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\begin{document}

\title{Multi-parameter-based Radiological Diagnosis of Chiari Malformation
using Machine Learning Technology}



\author[1]{Bora  Tetik}%
\author[2]{Güleç Mert Doğan}%
\author[1]{Ramazan Paşahan}%
\author[1]{Mehmet Akif Durak}%
\author[1]{Emek Güldoğan}%
\author[1]{Kaya  Saraç}%
\author[1]{Çağatay Önal}%
\author[1]{Ismail Okan Yıldırım}%
\affil[1]{İnönü Üniversitesi}%
\affil[2]{Malatya Eğitim ve Araştırma Hastanesi}%


\vspace{-1em}



  
  \date{May 24, 2024}


\begingroup
\let\center\flushleft
\let\endcenter\endflushleft
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\selectlanguage{english}
\begin{abstract}
Background: The known primary radiological diagnosis of Chiari
Malformation-I (CM-I) is based on the degree of tonsillar herniation (
TH) below the Foramen Magnum (FM). However, recent data also shows the
association of such malformation with smaller posterior cranial fossa
(PCF) volume and the anatomical issues regarding the Odontoid. This
study presents the achieved result regarding some detected potential
radiological findings that may aid CM-I diagnosis using several machine
learning (ML) algorithms. Materials and Methods: Between 2011 and 2020,
radiological examinations of 100 clinically/radiologically proved
symptomatic CM-I cases and 100 control were evaluated by matching age
and gender. A team of Neuroradiologists had reviewed the MR images of
the study population. A total of 11 different radiological parameters
were assessed for CM-I diagnosis. The parameters were defined and
examined in 5 designed different ML algorithms. Statistical analysis was
conducted for data analysis. Results: The mean age of patients was
29.92 \selectlanguage{ngerman}±\selectlanguage{english} 15.03 years. The primary presenting symptoms were headaches
(62\%). Syringomyelia and retrocurved-odontoid were detected in 34\% and
8\% of patients, respectively. All of the morphometric measures were
significantly different between the groups, except for the distance from
the dens axis to the posterior margin of FM. The Radom Forest model is
found to have the best 1.0 (14 of 14) ratio of accuracy in regard to 14
different combinations of morphometric features. Conclusion: This study
indicates the potential usefulness of ML-guided PCF measurements, other
than TH, that may be used to predict and diagnose CM-I accurately. Our
results support the view of TH as a single radiological parameter may
fail during the diagnosis of CM-I. Combining two or three preferable
osseous structure-based parameters may increase the accuracy of
radiological diagnosis of CM-I.%
\end{abstract}\selectlanguage{ngerman}%



\sloppy


\textbf{Multi-parameter-based Radiological Diagnosis of Chiari
Malformation using Machine Learning Technology}

\textbf{Abstract}

\textbf{Background:} The known primary radiological diagnosis of Chiari
Malformation-I (CM-I) is based on the degree of tonsillar herniation (
TH) below the Foramen Magnum (FM). However, recent data also shows the
association of such malformation with smaller posterior cranial fossa
(PCF) volume and the anatomical issues regarding the Odontoid. This
study presents the achieved result regarding some detected potential
radiological findings that may aid CM-I diagnosis using several machine
learning (ML) algorithms.

\textbf{Materials and Methods:} Between 2011 and 2020, radiological
examinations of 100 clinically/radiologically proved symptomatic CM-I
cases and 100 control were evaluated by matching age and gender. A team
of Neuroradiologists had reviewed the MR images of the study population.
A total of 11 different radiological parameters were assessed for CM-I
diagnosis. The parameters were defined and examined in 5 designed
different ML algorithms. Statistical analysis was conducted for data
analysis.

\textbf{Results:} The mean age of patients was 29.92 \selectlanguage{ngerman}±\selectlanguage{english} 15.03 years. The
primary presenting symptoms were headaches (62\%). Syringomyelia and
retrocurved-odontoid were detected in 34\% and 8\% of patients,
respectively. All of the morphometric measures were significantly
different between the groups, except for the distance from the dens axis
to the posterior margin of FM. The Radom Forest model is found to have
the best 1.0 (14 of 14) ratio of accuracy in regard to 14 different
combinations of morphometric features.

\textbf{Conclusion:} This study indicates the potential usefulness of
ML-guided PCF measurements, other than TH, that may be used to predict
and diagnose CM-I accurately. Our results support the view of TH as a
single radiological parameter may fail during the diagnosis of CM-I.
Combining two or three preferable osseous structure-based parameters may
increase the accuracy of radiological diagnosis of CM-I.

\textbf{Key Words:} Chiari Malformation; Machine Learning; posterior
fossa; tonsillar herniation.

\textbf{What is already known about this topic?}

Chiari malformation (CM) is known as the malformation of varying degrees
of the descent of the brain stem and cerebellum below the foramen magnum
(FM). The most common form of CM is type I, the elongation of the
tonsils of the cerebellum into the upper cervical canal. Although this
situation is usually presented as an incidental radiological finding,
many symptoms may also guide the practitioner to such a diagnosis. The
known primary radiological diagnosis of CM-I is relied on the degree of
tonsillar herniation (TH) below the FM. However, recent data also shows
the association of such malformation with smaller posterior cranial
fossa (PCF) volume and the anatomical issues regarding the Odontoid.
Recent studies suggest more radiological criteria that may aid to the
diagnosis of CM.

\textbf{What does this article add?}

Machine learning (ML) is one of the traditional methods of computer
systems that help to recognize and detect patterns in organizational and
commercial decisions (e.g., underlying dimensions/subgroups, nonlinear
associations/patterns, and so on). This situation can be used in
differentiation, classifying, and organizing many health problems. ML
offers an opportunity to overcome obstacles using conventional
statistical methods. This study presents the achieved results regarding
some detected potential radiological findings that may aid CM-I
diagnosis using several ML algorithms.

\textbf{Introduction}

Hans Chiari was the first who defined the term Chiari malformation (CM)
in 1891, specifying the malformation of varying degrees of the descent
of the brain stem and cerebellum below the foramen magnum (FM) (1). The
most common form of CM is type I, the elongation of the tonsils of the
cerebellum into the upper cervical canal. Although this situation is
usually presented as an incidental radiological finding, many symptoms
may also guide the practitioner to such a diagnosis (2).

The prevalent belief is that CM-I could result from an intrinsically
smaller overcrowded posterior fossa that predisposes the upper cervical
spine to eventual herniation of the cerebellar tonsils, resulting in
altered dynamics of Cerebrospinal fluid (CSF) flow (3). The known
primary radiological diagnosis of CM-I is relied on the degree of
tonsillar herniation (TH) below the FM. However, recent data also shows
the association of such malformation with smaller posterior cranial
fossa (PCF) volume and the anatomical issues regarding the Odontoid
(4-7). Recent studies suggest more radiological criteria that may aid to
the diagnosis of CM (5, 6, 7, 16, 18, 21).

Machine learning (ML) is one of the traditional methods of computer
systems that help to recognize and detect patterns in organizational and
commercial decisions (e.g., underlying dimensions/subgroups, nonlinear
associations/patterns, and so on) (8). This situation can be used in
differentiation, classifying, and organizing many health problems. ML
offers an opportunity to overcome obstacles using conventional
statistical methods.

This study presents the achieved results regarding some detected
potential radiological findings that may aid CM-I diagnosis using
several ML algorithms.

\textbf{Materials and Methods}

\textbf{Patient and Study Characteristics}

Between 2011 and 2020, the Neurosurgery Department database in Malatya
Inonu University, School of Medicine was searched to evaluate 100
patients with clinically and radiologically proved symptomatic CM-I
diagnosis. Also sex and age were matched to patients with normal MRI
reports to form the control group. Patients with missing clinical data
or with a history of prior cranial surgery were excluded from the study.

The study was approved by the Ethical Committee of Malatya Clinical
Researches in Malatya, Turkey (Protocol number: 2021/104). Since the
patients were retrospectively chosen and the MR images examined were
fully de-identified, the analysis did not require any informed consent.

\textbf{Magnetic Resonance Imaging (MRI) Protocol}

Three experienced Neuroradiologists who are blinded to patients' data
reviewed the MR images (1.5 T; Siemens, Magnetom-Avantou, Germany) of
all patients in the study, and 10 measurements other than TH were
obtained from this study. On repeated tests, high intraobserver
reliability was demonstrated (with 95 percent confidence intervals) in
20 randomly selected situations. Both the CM-I (n=100) and control
(n=100) groups were evaluated regarding the axial, sagittal and coronal
T1 and T2 weighted MRIs. The measurements were obtained manually from
the mid-sagittal images. These measurements consisted of; F1: Tonsillar
herniation; F2: Distance from the pons to FM; F3: Distance from corpus
callosum to FM; F4: Distance from Fastigium to FM; F5: Distance from the
pons to dens axis; F6: Distance from corpus callosum to dens axis; F7:
Distance from Fastigum to dens axis; F8: Distance from dorsum sella to
dens axis; F9: Clivus length; F10: Distance from dens axis to posterior
margin of FM; F11: Clivus canal angle (Weckenheim line- posterior
vertebral body line) (Figure 1).

\textbf{Supervised Machine Learning Models}

In the current study, each data point in the training set includes a
vector (X, Y), where X denotes the feature vector of\((x_{1},\ x_{2},\ \ldots,\ x_{n})\)
and Y expresses the output feature that takes values 0 (absence of CM)
and 1 (presence of CM). The following five supervised ML models were
constructed on the feature vectors of several sizes \((1,\ 2,\ \ldots,\ 11)\).
Single and the combined features achieved from the best performed
classifiers were constructed for each measurement.

\emph{XGBoost (Extreme Gradient Boosting) algorithm:} Xgboost is an
algorithm that employs a gradient boosting decision tree and can compute
boosted trees efficiently in parallel. XgBoost divides its tree models
into regression and classification trees (9). The biggest advantage of
XGBoost is its scalability in all situations. The method for measuring
timing helps to simulate distributed real-time applications with
millions of simultaneous connections. The efficacy of XGBoost is owing
to various well-differentiated systems and algorithmic optimizations. A
novel tree learning method is used to handle sparse data, and a
technically justified weighted quantile sketch technique is implemented
in approximate tree learning to handle instance weights (10). The
details of the XGBoost can be achieved from the relevant study (10).

\emph{Stochastic Gradient Boosting (SGB):} Gradient boosting is a
supervised machine learning approach for regression and classification
issues in the SGB algorithm, which creates a predictive model using a
collection of weak learners/classifiers, usually decision trees. SGB
builds the model in a stage-wise manner and constructs additive
regression models by fitting a simple parameterized function (base
learner) to the current pseudo-residuals by at least squares at each
iteration. The pseudo-residuals are the minimization of the functional
loss gradient. It's worth noting that integrating randomization into the
technique improves gradient boosting's approximation accuracy and
execution speed. For prediction models, the SGB parameters (depth of
interaction, tension number, and shrinkage) were optimized as soon as
possible (11). The entire information on the SGB was reported by the
related study (12).

\emph{Bagged classification and regression trees (Bagged CART):} CART
has been widely utilized for ML modeling with adequate results,
including potential prediction of the diseases in health field. As the
CART is regarded as an unstable model, the bagging method can
significantly increase its precision. The bagged CART effectively
eliminates the variance in estimation and greatly improves accuracy and
over-fitting of classification. Thus, it is predicted that promising
results can be obtained by employing the bagged CART in the new
application of potential classification problems (13). A comprehensive
explanation for the bagged CART was given in the concerned reference
(14).

\emph{Random Forest (RF):} An ensemble method, which constructs several
decision trees that will be used by the majority vote to classify a new
case, is Random Forest. A subset of attributes selected randomly from
the whole original set of attributes is used by each decision tree node.
Additionally, in the same way as bagging, each tree uses a different
bootstrap sample data. Besides, Random Forest is a technique that is
computer-efficient and can run rapidly over large datasets. It has been
used in diverse domains in many recent research projects and real-world
applications (14). The details of the Random Forest was introduced with
the relevant paper (15).

\emph{Logistic Regression (LR):} Logistic regression analysis is used to
obtain an ''odds ratio'' that incorporates two or more
covariates/features. The process is similar to multiple linear
regression, except that the response attribute is predicted from a
binomial distribution. The data and the results of each variable
indicate the strength of each predictor on the observed outcome of
interest. This method can be used to estimate the
probability\(P(Y\ |\ X)\) for an observation point of X and
considers a different transformation of a linear combination for the
input features. Here,\(\left(Y=1\ \right|X)=\frac{1}{\left[1+e^{-\left(b_{0}+b_{1}x_{1}+\ldots+b_{n}x_{n}\right)}\right]}\), where \(b_{0},\ b_{1},\ \ldots,\ b_{n}\) are
parameters of the model, which are calculated from the training stage
with maximum likelihood technique (16,17).

\textbf{Validation and performance evaluation}

Validation of the algorithms were performed using five-fold
cross-validation method. Hyperparameters of the interested models were
tuned by random search optimization in the current study. We computed
the following performance metrics to measure the quality of a classifier
using five -fold cross-validation: Accuracy, sensitivity, specificity,
positive/negative predictive values, F-measure, and G-mean. All
performance metrics were calculated through DTROC software. The
supervised ML algorithms mentioned earlier were implemented using R
Studio of R programming language.

\textbf{Statistical Analysis}

IBM SPSS Statistics 26.0 software was utulized for the analysis.
Quantitative data were given as mean, standard deviation, \%95
confidence intervals (CI), and qualitative data were given as numbers
(percentages). Conformity to normal distribution was made using the
Shapiro-Wilk test. Mann-Whitney U test, Independent Sample t-Test, and
Spearman Chi-square test were used in statistical analyzes as
appropriate. All results were reported in line with APA style. A p-value
of \textless{}0.05 was regarded as statistically significant.

\textbf{Results}

A total of 200 radiological examinations was evaluated in this work.
Table 1 represents the baseline characteristics of the CM-I group. The
mean age was 29.92\selectlanguage{english} +-\selectlanguage{english} 15.03 years, and the study population consisted of
55 females and 45 males. The primary presenting symptoms were headache
(62\%), neck pain (30\%), sensorial disturbance (18\%), and paraparesis
(15\%). Syringomyelia and retro-odontoid were detected in 34\% and 8\%
of patients, respectively.

The measured parameters were identified to ML algorithms, and all of the
morphometric measures were significantly different between the groups,
except for the distance from dens axis to posterior margin of FM (F10).
Table 2 represents the statistics regarding the measured parameters.

For the first parameter (F1) XGBoost, SGB, Bagged CART, Random Forest,
and Logistic Regression values were found to be 100\% as expected. For
the other parameters (F2-11), the most accurate values were 0.88 for F6
and F10 (Random Forest model), 0.87 for F5 (Random Forest model), and
0.86 for F2 (Random Forest model). The accuracy of the Logistic
Regression model for F2-11 was calculated as 0.89, whereas it was 100\%
for other models. Detailed data are presented in Table 3.

The results indicate that the Random Forest model has produced the best
1.0 (14 of 14) ratio of accuracy regarding 14 different combinations of
morphometric features. This ratio is found to be 0.50, 0.29, 0.21, and
0.07 in the Bagged CART, Stochastic Gradient Boosting, XGBoost, and
Logistic Regression models, respectively.

\textbf{Discussion}

Recent clinical and experimental studies have underlined the TH in CM-I
due to embryological developmental anomalies in the occipital bone and a
hypoplastic PCF (5,6,7,18,19). However, tonsillar herniation as a single
radiological diagnostic criterion for CM-I is insufficient and more
parameters are needed to prevent under or misdiagnosis. A reported study
by Alperin et al. identified four measures that distinguished CM-I
patients from a healthy cohort with 97 percent sensitivity and 100
percent specificity (4). Another study produced a probability predictor
based on a logistic regression (LR) model that took into account seven
PCF measures and had a sensitivity of 93\% and specificity of 92\% in
distinguishing patients with classic CM-I from those with a standard PCF
(16).

Many studies have searched for alternatives or adjunct diagnostic
radiological parameters for CM-I (4,5,16,20-23). In our study, a large
CM-I population was compared with a sex-age matched control group using
5 different supervised ML programs. The primary aim was to detect the
test with the most accurate result and minimal parameters.

Machine learning is a potential diagnostic tool that may be used in many
disorders. The quality of each classifier was tested using three-fold
cross-validation. Also, calculation of the variable importance for the
features can be divided into model-based and model-independent
approaches. The benefit of using a model-based method is that it is more
closely related to the performance of the model and that the association
structure between the predictors can be integrated into the estimation
of significance. Based on the advantages of model-based methods, we used
this approach for calculating the variable importance in the current
study.

It has been shown that cross-validation techniques significantly improve
the outcome of the models by helping to choose the best coefficients
taken into consideration for the model (24). To boost the efficiency of
the models, k-fold cross-validation is employed in the training stage.
In the present study, three-fold cross-validation was utulized for
assessing the predictive power of the supervised ML models. The random
search optimization approach deals with techniques for a given problem
to achieve the 'most favorable' solution and selects the most relevant
features with the output variable.

Bagged CART (F4\&F11) and Random Forest (F2\&F11) methods have revealed
a success rate of 98\% using two different parameters. This ratio
increased to 100\% when a third parameter was included in the analysis.
Also, the diagnostic ratio of the XGBoost method was 99\% using three
parameters (F2, F4, and F6) but increased to 100\% when a fourth
parameter was included. These results reflect the usefulness and
accuracy of such ML systems. The Random Forest method is found to be the
most accurate test using the parameters of distance from the pons to FM
(F2); fastigium to FM (F4), and Clivus canal angle (F11). This outcome
supports the latest report by Urbizu et al. but with augmented accuracy
(16). The high diagnostic ratio of our methods seems to be due to the
matched control group and the use of advanced ML algorithms.

It is known that the posterior basicranium undergoes retroflexion during
the fetal phase, pushing the basion upward and dorsally and decreasing
the PCF~ventral depth (25). Any developmental problem during this phase,
as the spheno-occipital synchondrosis closes, may impede the normal
growth of the basilar portion of the occipital bone until the 2nd decade
of life (25). In our study, the distance from Fastigum to FM (F4) was
the standard parameter that was used and obtained higher accuracy. This
result may support the suggested role of the decreased ventral depth of
PCF and hypoplastic PCF in CM-I etiology (2,5,6,7,18,21,25) .

It was suggested that the basion and the dens might grow in the embryo
jointly (sclerotome resegmentation), supporting the theory that a shift
in the location of the basion could result in a concomitant change in
the dens position, leading to more craniocervical changes in these
patients (26). This relation was concluded as a necessity to include the
Odontoid in such measurements (16). In our study, the Odontoid was
included as a parameter but provided different values of accuracy that
in Random Forest test no change was observed; but in Bagged CART test,
the value of accuracy was increased and decreased in different
combinations. Also, inclusion of clival and Corpus Callosum measurements
was found to increase the classification accuracy. The crowded PCF and
CSF dynamics may decrease the reliability of mobile points like pons
when compared with osseous structures like Clivus, dorsum sella and
odontoid. These findings should be evaluated in cooperation with
literature-based data that support the role of crowded PCF in the
etiology of CM-I (5,27,28,29).

The optimal surgical management of CM-I is still controversial.
Posterior fossa decompression with or without duroplasty is the most
recommended surgery (28, 30-32). However, our results may guide further
studies that anteriorly localized structures seem to influence the PCF
and etiology of CM-I as much as posterior ones. This may also aid
different surgical approaches and management ways.

Regarding the limitation of the study, even statistically matched, the
dominance of female cases in the study population might be considered as
a minor bias. A larger and more homogenous study population may be more
appropriate. Also, TH was calculated using midsagittal MR images,
excluding any possible asymmetry regarding parasagittal structures that
may influence symptomatology. Larger studies may be designed in order to
exclude any possible difference in race and regional factors that may
have an effect on morphometric anatomy.

\textbf{Conclusion}

Our study indicates the potential usefulness of ML-guided PCF
measurements, other than TH, that may be used to predict and diagnose
CM-I accurately. Our results support the view of TH as a single
radiological parameter may fail during the diagnosis of CM-I. Combining
two or three preferable osseous structure-based parameters may increase
the accuracy of radiological diagnosis of CM-I.

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106: 329-330.

32. Zhao JL, Li MH, Wang CL, Meng W: A systematic review of Chiari I
malformation: techniques and outcomes. World Neurosurg 2016; 88: 7--14

\textbf{Table 1.} Basic clinical characteristics of the CM-I group

\textbf{Demographics}\selectlanguage{english}
\begin{longtable}[]{@{}lll@{}}
\toprule
\textbf{Characteristic} & \selectlanguage{ngerman}\textbf{Mean ± SD} & \selectlanguage{ngerman}\textbf{Mean ±
SD}\tabularnewline
Age at diagnosis & 29.92 \selectlanguage{ngerman}±\selectlanguage{english} 15.03 & 29.92 \selectlanguage{ngerman}±\selectlanguage{english} 15.03\tabularnewline
\textbf{Characteristic} & \textbf{n} & \textbf{\%}\tabularnewline
Male & 55 & 55.0\tabularnewline
Female & 45 & 45.0\tabularnewline
\textbf{Signs and Symptoms} & \textbf{Signs and Symptoms} &
\textbf{Signs and Symptoms}\tabularnewline
\textbf{Characteristic} & \selectlanguage{ngerman}\textbf{Mean ± SD} & \selectlanguage{ngerman}\textbf{Mean ±
SD}\tabularnewline
Time elapsed from onset (mo) & 111.33\selectlanguage{ngerman}± 118.75 & 111.33\selectlanguage{ngerman}±
118.75\tabularnewline
\textbf{Characteristics} & \textbf{n} & \textbf{\%}\tabularnewline
Hydrosyringomyelia & 34 & 34.0\tabularnewline
Retrocurved odontoid & 8 & 8.0\tabularnewline
Headaches & 62 & 62.0\tabularnewline
Occipital headache/cervicalgia & 30 & 30.0\tabularnewline
Dizziness & 9 & 9.0\tabularnewline
Vertigo & 8 & 8.0\tabularnewline
Visual alterations & 3 & 3.0\tabularnewline
Kyphoscoliosis & 8 & 8.0\tabularnewline
Sensory loss & 18 & 18.0\tabularnewline
Motor weakness & 12 & 12.0\tabularnewline
Gait disturbances & 13 & 13.0\tabularnewline
Paresthesia/pain upper limbs & 13 & 13.0\tabularnewline
Paresthesia/pain lower limbs & 15 & 15.0\tabularnewline
\textbf{Therapeutic procedures} & \textbf{Therapeutic procedures} &
\textbf{Therapeutic procedures}\tabularnewline
\textbf{Characteristic} & \textbf{n} & \textbf{\%}\tabularnewline
Surgical treatment & 50 & 50.0\tabularnewline
\bottomrule
\end{longtable}

\textbf{Table 2.} Baseline characteristics of the study sample per the
groups\selectlanguage{english}
\begin{longtable}[]{@{}lllllllll@{}}
\toprule
\textbf{~Feature} & \textbf{Group} & \textbf{Group} & \textbf{Group} &
\textbf{Group} & \textbf{Group} & \textbf{Group} & \textbf{Group} &
\textbf{Group}\tabularnewline
\midrule
\endhead
& \textbf{Non-CM-I} \textbf{n=100} & \textbf{Non-CM-I} \textbf{n=100} &
\textbf{Non-CM-I} \textbf{n=100} & \textbf{Non-CM-I} \textbf{n=100} &
\textbf{CM-I} \textbf{n=100} & \textbf{CM-I} \textbf{n=100} &
\textbf{CM-I} \textbf{n=100} & \textbf{CM-I}
\textbf{n=100}\tabularnewline
& \textbf{Mean} & \textbf{SD} & \textbf{95.0\% Lower CL for Mean} &
\textbf{95.0\% Upper CL for Mean} & \textbf{Mean} & \textbf{SD} &
\textbf{95.0\% Lower CL for Mean} & \textbf{95.0\% Upper CL for
Mean}\tabularnewline
F\textsubscript{1} & -3.1\textsubscript{a} & 2.1 & -3.5 & -2.7 &
12.2\textsubscript{b} & 6.1 & 11.0 & 13.4\tabularnewline
F\textsubscript{2} & 40.5\textsubscript{a} & 4.2 & 39.7 & 41.4 &
33.9\textsubscript{b} & 5.2 & 32.9 & 35.0\tabularnewline
F\textsubscript{3} & 60.8\textsubscript{a} & 3.6 & 60.1 & 61.5 &
56.4\textsubscript{b} & 5.5 & 55.3 & 57.5\tabularnewline
F\textsubscript{4} & 27.0\textsubscript{a} & 2.9 & 26.4 & 27.6 &
22.7\textsubscript{b} & 4.6 & 21.8 & 23.6\tabularnewline
F\textsubscript{5} & 49.2\textsubscript{a} & 4.6 & 48.3 & 50.1 &
44.0\textsubscript{b} & 6.1 & 42.8 & 45.2\tabularnewline
F\textsubscript{6} & 65.8\textsubscript{a} & 3.8 & 65.1 & 66.6 &
61.5\textsubscript{b} & 5.7 & 60.4 & 62.7\tabularnewline
F\textsubscript{7} & 30.0\textsubscript{a} & 3.4 & 29.4 & 30.7 &
26.3\textsubscript{b} & 4.3 & 25.5 & 27.2\tabularnewline
F\textsubscript{8} & 47.5\textsubscript{a} & 4.5 & 46.6 & 48.4 &
46.1\textsubscript{b} & 4.6 & 45.2 & 47.0\tabularnewline
F\textsubscript{9} & 37.8\textsubscript{a} & 3.1 & 37.2 & 38.5 &
35.0\textsubscript{b} & 3.5 & 34.3 & 35.7\tabularnewline
F\textsubscript{10} & 36.6\textsubscript{a} & 3.8 & 35.8 & 37.3 &
36.3\textsubscript{a} & 5.6 & 35.2 & 37.4\tabularnewline
F\textsubscript{11} & 158\textsubscript{a} & 6 & 157 & 159 &
146\textsubscript{b} & 12 & 143 & 148\tabularnewline
Age & 29.9 & 15.0 & 27 & 33 & 29.9 & 15 & 15.0 & 33\tabularnewline
\textbf{Gender} & \textbf{n} & \textbf{\%} & & & \textbf{n} &
\textbf{\%} & &\tabularnewline
1 & 45 & 45.0 & & & 45 & 45.0 & &\tabularnewline
2 & 55 & 55.0 & & & 55 & 55.0 & &\tabularnewline
\bottomrule
\end{longtable}

Values in the same row and subtable not sharing the same subscript are
significantly different at p\textless{} .05 in the two-sided test of
equality for column means by APA style.

\textbf{Table 3:} Accuracy values of single and combined morphometric
measurements for the best performed classifiers\selectlanguage{english}
\begin{longtable}[]{@{}llllll@{}}
\toprule
\textbf{Feature(s)} & \textbf{XGBoost} & \textbf{Stochastic Gradient
Boosting} & \textbf{Bagged CART} & \textbf{Random Forest} &
\textbf{Logistic Regression}\tabularnewline
\midrule
\endhead
F\textsubscript{1} & 1 & 1 & 1 & 1 & 1\tabularnewline
F\textsubscript{2} & 0.845 & 0.82 & 0.855 & 0.86 & 0.74\tabularnewline
F\textsubscript{3} & 0.775 & 0.82 & 0.83 & 0.835 & 0.68\tabularnewline
F\textsubscript{4} & 0.83 & 0.815 & 0.835 & 0.84 & 0.69\tabularnewline
F\textsubscript{5} & 0.78 & 0.735 & 0.865 & 0.87 & 0.66\tabularnewline
F\textsubscript{6} & 0.805 & 0.845 & 0.875 & 0.88 & 0.69\tabularnewline
F\textsubscript{7} & 0.77 & 0.8 & 0.825 & 0.83 & 0.7\tabularnewline
F\textsubscript{8} & 0.785 & 0.755 & 0.785 & 0.795 & 0.57\tabularnewline
F\textsubscript{9} & 0.79 & 0.785 & 0.835 & 0.835 & 0.675\tabularnewline
F\textsubscript{10} & 0.84 & 0.85 & 0.88 & 0.88 & 0.555\tabularnewline
F\textsubscript{11} & 0.81 & 0.81 & 0.815 & 0.815 & 0.785\tabularnewline
Accuracy of the combined features achieved from the best performed
classifiers & Accuracy of the combined features achieved from the best
performed classifiers & Accuracy of the combined features achieved from
the best performed classifiers & Accuracy of the combined features
achieved from the best performed classifiers & Accuracy of the combined
features achieved from the best performed classifiers & Accuracy of the
combined features achieved from the best performed
classifiers\tabularnewline
2 & 0.99 & 0.84 & 0.98 & 0.98 & 0.815\tabularnewline
~3 & 0.955 & 0.84 & 1 & 1 & 0.82\tabularnewline
~4 & 1 & 0.895 & 1 & 1 & 0.815\tabularnewline
~5 & 0.995 & 0.975 & 1 & 1 & 0.835\tabularnewline
~6 & 0.995 & 0.89 & 0.995 & 1 & 0.865\tabularnewline
~7 & 1 & 0.775 & 1 & 1 & 0.875\tabularnewline
Features combination for the best performed classifiers & Features
combination for the best performed classifiers & Features combination
for the best performed classifiers & Features combination for the best
performed classifiers & Features combination for the best performed
classifiers & Features combination for the best performed
classifiers\tabularnewline
2 & 4,2 & 2,5 & 11,4 & 11,2 & 11,6\tabularnewline
~3 & 4,2,6 & 2,5,4 & 11,4,6 & 11,2,4 & 11,6,9\tabularnewline
~4 & 4,2,6,5 & 2,5,4,6 & 11,4,6,3 & 11,2,4,6 & 11,6,9,3\tabularnewline
~5 & 4,2,6,5,9 & 2,5,4,6,3 & 11,4,6,3,7 & 11,2,4,6,5 &
11,6,9,3,2\tabularnewline
~6 & 4,2,6,5,9,7 & 2,5,4,6,3,9 & 11,4,6,3,7,5 & 11,2,4,6,5,3 &
11,6,9,3,2,4\tabularnewline
7 & 4,2,6,5,9,7,8 & 2,5,4,6,3,9,8 & 11,4,6,3,7,5,9 & 11,2,4,6,5,3,10 &
11,6,9,3,2,4,8\tabularnewline
\bottomrule
\end{longtable}

\textbf{Figure Legends}

\textbf{Figure 1.} Sagittal T1-weighted MR images show the measurements
of structures related to posterior cranial fossa morphology. The numbers
represent the measured distance: 1. Tonsillar herniation; 2. Distance
from pons to FM; 3. Distance from corpus callosum to FM; 4. Distance
from Fastigium to FM; 5. Distance from pons to dens axis; 6.Distance
from corpus callosum to dens axis; 7. Distance from Fastigum to dens
axis; 8. Distance from dorsum sella to dens axis; 9. Clivus length; 10.
Distance from dens axis to posterior margin of FM; 11. Clivus canal
angle (Weckenheim line- posterior vertebral body line).

\textbf{Table 1.} Basic clinical characteristics of the CM-I group

\textbf{Table 2.} Baseline characteristics of the study sample per the
groups

\textbf{Table 3:} Accuracy values of single and combined morphometric
measurements for the best performed classifiers\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/Fig/Fig}

\end{center}
\end{figure}

\selectlanguage{english}
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