An automated image analysis methodology for classifying megakaryocytes in chronic myeloproliferative disorders.

This work describes an automatic method for discrimination in microphotographs between normal and pathological human megakaryocytes and between two kinds of disorders of these cells. A segmentation procedure has been developed, mainly based on mathematical morphology and wavelet transform, to isolate the cells. The features of each megakaryocyte (e.g. area, perimeter and tortuosity of the cell and its nucleus, and shape complexity via elliptic Fourier transform) are used by a regression tree procedure applied twice: the first time to find the set of normal megakaryocytes and the second to distinguish between the pathologies. The output of our classifier has been compared to the interpretation provided by the pathologists and the results show that 98.4% and 97.1% of normal and pathological cells, respectively, have testified an excellent classification. This study proposes a useful aid in supporting the specialist in the classification of megakaryocyte disorders.

Mathematical models for excitable systems in biology and medicine.

The excitable systems play a very important role in Biology and Medicine. Phenomena such as the transmission of impulses between neurons, the cardiac arrhythmia, the aggregation of amoebas, the appearance of organized structures in the cortex of egg cells, all derive from the activity of excitable media. In the first part of this work a general definition of excitable system is given; we then analyze some cases of excitability, distinguishing between electrical and chemical excitability and comparing experimental observations with simulations carried out by appropriate mathematical models. Such models are almost always formulated by partial differential equations of "reaction-diffusion" type and they have the characteristic to describe propagations of electrical waves (neurons, pacemaker cardiac cells, pancreatic b-cells) or chemical and mechanical waves (propagation of Ca++ waves or mechanical waves in the endoplasmic reticulum). The aim is to put in evidence that the biological systems can show not only excitability of electrical type, but also excitability of chemical nature, which can be observed in the first steps of development of egg cells or, for example, in the formation of pigments in vertebrate skin or in clam shells.

Reaction-diffusion equations for simulation of calcium signalling in cell systems.

Numerous experimental and theoretical studies have recently pointed to the importance of calcium signals and their propagation as waves of various kinds inside cells. This phenomenon has been particularly noted in fertilized egg cells. Ca2+ plays a fundamental role in these cells as it is capable of stimulating, by means of a first, large wave, the beginning of an organism's life at fertilization, immediately after sperm penetration. Furthermore, calcium is involved in numerous subsequent processes that are essential for the development of the future embryo, e.g. in contraction of cortical cytoplasm, protein synthesis and cell differentiation. Calcium waves, which are generated by self-oscillating pacemakers and propagate in excitable media, have been observed in some types of egg cells after fertilization. These waves adopt different shapes according to their emission frequency, wavelength, velocity and curvature, and they can occur as solitary waves, target waves or spiral waves. The mathematical models that study the progress of these waves have been developed by means of partial differential equations of the "reaction-diffusion" type. This study will discuss some significant models of intracellular Ca2+ dynamics. Some preliminary considerations will then be made in order to develop a model that describes the propagation of Ca2+ waves in ascidian eggs.

Rotating spiral waves in fertilized ascidian eggs.

Excitable systems modelled by reaction-diffusion equation may be expected to produce quite complex spatial patterns. Winfree [1974] demonstrated experimentally, in the Belousov-Zhabotinskii reaction, the existence of particular waves called rotating spiral waves. Later Keener and Tyson [1986] presented a thorough analysis of these waves in excitable systems. Spiral waves can also be observed in brain tissue (Shibata and Bures [1974]), while it seems that the precursor to cardiac fibrillation is the appearance of rotating waves of electrical impulses (Winfree [1983]). In this work we suppose the appearance of Ca++ spiral waves in the vegetal pole of ascidian egg cells after the first ooplasmic segregation. Previously we observed that (Ballarò and Reas [2000a]), when the myoplasm is completely localized in the vegetal region (excitable stage) and the ascidian egg cell is perturbed by an increase of Ca++ concentration in the culture medium, the cell reacts by showing persistent mechanical waves of contraction which exist as long as the cell is perturbed. Experimentally we observed the production of a polar lobe located in the vegetal region and the change of the inclination of mitotic furrow, after the appearance of a myoplasmic spiral wave in the vegetal pole. So we suppose that the myoplasmic spiral wave is due to a Ca++ spiral wave, and the myoplasmic spiral wave then causes the changes in the shape of the cell (polar lobe, inclination of mitotic furrow, etc.). Moreover we give a simple geometrical description of a spiral wave.