Surface Registration for Ventricular Morphometry

Analysis in Mild Cognitive ImpairmentJie Shi1, Cynthia M. Stonnington2, Paul M. Thompson3, Kewei Chen4, Boris Gutman3, Cole Reschke4,

Leslie C. Baxter5, Eric M. Reiman4, Richard J. Caselli6, and Yalin Wang1

1. CIDSE, Arizona State University 2. Department of Psychiatry and Psychology, Mayo Clinic Arizona 3. Imaging Genetics Center, Institute for Neuroimaging and Informatics,

University of Southern California 4. Banner Alzheimer’s Institute and Banner Good Samaritan PET Center 5. Human Brain Imaging Laboratory,

Barrow Neurological Institute 6. Department of Neurology, Mayo Clinic Arizona

jshi28@asu.edu

Introduction

We introduce a global conformal parameterization for the complex and

branching lateral ventricular surfaces with the hyperbolic Ricci flow

method. The parameterization minimizes angle distortions and has no

singularity points. From the conformal structure, we compute unique

and consistent geodesic curves on the ventricular surfaces. The

geodesic curves are then used as boundary conditions for ventricular

surface registration.

Methods

Fig. 1 summarizes the key steps in our ventricular surface registration

system.

Three boundaries are introduced on each ventricular surface as

shown in Fig. 1 (a). The process is called topology optimization.

Two paths connecting consistent endpoints of existing boundaries (as

show in Fig. 1 (b), points with the same colors) are traced on each

ventricular surface. The surface is then sliced open along the paths

and boundaries.

We compute hyperbolic metrics on ventricular surfaces after topology

optimization as shown in Fig. 1 (a) and embed them in the hyperbolic

space with the metrics and the simply connected surfaces as shown

in Fig. 1(b) with the hyperbolic Ricci flow method [1]. The hyperbolic

[3].

• Group comparison was performed in 71 mild cognitive impairment

(MCI) individuals who converted to incident AD in the subsequent 36

months, which we call the MCI converter group, and 62 MCI subjects

who did not convert to AD in the same period, which we call the MCI

stable group. All subjects are from the ADNI baseline dataset, as

summarized in Table 1.

Citations[1] Jin, M., et al., 2008. Discrete Surface Ricci Flow. IEEE Trans Vis

Comput Graph 14(5): 1030-1043.

[2] Chung, MK., et al., 2008. Tensor-Based Cortical Surface

Morphometry via Weighted Spherical Harmonic Representation. IEEE

Trans Med Imag 27, 1143-1151.

[3] Chung, MK., et al., 2005. Cortical thickness analysis in autism with

heat kernel smoothing. NeuroImage 25, 1256-1265.

[4] Chen, K., et al., 2011. Characterizing Alzheimer's disease using a

hypometabolic convergence index. Neuroimage 56, 52-60.

space is visualized with the Poincaré disk model as shown in Fig. 1

(c), which is the fundamental domain of a ventricular surface.

• Four fundamental domains at different periods are computed and

glued with the original fundamental domain to tile a finite portion of the

universal covering space, as shown in Fig. 1 (d).

• We recalculate the positions of the two paths in Fig. 1 (b) and their

complements as geodesics in the Poincaré disk, as shown in Fig. 1

(e). These geodesics are required to connect consistent endpoints of

existing geodesics, as shown in Fig. 1 (f).

We slice the universal covering space along the new geodesics and

form the canonical fundamental domain of the ventricular surface, as

shown in Fig. 1 (g).

The canonical fundamental domain is then converted a Euclidean

octagon with the Klein model, as shown in Fig. 1 (h). The octagon is

used as the parameter space for ventricular surface registration with

the constrained harmonic map.

• Permutation test with ventricular volume and surface area measures

did not detect significant differences between the two groups, the

permutation test corrected p-value is 0.0803 for the volume and

0.2922 for the surface area.

• Our method detected significant differences in the ventricular surface

shapes between the two groups. The permutation test corrected p-

value is 0.0172. Fig.2 shows the local areas with significant

differences on the ventricular surface.

• Correlation between ventricular morphology and the FDG-PET

derived brain functional biomarker, the hypometabolic convergence

index (HCI) [4] was performed to study the relationship between brain

structural morphology and functional changes in AD. Fig. 3 shows the

correlation p-map.

Figure 2. Statistical map showing local shape differences (p-values) between MCI

converter and MCI stable groups from the ADNI baseline dataset, based on tensor-

based morphometry (TBM) [2], which was smoothed by the heat kernel smoothing

method [3].

Figure 3. Correlation p-map between ventricular morphometry and HCI [4] with

smoothed TBM features [2,3].

Gender

(M/F)Education Age

MMSE at

Baseline

MCI

Converter

(n = 71)

45/26 15.99 ± 2.73 74.77 ± 6.81 26.83 ± 1.60

MCI Stable

(n = 62)44/18 15.87 ± 2.76 75.42 ± 7.83 27.66 ± 1.57

Table 1. Demographic information of studied MCI subjects in ADNI baseline dataset.

Experiments

• Surface deformations are measured by tensor-based morphometry

(TBM) [2], which is smoothed by the hear kernel smoothing method

Figure 1. System processing pipeline overview.