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14.4 Image Analysis 335
structures’ topology (i.e., connectivity or hierarchical nature) and its morphology
(i.e., measurement of various properties, such as branch segment lengths, di-
ameters, branching angles, vessel surface area, etc.). Being able to accurately
characterize these properties of the microvasculature, flow patterns may be un-
derstood, optimal design principles may be exposed, and model systems may be
fabricated.
The analysis of micro-CT images shares a great deal with other imaging modal-
ities. Many algorithms, theories, and methods designed for different problems
have been borrowed from other imaging methods and have seen success in their
application to micro-CT images. Of course, the image analysis of micro-CT images
continues to improve and contribute to the other imaging methods as well.
Many programs exist for performing image analysis, including the Analyze
software program [56], Skyscan’s (Kontich, Belgium) image analysis software,
Matlab (Mathworks Inc.), and the software program Mimics by Materialise (Leuven,
Belgium). Open source programs such as VTK can be used for visualization of
micro-CT image data; also, ITK offers a whole host of image analysis algorithms
for image registration as well as vascular segmentation and ImageJ is an excellent
tool for performing various measurements of components within an image.
In the following subsections, methods pertaining to vascular segmentation,
extraction of vascular centerlines, measurement of various geometrical properties,
and modeling principles are discussed.
14.4.1
Segmentation
The task of delineating what is and what is not vasculature in an image has been
studied by many research groups [8, 57, 58]. Typically, in microcirculation imaging
studies, this is a two-phase problem, in the sense that we are interested in the
vasculature and not interested in anything else (background). Owing to the use of
contrast agents, the simple method of thresholding is the most common technique
[47]. In this sense, the gray scale value of each voxel is considered and if it is
within a certain range, it is set to being a vessel voxel (a one for instance), whereas
if the voxel is outside of the specified range, it is not a vessel voxel (and set to
zero). The process of image segmentation converts a gray scale volume data set
into a binary data set, whereby the vasculature is easily represented as one distinct
phase. A connected component analysis (region growing) can then be used to
distinguish different vascular structures within the image. Shown in Figure 14.18
is a volume rendering of an intramyocardial cast from a human coronary artery.
Here, the volume is rendered at four different CT gray scale thresholds. Clearly,
significant differences in the vasculature are evident, which suggests that threshold
choice is an important processing step and must be carefully chosen. Nonetheless,
algorithmic approaches have been used to account for and alleviate the influence
of threshold choice on subsequent vascular measurements.
The problem of segmentation is compounded by beam hardening, aliasing
artifacts, partial volume effects, ring artifacts, and the nonideal MTF of the imaging
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336 14 Studying Microcirculation with Micro-CT
100
300 400
200
1 mm
Figure 14.18 Micro-CT image data (20 µm
isotropic voxels) of a corrosion cast of a
human coronary artery. The material used
to fix the specimen is seen at the bottom
of each image. Here, volume renderings of
the cast are displayed for different CT gray
scale threshold choices. This threshold sets
any voxel with a CT value greater than the
threshold such that it is considered when
creating the volume rendering (a rendering
of the surface of the vasculature). All voxels
with a value below the threshold are thus
not visualized. The nonuniform nature of
the CT gray scale is seen here, in particular,
the lower values for branches with smaller
diameters (since these are the first branches
to be removed on raising the threshold).
Also, it can be seen how all the branch seg-
ments become thinner as the threshold is
increased. This results from the partial vol-
ume effect (whereby the vessel may only
cross through part of a voxel and thus not
attain as high of a gray scale value as those
voxels that are fully within a vessel), as well
as from blurring by the imaging system’s
modulation transfer function. This blurring
has a larger effect on vessel segments with a
small diameter than it does on larger diame-
ter vessel segments.
system. This causes values of certain tissues (i.e., the lumen of vessel trees) to
not be a specific value, but rather take on a range of values. Methods developed
to overcome some of these problems include object tracking algorithms [57], local
adaptive region-growing methods [8], active contours [59], as well as tubularity
measure or Hessian-based filtering techniques [58]. The best approach depends on
the quality of the micro-CT data in terms of how well the object stands out from
the background and also just how complex the vascular structure is. For instance,
Hessian-based filtering methods (which characterize the degree to which a voxel
appears to pertain to a cylindrical type structure) have problems at bifurcation
points since the vessel tree does not appear tubular in these regions. Also, active
contour methods typically rely on user-specified parameters such as the number
of iterations that the algorithm should run through, as well as various weighting
parameters. Thus, a particular method should be chosen for each image analysis
study, which is reliable and repeatable.
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14.4 Image Analysis 337
14.4.2
Centerline Extraction
Another preprocessing step for the subsequent characterization of vascular branch-
ing geometry is known as centerline extraction. The 3D segmented data set is
used as the input for the extraction of the vascular tree’s lumen centerline (also
frequently termed, skeleton). The extraction of the vascular tree centerline allows
for the simplification of the complex tree structure from which the branch seg-
ment location within the tree and its connection to the other branch segments is
conveyed (essentially the first step in defining the vascular tree topology). Using
locations along the centerline within the segmented image, the tree’s hierarchical
nature, branch lengths, branch diameters, and branching angles can subsequently
be determined.
There exist many different methods for finding the centerline of vasculature.
The three main categories are (i) iterative thinning [60] (i.e., peeling away surface
voxels), (ii) mesh contraction [61] (i.e., shrinking), and (iii) methods based on ‘‘fast
marching’’ [62, 63]. The different methods have been shown to each have strengths
and weaknesses, and the different methods should be tested for their intended
application. A successful centerline method will be robust, will follow closely the
center of vessel lumens, and will not generate false branch segments (‘‘whiskers’’).
14.4.3
Measurements
The measurement of length, diameter, and the connectivity relationship between
interbranch segments lie at the foundation of most vascular geometry research
[64, 65]. Other properties such as branching angle, vessel volume, and vessel wall
surface area are also relevant parameters of vasculature, which can be produced
with knowledge of the former. Accurately measuring vascular branching geometry
is a task well suited to micro-CT image analysis. Manual-based methods can be
performed, such as using a software program to measure cross-sectional widths
of vessel tree lumens in two-dimensional slices. For high-throughput experiments,
automated methods are desirable in order to generate large amounts of data in a
relatively short amount of time. The data can therefore be reproducible and not
constrained to the problems that occur from user subjectivity.
14.4.3.1 Segment Length
Once a vessel tree’s centerline is extracted, measurements of the individual branch
segments’ length can easily be performed. The measurement of an individual
branch segment’s length can be determined by moving from one voxel to the
next in the list of ordered centerline voxels, calculating the Euclidean distance
between contiguous voxels, and summing the distances. This approximate method
is known as the sample-distance method [66], where geometrically the interbranch
segment’s length is being approximated by the connected polygonal curve whose
vertices are the branch segment’s centerline voxels. Another method, that of simply
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338 14 Studying Microcirculation with Micro-CT
counting voxels [56, 67], can significantly underestimate interbranch segment
length. Furthermore, smoothing of the centerline either through a moving average
type of approach or curve fitting can further improve the accuracy of interbranch
segment length measurements.
14.4.3.2 Segment Diameter
Several methods for measuring the branch diameter exist including distance map
computation, cross-sectional area determination (brightness area product-based
methods), and volume-based methods (where the diameter is calculated based on
the segment’s length and volume). Typically, these methods overestimate small
vessel diameters. Hoffman et al. [68] compared the various techniques for deter-
mining vessel diameters. The main conclusion was that no technique perfectly
characterized vessels over the full size range found in angiographic images; yet, it
was suggested that a derivative-based technique was the most accurate for larger
vessels. At a basic level, the convolution of a square wave function and a Gaussian
blurring function results in an image that has a correct width at exactly half the origi-
nal intensity (i.e., Full-width half-max (FWHM)). Therefore, the first-derivative edge
detection as well as a thresholding technique of the local FWHM accurately char-
acterize the input square wave’s width (for vessels with diameters greater than two
times the FWHM of the scanner’s MTF). Additional considerations must be incor-
porated in order to accurately measure small interbranch segment diameters, which
is typically done by using information pertaining to the imaging system’s MTF.
14.4.4
Erode/Dilate Analysis
Micro-CT offers an excellent framework from which to analyze intact microvascular
beds and a sequential ‘‘erode/dilate’’ technique [54, 69], which progressively
eliminates branches of increasing diameter, is one approach that greatly reduces
image analysis effort. By this method, the total luminal volume of different
diameter branches is calculated. The method operates on a segmented image of
the vasculature. The method uses the morphological operations of erosion and
dilation [70, 71] whereby the segmented vascular bed is eroded and then dilated
‘‘n’’ times, where ‘‘n’’ is the iteration number (which can be related to the diameter
of vessel segments lost at each iteration). Erosion involves removal of voxels from
the surface of the lumen and dilation involves adding voxels to the surface of the
lumens. After each iteration, the total vessel volume is measured. The results are
then binned according to the vessel volume ‘‘V’’ that was lost (i.e., V(n + 1) − V(n))
by removing individual branches 2nh in diameter (‘‘h’’ is the voxel size). This
method has the benefit of being able to easily deal with highly complex structures,
as well as images where multiple vascular trees exist.
As a few examples, the question of whether vasculature grows in proportion to
the myocardium, as the rat heart develops, was studied by this erode/dilate method
of analysis [69] and the results obtained were shown to compare accurately to the
results of more complex methods, as well as indicate what diameter interbranch
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14.5 Summary and Future Developments 339
segments trap a microsphere of a given size [54]. In addition, Ohuchi et al. [72]
used the morphological operation of dilation to deduce the volume of myocardial
tissue perfused by selected arterioles.
14.4.5
Modeling
14.4.5.1 Analytical
The data regarding branching geometry can be investigated by analyzing the
geometric properties of the vascular structures, in particular, with regard to
the model derived by Murray [73] on the basis that the fluid transport system
(vasculature) geometry is consistent with simultaneous minimization of both the
power loss of laminar flow and a cost function proportional to the total volume
of material needed to maintain the system (lumenal contents) – factors that have
opposing geometric consequences. The vessel tree structures can be modeled as a
binary tree in that, at each bifurcation, there exists one parent segment that divides
into two branches. The ‘‘level’’ (or generation) of the branches is one higher than
that of their parent branch segment.
The Hagen–Poiseuille equation [74] that describes laminar flow of an incom-
pressible Newtonian fluid, through a pathway with a circular cross section, can
also be used to calculate fluid flow resistance through different sections of vascula-
ture, local shear stresses on vascular walls [65], and also the pressure distribution
within vascular trees [48]. Shown in Figures 14.19 and 14.20 are the results of
hemodynamic flow calculations of pressure distributions, fluid flow magnitudes,
and shear stress distributions of vascular trees from placenta and lung vasculature
of mice. These were computed by considering the vessel trees as networks of
interconnected cylindrical pipes, taking into account the ‘‘pipes’’ series and parallel
arrangements.
14.4.5.2 Computational Fluid Dynamics
More computationally demanding methods to characterize vasculature exist
(Figure 14.21). These typically include fluid dynamic simulations. Owing to the
computational complexity, simple structures, such as a single root segment, which
bifurcates into two branches [75], or a mouse aorta composed of a main branch
segment and a couple side branches [76], are typically characterized. Software
programs such as ANSYS can be used to solve the Navier–Stokes equations. The
modeling process involves defining inlets and outlets of the system, as well as
other boundary conditions such as inlet flow magnitude and outlet pressure.
14.5
Summary and Future Developments
The important areas of scanner technologies (X-ray sources, geometries, and de-
tectors), specimen preparation and scanning processes, image analysis techniques
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340 14 Studying Microcirculation with Micro-CT
L1
L4 L5
L2 L3
1.0
0.8
0.6
0.4
0.2
0.0
20
15
10
5
0
Pressure (mmHg) Pressure (mmHg)
P1 P2
P4 P5
P3
1 mm
1 mm
Figure 14.19 Vascular tree pressure distributions can be
determined analytically by modeling the vasculature as a
network of cylindrical pipes (connected in series and in par-
allel). Here, the computed pressure distributions for five
placenta (P1–P5) and five lungs (L1 –L5) from mice speci-
mens are shown. (Source: This figure is from Ref. [48]).
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14.5 Summary and Future Developments 341
P4
P4 L5
L5
1 mm
1 mm
10
1
1
10
−1
10
−2
10
−3
10
−3
10
3
10
−6
10
−4
10
−5
Flow (mm
3
s
−1
)
Flow (mm
3
s
−1
)
45
30
15
0
Shear (dynes cm
−2
)
Shear (dynes cm
−2
)
600
500
400
300
200
100
0
Figure 14.20 Vascular tree flow magni-
tudes and shear stress distributions can
also be determined analytically by modeling
the vasculature as a network of cylindrical
pipes (connected in series and in parallel).
Here, the computed fluid flow magnitude
and shear stress distributions for a mouse
placenta and lung specimen are shown.
(Source: This figure is from Ref. [48]).
and simulations, as well as novel experimental designs are all fully open fields for
micro-CT research.
The phase delay of X-rays can be used to provide higher tissue contrast than
that achievable by attenuation-based X-ray imaging. Since X-rays travel at slightly
different velocities through different tissues, interference patterns in the detected
X-ray intensities develop, which can then be turned into actual phase delays that
can be used for higher sensitivity tissue differentiation.
Novel detector arrays can make energy-selective X-ray detection a practical option
for bench-top micro-CT imaging systems, and the capability of a detector to actually
count individual photons, of the order of 10
4
photons per detector pixel per second,
is also being realized.
The use of different contrast agents can be used to study vasculature in close
proximity. For instance, the hepatic artery, portal vein, and biliary tree in the liver all
follow essentially the same branching paths. By injecting different contrast agents
and imaging at different photon energies, closely related vascular structures could
be delineated and characterized.
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342 14 Studying Microcirculation with Micro-CT
220
200
180
160
140
120
100
80
60
2 mm
Figure 14.21 Wall shear stresses of vas-
culature can be computed through fluid
dynamic simulations of the segmented vas-
culature. Here, the mean wall shear stress
(in dynes cm
−2
) for two different mouse aor-
tas is shown. The wall shear stress vector
magnitudes were averaged over the full car-
diac cycle. Areas of relatively low wall shear
stress are observed in the inner curvature
of the aortic arch as well as the entrance
orifice. The lateral surfaces of the ascend-
ing aorta and the region of the arch around
the left common carotid artery are regions of
high wall shear stress. (Source: This figure is
from Ref. [76]).
The previously developed methods for performing a successful in vivo study have
already had to work on overcoming problems related to motion artifacts, which will
be useful for future in vivo longitudinal microcirculation studies. As an example,
longitudinal study, the remodeling of microvasculature, as the dynamic process
which it is, could be evaluated.
In addition, methods for cardiac gating could help answer the question of how
well a micro-CT scan of a vascular tree (which is a snapshot in time) represents the
‘‘true’’ dynamic tree geometry.
For example, just how important is the diameter change caused by the contracting
heart’s pressure pulses? Many questions, like this one, can only be answered by
doing in vivo scans at many time points within a single cardiac cycle.
Since physiological motion in a mouse (for instance) is 10× faster than in
humans, special care is needed to reduce motion blur. For example, short exposure
times with high fluency rates are needed; yet, lethal dose (or LD50) levels must
be considered to allow for the feasibility of longitudinal studies. Clearly, in vivo
micro-CT imaging is still in its infancy, which allows a great deal of room for future
research investigations.
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References 343
Fluid dynamic analysis of vasculature still has to overcome issues related to
the definition of boundary conditions (a highly complex problem when dealing
with hundreds or thousands of interbranch segments; a simulation which would
involve just as many outlet pressures, for instance, to be defined) and applying
physiologically realistic values to the simulation’s initial conditions. In the past,
these issues have required relatively simple structures to be characterized. Further,
methodological improvements are needed to fully and accurately characterize the
complex nature of fluid flow through vasculature.
The high spatial resolution data of micro-CT imaging is an important addition for
many other imaging modalities, and further improvements in all the collaborative
disciplines will help to further use micro-CT as a tool for studying microcirculation.
Acknowledgments
The authors would like to thank Ms Delories C. Darling for her help in the
preparation of this chapter. This work was supported in part by NIH Grant
EB000305 and The Mayo Foundation.
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