Dense feature deformation morphometry: Incorporating DTI data into conventional MRI morphometry

Abstract

Registration based mapping of geometric differences in MRI anatomy allows the detection of subtle and complex changes in brain anatomy over time that provides an important quantitative window on the process of both brain development and degeneration. However, methods developed for this have so far been aimed at using conventional structural MRI data (T1W imaging) and the resulting maps are limited in their ability to localize patterns of change within sub-regions of uniform tissue. Alternative MRI contrast mechanisms, in particular Diffusion Tensor Imaging (DTI) data are now more commonly being used in serial studies and provide valuable complementary microstructural information within white matter. This paper describes a new approach which incorporates information from DTI data into deformation tensor morphometry of conventional MRI. The key problem of using the additional information provided by DTI data is addressed by proposing a novel mutual information (MI) derived criterion termed diffusion paired MI. This combines conventional and diffusion data in a single registration measure. We compare different formulations of this measure when used in a diffeomorphic fluid registration scheme to map local volume changes. Results on synthetic data and example images from clinical studies of neurodegenerative conditions illustrate the improved localization of tissue volume changes provided by the incorporation of DTI data into the morphometric registration.

Fig. 1

An illustration of the derivation of different MI measures of similarity between multiple sets of images for conventional scalar images (top) and combined scalar and DTI data types (bottom). In conventional MRI data sets (T1W, PDW, T2W) there is appreciable shared information. For DTI data, there is little shared information between individual diffusion direction maps. We can therefore consider the simplified relationship between DTI directional measurements separately paired with conventional MRI.

Fig. 2

An illustration of different multi-channel formulations for measures relating the change in information in pairs of images. We can either consider the change in information between each of the images considered independently and when combined (top), or consider the change in information content between separately paired images and pairs combined (bottom). We name these diffusion paired mutual information (DPMI) and diffusion paired joint mutual information (DPJMI) respectively. The key difference is the constant factor indicated in grey for the DPMI measure, which is not a function of the mapping between studies.

Fig. 3

Digital phantom data for evaluation: Top two rows show orthogonal slices through synthetic image volumes created to simulate loss of tissue in T1W MRI data. Lower two rows show additional synthetic diffusion data in the form of an overlay of principal diffusion directions, illustrating the different diffusion properties in the left and right halves of the partially contracting sphere. These two diffusion regions have the same fractional anisotropy, but differ simply in their orientation. This simulates neighbouring tracts with different directions, but with the same strength of connectivity.

Fig. 4

Resulting maps of volume changes estimated when driving the fluid registration using conventional Mutual information (top) based on the T1W images only and using Diffusion Paired Mutual Information (DPMI) middle and Diffusion Paired Joint MI (DPJMI) bottom. Volume changes are shown as a simple grey scale with dark indicating contraction of the first time point to match the second, mid grey no change and white indicating expansion. Without the diffusion data there is no image structure to constrain the deformations within the bulk of tissue making up the sphere, resulting in a smooth gradient of contractions across the sphere. With DTI data, the orientation information provided by the diffusion tensors strongly partitions the pattern of contractions within the sphere so there is no inferred contractions in the opposite half of the sphere. The maps provided by DPMI and DPJMI (bottom two columns) are, within numerical rounding, the same, which confirms our observations in the derivation of the two measures.

Fig. 5

Data and results of applying deformation tensor morphometry to studies acquired on a subject before and after a period of abstinence from heavy drinking. Left two columns show enlarged view of the subtraction of rigidly aligned T1W MRI data. Right column shows estimated volume changes as a colour overlay on the first time point MRI of the determinant of the jacobian of the deformation sequence. Gross increases of tissue volume over bulk white matter are observed from T1W imaging alone. DTI-MRI morphometry created by maximising DPMI (top right) provides significant localisation of tissue volume changes, localizing changes in patterns around the ventricles and following the white matter tract structure seen in the DTI data.

Fig. 6

Axial slices through DTI (shown as principal diffusion direction) and MRI (left) at the two time points before and after abstinence from heavy drinking. Right: corresponding slices though volume change maps derived from MRI and MRI-DTI combined (using DPMI) displayed as a colour scale of percentage change overlaid onto the first time point MRI. Volume changes constrained by MRI data alone show diffuse increases in white matter volume after abstinence from heavy drinking. DTI-MRI constrained results show significantly localized volume increase patterns constrained to regions of tracts. Localization of greater changes are particularly visible in the corpus callosum (seen in mainly in red on the diffusion tensor maps).

Fig. 7

A subject diagnosed with Alzheimer's dementia scanned twice with an interval of 9 months (MMSE 25, age 61.7), exhibiting tissue loss and ventricular expansion. The scan pairs were fluidly aligned using MI (bottom row) and DPMI (top row). Sagittal and axial slices are shown along with a corresponding coronal slice through the DTI data at the same location. Here, in contrast to the alcohol recovery study, mainly tissue contractions are observed (blue). The incorporation of the additional structural information in white matter provided by DTI assists in constraining the local volume changes mapped by the fluid registration within a more focal region. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)