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

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.

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).

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.