registration algorithm we projected and overlaid the Paris atlas onto our reference volume. The probabilistic maps were then overlaid on the structures from the Paris atlas. The centroid of the maps as well as their shapes are compared and reported in the next section.

Results

Figure 1 shows the coronal, axial and sagittal slices centered on the Vim of the reference MRI volume overlaid with both the Paris atlas and the probabilistic maps of tremor control. The map built using Talairach coordinates is shown in the first row and that built using non-linear normalization is shown in the second row. We report quantitative results in Tables 1 and 2. Table 1 reports the location of the highest probability of tremor control for each normalization method. Table 2 gives information on the shape of the maps in terms of the dimensions of the major axes of the map.

Figure 1.

Coronal, axial and sagittal slices centered on the Vim of the reference MRI volume overlaid with both the Paris atlas and the probabilistic map of tremor control. Each row corresponds respectively to the Talairach coordinates and non-linear normalization method.

Table 1.

Location of the highest probability of tremor control obtained from the Talairach and non-linear normalization schemes (in mm from the mid-commissure; A-P: Anterior-Posterior, M-L: Medial-Lateral, S-I: Superior-Inferior).

	A-P	M-L	S-I
Talairach Coordinates based Normalization	−4.47	13.79	6.75
Non-Linear Normalization	−4.47	12.12	4.38

Table 2.

Dimensions (in mm) of the major and minor axes (A-P: Anterior-Posterior, M-L: Medial-Lateral, S-I: Superior-Inferior) of the probability map of successful tremor control.

			A-P	M-L	S-I
		Talairach Coordinates based Normalization	6.4	3.2	7.3
		Non-Linear Normalization	2.3	1.2	1.5

Discussion

Stereotactic and linear methods used to match different brains cannot match functional areas across individuals, because these are local sub-regions that are not well predicted by gross anatomical landmarks. Volumetric approaches such as the non-rigid registration algorithm used in this study can better align such regions allowing more accurate mapping of data from a population of patients and subsequent analyses as illustrated on Figure 1 and Tables 1 and 2. The results show that statistical maps created by non-linear normalization of data from several individuals are tighter than those created using the Talairach system commonly used by neurosurgeons as non-linear methods have more degrees of freedom. Furthermore, the non-linear normalization method generates a probability map built using intra-operatively collected tremor relief data points that correlates strongly with the anatomical Vim while the Talairach approach produces scattered results.

These findings illustrate the importance of the choice of the normalization scheme while analyzing such data and interpreting the results of such analyses. The use of Talairach coordinates is often favored to other methods because of its simplicity and its prevalence in the medical literature for a long time prior to the availability of more sophisticated normalization schemes. However, even though these new non-linear methods require additional processing they should be preferred to linear ones in order to accurately and reliably compare functional information across individuals. Recently, non-linear algorithms have been made more accessible to researchers and clinicians alike in user-friendly software packages allowing a wider use in clinical analyses. Their use will likely improve the accuracy of statistical studies and clinical conclusions in stereotactic and functional data analyses.