SUPPLEMENTAL MATERIAL

SpatialVascular Volume Fraction Imaging for Quantitative Assessment of Angiogenesis

Molecular Imaging and Biology

Junting Liu,1*Weiwei Fan,2*Muhan Liu,1Xiuduan Lin,1Yabin Wang,2Fu Wang,1

Xiaoyuan Chen,3Feng Cao,2#Jimin Liang1#

1School of Life Science and Technology, Xidian University, Xi’an, China;2Department of Cardiology, Xijing Hospital, Fourth Military Medical University, Xi’an, China; 3Laboratory of Molecular Imaging and Nanomedicine, National Institute of Biomedical Imaging and Bioengineering, National Institutes of Health, Bethesda, Maryland, USA

* Both contributed equally to this work.

Corresponding author:

Jimin LiangSchool of Life Science and Technology, Xidian University, Xi’an, China,P.O. Box 0528,266 Xinglong Section of Xifeng Rd, Xi’an, Shaanxi 710126, China

E-mail address:

Feng CaoDepartment of Cardiology, Xijing Hospital, Fourth Military Medical University, Xi’an, China,127 West Changle Rd, Xincheng District, 710032, Xi’an, China

E-mail address:

Supplemental Materials and Methods

SVVFmodeling

To quantitatively assess the angiogenesis and vascular density in deep tissue rather than in superficial planar DLPI, SVVF was defined as the fraction of microvascular enhancement of the 3D space based on the vascular volume data of hindlimb angiography at different time points and different spatial distances from the center of the stem cells. An icosahedron-based spherical quad-tree triangulation pattern was introduced to observe and analyze the hindlimb vasculature. The model is based on subdivision of a spherical icosahedrons, which originally used the analysis that had global coverage or covered the poles and provided a straightforward way of combining measurements from multiple observations in geosciences[1, 2]. According to the requirement of binning globally distributed measurements, the scheme was based on a network of evenly distributed grid points, which can be defined by repeated subdivision of spherical icosahedrons (The distribution of grid points as N=12 (Suppl. Figure1A) and N=42 (Suppl. Figure 1B). In this study, we chose N=42 grid points, to satisfy theappropriate measure points and resolution around the stem cell localization.

The spatial grid points on the spherical surface [2] were determined by:

(1)

These spherical harmonic transforms used colatitudes and longitude, where the basic functions were called the spherical harmonics of degree n and order m,

(2)

The grid points could be divided into ten levels from top to bottom on the spherical icosahedron, and the spatial locations of the small balls (the ball center locates the grid point) on every level were determined by the latitude (90-) of the large sphere.The polar coordinate system was established at the center of the reconstructed maximum source density point of the stem cells, thus we could determine every grid point coordinate as follows:

(3)

This spatial analysis model was adopted for the assessment of angiogenesis through vascular density development. A large sphere with a radius Rwas constructed whose center was determined by the reconstructed maximum source density point of the stem cells in the treatment group or by the ligation site in the controls, and R could be adjusted from 0.8 to 3 mm. Forty-two small balls (r = 0.3 mm) were located on the sphere with each grid point as the center respectively.

Supplemental Fig. 1.

A spherical scheme for binning globally distributed measurement points around the stem cells by repeated subdivision of spherical icosahedrons with (A) the distribution of grid points for N=12, (B) the distribution of grid points for N=42.

Supplemental Fig.2.

SVVF quantitative assessment results with the AD-MSCs’ survival and paracrine action at typical active radii (R=1.2, 1.7, 2.4mm) for 7, 14, 28 days and control (n=5 per group) after transplantation respectively.

References

1.Teanby NA (2006) An icosahedron-based method for even binning of globally distributed remote sensing data. Comput Geosci 32:1442-1450.

2.Blais JAR (2011) Discrete Spherical Harmonic Transforms of Nearly Equidistributed Global Data. JGeodetic Sci 1:251-258.