Mathematical abilities in children: an sMRI analysis with radiomics

Brain areas related to mathematical abilities in children have been mainly assessed through their activation in fMRI, while volume-based analysis have been employed in sMRI to discover structural differences. However, a recent technique in precision medicine allows to enhance the sMRI analysis by extracting a large number of features, also called radiomics, related to shape, intensity and texture from specific areas. In the present study, a structural neuroimaging analysis based on radiomics and machine learning models is presented with the aim of identifying brain areas related to different mathematical tests. A total of 77 schoolaged children from third to sixth grade were administered four mathematical tests: Math Fluency, Calculation, Applied Problems and Concepts as well as a structural brain imaging scan. The results confirmed and extended the involvement of brain areas found in sMRI and fMRI literature such as the frontal, parietal, temporal and occipital cortex, as well as basal ganglia and limbic system areas. For these areas, texture features were the most informative while volume repreV. Pina Faculty of Education, Economics and Technology in Ceuta. University of Granada. Cortadura del Valle s.n., 51001 Ceuta, Spain. V. M. Campello · K. Lekadir · S. Segúı Departament de Matemàtiques i Informàtica. Universitat de Barcelona. Gran Via de les Corts Catalanes, 585, 08007 Barcelona, Spain. J. M. Garćıa-Santos Radiology Service. Morales Meseguer Hospital. Av. Marqués de los Vélez s.n., 30008 Murcia, Spain. L. J. Fuentes Faculty of Psychology. University of Murcia. Campus Universitario de Espinardo, 30100 Murcia, Spain. E-mail: lfuentes@um.es sented less than 15% of the shape information. These findings emphasize the potential of radiomics for a more in-depth analysis of medical images for the identification of brain areas related to mathematical performance. The code used to obtain these results can be found at github.com/vicmancr/MathBrainRadiomics.


Introduction
Recent research has focused on determining the cognitive processes that are associated with mathematical performance, as well as the brain areas involved. The goal is not only to reach a more comprehensive understanding of how children and adults solve mathematical problems but also to better characterize disorders that affect mathematical abilities.
A bulk of evidence is currently available showing crucial brain areas related to mathematical abilities, with functional magnetic resonance imaging (fMRI) studies outweighing structural magnetic resonance imaging (sMRI) ones (Peters and Smedt 2017). fMRI studies have revealed active parietal and frontal areas, involved in attention and working memory (WM) when children perform mathematical tasks (Eriksson et al. 2015;Gazzaley et al. 2004). For instance, the right parietal lobe along with the cingulate gyrus and frontal areas, such as the left superior frontal gyrus, left inferior frontal gyrus (IFG), and right medial frontal gyrus (MFG), would be involved in calculation tasks, whereas the insula and claustrum are related to intrinsic motivation when performing mathematical tasks that require attentional effort (Arsalidou et al. 2017;Houdé et al. 2010). The relationship between attention/working memory and mathematical performance has further been established in some cognitive-training studies with children (Sánchez-Pérez et al. 2018).
Similar findings have also been reported with sMRI. Recent voxel-based morphometry (VBM) approaches, which measure the volume of white and gray matter, found that children with poor mathematical abilities showed reduced gray matter volume in several brain areas related to number processing, attentional control, and memory, such as the posterior parietal cortex, including the intraparietal sulcus (IPS), frontal areas such as IFG and MFG, hippocampal areas, and occipito-temporal areas (Fritz et al. 2019;Peters and Smedt 2017). Also, VBM has revealed that reduced gray matter in the left IPS, an area that is involved in attention, numerical processing and working memory, is associated with higher levels of mathematical anxiety (Hartwright et al. 2018). However, VBM techniques are prone to registration errors and inter-subject variability.
In the present study a radiomics approach is investigated for deeper analysis. Radiomics refers to a type of image analysis mainly applied in the field of precision medicine, that allows researchers to perform a more exhaustive analysis of medical images, by computing and mining a large pool (thousands) of advanced imaging features (Gillies et al. 2016). Thus far, radiomics-based analyses have been carried out mostly in oncology, and more recently for lung and cardiovascular applications (Guerrisi et al. 2020;Huang et al. 2016;Raisi-Estabragh et al. 2020). To date, few studies have explored this technique in the area of psychology (Chaddad et al. 2017;Sun et al. 2018;Cui et al. 2020). sMRI based techniques applied to mathematical performance have focused primarily on the analysis of volumetric measures, whereas radiomics includes additional shape and texture features that may provide extra value for the identification of brain areas involved in predicting children's mathematical abilities. Here, we describe a radiomicsbased approach to identify the structural brain areas involved in different mathematical abilities in schoolaged children.

Participants
One hundred and four 7 to 12 year-old children that participated in a larger project (Sánchez-Pérez et al. 2018), took part in the present neuroimaging study. Children were recruited from two primary education schools in the Región de Murcia (Spain), and were enrolled in grades 3 to 6. Data were collected from mathematical standardized tests and sMRI. The final sample reduced to 77 children (43 boys and 34 girls, mean age 9.7; SD 1.2), after excluding: data with excessive motion, children that refused to enter into the scanner at the moment of scanning, or equipment failures. The K-Bit test (Kaufman and Kaufman 1990) was administered to verify that all children had average intelligence. Children with special educational needs were not included in the overarching study.
The project was approved by the Ethics Committee of the University of Murcia and it was conducted in accordance with the approved guidelines and the Declaration of Helsinki. Written informed consent was obtained from the parents, and oral consent from the children at the moment of scanning.

Behavioral data
Mathematical ability tests. Children's math abilities were assessed through the Woodcock-Johnson III (WJ-III) Achievement battery for children aged 6 to 13 years in Spain (Diamantopoulou et al. 2012). It comprises four tests: Math Fluency, Calculation, Applied Problems, and Quantitative Concepts. Descriptive data are shown in Table 1. Math Fluency measures the ability to quickly solve a total of 160 simple addition, subtraction, and multiplication within 3 minutes. Calculation measures the ability to perform simple mathematical computations including 46 ascending difficulty addition, subtraction, multiplication, and division. Applied Problems measures the ability to analyze and solve 62 ascending difficulty math word problems. Quantitative Concepts measures the knowledge about mathematical concepts, symbols, vocabulary and numerical series in 57 items (Pina et al. 2015;Sánchez-Pérez et al. 2018). The scoring for all items was 0 (incorrect) and 1 (correct). The final score for each subtest is the sum of all correct answers.

Image Analysis
Several pre-processing steps were conducted prior to the cortical parcellation and features extraction (see Figure 1). First of all, possible low frequency intensity inhomogeneities were corrected using N4 Bias Field correction (

2017) with the default configuration (bin width of 25).
To see the complete list of extracted features see Table  3 in the supplementary material.
Machine learning-based area ordering In order to discover which brain areas are more involved for the mathematical tests under consideration, a regression-based analysis, with age as control variable, is proposed for predicting the final subtest score. For each regression and for each area, a prediction error is extracted using the absolute deviation from the real score (Mean Absolute Error, MAE), allowing the ordering of areas from more to less predictive. A Random Forest (RF) regression model is proposed to account for linear and non-linear relations of brain areas characteristics with mathematical abilities. This model reduces the prediction variance while preventing over-fitting with the increase of decision trees, becoming optimal for this dataset. Default values were used as hyperparameters for each model (100 decision trees, as in scikit-learn version 0.22.1), but for a maximum of 5 decision steps to prevent decision trees from being too specific for the training sample. Due to the rather small sample size and the large input feature space, a feature selection was conducted for each area during training. The final set of variables were selected sequentially, one by one. At each step, we removed the variables that had a squared correlation coefficient over 0.8 with the selected variable (see Figure 2). The final selected features accounted for a percentage in between 81% and 39% of the initial features, depending on the area under consideration. The selected features together with age were used as input variables. Fig. 2: Example of a correlation matrix for radiomics features before and after the feature reduction for a given area, showing significant reduction in the number of correlated features.
For each test and each area, the following pipeline was used to ensure the robustness of the final results (see Figure 3): (1) 20 random partitions of the dataset in training (80%) and testing (20%) were generated, (2) 100 different RF regression models were trained on each partition and the median MAE was extracted, and (3) the resulting MAE was obtained as the median across the 20 partitions. The median was chosen over the mean due to its robustness against outliers.

Results
For each mathematical test the most predictive and significant areas were selected. To do this, the resulting mean absolute errors (MAEs) were assumed to follow a normal distribution and those areas with an error below two standard deviations from the mean (p < 0.022) were classified as "most relevant". Then, the p-value associated to these areas was obtained comparing their performance against the noise distribution, obtained with the same methodology using random features as input variables. Results below three standard deviations from the noise distribution mean (p < 0.01) were classified as significant. Table 2 summarizes the final selected areas for each test.
For the Math Fluency test (Figure 4a), five areas were found below the two-sigma threshold with high significance (ps < 0.0014%), involving the two brain hemispheres. In particular, the right lateral sulcus (sylvian fissure), the left intraparietal sulcus and the right postcentral gyrus in the parietal lobe and the middle frontal sulci bilaterally.
For the Calculation test (Figure 4b), five areas were selected with a significance level ps between 0.0052 and 0.0015 from both hemispheres. The most relevant region was the left accumbens area, followed by the left middle cingulate gyrus and sulcus, the right suborbital sulcus, the right cuneus gyrus and the right postcentral gyrus .  For the Applied Problems test (Figure 5a), two very significant regions were obtained (ps < 0.000013%). In particular, the right rectus gyrus and the right inferior frontal gyrus were found.
Finally, for the Concepts test (Figure 5b), three areas from the left hemisphere were found with significance levels below 0.0029. In particular, the parahip- pocampal gyrus was the most relevant area, followed by the angular gyrus and Hesch gyrus.
In order to find out the relevance of each type of features for each of the brain areas analyzed, the Gini importance for age, shape, intensity, and texture features was calculated (see Figure 6). The area volume, used mainly in VBM, was considered apart from shape features, to assess its contribution independently. Our results show that texture features provide more information about areas, followed by shape and intensity features. Importantly, volume represents less than 15% of the shape features contribution in all cases.

Discussion
Most of sMRI studies that have explored the brain areas involved in mathematical abilities used mainly volume. However, by using a radiomics-based analysis we have demonstrated that volume contribution to identify the brain areas that predict children's math abilities is minimal compared with texture, shape and intensity measures. In particular, texture features are the most informative variables per area in our analysis. These features quantify the local heterogeneity of tissues often unrecognizable through visual assessment (Larroza et al. 2016) and have been found to be important biomarkers for cognitive traits such as autism spectrum disorder (Chaddad et al. 2017) or schizophrenia (Park et al. 2020).
Until now, fewer studies have used sMRI volume analysis in mathematical abilities and these have provided less information than fMRI activation analysis. Overall, our results highlight the involvement of frontal, and parietal cortex mainly but also temporal and occipital cortex, as well as basal ganglia and limbic system areas. According to fMRI studies, these areas seem to play a role in mathematical operations as well as in cognitive control and motivation (Arsalidou et al. 2017).
Math Fluency is based on basic arithmetic operations that depend on recovery of number facts from long-term memory (Andersson 2008), and therefore is expected to pose minimal demands on participants' attentional/WM capacity. Inferior frontal (IF) cortex, medial frontal (MF) cortex and parietal (PSTCG) cortex, mainly from the right hemisphere, are involved in mathematical abilities that are mainly based on automatized processes (Arsalidou et al. 2017). The left IPS plays also a central role in basic quantitative representation (Dehaene et al. 2004) and in addition and subtraction (Arsalidou and Taylor 2011), representing the basis of the Math Fluency test. In addition, the left frontoparietal network (MF cortex, IPS) might have been recruited to deal with the increased attentional effort required by the time constraint imposed by the test. Reduced attentional resources might explain why the left MF area shows lower volume in children with mathematical learning disorder (Rotzer et al. 2008) and reduced left IPS gray matter in children with math anxiety (Hartwright et al. 2018).  Calculation is based on the quick activation of the numerical magnitude of Arabic numerals, and arithmetic operations go in increasing order of complexity. Therefore, as with Math Fluency, important areas of the right frontal and parietal lobes involved in numerical automatized processes are also observed (the suborbital sulci, SS and postcentral gyrus, PSTCG), but more complex operations might recruit the posterior cingulate cortex, an area involved in memory retrieval (Rolls 2019). In addition, the involvement of the basal ganglia may be related to important motivational/affective components linked to the performance of this test. Accordingly, the NA has been associated with motivational behavior, and effort regulation (Salamone 1994;Nicola et al. 2005;Salamone et al. 2006). The involvement of the cuneus gyrus can be attributed to the visual recognition of objects but the involvement of the right cuneus gyrus has been related to the approximate calculation in children in previous studies .
Applied Problems requires both to hold information in memory and to integrate new information with previous one (Swanson 2011;Pina et al. 2014), and therefore it is expected to impose more demands on executive control capacity than the two previous tests. In accordance, in our case the SG and OIF seem to be implicated. SG is involved in attention control and its functions are integrated with the orbital cortex (Nestor et al. 2015). Liu et al. 2019 observed bilateral implication of the IF gyrus and the SG in arithmetic principles versus computation. Additionally, previous studies showed the involvement of the frontal lobe, specifically bilateral activation of the IF gyri, in mathematical word problems (Prabhakaran et al. 2001). Studies with larger sample sizes, and thus with greater statistical power, are needed to confirm the bilateral activation of these areas in sMRI with the presented methodology.
Finally, the Concepts test assesses the mathematical knowledge (e.g., formulas and terms) and quantitative reasoning. Poor performance on this test is expected when participants show limited vocabulary or insufficient conceptual development (Pina et al. 2015). Accordingly, brain areas involved in this test are lateralized in the left hemisphere, which could reflect a language mediation role (Grabner et al. 2007). Concretely, PHPG participates in remembering facts and rules (Squire et al. 2004) and this area has been proposed to maintain memory representations during the tests (Rivera et al. 2005). The left AG located near the IPS has been related to the language required in some arithmetic operations that use verbal coding or are based on verbally stored knowledge (Grabner et al. 2007). Finally, an important result is the involvement of HG which corresponds to the primary auditory cortex. This area was expected because only for this test were the statements read aloud, and just a drawing was available for each test item. Thus, children needed to be attentive to verbal information.
Our results involve different brain areas depending on the processes required by the different mathematical abilities, and the main areas observed agree with those observed in both functional and structural MRI studies. However, the present study has addressed the issue from a broader and novel perspective. First, we have used an ample range of mathematical tests that differ not only in the specific mathematical abilities, but also in the degree of complexity the arithmetic operations convey and the demands on participants' mental-attentional capacity. This makes the present study an important contribution to better understanding the brain areas that better predict the diverse skills required when people face mathematical facts. Also, despite the sample used here might be rather small (although clearly superior to other neuroimaging approaches), to the best of our knowledge, this is the first study that analyzes mathematical performance in school aged children with radiomics through sMRI images. The open-sourced radiomicsbased analysis proposed in this study can be easily automated and therefore potentially used by researchers and clinicians to make the most of radiological studies.
github.com/vicmancr/MathBrainRadiomics. Data will be available upon request to either the first author or the corresponding author.