Anthony G Christodoulou^{1}, George C Gabriel^{2}, Cecilia W Lo^{2}, and Yijen L Wu^{2,3}

The objective of this study is to develop 4D time-resolved high-resolution in utero MRI for simultaneous interrogation of placenta, heart and brain development and function in genetic mouse models of hypoplastic left heart syndrome. The structural and functional imaging of the fetal heart, brain, and placenta can be correlated with genotype. In addition, temporal and spatial characteristics of BOLD responses to acute hypoxia challenge can be derived.

**A. 4D Dynamic Fetal MRI: **

We use a hybrid^{1}
low-rank^{2} and sparse^{3} model to perform 4D BOLD imaging in utero. The low-rank model
expresses the image $$$\rho(\mathbf{r},t)$$$ (for voxel location $$$\mathbf{r}$$$ and time $$$t$$$) as:$$\rho(\mathbf{r},t)=\sum_{\ell=1}^L\psi_\ell(\mathbf{r})\varphi_\ell(t),$$where
$$$\{\psi_\ell(\mathbf{r})\}_{\ell=1}^L$$$ are $$$L$$$ spatial coefficient maps and where $$$\{\varphi_\ell(t)\}_{\ell=1}^L$$$
are $$$L$$$ temporal basis functions.
In matrix form, this becomes $$$\mathbf{X=\Psi\Phi}$$$, where $$$X_{ij}=\rho(\mathbf{r}_i,t_j)$$$,
$$$\mathit{\Psi}_{ij}=\psi_j(\mathbf{r}_i)$$$, and $$$\mathit{\Phi}_{ij}=\varphi_i(t_j)$$$.
We additionally model $$$\rho(\mathbf{r},t)$$$ as being transform sparse,
specifically in the spatial-spectral domain (i.e., we model $$$\mathcal{F}_t\{\rho(\mathbf{r},t)\}$$$
as sparse, where $$$\mathcal{F}_t$$$ is the temporal Fourier transform). This approach exploits both image correlation and transform sparsity to
allow high spatiotemporal resolution imaging.
We perform image reconstruction in two steps: first
determining the temporal basis $$$\mathbf{\Phi}$$$ from the singular value
decomposition (SVD) of interleaved training data, and second determining the
spatial coefficient maps $$$\mathbf{\Psi}$$$ by fitting the temporal basis to the
remainder of the imaging data. This second step is calculated according to$$\mathbf{\Psi}=\arg\min_\mathbf{\Psi}\|\mathbf{d}-E(\mathbf{\Psi\Phi})\|_2^2+\lambda\|\mathbf{\Psi\Phi{F}}\|_1$$where $$$\mathbf{d}$$$
are the measured data, $$$E$$$ is the
encoding operator comprising spatial encoding and undersampling, and $$$\mathbf{F}$$$
is the temporal Fourier transform.

**B.
Animal Model:
**

Digenic mouse model of
HLHS^{4} with
both *Pcdha9* and *Sap130* gene mutations were used in this study. The *pcdha9* gene encodes protocadherinA9
mediating cell-cell adhesion, whereas *Sap130*
encodes Sin3A-associated protein 130, a member of the histone deacetylase
(HDAC) complex mediating chromatin repression. Mouse fetuses with homozygous mutations in both *pcdha9* and *Sap130* exhibit
HLHS. Some HLHS mutant
mice show microcephaly and holoprosencephaly, similar to brain defects seen in
HLHS patients. Mice heterozygous for
both *pcdha9* and *Sap130* do not display HLHS phenotype. In this study, double heterozygous adult breeding
pairs were used to generate fetuses with various genotypes within the same
pregnancy.

1 Zhao B et al. IEEE-TMI 2012.

2 Liang Z-P. IEEE-ISBI 2007.

3 Lustig M et al. MRM 2007.

4 Liu, et al. Nature Gen. 2017.

4D *in utero*
MRI of pregnant female mice on E15.5 with lower (A,B: 200-micron) and higher
(C-E:146 micron) resolutions (A,B) multiple mouse fetuses and maternal kidney
(C) sagittal view of a fetus showing brain and anatomical structures (D) placenta (E) fetal heart. LV: left
ventricle; RV: right ventricle; RA: right atrium; LA: left atrium.

Blood oxygenation level dependent (BOLD) 4D MRI of a
double heterozygous mutant on embryonic day E12.5. (A) Oscillating hypoxia challenge was
conducted every 3 minutes. (B)
anatomical MRI (C) BOLD MRI (D) real BOLD signal of fetal brains (E) real BOLD
signal of placenta (F) imaginary BOLD signal of fetal brains (G) imaginary BOLD
signal of placenta. Fetus 1: blue; fetus
2: orange; fetus 3: yellow.