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IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL. 39, NO. 12, DECEMBER 2020 4425
Quantitative Classification of 3D Collagen Fiber
Organization From Volumetric Images
Woowon Lee , Amir Ostadi Moghaddam, Zixi Lin, Barbara L. McFarlin, Amy J. Wagoner Johnson ,
and Kimani C. Toussaint ,Jr.,
Senior Member, IEEE
Abstract
—Collagen fibers in biological tissues have a
complex 3D organization containing rich information linked
to tissue mechanical properties and are affected by muta-
tions that lead to diseases. Quantitative assessment of this
3D collagen fiber organization could help to develop reliable
biomechanical models and understand tissue structure-
function relationships, which impact diagnosis and treat-
ment of diseases or injuries. While there are advanced
techniques for imaging collagen fibers, published methods
for quantifying 3D collagen fiber organization have been
sparse and give limited structural information which cannot
distinguish a wide range of 3D organizations. In this article,
we demonstrate an algorithm for quantitative classifica-
tion of 3D collagen fiber organization. The algorithm first
simulates five groups, or classifications, of fiber organiza-
tion: unidirectional, crimped, disordered, two-fiber family,
and helical. These five groups are widespread in natural
tissues and are known to affect the tissue’s mechanical
properties. We use quantitative metrics based on features
such as preferred 3D fiber orientation and spherical variance
to differentiate each classification in a repeatable manner.
We validate our algorithm by applying it to second-harmonic
generation images of collagen fibers in tendon and cervix
tissue that has been sectioned in specified orientations,
and we find strong agreement between classification from
simulated data and the physical fiber organization. Our
approach provides insight for interpreting 3D fiber orga-
nization directly from volumetric images. This algorithm
could be applied to other fiber-like structures that are not
necessarily made of collagen.
Index Terms
—Biomechanical modeling, second-
harmonic generation imaging, collagen-fiber organization,
Manuscript received April 13, 2020; revised June 21, 2020 and
August 18, 2020; accepted August 19, 2020. Date of publication
August 24, 2020; date of current version November 30, 2020.
Kimani C. Toussaint, Ph.D., holds the 2017 Preterm Birth Research
Grant from the Burroughs Wellcome Fund (#1017300).
(Corresponding
author: Kimani C. Toussaint.)
Woowon Lee and Amir Ostadi Moghaddam are with the Depart-
ment of Mechanical Science and Engineering, University of Illi-
nois at Urbana–Champaign, Champaign, IL 61801 USA (e-mail:
wole9736@colorado.edu; amiro2@illinois.edu).
Zixi Lin and Kimani C. Toussaint, Jr., are with the School of
Engineering, Brown University, Providence, RI 02912 USA (e-mail:
zixi_lin@brown.edu; kimani_toussaint@brown.edu).
Barbara L. McFarlin is with the Department of Women, Children
and Family Health Science, College of Nursing, University of Illinois at
Chicago, Chicago, IL 60612 USA (e-mail: bmcfar1@uic.edu).
Amy J. Wagoner Johnson is with the Carle Illinois College of Medicine,
Champaign, IL 61820 USA, and also with the Carl R. Woese Institute for
Genomic Biology, Urbana, IL 61801 USA (e-mail: ajwj@illinois.edu).
This article has supplementary downloadable material available at
https://ieeexplore.ieee.org, provided by the authors.
Color versions of one or more of the figures in this article are available
online at https://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TMI.2020.3018939
quantification and estimation, structure-function relation-
ship, volumetric imaging.
I. INTRODUCTION
COLLAGEN is the most prevalent protein in the human
body and exists in a wide range of tissue types including
tendon, skin, muscle, bone, and blood vessels [1], [2]. There
are more than twenty types of collagen depending on their
molecular composition [3]; the most abundant collagen types
(I, II, III) form a hierarchical structure where the collagen
molecules assemble into fibrils and ultimately group into fibers
[1]–[3]. This fiber organization generally varies in three spatial
dimensions in collagenous tissues.
There are a handful of optical imaging techniques that
are well-suited for noninvasive imaging of fibrillar collagen.
Polarized light microscopy has been successful in provid-
ing 2D high-contrast images of these structures, where the
intrinsic birefringence of collagen provides an endogenous
contrast mechanism when viewed between cross polarizers.
This technique helped to evaluate the molecular organization
and alignment of collagen fibers as a function of anatomical
region and age in ligament and tendon [4]–[7]. While polar-
ized light microscopy does not provide 3D imaging capa-
bilities, polarization sensitive optical-coherence tomography
(PS-OCT), a polarization-sensitive, interferometric approach
based on the coherence-gating effect [8], has been routinely
used to image collagenous tissues in 3D [9]–[13]. PS-OCT
has been used to obtain morphological information of human
skin [12], [13] and to facilitate detection of diseases such
as occlusal lesions [9], macular degeneration [10], and glau-
coma [11].
Second-harmonic generation (SHG) microscopy is another
common technique used for noninvasive imaging of collagen
fibers in 3D. In contrast to polarized light microscopy and PS-
OCT, SHG microscopy is based on the process of nonlinear
second-order scattering, in particular degenerate three-wave
mixing, from noncentrosymmetric structures, such as collagen
fibers [14], myosin [15], and microtubules in cells [16]. The
nonlinear nature of the SHG process and the corresponding
optical frequency conversion results in high-contrast, submi-
cron, 3D images. Moreover, quantitative SHG imaging can
examine the spatial organization of collagen fibers [17]–[21],
which is particularly useful for imaging spatially heteroge-
neous 3D tissues such as uterine cervix [18], [20].
Studies show that analyzing collagen organization in 3D
is more effective than 2D analysis alone [22]–[24].
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4426 IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL. 39, NO. 12, DECEMBER 2020
For example, researchers found that analyzing the SHG density
and qualitative features over all the images in the 3D stack
helped to characterize pathological changes caused by fibrosis
progression more accurately compared to 2D analysis [22],
[23]. In another study, 3D collagen fiber data were used to
detect malignancy qualitatively in ovarian tissue [24]. Apart
from these studies, researchers were able to develop methods
to extract quantitative information directly from the 3D image
data. Liu et al. utilized the 3D orientation variance as a
parameter to characterize articular cartilage and differentiate
breast cancer tissue from normal tissue [21], [25]. In addition,
Lilledahl et al. quantified 3D morphological features of col-
lagen in cartilage for generalized biomechanical models [26].
Such models aim to predict the tissue mechanical behavior
based on the structural arrangement of collagen and give
insight to collagen structure-function relationship [27]–[29].
In spite of these approaches using 3D analysis, to the best
of our knowledge there is no published methodology that
quantitatively assesses and classifies the 3D collagen fiber
organization data based on natural tissue structures intuitively,
i.e., in a manner that is consistent with direct visualization
of fiber organization. Quantitatively classified 3D collagen
organizations from collagen-fiber images could improve the
accuracy of biomechanical models. Also, studies demonstrated
that the mechanical properties of extracellular matrix (ECM),
which exhibits a complex 3D architecture, has an effect on
cellular activities [30], [31] and this implies proper mechanical
property estimations could aid diagnosing physical injuries and
diseases [32]–[36].
In this study, we demonstrate an algorithm that quantita-
tively analyzes several tissue archetypes in an intuitive manner
based on differing 3D collagen fiber organizations. Herein,
we define five classifications of 3D collagen fiber organiza-
tions, namely, unidirectional, crimped, disordered, two-fiber
family (TFF), and helical. These classifications are chosen
due to the common identification in tissue engineering lit-
erature and their currently understood significance to tissue
mechanical properties [27], [35]–[47]. We first analyze the
preferred 3D fiber orientations on simulated volumetric images
generated for each classification. Next, we separate image
stacks into volume elements, and compute the preferred fiber
orientation in each volume element. Subsequently, a decision
process is implemented that differentiates each classification
by extracting quantitative features such as the number of
preferred fiber orientations detected in a volume element,
the 3D spread of preferred orientations, and the type of
distribution in the 2D polar plot. As an example, we apply our
decision process to experimentally obtained SHG images of
porcine tendon cut in three different orientations with respect
to the collagen fiber bundles and find our results to be in
agreement with the physical fiber organization. To evaluate the
capabilities of our approach for a complex tissue, we use our
decision process to classify the region-specific SHG images
of rat cervix.
II. METHODS
A. 3D Collagen Fiber Classification
We classify 3D collagen fiber organization into five dif-
ferent types as shown in Table I. These were identified
from common fiber arrangements found in biological tissues.
We define the “unidirectional” classification as fiber organi-
zations that have relatively straight fibers, with a deviation
of less than 20% relative to the aligned orientation. Tendon,
which transmits tensile load and also experiences rotational
forces, is mainly composed of unidirectional fibers [36], [37],
[46]. The “crimped” classification includes collagen fibers that
have a crimp pattern with more than 20% modulation in
amplitude with respect to the preferred fiber orientation. The
crimp pattern is not restricted to a single plane. In terms of
the mechanical function, crimped fibers help absorb shock and
contribute to the low stress, nonlinear stress-strain behavior in
the so-called toe region that is associated with un-crimping
[35], [39], [43], [47]. Ligament, tendon and the tumor-stromal
interface are all examples of tissues that contain crimped fibers
[35], [39], [40], [43], [47]. The “disordered” classification
includes fibers with no preferred orientation, as observed
in healing skin, tumors and the middle zone of cartilage,
as examples [40], [41], [44]. Tissues with disordered fiber
organization typically have a lower stiffness compared to
those with unidirectionally aligned fibers measured along the
preferred fiber direction and show nearly isotropic mechan-
ical behavior, i.e. have similar mechanical properties in all
orientations. The “TFF” classification encompasses tissues
with two distinct families of fibers that align in two major
directions. TFF organization occurs in arterial wall tissue, for
example [27], [42]. The TFF organization leads to a direction-
dependent mechanical behavior, with larger stiffness along
the two fiber directions compared to other directions. Lastly,
“helical” classification includes fibers that, as a group, are
aligned in a helical fashion in 3D. The representative image
in Table I shows only the case where the fibers form a
helical organization with different axes, however, our helical
classification includes the case where the helical fibers have
the same axis as well. This fiber organization resists multi-
directional forces. The anterior cruciate ligament [45] is an
example tissue that would be classified as having a helical fiber
organization.
B. 3D Orientation Analysis
We implement a custom MATLAB (MathWorks, Natick,
MA) code1that reads multiple images from 3D stacks in
order to measure the preferred fiber orientation within a
volume. A preconditioning step uses the Canny edge detection
algorithm [48] and detects the boundary of the fibers in the
image. Next, the filter bank method [49] is used to calculate
the preferred 3D orientation of fibers in the predetermined
localized volume elements. Specifically, the 3D Fourier trans-
form is used to convert images of fibers to a 3D spatial
frequency map, which is then sequentially cross-correlated
with an orientation filter. This is carried out for the entire
solid angle. The final estimated orientation is that with the
highest correlation value. A more detailed description of the
basic code is elsewhere [17]. The designated volume elements
are grouped by the following features: dark, 1-directional,
2-directional, or isotropic. Dark volume elements have an
1Detailed information on the accuracy of the MATLAB code is available
in the supporting documents/multimedia tab.
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: QUANTITATIVE CLASSIFICATION OF 3D COLLAGEN FIBER ORGANIZATION FROM VOLUMETRIC IMAGES 4427
TABLE I
3D COLLAGEN FIBER CLASSIFICATION
average intensity in the volume element that is below 12% of
the maximum intensity, whereas 1-directional, 2-directional,
and isotropic have one, two or no detected preferred fiber
orientation in the volume element, respectively. The preferred
fiber orientation is calculated only when the volume elements
are 1-directional or 2-directional and stores a single orientation
or two preferred fiber orientations, respectively.
The code stores the preferred orientation information
as two sets of angles (θ,φ), referring to the respective
in-plane (x-y) and out-of-plane (z)preferred orientations, and
the corresponding 3D vector. To visualize how the fibers
are aligned in the volume of interest collectively, we plot
the preferred 3D orientation data as a 3D histogram, which
consists of vector distribution represented as arrows [50] in a
x-y-zcoordinate reference frame. The direction of an arrow
indicates the preferred orientation in 3D space, whereas its
length represents the number of volume elements (magnitude)
within the volumetric image. This format provides a visual-
ization of the preferred orientation of fibers and their overall
spread in a fixed volume in a manner that is consistent with
observed image data.
To quantify the spread of the fiber direction (the arrows)
in 3D space, we employ the spherical variance (SV) parameter
[21], [51] defined as
SV =(n−R)/n,0≤R≤n,0≤SV ≤1,(1)
where the length of the resultant Ris given by
R={(n
i=1li)2+(n
i=1mi)2+(n
i=1ni)2}1/2
i=1,...,n,(2)
representing the magnitude of the vector (li,mi,ni)sum.
The vector components li,mi,niindicate the fiber orientation
and nis the number of volume elements, excluding dark
and isotropic volume elements. Dark and isotropic volume
elements are excluded from the calculation of SV since there
is no definite dominant orientation. We also limit the cases
when calculating SV to dark and isotropic volume elements
being less than 20% of the entire volume. The SV ranges from
0 to 1, where 0 corresponds to no spread and 1 corresponds
to completely random organization. We calculate the SV in
every hemisphere and use the smallest value as the final
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4428 IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL. 39, NO. 12, DECEMBER 2020
SV. A detailed method for obtaining SV is explained in
Supplementary file 1.
There are two conditions we apply when calculating SV.
First, the range of each angle (0◦<θ <360◦,0
◦<φ<90◦)
is defined to span the cases for z>0. This range of angles
limits the volume to the upper four quadrants, which prevents
having two coinciding arrows with opposite directions. Also,
we consider the cases where the 3D arrows are clustered
around the z-axis so the average φshould be greater than
40◦.
To represent the preferred 3D orientations in a 2D format,
we show θand φin a polar histogram. Each bin has a value
on the corresponding angular and radial axes. The radial axis
value represents the number of volume elements that have
the preferred orientation equal to the corresponding angular
axis value. We detect peaks in the θpolar plot based on the
radial axis values. A peak is defined by initially identifying
the radial axis values for each angular value and subsequently
choosing eight local maxima because in each z-layer we
assumed there would be at most two peaks and total four
z-layers are analyzed. Next, we calculate the average radial
axis value of the four neighboring bins, two on each side,
for the eight local maxima. A local maximum is defined as
a peak if the average value from the neighboring bins is less
than one third of the corresponding local maximum value.
Additional information from the polar plots can be determined
such as the mean θand φangle, peaks in the polar plot being
parallel or nonparallel, as well as their value and location.
C. Process of Distinguishing 3D Collagen Fiber
Classifications
To organize steps that quantitatively distinguish different
classifications, we apply the 3D orientation analysis to 25 dif-
ferent simulated images of each classification. Specifically,
for the unidirectional and TFF classification we alter φand
θfrom 40◦to 90◦and from 0◦to 180◦, respectively. Also
for disordered classification we select φto be 0◦∼90◦but
mostly in the 20◦∼90◦range. For the crimped classification
we modify the crimp amplitude to a maximum of 15 pixels,
while for the helical classification we alter the radius of the
helix to a maximum of 15 pixels and alter the shape of
the trajectory so the helix can form a trajectory of a spiral
which has an elliptical shape when observed from the top of
the z-axis. Subsequently, we construct a stack of images for
each classification that reflect the features chosen. With the
information from the 3D orientation analysis on the simulated
images, we extract quantitative metrics including the volume
element labels (1-directional, 2-directional, isotropic), SV,and
number of peaks in the θpolar plot.
D. Experimental Setup
1) Sample Preparation:
From a local abattoir, we purchased
frozen porcine feet and kept them frozen (−20◦C)for less than
24 hours. Then they were thawed and dissected. We prepared
three types of samples by cutting the deep digital flexor tendon
with a razor blade at angles of 0◦,45
◦, and 90◦with respect
to the orientation of the collagen fiber bundles. We chose
to use the digital flexor tendon due to the compact collagen
fibers resulting in a strong backward-SHG signal [52]–[54] and
also because the mechanical properties of tendon are strongly
related to its function [46], [55], [56]. All three samples were
cut from the same tendon with thickness of ∼5 mm. The final
step was to embed the samples in optimal cutting temperature
compound and cut 5-μm thin sections along the surface of the
samples to minimize roughness.
We harvested 12-week-old non-pregnant rat cervixes
(Sprague Dawley’s) and stored them at −80◦C. We embedded
the tissue in optimal cutting temperature compound and froze
the sample at −20◦C for cryosectioning. The samples were cut
perpendicular to the cervical canals in 3 mm thick sections.
2) SHG Microscopy:
We used a tunable Ti:Sapphire laser
(Spectra-Physics, Santa Clara, CA) producing 100-fs pulses
and centered at 780-nm wavelength. The 15-mW input power
beam focused on the sample with a 60X magnification and
a 1.0 numerical aperture water immersion objective lens
(Olympus, Tokyo, Japan). The backward SHG signal emitted
by the sample traveled through the same objective, and a
390-nm center wavelength, 18-25-nm bandwidth, bandpass
filter (Semrock, Rochester, NY) blocked any potential
autofluorescence from reaching the photomultiplier tube
(Hamamatsu, Hamamatsu City, Japan). The tissue samples
were placed in a No. 1.5 cover glass bottom dish (MatTek,
Ashland, MA) and the side to be imaged faced the bottom.
We imaged all the samples in 3D stacks of dimension 80
μm×80 μm×26 μm, where the step size along the
z-axis (axial direction) was 300 nm. The pixel size in the
SHG images is 310 nm ×310 nm. To prevent the sample
from dehydrating during image, the sample was partially
submerged in phosphate-buffered saline, which was collected
in the petri dish before imaging. Details of the optical setup
have been described elsewhere [57].
III. RESULTS AND DISCUSSION
A. 3D Orientation Analysis of Simulated Images for Each
Classification
Fig. 1 illustrates the volumetric spatial analysis of the simu-
lated images from the five classifications of fiber organizations
discussed in Ta bl e I. Row (a) through (e) show the unidirec-
tional, crimped, disordered, TFF, and helical classifications,
respectively. Each image consists of 6 ×6×4 volume
elements where one volume element is composed of 44 ×
44 ×44 voxels. The number of voxels is determined to create
simulated images with a length scale that agrees with a simple
biological fiber structure, tendon. Fig. 1 column (i) shows
the calculated preferred 3D orientation for each classification.
Here, we use the free open source software 3D slicer (4.9.0,
BSD-style license) [58] to visualize the five simulated fiber
organizations; the calculated preferred fiber orientations are
plotted as arrows overlaid on half of the volumetric image.
The orange arrows indicate the case of two dominant preferred
fiber orientations. The unidirectional fiber organization shows
similar arrow directions throughout the volume compared to
the other images. The arrows in the crimped fiber organization
show the crimp pattern whereas for the disordered fiber
organization, there is no identifiable preferred orientation.
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: QUANTITATIVE CLASSIFICATION OF 3D COLLAGEN FIBER ORGANIZATION FROM VOLUMETRIC IMAGES 4429
Fig. 1. Volumetric spatial analysis of simulated 3D fibers. (i) Five
classifications of simulated 3D fiber organization, where (a)-(e) refers to
unidirectional, crimped, disordered, two-fiber family (TFF), and helical,
respectively. For each simulated image, half the volume shows the
rendered fiber organization and half shows the calculated preferred 3D
fiber orientation. The arrows represent local preferred fiber orientations,
where the orange arrows specifically indicate the presence of two
dominant preferred fiber orientations. (ii) Label of each classification of
fiber organization per volume element as either 1-directional (green),
2-directional (cyan), or isotropic (red). All images have the same view
angle.
The TFF organization shows orange arrows in most of the
volume elements, whereas the helical fiber organization results
in a helical arrangement of arrows. The region labels in
Fig. 1 column (ii) show the result of labeling each volume
element into either 1-directional, 2-directional, or isotropic.
There are no volume elements labelled as dark since our
simulated images are designed to have dense fibers throughout
the volume.
In Fig. 1, the code identifies some of the volume elements on
the edge of the 3D images as 2-directional or isotropic where
they should be 1-directional and 2-directional, respectively.
This mislabeling resulted from the sharp contrast between
the background and fibers at the edge of the volume of
interest. Sharp contrast requires an infinite summation of
spatial harmonic waves to synthesize the edges, but instead
the code employed in the analysis approximates to a finite
number of spatial frequencies [59]. This approximation causes
the aforementioned erroneous labels; however, the percentage
of these inaccurate labels is less than 3% of the entire volume
and the by considering the inner volume elements only, there
are no mislabeled volume elements.
Fig. 2 shows the further analyzed preferred 3D orientation
data on the simulated images for each classification displayed
in rows (a) through (e). The 3D orientation histograms2are
in the first column of Fig. 2 and the projections in the
x-y,y-z,andx-zplanes are immediately to the right in
the same column. The colors for each arrow represent their
relative magnitude within the image, where the colors are blue,
cyan, yellow, and red in the ascending order of the relative
magnitude (see scale in the upper right corner of Fig. 2). The
polar plots are in the second column. The angular resolution
of each polar plot is 10◦.
The unidirectional classification [Fig. 2(a)] has a single
arrow in the 3D orientation histogram, representing its single
fiber direction. The fiber direction from the corresponding
polar plots is θ=180◦and φ=80◦. The 3D orientation
histogram for crimped classification [Fig. 2(b)] has two major
arrows, which correspond to the crimping directions of a band
of fibers. The θpolar plot shows that the crimped pattern
occurs in a single plane since the θpolar plot has two peaks
that are 180◦apart. The φpolar plot for the crimped fiber orga-
nization has an angular range from 55◦to 75◦,which reflects
the out-of-plane angles of the arrows in the 3D orientation
histogram. In the disordered classification [Fig. 2(c)], arrows
point multiple directions in the 3D orientation histogram and,
as a result, there is no particular fiber direction, which leads to
no distinct peak in the θpolar plot. This distribution trend is
also evident in the φpolar plot. The 3D orientation histogram
for the TFF classification [Fig. 2(d)] shows preferred orien-
tations of the 2-directional grouped volume elements (orange
arrows in Fig. 1). There are two peaks in the θpolar plot and
one angular bin in the φpolar plot. These configurations result
from the simulated TFF example having the same two fiber
directions in all the volume elements analyzed. The helical
classification [Fig. 2(e)] has four dominant arrows representing
the helical pattern for each z-layer. As a result, four peaks
are in the θpolar plot and each peak corresponds to one z-
layer of volume elements. The peaks in the θpolar plot rotate
either clockwise or counter clockwise as the z-layer increases.
This characteristic distinguishes the helical from the crimped
classification where the peaks do not rotate along the z-layer.
The φpolar plot has a single bin since the differences in the
out-of-plane angles among the arrows in the 3D orientation
are less than 10◦.
We employ a normalized spherical variance SV
N,whichfor
the representative classifications is 0, 0.2973, 0.8138, 0.3350,
and 0.1508 for unidirectional, crimped, disordered, TFF, and
helical, respectively. We define SV
Nby normalizing the SV to
0.4 since the maximum SV could not exceed 0.4, which is the
maximum SV we have plus standard deviation in disordered
classification.
Fig. 3(a) shows the volume fraction of each region label
(2-directional, isotropic, 1-directional) averaged for 25 cases
2To assist visualization, a 360◦rotational view of each of the 3D orien-
tation histograms in Fig. 2(a)-(e) could be found in the supporting docu-
ments/multimedia tab.
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4430 IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL. 39, NO. 12, DECEMBER 2020
Fig. 2. Quantitative 3D orientation analysis on each simulated collagen fiber classification. (a)-(e) represent unidirectional, crimped, disordered,
TFF, and helical classification, respectively. The 3D orientation histogram in the first column indicates the computed preferred 3D fiber orientations
for each classification (first column in Fig. 1) and the view angle is the same as Fig. 1. The corresponding x-y, y-z, and x-z projections are adjacent.
The color-scale in the top right indicates the relative contribution to a particular-preferred orientation. The polar plots in the second column indicate
the θand φangles (0◦<θ<360◦,0
◦<φ<90◦) for the corresponding 3D orientation histogram in the first column. A coordinate reference shows
the angles θand φrelative to the x, y, and z axes in the bottom right.
for each classification. The volume elements on the boundary
are not included. The average number of volume elements
labeled as 1-directional are more than 95% for the uni-
directional, crimped, disordered, and helical classifications.
The TFF classification has more than 95% of 2-directional
volume elements. Fig. 3(b) shows the average SV
Nfor each
classification where the unidirectional classification has the
minimum value, close to 0, and the disordered classification
has the maximum value, greater than 0.8. The SV
Nvalues of
crimped, TFF, and helical classification are similar, which is
greater than for the unidirectional classification and less than
the disordered and ranges from 0.21 to 0.32.
B. Quantitative Classification
Fig. 4 depicts our quantitative classification process. First,
a volumetric image, which has one of the already defined
classifications from Table 1, is input to the classification
process and, as a result, divided into one of three cases
depending on the labeled volume elements (1-directional,
2-directional, isotropic). If the volume elements are mostly
(>80%) 2-directional, then the 3D image is classified as TFF.
When the volume elements are mostly (>80%) isotropic,
it indicates that there is no preferred fiber orientation within
each volume element. The 3D images that primarily have
1-directional volume elements are divided into two groups
depending on the SV
N. 3D images with small SV
N(<0.075)
are considered unidirectional. The SV
Nthreshold we adopt,
0.075, is calibrated based on our simulation data. For applying
the analysis to experimentally obtained images from a range of
different fibrous tissues, the value may need recalibration from
the 3D orientation analysis. However, the general trend, which
is small SV
Nrepresenting unidirectional fiber organization
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: QUANTITATIVE CLASSIFICATION OF 3D COLLAGEN FIBER ORGANIZATION FROM VOLUMETRIC IMAGES 4431
Fig. 3. Quantitative metrics from the 3D orientation analysis for 25 sim-
ulated images per classification. (a) The average volume composition
and (b) the average
SVN
for each classification, presented as mean ±
standard deviation.
and medium and large SV
Nrepresenting crimped, helical, and
disordered fiber organization, would still be valid. 3D images
that have a SV
Ngreater than 0.075 require further analysis,
beginning with the θpolar plot. When the θpolar plot does
not have peaks, the 3D image classification is disordered. For
the plots that have peaks, we analyze the corresponding z-
layer for each peak. As previously mentioned, when the peaks
have an order rotating clockwise or counterclockwise in the
ascending z-layer, the 3D image classification is helical. The
3D images that do have peaks in the θpolar plot, but do
not rotate in the ascending z-layer, classify as crimped, as do
those with a θpolar plot with a single peak. One should
consider that the dominant fiber orientation for the images
we used are all along the z-axis in the image stack, which
is our axis of choice for this study. However, based on the
dominant fiber orientation, another preferred axis can always
be chosen. Thus, the fiber organization decision process could
be modified by changing the axis of choice to the preferred
orientation axis following the fiber orientation calculation.
Also, although in the simulated disordered classification data
the SV
Nis greater than all other classifications, we choose
not to use SV
Nalone to separate it from the others. This is
because the simulated images used in Fig. 3 only consider
disordered cases when the preferred fiber orientation in each
volume element is unidirectional. However, there are a variety
of disordered fiber organizations that have a wide range of
SV
N, thus relying only on SV
Nto distinguish disordered
classifications from others could be misleading. It is important
to note that Fig. 4 illustrates a decision process restricted
to the classifications we defined in Tabl e I. Since there are
numerous fiber organizations that are observed in biological
tissues, our five classifications could be considered as a basis
set where each classification yields a spectrum of variants. For
example, unique circumferential fibers in sclera and stroma
tissue [60], [61] would be classified as disordered. To add such
fiber organizations as a separate classification, one can divide
the image into sub-regions and analyze the peaks in the polar
plot of Fig. 4 to each of the sub-regions. Accordingly, future
work can extend the algorithm for new and more complex
cases, considering application-specific requirements.
The thresholds chosen for the process described in Fig. 4
are based on certain decisions about the fiber organization,
which can be predetermined by the user from a 3D rendered
image. For instance, the SV
Nvalue 0.075 for distinguish-
ing unidirectional from crimped classification was based on
our crimped definition previously mentioned which is 20%
modulation in amplitude with respect to the preferred fiber
orientation. This definition indicates that for crimped fibers,
the maximum φcan be 80◦in one volume element when the
preferred fiber orientation is along the z-axis. The maximum
φof 80◦results in a minimum SV
Nof 0.075. Also, for
the size of the volume elements, we chose approximately
25 fibers to be in one volume element, considering the typical
fiber distance in tissues that we image. We maintained the
maximum limit of the volume element size along zto be
1/4 of the crimped/helical wavelength according to the Nyquist
sampling theorem. For low-density fibers, it is possible for
the volume element size along zto be smaller than 1/4 of
the crimped wavelength while there are significantly less than
24 fibers in one volume element. In that case, the simulation
should be repeated to recalibrate the thresholds used for the
process described in Fig. 4. If the volume elements become
too large, the orientation will average out resulting in a
single orientation where the actual classification is crimped
for some cases. A grid size that is too small also affects
the analysis. For example, a TFF region of an image could
include unidirectional, dark, TFF, and isotropic elements if
divided into very fine regions. We have performed a parametric
study of simulated data and found that at least two fibers
should be present in each volume element to achieve an
accurate orientation analysis. Choosing a smaller grid size that
includes fewer fibers could potentially lead to an inaccurate
classification of the image. Details of the analysis are included
in Supplementary file 1. In addition, the bin size we chose
(10◦)in the polar plot was also related to our crimped fiber
definition. If the fibers differ in orientation more than 10◦(φ <
80◦)in each volume element, they are considered to be no
longer unidirectional fibers and the orientations should be
grouped separately. We use this criterion for the polar plot bin
size. Lastly, the criterion of volume elements being mostly
1-directional or 2-directional (>80%) was chosen from our
simulated images and also from dense collagen fiber images
of tendon. All of the 1-directional volume elements from
simulation and tendon tissue satisfied the 80% threshold.
Therefore, the thresholds are decided based on how the user
wants to distinguish each classification and some understand-
ing of the image, and thus requires a “human-in-the-loop”.
From a 3D rendered image, one can decide how much the
fiber orientation has to change in order to be classified as
non-unidirectional fibers, and also the number of fibers to fit in
one unit volume. Based on the user’s decision, the thresholds
including SV
N, size of unit volume and bin size is determined.
In essence, there is no absolute threshold that can be applied
to all fiber structures, but the threshold value is determined by
the user and the type of tissue.
C. 3D Orientation Analysis and Quantitative
Classification Applied to SHG Images
Fig. 5 illustrates the volumetric spatial results of the
3D orientation analysis for the 0◦(parallel), 45◦,and
90◦(perpendicular) cut samples, respectively [Fig. 5(a)-(c)].
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4432 IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL. 39, NO. 12, DECEMBER 2020
Fig. 4. Process guide for identifying 3D fiber classifications. A volumetric
image is assumed to have one of the already defined classifications. The
image is subsequently sorted into one of the three labels, 1-directional,
2-directional, and isotropic. 1-directional volumes are then separated
based on their computed
SVN
, where those with
SVN
<0.075 are
identified as unidirectional and otherwise a volume is classified as
crimped, helical, and disorderly oriented fibers by further analyzing the
θpolar plot. 2-directional volumes are classified as TFF.
Fig. 5 column (i) shows a representative SHG image from
the 3D image stacks, and the 3D rendered images in Fig. 5
column (ii) combine multiple 2D images. The preferred 3D
orientation arrows on top of the rendered image show the
fiber organization, where the calculated mean φangles are
8.26◦, 49.14◦, and 66.13◦for the 0◦,45
◦, and 90◦cut samples,
respectively. The mean φangle values match well with the
intended cut angle, where the 2D SHG images in the first
column give a sense of the dominant fiber direction through
general features, e.g., the length of the discernable fibers are
longest in Fig. 5(a) and shortest in Fig. 5(c). The potential
offset is due to sample heterogeneity and fiber misalignment
while cutting the sample. Fig. 5 column (iii) shows the region
labels of each sample, where most of the volume elements
are 1-directional and a few are dark and isotropic. The
considerable amount of dark and isotropic volume elements is
because of the irregular fibers within the sample and the lower
contrast in the SHG images, which is different from the ideal
simulated cases. In addition, an inherent artifact caused by the
sharp contrast in the simulated images mentioned above plays
a role in the appreciable amount of non 1-directional volume
elements. No volume elements are labeled as 2-directional in
all three samples.
Results from 3D orientation analysis from the tendon SHG
images are in Fig. 6,whereFig. 6(a)-(c) refers to the 0◦,
45◦, and 90◦cut samples, respectively. The 3D orientation
Fig. 5. Volumetric spatial analysis of SHG images of porcine ten-
don. Fresh tendon samples cut at (a) 0◦(parallel), (b) 45◦, and (c)
90◦(perpendicular) with respect to the collagen fiber bundles. (i) A
representative SHG image from the stack and (ii) the 3D rendered image
where the computed preferred 3D fiber orientations are plotted on half
of the volume. (iii) Label of each classification of fiber organization per
volume element as either dark (blue), 1-directional (green), and isotropic
(red). All images are in the same view angle. Scale bar is 20 μm.
histogram is in the first column of Fig. 6 and the projections
in x-y,y-z,andx-zplanes are immediately to the right in the
same column. The arrow colors (blue, cyan, yellow, and red)
represent their relative magnitude and the scale is located on
the right in Fig. 6. For all three cases, the arrows mainly have a
small deviation (≤40◦for both θand φ) with respect to their
main preferred orientation (red arrow). For the 0◦cut sample
[Fig. 6(a)], the range of θand φangles is −90◦<θ<90◦,
−90◦<φ<90◦. The range of θand φangles is defined
differently for visualization purpose since the mean φangle
is smaller than 40◦.Whenφ<40◦, the upper four quadrant
range (z>0) will give intuition that the SV is large, which is
misleading. By converting θ,φto θ±180◦,-φand changing
the angle ranges (−90◦<θ<90◦,−90◦<φ<90◦)the 3D
orientation histogram reflects the true SV value. The polar plots
for θand φin the second column have an angular resolution of
10◦and are drawn based on the θand φrange for each sample.
The θpolar plot for all samples has a peak at −20◦, 110◦,
and 60◦in Fig. 6(a)-(c), respectively. The φpolar plot shows
a narrow angular range, which reflects the small deviation of
arrows in the 3D orientation histogram.
Fig. 7 illustrates the volume fraction of each region label
(dark, isotropic, 1-directional) and SV
Nfor the SHG images
of tendon cut at 0◦,45
◦, and 90◦.InFig. 7(a), the majority
of the volume elements (>90%) are 1-directional for all
three samples. The volume elements on the boundary are
not included. In Fig. 7(b),theSV
Nis 0.0568, 0.0740, and
0.0432 for the 0◦,45
◦, and 90◦cut samples, respectively.
According to our classification procedure shown in Fig. 4,
all three images are classified as unidirectional. This result is
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LEE
et al.
: QUANTITATIVE CLASSIFICATION OF 3D COLLAGEN FIBER ORGANIZATION FROM VOLUMETRIC IMAGES 4433
Fig. 6. Quantitative 3D orientation analysis applied to SHG images of porcine tendon cut at (a) 0◦,(b) 45◦, and (c) 90◦relative to the long axis. The
3D orientation histogram in the first column indicates the computed preferred 3D fiber orientation for each sample and the view angle is the same
as in Fig. 5. The corresponding
x
-
y
,
y
-
z
, and
x
-
z
projections are on the right. The relative contribution to a particular-preferred orientation direction
is indicated by the color bar in the right panel. The polar plots in the second column indicate the θand φangles for the corresponding 3D orientation
histogram in the first column. The range of the angles are 0◦<θ<360◦and 0◦<φ<90◦except for (a) 0◦cut case where it is −90◦<θ<90◦
and −90◦<φ<90◦due to the low mean φangle.
Fig. 7. Quantitative metrics from the 3D orientation analysis for the SHG
images cut at 0◦,45
◦,90
◦with respect to the collagen fiber bundles.
(a) The volume composition and (b) the
SVN
for each sample.
because SV
Nfor all cases is less than 0.075 and also can be
deduced from the 3D orientation histograms in Fig. 6.
Cervix is a more complex tissue than tendon, exhibiting
strong spatial heterogeneity. Fig. 8(a) shows the cervical ring,
canal, a more random fiber structure (near septum), and septum
as approaching left to right. We select two distinct regions
(ring, near septum) and collect volumetric SHG images.
Fig. 8(b) and (c) display representative 2D images of the
ring and near septum regions, respectively. In the ring region,
the collagen fibers are preferentially aligned while in the
near septum region the SHG signal is lower and the fibers
Fig. 8. Rat cervix SHG images. (a) Cervix cross-section where the red
square on left is the ring region and on the upper right is the near septum
region. Zoomed in SHG images of the (b) ring region and (c) near septum
region. Scale bar is 250 μm and 20 μm, respectively.
are oriented more randomly. 87.5% of the volume elements
were 1-directional in the ring region while only 31.25% were
1-directional in the near septum region due to the high volume
of dark regions. The SV
Nis 0.0332 and 0.3684 for ring
region and near septum region, respectively. By using the
decision tree in Fig. 4 to classify the 3D organization, the
ring region is classified as unidirectional. The near septum
region cannot be classified due to the low 1-direction volume
elements (<80%) however shows the wider spread of fibers by
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4434 IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL. 39, NO. 12, DECEMBER 2020
aSV
Nhigher than the threshold 0.075. Cervix tissue has other
elements such as glycosaminoglycans, which has no SHG
signal, and results in a high number of dark volume elements
in the near septum region. Since the thresholds (>80%) of
volume elements was based on tendon, which is dense collagen
tissue, it can be readjusted for sparse tissue such as cervix.
By lowering the threshold to 30%, near septum region is
classified as disordered.
While we cannot verify the feasibility of our method for
every collagenous tissue, we demonstrated its feasibility for
several simulated images, a simple tissue (tendon), and a
much more complex tissue (cervix) with region-specific fiber
structure.
IV. CONCLUSION
In this article, we proposed an algorithm to quantitatively
classify 3D collagen fiber organization from volumetric images
into five common types of unidirectional, crimped, disordered,
TFF, and helical classifications. We demonstrated a method
that calculated the preferred 3D fiber orientation on simulated
images for each classification, and subsequently labeled the
volume elements to have features that were dark, 1-directional,
2-directional, or isotropic. With regards to the results of the
3D orientation analysis, we implemented a decision process
that distinguished the 3D collagen fiber classifications based
on quantitative metrics derived from features such as SV
and preferred 3D fiber orientation. Subsequently, we applied
the 3D orientation analysis to 3D SHG images of porcine
tendon and rat cervix. All three tendon samples, each with
a different orientation relative to the long axis of the tendon,
were classified as unidirectional. The image on the cervical
ring was classified as unidirectional. The five classifications
we defined could serve as a basis set, while our ongoing work
aims to improve the accuracy of our algorithm utilizing a more
diverse array of fiber organizations, and by employing machine
learning techniques. By incorporating such improvements,
our quantitative classification could potentially help in the
development of accurate biomechanical models through the
simplification of complex configurations of fibers within tis-
sues such as the cervix, which undergoes collagen remodeling
as a function of gestational age that can lead to preterm birth.
Also, our classification could assist in diagnosing diseases like
Ehlers-Danlos Syndrome by facilitating the identification of
structural defects in the collagen organization in the ECM of
tissues such as bones and tendons. Lastly, though validated
with collagen fibers, the algorithm is not restricted to these
fibers and could be adapted to other fiber types such as those
comprised of synthetic nanowires and fibrous polymers.
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