Background
PBC is a chronic inflammatory autoimmune disease [1] that evolves into cirrhosis via
four stages. These are determined by the successive implementation in hepatic tissue
of the following events: inflammation, destruction and regeneration of biliary tissue
CK7+ and fibrosis. This paper describes a method to study of the dynamics of the disease
histologic behaviour [2].
Materials and methods
We studied 58 liver biopsy samples, from the archives of Departments of Pathological
Anatomy of Istituto Clinico Humanitas IRCCS, Rozzano, Milan, Italy and the Department
of Gastroenterology of Milan’s Ospedale Policlinico IRCCS, of Caucasian subjects with
PBC in various stages. Each procedure was performed in accordance with the guidelines
of the Ethics Committees of the hospitals involved and diagnoses were defined by the
expert pathologists of these same hospitals.
Three consecutive 2-3 µm thick sections were obtained from each sample: the first
was used to identify inflammatory cells; the second was stained with Sirius red to
visualize collagen deposits and the third was used to visualize the biliary tree with
CK7 antibody.
The histological metrization method [3] was developed in the Laboratory for the Study
of Metric Methods in Medicine of the Istituto Clinico Humanitas (Rozzano, Milan, Italy).
The prototype of this computerized device called HM and its controlling software were
entirely designed and developed in our laboratory. The Metrizer is a totally computer-driven
machine that automates the focusing of the microscope and the exclusion of Glisson’s
capsule from the computation of fibrotic islets. It performs reproducible metric measurements
from digitalized images of the entire histological section, giving results within
a few minutes. This method measures all notable liver structures bared of any property
not involved in the measurement.
Statistical analysis
The data are given as numbers and percentages or mean or median values and ranges
where appropriate. All variables were log-transformed in order to approximate a Gaussian
distribution and normalized to a (0,1) range to allow for comparison between variables.
Thus the final data are expressed in percentage of the interval between 0 and 1. All
of the analyses were performed with Stata10 [http://www.stata.com].
Results and discussion
Inflammation
(Figure1A) was identified by defining the borders around clusters of mononuclear cells
(lymphocytes) with Delaunay's triangulation method [4].
Figure 1
Catalogue of the multifarious fragments of liver structures measured by HM.; A. Inflammation
cell clusters B. CK7; and C. fibrosis elements, The black image is a Glisson membrane
fragment excluded by the Metrizer.
This method identifies a line that connects the centers of outermost cells that are
distanced ≤20 μm. This line is arbitrarily considered the separator of the inflammatory
cells within a cluster from the mononuclear cells dispersed in the surrounding hepatic
tissue.
The inflammatory basin, which increases constantly due to the autoimmune process,
is the set of areas in a section that are covered by inflammatory cell clusters. The
area of the basin covered by cluster-resident cells is called the pure inflammatory
space, which varies with the number (density) of cells present in the clusters.
The
intra-hepatic biliary duct
area (Figure 1B) was metrically measured. During the course of PBC, the biliary tree
duct status is determined by two components: autoimmune destruction and regeneration
of intrahepatic CK7+ ductular segment.
The
collagen islets
forming fibrosis (Figure 1-C) were measured in linear meters; the result was corrected
by the fractal dimension [5] to include details of the irregularity of their shapes
The fractal dimension was obtained by means of the box counting method because the
objects to be measured were “truncated fractals” [6], the fractal dimension was used
as a dilation factor rather than an exponent [7] Three classes of islet magnitude
were arbitrarily identified: area from 10 and 103 μm2, from 103 to 104 μm2 and over
104 μm2.
The
tissue disorder
quantitative assessment was performed with a Tectonic Index (TI), which describes
the loss of tissue organization or any deviation from the natural order (a high TI
indicates a high degree of tissue disorder). The TI defines the organization of liver
tissues and is expressed with a range of values from 0 to 1. The TI was calculated
as 1 – H, where H is Hurst’s coefficient (range zero to 1) [8], defined as Dγ + 1
– D, where D is the fractal dimension and Dγ the Euclidean dimension of the observed
object. So TI = 1 – H = D - Dγ. Numerical results of all of these parameters are summarized
in Table 1.
Table 1
Summary of all of the metric data obtained from the structural measurements and the
data used for staging purposes. Minimum, median, and maximum values of tissue parameters
are given in % of total histologic section area of biopsy specimen.
Tissue parameters
Minimum
Median
Maximum
Area of the inflammatory basin
0.026
1.005
6.444
Area covered by resident cells
0.002
0.636
5.295
Area of intra-hepatic biliary ducts
0.003
0.114
0.882
Small areas (10-103 μm)
0
0.009
0.105
Medium-sized areas (103-104 μm)
0.001
0.006
0.033
Large areas (>104 μm)
0
0
0
Area of fibrosis
0.30
1.456
24.4
Small areas (10-103 μm)
0.008
0.092
0.521
Medium-sized areas (103-104 μm)
0.001
0.026
0.203
Large areas (>104 μm)
0.01
0.075
1.005
Neo-angiogenesis
0.030
0.586
3.474
Hemopoietic stem cells
0
0.006
0?
Tissue disorder (TI)
0.072
0.274
0.643
In order to approach the PBC behavioural dynamics [9], the first key was to set into
the interval (0,1) the logarithmic transformation and normalization of the measures
of CK7+; tissue and fibrosis, taken as the most representative structural elements
with which to metrically construct the liver state portrait that defines the grading
and staging of the semiquantitative subjective methodologies.
A second key is the transformation of portrait scalars into a single vector to reduce
the multiplicity of elements of the liver section into a dot-like geometrical figure.
This translation into vectorial arithmetic in classic dynamics is crucial for the
construction of the dot-like geometrical operator, called dynamic particola that represents
the whole system.
In order to gain a method to study the system’s behaviour dynamics [9], the immune
CK7+ biliary ductules resulting from the destruction-regeneration and intrahepatic
fibrosis, considered a set of phenomena that generates the irreversible tectonic disorder
leading to cirrhosis. The values of vectors representing irreversible parameters,
resulting from the HM measurement, were taken to create the particola. The vectorial
transformation is obtained by plotting the value of CK7 area on the y and the value
of fibrosis areas on the x orthogonal axes. The value of the modulus of this resultant
sum in the orthogonal space is taken as the Newtonian dot-like dynamic particola that
shows an instant of the PBC behaviour (Figure 2A). The set of points (each a particola)
on the x-y orthogonal space, resembles a Gibbs cloud of points, each expressing in
log scale the magnitude of the vectorial value of a particola with a scalar. These
scalars ordered on a real number line, the simplest state space, will graphically
show the trajectory that is the reference of the dynamic behavior of PBC process.
(Figure 2B).
Figure 2
A): The set of dynamic particulae resembling a Gibbs cloud-point obtained expressing
as vector magnitudes the normalised log value of CK7+ areas and the normalised log
value of fibrosis in our patients. B) The points are transferred to the oriented line
of real numbers representing the standardised trajectory of the process. C) An ogival
cumulative curve orders the dynamic particula within the three clouds in panel A.
This curve is sub-divided into three tertiles marked by blue points and represents
the trajectory of the overall dynamic process of PBC from α to ω.
Furthermore, we plotted the value of each particula on the y axis (ranging from 0
to 1) versus the disease timing, identified with all particulae, on the x axis (Figure
2C). Next, we identified the tertiles on this curve that discriminate three phases.
This term used in our new method is different from the ‘stages’ characterising semiquantitative
static descriptions. As a result, the three phases are extrapolated by increasing
amounts of particolae formed by fibrosis and CK7+ tissue. In particular, phases 1,
2, and 3 represent early, intermediate, and final disease to feature mean particula
values of 0.2075, 0.4722, and 0.7386, respectively.
The inflammation was excluded from the constitutive components of the trajectory describing
the course of PBC process, for its reversibility. This different behaviour is due
to the entropy produced in the interior of the inflammation process that is not transferred
across its boundaries into the surrounding environment [10].
Conclusions
The method we constructed, with its technology, strongly reduced the computational
time and improved the liver tissue structure recognition and description. As these
tools allowed this first study of PBC behaviour in terms of physics of dynamics, this
paper supports the hypothesis that the long periods of cessation in the history of
dynamic knowledge were due to the very higher rapid theoretic development toward facilitating
computation devices [11,12]. The technology introduced into our methodology facilitated
the study of PBC behaviour by the following points:
1) Exclusion of the inflammatory infiltrates from dynamic study, as they do not produce
topic stable entropy deposits. Collagen interstitial deposition generating fibrosis
is hepato-cellular necrosis dependent.
2) Standardization of a strictly objective evaluation producing scalars by metrizing
the images of the histological structures of the liver section.
3) Metrical measurement also of the smallest dispersed islets of fibrosis, and tiny
CK7+ biliary ducts normally undetected with optical microscope.
4) Transformation of scalars into vectors leading to vectorial PBC histological section
portraits. A homogeneity was created with this operation that maintains the concepts
of mixture and identity of the mixed elements in the sum of CK7+ biliary ducts and
fibrosis vectors that define the particola, geometric figure which graphically will
trace the process trajectory.
5) Description of PBC evolution by the cumulative curve of the particolae, each representing
an actual state of the processes and taking this planar curve as the ideal finite
trajectory α–ω) of entire PBC process.
6) Definition of past and future percentage of the disease course with its particola
on the trajectory.
7) The score of PBC evolution into three phases on its trajectory and describe the
ideal course of the process based on mathematical measurements.
To conclude let us say that any correlation is recognizable between the metrical data
of our case-list, divided into three phases by the rules of dynamics and the semi-quantitative
data, divided into four stages according to the rules of the method of Scheuer. (Table
2) For example the 20 specimen classified in our higher phase III included 9 patients
(45%) classified by the semi-quantitative Scheuer classification at minor levels of
staging. Where is the truth?
Table 2
Distribution in the three stadia of the dynamic trajectory of the patients’list classified
according to Scheuer’s classification.
Scheuer classification
Phase
1
2
3
4
I
19 (33%)
11 (58%)
7 (37%)
1 (5%)
0
II
19 (33%)
11 (58%)
1 (5%)
6 (32%)
1 (5%)
III
20 (34%)
9 (45%)
2 (10%)
5 (25%)
4 (20%)
List of abbreviations
PBC: Primary biliary cirrhosis; IRCCS: Institute for Scientific Research Hospitalisation
and Care; HM: Histologic Metrizer; TI: Tectonic Index
Competing interests
No conflicts of interest exists.
Authors’ contributions
ND wrote the manuscript and ideated the theory around the machine and dynamics and
the machine itself, CR ideated the software and constructed the machine, EM did the
statistical analysis and contributed to revision of the text, BF, SDB and SM did the
histological preparations, GB revised the text.