A new approach to symmetric registration of longitudinal structural MRI of the human brain

Abstract

Background: This paper presents the Automatic Temporal Registration Algorithm (ATRA) for symmetric rigid-body registration of longitudinal T₁-weighted three-dimensional MRI scans of the human brain. This is a fundamental processing step in computational neuroimaging.

New method: The notion of leave-one-out consistent (LOOC) landmarks with respect to a supervised landmark detection algorithm is introduced. An automatic algorithm is presented for identification of LOOC landmarks on MRI scans. Multiple sets of LOOC landmarks are identified on each volume and a Generalized Orthogonal Procrustes Analysis of the landmarks is used to find a rigid-body transformation of each volume into a common space where the volumes are aligned precisely.

Results: Qualitative and quantitative evaluations of ATRA registration accuracy were performed using 2012 volumes from 503 subjects (4 longitudinal volumes/subject), and on a further 120 volumes acquired from 3 normal subjects (40 longitudinal volumes/subject). Since the ground truth registrations are unknown, we devised a novel method for showing that ATRA's registration accuracy is at least better than 0.5 mm translation or 0.5° rotation.

Comparison with existing method(s): In comparison with existing methods, ATRA does not require any image preprocessing (e.g., skull-stripping or intensity normalization) and can handle conditions where rigid-body motion assumptions are not true (e.g., movement in eyes, jaw, neck) and brain tissue loss over time in neurodegenerative diseases. In a systematic comparison with the FSL FLIRT algorithm, ATRA provided faster and more accurate registrations.

Conclusions: The algorithm is symmetric, in the sense that any permutation of the input volumes does not change the transformation matrices, and unbiased, in that all volumes undergo exactly one interpolation operation, which precisely aligns them in a common space. There is no interpolation bias and no reference volume. All volumes are treated exactly the same. The algorithm is fast and highly accurate.

Keywords: Brain; Image registration; Inverse-consistent registration; Landmark detection; Longitudinal MRI; Symmetric registration; Unbiased registration.

Figure 1:

The z = 0 plane of a volume after transformation to PIL space. In this standard space, the x axis points to the posterior direction, the y axis points to the inferior direction, and the z axis (not shown) points from subject’s right to left.

Figure 2:

Flowchart for rigid-body transformation of an arbitrarily orientated volume V to the standard PIL space. The transformation is comprised of three steps that are combined into a single transformation T_Δ = T_lm ○ T_acpc ○ T_msp to obtain the transformed volume $V_{pil}=V○T_{\Delta }^{-1}$.

Figure 3:

The z = 0 plane in four longitudinal volumes acquired from the same individual after PIL transformation $V○T_{\Delta }^{-1}$. In each volume, the “+” marks indicate MSP projections of the eight landmarks {q₁, q₂, …, q₈} detected independently for each volume. Note that after PIL transformation of the 4 volumes a coarse registration has been achieved. However, small residual misalignments may remain that will be corrected by applying T_δ.

Figure 4:

Regions where the intra-cranial probability map P_ic(w) > 0.5 are shown in red superimposed on a coronal slice of a volume in PIL space. This method is used to to remove almost all non-brain regions from the analyses.

Figure 5:

Sagittal sections from 4 longitudinal volumes from an ADNI subject after registration with ATRA. After registration, one of the volumes (c) was deliberately misaligned by adding a 0.5mm translation to the registration matrix before realignment into a common space. We were then able to distinguish the deliberately misaligned volume by visual inspection, while being blind to its identity. In this example, the misaligned volume could be clearly discerned by examining, for example, the fastigium of the 4th ventricle as shown in the enlarged area.

Figure 6:

Sections through volume #20 of Stanford subject #3 (left column) and the average of all 40 volumes (right column) after ATRA registration. There is no perceptible loss of resolution in the average images, while the noise level has clearly reduced due to averaging of the 40 volumes.

Figure 7:

An illustration of the method used for comparing ATRA and FLIRT registration performance. First, we would note a feature that were different between to the registration outputs. In this case, we noted that the cut through the posterior cingulum on the mid-sagittal slice was distinctly different between FLIRT (top left) and ATRA (top right) outputs as shown by the white arrows. Then we would examine the reference scan at the same location (bottom left) to decide which registration more accurately matched the reference scan at those locations. This figure also presents an example where image regions cannot be modelled by rigid-body transformation, in this case, the subcutaneous neck fat indicated by the yellow arrows.