Lihan Wang, Honghong Liu, Weijia Liu, Qunxi Dong, Bin Hu
Abstract: The advantages of structural magnetic resonance imaging (sMRI)-based multidimensional tensor morphological features in brain disease research are the high sensitivity and resolution of sMRI to comprehensively capture the key structural information and quantify the structural deformation.However, its direct application to regression analysis of high-dimensional small-sample data for brain age prediction may cause “dimensional catastrophe”.Therefore, this paper develops a brain age prediction method for high-dimensional small-sample data based on sMRI multidimensional morphological features and constructs brain age gap estimation (BrainAGE) biomarkers to quantify abnormal aging of key subcortical structures by extracting subcortical structural features for brain age prediction, which can then establish statistical analysis models to help diagnose Alzheimer’s disease and monitor health conditions, intervening at the preclinical stage.
Keywords: brain age gap estimation (BrainAGE); Alzheimer’s disease (AD); structural magnetic resonance imaging (sMRI)
By 2019, the number of people with Alzheimer’s disease (AD) in China had been more than 10 million.It is estimated that by 2050, among every 85 people worldwide, there will be one person who suffers from Alzheimer’s disease [1].The risk of a person suffering from AD would double every five years.It can effectively reduce morbidity through early assessment and early intervention [2].An important characteristic of AD is the brain structure deformation.So early recognition of quantitative abnormal brain structure changes has great significance to prospect identification and improve treatment effects of patients at risk for cognitive decline.AD in general can be divided into the preclinical stage, the stage of mild cognitive impairment (MCI), and the stage of dementia [3].
Structural magnetic resonance imaging(sMRI) can get a high resolution of the human brain structure invasively.Many studies explore the AD-related biomarkers based on the sMRI,and brain age has been an emerging biomarker because of its good interpretation for AD pathology [4].Brain age can better predict the transition from MCI to AD by comparative analysis of the difference between brain age and actual age compared to traditional biomarkers.Meanwhile,an important symptom of AD is the morphological degeneration of brain structure, and sMRI can clearly show the internal structure of the brain, which is universal in the case of different field strengths and scanners.The aging process of the brain is a largely irreversible process resulting from the random accumulation of various types of neuro-degeneration, but the process is individualized heterogeneous with differences in both the type and extent of brain damage sustained by individuals [5].Therefore, the aging process of the brain is not completely synchronized with the physiological aging, but there are many different manifestations such as slow aging,normal aging, and accelerated aging of the brain.The main pipeline is to use the sMRI structure features of the normal control as independent variables and the chronological age as the dependent variables, to simultaneously establish a high-dimensional regression model by using the method of machine learning.This model transfers the quantitative image features to an easyunderstanding biomarker, that is brain age.Based on this constructed model, each new sample image data corresponds to a brain age and a chronological age.The difference between the brain age and chronological age, brain age gap estimation (BrainAGE), reflects the AD risk of this sample [6].
The BrainAGE index is a good indicator of the heterogeneous damage that exists during the neurodegeneration progress.Corresponding to this metric, the average BrainAGE of healthy controls with normal aging generally converges to 0.A BrainAGE greater than 0 indicates that the brain is older than its actual age, while a BrainAGE less than 0 indicates that the brain is younger.Based on this biomarker, researchers may be able to identify individuals at higher risk before they have a clinical condition and treat them with interventions before they experience a cognitive decline.Varikuti et al.[7] proposed a feature dimensionality reduction method based on nonnegative matrix factorization (NNMF) for brain age estimation.Wang et al.[8] conducted a longitudinal analysis of the open access series of imaging studies (OASIS) and Alzheimer’s disease neuroimaging initiative (ADNI) datasets by using a brain age prediction framework.It showed that accelerated brain aging leads to a decline in the expected cognitive ability.Gaser et al.[9] used the whole brain voxel features based on structural magnetic resonance images to train a brain age prediction model, and analyzed the predictive effect of brain age biomarkers and other traditional biomarkers for the transition from MCI to AD, showing that brain age biomarkers can better predict the transition from MCI to AD.Erickson et al.[10] used extracted hippocampal volume features from sMRI to build a brain age regression model and found a correlation between the predicted brain age from this regression model and the brain-derived neurotrophic factor in statistical analysis.Most current brain age studies take a global approach,that is, using the whole brain or the whole gray matter data to generate predicted age values in individual brains [11], which cannot effectively exploit the key brain structural features associated with AD.Thus it is necessary to develop higher precision brain structural feature extraction methods to better predict the brain age.
The advantages of sMRI-based multidimensional tensor morphological features in this study are their high accuracy, comprehensive capture of key structural information of the brain, and quantification of structural deformation, but no relevant techniques for the brain age prediction based on sMRI multidimensional tensor morphological features have been published.Current brain age prediction methods are not specifically designed to extract the critical information of multidimensional tensor morphological features of subcortical structures.If they were directly applied to regression analysis of high-dimensional small samples, they would cause “dimensional catastrophe”[12].The number of sMRI with an abnormal brain age is usually much higher than that of sMRI in healthy subjects.Therefore, the number of samples available for the model training and testing is much smaller than the dimensionality of the feature vector,which is one of the difficulties in this field to obtain ideal models based on available samples.
Therefore, the paper develops a brain age prediction method for high-dimensional small sample data based on sMRI multidimensional tensor morphological features, and constructs Brain-AGE biomarkers to quantify abnormal aging of key subcortical structures, which in turn can be used to build statistical analysis models to help diagnose AD and monitor health conditions for early-intervention.This study will significantly reduce the incidence of AD.
This paper contains the following parts: 1)Acquire the sample sMRI and construct the dataset for training and testing; 2) Perform the pre-processing, including alignment, correction,and smoothing; 3) Construct the model, including feature extraction, dimensionality reduction,building the model, and the performance analysis.Fig.1 is a flow chart of the overall idea.
Fig.1 Brain age prediction based on sMRI multidimensional tensor morphological features
2.1 Constructing the Dataset
T1-w sMRI of healthy subjects is screened from OASIS-1 and OASIS-3, the public database of neuroimaging of the brain, and the sMRI of healthy subjects covering a large range of age values was screened to form the dataset, ensuring that the age distribution of the subjects conformed to a normal distribution and covered a large range of age values to obtain the sample dataset.In Tab.1 the division of the dataset used in this example and the distribution of its demographic characteristics are given.
Tab.1 Classification of the dataset and its distribution of demographic characteristics
2.2 Pre-Processing
2.2.1 Building the Data Set
We selected images of three subcortical structures, hippocampus, amygdala, and voxel nucleus.Three independent sub-images of the hippocampus, amygdala, and voxel nucleus structures were automatically segmented in all T1-w sMRI using FIRST, an integrated library development tool for existing FMRIB Software Library software.(version 6.0, open source software; https://fsl.fmrib.ox.ac.uk/fsl/fslwiki)
2.2.2 sMRI Spatial Normalization
Linear variation was chosen to normalize the sample segmentation image.Here the normalization methods for different sub-images can be different, which means that the sample segmented images of different regions of interest can be processed separately in different standard spaces,but the sample standard space of the same region of interest from different samples should be identical [13].
2.2.3 Bias Field Correction
The brightness differences in sMRI may be caused by factors such as the scanner and bias in the scanning process, and failure to correct the bias field may result in the inaccurate output of imaging processing results.Perform position and image intensity correction for each of the sample standard segmentation images to obtain the corresponding sample target sMRI respectively, and perform the head movement correction alignment to facilitate the subsequent accurate extraction of multiple tensor morphological features on the standard segmented images of individual samples.The image intensity correction is then performed and the image intensity is balanced using a histogram equalization algorithm [14, 15].
2.2.4 Smooth Surface
The Gaussian smoothing function is applied to deconvolute and blur the data in space to eliminate and smooth out the subtle differences in the structural pieces of different samples.This method can eliminate noise, improve image quality, reduce interference, and provide satisfactory smoothing effect.
2.2.5 Quality Check
The shape of the structure of the interest in the sMRI of the sample target obtained from processing is rigorously checked to ensure that the normalized structural morphology matches the actual structural morphology, thus excluding segmentation errors and inaccurate structures.Fig.2 shows morphological diagrams of the three tissues.
Fig.2 Morphological diagrams of the three tissues
3.1 Feature Extraction
In the feature extraction stage, the multidimensional tensor morphological features of three subcortical structures (hippocampus, amygdala and nucleus accumbens) were extracted and the feature matrix was constructed using the Multivariate tensor-based subcortical morphometry(TBM) system [16].The system consists of three steps: the surface alignment, the feature computation, and the heat kernel smoothing [17].Then the training and test sets are divided.
3.2 Feature Dimension Reduction
The feature reduction stage includes a feature coding based on deep dictionary learning and a feature selection based on correlation analysis.A three-layer deep dictionary learning coding framework is constructed to sparsely encode the feature matrices of the three structures, and then the feature selection strategy based on correlation analysis is used to filter the feature of the sparsely encoded feature matrices, finally controlling the number of features and the number of samples to the same order of magnitude.
3.3 Prediction of Brain Age
In the brain age prediction phase, three independent optimal gradient-enhanced brain age prediction models were first trained for three subcortical structures: hippocampus, amygdala, and nucleus accumbens [18].
Taking hippocampus as an example, a 10-fold cross-validation scheme (9-fold for the training set and 1-fold for the validation set) was used to tune the parameters of the brain age prediction model on the training set after feature reduction for the training and test sets.The scheme was repeated 10 times to select the parameters with the best regression performance assessment to construct the optimal brain age prediction modelFM(xi).It used the gradient augmented regression model based onl1loss, and the regression model constructed is
wherehm(xi) is the estimator included in the gradient augmented regression model, also known as the weak learner.Mdenotes the number of estimators and the model uses a fixed size decision tree regressor as the weak learner.The training goal of the model is to make the predicted valueyˆiapproximate the true ageyi.
To better combine the features of the three subcortical structures for brain age prediction, a linear regression model was used to find the best linear combination of three independent brain age prediction models to predict brain age.The linear regression model is
whereyis the final predicted brain age, andxis a 3×1 input feature vector representing the predicted brain age of the three subcortical structures of hippocampus, amygdala and vomeronasal nucleus alone.wis the linear regression model parameter vector to be fitted.bis the bias, andwis fitted on the training set.The final predicted brain age is obtained by multiplying the three predicted brain ages obtained from the reduced-dimensional test set on three independent prediction models with the fitted parameterw.
3.4 Model Performance Analysis
The sMRI test set was used on the brain age prediction model obtained in Section 3.3 to evaluate the model’s predictive effect.Mean absolute error(MAE) was used to assess the error between the predicted brain age and the true physiological age.If the evaluation results do not meet the predefined conditions, the training is continued using other training samples according to the previous steps until the conditions are met.yˆiis the predicted brain age of theisamples andyiis the corresponding true physiological age.The MAE onntest samples is defined as
The coefficient of determinationR2was used to assess the degree of correlation and fit between predicted brain age and true physiological age,and thus the effect of the brain age prediction regression model.If the sample size is not very large, a largerR2indicates a better model fit.The results of the brain age prediction assessment using the three subcortical structures alone and in combination are presented in Tab.2.
Tab.2 Results of brain age prediction assessment using three subcortical structures alone and in combination
Fig.3 presents the results of brain age prediction assessment using the three subcortical structures alone and in combination.
Fig.3 Plot of predicted brain age and actual chronological age for the test set on the optimal model
In this paper, we develop a brain age prediction method for high-dimensional small-sample data by extracting subcortical structure features and construct BrainAGE biomarkers to quantify abnormal aging of key subcortical structures and reduce overfitting problems, which in turn can establish statistical analysis models to help diagnose brain diseases, and the evaluation of the regression model of the brain age prediction model can show that the model can effectively use the subcortical structure.The evaluation of the regression model of the brain age prediction model shows that the model can effectively use the multidimensional tensor morphological features of subcortical structures for brain age prediction, and there is a strong correlation between the predicted brain age and the actual physiological age, which has good application value.