# A deep-learning-based prediction model for the biodistribution of 90Y microspheres in liver radioembolization

Dimitris Plachouris, Ioannis Tzolas, Ilias Gatos, Panagiotis Papadimitroulas, Trifon Spyridonidis, Dimitris Apostolopoulos, Nikolaos Papathanasiou, Dimitris Visvikis, Kerasia-maria Plachouri, John D Hazle, et al.

► To cite this version:

Dimitris Plachouris, Ioannis Tzolas, Ilias Gatos, Panagiotis Papadimitroulas, Trifon Spyridonidis, et al. A deep-learning-based prediction model for the biodistribution of 90Y microspheres in liver radioembolization. Medical Physics: The international journal of medical physics research and practice, 2021, 48 (11), pp.7427 - 7438. 10.1002/mp.15270. hal-05272946

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RESEARCH ARTICLE

MEDICAL PHYSICS

# A deep-learning-based prediction model for the biodistribution of ⁹⁰Y microspheres in liver radioembolization

Dimitris Plachouris<fnref n="1" />

Ioannis Tzolas<fnref n="2" />

Ilias Gatos<fnref n="1" />

Panagiotis Papadimitroulas<fnref n="1" />,<fnref n="3" />

Trifon Spyridonidis<fnref n="4" />

Dimitris Apostolopoulos<fnref n="4" />

Nikolaos Papathanasiou<fnref n="4" />

Dimitris Visvikis<fnref n="5" />

Kerasia-Maria Plachouri<fnref n="6" />

John D. Hazle<fnref n="7" />

George C. Kagadis<fnref n="1" />,<fnref n="7" />

**Correspondence**

George C. Kagadis, Department of Medical Physics, School of Medicine, University of Patras, Rion, GR 265 04, Greece.
Email: gkagad@gmail.com

**Funding information**

European Regional Development Fund, Grant/Award Number: T11EPA4-00055; European Social Fund, Grant/Award Numbers: MIS-5000432, MIS-5033021

[Correction added on 19-10-22, after first online publication: The copyright line was changed.]

**Abstract**

**Background:** Radioembolization with ⁹⁰Y microspheres is a treatment approach for liver cancer. Currently, employed dosimetric calculations exhibit low accuracy, lacking consideration of individual patient, and tissue characteristics.

**Purpose:** The purpose of the present study was to employ deep learning (DL) algorithms to differentiate patterns of pretreatment distribution of ⁹⁹mTc-macroaggregated albumin on SPECT/CT and post-treatment distribution of ⁹⁰Y microspheres on PET/CT and to accurately predict how the ⁹⁰Y-microspheres will be distributed in the liver tissue by radioembolization therapy.

**Methods:** Data for 19 patients with liver cancer (10 with hepatocellular carcinoma, 5 with intrahepatic cholangiocarcinoma, 4 with liver metastases) who underwent radioembolization with ⁹⁰Y microspheres were used for the DL training. We developed a 3D voxel-based variation of the Pix2Pix model, which is a special type of conditional GANs designed to perform image-to-image translation. SPECT and CT scans along with the clinical target volume for each patient were used as inputs, as were their corresponding post-treatment PET scans. The real and predicted absorbed PET doses for the tumor and the whole liver area were compared. Our model was evaluated using the leave-one-out method, and the dose calculations were measured using a tissue-specific dose voxel kernel.

**Results:** The comparison of the real and predicted PET/CT scans showed an average absorbed dose difference of 5.42% ± 19.31% and 0.44% ± 1.64% for the tumor and the liver area, respectively. The average absorbed dose differences were 7.98 ± 31.39 Gy and 0.03 ± 0.25 Gy for the tumor and the non-tumor liver parenchyma, respectively. Our model had a general tendency to underpredict the dosimetric results; the largest differences were noticed in one case, where the model underestimated the dose to the tumor area by 56.75% or 72.82 Gy.

**Conclusions:** The proposed deep-learning-based pretreatment planning method for liver radioembolization accurately predicted ⁹⁰Y microsphere biodistribution. Its combination with a rapid and accurate 3D dosimetry method will render it clinically suitable and could improve patient-specific pretreatment planning.

This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

© 2021 The Authors. Medical Physics published by Wiley Periodicals LLC on behalf of American Association of Physicists in Medicine.

<footnote n="1">¹ Department of Medical Physics, School of Medicine, University of Patras, Rion, Greece</footnote>

<footnote n="2">² School of Electrical and Computer Engineering, University of Patras, Rion, Greece</footnote>

<footnote n="3">³ R&D Department, Bioemission Technology Solutions, Athens, Greece</footnote>

<footnote n="4">⁴ Department of Nuclear Medicine, School of Medicine, University of Patras, Rion, Greece</footnote>

<footnote n="5">⁵ LaTIM, INSERM, UMR1101, Brest, France</footnote>

<footnote n="6">⁶ Department of Dermatology, School of Medicine, University of Patras, Rion, Greece</footnote>

<footnote n="7">⁷ Department of Imaging Physics, The University of Texas MD Anderson Cancer Center, Houston, Texas, USA</footnote>
KEYWORDS

biodistribution prediction, deep learning, radioembolization, treatment planning, yttrium-90

# 1 | INTRODUCTION

Transarterial radioembolization (TARE) is one of the available locoregional therapeutic approaches for primary and metastatic liver tumors. In this procedure, microspheres containing the radioisotope ⁹⁰Y are injected into selected hepatic arteries. The normal liver parenchyma is supplied with blood mainly by the portal vein, while the tumor has mainly arterial supply.¹⁻³ Indeed, liver tumors larger than 3 mm receive 80-100% of their blood supply from the hepatic arteries rather than the portal vein.⁴ Current ⁹⁰Y-based TARE protocols involve a pretreatment workup after injection of technetium-99 m (⁹⁹mTc)-labeled macroaggregated albumin (MAA) into selected hepatic arteries.⁵ This procedure is most commonly followed by hybrid imaging with single-photon emission computed tomography (SPECT/CT) to assess lung shunt fractions and possible extrahepatic leaks.⁵ Post-treatment evaluation of the ⁹⁰Y microspheres' biodistribution is performed with positron emission tomography (PET)/CT imaging (or, if a PET scanner is not available, with ⁹⁰Y bremsstrahlung SPECT/CT).

At present, the pretreatment calculation of the expected absorbed dose is based on the application of the medical internal radiation dose (MIRD) formalism,⁶ which directly converts the radioactivity (in Bq) to the tissue-absorbed dose D (in Gy), and assuming uniform ⁹⁰Y distribution within both healthy and tumorous tissues.⁷ Based on this formalism, the partition model, which is the most frequently used pretreatment TARE planning model in clinical practice, calculates the mean absorbed doses for three areas of interest (tumor tissue, normal tissue, perfused area, whole liver, and lungs), erroneously assuming that the biodistribution in each of these areas is uniform.⁸⁻¹⁰

Moreover, multiple studies have demonstrated a substantial lack of consistency between the biodistribution

of ⁹⁹mTc-MAA and ⁹⁰Y microspheres.⁵,¹¹ Figure 1 shows a typical example of ⁹⁹mTc-MAA SPECT/CT and ⁹⁰Y PET/CT images of the same patient.

While the treatment response depends on the dose absorbed by the tumor, serious treatment complications such as radioembolization-induced liver disease (REILD) are mainly associated with the dose absorbed by the healthy liver parenchyma.⁵ In a recent clinical study by Haste et al.,⁵ ⁹⁹mTc-MAA SPECT/CT and ⁹⁰Y PET/CT showed significant differences in the tumor and healthy liver tissue absorbed doses. Similar results were documented in several other studies.¹¹⁻¹³ Thus, current protocols cannot accurately predict dose distributions in both tumor tissue and normal liver parenchyma.

These deficits can be eliminated via the implementation of artificial intelligence (AI) and machine learning (ML)-based approaches. AI is a field that has gained significant attention over the past few years. Its implementation in medical imaging through the use of deep learning (DL) algorithms, to process handcrafted data, has evolved into an area of vast research. The aim of these algorithms is to execute specific actions, following training based on processing and interpretation of input data. The application of AI algorithms in medicine is particularly useful, due to their ability to handle large data volumes, while minimizing human bias and staying current with subsequent alterations.¹⁴,¹⁵ AI and ML make predictions using larger amounts of data than that can be incorporated by other methods. DL is a type of ML in which biomedical data are transformed through a multilayer module into clinically relevant representations.¹⁶ There are two main types of DL algorithms: supervised (as in our case) and unsupervised. Supervised learning consists of providing the algorithms with specified, labeled, input and output data for the training process and then determine the variables that need to be assessed from the algorithms for any possible correlations. The architecture of supervised convolutional

<figure><img src="image_2.png" /><figcaption>FIGURE 1 (a) Pretreatment SPECT/CT showing biodistribution of ⁹⁹mTc-MAA vs. (b) post-treatment PET/CT showing biodistribution of ⁹⁰Y microspheres in patient 14 of our dataset</figcaption></figure>
neural networks (CNNs) —also known as U-net— consists of the following layers: first, an input layer that receives the input data in its initial form. This layer is followed by a series of convolutional and pooling feature processing layers that aim to extract critical features of the inserted input data to generate high-order features. Finally, the output layer—or classification layer—combines the generated high-order features to produce the desired output data.¹⁵ In molecular imaging, DL can recognize critical biomarkers within vast quantities of multidimensional data and then trans- late them into highly accurate predictive information regarding patient outcomes.¹⁷,¹⁸

Nonetheless, certain challenges must be overcome for DL to produce an accurate visualization of a biological process.¹⁵,¹⁶,¹⁹⁻²² Mainly, these challenges derive from the ambiguity of the ground-truth data, which can be interpreted differently and/or classified as normal or disease on the basis of the subjective criteria. Although the most common DL models currently used were cre- ated using data with uniform classes, the DL training for molecular imaging data typically uses irregular diagnos- tic classes.¹⁹ Molecular imaging is sometimes used to identify unusual conditions or cases, and this requires special training techniques to resolve possible class imbalances. Another limitation is the variability of molec- ular imaging compared to other types of imaging, e.g., CT or X-rays; molecular imaging involves a wide range of biological areas of interest and several different imag- ing modalities, such as PET, SPECT, and magnetic res- onance imaging. For these reasons, molecular imaging requires DL training with limited input data and an appro- priately adjusted architecture for the training of the neu- ral network.

In nuclear medicine and molecular imaging, Al and DL have been implemented mainly in the diagnostic process.¹⁹,²⁰,²³ However, recent studies have demon- strated several models and methods for applying DL methods for dosimetry purposes with promising results.²⁴,²⁵ The present study introduces a DL-based prediction model that uses pretreatment ⁹⁹mTc-MAA SPECT/CT data to predict the biodistribution of ⁹⁰Y microspheres. This model can accurately predict the absorbed dose in both tumorous and healthy liver tissue. Moreover, this model can assess the implementation of an alternative pretreatment planning method based on our proposed guided generative adversarial networks (GGAN), which addresses the challenging issue of pre- dicting ⁹⁰Y biodistribution during TARE treatments for hepatic tumors.

## 2 | MATERIALS AND METHODS

### 2.1 | Training parameters

A generative adversarial network (GAN) is a DL model that is based on the adversarial training of convolutional

("generator") and deconvolutional ("discriminator") neu- ral networks to reach highly accurate predictions. These two models are simultaneously trained by an adversar- ial process until a Nash equilibrium is reached. Basically, GAN's functionality is inspired by the zero-sum non- cooperative game between players. This means that if one player wins, the other loses. A zero-sum game is also known as minimax.²⁶ While the generator produces data, the discriminator evaluates whether an image was derived from the true training data pool or was artifi- cially synthesized by the generator. This process results in a feedback loop in which the generator progressively improves its ability to produce high-quality data that can "fool" the discriminator and the discriminator enhances its ability to distinguish "fake" from "real" data.²⁶ Pix2Pix is a special type of conditional GAN designed to per- form image-to-image translation.²⁷,²⁸ In this framework, the generator receives an image of a specific Type A input domain and then translates it into an image of a specific Type B target domain using pixel-by-pixel transformation.²⁸ More specifically, the objective function of Pix2Pix $L_{GAN}(G, D)$ can be expressed with the use of the generator G and the discriminator D as shown in Equation (1):

$$L_{GAN}(G, D) = E_{x,y}[\log D(x, y)] + E_x[\log(1 - D(x, G(x)))], \quad (1)$$

where x is the image used as a source (i.e., the CT image), y is the image used as a target (i.e., the cor- responding RT-dose image), $D(x)$ is the dose image created by the generator, $D(x,y)$ is the probability that the real pair $(x,y)$ is correctly labeled as real by the discriminator, while $D(x,G(x))$ is the probability that the fake pair $(x,G(x))$ is correctly labeled as fake, respec- tively. The probability $D(D(x,y)$ or $D(x,G(x))$ is charac- terized as a binary problem, i.e., $D \rightarrow [1, 0]$, where 1 means that the discriminator labeled the input-paired images as real and 0 means that the discriminator labeled the input-paired images as fake. The objective function would increase its value if the discriminator completely identified the input images as real or fake. On the other hand, the generator tries to minimize the objective function and produce an image that fools the discriminator (i.e., $D(x,G(x)) \rightarrow 1$). The relationships can be expressed by $min_G max_D L_{GAN}(G, D)$, as in a minimax game. To attain the network's stability and fast conver- gence, the generator measures how close the real dose distribution y images are to the generated dose distribu- tion $G(x)$ images by using the L1-distance as shown in Equation (2):

$$L_{L1}(G) = E_{x,y}[\|y - G(x)\|_1]. \quad (2)$$

The final objectives function of the Pix2Pix $\hat{G}$ can be expressed by combining Equations (1) and (2):
Training Data

<figure><img src="image_3.png" /><figcaption>FIGURE 2 A schematic depiction of the model's architecture</figcaption></figure>

$$ \hat{G} = \arg \min_G \max_D L_{GAN}(G, D) + \lambda L_1(G), \quad (3) $$

where $\lambda$ is the L1 term weight for the generator. More information on the architecture is provided in Isola et al.²⁸ In the current study, we developed a voxel-based variation of the Pix2Pix model, a Vox2Vox GAN. Our model, therefore, performs the training process in a way that allows the translation of the radionuclide distribution not in a two-dimensional (2D), but in a three-dimensional (3D) format.

The generator network in our model was built with a U-Net architecture, whereas the discriminator was built with a PatchGAN²⁷,²⁹ architecture style. The input domain included a 3D image consisting of the following 3D multichannel volumes: the patient's pretreatment ⁹⁹mTc SPECT and CT scans followed by 3D labeling of the tumor area. This approach allowed us to take into consideration as many parameters as possible, such as the patient's anatomy, tissue heterogeneities, and the volumetric biodistribution of the radionuclide. The output consisted of a 128 × 128 × 128-resolution image, here called the predicted PET scan, that depicted the biodistribution of the ⁹⁰Y in the liver area. Figure 2 presents a schematic depiction of the algorithm's architecture.

Our model was trained for ≈39 000 iterations, each followed by batch normalization with a dropout rate of 0, a batch size of 2, and an adaptive learning rate of 0.002. Both the generator and the discriminator were trained using the Adam optimizer,³⁰ which included the following parameters: $\lambda = 2 \times 10^{-4}$, $\beta_1 = 0.5$, and $\beta_2 = 0.999$.

Our GGAN used a mean aggregate categorical cross-entropy loss function from the discriminator and a voxel-to-voxel (L1) loss function from the generator to update network parameters during the training process. The number of trained parameters was measured as 178 337 000 (≈167 million for the generator and ≈11 million

for the discriminator). Figure 3 shows a schematic depiction of the generator's and discriminator's network architectures.

To improve the training of our model, several on-the-fly augmentation methods were used. These applied augmentation methods were divided into two groups: (1) the “movement” group, which consisted of several random shifts, such as flipping or 3D rotation (from -20° to 20° for the azimuthal $\theta$ and from -6° to 6° for the polar $\varphi$ angle), and (2) the “imaging” group, which consisted of image-deformation methods such as applying random Gaussian filter, noise, and contrast levels. Every group was activated on the fly with a 50% chance of being used and an additional 50% chance of using a random variant of the opposite group. Our model was evaluated using the leave-one-out method.¹⁷ The training process of our prediction model took approximately 9 h and was implemented on a Nvidia GTX 1060 graphics processor unit (GPU) with 6 GB RAM.

## 2.2 | Clinical data

The patient pool consisted of 18 male patients and 1 female patient, with a mean age of 72 years, that were treated with ⁹⁰Y radioembolization with resin microspheres (SIR-Spheres; Sirtex) from November 2017 to December 2020. Out of 19 cases, 15 were diagnosed with primary liver cancer (10 HCC, 5 ICC), and 4 with liver metastasis (1 from neuroendocrine tumor, 3 from colorectal cancer). The injected radioactivity of ⁹⁰Y ranged from 1.26 to 4.76 GBq. An image preprocessing step was conducted before the GGAN training process. The SPECT and PET scans were normalized between 0 and 1 and the CT scans were normalized between -1 and 1. All images were resized to 128 × 128 × 128. To minimize data loss during the resizing process, PET and CT
<figure><img src="image_4.png" /><figcaption>FIGURE 3 Schematic depiction of the network architectures of the generator and discriminator</figcaption></figure>

scans were resized using linear and bicubic interpolation, respectively. Overall, our dataset consisted of 76 3D volumes (i.e., 19 patients with 4 sequences each) for a total of 9,728 2D images (Figure 2). For the present study, we used data only from the University Hospital of Patras departmental database. Our Institutional Review Board approved the study, and written informed consent was given by all patients to use their data.

## 2.3 | Validation methods

We validated our model by applying an image-based dosimetry method to both real and predicted PET images and by comparing the absorbed doses in the areas of interest, in our case the healthy liver and the tumor areas. Both the liver and the tumor on each case were manually segmented by two expert CT radiologists. The second expert's manual segmentations were used to assess the experts' inter-observer variability by means of Jaccard similarity coefficient (JSC) on their pairs of segmented areas per patient.31,32 The JSC from the inter-observer variability study on the two experts was calculated as 0.87. Furthermore, the tumor label drawn by the first expert was used as the input data for the training of our model mentioned above. Those segmentations, manually drawn by the first radiologist expert, were also used to measure the absorbed dose in the generated predicted PET images. This dosimetry method was analytically described in a recently published study by our group.33 Briefly, instead of executing a direct Monte Carlo simulation, with the help of a Geant4 application for emission tomography (GATE) v.8.0 simulation toolkit,34–36 a dose voxel kernel (DVK)6 was created. Specifically, a non-monoenergetic uniform $^{90}$Y $\beta$ pure emitter voxel source was simulated at the center of a homogeneous spherical medium. As the $^{90}$Y

$\beta$ particles range in water is 11 mm,37 the radius of the sphere was set to 11.5 mm. This way we ensured that all the emitted energy from the central voxel is deposited inside the generated sphere. Also, liver tissue ($\rho_{liver}$ = 1.06 g/cm$^3$) was used as the sphere's medium. The continuous beta spectrum of $^{90}$Y ranged from 0 to 2.2 MeV with a mean energy of 0.9337 MeV and a half-life of 64.1 h.38,39 The generated DVK (DVK$_{liver}$) was convoluted with the activity maps by using Equation (4):

$$D_{(x,y,z)} = \frac{1}{\lambda} (A_{PS} \otimes DVK_{liver})_{(x,y,z)} \\ = \frac{1}{\lambda} \left( \sum_{x'} \sum_{y'} \sum_{z'} A_{PS}(x', y', z') \right) \\ \times DVK_{liver}(x-x', y-y', z-z'), \quad (4)$$

where $\lambda$ is the $^{90}$Y decay constant and $A_{PS}$ is an activity percentage scaling map, on which each voxel was the correspondent proportion of the total activity of the original PET scans. For the generation of the DVK$_{liver}$ $2 \times 10^9$ primary events were simulated with a statistical uncertainty of < 0.75%. Moreover, random activity rate profiles were drawn and compared on different geometrical views to estimate the $^{90}$Y distribution in the liver and the tumor tissue.

## 3 | RESULTS

The real PET scans showing the $^{90}$Y biodistribution were considered the ground truth for all comparisons with our generated predicted PET images. Figure 4 presents an initial visual comparison of the two sets of images and their activity rate profiles in all axes concerning the amount of the total counts in the selected areas.
<figure><img src="image_5.png" /><figcaption>**FIGURE 4** (Left) Pretreatment, fused ⁹⁹mTc-MAA SPECT/CT vs. post-treatment real, fused ⁹⁰Y PET/CT vs. predicted ⁹⁰Y PET/CT images (top to bottom: axial, coronal, and sagittal views) and (Right) their corresponding activity rate profiles. Solid lines: real PET, dotted lines: predicted PET</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>**FIGURE 5** Absolute dose differences between real and predicted post-treatment PET scans in (left to right) axial, coronal, and sagittal views for two random representative slices</figcaption></figure>

Figure 4 shows that our approach accurately predicted the distribution of ⁹⁰Y and even predicted its heterogeneous distribution both within the tumor tissue and within the liver as a whole, although the predicted images appeared to be more homogenous than the real images. Nonetheless, our model was still able to predict a realistic dose map, as shown in Figure 5.

Figure 5 shows a detailed voxel-by-voxel comparison of the ⁹⁰Y distribution in the tumor tissue between the real and the predicted post-treatment PET scans. It also shows that there was no significant difference in the ⁹⁰Y distribution in the healthy liver tissue between the real and the predicted images.

Analytical results comparing absorbed dose in tumors and non-tumor liver parenchyma for all patient cases are shown in Figure 6.

Our model delivered very good agreement for the absorbed dose in the healthy liver tissue, as we observed no differences of more than 1 Gy in any patient case (Figure 6). However, our model had a tendency to slightly underestimate the predicted dose to the tumor area.

Figure 7 further illustrates the dosimetric accuracy of our model. Here, we present a point-by-point comparison of each patient case with regard to the relative and absolute dose differences between the real and predicted ⁹⁰Y biodistribution within the tumorous and healthy liver areas.

For the tumor area, the mean difference between the real and predicted dose was 5.42% ± 19.31% (range; -56.75% to +36.16%) using the absolute values, while the average absorbed dose difference was
<figure><img src="image_7.png" /><figcaption>FIGURE 6 Comparisons of real and predicted absorbed dose (Gy) in tumor (top) and healthy liver tissue (bottom) for each of the 19 patients included in this study</figcaption></figure>

7.98 ± 31.39 Gy (range; -72.82 Gy to +64.81 Gy). For the healthy liver tissue, our model delivered an almost perfect prediction, with differences of 0.44% ± 1.64% (-2.93% to 4.46%) and 0.03 ± 0.25 Gy (-0.52 Gy to +0.45 Gy), respectively. In 16 of the 19

(84%) patient cases, we found less than 20% differ-
ence in dose in the tumor area, with an average dif-
ference of 4.71% ± 8.03%. Our model had a general
tendency to underpredict the dosimetric results; the
largest differences were noticed in case 16, where the
<figure><img src="image_8.png" /><figcaption>**FIGURE 7** Differences between the real and the predicted ⁹⁰Y biodistribution in (a) tumor and (b) the whole normal liver. The differences are presented as absorbed dose (Gy) on the top and relative differences (%) on the bottom for each patient</figcaption></figure>

model underestimated the dose to the tumor area by 56.75% or 72.82 Gy.

## 4 | DISCUSSION

The current study presents the application of a GGAN as a method of obtaining accurate predictions of the biodistribution of ⁹⁰Y microspheres during TARE of hepatic tumors. This DL prediction model used a combination of pretreatment ⁹⁹mTc-MAA SPECT scan data and patient anatomical information as the input data to accurately predict the distribution of the ⁹⁰Y within the tumor area as well as within the entire liver. This method also allowed us to calculate the absorbed dose in the areas of interest. Our approach provides more accurate predictions than currently used dose-only prediction methods. To our knowledge, this is the first study to assess an alternative pretreatment planning method based on a DL algorithm for the challenging problem of predicting ⁹⁰Y biodistribution during TARE treatments for hepatic tumors.

One of the main drawbacks of current clinical practice is that treatment plans are based on basic and simplified dosimetry methods. The most frequently used

method is the simplistic partition model, which assumes homogeneous uptake of the radionuclide and does not consider individualized patient parameters. This simplified assumption, which is the basic concept of widely used treatment planning methods, such as BSA or MIRD,⁶,⁹,¹⁰ fails to take into consideration the differences in the microsphere distribution among tumor and non-tumor liver tissue, and may result in treatment underdosing, mostly in an effort to maximize patient safety.⁴⁰⁻⁴² It was also shown that the BSA model could not accurately incorporate liver volume, and therefore patients with large liver volumes ended up receiving insufficient doses, while patients with small liver volumes received disproportionate high doses.⁴³ The most frequently used method is the simplistic partition model, which assumes homogeneous uptake of the radionuclide and does not consider individualized patient parameters. Additionally, most studies that have attempted to deliver more accurate dosimetric models focused on the biodistribution of ⁹⁹mTc-MAA on SPECT/CT. This biodistribution, however, often substantially deviates from the real distribution of ⁹⁰Y. One of the contributing factors that lead to this discrepancy is the significant, catheter-positioning-dependent deviation that is observed between the absorbed and
$^{99m}$Tc MAA SPECT/CT-predicted dose, especially when it comes to treating small lesions. It has been demonstrated that the 95% confidence interval of the variations among the predicted and the real absorbed dose in the target tissue can have a range of several hundreds of Grays,$^{5,13,44–46}$ a fact that can result in considerably inaccurate response predictions. Notably, even in the case of accurate catheter positioning, this disagreement may persist.$^{47–49}$ This fact implies that other parameters might also be playing a role, such as the administration of two distinctive particle types in two sessions. The most recent study assessing this topic is the one by Haste et al.,$^{5}$ which involved 83 patients. The reported results were mostly estimations, with an average deviation of –14 ± [–355; 327] Gy for the tumor tissue and 0 ± 15 Gy for healthy liver tissue and a range of differences extending from +400 to –500 Gy and +20 to –30 Gy, respectively. Specifically, these estimations corresponded to a range of –160% to 100%, and –75% to 50% for the tumor tissue and for the whole liver, respectively.$^{5}$ Similar observations were also reported in studies by Richetta et al.$^{12}$ and Wondergem et al.$^{13}$

Given these findings, it is evident that the distri-
bution of <sup>90</sup>Y microspheres used in TARE cannot
always be simulated by <sup>99m</sup>Tc-MAA SPECT/CT, espe-
cially with regard to the distribution in the tumor tissue.
The approach used in our 3D-based model succeeded
in eliminating potential discrepancies among different
slices, which can occur with 2D-based algorithms, by tak-
ing into consideration the spatially heterogeneous dis-
tribution of the <sup>99m</sup>Tc-MAA (using the information from
the SPECT scans), the individual patient anatomy, and
the tissue heterogeneities in the area of interest (using
the information from the CT scans). Our method was,
therefore, able to predict the dose to the involved liver
regions: it almost perfectly predicted the absorbed dose
in the healthy liver area, with an accuracy of 0.44% ±
1.64%. For the tumorous area, our model predicted the
absorbed dose with an average accuracy of 5.42% ±
19.31%. Our model predicted an average difference of
7.98 ± 31.39 Gy in the tumor area and 0.03 ± 0.25 Gy in
the healthy liver area, meaning that it is more accurate
than the existing treatment planning modalities.<sup>2,8–10</sup> As
already described in the previous sections, our algorithm
was trained with the use of patient CTs as input data.
The parameters that lead to this minor dose underes-
timation are few. Both the type of tumor under investi-
gation, as well as the presence of other tumor-related
complications, may result in substantial differences in
the tumorous area tissue characteristics.<sup>50</sup> Additionally,
further limitations to the accuracy of dose prediction
derived from the <sup>90</sup>Y catheterization procedure that may
not be always optimal, i.e., during catheterization slight
differences in catheter position and angle can result in
differences in the microsphere distribution. These pro-
cedural limitations can result in significant variations in

dose predictions.<sup>4,13,36</sup> Based on the findings of this
study, DL approaches in such an application can provide
high accuracy in the prediction of the Y<sup>90</sup> microspheres
distribution, compared to other methods (e.g., DVK, MC,
partition model). In general, the main difference in the
accuracy of the result lies in the different approaches
used. The DVK approach lies on the distribution of the
<sup>99m</sup>Tc-MAA (SPECT) image, while the DL is a prediction
of the Y<sup>90</sup> (PET) distribution, using a dataset that has
been trained, on real PET data.

The guided mechanisms that were applied in our
model not only successfully provided highly accurate
dose predictions in the areas of interest but also pre-
cisely depicted the heterogeneous ⁹⁰Y biodistribution in
both healthy and tumorous tissues, which could improve
pretreatment decision making. To our knowledge, ours is
the only model that can depict the exact spatial biodis-
tribution of ⁹⁰Y in the liver area, making our model espe-
cially useful for centers where PET/CT is not available.
These centers must rely on post-treatment SPECT/CT
imaging, which has been shown to be inaccurate.<sup>11,48,51</sup>

Regarding the specific training and validated data
input profile of our study, three important aspects and
limitations should be noted. First, we used only data from
the University Hospital of Patras database, so that pro-
tocol consistency would enable stable training for our
model. Several studies, for instance, have shown that
parameters such as the catheter position can result in
significant variations in dose predictions.<sup>4,13,52</sup> There-
fore, to reduce the effect of such deviations to the
maximum extent possible, we used data from a sin-
gle source. The use of this dataset, which was simi-
lar in size to those used in several other DL studies in
nuclear medicine,<sup>53</sup> did not negatively affect our dosi-
metric results. However, our method was less accurate
at predicting (and thus at depicting) heterogeneity in the
tumorous area than in the healthy liver area. Second, to
establish the model architecture of the applied hyperpa-
rameters, such as volume depths, our model architecture
was adapted to the limited memory capacity of the GPU
hardware used. Third, no registration between SPECT
scans with the other images used for the training of our
model was performed. We relied on the ability of con-
volutional layers within deep neural networks (such as
GANs) with millions of parameters, to identify patterns
in a 3D image irrespective of their position within the
image. We anticipate that registration of all our image
data per patient would further optimize and improve our
model’s ability to predict. Finally, our study did not include
patients with extended lung shunt function because pre-
dicting lung dose was outside of our current aims. To
resolve these limitations, our future goals are to: (i) aug-
ment our dataset with cases from other hospitals so that
our model can be generalized, (ii) use GPUs with larger
memory capacity that can perform more complicated
calculations with higher-resolution images, (iii) perform
image registration on all images that will be used for
training, and (iv) incorporate cases with extended lung shunt function to estimate dose to the lungs as well.

Cutting-edge radiotherapy modalities such as intensity-modulated radiation therapy and elaborated automated treatment planning algorithms are already being gradually implemented in everyday clinical practice, improving efficacy and safety.⁵⁴⁻⁵⁷ However, pretreatment planning remains a challenge in nuclear medicine, mostly owing to the difficulty of accurately predicting the radionuclide biodistribution. Further studies are needed to be able to draw definite conclusions concerning the efficient implementation of automated models in nuclear medicine treatments.¹⁹,⁵³ As hardware dead-end issues (e.g., GPU capacity) are resolving, DL algorithms, such as our proposed GGAN, can be applied to perform post-treatment evaluation while also offering accurate dosimetry and biodistribution calculations.

## 5 | CONCLUSION

The use of an accurate planning agent before ⁹⁰Y microsphere TARE treatment is crucial for optimal personalized dosimetry. The absorbed dose calculated from a planning agent must correlate to the absorbed dose actually delivered by the ⁹⁰Y microspheres. Sufficiently accurate pretreatment dosimetry would allow the selection of administered activity levels that give the best chance for effective tumor control while limiting liver toxicity. In the current study, we proposed a 3D multimodal GGAN as an elaborated alternative to existing dose prediction models, which are not always accurate. Our method enhanced model performance and reduced network redundancy by efficiently covering parameters such as individual anatomy and tissue heterogeneities. Thus, by optimizing dose predictions and enhancing the safety and efficacy of TARE treatment, it could improve patient outcomes. More patients' data should be processed in future studies to further validate this model for use in everyday clinical practice.

## ACKNOWLEDGEMENTS

The authors thank Editing Services, Research Medical Library at MD Anderson Cancer Center for their professional language editing on the article.

## FUNDING INFORMATION

This research was co-financed by:

(a) Greece and the European Union (European Social Fund- ESF) through (i) the Operational Programme «Human Resources Development, Education and Lifelong Learning» in the context of the project "Strengthening Human Resources Research Potential via Doctorate Research" (MIS-5000432), implemented by the State Scholarships Foundation (IKY),

and (ii) the Operational Programme «Human Resources Development, Education and Lifelong Learning» in the context of the project "Reinforcement of Postdoctoral Researchers-2nd Cycle" (MIS-5033021), implemented by the State Scholarships Foundation (IKY)”, and

(b) the European Regional Development Fund (ERDF), Greek General Secretariat for Research and Innovation, Operational Programme "Competitiveness, Entrepreneurship and Innovation" (EPAnEK), under the frame of ERA PerMed (project POPEYE T11EPA4-00055).

## CONFLICTS OF INTEREST

The author declares that there is no conflict of interest that could be perceived as prejudicing the impartiality of the research reported.

## DATA AVAILABILITY STATEMENT

The data that support the findings of the present study are not publicly available to preserve the privacy of patients' personal medical information. It can, however, be obtained from the corresponding author upon reasonable request.

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How to cite this article: Plachouris D, Tzolas I, Gatos I, et al. A deep-learning-based prediction model for the biodistribution of ⁹⁰Y microspheres in liver radioembolization. *Med. Phys.* 2021;48:7427–7438.

https://doi.org/10.1002/mp.15270