STATISTICAL PARAMETRIC MAPS IN IDENTIFICATION OF REGIONAL CEREBRAL ACTIVITY IN PET STUDY

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1 Krynica Morska 23 rd 27 th September 2012 STATISTICAL PARAMETRIC MAPS IN IDENTIFICATION OF REGIONAL CEREBRAL ACTIVITY IN PET STUDY Marek Wróbel 1 Piotr Boguś 2 Anita Markowska 3 Bogdan Małkowski 1 Łukasz Bałszewski 1 Monika Kempińska 4 Artur Kachniarz 1 1 Department of Nuclear Medicine Oncology Centre Prof F. Łukaszczyk Memorial Hospital ul. dr I. Romanowskiej Bydgoszcz 2 Department of Physics and Biophysics Medical University of Gdańsk ul. Dębinki Gdańsk 3 Department of Psychiatric Nursing CM Nicolaus Copernicus Universityin Toruń ul. Jagiellońska Bydgoszcz 4 Department of Nuclear Medicine and Radiology Informatics Medical University of Gdańsk ul. Dębinki Gdańsk 1 wrobelm@co.bydgoszcz.pl 2 piotr.bogus@gumed.edu.pl ABSTRACT The paper presents the application of statistical parametric maps as a tool for the determination of changes in regional cerebral blood flow during Stroop colour word interference test in [15O]H2O PET study. It describes the general linear model used for preparing classical inferences on regional specific responses. The paper presents only some preliminary results of the SPM application. The results are obtained by using Statistical Parametric Mapping package (SPM Wellcome Department of Cognitive Neurology London UK) implemented in Matlab (Mathworks; Sherborn MA). INTRODUCTION In recent years the positron emission tomography (PET) has been widely used for functional brain studies. One of the foci identification processing methods in PET activation studies is the statistical parametric maps (SPMs). It includes two earlier ideas: the distribution analysis change [1] and the mapping probability significance [2]. The statistical parametric maps are an alternative estimation method for region of interest (ROI). Moreover it allows one to find the differences in PET images without a prior knowledge about the activation foci. There are spatially extended statistical processes that are used to hypotheses test of regionally specific effects in neuroimaging data [3]. PET activation studies consist of two modes: baseline (B) and activation (A). During the activation part the subject is under stimulus (e.g. reading words) whereas without stimulus subject is under the baseline part. The SPM compares voxels in the baseline and in the activation images to localize the differences in regional cerebral activity. In the voxel-based approach is calculated the statistical parameters e.g. t-value. It is done for every voxel by using the general linear model. Finally the sets of t-values constitute a statistical image. The contribution of the present paper is that it proposes to use a statistical method to identification activation foci in brain using a PET studies.

2 GENERAL LINEAR MODEL The General Linear Model (GLM) [4] provides a unified procedure for fitting the models to the likelihood based data. The GLM approach generalizes models such as: variance analysis covariance analysis linear regression multiple regression t-test etc. The common goal is to predict and explain the dependent random variables from independent variables. The first is quantitative the second is categorical or quantitative. The GLM approach is described by the equation: where the dependent variable is treated as a linear combination of independent variable. Vector expresses additive noises whereas vector represents regression parameter (Fig. 2). Let us assume that the dependent variables represent the regional cerebral distribution of radioactivity in individual pixels. Then the quantity is a vector containing observed data. The can be understood as a voxel with the values of the pixels at specific coordinates in the brain among the sequential regional cerebral blood flow (rcbf) PET measurements (Fig. 1). So that is the total number of sequential rcbf PET measurements. voxel y PET studies Figure 1. The voxel in a PET activation study for a single subject. The matrix is composed of explanatory variables (covariates indicator variable) such as each column corresponds to one effect of the built-in experiment. The variables values are known and contain all effects that can affect the pixel values [9]. The explanatory variable reflects the conditions under which the PET scans were performed. The parameter is an vector of independent and identically (normally) distributed (iid) additive noises. The parameter is a vector containing the regression parameters that are estimated using the least square method. The regression parameters are determined by the best fit of to linear combination in the least square sense. The solution is described by [9]: where is: denotes the pseudo inverse. It can be shown that the variance-covariance matrix of in assumption that the observations are independent the mean is zero and variance is constant. The predicted data can be written as and describes what is predicted by the model. The estimated variances are given by: where.

3 A) PET data / B) Design matrix (for ) C) Regression parameters and errors E) Contrast vector D) General Linear Model F) The map of T-values G) Statistic image H) Inference/significance of voxels α and p-value Figure 2. The general scheme of the idea SPMs. A) The voxel y is an element of Y matrix. The matrix Y containing N scans (rows) and M voxels; the total number of voxels M is equal to the dimension of the matrix in PET protocol study). B) The X is a matrix of known constants: continuous discrete or indicating the levels of an experimental factor [9]. C) Estimated regression parameters and independent errors. D) The equation of GLM for one voxel. The GLM is applied for each voxel. E) Contrast the result of the linear combinations of parameters allows to select the effect to the statistical test. The column shape vector c is called contrast vector and function is called contrasts parameter estimates. F and G) Statistical t-test is performed on random variables. H) The null hypothesis is specified with a contrast against the one-sided alternative. In tests the null hypothesis is rejected at significance level α i.e. it verifies is estimated whether contrast values differ from zero. This means that the certain areas of the brain are activated by the task.

4 INFERENCE The next step is to assess whether a voxel is active or not. Using a GLM in the statistical analysis the inference is carried out on the parameters. This is achieved using the t-statistic and a linear combination of parameter estimates and contrast vector. The contrast allows to test the research hypothesis where the differences in the reaction is caused by various factors (e.g. activation - baseline) are compared. The specific hypothesis for the linear compounds of the model parameters can be assessed by T-value: where is estimated. The degree of freedom (df) is equal [9]. The decision about rejection of the null hypothesis is made using a significance level for one-tiled t-test and p- value. If the T-value is greater than the t-value at the level of significance the null hypothesis is rejected and it can be written as:. The is the quantile of the t-distribution with degrees of freedom. In the SPM the null hypothesis is always is true determines the p-value.. The probability of the null hypothesis rejection when it PET SCANNING PROTOCOL AND DATA ACQUISITION [15O]H2O PET studies are performed using a high-resolution time-of-flight 3-rings Biograph128 mct scanner (Siemens Medical Solutions USA Inc) equipped with lutetium oxyorthosilicate crystals and a 2x64-slice spiral CT scanner. The axial field of view (FOV) of the PET detector is 16.2 cm. Six sequential rcbf PET measurements with 15O-labelled water are obtained for one subject during the two conditions (A1 - reading color names in black and A2 - naming color of word different) [8] repeated two times in alternative order. Between each of two conditions the baseline emission scan (B) is performed. The sequence of scans is as following: BA1A2BA1A2. A bolus of 400 MBq of [15O]H 2 O in 3 ml of normal saline was injected for each emission scan. It is done via the intravenous cannula over 15s and then the solution is flushed in with the automatic pump at a rate 60 ml/min for 10s. The emission data is acquired after 15s of the end phase of the injection. The acquisition is performed in a list mode in 120s epochs began 5s before the raising phase of the radioactivity head curve. The subject initiates the task 15s before the onset of the injection phase in order to ensure that the performance of the task is coincided with the maximum activity level of isotope in the brain. The time gap (10 min.) between each scan allows for the radioactive decay to the level of background. Patients are positioned within a head holder to minimize artefacts arising from head motions. The images are reconstructed with iterative techniques for the transmission scan and 3D OSEM (the ordered subset expectation maximization consist of 2 iterations with 21 subsets 2i21s) for the emission scan. A modulation of the point spread function (PSF) is used in order to increase the reconstructed spatial resolution. Corrections for attenuation scatter and random with an 5-mm FWHM Gaussian smoothing filter are applied. The final reconstructed volume set has a matrix size of pixels resulting in a voxel size of mm. The image pixels count is calibrated for the activity concentrations (Bq/mL) and decay is corrected using the time of traces injection as a reference. Data is analyzed with Statistical Parametric Mapping software. Before the statistical analysis the images are spatially pre-processed. The voxel-based approach requires the data to be in the same anatomical place in a image space. That is the reason why before statistical analysis using SPM the pairs of rest-activation images are realigned using a least-squares approach and a 6 parameter rigid body spatial transformations [5]. This allows one to remove the movement artefacts in PET time-series. Next stereotactic normalization is performed [6] where each

5 image is transformed into the standard space. The space is defined by some ideal model or template images (reference). This transformation matches each scan to the template image in a least squares sense. The matching involves a 12-parameter linear affine transformation and a nonlinear quadratic transformation in three dimensions followed by a 2-dimensional piece-wise nonlinear matching in the transverse planes. The normalization facilitates inter-subject averaging and precise characterization of functional anatomy [7]. The transformed 3D data were smoothed with a Gaussian filter (7 7 7 mm FWHM). RESULTS AND CONCLUSIONS Fig. 3 is showing some results of the analysis for a single patient during the activation A1 and A2. Maps of areas of increased rcbf associated with the activations A1 and A2 are shown in three projections: sagittal (side view) coronal (front view) and transverse (top view). The threshold level is p < but it is uncorrected for multiple independent comparisons. That means in this case the random fields theory [11] has been not applied. The g ray scale is arbitrary and the space is consistent with the described in Talairach and Tournoux atlas [10]. Figure 3. The SPM results for activation A1 and A2. The main goal of the paper was to present mathematical basis of SPM methods applied to analysis of PET images. The presented results are only introductory because the study considered the data only form one patient. But although only one patient was taken into account in PET study the SPM analysis can distinguish in the brain activation foci coming from A1 and A2. Number of subjects in PET activation studies affects the sensitivity of the finding of an increased rcbf. Therefore further PET study changes in rcbf during Stroop test should be performed on a larger group of subjects than in presented case. ACKNOWLEDGMENTS We are grateful for helpful comments from Ph.D. Mateusz Wędrowski from the Department of Nuclear Medicine Oncology Centre in Bydgoszcz.. REFERENCES [1] P.T. Fox M.A. Mintun: Noninvasive functional brain mapping by change-distribution analysis of averaged PET images of H215O tissue activity Journal of nuclear medicine 30 (1989)

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