Identifying Sex-specific Risk Architectures for Predicting Amyloid Deposition using Neural Networks

Abstract

In older adults without dementia, White Matter Hyperintensities (WMH) in MRI have been shown to be highly associated with cerebral amyloid deposition, measured by the Pittsburgh compound B (PiB) PET. However, the relation to age, sex, and education in explaining this association is not well understood. We use the voxel counts of regional WMH, age, one-hot encoded sex, and education to predict the regional PiB using a multilayer perceptron with only rectilinear activations using mean squared error. We then develop a novel, robust metric to understand the relevance of each input variable for prediction. Our observations indicate that sex is the most relevant predictor of PiB and that WMH is not relevant for prediction. These results indicate that there is a sex-specific risk architecture for Aβ deposition.

1. Introduction

Alzheimer’s Disease (AD) is the 7^th leading cause of death worldwide¹. More than 44 million people are living with AD, requiring over US$ 1 trillion of AD and dementia related yearly healthcare costs^1,2. These numbers are expected to double by 2050^3,4. The increase in AD prevalence combined with modestly effective, symptom-focused treatment options, accentuates the urgent need for the development of neurobiologically informed treatment strategies^5,6. Thus, research examining neuropathological hallmarks of AD is of critical importance, as it will form the basis for the development of more efficient treatments which will primarily target the progression of AD.

Pathologic brain changes characteristic of AD, such as cerebral beta-amyloid (Aβ) deposition and white matter hyperintensities (WMH), are often observed in cognitively intact older adults^3,7–11. Extracellular deposition of Aβ in the form of neuritic plaques is one of the pathologic hallmarks of AD. As suggested by the amyloid cascade hypothesis, Aβ accumulation initiates a cascade of neuropathological alterations, resulting in cognitive decline and personality changes over time^7,12. WMHs are a biomarker of cerebral small vessel disease, representing the resulting ischemic tissue damage^9,13. Even though both Aβ and WMH are recognized as important factors in healthy aging and neurodegeneration, the nature of their associations has remained elusive. While some conceptualize Aβ and WMH as independent yet additive processes in AD, others argue that WMH are strongly associated with Aβ and as such are an integral part of the AD pathological cascade^{3,9,10,13–15}. Similarly, the association between Aβ and WMH in healthy aging remains poorly understood¹³. These associations are complicated by the effects of sex and other demographic factors such as age and education. Characterizing the relationship between Aβ and WMH in cognitively intact adults can inform the development of neurobiologically driven therapeutic approaches primarily focused on delaying or eliminating AD onset and progression.

To characterize the association between Aβ and WMH in cognitively normal older adults, we hypothesized that, if WMH is a precursor and/or if it is strongly associated with Aβ in older adults with intact cognition, it should act as a strong predictor of amyloid burden. To test this hypothesis, we first developed a novel method for determining feature relevance among a complex set of interrelated features. Next, we tested this novel method by implementing a multilayer perceptron and used both regional and global voxel counts of WMH, sex, age, and education to predict regional and global Aβ as measured by positron emission tomography (PET) imaging with [¹¹C]PiB (Pittsburgh Compound-B). Critically, this method allowed us to project the gradients from each layer onto the input variables to precisely determine the predictive contribution of each input variable, thus allowing us to examine if global and regional WMHs serve as a reliable predictor of Aβ while accounting for important demographic factors.

2. Material and Methods

2.1. Participants

This study included 72 cognitively normal older adults (age range: 65-93 years, age mean ± standard deviation: 74.8 ± 6.2, 50 (68.5%) female) detailed in table 1. Inclusion criteria and exclusion criteria were previously described in detail¹⁶. In brief, inclusion criteria were age ≥ 65 years, education ≥ 12 years, and fluency in English. Exclusion criteria were diagnosis of MCI or dementia, history of a major psychiatric or neurological condition, conditions affecting cognition or cognitive test performance, and contraindications for magnetic resonance (MR) imaging. A comprehensive neuropsychological testing battery was conducted on all participants in multiple cognitive domains including memory, visuospatial construction, language, and attention and executive functions ¹⁷. PiB status was determined using plasma Aβ42/40 ratios with a positivity threshold of 1.57¹⁸. This study was approved by the Human Use Subcommittee of the Radioactive Drug Research Committees and the Institutional Review Board of the University of Pittsburgh.

Table 1.

Table of demographics of the dataset with baseline values grouped by sex.

Variables		Mean (SD)	F (n=49)	M (n=23)
Age (years), mean (SD)		75.0 (6.1)	74.8 (6.4)	75.4 (5.6)
Whole Brain WMH, mean (SD)		2648.4 (3415.4)	2694.6 (3646.2)	2550.0 (2936.6)
Education (years), mean (SD)		14.8 (2.4)	14.5 (2.4)	15.7 (2.3)
Global PiB SUVR, mean (SD)		1.6 (0.5)	1.6 (0.5)	1.6 (0.5)
Geriatric Depression Score Total, mean (SD)		2.6 (2.4)	2.7 (2.4)	2.4 (2.3)
Mini Mental State Exam: mean (SD)		28.5 (1.5)	28.5 (1.5)	28.5 (1.6)
Sex, n (%)	F	49 (68.1)	49 (100.0)
Sex, n (%)	M	23 (31.9)		23 (100.0)
Race, n (%)	African American or Black	8 (11.1)	6 (12.2)	2 (8.7)
Race, n (%)	Asian	1 (1-4)	1 (2.0)
Race, n (%)	Caucasian White	63 (87.5)	42 (85.7)	21 (91.3)
APOE Status, n (%)	At Least One E4 Allele	18 (26.1)	9 (19.6)	9 (39.1)
APOE Status, n (%)	No E4 Allele	51 (73.9)	37 (80.4)	14 (60.9)
Global PiB Status, n (%)	Negative	57 (79.2)	40 (81.6)	17 (73.9)
Global PiB Status, n (%)	Positive	15 (20.8)	9 (18.4)	6 (26.1)

2.2. Image Acquisition and Preprocessing

2.2.1. MRI acquisition

All MR scanning was performed on a 3T Siemens Trio scanner with 12-channel head coil at the University of Pittsburgh Magnetic Resonance Research Center. T₁-weighted (T₁w) structural images were acquired axially using a magnetization-prepared rapid gradient echo sequence (T₁w MPRAGE): TR = 2300 ms, TE = 3.4 ms, flip angle (FA) = 9°, FOV = 240 × 256 mm², matrix = 240 x 256, slice thickness/gap = 1/0 mm, and 160 slices. T₂-weighted (T₂w) fluid-attenuated inversion recovery images were acquired axially (T₂w FLAIR): TR = 9160 ms, TE = 90 ms, TI = 2500 ms, FA = 150°, FOV = 256×212 mm², matrix = 256×212. slice thickness/gap = 3/0 mm, and 48 slices.

2.2.2. White Matter Hyperintensities

WMH on T2 FLAIR images were segmented using an automated method, developed based on our previous work^{19, 20}. Cerebral and cerebellar white matter (WM) were segmented on individual T₁w MPRAGE images and mapped into T₂w FLAIR image space using SPM12 and FreeSurfer (version 7.1.1). Given the observation that there were very few lesions in the cerebellum in our sample, cerebellar WM represented normal appearing white matter, and its mean and standard deviation were used to Z-transform the T₂w FLAIR image (Z- T₂w FLAIR). Voxels with a Z-score >= 2 and within the cerebral WM mask were identified as WMH. Using signals from normal cerebellar WM to standardize FLAIR images has several advantages, including reducing intensity variations across individual FLAIR images and avoiding systematic bias in histogram-based seed selection (between individuals with significant WMH burden versus those with minimum WMH burden). Further, white matter was also parcellated according to its nearest cortex with the Deskian/Killiany atlas in FreeSurfer. These parcellations were combined to generate the cortical white matter masks for frontal, temporal, parietal, and occipital lobes. These non-overlapping lobular cortical white matter masks were combined to create an overall cortical/deep white matter mask. White matter surrounding the ventricles that was not included in the cortical/deep white matter mask comprised the periventricular white matter mask. These lobular cortical and periventricular white matter masks allowed us to localize and quantify regional WMH in the brain.

2.2.3. PiB PET imaging

[¹¹C]PiB was synthesized by a simplified radiosynthetic method described in Wilson et al²¹. Fifteen mCi of [¹¹C]PiB with high specific activity [~2.1 Ci/μmol at end of synthesis (EOS)] was injected intravenously over 20 seconds. Beginning 50 minutes after injection, a 20-min PiB PET scan was acquired on a Siemens/CTI ECAT HR+ scanner (Siemens Medical Solutions, Knoxville, TN) in 3D imaging mode: 4 x 300 second frames, 63 axial slices, slice thickness = 2.4 mm, field of view (FOV) = 15.2 cm, intrinsic in-plane resolution = 4.1 mm full-width at half-maximum (FWHM) at FOV center.

2.2.4. Image processing

3T MPRAGE MR images were processed using FreeSurfer (version 7.1.1) to obtain a brain parcellation atlas for PET image sampling as previously described^{22, 23}. Briefly, [¹¹C]PiB PET images were corrected for interframe motion and summed over the 50-70 min post-injection interval²⁴. Summed PET images were subsequently registered to a subject-specific reference MR image using the normalized mutual information algorithm²⁵. The FreeSurfer parcellation template was used to sample summed PET images using PMOD software (PMOD Technologies, Zurich, Switzerland). Regional [¹¹C]PiB standardized uptake value ratio (SUVR) outcomes were calculated using cerebellar grey matter as reference²⁶ for nine composite regions (anterior cingulate, posterior cingulate, insula, superior frontal cortex, orbitofrontal cortex, lateral temporal cortex, parietal cortex, precuneus, and ventral striatum) as previously described²², as well as a global [¹¹C]PiB retention index based on a volume-weighted average of these nine composite regions (GBL9).

2.3. Machine Learning and Model Interpretability

2.3.1. Architecture

We used a multilayer perceptron (MLP) neural network with four, fully connected hidden layers of 256, 128, 64, and 32 artificial neurons respectively. Between the input layer and the first hidden layer, we included a dropout layer that randomly sets the inputs to zero to simulate noisy data and reduce the amount of overfitting in the model. All fully connected hidden layers used a ReLu activation which is a non-linearity that only accepts positive outputs from the artificial neurons as shown in equation 1. This has become the preferred activation function in the literature due to its ability to overcome the vanishing gradient problem²⁷. This also adds sparsity to the gradients which allows us to better understand which variables are most relevant for learning.

$$ReLu\left(x\right)=\max \left(0,x\right)$$

$$\frac{dReLu\left(x\right)}{dx}=\left\{\begin{array}{c}1ifReLu\left(x\right)>0\hfill \\ 0ifReLu\left(x\right)=0\hfill \end{array}\right.$$

2.3.2. Model Training

We trained multiple models to jointly predict regional PiB SUVR using regional WMH voxel counts, age, sex, and education shown in figure 1. Each region was normalized by dividing the WMH count by the maximum WMH count of that region in the training set. Our data was split up into train, validation, and test sets with 80%, 10%, and 10% of the total data in each split respectively, each of which maintained the sex imbalance of the overall dataset. There were no significant differences between males and females for all regional PiB SUVR, regional WMH voxel counts, age, sex, and education. The p-values from a two-sample student t-test between males and females are shown in table 2.

Figure 1:

Diagram of model input and outputs

Table 2.

Table of input variables and prediction targets.

Input Variables	Mean (SD)	F (n=49)	M (n=23)	P-Value
Whole Brain WMH, mean (SD)	2648.4 (3415.4)	2694.6 (3646.2)	2550.0 (2936.6)	0.858
Left Frontal WMH, mean (SD)	145.1 (305.8)	170.7 (360.3)	90.6 (118.3)	0.165
Left Occipital WMH, mean (SD)	34.6 (38.6)	29.2 (36.9)	46.1 (40.5)	0.097
Left Parietal WMH, mean (SD)	109.6 (261.2)	109.5 (274.8)	109.6 (235.4)	0.999
Left Temporal WMH, mean (SD)	67.3 (110.5)	71.7 (125.4)	58.0 (70.7)	0.556
Periventricular WMH, mean (SD)	1920.2 (2158.4)	1921.2 (2240.2)	1918.2 (2021.1)	0.996
Right Frontal WMH, mean (SD)	154.8 (362.3)	179.3 (412.3)	102.7 (220.2)	0.308
Right Occipital WMH, mean (SD)	51.1 (58.4)	45.8 (58.6)	62.4 (57.7)	0.261
Right Parietal WMH, mean (SD)	111.4 (229.4)	112.7 (239.4)	108.6 (211.6)	0.941
Right Temporal WMH, mean (SD)	54.3 (79.9)	54.5 (76.7)	53.9 (88.1)	0.976
Age (years), mean (SD)	75.0 (6.1)	74.8 (6.4)	75.4 (5.6)	0.679
Education (years), mean (SD)	14.7 (2.4)	14.4 (2.5)	15.4 (2.2)	0.102
Prediction Targets
Anterior Cingulate PiB SUVR, mean (SD)	1.7 (0.6)	1.7 (0.6)	1.6 (0.7)	0.612
Anterior Ventral Striatum PiB SUVR, mean (SD)	1.1 (0.5)	1.1 (0.5)	1.2 (0.4)	0.679
Superior Frontal PiB SUVR, mean (SD)	1.6 (0.6)	1.7 (0.6)	1.6 (0.6)	0.856
Orbitofrontal PiB SUVR, mean (SD)	1.6 (0.5)	1.6 (0.5)	1.7 (0.6)	0.752
Insula PiB SUVR, mean (SD)	1.2 (0.4)	1.2 (0.4)	1.2 (0.4)	0.825
Lateral Temporal PiB SUVR, mean (SD)	1.5 (0.4)	1.5 (0.4)	1.5 (0.5)	0.962
Parietal PiB SUVR, mean (SD)	1.6 (0.5)	1.6 (0.5)	1.6 (0.5)	0.984
Posterior Cingulate PiB SUVR, mean (SD)	1.6 (0.5)	1.6 (0.5)	1.6 (0.5)	0.97
Precuneus PiB SUVR, mean (SD)	1.6 (0.7)	1.6 (0.8)	1.6 (0.7)	0.999
Global PiB SUVR, mean (SD)	1.6 (0.5)	1.6 (0.5)	1.6 (0.5)	0.951

We used the average mean squared error (MSE) of each PiB SUVR to optimize the weights and a Root Mean Squared Propagation optimizer with a learning rate of 0.0003. The inclusion of multiple PiB SUVR values makes it difficult for the model to overfit on a single label, thus functioning similarly to regularization. To compensate for the imbalance of sexes in the data (67.2% Female), we implemented image oversampling for men using the SMOTE²⁸ algorithm which creates synthetic male data using a decision tree and k nearest neighbors that are representative of the sample population. Additionally, to evaluate and control for the effect of the dataset sex imbalance on feature relevance metrics, we ran a separate analysis by undersampling women using the NearMiss3²⁹ algorithm which uses k-means to use the most representative samples from the population. Oversampling and undersampling were only performed on the training dataset to avoid inflating the model performance.

2.3.3. Validation

The methods and models were validated by randomly selecting seeds to resample the dataset splits, reinitialize the model, and reinitialize any random component of the code (e.g., oversampling and undersampling initialization). We tracked each seed in a configuration file and log files of each respective validation run. All models were trained until there was no improvement in the validation error for 10 epochs.

Feature Importance and Relevance

After training the models, we investigated which features are the most important for the prediction of PiB SUVR. We first computed the permuted feature importance of our model by augmenting each data feature with the method proposed by Fisher, Rudin, and Dominici³⁰. Despite being commonly used, this metric is not robust to retraining and can lead to different values due to differences in the model convergence. The data was augmented by swapping each instance of a feature for every other instance of that feature within the dataset and averaging the change in the error. By doing so, we can observe the relative change in the error. A larger change indicates that a particular feature is more important for the final prediction. On the contrary, if swapping a particular feature causes a small change in the error, then the model does not heavily rely on that feature for the final prediction.

Our feature relevance metric projects the model gradients from each layer onto the previous layer. The equation below represents a single neuron in our model which takes an input vector $\mathit{x}$ of length $n$.

$$f\left(\mathit{x}\right)=ReLu(\sum _{i=0}^n{w}_i{x}_i)$$

The impact of an input variable $x_i$ is proportional to its associated weight $w_i$ if the output is positive. If this neuron is an output neuron, then for some loss function $g\left(f(\mathit{x}),y\right)$ the gradient of each weight, $w_i$ is $g^{\prime }\left(f\left(\mathit{x}\right),y\right)x_i$ for a positive output. In our case, the derivative of the MSE is simply $\frac{2}{N}(f\left(\mathit{x}\right)-y)$, which is the difference between the predicted and actual values divided by the number of predicted values. This gradient, which is used to update a particular weight, represents the relevance of a particular input $x_i$ with respect to the output. Through backpropagation we calculate the gradients of the input layer, we then sum all the weights associated with a particular input variable and normalize these gradients by the sum of all gradients in the input layer. The normalized values are then treated as the relevance of a particular feature. This method can be performed significantly quicker than permuted feature importance as it only requires a single pass over the test dataset compared to passes equal to the length of the dataset. To analyze feature relevance values, we performed a Wilcoxon ranked sign test between pairs of features with the same train-test split. We will perform this for both the permuted feature importance and the feature relevance values to show the stability of our feature relevance metric compared to permuted feature importance.

3. Results

For each trained model, we loaded the set of weights associated with the lowest MSE for evaluation. We exclude runs that produced test MSEs greater than 2.5 median absolute deviations away from the median³¹. The best MSE for each oversampled model was between .07 and .755 with a mean of .35. In figure 2, we can see a box plot for the permuted feature importance values of all our models. We can see a significant overlap between the importance values for each of the input features which suggests that there is not a clear ranking of the features. The Wilcoxon ranked sign tests performed between feature importance values found that only 8 of the 78 pairs of input features were significantly different from each other at a significance level of 0.05 with Bonferroni correction.

Figure 2.

a: Permuted feature importance box plot for predicting regional PiB shows no significant predictors.

b: The W-table of permuted feature importance value comparisons reflects the lack of significant predictors in 2a.

We then obtained feature relevance values for our models to compare with the permuted feature importance results (figure 3). We treated the one-hot encoded male and female variables as separate for this analysis since they are distinct inputs. This is to disentangle the effects of each sex when observing the feature relevance values. For the feature relevance comparisons, the one-hot encoded female variable was significantly different from all other input features. We also found that age was significantly different from all WMH features. While education and one-hot encoded male appear to be more important than other WMH features, those comparisons did not survive multiple comparisons corrections. The Wilcoxon ranked sign tests performed between feature relevance values found that only eight of the 57 of the 91 pairs of input features were significantly different from each other at a significance level of 0.05 with Bonferroni correction.

Figure 3.

a: Feature relevance box plot for predicting regional PiB shows a strong effect for females.

b: W-table of feature relevance value comparisons reflects the strong effect in females.

Our results suggest that sex, specifically being assigned female at birth, is the most reliable predictor of amyloid deposition in cognitively healthy older adults. Critically, we found the same results when oversampling males as we did when undersampling females, suggesting our results are not driven by the sex disbalance present in the dataset. We observed almost identical results when comparing the MSE, feature importance, and feature relevance values between the undersampled and oversampled datasets. Again, we find that 8 out of 78 feature importance comparisons and 57 out of 91 feature relevance comparisons are significant.

4. Discussion and Conclusion

4.1. Discussion

This study employed a data driven approach to investigate the relationship between WMH burden and PiB SUVR. We implemented an MLP with a novel feature relevance metric to determine which features most strongly predict Aβ deposition in cognitively intact older adults.

Our model was able to consistently predict the PiB SUVR of multiple regions at the same time. By bootstrapping our validation, we were able to better estimate the true performance of our model. This also allows us to better understand the relationship between WMH, age, sex, and education. Age is the most well-known predictor of AD pathology and sex differences are also well-studied in the literature³². However, due to the age of our population, we are unable to study the effects of various pathologies on Aβ burden in midlife which may reduce the effect size that we observe for some of our variables of interest. Education was included as it is associated with cognitive reserve and the use of a neural network allowed us to include it as a variable without degrading the performance of our model³³. However, since our population is highly educated, this likely reduces the relevance of education in this study. While there have been other studies that show significant racial effects on Aβ burden³⁴, our methods do not investigate the effects of race in this study because our sample only included nine non-Caucasian participants. The relationship between WMH and amyloid burden has only been studied relatively recently^35–37. Our method uses a unique metric to evaluate how important a variable is for the optimization of the complex neural network. This is similar to other gradient interpretability methods such as guided backpropagation³⁸ and gradient-weighted class activation maps³⁷ which are commonly used in convolutional neural networks. In our model, we also leverage the ReLu non-linearity to make the values of the gradients more meaningful. Permuted feature importance investigates how the weights of the model are related to the output by observing the change in error associated with permuting the input. Other weight-based interpretability methods have been shown to be unreliable since reinitializing the model can cause conflicting explanations³⁸. This can be attributed to the different convergence points for the model. We expected that gradients would be a more stable and robust explanation than the weights of the model.

We found that WMH burden is not an important predictor of PiB SUVR compared to age, sex, and education. These results are consistent with other findings in the literature that show that WMH and amyloid burden are largely independent and additive effects^35–37. We used regional WMH values in the input since we believed this would improve the accuracy of our model. In addition, we include the total number of WMH voxels found since prior work has found that artificial neural networks are not good at aggregating multiple sources of information^{41, 42}. It is possible that our models underestimate the importance of WMH compared to other more direct variables due to the collinearity between many of our variables. However, we believe this is not the case since we would observe strong outliers in the feature importance values for some of the WMH variables since we should expect our model to overfit. In our results, we only found strong outliers for the left frontal lobe feature importance values. In addition, collinearity shouldn’t be a significant issue since we are looking at the gradients of nonlinear functions. Although may be possible that WMH could better predict white matter PiB SUVR due to the localized effects of demyelination, this is beyond the scope of this paper and warrants future investigation.

We also investigated the stability of the feature relevance metric compared to permuted feature importance, which is a widely used, model-agnostic method for interpreting model predictions. While the importance values do not match our feature relevance values, we show via bootstrapped validation that feature relevance presents a more reliable explanation of how our model predicts PiB SUVR.

While our results show a significantly higher feature relevance value for females, this could be due to the larger number of females in our dataset. To compensate we chose to compare feature relevance values between models that used a dataset where females were undersampled and a dataset where men were oversampled. We primarily reported the oversampled dataset as it does not exclude samples from the analysis. Both methods reduce the effect of the sex imbalance in our dataset in different ways, but we find that there is a higher feature relevance for women compared to men in both. We do not adjust for WM volume even though many studies have shown that WMH relative to WM volume is higher in women compared to men⁴³. This is because we believe that this would introduce significant interactions between input variables which would make it difficult to investigate the independent relevance of each feature and validate our method. Higher feature relevance for women suggests there may be a female-specific risk architecture for Aβ burden. Many factors may contribute to this sex difference, including a dramatic drop of estrogen during menopause in women, compared to a gradual decline of testosterone in men. During the menopausal transition, women also experience hot flashes which has been associated with greater WMH burden⁴⁴. Hot flashes negatively impact the quality of sleep which is well known to greatly affect brain health and the clearance of toxins⁴⁵. These events in midlife can accumulate to cause differences in the presentation of Aβ pathology which seem to be more impactful than WMH burden. Our findings are consistent with the literature³¹, the use of a neural network allows us to investigate multiple independent features simultaneously.