Introduction

Abnormalities of placental development and function can result in fetal growth restriction and preeclampsia^1-3. A large body of evidence stresses the importance of placental insufficiency in the lifelong health of both mother and offspring⁴. Nevertheless, our knowledge regarding placental growth and function remains limited. Understanding the structure and function of the placenta during gestation is important to detect placental insufficiency. Advances in technology allow safe monitoring of placental growth and function in-vivo. In addition, new MR imaging techniques enable non-invasive measurement of fetal oxygen saturation⁵ but these have not been yet validated. Because of the invasiveness of the tests required, validation in human subjects is not possible. However, preclinical studies and testing in sheep models can define the accuracy of the MRI technique³ and its suitability for clinical use.
Herein, we aimed to implement and assess Bayesian shrinkage prior (BSP) inference^6,7 for placentome-specific signal modelling and compare its performance to least-squares (LSQ) fitting. Bayesian analysis yields improved parameter maps relative to conventional least-squares fitting and thus can reduce the number of individual experiments required to validate new imaging markers of placental function.

Methods

Subjects
The study was approved by the Animal Ethics Committee of the South Australian Health and Medical Research Institute (SAHMRI) and abided by the Australian Code of Practice for the Care and Use of Animals for Scientific Purposes developed by the National Health and Medical Research Council. Nine ewes with normal singleton pregnancy at 105-110 days gestation were included.

Image Acquisition
MRI was performed on a 3T Siemens Skyra Scanner (Erlangen, Germany). DECIDE⁵ imaging was performed at 11 b-values (0,10,20,30,50,70,100,150,200, 300,500,600s.mm^-2) and 10 echo times (T_E) (81,90,96,120,150,180,210,240,270,300 ms). All T_E were acquired at b=0 to allow T2 fitting and all b-values at T_E=96ms. In addition, data acquired at b=50s.mm-2 and 2000s.mm^-2 for T_E=(81,90,120,150,180,210,240 ms). Voxel resolution was $$$0.9 \times 0.9 \times 2.5$$$ mm.

Signal Model
Sheep placentomes comprise a 6-layer epitheliochorial structure with two inter-digitating villous capillary trees; fetal and maternal blood both remain intervascular. Based on DECIDE⁵, we define a sheep-specific placentome signal model:

$$S({\bf b},{\bf T_E}) = S_0 \left[ e^{-{\bf b}d^*}\left(fe^{{\bf -T_E}R_2^{f_b}}+ve^{{\bf -T_E}R_2^{mb}}\right)+(1-f-v) ve^{-{\bf b}d-{\bf T_E}R_2^{ts}}\right],$$

where $$$S$$$ is the measured MR signal and $$$S_0$$$ is the signal with b=0. The five model parameters are the fetal volume fraction $$$f$$$, diffusivity $$$d$$$, pseudo-diffusivity $$$d^*$$$, fetal blood relaxation $$$R_2^{f_b}=1/T_2^{f_b}$$$ and maternal blood volume $$$v$$$. We used literature based values for highly-saturated blood relaxation $$$R_2^{mb}=(240 ms)^{-1}$$$ and tissue relaxation $$$R_2^ts=(46ms)^{-1}$$$.

Image-Processing
A nonrigid registration algorithm⁸ was used to correct for motion. The sheep placentomes were manually segmented (ITK-SNAP, 2017) from the unregistered baseiline image (lowest T_E, b=0).

LSQ-Fitting
The LSQ fitting is implemented in Matlab (MathWorks,Natick) using a Levenberg-Marquardt algorithm. To stabilise the voxelwise fitting the following constraints were chosen: $$$0<f<1$$$ (no units), $$$0<d<1 $$$ $$$(mm^2s^-1)$$$, $$$0<d*<1$$$ $$$(mm^2s^-1)$$$, $$$0<$$$T2 fetal blood$$$< 240$$$ (ms), $$$0<v<1$$$ (no units).

BSP Inference
Our method⁶uses a hierarchical prior in which spatial correlation is introduced by modelling regions as containing voxels with similar values. This correlation is incorporated in the parameter inference leading to large-scale spatial smoothness. We used a Monte Carlo Markov Chain approach to perform inference using Gibbs sampling. This is initialised with the voxel-wise LSQ estimates.

The effect of BSP method was evaluated by visual comparison of parameter maps calculated with BSP and LSQ methods. Mean value and standard deviation were calculated over the 9 subjects.

Results

Fig.1 and Fig.2 show examples of the parameter maps obtained with the LSQ and BSP approaches respectively. All LSQ parameter maps appear noisy and artefact-prone, where BSP fitting notably improved all the parameter maps. Fig.3 shows corresponding histograms of the 5 parameters calculated with LSQ and BSP method. The proportions of the LSQ estimated in the edge-most bins are 4% for $$$f$$$, 7.1% for $$$d^{*}$$$, 17.3% for T2 and 19.5% for $$$v$$$. ROI mean estimated values derived using BSP approach are comparable to LSQ estimates but the precision of the parameters has been improved.

Discussion

To minimise variability related to noise we evaluated our data averaged over all ROIs drawn around placentomes. Even then, applying LSQ fitting resulted in poor measurement of the parameters. The improvement in BSP derived parameter maps was typical for all the in-vivo sheep placentomes. The shrinkage effect of the prior distribution in BSP approach is clearly seen in Fig.3 where the outlying LSQ estimates have been brought into the bulk of the distribution. In contrast to LSQ method which allows data processing in a pixel-wise fashion, BSP approach requires pre-segmentation of the data which makes automation in image-processing workflow more challenging. The BSP approach is applicable to many forms of image contrast where model fitting is necessary. Further work is needed to evaluate the effect of the BSP method on the diagnostic quality of the estimated parameter maps with histological data.

Conclusion

BSP method yields improved parameter maps relative to conventional LSQ fitting in the sheep placentomes. Further in-vivo studies are necessary to assess the performance of the method at a wider range of gestational ages. This information will help demonstrate the longitudinal trend between the MR parameters during pregnancy that may aid in the assessment of novel treatments for placental dysfunction.

Acknowledgements

This research was supported by the Wellcome Trust (210182/Z/18/Z), Wellcome Trust/EPSRC (NS/A000027/1) and the Radiological Research Trust.