An adaptive complex independent component analysis to analyze dynamic contrast enhanced-MRI

Using independent components analysis to calculate intravascular contrast agent concentration in prostate cancer

“…ICA algorithms try to find an unmixing matrix such that where columns of and are different only in scaling and permutation [11]. We developed and validated an adaptive complex ICA (ACICA) technique to calculate the intravascular contrast agent concentration in the tissue of interest [7][8][9]. The major assumption in this method was the spatial independence of the intravascular and extravascular MR signals.…”

“…The major assumption in this method was the spatial independence of the intravascular and extravascular MR signals. It also assumed that the distribution of the real and imaginary parts of the MRI signal can be approximated with a linear combination of a number of (usually 3 to 5) generalized Gaussian distributions [8][9] which is given as follows:…”

“…It then uses this probability density function to derive the non-linearity in ICA algorithm. Finally the non-linearity is used in the fixed point update rule of complex ICA given as [8,9,12]:…”

“…Measuring such a signal in the prostate area is extremely difficult and thus it is usually approximated from a major artery adjacent to the tumor [4], a standard AIF [5], population averaged AIF [6], etc. In a previous study we proposed a method based on an adaptive complex independent components analysis (ACICA) method to calculate the intravascular concentration in the tissue of interest [7][8][9]. This method provided a good estimate to the intravascular signal both temporally and spatially.…”