Integral curves from noisy diffusion MRI data with closed-form uncertainty estimates

Owen Carmichael, Lyudmila Sakhanenko

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


We present a method for estimating the trajectories of axon fibers through diffusion tensor MRI (DTI) data that provides theoretically rigorous estimates of trajectory uncertainty. We develop a three-step estimation procedure based on a kernel estimator for a tensor field based on the raw DTI measurements, followed by a plug-in estimator for the leading eigenvectors of the tensors, and a plug-in estimator for integral curves through the resulting vector field. The integral curve estimator is asymptotically normal; the covariance of the limiting Gaussian process allows us to construct confidence ellipsoids for fixed points along the curve. Complete trajectories of fibers are assembled by stopping integral curve tracing at locations with multiple viable leading eigenvector directions and tracing a new curve along each direction. Unlike probabilistic tractography approaches to this problem, we provide a rigorous, theoretically sound model of measurement uncertainty as it propagates from the raw MRI data, to the tensor field, to the vector field, to the integral curves. In addition, trajectory uncertainty is estimated in closed form while probabilistic tractography relies on sampling the space of tensors, vectors, or curves. We show that our estimator provides more realistic trajectory uncertainty estimates than a more simplified prior approach for closed-form trajectory uncertainty estimation due to Koltchinskii et al. (Ann Stat 35:1576–1607, 2007) and a popular probabilistic tractography method due to Behrens et al. (Magn Reson Med 50:1077–1088, 2003) using theory, simulation, and real DTI scans.

Original languageEnglish (US)
JournalStatistical Inference for Stochastic Processes
StateAccepted/In press - Aug 27 2015
Externally publishedYes


  • Asymptotic normality
  • Diffusion tensor imaging
  • Integral curve
  • Kernel smoothing

ASJC Scopus subject areas

  • Statistics and Probability


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