Automatic measurement of the evolutionary process dynamics of primary of biliary cirrhosis

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].

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.

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].

Inflammation (Figure1A) was identified by defining the borders around clusters of mononuclear cells (lymphocytes) with Delaunay's triangulation method [4].

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 D_γ + 1 – D, where D is the fractal dimension and D_γ the Euclidean dimension of the observed object. So TI = 1 – H = D - D_γ. Numerical results of all of these parameters are summarized in Table 1.

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.

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).

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].

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.

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?