Registration, atlas generation, and statistical analysis of high angular resolution diffusion imaging based on riemannian structure of orientation distribution functions 6

Firstly, we proposed a novel large deformation diffeomorphic registration algorithm to align HARDI data characterized by ODFs.. We incorporated theRiemannian metric of ODFs for quantifyi

Conclusion and Future Work

Recent advances in diffusion-weighted imaging (DWI), such as High Angular lution Diffusion Imaging (HARDI), allows us to model the water diffusion at a voxelwith an orientation distribution function (ODF) that can capture multiple orientation at

Reso-a voxel MReso-ajor reseReso-arch questions Reso-are: how would one Reso-anReso-alyze the HADRI dReso-atReso-a Reso-andmake the correct inferences from the rich information provided? Whether new insightsinto the human brain, in particular white matter, would surface? Before HARDI can beuseful in both diagnosis and clinical applications, an ODF-based computational frame-work, including registration, atlas generation and regression analysis, etc, is needed forHARDI-based analysis across populations

Firstly, we proposed a novel large deformation diffeomorphic registration algorithm

to align HARDI data characterized by ODFs The proposed algorithm seeks an optimaldiffeomorphism of large deformation between two ODF fields in a spatial volumedomain and at the same time, locally reorients an ODF in a manner such that it remainsconsistent with the surrounding anatomical structure To this end, we first reviewedthe Riemannian manifold of ODFs We then defined the reorientation of an ODF when

an affine transformation is applied and subsequently, defined the diffeomorphic groupaction to be applied to the ODFs based on this reorientation We incorporated theRiemannian metric of ODFs for quantifying the similarity of two HARDI images into avariational problem defined under the large deformation diffeomorphic metric mapping(LDDMM) framework We finally derived the gradient of the cost function in bothRiemannian spaces of diffeomorphisms and the ODFs, and presented its numericalimplementation Both synthetic and real brain HARDI data were used to illustrate theperformance of our registration algorithm.

We also presented a Bayesian probabilistic model to estimate the HARDI atlas ofthe brain white matter First of all, we assumed that the HARDI atlas is generatedfrom a known hyperatlas through a flow of diffeomorphisms A shape prior of theHARDI atlas can thus be constructed based on LDDMM LDDMM characterizes anonlinear diffeomorphic shape space in a linear space of initial momentum that uniquelydetermines diffeomorphic geodesic flows from the hyperatlas Therefore, the shapeprior of the HARDI atlas can be modeled using a centered Gaussian random field(GRF) model of the initial momentum In order to construct the likelihood of observedHARDI datasets, it is necessary to study the diffeomorphic transformation of individualobservations relative to the atlas and the probabilistic distribution of ODFs To this end,

we constructed the likelihood related to the transformation using the same construction

as discussed for the shape prior of the atlas The probabilistic distribution of ODFswas then constructed based on the ODF Riemannian manifold We assumed that theobserved ODFs are generated by an exponential map of random tangent vectors atthe deformed atlas ODFs Hence, the likelihood of the ODFs can be modeled using aGRF of their tangent vectors in the Riemannian manifold of ODFs We solved for themaximum a posteriori using the Expectation-Maximization algorithm and derive the

corresponding update equations Finally, we illustrated the HARDI atlas constructedbased on a Chinese aging cohort of94 adults and compared it with that generated byaveraging the coefficients of spherical harmonics of the ODFs across subjects.

We further proposed a geodesic regression algorithm on the Riemannian manifold

of ODFs We derived the algorithm for the geodesic regression of ODFs and conductedthe simulation experiment to evaluate its performance We then examined the effects

of aging via geodesic regression of ODFs in a large group of healthy men and women,spanning the adult age range Results show that the proposed method is able to capturemore regions with age effect on white matter changes as compared to the conventionalregression based on DTI The evolution of ODF fields along the geodesic regressionline depicts in great detail the changes of white matter including the breakdown of themyelin sheath with aging and the anterior-posterior gradient of corpus callosum Inthe investigation of the regional aging effects where corpus callosum and corticospinaltracts come across, the result suggests that the diffusivity in corpus callosum declinesmore than in corticospinal tracts in the selected region To sum up, experiments haveshown that the HARDI-based computational framework offers valuable clues aboutthe changes of white matter in population studies that were previously undetected withexisting methods

Future work will aim to find new biomarkers sensitive to white-matter pathologiesrelated to neuropsychiatric disorders such as Alzheimer’s disease (AD) Together withthe HARDI-based tractography e.g., [32], we can quantify in detail the strength ofconnections along a specific pathway, which can be useful in the diagnosis and prognosis

of AD In addition, there were a few methods proposed for the reconstruction ofensemble average propagator (EAP) from original DWI images recently [e.g 114,

115, 116] In order to accurately reconstruct the diffusion signal and EAP, a thorough

exploration of q-space is needed, which requires multiple b-value diffusion weightedimaging (mDWI) MDWI can characterize more complex neural fiber geometries whencompared to single b-value techniques like diffusion tensor imaging (DTI) or highangular resolution diffusion imaging (HARDI) Hybrid diffusion imaging (HYDI) [117]

is a mDWI technique that samples the diffusion signal along concentric spherical shells

in q-space, with the number of encoding directions increased with each shell to increasethe angular resolution with the level of diffusion weighting MDWI techniques likeHYDI, however, have not been widely used by clinicians and neuroscientists partiallydue to their relatively long acquisition times In addition, there is a lack of fundamentalimage analysis tools, such as registration, that can fully utilize their information Ourfuture work will also include the extension of our framework to HDYI dataset

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