Development and validation of the random walk algorithm: application to the classification of diffuse heterogeneity in brain SPECT perfusion images.

UNLABELLED: Heterogeneity analysis has been studied for radiological imaging, but few methods have been developed for functional images. Diffuse heterogeneous perfusion frequently appears in brain single photon emission computed tomography (SPECT) images, but objective quantification is lacking. An automatic method, based on random walk (RW) theory, has been developed to quantify perfusion heterogeneity. We assess the robustness of our algorithm in differentiating levels of diffuse heterogeneity even when focal defects are present. METHODS: Heterogeneity is quantified by counting R (percentage), the mean rate of visited pixels in a fixed number of steps of the stochastic RW process. The algorithm has been tested on the numerical anthropomorphic Zubal head phantom. Seven diffuse cortical heterogeneity levels were simulated with an adjustable Gaussian function and 6 temporoparietal focal defects simulating Alzheimer Disease, leading to 42 phantoms. Data were projected and smoothed (full width at half maximum, 5.5 mm), and Poisson noise was added to the 64 projections. The SPECT data were reconstructed using filtered backprojection (Hamming filter, 0.5 c/p). R values for different levels of perfusion defect and diffuse heterogeneity were evaluated on 3 parameters: the number of slices studied (20 vs 40), the use of Talairach normalization versus original space, and the use of a cortical mask within the Talairach space. For each parameter, regression lines for heterogeneity and temporoparietal defect quantification were analyzed by covariance statistics. R values were also evaluated on SPECT images performed on 25 subjects with suspected focal dementia and on 15 normal controls. Scans were blindly ranked by 2 experienced nuclear physicians according to the degree of diffuse heterogeneity. RESULTS: Variability of R was smaller than 0.17% for repeated measurements. R was more particularly influenced by diffuse heterogeneity compared with focal perfusion defect. The Talairach normalization had a significant influence on the heterogeneity quantification. The number of slices visited by the RW and the cortical masking have a weak influence on the heterogeneity quantification but only for very low heterogeneity levels. The Spearman coefficient between physicians' consensus and RW automatic ranking is 0.85, in the same order of magnitude as the Spearman coefficient between the rankings of the 2 senior physicians (0.86). CONCLUSIONS: Random walk is an original and objective method and is able to quantify heterogeneous brain perfusion, even in presence of cortical defects. This method is repeatable, robust, and mainly influenced by spatial normalization.

Comparison of heterogeneity quantification algorithms for brain SPECT perfusion images.

BACKGROUND: Several algorithms from the literature were compared with the original random walk (RW) algorithm for brain perfusion heterogeneity quantification purposes. Algorithms are compared on a set of 210 brain single photon emission computed tomography (SPECT) simulations and 40 patient exams. METHODS: Five algorithms were tested on numerical phantoms. The numerical anthropomorphic Zubal head phantom was used to generate 42 (6 × 7) different brain SPECT simulations. Seven diffuse cortical heterogeneity levels were simulated with an adjustable Gaussian noise function and six focal perfusion defect levels with temporoparietal (TP) defects. The phantoms were successively projected and smoothed with Gaussian kernel with full width at half maximum (FWHM = 5 mm), and Poisson noise was added to the 64 projections. For each simulation, 5 Poisson noise realizations were performed yielding a total of 210 datasets. The SPECT images were reconstructed using filtered black projection (Hamming filter: α = 0.5).The five algorithms or measures tested were the following: the coefficient of variation, the entropy and local entropy, fractal dimension (FD) (box counting and Fourier power spectrum methods), the gray-level co-occurrence matrix (GLCM), and the new RW.The heterogeneity discrimination power was obtained with a linear regression for each algorithm. This regression line is a mean function of the measure of heterogeneity compared to the different diffuse heterogeneity and focal defect levels generated in the phantoms. A greater slope denotes a larger separation between the levels of diffuse heterogeneity.The five algorithms were computed using 40 99mTc-ethyl-cysteinate-dimer (ECD) SPECT images of patients referred for memory impairment. Scans were blindly ranked by two physicians according to the level of heterogeneity, and a consensus was obtained. The rankings obtained by the algorithms were compared with the physicians' consensus ranking. RESULTS: The GLCM method (slope = 58.5), the fractal dimension (35.9), and the RW method (31.6) can differentiate the different levels of diffuse heterogeneity. The GLCM contrast parameter method is not influenced by a focal defect contrary to the FD and RW methods. A significant correlation was found between the RW method and the physicians' classification (r = 0.86; F = 137; p < 0.0001). CONCLUSIONS: The GLCM method can quantify the different levels of diffuse heterogeneity in brain-simulated SPECT images without an influence from the focal cortical defects. However, GLCM classification was not correlated with the physicians' classification (Rho = -0.099). The RW method was significantly correlated with the physicians' heterogeneity perception but is influenced by the existence of a focal defect.

Brain perfusion heterogeneity measurement based on Random Walk algorithm: choice and influence of inner parameters.

UNLABELLED: A Random Walk (RW) algorithm was designed to quantify the level of diffuse heterogeneous perfusion in brain SPECT images in patients suffering from systemic brain disease or from drug-induced therapy. The goal of the present paper is to understand the behavior of the RW method on different kinds of images (extrinsic parameters) and also to understand how to choose the right parameters of the RW (intrinsic parameters) depending on the image characteristics (i.e. SPECT images). "Extrinsic parameters" are related to the image characteristics (level/size of defect and diffuse heterogeneity) and "intrinsic" parameters are related to the parameters of the method (number (N(rw)) and length of walk (L(rw)), temperature (T) and slowing parameter (S)). Two successive studies were conducted to test the influence of these parameters on the RW result. In the first study, calibrated checkerboard images are used to test the influence of "extrinsic parameters" (i.e. image characteristics) on the RW result (R-value). The R-value was tested as a function of (i) the size of black & white (B&W) squares simulating the size of a cortical defect, (ii) the intensity level gaps between the B&W squares simulating the intensity of the cortical defect and (iii) intensity (=variance) of noise, simulating the diffuse heterogeneity. The second study was constructed with simulated representative brain SPECT images, to test the "intrinsic" parameters. The R-value was tested regarding the influence of four parameters: S, T, N(rw) and L(rw). The third study is constructed so as to see if the classification by diffuse heterogeneity of real brain SPECT images is the same if it's made by senior clinicians or by RW algorithm. RESULTS: Study 1: the RW was strongly influenced by all the characteristics of the images. Moreover, these characteristics interact with each other. The RW is influenced most by diffuse heterogeneity, then by intensity and finally by the size of a defect. Study 2: N(rw) and L(rw) values of 1000 give an optimal reproducibility of the measurement (mean standard deviation<0.1), a fast computation time (time<0.5s/image) and have a maximum difference in terms of R-value between the two extreme images corresponding to the range of the population studied. The best S and T values for SPECT images are 3 and 15, respectively. Study 3: A significant correlation was found between RW ranking and the physicians' consensus (rho=0.789; p<0.0001). CONCLUSION: This study confirms that the RW method is able to measure the heterogeneity of brain SPECT images even in the presence of a large defect. However, the result of the method is strongly influenced by the "intrinsic" parameters, so the program should be calibrated for each different type of image.