Soft Null Hypotheses: A Case Study of Image Enhancement Detection in Brain Lesions

<div><p>This work is motivated by a study of a population of multiple sclerosis (MS) patients using dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) to identify active brain lesions. At each visit, a contrast agent is administered intravenously to a subject and a series of images are acquired to reveal the location and activity of MS lesions within the brain. Our goal is to identify the enhancing lesion locations at the subject level and lesion enhancement patterns at the population level. We analyze a total of 20 subjects scanned at 63 visits (∼30Gb), the largest population of such clinical brain images. After addressing the computational challenges, we propose possible solutions to the difficult problem of transforming a qualitative scientific null hypothesis, such as “this voxel does not enhance”, to a well-defined and numerically testable null hypothesis based on the existing data. We call such procedure “soft null” hypothesis testing as opposed to the standard “hard null” hypothesis testing. This problem is fundamentally different from: 1) finding testing statistics when a quantitative null hypothesis is given; 2) clustering using a mixture distribution; or 3) setting a reasonable threshold with a parametric null assumption.</p></div

Properties of the GLSR statistic computed for each of the registration algorithms (higher is worse).

<p>The values in the brackets show the corresponding statistic computed while filling the lesions with average NAWM before registration.</p><p>Properties of the GLSR statistic computed for each of the registration algorithms (higher is worse).</p

The histogram of brain lesions for 98 patients based on a rigid registration of the images to a template brain indicating the number of patients out of 98 having lesions at each voxel.

<p>The histogram of brain lesions for 98 patients based on a rigid registration of the images to a template brain indicating the number of patients out of 98 having lesions at each voxel.</p

Descriptive statistics of the demographic information on the patients.

<p>Descriptive statistics of the demographic information on the patients.</p

Histograms of EDSS scores, age (in years), sex, and duration from disease onset (in years) for the 98 patients in the study.

<p>Histograms of EDSS scores, age (in years), sex, and duration from disease onset (in years) for the 98 patients in the study.</p

P-values (uncorrected) for testing using models –.

<p>From left to right: spatial registrations “rigid”, “ANTS affine”, “ANTS diffeo”, “FSL nonlinear”, and “DARTEL”. Bright red: p-values close to 0 to black: p-values close to 1. The p-value maps are overlaid on a grayscale template.</p

The lesion histograms for 98 patients (showing the number of patients out of 98 having lesions at each voxel) based on “ANTS affine” (top left), “ANTS diffeo” (top right), “FSL nonlinear” (bottom left) and “DARTEL” (bottom right) spatial registration algorithms.

<p>Red: voxels where more patients have lesions; Blue and light blue: voxels where fewer patients have lesions.</p

P-values for testing using models – after applying Bonferroni and FDR corrections.

<p>From left to right: spatial registrations “rigid”, “ANTS affine”, “ANTS diffeo”, “FSL nonlinear”, and “DARTEL”. Red: small p-values ().</p

Review of the steps behind the five algorithms.

<p>Review of the steps behind the five algorithms.</p

One slice from five different registration methods for three subjects (one subject on each row).

<p>The MNI template brain is shown on the first row (left).</p