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the left asymptote is zero). While the inflection point lies in the range from 4 to
6 months for T1W images, it takes on a much higher value of over 9 months for
T2W images. Analysis of the inflection point parameter also numerically con-
firms the visual finding that temporal and frontal lobes follow delayed maturation
trajectories compared with occipital and parietal lobes. The rate parameter is a
numerical scale parameter on the input time axis. This parameter approximates
to the time taken in months for change from 50 percent to 73 percent of the
maximum value [ 16 ]. The rate parameter ranges between half and 1 month for
T1W images and between 2 and 3 months for T2W images, indicating that the
rate of change after the inflection point in T1W images is much higher than
the rate of change in T2W images. The SIR (Signal Intensity Ratio) of major
brain regions is used in addition to NLME modeling of contrast magnitude to
characterize directionality of relative intensity gradient between white and gray
matter tissue classes. A linear mixed effects model is used to estimate the general
population trend observed in SIR as seen in Fig. 6 . This LME model is similar to
the NLME model described above except that the nonlinear growth function is
replaced by a linear function. It can be observed that for T1W images the SIR is
predominantly greater than 1, indicating that white matter is of higher intensity
compared with gray matter on average. The SIR is less than 1 for most T2W
images, indicating the inverted nature of white-gray matter contrast. The slope
of the SIR trends for T1W and T2W scans further illustrates the knowledge that
contrast changes in these two modalities take place in opposite directions. The
CONTDIR value which measures gradient relative to intensity gradient in the
adult-like image is also computed at each time point and adds the sign for the
contrast value.
4 Discussion and Conclusions
The multivariate NLME modeling of multimodal contrast change demonstrates
that T1W and T2W modalities show distinctly different patterns of contrast
change. The average growth function parameters estimated using NLME serve as
numerical indicators of these differential patterns and conform to existing studies
of the developing brain [ 1 ]. Statistical hypothesis testing further substantiates
the claim that the timing parameters of contrast change are significantly differ-
ent for the two modalities studied. Our choice of the logistic function to model
contrast change is based on comparison of AIC values with a few other com-
monly used biological growth functions. Prior knowledge that maturation takes
place in a highly asymptotic manner and reaches a saturation value around 2
years of age further strengthens our choice. Our method faces limitations since
contrast as a measure of appearance could be adversely affected by intensity
inhomogeneities. In this study contrast is analyzed in a regional manner but a
voxel-level appearance measure could give rise to new interesting insights at a
finer anatomical scale, particularly since large variability can exist even within
a lobar region as applied here.
This work presents a complete framework for the joint modeling of multi-
modal MR image appearance change in longitudinal datasets using multivariate
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