Model Brain Anomaly with Machine Learning Uncertainty

Model Brain Anomaly with Machine Learning Uncertainty

Can we guess the age of a person based on their appearance? Aging affects our bodies in ways that make this possible. For example, if we see a man with wrinkles in his face and white hair we could guess that this man is over 60 years old. On the other hand, if we see a very small person, with very little hair and which is unable to walk we might guess that it is a baby under 2 years old. Not surprisingly, machine learning researchers have found out that an age of a person can be estimated based only on a picture of their face.

In a similar way that it affects our appearance, aging  has a profound effect on the structure of our brain. Different brain structures grow or shrink at different ranges during our lifespan, meaning that if we look at the shape and size of these structures we can make an educated guess about the real age of a person. Leveraging on this, and in a similar way that machine learning techniques have been used to estimate the age of a person based on a picture of their face, recent methods have been developed which are able to estimate the age of a person based on a Magnetic Resonance Image (MRI) of their brains with reasonable accuracy. More importantly, these studies have found that these models can be used to detect abnormal brain appearances caused by a variety of conditions like Alzheimer’s disease schizophreniadiabetes, etc.

The standard strategy to use age prediction models to detect these abnormalities is to: 1) extract image-based features from a collection of scans, 2) train an age prediction model using images of healthy controls, 3) use the trained model to predict age on test subjects, 4) measure the prediction error for each test subject and 5) look for group differences in prediction error between controls and individuals diagnosed with a specific condition. This approach of measuring brain abnormality is attractive due to its simplicity and because models can be trained using only images of healthy controls without the need of recruiting patients suffering from a specific condition.

Although these studies suggest that the use of age prediction models is a promising tool for measuring abnormalities in  brain development, they rely on a rather strong assumption that changes caused by disease are equivalent to an accelerated aging process. Although this assumption is partially true since many diseases seem to have similar deterioration patterns as aging for some brain structures, diseases generally do not affect the whole brain in the same way that ageing does.  Take for example the case of Alzheimer’s disease.  After 50 years, the volume of many brain structures including the cerebellum and the hippocampus decrease consistently. This decrease in hippocampus volume is accelerated for individuals suffering from Alzheimer’s disease, making the hippocampus of a 60-year old have a similar volume to that of a healthy 80-year old person.  However, this accelerated aging does not have an effect in the volume of the cerebellum. This means that 60-year-olds have a similar amount of cerebellum white matter whether they are suffering from Alzheimer’s disease or not (see the boxplots to observe these patterns) .

 

Using uncertainty to measure brain abnormalities.

Age prediction models are attractive tools to assess brain abnormalities, however using prediction error might not be the best approach due to their very strong assumptions about how disease affect the brain in a similar way to aging. In our recent paper: Gaussian Process Uncertainty in Age Estimation as a Measure of Brain Abnormality, we propose to use this prediction models in a different way:  instead of using prediction error as a measure of abnormality, we propose the use of prediction uncertainty.

What is prediction uncertainty? Prediction uncertainty can be described as how confident is a model about a prediction. In general, a model will have low uncertainty values when the test point is very similar to previously seen training examples, whereas it would have high uncertainty values for test points that are different to the training set. In our case we measure uncertainty using a Gaussian Process Regression (GPR) model. In a GPR model, the uncertainty of the predictions is measured by looking at the density of samples of the training set falling in a specific region of the feature space.

What this means in practice is that a GPR model will be more confident of a prediction if it has already seen many similar cases before.  On the other hand, if we ask for a prediction on a testing case which is completely different to what the model has seen before, we will get a prediction but with a high level of uncertainty.

 

 

Going back to our Alzheimer’s disease example, you can see in the video in this page an example of how our uncertainty based framework operates. First, image based features are obtained for a set of healthy individuals (blue dots in the scatter plot). Given these training samples we can calculate an uncertainty map of the predictor at each point of the feature space (shaded area: blue corresponds to low uncertainty, red to high uncertainty). See how those areas with a large number of samples correspond to areas with low levels of uncertainty?. We assume that areas with low uncertainty levels correspond to areas with common-looking brains.

Finally we perform age prediction on  test subjects. Crosses correspond to healthy individuals and circles to individuals diagnosed with Alzheimer’s disease. In our experiments we observed that predictions on healthy individuals tend to stay in areas with low uncertainty (the blueish area), while individuals suffering from Alzheimer’s disease tended to drift towards areas with larger uncertainties. This happens because the feature extracted from healthy individuals are in general more like those in the training set, whereas individuals diagnosed with Alzheimer’s disease tend to have abnormal brain development which make their brains look different to those in the training set.

How does this compare to the previous approaches we mentioned which use prediction error to measure brain abnormalities? In the experiments shown our paper we observed that prediction uncertainty is able to find more consistent statistical significant differences between healthy controls and individuals with Alzheimer’s disease when compared to prediction error. Similarly, we found differences in prediction uncertainty between healthy controls and patients diagnosed with autism.

One of the big advantages of age prediction based methods to predict brain abnormalities is that models can be trained using images only of healthy individuals, and the same model can be used to predict abnormal development caused by very different diseases. In our work, we have used the same prediction model for Alzheimer’s disease and autism, and given our results we are excited to test if our proposed method can be used to perform predictions in some other diseases affecting the structure of the brain.

 

 

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