Improved Prediction of Imminent Progression to Clinically Significant Memory Decline Using Surface Multivariate Morphometry Statistics and Sparse Coding

INTRODUCTION

Even though simple blood tests [1–3] promise to become a useful and less expensive tool for assessing a person’s diagnosis and prognosis in the early clinical and preclinical stages, structural magnetic resonance imaging (MRI) remains the most common biomarker assessment tool in current clinical practice. Typically, volumetric methods have utilized mass-univariate or region of interest methods to detect cortical thickness, grey matter volume, and surface areas. Accordingly, we recently reported findings from a prospective cohort of cognitively unimpaired individuals to estimate a priori MRI regions of interests (preferentially affected in the preclinical and clinical stages of Alzheimer’s disease (AD)) for differences between those individuals who subsequently progressed to clinically significant memory decline in approximately 2 years and those who did not. Additionally, the same study also used Statistical Parametric Mapping (SPM) (http://www.fil.ion.ucl.ac.uk/spm/) to examine the ¹⁸F-flu-orodeoxyglucose (FDG) positron emission tomography (PET) measured cerebral metabolic rate for glucose (CMRgl) differences between progressors and nonprogressors. Based on receiver operating characteristic, binary logistic regression, and leave-one-out procedures, hippocampal volume best predicted an individual’s imminent progression to the clinically significant memory decline, with 79%sensitivity/78%specificity among the APOE-matched cohort [4].

Multivariate methods appear to improve detection of subtle changes in MRI-based morphological features of structures relevant to preclinical detection of AD [5–7]. Machine learning methods promise to improve the accuracy of prediction for individual patients, particularly when applied to MRI based multiple features as with multivariate morphometry statistics (MMS), in the preclinical stages of AD [8–10]. In this study, we aimed to improve prediction from prior studies by employing the hippocampal surface MMS features, which have been shown to outperform the hippocampal volume measure [6, 11], and the patch based sparse coding algorithm to predict clinically significant memory impairment within two years, even in the absence of other amyloid, tau, PET, cerebrospinal fluid (CSF), or emerging blood-based bio-markers.

METHODS

Hippocampus segmentation and surface reconstruction

All the T1-weighted MR images were automatically segmented by using FIRST [16], which is a model based subcortical structure registration and segmentation tool that we have used in our previous hippocampal morphometry research [6, 11]. In comparison to FreeSurfer, FIRST is capable of generating topologically sound segmentation results with classification of relatively large, scaled databases. FIRST is one part of FSL library developed mainly by Analysis Group, FMRIB, Oxford, UK. With default parameters, we ran the run_first_all command and extracted the segmentation of left and right hippocampi. Then all the extracted images were binarized with a simple thresholding process. With the binary images, hippocampal surfaces were constructed with a topology-preserving level set method [18] and triangular surface meshes were further acquired based on marching cubes algorithm [19]. We then refined the meshes [6] to get the smooth surfaces which are suitable for generating conformal grids. Finally, all these smoothed meshes were aligned into the MNI standard space with a 9-DOF (degree of freedom) global affine transformation (Fig. 1).

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Fig. 1

Hippocampus segment. The blue and green parts in these images represent the left and right hippocampus that FIRST segments of the image. The bottom right picture shows the shape of the hippocampal surface, which fits the segmented image well.

Surface conformal representation

On each hippocampal surface, we generated a conformal grid as a canonical space for surface registration and multivariate statistical analysis [6]. Firstly, two cuts were introduced on the hippocampal surface (Fig. 2) and thus the surface could be converted into a tube-like genus zero surface. The two cuts locate at the front and back of the hippocampal surfaces, representing anterior junction with the amygdala, and its posterior limit as it turns into the white matter of the fornix. Thus, they are biologically valid and can be used as consistent landmarks across subjects. With the tube-like surface, the landmark curves can be automatically determined by locating the extreme points and searching along the first principle direction of geometric moments of the surface [7, 21]. Finally, we calculated the holomorphic 1-form basis of each tube-like surface and conformally mapped the hippocampal surface to a planar surface.

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Fig. 2

Hippocampal surface morphometry pipeline. (a) The hippocampus is segmented from T1-weighted images and a conformal grid is built on the surface. Here examples are shown for 2 different subjects. (b) Examples of features selected in the image for the two subjects in (a). (c) From left to right: Intensity map on the surface 1 in (a). Forward map f(x) for the conformal grid fluid registration to the image 2. Backward map b(x) from the image 2 to image 1. Intensity map on the surface 2. (d). Surface multivariate morphometry statistics is applied to analyze morphometric changes.

Many of the geometric features of the surface could be contained in the conformal parameterization. In this paper, we calculated the local conformal factor and mean curvature, which represents the intrinsic and extrinsic features of the surface respectively. The conformal factor is the area ratio of the infinitesimal region around the same point on the original hippocampal surface and the conformal planar surface. Mean curvature is an extrinsic measure of curvature which comes from differential geometry and can represent the flatness of the surface around a vertex. Both the conformal factor and mean curvature are local features defined on each vertex. The conformal factor and mean curvature are called the surface conformal representation because they can encode both intrinsic structure and 3D embedding information.

Patch selection with sparse coding

After registering each hippocampal surface to a uniformed grid, each surface contains 150 ^* 100 vertices and the feature dimension of each hippocampal surface is 60,000, where each vertice has 1 ^* 4 dimensional MMS features. We then randomly generated 10×10 square windows on each hippocampal surface and collected 504 surface patches with different amounts of overlapping on each side of the hippocampus. We randomly selected 1008 patches on each subject’s hippocampal surfaces (1008 for both left and right). For different subjects, we used the same random seed to choose the patches. In other words, the distribution for the random-selected patches is the same on the hippocampal surfaces for all the subjects. Then we reformed these patches of features to a vector, of which the dimension is 400×1008. The dictionary was initialized by randomly selecting patches [43], which has proved to be an efficient method in practice, and then we started learning the dictionary and sparse codes by stochastic coordinate coding [42]. The size of the batch is one and the model is trained for ten epochs. After sparse coding, we acquired 1008 samples, each of which has 1800 features on each subject. Finally, with max-pooling, we chose the maximum values for each feature over 1008 patches and obtained 1800-dimensional features for each subject.

In this study, we chose random forest algorithm [44]. Random forests are a combination of tree predictors such that each tree depends on the values of a random vector sampled independently and with the same distribution for all trees in the forest (Fig. 3). This algorithm adapts a learning process called “feature bagging.” In this process, we selected a random subset of the features for several times and then trained a decision tree for each subset. If some features are strong predictors for the response, they will be selected in many decision trees and thus make them correlated. In comparison with decision trees, random forests have the same bias but lower variance, which means it can overcome the drawback of overfitting caused by the small data set. For our sparse surface features, when the training number becomes smaller, diversification becomes more subtle, and the method can better detect these subtle differences. Finally, we employed cross-validation to evaluate the performance of the classification. For the k-fold cross-validation, we randomly shuffled the dataset and split it to k groups. For each group, we take it as the test data set and use the remaining groups to train a model. Then, the model is evaluated by the test group. In this way, we can get a predicted class label for all the samples. To indicate the number of correct class labels, we built a contingency table, of which the rows are the true classes and the columns represent assigned classes. And then, we could represent the combination of ground truth and predicted result as { C 11 C 12 C 21 C 22 } and compute the following performance measures, Sensitivity = C₁₁/(C₁₁ + C₁₂) , Specificity = C₂₂/ (C₂₁ + C₂₂) and Accuracy = (C₁₁+ C₂₂)/(C₁₁ + C₁₂ + C₂₁ + C₂₂).

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Fig. 3

Patch-based sparse coding system. (a) Surface multivariate morphometry statistics. (b) Generate patches and randomly select patches on the surface. (c) Dictionary learning and sparse coding. (d) Sparse patch-based features got from (c). (e) Max-pooling to resize the features in (d). (g) Classification by using random forest classifier with the features after Max-pooling.

RESULTS

Characteristics of the progressors and nonprogressors are shown in Table 1. Overall, the ADNI participants were older and had a greater percentage of males and APOE4 non-carriers than the Arizona participants.

Prediction results are shown in Tables 2and 3 . In the Arizona cohort, the prediction result of progression to clinically significant decline using hippo-campal surface MMS features was achieved with 92%accuracy and 89%sensitivity and 95%specificity. The same method with the ADNI cohort achieved 92%accuracy, 88%sensitivity, and 97%specificity. Combining the Arizona and ADNI coh-orts (78 progressors and 80 nonprogressors) achieved 90%prediction accuracy, 90%sensitivity, and 90%specificity.

A post-hoc analysis using random forest classification and leave-one-out cross-validation showed that AVLT long-term memory (LTM) scores predicted progression with only 74%prediction accuracy (65%sensitivity and 83%specificity) in the Arizona cohort, and 62%prediction accuracy (59%sensitivity and 65%specificity) in the ADNI cohort despite the potential bias of using that same measure (along with other criteria) when making the diagnosis of aMCI. Furthermore, as a comparison to our new methods that utilize surface multivariate morphometry, prediction of aMCI using baseline hippocampal volume, random forest classification with leave-one-out cross-validation in the same data sets yielded only 79%prediction accuracy in the Arizona cohort and 72%in the ADNI cohort (Table 4).

DISCUSSION

This study extended previous work by showing that combining hippocampal surface MMS and machine learning methods affords improved prediction of imminent clinically significant cognitive decline compared to typical automated volumetric MRI methods and standard statistics. Our methods achieved high prediction accuracy in two separate and independent data sets, each balanced for age, sex, and presence or absence of the APOE4 allele, even in the absence of other brain imaging or fluid biomarkers of AD. Furthermore, we retained accuracy when the two data sets, which differed from each other in age, sex, and percentage APOE4 carriers, were combined. The predictions using hippocampal surface MMS and machine learning methods were also much better than predictions using either hippocampal volume or baseline cognitive scores, even though the latter are biased due to the circularity of using the same measure when making the diagnosis of aMCI. Although lacking amyloid and tau biomarker confirmation of AD pathology in this study, the data set from Arizona is well-defined, with high confidence regarding the likelihood of AD in those who subsequently developed aMCI. Thus far, the majority of those in the Arizona progressor group later developed definite or probable AD, with the exception of one person who developed dementia with Lewy bodies and one aMCI individual who 2 years later had slight improvement in cognition. Although we do not know how many of those in the nonprogressor group will ultimately develop AD, we have high confidence that none developed MCI for 4 years following the scan. To date, 3 in the Arizona nonprogressor group subsequently developed MCI and none have progressed to dementia. Thus, the training and testing groups were well defined and mostly accurate, which mirrors the accuracy of our novel feature-based sparse coding methods. Instead of using the automated brain mapping algorithmic programs FreeSurfer (http://surfer.nmr.mgh.harvard.edu/) and Statistical Parametric Mapping (http://www.fil.ion.ucl.ac.uk/spm/) as we did in our prior study with the same data set [4], in this study we utilized arguably more sensitive methods involving MMS to discover subregional hippocampal surface differences, patched-based sparse coding for feature selection, and the random forest machine learning classifier. We were able to replicate our improved results in a completely independent data set from ADNI that differed from the Arizona data set in age, sex, and percentage APOE4 carriers.

Because the Arizona data set was identical to our prior study [4], the improved accuracy in this study can be explained by our use of hippocampal surface MMS combined with patch-based sparse coding algorithms. Similar to the methods from our most recent work [36], in this paper we propose a novel Patch Analysis-based Surface Correntropy-induced Sparse coding, PASCS, to help predict future cognitive decline. We demonstrate that PASCS is surprisingly useful for surface features classification and surface multivariate morphometry statistics features consisting of surface multivariate tensor-based morphometry and radial distance (the distance from the medial core to each surface point), and we also move a step forward from group difference to that of individual subject classification. Unlike other sparse coding work [37–40], PASCS takes advantage of surface morphometry features that practically encode neighboring intrinsic 3D geometry information. Meanwhile, MMS features also benefit from the succinct representation and strong discrimination power that sparse coding provides for effective AD classifications, i.e., capturing more important information so that MMS features not only have the significant group difference but also have an effective classification power.

In this work, we adopted FIRST for hippocampus segmentation, which, having previously explored different segmented hippocampal data as input, appears to most reliably generate topologically sound segmentation results. For example, our earlier work used manually segmented hippocampi to build surface meshes [26, 45]. Later, we adopted FIRST for automatic hippocampus segmentation [6] and used it in almost all our hippocampal morphometry research. Meanwhile, we also used FreeSurfer segmented hippocampi to build hippocampal surface meshes [17]. All achieved reasonable results in group difference studies, thus demonstrating that our pipeline is robust to segmentation methods. However, FIRST can always generate topologically sound segmentation results, whereas FreeSurfer does not guarantee topologically correct results. Therefore, manual quality control is necessary to incorporate FreeSurfer in our pipeline. Thus far, our related prediction/classification work adopted FIRST segmented hippocampal surfaces in order to more efficiently work with relatively large-scaled datasets [10, 11]. Since the input of our MMLC is the surface features rather than the output from segmentation tools, it is reasonable for us to expect that our method is not sensitive to the hippocampus segmentation tools used.

To evaluate the influence of these random-select patches on the classification accuracy and the stability of our framework, we repeated the experiments ten times with ten different patch selection on both sides of the hippocampal surface. The mean and standard deviation of the results are shown in Table 5. The results show our method is relatively stable with different patch selection and comparable to the best accuracy results reported in Tables 2and 3 . It is worth noting that the variance results were not purely caused by the patch selection, since other components in the pipeline, such as random forest and cross-validation parts, may also perturb the final results. For example, during the training of random forest, the classifier will randomly select a subset of features to build a decision tree. Similarly, in the 5-fold cross-validation, the training data may be different. Considering the small dataset size in the current experiments, the minor variance in our results demonstrates that the influence of random patch selection is in a reasonable range and does not appreciably affect the stability of the results. In future, we will further explore the random patch selection issue with larger imaging cohorts.

Future directions will include integrating convolutional neural network (CNN) with our proposed ap-proach. CNN is considered one of the most successful deep models for identifying, classifying, and quantifying patterns in medical images [46, 47]. Based on promising results from our most recent work [48, 49], integrating CNN with the proposed approach could further improve the PASS results. Specifically, we applied CNN and an unsupervised learning method (multi-task stochastic coordinate coding) algorithm to the ADNI dataset to predict future cognitive clinical measures with baseline hippocampal/ventricle mTBM features and cortical thickness, achieving accurate predictions of MMSE/ADAS-Cog scales [48, 49]. However, there is a trade-off between com-putation efficiency and prediction performance. Training a CNN model usually requires substantial computational resources (multiple GPUs). Our PASS-MP is a generative toolbox for brain image analysis with fast running time and does not require GPU for training. It can apply to different subcortical of brain images with relatively high performance. We therefore will continue to explore the efficient CNN based sparse coding method that could both improve the prediction power and maintain a low-cost of computational resources and fast running time as PASS-MP for better help with clinical diagnosis and prognosis.

Although there are many other sensitive biomarkers to detect the pathology associated with AD, this method capitalizes on MRI scans, which is a clinical diagnostic capability that virtually all clinicians have access to. Further testing is needed to verify the results in larger data sets, but our method appears to accurately predict whether an individual will progress to the clinical stages of AD within the next 2 years. Thus, this method has the potential to be developed into a clinically useful tool. We currently have no proven medication treatments for AD; however, well-tested behavioral programs that provide lifestyle and behavioral training to adapt to memory loss associated with MCI are available [50]. These behavioral programs appear to be most effective when done prior to significant memory decline [51]. If we had an accurate and inexpensive tool to predict likelihood of clinically significant decline, we could target those individuals who would most benefit from a similar intervention that is delivered preclinically.

Limitations of this study include relatively small numbers of progressors and nonprogressors in both cohorts and thus this method will need to be replicated in other, larger data sets. Importantly, we also did not include other biomarkers such as amyloid or tau to verify that progressors had MCI due to AD or include other imaging, CSF, and emerging, less expensive and more scalable blood-based biomarkers of amyloid, tau, and neurodegeneration [1–3], and future applications of this technique should do so to ensure accurate training sets and generalizable results. However, we were interested in seeing the “added value” of this MRI based image analysis technique as a complement to those emerging methods. We did not test brain regions other than hippocampus, but the purpose of this study was to evaluate the utility of prediction using hippocampal surface multivariate morphometry statistics combined with patch-based sparse coding algorithms. It was therefore convenient to compare these methods using the same data set that we had previously evaluated with standard automated brain mapping algorithmic programs, binary logistic regression, and leave-one-out procedures. Also, our previous study did explore other imaging-based biomarkers and found that the hippocampus was the best predictor 2 years prior to clinically significant decline (including both FDG-PET and MRI biomarkers). Finally, because of the overlapping patch selection and max-pooling scheme, we generally cannot visualize the selected features, which may decrease the interpretability of biomarkers and, in turn, translation to clinical applications. However, we can always visualize statistically significant regions using group differences [6]. In addition, our recent work [52] better addresses this problem with the adoption of group lasso screening [53] to select the most significant features. It was not adopted in our current study because of its relatively small sample size. In the future, we will incorporate this approach into our current framework to improve its interpretability.