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DeepSPIO: A SPIO particles quantification method using Deep Learning
Gabriel della Maggiora1,2,3, Carlos Castillo-Passi1,2,3, Qiu Wenqi4, Masaki Sekino4, Carlos Milovic1,2,3, and Pablo Irarrazaval1,2,3,5

1Department of Electrical Engineering, Pontificia Universidad Católica de Chile, Santiago, Chile, 2Biomedical Imaging Center, Pontificia Universidad Católica de Chile, Santiago, Chile, 3Millennium Nucleus for Cardiovascular Magnetic Resonance, Santiago, Chile, 4Department of Bioengineering, School of Engineering, University of Tokyo, Tokyo, Japan, 5Institute for Biological and Medical Engineering, Pontificia Universidad Católica de Chile, Santiago, Chile

### Synopsis

In this study we propose a method to quantify the distribution of Super Paramagnetic Iron Oxide (SPIO) particles with MRI. This task is particularly challenging due to the extreme distortion that these particles produce in the image. Our method is based on a supervised feed-forward deep learning model. The estimation of total quantity of SPIO was in the order of 9% error. This is potentially useful for detecting breast cancer metastasis by identifying residual particles in the breast and eventually other organs.

### Introduction

Super Paramagnetic Iron Oxide (SPIO) nanoparticles generate a distortion in the main magnetic field as well as in the gradients. There are different applications for SPIO particles in MRI. One of them is the detection of breast cancer metastasis by recognizing residues in the lymph nodes1,2. In this study we propose a new way to quantify SPIO. First we designed a sequence to measure the inhomogeneities produced by the particles in the direction of the main field. Afterwards through simulated data we train a deep learning model to solve the inverse of the problem, to get a concentration distribution.

### Methods

The main idea is to directly visualize the field distortion, and from there the SPIO distribution. To measure the field map produced by the SPIO particles we acquire 25 slices perpendicular to the excitation plane to create an image of two channels where the odd numbered slices go into the first channel and the even numbered go into second channel. This is a descriptor of the distortion produced by the particles. We know that In MRI, the local magnetic field is the convolution of the dipole kernel with the susceptibility, which is proportional to the distribution of SPIO3 $C(\mathbf{r})$. This is

$$\Delta B_z (\mathbf{r})\propto C(\mathbf{r})*D(\mathbf{r}), \quad\text{with}\quad D(r, \theta) = \frac{3\cos^2(\theta)-1}{4\pi r^3} .$$

We use this to simulate the distortion produced by a given distribution of particles. With this we created the required amount of data to train a deep learning model. We use U-Net4, inspired in the success of DeepQSM5 and QSMnet6, as the base model. We extend the bottleneck of the neural network (central section) using residual blocks7 to increase the convergence rate of the model and to remove the depth concatenation operations. We call our method DeepSPIO. To train the network we used a modified MSE loss function to account for the unnormalized training set and give every sample the same weight.

$$L = \frac{1}{2N}\sum_{i=1}^N \Bigg | \Bigg | P \odot \Bigg(\frac{\alpha_i}{S_i} - \frac{\hat{\alpha_i}(w)}{S_i}\Bigg)\Bigg | \Bigg |_F^2 + \lambda \sum_{l=1}^L||w_l||_2^2.$$

Where

$$S_i = ||C_i||_1\quad\text{and}\quad C_i = \Psi^{-1}\alpha_i.$$

$\alpha_i$ corresponds to the wavelet transform (Daubechies 4 of 5 levels) of the sample $i$ of SPIO distribution. $P$ is a preconditioner. $\Psi$ corresponds to the wavelet transform. $L$ is the number of layers. $N$ is the number of training samples. Figure 1 shows a summary of the problem.

The method is robust enough such that other anatomies can be used as training. Therefore, we simulated SPIO distortions with brain and water proton density images, but other contrasts can also be used. We generated a uniform concentration of SPIO in two different shapes: metaballs and toruses. We sampled exponentially between 0.2734 and 17.5 $\frac{\mu\text{g}}{\text{mm}^3}$ with 400,000 samples. We generated a SPIO distribution mixing the geometric figures with overlapping (in case of overlap the concentrations are added) with random positions, rotations and sizes. The output is a wavelet transform of the middle slice ($256 \times 256$ coefficients). We generated 2 million samples in this way.

We used the following metrics to measure the quality of the estimation:

$$\text{NMAE}:= \frac{||C - \hat{C}||_1}{||C||_1} \quad\text{and}\quad \text{Integral Error}:= \frac{| \text{ } ||C||_1 - ||\hat{C}||_1 \text{ }|}{||C||_1}.$$

We also used the dice’s similarity coefficient with binarized $C$ and $\hat{C}$:

$$\text{Dice}:= \frac{2|B_C \cap B_{\hat{C}}|}{|B_C| + |B_{\hat{C}}|}.$$

### Results

We constructed a test dataset comprising only of unseen simulations from brain images, with a linear distribution of SPIO particles concentration in the same range as the training set. And we obtained the following result:

• NMAE: $26.02\% \pm 9.82\%.$
• Integral Error: $8.83\% \pm 8.51\%.$
• Dice: $91.28\% \pm 4.82\%.$

Furthermore, to show the ability of the algorithm to perform in images with different intensities, textures and shapes we quantified the SPIO distribution in simulated breast and brain images (Figures 3 and 4). We also scanned an agar phantom with SPIO particles in it to test the method as is seen in Figure 5.

### Discussion and Conclusion

The results shown by DeepSPIO indicate that the excitation profile is a good feature to describe the distribution of SPIO. Furthermore, we have shown that our model is robust enough to perform well in different images from the training set. Resulting in a fast method capable of estimating a SPIO concentration in the profile images. In the future, a bigger and diverse database will allow for more precise results. Continued experiments will use different networks architectures and compositions of features. Moreover, we need to speed up the acquisition process. We want to change our acquisition method from an image formed by multiple slice profiles to a tagging method to obtain a similar image in a faster way. Such work will improve the SPIO estimation and making a faster and a more robust method.

### Acknowledgements

This publication has received funding from Millenium Science Initiative of the Ministry of Economy, Development and Tourism, grant Nucleus for Cardiovascular Magnetic Resonance, and from CONICYT - PIA - Anillo ACT1416.

### References

1. Wáng, Y. X., & Idée, J. (2017). A comprehensive literatures update of clinical researches of superparamagnetic resonance iron oxide nanoparticles for magnetic resonance imaging. Quantitative Imaging in Medicine and Surgery, 7(1), 88-122. doi:10.21037/qims.2017.02.09.
2. Langley, J., Liu, W., Jordan, E. K., Frank, J. A., & Zhao, Q. (2010). Quantification of SPIO nanoparticles in vivo using the finite perturber method. Magnetic Resonance in Medicine, 65(5), 1461-1469. doi:10.1002/mrm.22727.
3. Salomir, R., Senneville, B. D., & Moonen, C. T. (2003). A fast calculation method for magnetic field inhomogeneity due to an arbitrary distribution of bulk susceptibility. Concepts in Magnetic Resonance, 19B(1), 26-34. doi:10.1002/cmr.b.10083.
4. Ronneberger, O., Fischer, P., & Brox, T. (2015). U-Net: Convolutional Networks for Biomedical Image Segmentation. Lecture Notes in Computer Science Medical Image Computing and Computer-Assisted Intervention – MICCAI 2015, 234-241. doi:10.1007/978-3-319-24574-4-28.
5. Rasmussen, K. G., Kristensen, M. J., Blendal, R. G., Ostergaard, L. R., Plocharski, M., Obrien, K., Bollmann, S. (2018). DeepQSM - Using Deep Learning to Solve the Dipole Inversion for MRI Susceptibility Mapping. doi:10.1101/278036.
6. Yoon, J., Gong, E., Chatnuntawech, I., Bilgic, B., Lee, J., Jung,W., Lee, J. (2018). Quantitative susceptibility mapping using deep neural network: QSMnet. NeuroImage, 179, 199-206. doi:10.1016/j.neuroimage.2018.06.030.
7. He, K., Zhang, X., Ren, S., & Sun, J. (2016). Deep Residual Learning for Image Recognition. 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR). doi:10.1109/cvpr.2016.90.

### Figures

Figure 1. Summary of the problem. We simulate the presence of SPIO artificially on the breast image. We obtain a distorted version due to the inhomogeneities produced by the particles. Using these images we try to obtain a distribution of SPIO particles in the image using deep learning.

Figure 2. Example of simulation. The original image corresponds to a MR brain image. We then perform the simulation of the distortion produced by the SPIO shown in the figure. Afterwards, we do the MRI simulation and obtain the final image. In the simulation we considererd raised cosine excitations, fractionary voxel displacements, and the nonlinear gradient effects over the image.

Figure 3. Simulation of a metaball in a breast image. NMAE: $11.76\%$, Integral Error: $4.60\%$, Dice: $93.55\%$.

Figure 4. Simulation of a composite figure in a brain image. NMAE: $18.55\%$, Integral Error: $0.02\%$, Dice: $92.40\%$.

Figure 5. MRI image of SPIO of the phantom shown in the left image (SPIO) concentration of $13.9 \frac{\mu\text{g}}{\text{mm}^3}$. Middle: MR acquisition. Right: prediction done by DeepSPIO. Average concentration $11.69 \frac{\mu\text{g}}{\text{mm}^3}$

Proc. Intl. Soc. Mag. Reson. Med. 27 (2019)
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