# Optimizing Prediction of MGMT Promoter Methylation from MRI Scans using
Adversarial Learning

Sauman Das  Thomas Jefferson High School for Science and Technology

(January 2022)

###### Abstract

Glioblastoma Multiforme (GBM) is a malignant brain cancer forming around 48%
of all brain and Central Nervous System (CNS) cancers. It is estimated that
annually over 13,000 deaths occur in the US due to GBM, making it crucial to
have early diagnosis systems that can lead to predictable and effective
treatment. The most common treatment after GBM diagnosis is chemotherapy,
which works by sending rapidly dividing cells to apoptosis. However, this form
of treatment is not effective when the MGMT promoter sequence is unmethylated,
and instead leads to severe side effects decreasing patient survivability.
Therefore, it is important to be able to identify the MGMT promoter
methylation status before deciding on the treatment plan. In this research, we
aim to detect the methylation status through non-invasive magnetic resonance
imaging (MRI) based machine learning (ML) models. This is accomplished using
the Brain Tumor Segmentation (BraTS) 2021 dataset, which was recently used for
an international Kaggle competition. We developed four primary models - two
radiomic models and two CNN models - each solving the binary classification
task with progressive improvements. We built a novel ML model termed as the
Intermediate State Generator which was used to normalize the slice thicknesses
of all MRI scans. With further improvements, our best model was able to
achieve performance significantly ($p<0.05$) better than the best performing
Kaggle model with a 6% increase in average cross-validation accuracy. This
improvement could potentially lead to a more informed choice of chemotherapy
as a treatment option, prolonging lives of thousands of patients with GBM each
year.

##  1 Introduction

A recent survey conducted by GLOBOCAN in 185 countries, estimates that there
were 308,102 new cases of brain cancer and 251,329 deaths in 2020 alone in 185
countries (Sung et al.,, 2021). _Glioblastoma Multiforme (GBM)_ is one of the
most stubborn and aggressive forms of malignant brain cancer, with very few
effective treatment options. The World Health Organization has classified it
as a grade IV, the highest grade brain tumor, accounting for 48% of all
primary malignant brain tumors (Ostrom et al.,, 2014). More than 13,000
Americans are expected to receive a GBM diagnosis each year. It is also
estimated that more than 10,000 Americans will die from GBM every year.

The typical recommended treatment for GBM patients include surgical removal of
the tumor followed by radiotherapy and chemotherapy. With this standard care,
the patients have an median survival time of 15 months as compared to a mere 4
months if left untreated once diagnosed (Bleeker et al.,, 2012). Chemotherapy,
a standard and often used treatment option, works by killing rapidly dividing
cells but cannot always differentiate between tumor cells from normal cells.
This can result in adverse side effects (MacDonald,, 2009) (Taal et al.,,
2015). According to the American Cancer Society, for GBM treatment, these side
effects may include peripheral neuropathy, which includes symptoms causing
damage to the central nervous systems and impaired body movements,
significantly deteriorating patient quality of life. Therefore, before the
patient starts chemotherapy treatment, it is critical to know if it would be
effective in curbing the disease progress.

Chemotherapy relies on Temozolomide (TMZ) which places a side product on a
Guanine molecule of the DNA. This additional molecule prevents the synthesis
of new DNA and leads to apoptosis of the cancer cells. However, an enzyme,
known as $\text{O}^{6}$-methylguanine DNA methyltransferase (MGMT), can remove
the additional molecule. If the MGMT protein is transcribed, then cells will
not be led to apoptosis because of the absence of the additional molecule and
chemotherapy will be ineffective. Sometimes, however, the promoter region of
the MGMT gene is methylated and that prevents transcription of the enzyme. As
a result, chemotherapy will likely be effective, since the side product
molecule will remain attached to the Guanine molecule.

Unfortunately Temozolomide has severe side effects, especially in patients
with pre-existing comorbidities. Hence, detection of MGMT promoter methylation
status may help tailor the best Temozolomide dosage or schedule for the GBM
patient. The MGMT promoter methylation status can be found through invasive
surgeries; however, this is time-taking and can lead to side effects caused by
the surgery itself. However, with the increasing amount of biomedical imaging
data along with recent advances in deep learning, the process of MGMT promoter
methylation detection can be largely simplified. This work aims to discover if
MGMT promoter methylation can be detected from MRI scans and reveal certain
biomedical markers extracted from images that strongly correlate with the
methylation status. This approach could potentially result in a non-invasive
and more efficient form of prognosis leading to better treatment for GBM.

In this work, we aim to improve the accuracy of MGMT promoter methylation
prediction, but achieve this using data that is noisy and more representative
of what would be provided in a real medical setting. We begin by summarizing
prior research done on this topic in Section 2. Then, we will go into detail
about methodologies used in this work including the explanation of an original
preprocessing strategy in Section 3.4. Furthermore, we train and test 4
different models and summarize their results. Finally, we discuss the results
shown in this paper with respect to work from prior research.

##  2 Existing Research

During the summer of 2021, the Radiological Society of North America hosted a
prestigious Kaggle competition to encourage renewed research on MGMT promoter
methylation detection using data science and machine learning techniques. The
challenge received over 1,500 submissions from researchers around the world.
Firas Baba used an ML model known as _ResNet_ and was declared as the eventual
winner of the competition. The model generated the highest area under the ROC
curve score of 0.62714.

Prior to this Kaggle challenge, researchers have primarily followed two
distinct approaches to detect MGMT Promoter methylation. The first approach is
outlined in Figure 1.

Figure 1: Overview of Radiomic Feature Extraction Approach

A brain tumor segmentation model is created to identify the region of interest
(ROI). Then, radiomic features, such as tumor location, tumor shape, and
several histogram and gray level coocurrence matrix (texture descriptors) are
extracted. These features are then processed by machine learning models to
predict the methylation status.

During the Kaggle competition, some researchers found that radiomic feature
extraction did not provide the most optimal results. Instead, they followed an
alternate approach which involved using Convolutional Neural Networks (CNNs)
rather than extracting radiomic features. This method does not require tumor
segmentation masks which the previous method relied upon. The CNN method is
outlined in Figure 2.

Figure 2: Overview of CNN Approach

Ahn et al., (2014) was one of the earliest to study and analyze the MGMT
promoter methylation from MRI scans. They studied the MRI scans of 43 patients
diagnosed with GBM and were provided with the methylation status for each
patient. They extracted features including the rate transfer coefficient,
apparent diffusion coefficient, and fractional anisotropy from a defined ROI.
Using Chi-Square and Mann-Whitney tests, they found the correlation between
the extracted imaging features and the MGMT promoter methylation status. They
achieved sensitivity and specificity values of 56.3% and 85.2%, respectively.

Sasaki et al., (2019) did a more thorough analysis in describing the
effectiveness of radiomic features for methylation status detection. They
extracted 489 texture features from the ROI along with location features.
Through Principal Component Analysis (PCA), they were able to identify 22
features that contributed most to the MGMT promoter methylation. They were
able to achieve a high accuracy of 67% with their LASSO regression model.

Han and Kamdar, (2018) followed the Convolutional Neural Network (CNN) feature
extraction method (Figure 2). They proposed a novel bi-directional CNN
architecture to predict MGMT promoter methylation. The benefit of using this
type of network is that any number of MRI slices can be passed through due to
the recurrent nature of the network. In contrast, a 3-dimensional CNN would
require a uniform number of slices to work. They tested their model on 21
patients and achieved a 62% accuracy.

##  3 Materials and Methods

###  3.1 Dataset

For this research We utilized the MRI datasets provided by the Brain Tumor
Segmentation (BraTS) Challenge in 2020 and 2021. To build a segmentation model
to detect the tumour region, BraTS 2020 Challenge dataset was used. 369 MRI
scans were provided in four modalities, namely Fluid-attenuated inversion
recovery (FLAIR), T1-weighted (T1w), T2-weighted (T2w), and T1-weighted
contrast enhanced (T1wCE). Both the scans and the segmentation masks were
given in the NIfTI file format and in the coronal orientation. The masks
provided four class labels including non-tumor, non-enhancing tumor core,
peritumoral edema, and enhancing tumor. For our research, we combined the
latter three classes since we were only concerned with the general tumor
region.

In 2021, the Radiological Society of North America (RSNA) along with the
Medical Image Computing and Computer Assisted Intervention (MICCAI) Society
introduced the MGMT promoter methylation detection aspect to the BraTS
challenge hosted on Kaggle. They provided a pre-selected dataset of 585 MRI
scans in the same four modalities as in 2020. The scans were collected from
various institutions with different equipment in order to represent the
diverse clinical practices across the world (Baid et al.,, 2021). For the
classification task, we used these dataset which were in the DICOM format
labelled with their methylation status. The MGMT methylation status was
confirmed by laboratory assessment of the surgical brain tumor specimen. The
four modalities remained the same from the previous dataset described, but the
T1w scans were not used due to consistently large thicknesses contributing to
more noise than information.

Unlike many prior research on methylation detection, our MRI scans were very
messy containing varying slice thicknesses and orientations. This messiness is
typically observed in real-world clinical data. Although preprocessing of
messy data is challenging, an autonomous deep learning model should apply
adequate correction to avoid any intervention from the medical practitioners.
The practitioner should be able to specify these messy MRI scans to the ML
model in order to generate the methylation status.

###  3.2 Overview of Models

The objective of this research is to improve the accuracy of MGMT prediction
using ML models for messy real-world MRI data. For this purpose we
investigated potential improvements that can be introduced at various stages
of the processing to arrive at the final methylation decision. Figure 3
provides an overview of the four specific models we developed to study and
compare the performance using the same messy dataset. The first two models
relied on radiomic feature based approach as adopted by many of researchers
recently. Unlike these models, the latter two models used CNN directly without
explicit feature extraction. The first and third models are mere replications
of known prior approaches. The third model in particular has gained a lot of
recognition as the winner of the 2021 Kaggle challenge.

Figure 3: Overview of ML modeling approaches for MGMT detection.

The second and fourth models are based on the basic prior approaches of first
and third models respectively. These new models exhibited improved performance
when the messy data is first corrected and then used for classification. The
correction is applied by a new proposed method called Intermediate State
Generator or IS-Gen which fills in missing images in a particular MRI scan
with images imputed from adjacent real images. This way all MRI scans are
normalized to have the same number of images with equal thickness. The
normalization is fully complete when all the images are rotated to be in the
coronal plane. Rotating the images after application of IS-Gen prevents undue
blurring of the rotated images.

The traditional CNN approach of third model considers the 64 slices around the
middle image for use by CNN for classification. One potential issue with this
approach is the assumption that the tumor region is more or less centrally
located. Furthermore, these 64 slice selection does not consider the absence
of slices in heterogeneous messy MRI scans. The fourth and final model
corrects these issues by first applying IS-Gen to fill in the missing images,
then finding the tumor region to detect the location of maximal presence of
the disease. The final 64 slices are selected surrounding the maximal presence
of the tumor for the CNN classification

###  3.3 Baseline Radiomic Feature Based Model

In Section 2, two approaches to achieve MGMT promoter methylation prediction
were discussed. For the first model, we use the radiomic feature extraction
approach. The first step was to build a segmentation model to define the tumor
ROI. We used a 2D U-Net that was originally designed by
Rastislav111https://www.kaggle.com/rastislav/3d-mri-brain-tumor-segmentation-
u-net. We optimized the model for better use in the complete pipeline. The
primary modification we made was to combine the three non-background classes
into one tumor class. Furthermore, we cropped all MRI scans to the smallest
rectangular prism containing the full brain (i.e. removed all black padding).

The U-Net was trained for 35 epochs on MRI scans provided in the coronal
plane. We monitored the Intersection Over Union (IOU) and dice coefficient
which are frequently used metrics to measure image segmentation performance.
Given a predicted mask $A$ and labelled region $B$, the following equations
can be used to calculate IOU and the dice score.

$\text{IOU}=\frac{|A\cap B|}{|A\cup B|}$ $\text{Dice
Coefficient}=\frac{2|A\cap B|}{|A|+|B|}$

The final U-net exhibited validation IOU and dice scores of 0.832 and 0.626,
respectively.

The segmentation model was then applied to the MRI scans in the BraTS 2021
dataset which contained methylation status labels. The model was applied to
each individual slice reoriented into the Coronal plane in the MRI scan
because of the 2D U-net architecture. Once masks were defined, we began
extracting radiomic features. Radiomics refers to the idea of extracting
features from biomedical images such as computed tomography, positron emission
tomography, or MRIs in order to build “models relating image features to
phenotypes or gene–protein signatures” (Kumar et al.,, 2012). We extracted 39
features from 3 modalities of MRI scans using the Python library known as
PyRadiomics (Van Griethuysen et al.,, 2017). We included both first-order
features such as energy and entropy of the tumor region and included some
texture features using the Gray Level Co-occurrence Matrix (GLCM) and Run
Length Matrix (GLRLM). Additionally, we calculated the tumor region centroid
coordinates along with shape features of the tumor. The centroid coordinates
were treated as 3 separate features which were calculated using the formulas
below where $T$ represents the $x$, $y$, or $z$ coordinate of the $i$th pixel
located in the tumor and $n$ is the total number of pixels in the tumor.

$\displaystyle X_{c}=\frac{\sum_{i=1}^{n}T_{x}(i)}{n}$ $\displaystyle
Y_{c}=\frac{\sum_{i=1}^{n}T_{y}(i)}{n}$ $\displaystyle
Z_{c}=\frac{\sum_{i=1}^{n}T_{z}(i)}{n}$

We used another 3 shape features including approximate mesh volume (V),
surface area (A), and sphericity (closeness to a sphere) using PyRadiomics.
Out of the 39 total features extracted, the 7 features which produced the
highest accuracies during cross-validation were the following: $X_{c}$,
$Y_{c}$, $Z_{c}$, Volume, Surface Area, Sphericity, and Total Energy
calculated from the FLAIR modality.

After doing preliminary experimentation with multiple machine learning models
including Decision Trees, Random Forests, AdaBoost, Support Vector Machines,
and Extreme Gradient Boosting (XGBoost), we further fine-tuned the Random
Forest since it showed the most promising results. All these models were
implemented using the Scikit Learn package. The following set of
hyperparameters were experimented with for the Random Forest using a Grid
Search:

Hyperparameter | Values
---|---
n-estimators | [50, 150, 200, 250, 300]
criterion | [‘gini’, ‘entropy’]
max-depth | [10, 15, 20, 25, 30, 35, 40, 45, 50]
max-leaf-nodes | [5, 10, 15, 20, 30, None]
class-weight | [‘balanced’, None]
min-samples-split | [2, 4, 6, 8]
Table 1: Parameter grid for random forest fine-tuning.

The bolded values produced the optimal results. A 5-fold Cross Validation (CV)
was conducted for concrete model evaluation. The average results are shown
below.

Accuracy | Sensitivity | Specificity | PPV | NPV | AUROC
---|---|---|---|---|---
0.564102564 | 0.678241587 | 0.418761311 | 0.615846663 | 0.678241587 | 0.548501449
Table 2: Average Cross Validation Results for Baseline Radiomic Feature
Extraction Model.

One possible explanation for the poor results was the varying slice thickness
and general noise prevalent in the MRI scans. The radiomic approach heavily
relies on the accuracy of segmentation and clarity of images because radiomic
features are extracted based on pixel values. Thrower et al., (2021) show that
a MRI slice thickness greater than 1 mm effects segmentation of brain lesions.
Therefore, being able to have MRI scans with minimal slice thickness could
potentially provide more tumor information resulting in a better radiomic
feature extractor.

However, we cannot rely on alternative data sources such as TCIA which provide
higher quality MRI scans. Data provided in real-world medical conditions will
not necessarily be processed to the way that benefits our model. Most likely,
we will be faced with varying slice thicknesses and orientations just as the
BraTS 2021 dataset presents. This problem led to the creation of a new
architecture used for preprocessing called the Intermediate State Generator.

###  3.4 Intermediate State Generator (IS-Gen)

In this paper, we consider the orientation and slice thickness problems
inherent in the messy data. Orientation refers to the plane in which an MRI
scan is provided. There are three distinct orientations through which MRI
scans can be interpreted, namely sagittal, axial, and coronal. The diagram
below shows which plane each of the three orientations refer to.

Figure 4: Three different MRI planes. The axial plane is sometimes referred to
as the transverse plane. Source: My-MS.org

Although orientation does not have to remain constant when passed through a
model, the model can benefit by removing the orientation variable to learn
from. Furthermore, the segmentation dataset provides all images in the coronal
orientation which results in more accurate tumour region segmentation for the
classification images in that orientation.

The process of modifying orientations to be constant throughout the data
directly relates to problems caused by slice thickness. A larger slice
thickness indicates the availability of less 2D slices to represent the brain
volume. We can see the consequence of changing orientation with large slice
thicknesses in the following figure.

(a)

(b)

Figure 5: Image (a) is created by changing orientation of an axial T1w MRI
with 33 total slices. Image (b) is created by changing orientation of a
sagittal T2w MRI with 274 slices. The images are presented in the figure in
the coronal plane.

Figure 5(a) is very blurry and pixelated because only 33 slices were
originally provided in the axial orientation. The minimal amount of slices is
not enough to produce a clear image of the brain when reinterpreted into the
coronal orientation. The image would not be good enough for a segmentation
model to locate the tumor due to extremely low level of detail. Because there
were several T1w images with large slice thickness, we excluded them from our
dataset. However, Figure 5(b) also shows an image that has been reinterpreted
into the coronal plane and the level of detail that is preserved is greatly
improved because of a significantly lower slice thickness.

In order to get automated MGMT promoter methylation detection to the level of
deployment, the input should be as generalized as possible. The goal is to be
able to provide a prognosis given any form of the MRI scans in the three
modalities (i.e. T1wCE, T2w, FLAIR). Consequently, we developed a
preprocessing algorithm that could adjust the slice thickness by inserting
synthetic MRI slices based on the real MRI sequence. We hypothesized that this
would be able to provide more accurate segmentation and also increase accuracy
of texture analysis. Three millimeter slice thickness is generally what is
required for accurate texture analysis (Savio et al.,, 2010).

We assume that this task is reasonable due to biological continuity that
naturally exists. In other words, there must be well-defined relationships
between 3 consecutive slices of an MRI sequence provided their distance
between each other is not too large. Our goal was to create synthetic slices
that provide more information than what existed previously. So, once tested,
it should be more accurate than what we call the “copy imputer”: the process
of filling in intermediary slices by duplicating adjacent slices that already
exist.

####  3.4.1 Initial Model Architecture

We planned to create synthetic slices with a model called the Intermediate
State Generator (IS-Gen). The IS-Gen takes in 2 images $x_{1}$ and $x_{2}$ as
input, and attempts to produce the MRI slice belonging between the two inputs
denoted by $\hat{y}$. Our initial model contained two separate convolutional
feature extractors that each took in a 256x256 sized MRI scan and extracted 2
feature maps of size 16x16x64. These feature maps were then concatenated and
passed through upsampling convolutions resulting in a 256x256 sized
reconstruction of the original image.

Figure 6: Initial IS-Gen model outline.

The model was trained using a supervised algorithm by taking sequences of 3
images separated by an equal width and using the second image ($y$) as the
label. The spacing between the images passed through the model was randomly
selected during training to provide a variety of slice thicknesses since the
model would need to work on a variety of slice thicknesses when used during
preprocessing.

We defined the loss function as the mean squared error in order to achieve the
most accurate reconstruction.

$\mathcal{L}_{RL}(y,\hat{y})=(y-\hat{y})^{2}$

However, due to overrepresentation of black pixels, the model began returning
pure black images providing zero additional information. To combat this issue,
we introduced a piecewise loss function that adapted to the pixel values.

$\mathcal{L}_{RL}(y,\hat{y})=\begin{cases}\hat{y}^{2}&y=0\\\
5*(y-\hat{y})^{2}&y\neq 0\end{cases}$

Training this model allowed the model to learn fine details of the brain.
After training the model for 40 epochs, the following results were achieved.

(a)

(b)

Figure 7: Example results from mean squared error training. Image (a)
represents the actual intermediary label. Image (b) is the output of the IS-
Gen with two adjacent slices provided as input. Notice the blurriness that is
present in the image.

The images are able to maintain relative shape and color shade of the scan;
however, the detail in the center is completely blurred. A segmentation model
would likely not be able to accurately extract the tumor region from the
generated slice because there is very little resemblance to a brain at this
stage.

####  3.4.2 Discriminator Introduction

In order to combat the problems with the current synthetic imputations, we
added a new adversarial component to the IS-Gen called the discriminator. A
discriminator, in adversarial models, is typically used to detect whether the
produced image/result is real or fake. During training, the generator (i.e.
component described in Figure 8) attempts to create a synthetic image that is
close to the label defined by $\mathcal{L}_{RL}$, but it also tries to create
an image that can trick the discriminator into thinking it is real.
Simultaneously, the discriminator is learning how to discriminate between real
and fake images. The discriminator is a basic binary classification CNN with 3
convolutional layers, a fully connected layer, and a single neuron sigmoid
output layer.

Figure 8: Full IS-Gen model with discriminator to ensure crisp image creation.

The model architecture has some similarities to a Generative Adversarial
Network (GAN) (Goodfellow et al.,, 2014), but adds a reconstruction loss to
the generated image. Furthermore, this is trained in a supervised manner
whereas GANs use an unsupervised training algorithm.

####  3.4.3 IS-Gen Training

Our initial approach towards training the IS-Gen was similar to that of the
GAN training algorithm. The sequences of three images ($x_{1},x_{2},y_{g}$)
are selected in the same way described in Section 3.4.1. Then, the generator
$G$ produces an intermediary slice prediction $\hat{y_{g}}$. The discriminator
takes $\hat{y_{g}}$ and $x_{1}$ as input and produces a binary prediction for
each of the images. The goal for the discriminator is to predict each
generated image as belonging to class 0 and real image belonging to class 1.
It is trained with the following loss function:

$\mathcal{L}_{D}(y_{d},\hat{y_{d}})=-\frac{1}{N}\sum_{i=1}^{N}y_{di}\cdot\log(\hat{y_{di}})+(1-y_{di})\cdot\log(1-\hat{y_{di}})$

In our experimentation, the value of $N$ was 2 because we passed in exactly
one synthetic and one real image in each batch. Additionally, the generator
loss function was expanded to include the adversarial component. The labels
for the real vs. synthetic images were inverted for the generator because the
generator’s task is the opposite of the discriminators. The following equation
represents the loss function for the generator:

$\mathcal{L}_{G}(y_{g},\hat{y_{g}},\overline{y_{d}},\hat{y_{d}})=\mathcal{L}_{RL}(y,\hat{y})+\lambda\mathcal{L}_{D}(\overline{y_{d}},\hat{y_{d}})$

Note that we added the extra $\lambda$ factor to the adversarial loss function
term. Originally we set $\lambda=1$, but the model was not able to learn
useful information. The generator was not able to learn fast enough relative
to the discriminator which again resulted in the creation of black images.
Consequently, we introduced the regularization term and set $\lambda=0.03$ to
scale down the impact of the discriminator. The adversarial training algorithm
is shown below:

Algorithm 1 Adversarial IS-Gen Training Step

1: for all $x_{1},x_{2},y_{g}\in Data$ do

2: $\hat{y_{g}}\leftarrow G(x_{1},x_{2})$

3: $\hat{y_{d}}\leftarrow D(\hat{y_{g}},x_{1})$

4: $y_{d}\leftarrow[0,1]$

5: Update: $[w_{g}\leftarrow
w_{g}-\eta\nabla\mathcal{L}_{G}(y_{g},\hat{y_{g}},\overline{y_{d}},\hat{y_{d}})]$

6: Update: $[w_{d}\leftarrow
w_{d}-\eta\nabla\mathcal{L}_{D}(y_{d},\hat{y_{d}})]$

7: end for

These modifications successfully decreased the blurriness of the IS-Gen
output. However, after 10 epochs of purely adversarial training (i.e. training
with $\lambda=0.03$), the model began to decrease in accuracy as measured by
the reconstruction loss.

(a)

(b)

Figure 9: Sample synthetic image generated after 10 epochs of adversarial
training. We can clearly see decreased accuracy compared to Figure 7(b), but
the blurriness has significantly reduced.

We used one final modification to improve the training of the IS-Gen called
“On-Off Training”. During On-Off training, the model does not consistently
learn using adversarial training; instead, it switches back and forth between
adversarial and non-adversarial training to increase clarity while maintaining
pixelwise accuracy.

For the first 5 epochs, the model was trained with $\lambda=0$ and gradients
were not backpropagated through discriminator enabling the generator to get a
head start (Algorithm 2). For the following 5 epochs, we again set
$\lambda=0.03$ and allowed backpropagation of gradients through the
discriminator (Algorithm 1). This 10 epoch pattern was repeated 10 times
resulting in 100 total epochs of training.

Algorithm 2 Non-Adversarial IS-Gen Training Step

1: for all $x_{1},x_{2},y_{g}\in Data$ do

2: $\hat{y_{g}}\leftarrow G(x_{1},x_{2})$

3: Update: $[w_{g}\leftarrow
w_{g}-\eta\nabla\mathcal{L}_{RL}(y_{g},\hat{y_{g}})]$

4: end for

Using this process prevented the model from losing too much clarity and
maintained accuracy in its predictions.

(a)

(b)

Figure 10: The produced image (b) is significantly more accurate than Figure
9(b) and maintains clarity unlike Figure 7(b). Image (a) is the provided
intermediary image.

This process was applied to three different IS-Gen models that were specific
to 3 modalities of MRI scans, namely FLAIR, T1wCE, and T2w.

The updated results show that both shape and clarity have been conserved to an
extent. We can also see that the color distribution remains relatively
accurate indicating that a segmentation model could also work for the
generated slices.

We wanted to confirm that the model was contributing more information than
what already existed in the MRI sequence. Consequently, we compared the IS-Gen
to a basic “copy imputer”. The copy imputer filled in missing slices by simply
adding a copy of an adjacent slice that already existed, therefore
contributing no new information, yet filling in slices with some level of
accuracy.

| T1wCE | FLAIR | T2w
---|---|---|---
IS-Gen | 4.820610455 | 6.069807723 | 6.204056403
Copy Imputer | 22.25231586 | 27.96860923 | 28.92950342
Table 3: Average Mean Absolute Pixelwise Error from 1,250 test cases. All
pixel values were scaled between 0-255 before score calculation.

The results of the IS-Gen were significantly better ($\alpha=0.05$) than
naively copying adjacent slices. This shows that the IS-Gen was able to
contribute information that did not previously exist while maintaining a
relatively low average pixelwise error.

####  3.4.4 Applying the IS-Gen

For all of the models that we design, we resize the MRI scans to contain 128
slices. Based on provided metadata, 128 slices in the coronal plane represents
a slice thickness of approximately 2.5 mm.

The goal of the IS-Gen is to standardize the slice thickness of the MRI scans
by providing synthetic images to scans with a large slice thickness. For scans
that contain less than 128 slices in the provided orientation, the IS-Gen was
used iteratively to impute intermediary slices. During the first round of
imputation, existing adjacent pairs of slices were used as input to the IS-Gen
to impute new slices (Figure 11).

(a)

(b)

(c)

Figure 11: Image (a) and (c) are two adjacent slices in ad MRI scan. Image (b)
represents the middle slice produced by passing in (a) and (c) as input to the
IS-Gen trained with On-Off training.

If the first round of imputation did not result in at least 128 slices, the
same process was repeated with the current MRI scan until it has all 128
slices in the provided plane. If the imputation resulted in more than 128
slices, exactly 128 slices were selected in uniform from the existing scan.
Once the slices were selected, the MRI scan was reoriented into the coronal
plane, if necessary. The final MRI scan dimensions were 128x128x128.

###  3.5 Enhanced Radiomic Feature Based Model

We hypothesized that the IS-Gen could contribute new information to the MRI
allowing for a more detailed and representative set of radiomic features.
Especially for the shape features, we believe that the IS-Gen could be used to
preprocess and enhance the provided MRI scans to improve the quality of these
features. In this paper, we will refer to an MRI scan that has been
preprocessed by the IS-Gen as enhanced.

The pipeline for radiomic feature extraction presented in Section 3.3 was
reused to build another model with one modification. We enhanced all the MRI
scans before passing them through the segmentation model and all other factors
remained constant. The radiomic features were now going to be extracted from
MRIs with equal slice thickness and additional information.

Similar to the previous baseline radiomic feature model, 39 features were
extracted but the 6 shape and location features provided the optimal
preliminary results when trained with the random forest classifier. We
performed a grid search with the hyperparameters presented in Table 1 and the
final hyperparameters are presented in the table below.

Hyperparameter | Optimal Value
---|---
n-estimators | 200
criterion | ‘gini’
max-depth | 10
max-leaf-nodes | 5
class-weight | None
min-samples-split | 4
Table 4: Parameter grid for random forest fine-tuning.

The results of the 5-fold CV for the enhanced radiomic feature extraction
model are shown in the table below.

Accuracy | Sensitivity | Specificity | PPV | NPV | AUROC
---|---|---|---|---|---
0.606837607 | 0.770721608 | 0.401783756 | 0.636609161 | 0.566618256 | 0.586252682
Table 5: Average Cross Validation Results for Enhanced Radiomic Feature
Extraction Model.

These results show a borderline statistically significant improvement
($p=0.049$) from the baseline radiomic model as shown by a 2-way ANOVA with 5
replications (5 folds of CV); however, the results need significant
improvement because certain metrics such as the specificity are around 40% for
both models. The increase in accuracy can primarily be credited to the 10%
increase in sensitivity.

Although the radiomic feature extraction process was not the most successful
in terms of performance, it showed that the IS-Gen preprocessing has the
potential to contribute additional information towards the methylation status
prediction because that was the only variable modified from the baseline
model.

###  3.6 Baseline ResNet-10

As discussed in Section 2, two modeling approaches are commonly followed to
detect MGMT promoter methylation prediction, viz. radiomic feature extraction
and CNN feature extraction. As described in the previous section, radiomic
feature extraction based approach resulted in only modest improvement in MGMT
detection accuracy. We therefore proceeded to experiment with the alternative
latter approach.

As mentioned earlier, we utilized the dataset used in the Kaggle competition
hosted during the summer of 2021. Incidentally, the winner, Firas Baba,
described his results in a Kaggle discussion
post222https://www.kaggle.com/c/rsna-miccai-brain-tumor-radiogenomic-
classification/discussion/281347. At the time of our research, there did not
exist any peer-reviewed publications describing results of the recently
concluded competition. However, we were able to replicate the methodologies
used by Baba using information from his discussion post along with his GitHub
repository333https://github.com/FirasBaba/rsna-ResNet10.

The winner experimented with several models before using a surprisingly simple
approach with the 3-Dimensional ResNet-10 as the winning solution. It is
important to consider how he dealt with the variable slice thickness problem.
His solution was to find the slice that contained the largest cross-sectional
brain image and treat this as the central slice. This was called the “Central
Image Trick”. Then, $n$ images centered around that image were selected as
input to the model. The rationale behind this method was that the tumor would
be located in the brain area surrounded by the central imaged covered by the
selected images. Baba used 64 slices centered around the middle image as the
input for his classification CNN model. No further preprocessing was done
which indicates that the variable orientations in which the images were
provided remained the unchanged when passed into the model. This means that
the model would have to learn to predict methylation status from MRI scans
provided in various orientations.

The overall process of selecting the 64 images is a simple two-step process
depicted in Figure 12.

(a)

(b)

Figure 12: Standard 64 image selection approach using the Central Image Trick.
(a) The central image, marked by the orange star, is identified from the
original set of images. (b) 64 images used in classification are selected
around the central image.

The ResNet-10 was designed using PyTorch and trained for 15 epochs to select
the best model used for testing. The results for the baseline ResNet-10 are
displayed in the table below.

Accuracy | Sensitivity | Specificity | PPV | NPV | AUROC
---|---|---|---|---|---
0.60991453 | 0.701628664 | 0.508633094 | 0.615179617 | 0.61794551 | 0.605130879
Table 6: Average Cross Validation Results for Baseline ResNet-10 Model.

These results are consistent with those self-reported by Firas Baba in his
blog post. He obtained average AUROC scores of 0.62 over 5 folds of cross
validation. Although his accuracy was at the same level as the enhanced
radiomic feature extractor, he observed a 10% increase in average specificity.

###  3.7 Enhanced ResNet-10

Although the baseline ResNet-10 CNN model improves the MGMT classification
accuracy for messy MRI data, there are inherent issues with the approach. It
is a prevalent clinical practice to examine biopsy tissue sample of the tumor
to determine methylation status. Thus, the central issue is that the approach
does not rely on the clinical fact that the methylation molecular
characteristics are manifested only in the tumor region. The region of brain
outside of the tumor should not contain any of these characteristics. By
selecting generic brain regions without any emphasis on tumor regions dilutes
the information pertinent for MGMT detection. In many cases, the 64 slices
selected as classification input, pivoting on the largest brain image may have
little or no tumor region. Additionally, selecting 64 slices ignoring the
slice thickness of the scan, results in a different width of the brain being
represented for each input. This could misguide the learning process for the
model since it is provided potentially with a different width of brain every
training iteration. Finally, the input could be in any of the three spatial
orientation forcing the model to consider an extra variable.

In the improved enhanced ResNet-10 model, we address the central issue of the
baseline model by using only the segmented tumor region as classification
input. All non-tumor regions are ignored for this purpose. In order to keep a
fixed width of the brain as the input to classification, we normalize the
scans to synthetically fill in the intermediary missing slices by harnessing
previously described IS-Gen algorithm. Depending on the number of slices
provided by the BraTS 2021 dataset for each MRI, we apply the IS-Gen
repeatedly to represent the entire brain as a 128x128x128 volume to maintain
identical slice thickness for each scan. Thus we create a complete set of MRI
scans with uniform slice thickness. In this approach we always maintain a
fixed width of the brain when 64 images are selected for classification unlike
the baseline model.

We then fully normalize the scans by applying rotational transformation to
non-coronal images to coronal plane. Once the scans are normalized, the U-Net
based segmentation model as described in Section 3.3 is used to extract the
tumor regions. It is worth mentioning that the segmentation model is trained
using BraTS 2020 images in coronal plane. It is expected to perform better
since all classification input images are also normalized to the same plane.

With segmentation mask for each of the 128 slices in the tumor region of the
brain, we need to consider pros and cons of using only a subset of these masks
to be used for classification. One can pass in every slice where there is a
portion predicted as a tumor region. However, an imperfect segmentation model
can cause cases where several slices have small predictions of false tumor
regions. Figure 13 depicts an example of the segmentation model’s imprecise
prediction where a non-tumor region has been wrongly predicted as tumor. Using
such a slice for classification will deteriorate model’s performance.

Figure 13: An example false segmentation prediction.

Alternatively, we can sort each slice based on the size of the predicted mask
and choose a subset of the largest tumor regions for classification. However,
this could cause a non-continuous region of the brain to be passed in as
input. The non-continuous region would result in unrealistic and inaccurate
features to be extracted internally by the 3D convolutions.

We make the assumption that tumor region is a single and continuous region of
the brain. In order to maintain contiguity, we select the biggest tumor image
and then use the 64 images around this center image. We assume that 64 images
will adequately capture the entire tumor region without including too much
non-tumor region or excluding too much tumor region for classification. The
multistage intelligent tumor selection process is demonstrated in the
following Figure 14.

Figure 14: Intelligent image selection procedure used for Enhanced ResNet-10
input. The green star represents the center of the 64 selected images.

Finding the optimal selection of these images is a future area of our
research. For example, one could use a sliding window based algorithm to find
a continuous subset of images that will cover the tumor region with 95%
confidence.

We used the enhanced ResNet-10 for a direct comparison to the baseline model
results. We preprocessed the MRI scans just once before training and stored as
.npy files to prevent repeated computation. We then trained the model for 40
epochs while saving the model with the highest accuracy after the iteration.
We used a NVIDIA K80 GPU to train the model for computational efficiency. As
shown in in Table 7, we observed more than 6% increase in overall accuracy
relative to the baseline ResNet-10 model.

Accuracy | Sensitivity | Specificity | PPV | NPV | AUROC
---|---|---|---|---|---
0.664957265 | 0.783236383 | 0.533116883 | 0.654363102 | 0.746775701 | 0.663826516
Table 7: Average Cross Validation Results for Enhanced ResNet-10 Model.

##  4 Results and Discussion

Finally, we compile model performance results in tabular and graphical formats
in Table 8 and Figure 15, respectively. We notice that our proposed enhanced
ResNet-10 model outperforms the other three models we studied in all five
performance dimensions. Using Microsoft Excel’s Data Analysis package, we
conducted a 2-way ANOVA with 5 repetitions to compare the enhanced and
baseline ResNet-10 models, the top two performing models. The ANOVA result is
provided in Table 9 and confirms that the enhanced ResNet-10 outperforms the
Kaggle’s best model by a statistically significant margin ($p<0.05$).

| Accuracy | Sensitivity | Specificity | PPV | NPV | AUROC
---|---|---|---|---|---|---
Model 1 | 0.564 | 0.678 | 0.419 | 0.616 | 0.678 | 0.549
Model 2 | 0.607 | 0.771 | 0.402 | 0.637 | 0.567 | 0.586
Model 3 | 0.610 | 0.702 | 0.509 | 0.615 | 0.618 | 0.605
Model 4 | 0.665 | 0.783 | 0.533 | 0.654 | 0.747 | 0.664
Table 8: Model specific average cross validation results. Figure 15: Comparative plot of accuracy, sensitivity, specificity, PPV, NPV, and AUROC scores.  Source of Variation | F | P-value | F crit
---|---|---|---
Model Selection | 6.261825405 | 0.015796413 | 4.042652129
Table 9: 2-way ANOVA test results ($\alpha=0.05$).

By introducing the improvements in the enhanced model, we ensured that we
overcome the shortcomings of the baseline ResNet-10 model. These include
normalizing the slice thickness of the brain, maintaining a constant MRI
orientation in coronal plane, and intelligently selecting slices containing
the tumor region. By reducing the number of variables and enforcing focus on
the tumor region only, the enhanced ResNet-10 was able to learn more
effectively than the other models.

For the BraTS 2021 dataset, radiomic feature extraction did not show strong
correlations with MGMT promoter methylation. However, we were able to
determine that tumor location and shape characteristics were important
biomarkers for methylation prediction. Experimenting with the two radiomic
feature based models corroborated that the IS-Gen enhances the information
content and increases the quality of extracted radiomic features. This was
conclusively established with the statistical test described in Section 3.5.

It is worthwhile to note that many different approaches have been reported in
literature for classifying MGMT promoter methylation which did not utilize the
BraTS 2021 dataset. The reported results for these studies are summarized in
Table 10.

Author |  Performance |  Methodology |  Data Description
---|---|---|---
Ahn et al., (2014) |  Sensitivity - 0.56 Specificity - 0.85 AUROC - 0.756 |  Mann-Whitney and Chi-Square analysis on extracted image biomarkers. |  Dynamic contrast-enhanced MRI and Diffusion Weighted Imaging (DWI) from 43 patients.
Han and Kamdar, (2018) |  Accuracy - 0.61 Precision - 0.67 Recall - 0.67 |  Convolutional Recurrent Neural Network |  159 unique patient MRI scans acquired in 3 modalities from The Cancer Genome Atlas Glioblastoma Multiforme (TCGA-GBM) project. All scans were in the Axial plane. Scans contained varying slice thickness.
Sasaki et al., (2019) |  Accuracy - 0.67 Sensitivity - 0.66 Specificity - 0.66 PPV - 0.67 NPV - 0.67 |  Radiomic Feature Extraction + LASSO |  181 MRI scans in 3 different modalities collected from 10 institutions. Slice thicknesses for MRI scans were 1 mm.
Han et al., (2018) |  Accuracy - 0.805 Sensitivity - 0.857 Specificity - 0.852 AUROC - 0.877 |  Logistic Regression on extracted image biomarkers. |  Study used 77 patient data including 3 modalities of MRI scans in the axial orientation with 1.5 mm thickness. Also used DWI scans.
Le et al., (2020) |  Accuracy - 0.887 Sensitivity - 0.88 Specificity - 0.887 |  Radiomic Feature Extraction + XGBoost Classifier |  Used 262 MRI scans of 4 modalities acquired from the TCGA-GBM project. Do not account for varying slice thicknesses.
Table 10: Summary of existing models that experimented with clean MRI dataset.

Each author above uses different set of images to determine methylation
status. Two of them use DWI which is another form of MRI scans. A few of them
make use of the Apparent Diffusion Coefficient (ADC), a value clinically
calculated from DWI scans. The ADC is strongly correlated with the MGMT
methylation status. Some reported high performance with multimodal MRI scans
similar to those provided in the BraTS 2021 dataset. We assume that higher
accuracy is a result of using clean nature of the data used for training and
classification. For example, Le et al., (2020) used MRI scans acquired from
the TCGA-GBM project, a repository of MRI scans labelled with several genetic
labels. The authors do not take into account varying slice thicknesses and all
images are provided in a constant orientation.

We attempted to replicate the feature extraction process based on the top 9
radiomic features proposed in this paper. These included first order and GLRLM
radiomic values. We did not obtain high performance when applied to our messy
dataset. This indicates that the dataset selected could potentially contribute
to the level at which MGMT promoter methylation could be learned. The
Radiological Society of North America collected images from varying sources
without any standard extraction process defined. This can explain the
difference in results.

However, for a more consistent comparison to other research, we compared our
results to others studies utilizing the BraTS 2021 dataset. Similar to our
research Saeed et al., (2021) conducted their study after the Kaggle contest
was completed in 2021. Not surprisingly, they analyzed the Kaggle winner’s
solution and made optimizations to the winning solution.

| Accuracy | Sensitivity | Specificity | PPV | NPV | AUROC
---|---|---|---|---|---|---
Saeed et al., (2021) | - | - | - | - | - | 0.630
Pálsson et al., (2021) | - | - | - | - | - | 0.598
Kaggle Winner | 0.610 | 0.702 | 0.509 | 0.615 | 0.618 | 0.605
Proposed Model | 0.665 | 0.783 | 0.533 | 0.654 | 0.747 | 0.664
Table 11: Comparison with existing models using the BraTS 2021 dataset. Due to
the recent date of the competition, Saeed et al. and Palsson et al. have not
been peer reviewed.

Compared to the performance of models developed by prior research, our
proposed model exhibits a significantly higher AUROC score. In future we plan
to apply our methodology to the datasets described in Table 10 starting with
TCGA-GBM. Due to the fundamental changes in our approach, We expect that our
proposed model will work equally well or even better than the other models on
clean dataset.

##  5 Conclusion

This study presents a new preprocessing method that improves classification of
MGMT promoter methylation directly from MRI scans. We develop a method that
can be used to normalize MRI scans into one spatial plane with equal slice
thickness by artificially synthesizing missing slices. The proposed method can
be beneficial for other tasks aside from MGMT promoter methylation detection.
For example, diagnosis of GBM or Alzheimer’s Disease can be performed directly
from MRI scans (Islam and Zhang,, 2018). With the normalization procedure made
possible by the IS-Gen, these methodologies can also be applied to MRI scans
produced by a variety of different clinical conditions. The IS-Gen can be
adapted for wide range of deep learning models based on MRI scan analysis.

Furthermore, the IS-Gen algorithm is not just limited to MRI scans. It can be
applied to any three dimensional dataset to iteratively impute intermediary
data layers to form a more continuous volumetric dataset. For example, with
some update to IS-Gen algorithm, it could possibly be used to impute missing
frames in a video resulting in higher frames per second. This increases
clarity and smoothness of a video.

Although the IS-Gen proved to contribute additional information, the slices
were not always accurate. These inaccuracies caused granular images when
reoriented into the coronal plane. We intend to optimize the IS-Gen further by
adding more complex CNN feature extractors to increase details of the
predicted image. Additionally, we developed a method called On-Off training
for the IS-Gen; however, to increase IS-Gen output quality even further, we
can design a generator and discriminator to learn at similar rates to remove
the need for such training.

In the future, it may be possible to achieve increased performance by applying
only the IS-Gen, but removing the reorienting step used in the preprocessing
pipelines. This step was done because our segmentation model was trained on
MRI scans in the coronal plane. However, with a better segmentation model, we
could use only the IS-Gen to normalize slice thickness and pass in the MRI in
it original orientation state. Consequently, we would not lose any
segmentation accuracy and images would be crisp. Although this forces the
ResNet-10 to distinguish between the distinct orientations, it will likely
perform better due to higher image clarity. Finally, we will investigate if
improving the performance of the segmentation model further improves
prediction accuracy. Specifically, we plan to experiment with the best
performing segmentation model from BraTS challenge.

Figure 16: Impact of proposed model when extrapolated to global GBM
population.

Overall, our proposed improvements to the winning Kaggle solution exhibit a 6%
increase in accuracy relative to the prior state-of-the-art. Using statistics
provided by the GLOBOCAN 2020 report and sensitivity/specificity values for
the baseline and enhanced ResNet-10 models determined by cross-validation, we
were able to measure the impact of our proposed model to the global GBM
population of approximately 147,889. Specifically, the enhanced ResNet-10 is
able to correctly recommends chemotherapy treatment option to 46,141 patients
compared to only 41,409 patients by the baseline model. On the contrary, our
enhanced model correctly discourages chemotherapy for 47,029 patients compared
to only 45,254 patients by the baseline model. In other words, if both models
were used to predict cancer treatment in 2020, our proposed model would be
able to recommend the correct treatment option to approximately 6,507 more GBM
patients than the previous best. If the new model is clinically adopted, it
could bring remarkable change in the way GBM patients are treated increasing
the lifespan and quality of life for thousands of patients.

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deco | weak | $\\{1|00\frac{1}{2}\\}*$ | $6^{001}*$ | $2^{010}$ | $2^{1\bar{1}0}*$ |  |  |
$Z_{2}$ | ($0$$0$$0$) | $1$ | $1$ | $0$ | $1$ |  |  |
183.185 $P6mm$ Classification = $\mathbb{Z}_{M}^{2}$
deco | weak | $6^{001}$ | $Cm^{100}_{(0)}$ | $Cm^{\bar{1}20}_{(0)}$ |  |  |  |
$Z_{2}$ | ($0$$0$$0$) | $0$ | $1\bar{1}$ | $1\bar{1}$ |  |  |  |
M$(100;0)$ | ($0$$0$$0$) | $0$ | $2\bar{2}$ | $00$ |  |  |  |
M$(\bar{1}20;\frac{1}{2})$ | ($0$$0$$0$) | $0$ | $00$ | $2\bar{2}$ |  |  |  |
183.187 $P6^{\prime}m^{\prime}m$ Classification = $\mathbb{Z}_{M}$
deco | weak | $6^{001}*$ | $m_{\bar{1}20}*$ | $Cm^{100}_{(0)}$ |  |  |  |
$Z_{2}$ | ($0$$0$$0$) | $1$ | $0$ | $1\bar{1}$ |  |  |  |
M$(100;0)$ | ($0$$0$$0$) | $0$ | $0$ | $2\bar{2}$ |  |  |  |
183.188 $P6^{\prime}mm^{\prime}$ Classification = $\mathbb{Z}_{M}$
deco | weak | $6^{001}*$ | $m_{1\bar{1}0}*$ | $Cm^{\bar{1}20}_{(0)}$ |  |  |  |
$Z_{2}$ | ($0$$0$$0$) | $1$ | $0$ | $1\bar{1}$ |  |  |  |
M$(\bar{1}20;\frac{1}{2})$ | ($0$$0$$0$) | $0$ | $0$ | $2\bar{2}$ |  |  |  |
183.190 $P_{c}6mm$ Classification = $\mathbb{Z}_{M}^{2}$
deco | weak | $\\{1|00\frac{1}{2}\\}*$ | $6^{001}$ | $Cm^{100}_{(0)}$ | $Cm^{\bar{1}20}_{(0)}$ |  |  |
$Z_{2}$ | ($0$$0$$0$) | $1$ | $0$ | $1\bar{1}$ | $1\bar{1}$ |  |  |
M$(100;0)$ | ($0$$0$$0$) | $0$ | $0$ | $2\bar{2}$ | $00$ |  |  |
M$(\bar{1}20;\frac{1}{2})$ | ($0$$0$$0$) | $0$ | $0$ | $00$ | $2\bar{2}$ |  |  |
184.191 $P6cc$ Classification = $\mathbb{Z}_{2}$
deco | weak | $6^{001}$ | $g^{\bar{1}20}_{00\frac{1}{2}}$ | $g^{1\bar{1}0}_{00\frac{1}{2}}$ |  |  |  |
$Z_{2}$ | ($0$$0$$0$) | $0$ | $1$ | $1$ |  |  |  |
184.193 $P6^{\prime}c^{\prime}c$ Classification = $\mathbb{Z}_{2}$
deco | weak | $6^{001}*$ | $g^{\bar{1}20}_{00\frac{1}{2}}*$ | $g^{1\bar{1}0}_{00\frac{1}{2}}$ |  |  |  |
$Z_{2}$ | ($0$$0$$0$) | $1$ | $0$ | $1$ |  |  |  |
184.194 $P6^{\prime}cc^{\prime}$ Classification = $\mathbb{Z}_{2}$
deco | weak | $6^{001}*$ | $g^{\bar{1}20}_{00\frac{1}{2}}$ | $g^{1\bar{1}0}_{00\frac{1}{2}}*$ |  |  |  |
$Z_{2}$ | ($0$$0$$0$) | $1$ | $1$ | $0$ |  |  |  |
184.196 $P_{c}6cc$ Classification = $\mathbb{Z}_{2}$
deco | weak | $\\{1|00\frac{1}{2}\\}*$ | $6^{001}$ | $m_{\bar{1}20}*$ | $m_{1\bar{1}0}*$ |  |  |
$Z_{2}$ | ($0$$0$$0$) | $1$ | $0$ | $0$ | $0$ |  |  |
185.197 $P6_{3}cm$ Classification = $\mathbb{Z}_{M}$
deco | weak | $6^{001}_{00\frac{1}{2}}$ | $g^{\bar{1}20}_{00\frac{1}{2}}$ | $Cm^{100}_{(0)}$ |  |  |  |
$Z_{2}$ | ($0$$0$$0$) | $0$ | $1$ | $1\bar{1}$ |  |  |  |
M$(100;0)$ | ($0$$0$$0$) | $0$ | $0$ | $2\bar{2}$ |  |  |  |
185.199 $P6_{3}^{\prime}c^{\prime}m$ Classification = $\mathbb{Z}_{M}$
deco | weak | $6^{001}_{00\frac{1}{2}}*$ | $g^{\bar{1}20}_{00\frac{1}{2}}*$ | $Cm^{100}_{(0)}$ |  |  |  |
$Z_{2}$ | ($0$$0$$0$) | $1$ | $0$ | $1\bar{1}$ |  |  |  |
M$(100;0)$ | ($0$$0$$0$) | $0$ | $0$ | $2\bar{2}$ |  |  |  |
185.200 $P6_{3}^{\prime}cm^{\prime}$ Classification = $\mathbb{Z}_{2}$
deco | weak | $6^{001}_{00\frac{1}{2}}*$ | $g^{\bar{1}20}_{00\frac{1}{2}}$ | $m_{1\bar{1}0}*$ |  |  |  |
$Z_{2}$ | ($0$$0$$0$) | $1$ | $1$ | $0$ |  |  |  |
185.202 $P_{c}6_{3}cm$ Classification = $\mathbb{Z}_{M}$
deco | weak | $\\{1|00\frac{1}{2}\\}*$ | $6^{001}*$ | $m_{\bar{1}20}*$ | $Cm^{100}_{(0)}$ |  |  |
$Z_{2}$ | ($0$$0$$0$) | $1$ | $1$ | $0$ | $1\bar{1}$ |  |  |
M$(100;0)$ | ($0$$0$$0$) | $0$ | $0$ | $0$ | $2\bar{2}$ |  |  |
186.203 $P6_{3}mc$ Classification = $\mathbb{Z}_{M}$
deco | weak | $6^{001}_{00\frac{1}{2}}$ | $g^{1\bar{1}0}_{00\frac{1}{2}}$ | $Cm^{110}_{(0)}$ |  |  |  |
$Z_{2}$ | ($0$$0$$0$) | $0$ | $1$ | $1\bar{1}$ |  |  |  |
M$(110;\frac{1}{2})$ | ($0$$0$$0$) | $0$ | $0$ | $2\bar{2}$ |  |  |  |
186.205 $P6_{3}^{\prime}m^{\prime}c$ Classification = $\mathbb{Z}_{2}$
deco | weak | $6^{001}_{00\frac{1}{2}}*$ | $m_{\bar{1}20}*$ | $g^{1\bar{1}0}_{00\frac{1}{2}}$ |  |  |  |
$Z_{2}$ | ($0$$0$$0$) | $1$ | $0$ | $1$ |  |  |  |
186.206 $P6_{3}^{\prime}mc^{\prime}$ Classification = $\mathbb{Z}_{M}$
deco | weak | $6^{001}_{00\frac{1}{2}}*$ | $g^{1\bar{1}0}_{00\frac{1}{2}}*$ | $Cm^{110}_{(0)}$ |  |  |  |
$Z_{2}$ | ($0$$0$$0$) | $1$ | $0$ | $1\bar{1}$ |  |  |  |
M$(110;\frac{1}{2})$ | ($0$$0$$0$) | $0$ | $0$ | $2\bar{2}$ |  |  |  |
186.208 $P_{c}6_{3}mc$ Classification = $\mathbb{Z}_{M}$
deco | weak | $\\{1|00\frac{1}{2}\\}*$ | $6^{001}*$ | $m_{1\bar{1}0}*$ | $Cm^{\bar{1}20}_{(0)}$ |  |  |
$Z_{2}$ | ($0$$0$$0$) | $1$ | $1$ | $0$ | $1\bar{1}$ |  |  |
M$(\bar{1}20;\frac{1}{2})$ | ($0$$0$$0$) | $0$ | $0$ | $0$ | $2\bar{2}$ |  |  |
187.211 $P\bar{6}^{\prime}m^{\prime}2$ Classification = N/A
deco | weak | $\bar{6}^{001}*$ | $m_{\bar{1}20}*$ | $2^{1\bar{1}0}$ |  |  |  |
187.212 $P\bar{6}^{\prime}m2^{\prime}$ Classification = $\mathbb{Z}_{M}$
deco | weak | $\bar{6}^{001}*$ | $2^{1\bar{1}0}*$ | $Cm^{110}_{(0)}$ |  |  |  |
$Z_{2}$ | ($0$$0$$0$) | $0$ | $1$ | $1\bar{1}$ |  |  |  |
M$(110;\frac{1}{2})$ | ($0$$0$$0$) | $0$ | $0$ | $2\bar{2}$ |  |  |  |
188.217 $P\bar{6}^{\prime}c^{\prime}2$ Classification = N/A
deco | weak | $\bar{6}^{001}_{00\frac{1}{2}}*$ | $g^{\bar{1}20}_{00\frac{1}{2}}*$ | $2^{1\bar{1}0}$ |  |  |  |
188.218 $P\bar{6}^{\prime}c2^{\prime}$ Classification = $\mathbb{Z}_{2}$
deco | weak | $\bar{6}^{001}_{00\frac{1}{2}}*$ | $g^{\bar{1}20}_{00\frac{1}{2}}$ | $2^{1\bar{1}0}*$ |  |  |  |
$Z_{2}$ | ($0$$0$$0$) | $0$ | $1$ | $1$ |  |  |  |
189.223 $P\bar{6}^{\prime}2^{\prime}m$ Classification = $\mathbb{Z}_{M}$
deco | weak | $\bar{6}^{001}*$ | $2^{010}*$ | $Cm^{100}_{(0)}$ |  |  |  |
$Z_{2}$ | ($0$$0$$0$) | $0$ | $1$ | $1\bar{1}$ |  |  |  |
M$(100;0)$ | ($0$$0$$0$) | $0$ | $0$ | $2\bar{2}$ |  |  |  |
189.224 $P\bar{6}^{\prime}2m^{\prime}$ Classification = N/A
deco | weak | $\bar{6}^{001}*$ | $2^{010}$ | $m_{1\bar{1}0}*$ |  |  |  |
190.229 $P\bar{6}^{\prime}2^{\prime}c$ Classification = $\mathbb{Z}_{2}$
deco | weak | $\bar{6}^{001}_{00\frac{1}{2}}*$ | $2^{010}*$ | $g^{1\bar{1}0}_{00\frac{1}{2}}$ |  |  |  |
$Z_{2}$ | ($0$$0$$0$) | $0$ | $1$ | $1$ |  |  |  |
190.230 $P\bar{6}^{\prime}2c^{\prime}$ Classification = N/A
deco | weak | $\bar{6}^{001}_{00\frac{1}{2}}*$ | $2^{010}$ | $g^{1\bar{1}0}_{00\frac{1}{2}}*$ |  |  |  |
191.235 $P6/m^{\prime}mm$ Classification = $\mathbb{Z}_{M}^{2}$
deco | weak | $6^{001}$ | $2^{010}*$ | $i*$ | $2^{1\bar{1}0}*$ | $Cm^{100}_{(0)}$ | $Cm^{\bar{2}10}_{(0)}$ |
$Z_{2}$ | ($0$$0$$0$) | $0$ | $1$ | $0$ | $1$ | $1\bar{1}$ | $1\bar{1}$ |
M$(100;0)$ | ($0$$0$$0$) | $0$ | $0$ | $0$ | $0$ | $2\bar{2}$ | $00$ |
M$(\bar{2}10;0)$ | ($0$$0$$0$) | $0$ | $0$ | $0$ | $0$ | $00$ | $2\bar{2}$ |
191.241 $P6/m^{\prime}m^{\prime}m^{\prime}$ Classification = N/A
deco | weak | $6^{001}$ | $2^{010}$ | $i*$ | $2^{1\bar{1}0}$ | $m_{010}*$ |  |
192.245 $P6/m^{\prime}cc$ Classification = $\mathbb{Z}_{2}$
deco | weak | $6^{001}$ | $2^{010}_{00\frac{1}{2}}*$ | $i*$ | $2^{1\bar{1}0}_{00\frac{1}{2}}*$ | $g^{010}_{00\frac{1}{2}}$ |  |
$Z_{2}$ | ($0$$0$$0$) | $0$ | $1$ | $0$ | $1$ | $1$ |  |
192.251 $P6/m^{\prime}c^{\prime}c^{\prime}$ Classification = N/A
deco | weak | $6^{001}$ | $2^{010}_{00\frac{1}{2}}$ | $i*$ | $2^{1\bar{1}0}_{00\frac{1}{2}}$ | $g^{010}_{00\frac{1}{2}}*$ |  |
193.255 $P6_{3}/m^{\prime}cm$ Classification = $\mathbb{Z}_{M}$
deco | weak | $6^{001}_{00\frac{1}{2}}$ | $2^{010}_{00\frac{1}{2}}*$ | $i*$ | $2^{1\bar{1}0}*$ | $Cm^{100}_{(0)}$ |  |
$Z_{2}$ | ($0$$0$$0$) | $0$ | $1$ | $0$ | $1$ | $1\bar{1}$ |  |
M$(100;0)$ | ($0$$0$$0$) | $0$ | $0$ | $0$ | $0$ | $2\bar{2}$ |  |
193.261 $P6_{3}/m^{\prime}c^{\prime}m^{\prime}$ Classification = N/A
deco | weak | $6^{001}_{00\frac{1}{2}}$ | $2^{010}_{00\frac{1}{2}}$ | $i*$ | $2^{1\bar{1}0}$ | $m_{010}*$ |  |
194.265 $P6_{3}/m^{\prime}mc$ Classification = $\mathbb{Z}_{M}$
deco | weak | $6^{001}_{00\frac{1}{2}}$ | $2^{010}*$ | $i*$ | $2^{1\bar{1}0}_{00\frac{1}{2}}*$ | $g^{010}_{00\frac{1}{2}}$ | $Cm^{110}_{(0)}$ |
$Z_{2}$ | ($0$$0$$0$) | $0$ | $1$ | $0$ | $1$ | $1$ | $1\bar{1}$ |
M$(110;0)$ | ($0$$0$$0$) | $0$ | $0$ | $0$ | $0$ | $0$ | $2\bar{2}$ |
194.271 $P6_{3}/m^{\prime}m^{\prime}c^{\prime}$ Classification = N/A
deco | weak | $6^{001}_{00\frac{1}{2}}$ | $2^{010}$ | $i*$ | $2^{1\bar{1}0}_{00\frac{1}{2}}$ | $g^{010}_{00\frac{1}{2}}*$ |  |
195.1 $P23$ Classification = N/A
deco | weak | $3^{111}$ | $2^{100}$ |  |  |  |  |
195.3 $P_{I}23$ Classification = $\mathbb{Z}_{2}$
deco | weak | $\\{1|\frac{1}{2}\frac{1}{2}\frac{1}{2}\\}*$ | $3^{111}$ | $2^{100}$ |  |  |  |
$Z_{2}$ | ($0$$0$$0$) | $1$ | $0$ | $0$ |  |  |  |
196.4 $F23$ Classification = N/A
deco | weak | $3^{111}$ | $2^{100}$ |  |  |  |  |
196.6 $F_{S}23$ Classification = $\mathbb{Z}_{2}$
deco | weak | $\\{1|\frac{1}{2}\frac{1}{2}\frac{1}{2}\\}*$ | $3^{111}$ | $2^{100}$ |  |  |  |
$Z_{2}$ | ($0$$0$$0$) | $1$ | $0$ | $0$ |  |  |  |
197.7 $I23$ Classification = N/A
deco | weak | $3^{111}$ | $2^{100}$ |  |  |  |  |
198.9 $P2_{1}3$ Classification = N/A
deco | weak | $3^{111}$ | $2^{100}_{\frac{1}{2}\frac{1}{2}0}$ |  |  |  |  |
198.11 $P_{I}2_{1}3$ Classification = $\mathbb{Z}_{2}$
deco | weak | $\\{1|\frac{1}{2}\frac{1}{2}\frac{1}{2}\\}*$ | $3^{111}$ | $2^{100}_{00\frac{1}{2}}*$ |  |  |  |
$Z_{2}$ | ($0$$0$$0$) | $1$ | $0$ | $1$ |  |  |  |
199.12 $I2_{1}3$ Classification = N/A
deco | weak | $3^{111}$ | $2^{100}_{00\frac{1}{2}}$ |  |  |  |  |
200.16 $Pm^{\prime}\bar{3}^{\prime}$ Classification = N/A
deco | weak | $3^{111}$ | $2^{100}$ | $i*$ |  |  |  |
201.20 $Pn^{\prime}\bar{3}^{\prime}$ Classification = N/A
deco | weak | $3^{111}$ | $2^{100}_{0\frac{1}{2}\frac{1}{2}}$ | $i*$ |  |  |  |
202.24 $Fm^{\prime}\bar{3}^{\prime}$ Classification = N/A
deco | weak | $3^{111}$ | $2^{100}$ | $i*$ |  |  |  |
203.28 $Fd^{\prime}\bar{3}^{\prime}$ Classification = N/A
deco | weak | $3^{111}$ | $2^{100}_{0\frac{1}{4}\frac{1}{4}}$ | $i*$ |  |  |  |
204.32 $Im^{\prime}\bar{3}^{\prime}$ Classification = N/A
deco | weak | $3^{111}$ | $2^{100}$ | $i*$ |  |  |  |
205.35 $Pa^{\prime}\bar{3}^{\prime}$ Classification = N/A
deco | weak | $3^{111}$ | $2^{100}_{\frac{1}{2}\frac{1}{2}0}$ | $i*$ |  |  |  |
206.39 $Ia^{\prime}\bar{3}^{\prime}$ Classification = N/A
deco | weak | $3^{111}$ | $2^{100}_{00\frac{1}{2}}$ | $i*$ |  |  |  |
207.40 $P432$ Classification = N/A
deco | weak | $3^{111}$ | $4^{100}$ | $2^{110}$ |  |  |  |
207.42 $P4^{\prime}32^{\prime}$ Classification = $\mathbb{Z}_{2}$
deco | weak | $3^{111}$ | $4^{100}*$ | $2^{110}*$ |  |  |  |
$Z_{2}$ | ($0$$0$$0$) | $0$ | $1$ | $1$ |  |  |  |
207.43 $P_{I}432$ Classification = $\mathbb{Z}_{2}$
deco | weak | $\\{1|\frac{1}{2}\frac{1}{2}\frac{1}{2}\\}*$ | $3^{111}$ | $4^{100}$ | $2^{110}$ |  |  |
$Z_{2}$ | ($0$$0$$0$) | $1$ | $0$ | $0$ | $0$ |  |  |
208.44 $P4_{2}32$ Classification = N/A
deco | weak | $3^{111}$ | $4^{100}_{\frac{1}{2}\frac{1}{2}\frac{1}{2}}$ | $2^{110}_{\frac{1}{2}\frac{1}{2}\frac{1}{2}}$ |  |  |  |
208.46 $P4_{2}^{\prime}32^{\prime}$ Classification = $\mathbb{Z}_{2}$
deco | weak | $3^{111}$ | $4^{100}_{\frac{1}{2}\frac{1}{2}\frac{1}{2}}*$ | $2^{110}_{\frac{1}{2}\frac{1}{2}\frac{1}{2}}*$ |  |  |  |
$Z_{2}$ | ($0$$0$$0$) | $0$ | $1$ | $1$ |  |  |  |
208.47 $P_{I}4_{2}32$ Classification = $\mathbb{Z}_{2}$
deco | weak | $\\{1|\frac{1}{2}\frac{1}{2}\frac{1}{2}\\}*$ | $3^{111}$ | $4^{100}*$ | $2^{110}*$ |  |  |
$Z_{2}$ | ($0$$0$$0$) | $1$ | $0$ | $1$ | $1$ |  |  |
209.48 $F432$ Classification = N/A
deco | weak | $3^{111}$ | $4^{100}$ | $2^{110}$ |  |  |  |
209.50 $F4^{\prime}32^{\prime}$ Classification = $\mathbb{Z}_{2}$
deco | weak | $3^{111}$ | $4^{100}*$ | $2^{110}*$ |  |  |  |
$Z_{2}$ | ($0$$0$$0$) | $0$ | $1$ | $1$ |  |  |  |
209.51 $F_{S}432$ Classification = $\mathbb{Z}_{2}$
deco | weak | $\\{1|\frac{1}{2}\frac{1}{2}\frac{1}{2}\\}*$ | $3^{111}$ | $4^{100}$ | $2^{110}$ |  |  |
$Z_{2}$ | ($0$$0$$0$) | $1$ | $0$ | $0$ | $0$ |  |  |
210.52 $F4_{1}32$ Classification = N/A
deco | weak | $3^{111}$ | $4^{100}_{\frac{1}{4}\frac{1}{4}\frac{1}{4}}$ | $2^{110}_{\frac{1}{4}\frac{1}{4}\frac{1}{4}}$ |  |  |  |
210.54 $F4_{1}^{\prime}32^{\prime}$ Classification = $\mathbb{Z}_{2}$
deco | weak | $3^{111}$ | $4^{100}_{\frac{1}{4}\frac{1}{4}\frac{1}{4}}*$ | $2^{110}_{\frac{1}{4}\frac{1}{4}\frac{1}{4}}*$ |  |  |  |
$Z_{2}$ | ($0$$0$$0$) | $0$ | $1$ | $1$ |  |  |  |
210.55 $F_{S}4_{1}32$ Classification = $\mathbb{Z}_{2}$
deco | weak | $\\{1|\frac{1}{2}\frac{1}{2}\frac{1}{2}\\}*$ | $3^{111}$ | $4^{100}_{\frac{1}{4}\frac{1}{4}\frac{1}{4}}$ | $2^{110}_{\frac{1}{4}\frac{1}{4}\frac{1}{4}}$ |  |  |
$Z_{2}$ | ($0$$0$$0$) | $1$ | $0$ | $0$ | $0$ |  |  |
211.56 $I432$ Classification = N/A
deco | weak | $3^{111}$ | $4^{100}$ | $2^{110}$ |  |  |  |
211.58 $I4^{\prime}32^{\prime}$ Classification = $\mathbb{Z}_{2}$
deco | weak | $3^{111}$ | $4^{100}*$ | $2^{110}*$ |  |  |  |
$Z_{2}$ | ($0$$0$$0$) | $0$ | $1$ | $1$ |  |  |  |
212.59 $P4_{3}32$ Classification = N/A
deco | weak | $3^{111}$ | $4^{100}_{\frac{3}{4}\frac{3}{4}\frac{1}{4}}$ | $2^{110}_{\frac{1}{4}\frac{3}{4}\frac{3}{4}}$ |  |  |  |
212.61 $P4_{3}^{\prime}32^{\prime}$ Classification = $\mathbb{Z}_{2}$
deco | weak | $3^{111}$ | $4^{100}_{\frac{3}{4}\frac{3}{4}\frac{1}{4}}*$ | $2^{110}_{\frac{1}{4}\frac{3}{4}\frac{3}{4}}*$ |  |  |  |
$Z_{2}$ | ($0$$0$$0$) | $0$ | $1$ | $1$ |  |  |  |
212.62 $P_{I}4_{3}32$ Classification = $\mathbb{Z}_{2}$
deco | weak | $\\{1|\frac{1}{2}\frac{1}{2}\frac{1}{2}\\}*$ | $3^{111}$ | $4^{100}_{\frac{1}{4}\frac{1}{4}\frac{3}{4}}*$ | $2^{110}_{\frac{3}{4}\frac{1}{4}\frac{1}{4}}*$ |  |  |
$Z_{2}$ | ($0$$0$$0$) | $1$ | $0$ | $1$ | $1$ |  |  |
213.63 $P4_{1}32$ Classification = N/A
deco | weak | $3^{111}$ | $4^{100}_{\frac{1}{4}\frac{1}{4}\frac{3}{4}}$ | $2^{110}_{\frac{3}{4}\frac{1}{4}\frac{1}{4}}$ |  |  |  |
213.65 $P4_{1}^{\prime}32^{\prime}$ Classification = $\mathbb{Z}_{2}$
deco | weak | $3^{111}$ | $4^{100}_{\frac{1}{4}\frac{1}{4}\frac{3}{4}}*$ | $2^{110}_{\frac{3}{4}\frac{1}{4}\frac{1}{4}}*$ |  |  |  |
$Z_{2}$ | ($0$$0$$0$) | $0$ | $1$ | $1$ |  |  |  |
213.66 $P_{I}4_{1}32$ Classification = $\mathbb{Z}_{2}$
deco | weak | $\\{1|\frac{1}{2}\frac{1}{2}\frac{1}{2}\\}*$ | $3^{111}$ | $4^{100}_{\frac{1}{4}\frac{1}{4}\frac{3}{4}}$ | $2^{110}_{\frac{3}{4}\frac{1}{4}\frac{1}{4}}$ |  |  |
$Z_{2}$ | ($0$$0$$0$) | $1$ | $0$ | $0$ | $0$ |  |  |
214.67 $I4_{1}32$ Classification = N/A
deco | weak | $3^{111}$ | $4^{100}_{\frac{1}{4}\frac{1}{4}\bar{\frac{1}{4}}}$ | $2^{110}_{\bar{\frac{1}{4}}\frac{1}{4}\frac{1}{4}}$ |  |  |  |
214.69 $I4_{1}^{\prime}32^{\prime}$ Classification = $\mathbb{Z}_{2}$
deco | weak | $3^{111}$ | $4^{100}_{\frac{1}{4}\frac{1}{4}\bar{\frac{1}{4}}}*$ | $2^{110}_{\bar{\frac{1}{4}}\frac{1}{4}\frac{1}{4}}*$ |  |  |  |
$Z_{2}$ | ($0$$0$$0$) | $0$ | $1$ | $1$ |  |  |  |
215.72 $P\bar{4}^{\prime}3m^{\prime}$ Classification = N/A
deco | weak | $3^{111}$ | $\bar{4}^{100}*$ | $m_{110}*$ |  |  |  |
216.76 $F\bar{4}^{\prime}3m^{\prime}$ Classification = N/A
deco | weak | $3^{111}$ | $\bar{4}^{100}*$ | $m_{110}*$ |  |  |  |
217.80 $I\bar{4}^{\prime}3m^{\prime}$ Classification = N/A
deco | weak | $3^{111}$ | $\bar{4}^{100}*$ | $m_{110}*$ |  |  |  |
218.83 $P\bar{4}^{\prime}3n^{\prime}$ Classification = N/A
deco | weak | $3^{111}$ | $\bar{4}^{100}_{\frac{1}{2}\frac{1}{2}\frac{1}{2}}*$ | $g^{110}_{\frac{1}{2}\frac{1}{2}\frac{1}{2}}*$ |  |  |  |
219.87 $F\bar{4}^{\prime}3c^{\prime}$ Classification = N/A
deco | weak | $3^{111}$ | $\bar{4}^{100}_{\frac{1}{2}\frac{1}{2}\frac{1}{2}}*$ | $g^{110}_{\frac{1}{2}\frac{1}{2}\frac{1}{2}}*$ |  |  |  |
220.91 $I\bar{4}^{\prime}3d^{\prime}$ Classification = N/A
deco | weak | $3^{111}$ | $\bar{4}^{100}_{\frac{1}{4}\frac{1}{4}\bar{\frac{1}{4}}}*$ | $g^{110}_{\bar{\frac{1}{4}}\frac{1}{4}\frac{1}{4}}*$ |  |  |  |
221.96 $Pm^{\prime}\bar{3}^{\prime}m^{\prime}$ Classification = N/A
deco | weak | $3^{111}$ | $4^{100}$ | $i*$ | $2^{110}$ | $\bar{4}^{100}*$ | $m_{101}*$ |
222.102 $Pn^{\prime}\bar{3}^{\prime}n^{\prime}$ Classification = N/A
deco | weak | $3^{111}$ | $4^{100}_{0\frac{1}{2}0}$ | $i*$ | $2^{110}_{00\frac{1}{2}}$ | $\bar{4}^{100}_{0\frac{1}{2}0}*$ | $g^{101}_{0\frac{1}{2}0}*$ |
223.108 $Pm^{\prime}\bar{3}^{\prime}n^{\prime}$ Classification = N/A
deco | weak | $3^{111}$ | $4^{100}_{\frac{1}{2}\frac{1}{2}\frac{1}{2}}$ | $i*$ | $2^{110}_{\frac{1}{2}\frac{1}{2}\frac{1}{2}}$ | $\bar{4}^{100}_{\frac{1}{2}\frac{1}{2}\frac{1}{2}}*$ | $g^{101}_{\frac{1}{2}\frac{1}{2}\frac{1}{2}}*$ |
224.114 $Pn^{\prime}\bar{3}^{\prime}m^{\prime}$ Classification = N/A
deco | weak | $3^{111}$ | $4^{100}_{\frac{1}{2}0\frac{1}{2}}$ | $i*$ | $2^{110}_{\frac{1}{2}\frac{1}{2}0}$ | $\bar{4}^{100}_{\frac{1}{2}0\frac{1}{2}}*$ | $g^{101}_{\frac{1}{2}0\frac{1}{2}}*$ |
225.120 $Fm^{\prime}\bar{3}^{\prime}m^{\prime}$ Classification = N/A
deco | weak | $3^{111}$ | $4^{100}$ | $i*$ | $2^{110}$ | $\bar{4}^{100}*$ | $m_{101}*$ |
226.126 $Fm^{\prime}\bar{3}^{\prime}c^{\prime}$ Classification = N/A
deco | weak | $3^{111}$ | $4^{100}_{\frac{1}{2}\frac{1}{2}\frac{1}{2}}$ | $i*$ | $2^{110}_{\frac{1}{2}\frac{1}{2}\frac{1}{2}}$ | $\bar{4}^{100}_{\frac{1}{2}\frac{1}{2}\frac{1}{2}}*$ | $g^{101}_{\frac{1}{2}\frac{1}{2}\frac{1}{2}}*$ |
227.132 $Fd^{\prime}\bar{3}^{\prime}m^{\prime}$ Classification = N/A
deco | weak | $3^{111}$ | $4^{100}_{\frac{1}{4}0\frac{1}{4}}$ | $i*$ | $2^{110}_{\frac{1}{4}\frac{1}{4}0}$ | $\bar{4}^{100}_{\frac{1}{4}0\frac{1}{4}}*$ | $g^{101}_{\frac{1}{4}0\frac{1}{4}}*$ |
228.138 $Fd^{\prime}\bar{3}^{\prime}c^{\prime}$ Classification = N/A
deco | weak | $3^{111}$ | $4^{100}_{\frac{1}{4}\frac{1}{2}\frac{1}{4}}$ | $i*$ | $2^{110}_{\frac{1}{4}\frac{1}{4}\frac{1}{2}}$ | $\bar{4}^{100}_{\frac{1}{4}\frac{1}{2}\frac{1}{4}}*$ | $g^{101}_{\frac{1}{4}\frac{1}{2}\frac{1}{4}}*$ |
229.144 $Im^{\prime}\bar{3}^{\prime}m^{\prime}$ Classification = N/A
deco | weak | $3^{111}$ | $4^{100}$ | $i*$ | $2^{110}$ | $\bar{4}^{100}*$ | $m_{101}*$ |
230.149 $Ia^{\prime}\bar{3}^{\prime}d^{\prime}$ Classification = N/A
deco | weak | $3^{111}$ | $4^{100}_{\frac{1}{4}\frac{1}{4}\bar{\frac{1}{4}}}$ | $i*$ | $2^{110}_{\bar{\frac{1}{4}}\frac{1}{4}\frac{1}{4}}$ | $\bar{4}^{100}_{\frac{1}{4}\frac{1}{4}\bar{\frac{1}{4}}}*$ | $g^{101}_{\frac{1}{4}\frac{1}{4}\bar{\frac{1}{4}}}*$ |