**ABSTRACT** Advancements in
image analysis have recently made it possible to segment the cells and
nuclei, of a wide variety of tissues, from 3D images collected using fluorescence
confocal microscopy [Ortiz de Solorzano et al. J. Microscopy 193:212-226,
1999]. This has made it possible to analyze the spatial organization of
individual cells and nuclei within the natural tissue context. We present
here a spatial statistical method which examines an arbitrary 3D distribution
of cells of two different types and determines the probability that the
cells are randomly mixed, cells of one type are clustered, or cells of
different types are preferentially associated. Beginning with a segmented
3D image of cells (or nuclei), the Voronoi diagram is calculated to indicate
the nearest neighbour relationships of the cells. Then, in a test image
of the same topology, cells are randomly assigned a type in the same proportions
as in the actual specimen and the ratio of cells with nearest neighbours
of the same type versus the other types is calculated. Repetition of this
random assignment is used to generate a distribution function which is
specific for the tissue image. Comparison of the ratios for the actual
sample to this distribution assigns probabilities for the conditions defined
above. The technique is being used to analyze the organization of genetically
normal versus abnormal cells in cancer tissue.
Keywords: 3D spatial analysis,
tissue organization, tissue segmentation, fluorescence confocal microscopy
------------------------------
**INTRODUCTION **Recent technologies
in three dimensional (3D) fluorescence imaging, specific fluorescent bio-markers
combined with an ever increasing computational power has ensured that acquisition
of large, detailed, multi-probe, 3D images is becoming routine in biomedical
research. This technology is providing images of the spatial relationships
between cells in their natural tissue context together with details of
their subcellular and extracelluler properties. However, what is lagging
are the tools for analyzing such large and complex images. We present here
a spatial statistical method which examines an arbitrary 3D distribution
of cells of two different types, or cells exhibiting two different types
of features, and determines the probability that the cells are randomly
mixed, cells of one type are clustered, or cells of different types are
preferentially associated. The analysis involves a process by which structures
in the tissue are segmented and then individually scored based on measurements
of a given property. The measured property of interest may involve the
segmented structure itself, for example its size or directional polarity,
or might involve the abundance or distribution of other cellular components.
Currently, we are studying the spatial organization of genetically aberrant
cells relative to genetically normal cells in cancer. The image analysis
technique has allowed us to quantitate the high cell-to-cell heterogeneity
observed in the copy numbers of specific DNA sequences in human breast
tumors [1]. For this report, we use images from our breast cancer work
to demonstrate the spatial statistical analysis technique and to show that,
even in 2D, this technique easily detects spatial associations that are
not obvious by eye.
**METHODS & RESULTS** The
input for this analysis is a 3D image containing individually segmented
structures which have been classified into one of two types in terms of
a measured property. In the case of our breast cancer work, the structures
segmented were cell nuclei and the measured property was the normal or
abnormal copy number of specific DNA sequences. For illustration, the implementation
of our spatial statistical analysis technique is done on a 2D slice from
a 3D image stack of ToPro (Molecular Probes, Eugene, OR) labeled DNA in
human breast tissue (Figure 1A). Staining the total DNA allowed the nuclei
within the tissue to be segmented by a semi-automated algorithm [2]. Segmentation
produces an image mask, referred to as a labeled image (Figure 1B), where
all pixels within each nuclei are assigned a constant but unique value
in a black background. This value is used to identify individual nuclei
by number.
**FIGURE 1**
To determine the nearest-neighbour
relationships specific for these nuclei, segmented nuclei in the labeled
image are dilated, one voxel layer at a time, for a fixed number of iterations.
Dilation is only allowed into the background, not into other structures
and thus their shape was not necessarily conserved. The Voronoi diagram-like
surfaces that form between two dilated nuclei (Figure 2A) are used to infer
which pairs of nuclei are nearest neighbours. For the breast tumor tissue,
nuclei were large compared to the size of the cells and thus a relatively
small number of dilation iterations were required to detect the nearest
neighbour interactions. |
Generally, the number of dilation
steps equals the radius, in voxels, of an average nuclei. The set of nearest-neighbour
pairs are then tabulated in a triangular look-up-table (LUT) (Figure 2B).
Rows and columns of the LUT are labeled with the numbers representing the
segmented nuclei and elements of the LUT are assigned the value 1 when
the nuclei corresponding to the row and column number are neighbours. This
provides quick reference to which nuclei are adjacent to which others.
**FIGURE 2**
Nuclei in the labeled image are
then scored as either dark (d), for normal nuclei with 2 copies of each
chromosome, or light (l) for an aberrant number of chromosomes (Figure
3). To quantitate the spatial organization of the dark and light nuclei
in the image, we compute the fractions (Fdd, Fll, and Fdl) of dark-dark,
light-light and dark-light nearest-neighbour interactions by dividing the
number of each such interaction, respectively, by the total number of interactions.
As illustrated in figure 3, there are 18 nuclei, of which 9 are dark (normal
nuclei) and 9 are light (aberrant nuclei). There are 22 nearest-neighbour
interactions (the number of non-zero elements in the LUT), 1 dark-dark
interaction, 4 light-light interactions and 17 dark-light interactions.
These result in: Fdd=0.05, Fll=0.18 and Fdl=0.77, respectively. Note that
Fdd + Fll + Fdl =1.
**FIGURE 3**
We then ask how these values would
compare if the labeled image had the same numbers of dark and light nuclei
but the assignment to specific nuclei was random. To answer this, the labeled
image is randomly assigned to generate an ensemble of random states. For
the breast cancer work, this was done 1000 times. For each random assignment
the fraction of each type of nearest-neighbour interaction, Fdd, Fll and
Fdl, is calculated and used to generate probability histograms (Figures
4A, 4B, 4C) respectively. Each distribution shows the range and most probable
fraction of nearest-neighbour interactions. A typical random scoring of
the topology is shown in figure 4D.
**FIGURE 4**
In order to determine if nuclei
of the same type are clustered, randomly mixed or nuclei of different types
are preferentially associated, the values, Fdd, Fll and Fdl, from the actual
image are compared to their respective distributions. If the fraction of
any interaction type Fxy, for example, is significantly above its random
distribution it would imply that nuclei of type x and y are preferentially
clustered. If Fxy falls within the distribution then nuclei types x and
y are randomly distributed. However, if Fxy is significantly below the
distribution, it implies that there are fewer x-y type neighbouring interactions
than in the random case and that x and y nuclei are distributed so that
they are not likely to be neighbours. Integrating the random probability
distributions, from zero to their appropriate fractions Fxy, result in
confidence probabilities. Low confidence probabilities indicate that the
distribution of nuclei is not random because the nuclei are organized such
that there are few x-y type interactions. High values (close to 1) of the
confidence probability indicate that the nuclei are organized such that
there are many x-y type interactions. Intermediate values indicate randomness.
For the image in figure 3 the fractions
of nearest-neighbour interactions (Fdd=0.05, Fll=0.18 and Fdl=0.77) result
in confidence probabilities of 0.002, 0.3712 and 0.9964 respectively. These
clearly indicate that the distribution of the two types of nuclei is far
from random. |
Both Fdd and Fdl lie outside their
corresponding random probability distribution functions and indicate that
in the actual image the fraction of normal-normal interactions, Fdd, is
too low and the fraction of normal-aberrant interactions, Fdl, is too high
for this scoring to be random. Rather, these data clearly indicate that
normal and aberrant nuclei are preferentially anti-clustered. In contrast,
for a typical random image in figure 4D Fdd=0.14, Fll=0.32 and Fdl=0.54
and the corresponding confidence probabilities are 0.20, 0.88 and 0.66,
respectively. Since none of these data are close to either probabilities
of zero or one, they demonstrate that the image in figure 4D is random.
**DISCUSSION** In this study
we implemented an algorithm that calculates a statistical probability that
cells of one type are clustered, randomly mixed with cells of another type
or cells of different types are spatially associated with each other. What
distinguishes this technique from other spatial statistical analysis methods
[3 & 4] is that it makes no assumptions about how the objects are distributed
in space. This makes it particularly suitable for spatial analysis of cell
in tissue. Further, errors resulting from the analysis (for example undetected
nuclei, assignment of nuclei to the wrong type, or selection of a region
of tissue dominated by one type), bias the results towards the random case.
Consequently, this gives additional confidence that a non-random result
is correct.
We foresee several useful extensions
to the current method. These include analysis of three or more cell types,
use of the area of the surface between dilated segmented structures as
a measure of the strength of the nearest neighbour interaction and the
spatial analysis of non nearest-neighbours. Non-random, non-nearest-neighbours
could conceivably exist in complex tissue, yet would be difficult to observe
visually.
The current application of this
technique is the analysis of the spatial patterns of genetically aberrant
versus genetically normal cells in breast cancer tissue [1]. Spatial clustering
of the genetically aberrantly cells may be indicative of their clonal expansion.
On the other hand the deliberate association of genetically aberrant and
normal cells should not be unexpected, given the high level of cell-to-cell
communication that takes place in normal and cancerous tissue. Other potential
applications could be to study the pattern of progesterone receptor and
estrogen receptor positive cells, which are known to be heterogeneously
distributed in mouse mammary epithelium [5 & 6].
**ACKNOWLEDGMENTS **This work
has been supported by the Director, Office of Energy Research, Office of
Health and Environmental Research of the U.S. Department of Energy under
contract number DE-AC03-76SF00098, NIH grant CA-67412 and a contract with
Carl Zeiss Inc.
**REFERENCES**
[1] S.J. Lockett, E. G.Rodriguez,
C. Ortiz de Solorzano, A Jones, K. Chin, J Gray 1999
Technology for histogenetic analysis
of breast cancer
Proc. Amer. Ass. for Cancer Res.
40:#480
Chin K, Kuo w-l, Garcia Rodriquez
E, Ortiz de Solorzano C, Lockett S, Gray JW 1999
Rates of genome instability in
human breast cancers: FISH analysis in vitro and in vivo.
Breast Cancer Reserch and Treatment
57, 1:133
[2] C. Ortiz de Solorzano, E.G.
Rodriguez, A. Jones, D. Pinkel, J.W. Gray, D. Sudar, S.J. Lockett 1999
Segmentation of confocal microscope
images of cell nuclei in thick tissue sections.
J. Microscopy 193:212-226
[3] R. Albert, T. Schindewolf, I
Baumann, H. Harms 1992
Three-dimensional image processing
for morphometric analysis of epithelium sections
Cytometry 13:759-765
[4] B. Weyn, G. van de Wouwer, S.
Kumar-Singh, A. van Daele, P. Scheunders, E. van Mark, W. Jacob 1999
Computer-assisted differential
diagnosis of malignant mesothelioma based on syntactic structure analysis
Cytometry 35:23-29
[5] Shyamala, G. 1999
Progesterone signaling and mammary
gland morphogenesis.
J Mammary Gland Biol Neoplasia,
4(1):89-104.
[6] Silberstein, GB; Van Horn, K;
Shyamala, G; Daniel, CW. 1996
Progesterone receptors in the mouse
mammary duct: distribution and developmental regulation.
Cell Growth and Differentiation, 7(7):945-52. |