A spatiotemporal atlas of MR intensity, tissue probability and shape of the fetal brain with application to segmentation

Abstract

Modeling and analysis of MR images of the developing human brain is a challenge due to rapid changes in brain morphology and morphometry. We present an approach to the construction of a spatiotemporal atlas of the fetal brain with temporal models of MR intensity, tissue probability and shape changes. This spatiotemporal model is created from a set of reconstructed MR images of fetal subjects with different gestational ages. Groupwise registration of manual segmentations and voxelwise nonlinear modeling allow us to capture the appearance, disappearance and spatial variation of brain structures over time. Applying this model to atlas-based segmentation, we generate age-specific MR templates and tissue probability maps and use them to initialize automatic tissue delineation in new MR images. The choice of model parameters and the final performance are evaluated using clinical MR scans of young fetuses with gestational ages ranging from 20.57 to 24.71 weeks. Experimental results indicate that quadratic temporal models can correctly capture growth-related changes in the fetal brain anatomy and provide improvement in accuracy of atlas-based tissue segmentation.

Fig. 1

Axial and coronal views from reconstructed T2w MR images of typical fetal brain anatomies at around 21, 22, 23 and 24 weeks gestational age.

Fig. 2

Axial views from an MR intensity image i_s(x), its full manual segmentation p_s(x) as well as components $m_s^{(\text{GM})}(\mathbf{x})\text{and}{m}_s^{(\text{WM}+\text{GMAT})}(\mathbf{x})$ of a smooth tissue map m_s(x) used for spatial normalization.

Fig. 3

Voxelwise modeling of temporal changes in shape, MR intensity and tissue probabilities from a set of S registered fetal brain anatomies with different gestational ages t.

Fig. 4

Fitting of temporal polynomials p(¹⁾(x,t) (green line) and p⁽²⁾(x,t) (red line) to subject-specific probabilities $p_s^{(k)}(\mathbf{x})$ of two abstract mutually exclusive classes (green and red dots, respectively). (A) Unconstrained modeling directly in the probability space may result in p^(k)(x,t) values that are not valid probabilities (p^(k)(x,t)<0 or p^(k)(x,t)>1). (B) Alternatively, data points p_s(^k)(x) can be transferred to the space of LogOdds using 𝒪(·) where unconstrained temporal modeling is performed. (C) Age-specific p^(k)(x,t) values transferred back from the space of LogOdds using 𝒪⁻¹(·) and normalized across all tissue classes are, unlike in (A), legitimate probabilities. (For interpretation of the references to colour in this figure legend, the reader is referred to the web of this article.)

Fig. 5

Synthesis of a complete fetal brain anatomy with application to segmentation of new fetal MRI. (A) An age-specific MR intensity template and tissue probability maps are synthesized from model parameters in the space of the spatiotemporal atlas. (B) Age-specific shape deformation and linear scaling transform the MR image and tissue maps to the expected size and shape of the new subject. (C) The new subject MRI is registered to the synthetic MR template. (D) Using an inverse transformation, the age-specific tissue probability maps are warped to the space of the new subject and used as priors for atlas-based segmentation of the new subject MRI.

Fig. 6

The number of training fetal anatomies as a function of the gestational age.

Fig. 7

Tissue maps $m_s^{(\text{WM}+\text{GMAT})}(\mathbf{x})$ of 8 fetal subjects after rigid registration (top row), global linear registration (middle row) and groupwise multiple elastic registration (bottom row).

Fig. 8

Temporal modeling of global linear scaling in three orthogonal directions using linear models (D_a=1, dashed lines) and quadratic models (D_a=2, solid lines).

Fig. 9

Smoothed maps of R² coefficient for temporal models of shape changes with D_u=1, D_u=2, and D_u=3. Cooler colors represent lower R² values while warmer colors represent higher values of the R² coefficient. Maps were automatically masked to the brain region where $R_a^2$ values were calculated.

Fig. 10

Smoothed maps of R² coefficient for temporal models of intensity changes with D_i=1, D_i=2, and D_i=3. Cooler colors represent lower R² values while warmer colors represent higher values of the R² coefficient. Maps were automatically masked to the brain region where $R_a^2$ values were calculated.

Fig. 11

Axial and coronal views from age-specific T2w MR images i(x,t) of the fetal brain synthesized from a spatiotemporal atlas with D_a=2, D_u=2, and D_i=2 for gestational ages t from 21 to 24 weeks. Images were transformed from the average space using age-specific shape deformation u(x,t) and global linear scaling a(t).

Fig. 12

Average tissue probability maps p^(k)(x) for developing gray matter (GM), developing white matter (WM), the germinal matrix (GMAT) and ventricles (VENT) generated in the average space from a spatiotemporal atlas with D_p=0 (no temporal dependency).

Fig. 13

Age-specific tissue probability maps p^(k) (x,t) for developing white matter (WM) and the germinal matrix (GMAT) generated in the average space from a spatiotemporal atlas with D_p=2.

Fig. 14

3D visualization of main tissue types in the fetal brain for gestational ages from 21.0 to 24.5 weeks. The geometry of each age-specific surface was derived from a spatiotemporal atlas with D_a=2, D_u=2 and D_p=2.

Fig. 15

The impact of the degree of the tissue probability model (D_p) on automatic atlas-based tissue segmentation of a fetal subject at 24 weeks GA. Arrows indicate areas where the use of age-specific atlases generated from models with D_p=1 and D_p=2 improves segmentation of the germinal matrix.