Joint Longitudinal Modeling of Brain Appearance in Multimodal MRI for the Characterization of Early Brain Developmental Processes - Longitudinal Registration and Shape Modeling - page 51

Contrast computed in our analysis is region-specific and time point-specific
in addition to being modality-specific. The tissue intensity distributions and con-
trast measures are independently generated and studied for each major cortical
region of the brain to better capture spatial variability. Subject i 's contrast in the
region R , for the j th scan obtained at time point t i,j

of modality m , is denoted

as CONT i,m ( t i,j ).

2.3 Direction of Relative Intensity Gradient of White-Gray Matter
Tissue
The relative white-gray matter intensity gradients in T1W and T2W scans have
opposite directions. Generally, the intensity of white matter is greater than gray
matter in adult-like T1W scans, while the reverse applies to adult-like T2W
scans. In this paper, we use the Signal Intensity Ratio (SIR) of white matter to
gray matter to characterize this gradient direction and hence distinguish between
reversed appearance patterns seen in different modalities, as shown in Fig. 4 .
Regional SIR is the ratio of the mean intensity of WM voxels to the mean
intensity of GM voxels in a region. Consider the SIR for the modality m scan of
the i th subject taken at time t i,j , such that the intensity of a voxel x in this scan
is given by Int i,m ( x, t i,j ). If the SIR in a region R is greater than 1, it implies
that the mean intensity of WM is greater than the mean intensity of GM in that
region.

xW M,R Int i,m ( x,t i,j )
N R ( WM )
xGM,R Int i,m ( x,t i,j )
N R ( GM )

SIR i,m ( t i,j )=

(4)

The terms N R ( WM )and N R ( GM ) in the above equation denote the total num-
ber of voxels in a region R belonging to WM and GM tissue classes respectively.
It has also been observed that the direction of white-gray intensity gradient
undergoes a reversal during early development. A quantity CONTDIR charac-
terizes this reversal by comparing direction of intensity gradient at each time

Fig. 4. a) Examples of two histograms with the same contrast value, but inverted
white-gray intensity gradient directions. The SIR values capture gradient direction. b)
Contrast change trajectory with directional information of intensity gradient relative
to the adult-like scan provided by CONTDIR.