Pranay Prabhakar BS, Hua Zhang MD, De Chen PhD, …10.1007/s10456-014-9449... · Pranay Prabhakar...
Transcript of Pranay Prabhakar BS, Hua Zhang MD, De Chen PhD, …10.1007/s10456-014-9449... · Pranay Prabhakar...
Online supplemental material
Genetic variation in retinal vascular patterning predicts variation in pial collateral extent and stroke severity.
Pranay Prabhakar BS, Hua Zhang MD, De Chen PhD, James E. Faber PhD
Detailed materials and methods
Online Appendix 1. MATLAB code used to calculate fractal dimension and lacunarity.
Online Table 1. Collateral number, collateral diameter and retinal patterning metrics vary with genetic background.
Online Figure 1. Retinal tree segmentation.
Online Figure 2. Collateral number, collateral diameter and retinal patterning metrics vary with genetic background.
Online Figure 3. Among 4 strains of mice with large differences in collateral extent, the range of values is greater and
variance (SEMs) smaller for fractal dimension (panel C) determined for a randomly selected region of interest on arterial tree
(ROI) (inset in A) than for whole retina (B).
Online Figure 4. Fractal dimension of the distal-most region of the vasculature between adjacent artery and vein trees (ie, the
“capillary bed”) lacks strain-dependent differences shown in Online Figure 2 for whole retina or individual artery trees.
Online Figure 5. Complexity of genetic-dependent vascular patterning, as indicated by fractal dimension of randomly
selected artery trees, is not altered by removal of the distal-most region of the vasculature between adjacent artery and vein;
however, variance (SEMs) is reduced.
Online Figure 6. Comparison of fractal dimension (FD) and lacunarity (Lac) obtained from 3, 2 and 1 randomly chosen
arterial tree(s).
Online Figure 7. Retinal patterning predicts pial collateral number (COL-N) and diameter (COL-D).
Online Figure 8A. Differences in fractal dimension (FD) and lacunarity (L) of retinal artery trees are associated with
differences in retinal patterning metrics (RPMs). Online Figure 8B-I. Among RPMs characterizing retinal arterial tree
complexity, differences in FD and L are most strongly associated with differences in CRAE and average length of branch
segments, respectively.
Online supplemental material (continued)
Online Figure 9. Both retinal patterning metrics (RPMs) and middle-cerebral artery patterning metrics (MCAM) vary with
genetic background, but only half showed significant or suggestive correlations with each other).
Online Figure 10. Middle cerebral artery patterning metrics (MCAMs) predict pial collateral number (COL-N) and diameter
(COL-D).
Online Figure 11. Among the most predictive MCAMs, average number of MCA tree branch segments per unit MCA area (ie,
MCA branching density) contributes the most, statistically, to predicting collateral number and diameter (COL-N and COL-
D). MCA trees with larger branch angle, larger caliber of branching vessels (D1, D2), and larger cerebral hemisphere areas
tend to have greater collateral extent (COL-N and/or COL-D).
References for supplemental material.
Detailed materials and methods
Pial collateral number and diameter. Brains were obtained from a population of ~3 month-old male mice (n=81) composed of
10 strains that differ widely in collateral extent.1-3 The deficient strains were: VEGFAlo/+ A/J, AKR/J, CLIC4-/-, and BALB/cBy/J;
the abundant strains were: C57BLKS/J, DBA/2J, VEGFAhi/+, C57BL/6, and CD1/CR (this is the background strain for VEGFAlo/+,
VEGFAhi/+, and CLIC4-/-) (Figure 1). As described in detail elsewhere,1 mice were anesthetized with ketamine and xylazine (100
and 10 mg/kg ip), heparinized, and the cerebral vasculature perfused via the thoracic aorta at 100 mmHg with phosphate buffered
saline (PBS) containing 10-4M nitroprusside to produce maximal vasodilation and Evans blue to stain the endothelium. While this
proceeded, a craniotomy was performed and the dorsal surface of the neocortex was treated topically with 4% paraformaldehyde
(PFA) to fix the vasculature at maximal diameter. Under a stereomicroscope, the cerebral arterial vasculature was then filled with
yellow MicroFilR with a viscosity set to minimize capillary transit to allow filling of the entire pial arterial circulation. After the
microFil had set, the brain was fixed overnight in 4% PFA and imaged under a stereomicroscope to count the number of collaterals
(COL-N) interconnecting the middle and anterior cerebral arterial (MCA, ACA) trees. The brain was then immersed in Evans blue
in PBS to stain the brain parenchyma for contrast. Digital images were collected and collateral diameter (COL-D) was obtained as
the average of 3 points along the center-most length of each collateral using ImageJ software. The brain was oriented to present
the MCA tree in focus, and images were obtained for digital segmentation as describe below for the retina.
Mouse retina preparation. Before the above procedures, retinas were collected from one eye of each of the above mice (n=81).
Enucleation. Mice were anesthetized with ketamine and xylazine, and eyelids were reflected with a curved forceps. Using a
stereomicroscope, the optic-nerve was severed with irridectomy scissors and the eyeball was removed and immersed in 2% PFA for
2 hours or 4% PFA for 1 hour. Eyeballs were stored at 4C in PBS if necessary for 8 days. Removal of retina. The eyeball was
held in place with corneal side up in a Silastic-bottom glass petri dish using micropins (#26002-20, FST) passed through
connective tissue attached to the sclera, and kept moist with PBS throughout the procedure. Using a 27 gauge needle, a 1 mm slit
was cut at an oblique angle through the cornea at a point above the equator of the eye ball. The cornea was circumcised from the
sclera by placing one blade of a Vannas scissors into the slit and hinging it on the petri dish edge, positioning the scissors tangential
to the cornea and parallel to the surgical table surface, gradually cutting along the cornea’s circumference while rotating the dish
one whole turn in order to hemisect the eye just above the ora serrata. The lens and vitreous were gently suctioned using a
micropipette followed by rinsing the retinal cup with PBS without disrupting the retina. This process was repeated 2-3 times to
ensure maximum removal of the vitreous from the retinal surface. The sclera was further fastened to the silastic bottom using
additional pins. The retina was gradually separated from the sclera with the ora serrata intact, using fine forceps. The retinal cups
were transferred to 96 well-plates containing PBS. Staining. Following removal of PBS, retinal cups were incubated in ice cold
70% methanol for 10 minutes, rinsed with PBS 3 times for 5 minutes and incubated in PBS with 1% Triton X-100 for 30 minutes.
After an additional rinse with PBS, retinal cups were incubated overnight in Alexafluor 568 GS-IB4 (l21412, Invitrogen) at 10
μg/mL in PBS on a rotator at 4ºC in the dark. Retinas were then rinsed with PBS, incubated in 1% Triton X-100 in PBS for 20
minutes, and then re-rinsed 3 times for 5 minutes in PBS.
Detailed materials and methods (continued)
Mouse retina preparation. Mounting. Retinal cups were carefully lifted with fine forceps and placed onto Superfrost-Plus
charged slides in a PBS bubble within a Pap-Pen-marked hydrophobic boundary. Using the Vannas scissors, four deep cuts were
made along the circumference of the cup, extending from the ora serrata towards the optic nerve opening in order to sufficiently
flatten the retina. Flattened retina was mounted onto another Superfrost-Plus slide with Vectashield under a coverslip, which was
sealed with fingernail polish. Imaging. Slides were stored in paper folders in the dark at 4ºC and imaged and optically flattened
using a 10x objective lens on a Nikon Surveyor microscope within 5 days of cover-slipping.
Infarct volume. Permanent occlusion of the right MCA trunk by micro-cautery midway between the zygomatic arch and the pinna
of the ear, as detailed previously,2-3 was done on different mice from those used for the above procedures. Briefly, mice were
anesthetized with ketamine and xylazine and maintained at 37C rectal temperature. A 4mm skin incision was made, the midpoint
of the temporal muscle separated, and a 2mm burr-hole was made over the trunk of the MCA. The MCA was cauterized and
transected, the incision closed, cephazolin and buprenorphine administered, and mice were maintained at 37C rectal temperature
until awake. After an overdose of ketamine (100mg/kg ip) and xylazine (15 mg/kg ip) 24 hours later, brains were removed and
cooled on dry ice until the tissue became stiff, and 1 mm coronal slices were incubated in 1% 2,3,5-tripenyltetrazolium chloride in
PBS at 37C for 20 minutes, then fixed with 1% PFA overnight. Infarct volume was calculated as the sum of the unstained
volumes and expressed as a percent of total right cortical volume.
C57BLKS (8) DBA/2 (8) VEGFAhi/+
(10) C57BL/6 (8) CD-1 (8) VEGFAlo/+
(7) A/J (8) AKR (8) CLIC4-/-
(8) BALB/c (8) Adjusted R2 p-value
N Collateral number 24.75 (22.42, 27.08) 19.75 (17.42, 22.08) 20.60 (18.51, 22.69) 18.75 (16.42, 21.08) 18.13 (15.79, 20.46) 10.43 (7.93, 12.92) 6.13 (3.79, 8.46) 5.00 (2.51, 7.50) 2.75 (0.42, 5.08) 0.88 (-1.46, 3.21) 0.86 <.0001
DAverage collateral
diameter (µm)22.03 (20.97, 23.09) 20.73 (19.67, 21.79) 20.41 (19.47, 21.36) 20.71 (19.65, 21.77) 18.90 (17.85, 19.96) 17.23 (16.10, 18.36) 11.74 (10.69, 12.80) 11.94 (10.81, 13.07) 12.90 (11.84, 13.96) 13.92 (12.58, 15.26) 0.87 <.0001
1 Do (µm) 25.97 (24.27, 27.67) 22.51 (20.81, 24.22) 22.38 (20.85, 23.90) 18.93 (17.22, 20.63) 21.32 (19.62, 23.02) 17.70 (15.89, 19.52) 18.70 (17.00, 20.40) 18.17 (16.35, 19.99) 13.11 (11.41, 14.81) 16.05 (14.34, 17.75) 0.67 <.0001
2 D1 (µm) 12.04 (11.39, 12.69) 11.21 (10.56, 11.86) 10.44 (9.86, 11.02) 10.47 (9.82, 11.13) 9.95 (9.30, 10.60) 10.19 (9.50, 10.89) 11.02 (10.37, 11.67) 11.49 (10.80, 12.19) 8.58 (7.93, 9.23) 10.33 (9.68, 10.99) 0.46 <.0001
3 D2 (µm) 25.59 (23.97, 27.21) 22.29 (20.67, 23.91) 21.42 (19.98, 22.87) 18.51 (16.89, 20.13) 20.87 (19.25, 22.49) 17.37 (15.64, 19.10) 17.92 (16.30, 19.53) 17.60 (15.87, 19.33) 12.58 (10.96, 14.20) 15.53 (13.92, 17.15) 0.69 <.0001
4Tortuosity index (inner
zone)1.02 (1.01, 1.03) 1.01 (1.00, 1.02) 1.02 (1.02, 1.03) 1.01 (1.00, 1.02) 1.01 (1.01, 1.02) 1.02 (1.01, 1.03) 1.01 (1.00, 1.02) 1.02 (1.01, 1.03) 1.02 (1.01, 1.02) 1.02 (1.01, 1.03) 0.03 0.274
5 CRAE (µm) 46.03 (43.30, 48.77) 41.13 (38.40, 43.87) 42.61 (40.17, 45.06) 33.23 (30.50, 35.96) 41.18 (38.45, 43.92) 31.89 (28.97, 34.82) 33.14 (30.41, 35.88) 34.44 (31.52, 37.36) 25.45 (22.72, 28.18) 27.46 (24.72, 30.19) 0.73 <.0001
6 CRVE (µm) 77.63 (72.70, 82.57) 70.98 (66.05, 75.92) 63.49 (59.08, 67.91) 51.54 (46.61, 56.48) 59.61 (54.67, 64.54) 61.31 (56.03, 66.58) 51.01 (46.08, 55.94) 59.38 (54.11, 64.66) 38.18 (33.24, 43.11) 39.01 (34.08, 43.95) 0.74 <.0001
7 AVR 0.60 (0.55, 0.66) 0.58 (0.53, 0.64) 0.68 (0.63, 0.72) 0.65 (0.59, 0.70) 0.70 (0.65, 0.76) 0.53 (0.47, 0.59) 0.65 (0.60, 0.71) 0.58 (0.53, 0.64) 0.67 (0.61, 0.72) 0.71 (0.65, 0.76) 0.28 0.0001
8 Branch angle 83.74 (77.42, 90.07) 97.47 (91.15, 103.80) 75.85 (70.19, 81.51) 79.84 (73.52, 86.17) 80.45 (74.12, 86.77) 78.68 (71.91, 85.44) 68.39 (62.07, 74.72) 83.72 (76.95, 90.48) 66.25 (59.93, 72.58) 75.37 (69.04, 81.69) 0.43 <.0001
9 Optimality 0.83 (0.78, 0.88) 0.97 (0.92, 1.02) 0.81 (0.76, 0.85) 0.84 (0.79, 0.89) 0.85 (0.80, 0.90) 0.85 (0.80, 0.91) 0.84 (0.79, 0.89) 0.99 (0.94, 1.05) 0.86 (0.81, 0.91) 0.87 (0.82, 0.92) 0.35 <.0001
10 Retinal area (µm2)
1.66E+07 (1.53E+07,
1.79E+07)
1.61E+07 (1.49E+07,
1.74E+07)
1.72E+07 (1.61E+07,
1.84E+07)
1.62E+07 (1.50E+07,
1.75E+07)
1.64E+07 (1.51E+07,
1.77E+07)
1.60E+07 (1.46E+07,
1.74E+07)
1.56E+07 (1.43E+07,
1.69E+07)
1.57E+07 (1.43E+07,
1.70E+07)
1.48E+07 (1.35E+07,
1.61E+07)
1.35E+07 (1.22E+07,
1.48E+07)0.16 0.009
11 Fractal dimension 1.503 (1.490, 1.517) 1.481 (1.467, 1.495) 1.488 (1.475, 1.500) 1.469 (1.455, 1.482) 1.484 (1.470, 1.497) 1.472 (1.458, 1.487) 1.472 (1.459, 1.486) 1.470 (1.456, 1.485) 1.446 (1.433, 1.460) 1.464 (1.450, 1.477) 0.32 <.0001
12 Lacunarity 15.82 (13.48, 18.17) 21.05 (18.71, 23.40) 18.05 (15.95, 20.15) 21.13 (18.79, 23.48) 18.32 (15.97, 20.66) 21.10 (18.59, 23.61) 21.62 (19.27, 23.96) 19.98 (17.47, 22.49) 23.64 (21.29, 25.98) 19.29 (16.94, 21.64) 0.23 0.001
13 Arterial tree area (µm2)2.04E+05 (1.80E+05,
2.27E+05)
1.61E+05 (1.37E+05,
1.85E+05)
1.82E+05 (1.61E+05,
2.04E+05)
1.71E+05 (1.47E+05,
1.94E+05)
2.12E+05 (1.88E+05,
2.36E+05)
1.90E+05 (1.64E+05,
2.15E+05)
1.64E+05 (1.40E+05,
1.88E+05)
1.51E+05 (1.26E+05,
1.77E+05)
1.09E+05 (8.47E+04,
1.33E+05)
1.43E+05 (1.20E+05,
1.67E+05)0.38 <.0001
14Skeltonized arterial tree
area (µm2)
1.46E+04 (1.27E+04,
1.65E+04)
1.08E+04 (8.86E+03,
1.27E+04)
1.41E+04 (1.24E+04,
1.58E+04)
1.35E+04 (1.16E+04,
1.54E+04)
1.60E+04 (1.41E+04,
1.79E+04)
1.50E+04 (1.29E+04,
1.70E+04)
1.28E+04 (1.09E+04,
1.47E+04)
1.11E+04 (9.10E+03,
1.32E+04)
9.49E+03 (7.59E+03,
1.14E+04)
1.23E+04 (1.04E+04,
1.42E+04)0.29 <.0001
15Average arterial tree
diameter (µm)14.02 (13.21, 14.84) 15.20 (14.38, 16.02) 13.06 (12.33, 13.79) 12.62 (11.80, 13.43) 13.25 (12.43, 14.06) 12.62 (11.75, 13.49) 12.87 (12.05, 13.68) 13.63 (12.76, 14.50) 11.53 (10.71, 12.34) 11.70 (10.88, 12.52) 0.40 <.0001
16
Number of arterial tree
branch segments/tree
area (µm2)
1.24E-03 (1.11E-03,
1.37E-03)
1.13E-03 (1.00E-03,
1.26E-03)
1.43E-03 (1.32E-03,
1.54E-03)
1.46E-03 (1.33E-03,
1.59E-03)
1.33E-03 (1.21E-03,
1.46E-03)
1.45E-03 (1.32E-03,
1.59E-03)
1.21E-03 (1.08E-03,
1.34E-03)
1.37E-03 (1.23E-03,
1.50E-03)
1.44E-03 (1.32E-03,
1.57E-03)
1.37E-03 (1.24E-03,
1.49E-03)0.20 0.0025
17Average tortuosity of
branch segments 1.07 (1.07, 1.07) 1.07 (1.06, 1.07) 1.07 (1.07, 1.07) 1.07 (1.06, 1.07) 1.07 (1.07, 1.07) 1.07 (1.06, 1.07) 1.07 (1.07, 1.07) 1.07 (1.07, 1.07) 1.07 (1.07, 1.07) 1.08 (1.07, 1.08) 0.33 <.0001
18
Skewness of distrubtion
of branch segment
tortuosity
3.64 (2.61, 4.66) 0.78 (-0.24, 1.81) 2.03 (1.11, 2.95) 0.99 (-0.04, 2.02) 3.02 (1.99, 4.05) 1.06 (-0.03, 2.16) 1.61 (0.59, 2.64) 2.00 (0.91, 3.10) 1.28 (0.26, 2.31) 3.51 (2.49, 4.54) 0.27 0.0002
19
Kurtosis of distribution
of branch segment
tortuosity
37.29 (23.53, 51.06) 2.92 (-10.84, 16.68) 15.10 (2.79, 27.41) 4.91 (-8.85, 18.68) 31.61 (17.85, 45.37) 4.92 (-9.79, 19.64) 9.61 (-4.15, 23.37) 10.84 (-3.87, 25.55) 5.84 (-7.92, 19.61) 28.47 (14.70, 42.23) 0.21 0.002
20Avg length of branch
segments (µm)66.26 (62.42, 70.10) 69.09 (65.25, 72.93) 62.29 (58.85, 65.72) 63.40 (59.56, 67.24) 66.21 (62.37, 70.05) 63.57 (59.46, 67.67) 76.04 (72.20, 79.88) 63.17 (59.07, 67.28) 71.37 (67.53, 75.21) 73.57 (69.73, 77.41) 0.38 <.0001
21
Skewness of distribution
of branch segment
lengths
3.19 (2.71, 3.67) 3.42 (2.95, 3.90) 3.11 (2.68, 3.53) 3.12 (2.64, 3.60) 3.04 (2.56, 3.51) 3.19 (2.68, 3.70) 2.66 (2.19, 3.14) 4.36 (3.85, 4.87) 2.47 (2.00, 2.95) 2.73 (2.25, 3.20) 0.28 0.0002
22
Kurtosis of distribution
of branch segment
lengths
17.68 (12.06, 23.30) 19.42 (13.80, 25.05) 17.40 (12.37, 22.43) 17.08 (11.45, 22.70) 16.31 (10.68, 21.93) 16.36 (10.35, 22.38) 11.56 (5.93, 17.18) 30.50 (24.49, 36.51) 9.84 (4.22, 15.47) 12.49 (6.87, 18.12) 0.24 0.0007
ANOVACOL-D, COL-N and
RPMs (Mean and
95% CI)
Mouse strain (n size)
Online Table 1. Collateral number, collateral diameter and retinal patterning metrics vary with genetic background. Table shows averages,
95% confidence intervals, and bivariate regression of COL-N, COL-D, and 22 RPMs versus 10 mouse strains (one-way ANOVA - adjusted R2 and
p-value). Strains arranged left-to-right according to strains with the largest and smallest number of pial collaterals (n = number of mice studied).
Shading in ANOVA column reflects relative strength of association (adjusted R2 value; shading same as black bars shown in Figure 5).
Online Figure 1. Retinal tree segmentation. Image of flat-mounted stained retina (A) is segmented using Photoshop CS4, 3
retinal trees are randomly selected and capillaries are manually pruned away using specified segmentation rules so that only 1st,
2nd, 3rd, and the half-length of 4th order arterioles are retained (B). Using a combination of the Leveling tool and optimization of
brightness and contrast, background is eliminated, dark or missing segments of trees are filled in and the image is thresholded (C).
A B
C
*0.86 (<.0001)
0.87 (<.0001) 0.67 (<.0001) 0.46 (<.0001)
0.69 (<.0001) 0.03 (0.274) 0.73 (<.0001) 0.74 (<.0001)
0.28 (0.0001) 0.43 (<.0001) 0.16 (0.009)
0.32 (<.0001) 0.23 (0.001) 0.38 (<.0001)
0.4 (<.0001) 0.2 (0.0025) 0.33 (<.0001) 0.27 (0.0002)
0.21 (0.002) 0.38 (<.0001) 0.28 (0.0002) 0.24 (0.0007)
0.35 (<.0001)
0.29 (<.0001)
Strain: (A) A/J; (B) AKR; (C) BALB/c; (D) C57BLKS; (E) C57BL/6; (F) CLIC4-/-; (G) DBA/2; (H) VEGFAhi/+; (I) VEGFAlo/+; (J) CD-1
Online Figure 2. Collateral number, collateral diameter and retinal patterning metrics vary with genetic
background. Graphs show averages, 95% confidence intervals, and bivariate regression of COL-N, COL-D, and 22 RPMs
versus 10 mouse strains (one-way ANOVA - adjusted R2 and p-value are given on the graphs). Horizontal line across each
graph represents mean of the metric across all strains. Top and bottom points of diamond represent the 95% confidence
interval of the mean for each strain. Diamond width is proportional to the n-size of the strain. Relative variation in vertical
position of diamonds reveals degree to which COL-N, COL-D, and RPMs vary across all strains.
Note, Figure 3D in the manuscript proper shows 1 of 3-4 selected arterial trees chosen randomly from a retina. The
distribution displayed for this arterial tree happens to lack branch segments measuring 175-200 microns length, which makes
the distribution appear to have two peaks, ie, one large population of small branches and another smaller population with
really large branches. This is an incidental finding secondary to biological variation and experimental error. The consistently
positive skewness of distribution of branch segment lengths for all arterial trees reflects continued branching of the central
retinal artery into a few large parent trunks which, in turn, further divide into smaller daughters as terminal branching
approaches capillaries.
0 1 2 3 4 5 6 7 80
2
4
6
8 BC
BLKS
DBA/2
AKR
Log2 (r)
La
cu
na
rity
of
RO
I
A B
D
1.72
1.74
1.76
1.78
1.80
1.82
1.84
1.86
BC AKR BLKS DBA/2
Fra
cta
l d
ime
ns
ion
of
wh
ole
re
tin
a1.56
1.60
1.64
1.68
1.72
1.76
1.80
1.84
BC AKR BLKS DBA/2
Fra
cta
l d
imen
sio
n o
f R
OI
C
Online Figure 3. Among 4 strains of mice with large differences in collateral extent, the range of values is greater and
variance (SEMs) smaller for fractal dimension (panel C) determined for a randomly selected region of interest on arterial
tree (ROI) (inset in A) than for whole retina (B). Thus, the complexity of the branching pattern of arterial trees likely contain
more genetic background-specific features than the capillary bed and venous trees. Removal of the capillaries and venules/veins
will therefore increase the statistical power to test for association of retinal vascular patterning metrics with pial collateral number
and diameter among genetically distinct strains. A, representative image stained with IB4 lectin and converted to gray-scale. Distal
arterial trees were randomly selected and analyzed for an ROI of constant dimension. See Figure 3 for determination of fractal
dimension and lacunarity. Values here and in other on-line figures are means ± SEM unless indicated otherwise. Fractal dimension
and lacunarity varied with strain (ANOVA, p < 0.05). BC, BALB/c strain; BLKS, C57BLKS strain. N = 5 mice per strain.
Online Figure 4. Fractal dimension of the distal-most region of the vasculature between adjacent artery and vein trees (ie,
the “capillary bed”) lacks strain-dependent differences shown in Online Figure 2 for whole retina or individual artery trees.
The lower values than in Online Figure 3 indicate that patterning of the capillary bed has less complexity than individual arterial
trees or whole retina. Fractal dimension was determined for randomly selected ROIs of constant dimension that encompassed the
capillary bed between an artery and vein tree (See Online Figure 1 for methods). These findings indicate that removal of capillaries
from each artery tree during image processing (“pruning”) is required to obtain arterial patterning metrics to test for association with
genetic background-dependent differences in collateral number and diameter. A representative ROI showing Alexa-568 isolectin B4
staining is shown above left. N = 5 mice per strain. The absence of strain dependent differences in fractal dimension for the
capillary bed is consistent with evidence that angiogenesis (capillary formation) is dominated by stochastic processes. 4 The
findings in Online Figures 2-4 that the more mesh-like capillary network must be removed to accurately measure fractal dimension
of a dichotomously branching artery tree is intuitive and also supported elsewhere.5
1.20
1.24
1.28
1.32
1.36
1.40
1.44
1.48
1.52
1.56
1.60
BALB/c AKR C57BLKS DBA/2
Fra
cta
l d
imen
sio
n
connect to vein
connect to artery
Data at right, taken from Online
Figure 2, shows FD and Lac for fully
processed arterial trees used in the
main analysis in this study (Figure 5)
– for comparison to the above data.
Strains: B – AKR, C – BALB/c, D –
C57BLKS, G – DBA/2 (red boxes).
Type I Type II BC B6
Type I Type II BC B6
1.40
1.42
1.44
1.46
1.48
1.50
1.52
1.54
1.56
BC B6
*
5 5
Fra
cta
l d
ime
ns
ion
1.40
1.42
1.44
1.46
1.48
1.50
1.52
1.54
1.56
BC B6
**
5 5
Fra
cta
l d
ime
ns
ion
A
C
B
D
Online Figure 5. Complexity of genetic-dependent vascular patterning, as indicated by fractal dimension of randomly
selected artery trees, is not altered by removal of the distal-most region of the vasculature between adjacent artery and
vein; however, variance (SEMs) is reduced. A,B, representative binarized images and summary data after pruning away the
venous side of the “capillary” bed back to the capillary midpoints. C,D, images and data of artery trees after pruning away
capillaries and distal-most arterioles to just before joining the parent arteriole. Thus, pruning away of capillaries and distal-
most arterioles of each retinal artery tree during image processing yields genetic-dependent arterial patterning metrics with the
least variance. N = 5 mice per strain. , p <0.05, 0.01. BC, BALB/c strain; B6, C57Bl/6 strain. Fractal dimension,
lacunarity and the Image J “plug-in” metrics reported in figures and tables in the paper and in the on-line section were obtained
from artery tree images processed as shown in Figure 2 and On-line Figures 1 and 5A,C.
Online Figure 6. Comparison of fractal dimension (FD) and lacunarity (Lac) obtained from 3, 2 and 1 randomly chosen
arterial tree(s). Tree segmentation for obtaining semi-automated retinal patterning metrics (Online Figure 1) is a labor-intensive
process. Average FD and Lac, two dimensionless measures of image complexity (Figure 3), were measured from 3 randomly
chosen tree(s) from 5 mouse retinas each for 4 strains (AKR, BALB/c, C57BLKS, and DBA/2) that vary widely in collateral
number (n=20) (Online Table 1). The above data show a strong correlation between average FD and lacunarity obtained from 3
versus 2 trees (A, C) (adjusted R2 of 0.86 and 0.83, respectively), which drops significantly when comparing 3 versus 1 tree (B,
D) (adjusted R2 of 0.64 and 0.55, respectively). Thus, for the remaining 60 mice in the study, only 2 randomly chosen arterial
trees were segmented in order to achieve an optimal trade-off between accuracy and time required for image segmentation.
Adjusted R2 = 0.86
P value = <0.0001
Adjusted R2 = 0.64
P value = <0.0001
Adjusted R2 = 0.83
P value = <0.0001
Adjusted R2 = 0.55
P value = <0.0001
A Strain
B. AKR
C. BALB/c
D. C57BLKS
G. DBA/2
B
C D
Fra
cta
l d
ime
ns
ion
L
ac
un
ari
ty
Online Figure 7. Retinal patterning predicts pial collateral number (COL-N) and diameter (COL-D). Figure shows results of forward, backward, and mixed
direction stepwise multivariate regression of COL-N and COL-D versus retinal patterning metrics (RPMs) using different stopping rules—minimum AIC, minimum
BIC, and p-value cutoffs (p<0.25 for RPM to enter and >0.10 to leave model) before (RM1) and after (RM2 and 3) removal of influential outliers (Figure 4). Predictive
performance across all models (RM1, RM2, and RM3) as determined by K-fold R2 calculated from leave-one-out cross validation was strong (0.73-0.83 for COL-N
and 0.59-0.73 for COL-D) and confirmed our hypothesis that RPMs can be used to predict COL-N and COL-D. Removal of outliers improved K-fold R2 but did not
change our conclusion. Directionality, strength, and significance of correlation of RPMs with COL-N and COL-D across all models is displayed and highlights the
RPMs that remained predictive throughout all models. 11 of the 16 RPMs found to predict COL-N also predicted and correlated with COL-D in a similar direction,
consistent with the covariance of COL-N and COL-D in the mouse population (Figure 1) suggesting that genetic determinants of variation in collateral extent also
influence variation in key features of retinal vascular patterning. The most predictive models based on highest K-fold R2 was used to calculate a Retinal Predictor Index
for COL-N and COL-D (RPIn and RPId, respectively) and further examined to determine comparative predictive ability of individual RPMs (Figure 6).
a b c d e f g a b c d e f g a b c d e f g a b c d e f g a b c d e f g a b c d e f g
1 Do (µm) ↓ ↓
2 D1 (µm)
3 D2 (µm) ↑ ↑
4 Tortuosity index (inner zone)
5 CRAE (µm) ↑
6 CRVE (µm) ↑ ↑
7 AVR ↑
8 Branch angle ↑ ↑
9 Optimality ↓ ↓
10 Retinal area (µm2) ↑ ↑
11 Fractal dimension ↑
12 Lacunarity ↑
13 Arterial tree area (µm2) ↓ ↓
14 Skeltonized arterial tree area (µm2)
15 Average arterial tree diameter (µm)
16 Number of arterial tree branch segments/tree area (µm2)
17 Average tortuosity of branch segments ↓ ↓
18 Skewness of distrubtion of branch segment tortuosity
19 Kurtosis of distribution of branch segment tortuosity ↑
20 Avg length of branch segments (µm) ↓ ↓
21 Skewness of distribution of branch segment lengths ↓ ↓22 Kurtosis of distribution of branch segment lengths ↓ ↓
RM2 RM3R elat io nship
with C OL-N
RM1 RM2 RM3R elat io nship
with C OL-D
RM1Retinal Patterning Metric (RPM)
Collateral number (COL-N) Collateral diameter (COL-D)
p<0.001
p<0.01
p<0.05
p>0.05
P-valueDirection Criteria
a Forward
b Backward
c Forward
d Backward
e Forward
f Backward
g Mixed
ModelStewise Regression
Minimum AIC
Minimum BIC
P-value (<0.25 to enter
and <0.10 to leave
model)
0.55
0.65
0.75
0.85
0.55
0.65
0.75
0.85
RPIn
RPId
K-f
old
R2
= Most predictive models
0.4
0.5
0.6
0.7
p<0.001
p<0.01
p<0.05
p>0.05
P-valueDirection Criteria
a Forward
b Backward
c Forward
d Backward
e Forward
f Backward
g Mixed
ModelStewise Regression
Minimum AIC
Minimum BIC
P-value (<0.25 to enter
and <0.10 to leave
model)
RPMFD
K-f
old
R2
= Most predictive models
0.4
0.5
0.6
0.7
RPMLac
Online Figure 8A (below) and 8B-I (next page). See subsequent pages for legend.
A
a b c d e f g a b c d e f g
1 Do (µm)
2 D1 (µm)
3 D2 (µm) ↑ ↓
4 Tortuosity Index (Inner zone) ↓
5 CRAE (µm) ↑ ↓
8 BranchAngle ↓
9 Optimality
13 Arterial tree area (µm^2) ↑
14 Skeltonized arterial tree area (µm) ↑
15 Average arterial tree diameter (µm) ↑ ↑
16 Number of arterial tree branch segments/tree area (µm^2) ↑
17 Average tortuosity of branch segments ↑ ↓
18 Skewness of distrubtion of branch segment tortuosity ↑
19 Kurtosis of distribution of branch segment tortuosity ↓
20 Average length of branch segments (µm) ↓ ↑
21 Skewness of distribution of branch segment lengths ↓ ↑22 Kurtosis of distribution of branch segment lengths ↓
RMR elat io nship
with L
RMRetinal Patterning Metric (RPM)
Fractal dimension (FD) Lacunarity (Lac)
R elat io nship
with F D
B
D
C
E
Predicted Lacunarity (RPMLac)
Predicted Fractal dimension (RPMFD)
K-fold R2=0.64****
K-fold R2=0.49****
F
G
Strain
A. A/J
B. AKR
C. BALB/c
D. C57BLKS
E. C57BL/6
F. CLIC4-/-
G. DBA/2
H. VEGFAhi/+
I. VEGFAlo/+
J. CD-1
Lacu
nar
ity
(Lac
) Fr
acta
l dim
en
sio
n (
FD)
Par
eto
plo
t Sc
ale
d p
aram
ete
r e
stim
ates
Lacu
nar
ity
(Lac
)
Par
eto
plo
t Sc
ale
d p
aram
ete
r e
stim
ates
Frac
tal d
ime
nsi
on
(FD
)
Term Scaled Estimate Std Error P-value
Intercept 1.475 0.001 <.0001
Average tortuosity of branch segments 0.030 0.005 <.0001
CRAE (µm) 0.025 0.005 <.0001
Average arterial tree diameter (µm) 0.022 0.005 <.0001
Kurtosis of distribution of branch segment tortuosity -0.021 0.006 0.0007
Skewness of distribution of branch segment lengths -0.014 0.005 0.004
Skeltonized arterial tree area (µm) 0.013 0.003 0.0002
Average length of branch segments (µm) -0.011 0.004 0.011
TermOrthogonalized
Estimate
CRAE (µm) 0.0163
Skeltonized arterial tree area (µm) 0.0058
Kurtosis of distribution of branch segment tortuosity -0.0050
Average tortuosity of branch segments 0.0045
Average length of branch segments (µm) -0.0038
Average arterial tree diameter (µm) 0.0038
Skewness of distribution of branch segment lengths -0.0034
H FD = 1.41; L = 27.0 FD = 1.54; L ac= 13.7 I
1 mm 1 mm 0.5 mm 0.5 mm
Term Scaled Estimate Std Error P-value
Intercept 19.937 0.287 <.0001
Skewness of distribution of branch segment lengths 11.609 4.175 0.0069
Number of arterial tree branch segments/tree area (µm2) 10.455 4.303 0.0176
Kurtosis of distribution of branch segment lengths -8.870 3.816 0.023
Average length of branch segments (µm) 8.116 2.426 0.0013
Average tortuosity of branch segments -5.663 1.094 <.0001
Average arterial tree diameter (µm) 4.659 2.737 0.0931
CRAE (µm) -3.313 1.064 0.0027
Kurtosis of distribution of branch segment tortuosity 1.938 1.157 0.0984
TermOrthogonalized
Estimate
Average length of branch segments (µm) 1.775
Average tortuosity of branch segments -1.569
Kurtosis of distribution of branch segment lengths -1.068
CRAE (µm) -0.776
Number of arterial tree branch segments/tree area (µm2) 0.579
Kurtosis of distribution of branch segment tortuosity 0.480
Average arterial tree diameter (µm) 0.475
Skewness of distribution of branch segment lengths 0.433
Online Figure 8A. Differences in fractal dimension (FD) and lacunarity (Lac) of retinal artery trees are associated with
differences in retinal patterning metrics (RPMs). Online Figure 8B-I. Among RPMs characterizing retinal arterial tree
complexity, differences in FD and Lac are most strongly associated with differences in CRAE and average length of branch
segments, respectively.
Fractal dimension and lacunarity are global, non-Euclidean dimensionless metrics that have been used to define complexity of the
retinal vasculature in association studies. In the present study we found that differences in fractal dimension and lacunarity were
associated with differences in retinal patterning metrics (RPMs) (Figure 5B,C; orange boxes). Thus, our data set offers a unique
opportunity to identify the relationship between these global metrics and Euclidean metrics in a complex branching network, ie the
retinal vasculature. Fractal dimension was not found to be a significant predictor of COL-N and COL-D across most models (Online
Figure 7), and lacunarity was only moderately predictive of COL-N (Figure 8B). These findings were likely due to the narrow range
of fractal dimension (1.41-1.54) and high covariance of it and lacunarity with other RPMs (Figure 5B), many of which were more
specific features of arterial tree complexity and thus emerged as stronger predictors of COL-N and COL-D. To better characterize
global differences in complexity of the retinal artery trees, as measured by FD and Lac, in terms of Euclidean metrics that are more
intuitive and visualizable, we examined the association between RPMs and fractal dimension and lacunarity (Online Figure 8). We
performed forward, backward, and mixed stepwise multivariate regression modeling of fractal dimension and lacunarity versus RPMs
using a variety of criteria as detailed in Online Figure 7. Average fractal dimension and lacunarity of retinal artery trees (dependent
variables) from 80 mice were modeled versus other RPMs (independent variables) that strictly characterize only arterial tree
patterning (ie, we excluded CRVE, AVR, and retinal area) (Online Figure 8A). Significance of RPMs for a given model and their
strength of association with fractal dimension and lacunarity, as measured by K-fold R2, were identified.
Differences in many RPMs defining retinal arterial tree patterning (vessel caliber, branch angle, tortuosity, etc.) were associated
with differences in fractal dimension and lacunarity (ie, K-fold R2 was 0.60-0.64 and 0.47-0.49, respectively) (Online Figure 8A).
When a given RPM was associated with both fractal dimension and lacunarity, it correlated with both metrics in an opposite
direction, consistent with the inverse relationship between fractal dimension and lacunarity (Figure 8A). The only exception to this
observation was average arterial tree diameter, which was directly associated with both fractal dimension and lacunarity. To compare
relative strength of association of specific RPMs with fractal dimension and lacunarity, parameter estimates from the 2 most
predictive models (Online Figure 8A, RPMFD and RPMLac) were obtained and plotted as scaled estimates (ie, centered by mean and
normalized to have identical range) (Online Figure 8B,D). In addition, parameter estimates were standardized to have equal
variances, orthogonalized to be uncorrelated, and plotted—in descending order of scaled estimates—as a pareto plot (Online Figure
8C,E). The scaled estimates show the relative extent of change in fractal dimension and lacunarity as a specific RPM is varied from
the lowest to highest value in the population of mice.
Online Figure 8 legend (continued)
The pareto plot accounts for covariance and extent of variability of an RPM in the mouse population to estimate and arrange the
RPMs in descending order of “explanatory power” for fractal dimension and lacunarity. Plots of predicted (ie expected) fractal
dimension and lacunarity based on models from strongly correlated and explanatory RPMs, along with K-fold R2, reveals the spread
of data and the strength of correlation (Online Figure 8F,G; ****P<0.0001). In addition, segmented arterial trees from two retinas in
our study with the widest difference in fractal dimension (1.41 vs 1.54) and lacunarity (27.0 vs 13.7) were also compared to better
visualize differences in arterial tree patterning in the context of respective differences in RPMs (Online Figure 8H,I).
The pareto plot (Online Figure 8D) and comparison of retinas (Online Figure 8H,I) shows that fractal dimension is
disproportionately sensitive to changes in caliber of the central artery (CRAE) in comparison to other RPMs. In general, mice with
retinal arterial trees with a larger CRAE, shorter and greater proportion of shorter branch segment lengths (as measured by average
length of branch segments and skewness of distribution of branch segment lengths), more tortuous branch segments and a wider
distribution of branch segment tortuosity (as measured by average tortuosity of branch segments and kurtosis of distribution of branch
segment tortuosity) tend to have a higher FD and lower lacunarity. Higher FD (Online Figure 8A,B,I) is also associated with greater
extent of coverage of arterial tree (as measured by skeletonized arterial tree area). Other associated differences in RPMs are less
visually appreciable, consistent with their relatively lower rank on the pareto plots (Online Figure 8B,C,E); for example, low
lacunarity is also associated with a lower branch density (as measured by number of arterial tree branch segments/tree area) and a
greater proportion of branch segments with a similar length (as measured by kurtosis of distribution of branch segment lengths). As
found across all significant models (Online Figure 8A), a high fractal dimension and lacunarity were both associated with larger
vessel caliber (as measured by average arterial tree diameter). RPMs had a lower strength of association with lacunarity in
comparison to fractal dimension (Online Figure 8F,G) (K-fold R2 0.49 vs 0.64), suggesting that, in the context of our study, lacunarity
captures additional information on arterial tree patterning beyond the most descriptive RPMs.
Adjusted R2 p-value Adjusted R2 p-value Adjusted R2 p-value Adjusted R2 p-value
N Collateral number 0.86 <.0001 0.93 <.0001 0.93 <.0001
D Average collateral diameter (µm) 0.87 <.0001 0.95 <.0001 0.95 <.0001
1 Do (µm) 0.67 <.0001 0.80 <.0001 0.54 0.001 0.02 0.5
2 D1 (µm) 0.46 <.0001 0.51 0.0015 0.30 0.03 0.17 0.04
3 D2 (µm) 0.69 <.0001 0.79 <.0001 0.38 0.011 0.04 0.7
8 Branch angle 0.43 <.0001 0.06 0.3 0.66 <.0001 0.01 0.8
9 Optimality 0.35 <.0001 0.72 <.0001 0.09 0.21 0.05 0.8
10Retinal area or cerebral hemisphere
area (µm2)0.16 0.009 0.24 0.052 0.73 <0.0001 0.03 0.2
11 Fractal dimension 0.32 <.0001 0.48 0.003 0.36 0.013 0.21 0.02
12 Lacunarity 0.23 0.001 0.44 0.005 0.10 0.19 0.11 0.08
13 Arterial tree area (µm2) 0.38 <.0001 0.17 0.11 0.59 0.0004 0.06 0.3
14 Skeltonized arterial tree area (µm) 0.29 <.0001 0.05 0.3 0.41 0.008 0.05 0.8
15 Average arterial tree diameter (µm) 0.40 <.0001 0.50 0.002 0.38 0.01 0.17 0.04
16Number of arterial tree branch
segments/tree area (µm2)0.20 0.0025 0.21 0.074 0.40 0.008 0.04 0.2
17 Average tortuosity of branch segments 0.33 <.0001 0.24 0.054 0.14 0.14 0.05 0.8
18Skewness of distrubtion of branch
segment tortuosity0.27 0.0002 0.31 0.02 0.17 0.11 0.05 0.9
19Kurtosis of distribution of branch
segment tortuosity0.21 0.002 0.27 0.04 0.14 0.14 0.04 0.6
20 Avg length of branch segments (µm) 0.38 <.0001 0.59 0.0004 0.22 0.066 0.05 0.9
21Skewness of distribution of branch
segment lengths0.28 0.0002 0.36 0.014 0.01 0.4 0.18 0.03
22Kurtosis of distribution of branch
segment lengths0.24 0.0007 0.31 0.025 0.02 0.37 0.13 0.06
Bivariate ANOVAOneway ANOVA
N/A
4 strains, n=2110 strains, n=80
RPM vs strain RPM vs strain MCAM vs strain RPM vs MCAMCOL-N, COL-D, Retinal patterning metrics
(RPM) or Middle cerebral artery metrics
(MCAM)
Online Figure 9. Both retinal patterning metrics (RPMs) and middle-cerebral artery patterning metrics (MCAM) vary with genetic background, but only half
showed significant or suggestive correlations with each other. A subset of 18 MCAMs analogous to patterning metrics derived from the retina (RPMs) were measured in a
subset of 21 mice belonging to 4 strains (BALB/c, C57BLKS, AKR, and C57BL/6). Using definitions and methods previously detailed for the derivation of RPMs (Figure 2,
4), inner-zone metrics (RPMs/MCAMs 1-3, 8, 9) were measured on the 1st order of the MCA trunk and extended zone metrics (RPMs/MCAMs 11-22) were derived from
segmented MCA trees (Online Figure 11). Cerebral hemisphere area, the area of the hemisphere supplied by the MCA, is analogous to retinal area (RPM/MCAM 10)
supplied by the retinal arterial tree and was measured as described previously3 (Online Figure 11). Bivariate regression (one-way ANOVA adjusted R2 and p-value) of COL-
N, COL-D, and MCAMs versus mouse strain shows that COL-N, COL-D and at least 9 out of 18 MCAMs vary with genetic background (red dashed line, cutoff for adjusted
R2 of >0.35, p = 0.0001-0.13), comparable to the 10 out of 22 metrics found to strongly vary with genetic background in the retina (Figure 5). Black boxes reflect relative
strength of correlation. These data suggest that similar to its contribution to the variation in COL-N, COL-D and RPMs, genetic background also plays a significant role in
specifying variation in features of the MCA tree, such as vessel caliber, branch angle, fractal dimension, and MCA tree area. Optimality of the MCA tree did not vary with
genetic background as it did in the retina, and unlike in the retina, area of the skeletonized MCA tree and cerebral hemisphere and number of arterial tree branch segments per
unit tree area showed strong variation with genetic background. Bivariate regression of MCAMs versus analogous RPMs (Bivariate ANOVA adjusted adjusted R2 and p-
value) shows little to no correlation (adjusted R2 of 0.02- 0.21), with only fractal dimension showing some degree of correlation (adjusted R2 of 0.21, p = 0.02). The low
MCAM-RPM correlation may be attributable to low overall n-size (22), measurement of only 1 MCA tree versus 2-3 trees in the retina, truly flat-mounted 2D measurement in
retina versus 3D angular view of the MCA, possible lack of true analogy between MCAMs and RPMs, and reasons related to different times of formation (see Discussion).
MCA
a b c d e f g a b c d e f g
1 Do (µm) ↓ ↓
2 D1 (µm) ↑ ↑
3 D2 (µm) ↑ ↑
8 Branch angle ↑ ↑
9 Optimality ↓
10 Cerebral hemisphere area (µm2) ↑ ↑
11 Fractal dimension ↑
12 Lacunarity ↑ ↑
13 Arterial tree area (µm2) ↑ ↓
14 Skeltonized arterial tree area (µm2) ↓
15 Average arterial tree diameter (µm) ↑
16 Number of arterial tree branch segments/tree area (µm2) ↑ ↑
17 Average tortuosity of branch segments ↑
18 Skewness of distrubtion of branch segment tortuosity ↓ ↓
19 Kurtosis of distribution of branch segment tortuosity ↓
20 Avg length of branch segments (µm) ↑ ↑
21 Skewness of distribution of branch segment lengths ↑22 Kurtosis of distribution of branch segment lengths ↓
R elat io nship
with C OL-N
RMR elat io nship
with C OL-D
RMMiddle cerebral artery metrics (MCAM)
Collateral number (COL-N) Collateral diameter (COL-D)
0.55
0.65
0.75
0.85
0.95
0.55
0.65
0.75
0.85
0.95
Direction Criteria
a Forward
b Backward
c Forward
d Backward
e Forward
f Backward
g Mixed
ModelStewise Regression
Minimum AIC
Minimum BIC
P-value (<0.25 to enter
and <0.10 to leave
model)
K-f
old
R2
p<0.001
p<0.01
p<0.05
p>0.05
P-value
Co
rre
lati
on
S
ign
ific
an
ce
+/- R2
P-value
A
B
C
Online Figure 10. Middle cerebral artery patterning metrics (MCAMs) predict pial collateral number (COL-N) and diameter (COL-D). Multivariate correlation
matrices (A and B) of COL-N (N), COL-D (D) and MCA patterning metrics (MCAMs 1-3, 8-22) show significant covariance, similar to RPMs (Figure 5); matrices show
direction and strength (+/- adjusted R2 (A)), and significance (p-value, (B)) of covariance. Highlighted regions of matrices (A,B; yellow boxes) show that a number of
MCAMs (2, 8, 10, 15, 16, 20) also vary strongly with COL-N and COL-D, suggesting that they may also predict collateral extent. Thus, similar to methods detailed for
RPMs (Online Figure 7), forward, backward, and mixed direction stepwise multivariate regression of COL-N and COL-D versus MCAMs was performed using different
stopping rules—minimum AIC, minimum BIC, and p-value cutoffs (p<0.25 for RPM to enter and >0.10 to leave model). Predictive performance across all models as
determined by K-fold R2 calculated from leave-one-out cross validation was strong (0.61-0.78 for COL-N and 0.60-0.86 for COL-D) and confirmed our hypothesis that
similar to features of retinal patterning, features of MCA tree patterning strongly associate with and can predict COL-N and COL-D. Directionality, strength, and
significance of correlation of MCAMs with COL-N and COL-D across all models is displayed and highlights a select few MCAMs that remained significantly predictive for
either COL-N or –D throughout all models; thus, MCA trees with greater branching density (MCAM 16), at wider branch angles (MCAM 8), with smaller parent
(D0) but larger daughter vessel calibers (D1, D2) (MCAMs 1-3), supplying larger cerebral hemispheres (MCAM 10) were associated with a greater number of
collaterals. The most predictive models based on highest K-fold R2 was used to calculate an “MCA predictor index” for COL-N and COL-D similar to the retinal predictor
index (MCAPIn and MCAPId, respectively) to further examine and determine comparative predictive ability of individual features of MCA patterning (Online Figure 11).
MCAPIn MCAPId
Intercept 13.10 0.72 <.0001
D0 (µm) -53.91 11.41 0.0011
Number of MCA tree branch segments/MCA area (µm2) 28.70 6.94 0.0025
D2 (µm) 25.36 7.48 0.0080
Average length of MCA branch segments (µm) 18.94 6.51 0.0173
D1 (µm) 18.40 3.47 0.0005
Average tortuosity MCA branch segments 17.27 3.60 0.0010
Cerebral hemisphere area (µm2) 17.15 2.96 0.0003
Branch angle 11.17 3.99 0.0208
Skewness of distribution of MCA branch segment tortuosity -11.16 3.28 0.0079
MCA tree area (µm2) 10.62 3.46 0.0134
Optimality -9.26 2.92 0.0114
Number of MCA tree branch segments/MCA area (µm2) 6.36
Cerebral hemisphere area (µm2) 5.94
D1 (µm) 3.71
Optimality -2.28
Average tortuosity MCA branch segments 1.99
Branch angle 1.35
Skewness of distribution of MCA branch segment tortuosity -1.22
MCA tree area (µm2) 1.19
D2 (µm) -0.39
Average length of MCA branch segments (µm) -0.2
D0 (µm) 0.03
TermOrthogonalized
Estimate
Term Scaled Estimate Std Error P-value
Intercept 17.59 0.36 <.0001
Branch angle 6.39 0.98 <.0001
Number of MCA tree branch segments/MCA area (µm2) 5.92 0.76 <.0001
Lacunarity 3.29 0.84 0.0016
D1 1.96 1.03 0.0763
Branch angle 2.99
Number of MCA tree branch segments/MCA area (µm2) 2.60
Lacunarity 1.39
D1 0.69
Term Scaled Estimate Std Error P-value
TermOrthogonalized
Estimate
Predicted collateral diameter (MCAPId)
Par
eto
plo
t
Scal
ed
par
ame
ter
est
imat
es
Par
eto
plo
t
Scal
ed
par
ame
ter
est
imat
es
A
C
Predicted collateral number (MCAPIn)
K-fold R2=0.78****
K-fold R2=0.86****
B
D
E
F
Co
llate
ral
nu
mb
er
Co
llate
ral
dia
me
ter
Ave
rage
co
llate
ral
dia
me
ter
(µm
) A
vera
ge c
olla
tera
l n
um
ber
Strain
B. AKR
C. BALB/c
D. C57BLKS
E. C57BL/6
Figure 11. Among the most predictive MCAMs, average number of MCA tree branch segments per unit MCA area (ie, MCA branching density)
contributes the most, statistically, to predicting collateral number and diameter (COL-N and COL-D). MCA trees with larger branch angle, larger
caliber of branching vessels (D1, D2), and larger cerebral hemisphere areas tend to have greater collateral extent (COL-N and/or COL-D). To
compare the relative predictive power of the MCAMs, parameter estimates from the 2 most predictive models for MCAPIn and MCAPId (Online Figure 10)
were obtained and plotted as scaled estimates (ie centered by mean and normalized to have identical range) (A,C); in addition, the parameter estimates were
standardized to have equal variances, orthogonalized to be uncorrelated, and plotted—in descending order of scaled estimates—as a pareto plot (B,D). The
scaled estimates show the relative extent of change in COL-N or COL-D as a specific MCAM is varied from the lowest to highest value in the population of
mice. The pareto plot accounts for covariance and extent of variability of an RPM in the mouse population to estimate and arrange the MCAMs in descending
order of relative “explanatory power.” Plots of predicted COL-N and COL-D versus MCAPIn and MCAPId, along with K-fold R2 reveals the spread of data
and the strength of correlation (E,F). ****P<0.0001. Therefore, mice with greater MCA tree branching density, larger branch diameter at bifurcations (D1),
and larger branch angles tend to have greater collateral extent (COL-N and COL-D). Mice with relatively larger cerebral hemisphere areas also tend to have
greater COL-N.
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