MRI based on more sophisticated imaging methodologies, is able to create substantial maps in which a lot of information on the various patho/physiological parameters have been transpired. For instance, a comprehensive analysis of breast cancer concerning at all stages by the MRimages is of great importance in medicine. A number of new indexes may be employed to investigate quantitatively the trend of the growth rate of abnormal tissues on the improved maps obtained by the complex combination T1 and T2-weigthed MRimages along with the amounts of their improved SNR. 

Essentially, these indexes are based on the parametric function of the convolution integral of the functions of the relaxation times on the limits of integrand zero to r. Then, the signal-to-noise function on this parametric function is computed in terms of r, and by applying the Fourier transform and derivative operator, the FDC function will be formed. The area under the FDC curve is denoted as SFDC. Furthermore, for more investigation in different conditions, the FWxM function is also introduced on the FDC function. In other words, the FWxM defined as full width in a fraction (x) of the maximum value of the FDC function. 

The FWxM is as the parabolic curve that the slope and the area under the FDC curve at x = 0 are referred as S0, and SFWxM, respectively. The proposed indexes were simulated by means of Matlab software for two T1- and T2- weighted MR-breast images, and the amounts of S0, SFDC and SFWxM were calculated, as shown in the following figures and table. The indexes may employ to estimate of the growth rate of abnormal tissues at different conditions as well as to contribute to better diagnosis of breast cancer and to investigate tissues performance and identifying related detrimental influences.

Mansour Ashoor has completed his PHD at nuclear engineering department from Sharif University of Technology, Tehran, Iran. He is associate professor at radiation application research school, and an expert in medical imaging, MRI, health physics, and fuzzy mathematics who works at Nuclear Science and Technology Research Institute of Iran.