Longitudinal modeling of appearance and shape and its potential for clinical use

Abstract

Clinical assessment routinely uses terms such as development, growth trajectory, degeneration, disease progression, recovery or prediction. This terminology inherently carries the aspect of dynamic processes, suggesting that single measurements in time and cross-sectional comparison may not sufficiently describe spatiotemporal changes. In view of medical imaging, such tasks encourage subject-specific longitudinal imaging. Whereas follow-up, monitoring and prediction are natural tasks in clinical diagnosis of disease progression and of assessment of therapeutic intervention, translation of methodologies for calculation of temporal profiles from longitudinal data to clinical routine still requires significant research and development efforts. Rapid advances in image acquisition technology with significantly reduced acquisition times and with increase of patient comfort favor repeated imaging over the observation period. In view of serial imaging ranging over multiple years, image acquisition faces the challenging issue of scanner standardization and calibration which is crucial for successful spatiotemporal analysis. Longitudinal 3D data, represented as 4D images, capture time-varying anatomy and function. Such data benefits from dedicated analysis methods and tools that make use of the inherent correlation and causality of repeated acquisitions of the same subject. Availability of such data spawned progress in the development of advanced 4D image analysis methodologies that carry the notion of linear and nonlinear regression, now applied to complex, high-dimensional data such as images, image-derived shapes and structures, or a combination thereof. This paper provides examples of recently developed analysis methodologies for 4D image data, primarily focusing on progress in areas of core expertise of the authors. These include spatiotemporal shape modeling and growth trajectories of white matter fiber tracts demonstrated with examples from ongoing longitudinal clinical neuroimaging studies such as analysis of early brain growth in subjects at risk for mental illness and neurodegeneration in Huntington's disease (HD). We will discuss broader aspects of current limitations and need for future research in view of data consistency and analysis methodologies.

Keywords: Longitudinal imaging; Mixed-effects modeling; Shape analysis; Shape regression.

Fig. 1

Modeling of longitudinal data. Left: Nonlinear least squares (NLS) regression without considering repeated time points. Middle: Nonlinear mixed-effects modeling (NLME) with fixed effect (black) and subject-specific random effects (colored curves). Right: Regression result overlaid on NLME result. The figures indicate that regression provides a plausible model would one not know about repeated time points, but that mixed-effects modeling provides a significantly different result that reflects the average of the individual trajectories. The data, used here as an example, represents radial diffusivity changes of a brain subregion in longitudinal infant DTI datasets taken at neonate, 1 year and 2 years of age.

Fig. 2

Comparison of different growth models for longitudinal RD data of posterior thalamic radiation. Top: Posterior thalamic radiation is shown as red label on the longitudinal FA images of one subject. Images taken at 2 weeks, 1 year and 2 years. Bottom left: Linear mixed-effects models of RD. Bottom right: nonlinear mixed-effects models.

Fig. 3

Subject-specific interval compared to the overall prediction for RD of posterior thalamic radiation. Left: Subject-specific interval calculated based on only one time point (neonate). Right: Subject-specific interval calculated based on scans at neonate and 1 year. Subject-specific 95% prediction intervals (light blue) are compared to the overall prediction interval (gray shaded) for RD of posterior thalamic radiation. Solid blue curves illustrate the predicted subject trajectories based on NLME analysis. Red dots indicate subject’s test data left out for analysis but available for testing.

Fig. 4

Average development of genu fiber tract from 2 to 24 months. A) Observed data for all subjects, which is clustered around 2, 12, and 24 months. B) Genu fiber tracts estimated at several time points with velocity of fiber development displayed on the surface of the estimated fibers.

Fig. 5

A) Shape data used for model estimation in addition to image data. B) Evolution estimated for an HD subject at baseline, 3 years, and 6 years.

Fig. 6

Left: LME modeling of control versus risk Hungtinton’s groups. Right: Fixed effects trends from linear mixed-effects shape modeling. Example illustrates LME modeling of longitudinal segmentations of subcortical structures with three time points over two years from 7 controls and 6 Huntington’s subjects. Colormaps of fixed effects slopes for controls and HD indicate local expansion (blue) or contraction (yellow). Data and analysis courtesy of PREDICT-HD study and PhD thesis of Manasi Datar, Utah 2013.

Fig. 7

Scanner comparison via traveling phantom. Left: Subset of sagittal MRI of 3T Allegra and 3T Trio brain scans (top) and tissue segmentations (bottom). Right: Graph of normalized percentage tissue volumes for Tim Trio and Allegra data. White matter, gray matter, cerebrospinal fluid and intracranial volume are indicated as GM, WM, CSF and ICV. The Allegra results are plotted as open squares. Statistical analysis shows that the Allegra data differs significantly from the Trio data for WM, CSF and ICV. Results from 3 sites with 2 repetitions and 2 phantoms with Trio and 1 site with 2 repetitions and 2 phantoms with Allegra scanners are shown.