A New Non-Equilibrium Thermodynamic Fractional Visco-Inelastic Model to Predict Experimentally Inaccessible Processes and Investigate Pathophysiological Cellular Structures

Abstract

Abstract:After remarking on non-equilibrium thermodynamics with internal variables, this paper highlights the importance of these variables to the study of biological systems. Internal variables can provide a more detailed description of biological processes that occur inside cells, tissues and organs. In order to introduce a fractional model on a visco-inelastic medium based on Kluitenberg's non-equilibrium thermodynamics, the origin of the complex dynamic modulus is shown by means of linear response theory. This research recalls our previous work to develop an ultrasound wave technique that allows us to investigate biological systems, and introduces the fractional visco-inelastic model and relative generalized relaxation time, to show that it is possible to obtain the Cole-Cole model in a particular case.

A New Model for Thermodynamic Characterization of Hemoglobin

“…In a frequency range between 2.5 × 10 7 Hz and 10 8 Hz, the difference between the two curves (28) and (29) is due to a type of phenomena emerging when the thermodynamic coefficient L (1,1) is used. In line with our studies [4,5,[10][11][12][13][14][15][16][17][18], the introduced coefficients (not only L (1,1) ) show phenomena not detectable with ε, because ε is the sum of many phenomena. The above on L (1,1) and ε is reported in the previous paper [4].…”

“…The choice of the variables on which the entropy depends leads to different developments of non-equilibrium thermodynamics. In all our researches, we chose to use the non-equilibrium thermodynamics with hidden internal variables formulated by Klutenberg in its theoretical aspects [5][6][7][8][9] and further developed by us [10][11][12][13][14][15][16][17][18]. This choice was made because we think this theory is more suitable in the study of biological systems [12] and it is a more physical-mathematical approach in regard to the classical meaning of this term.…”

Expanding the Repertoire of Dielectric Fractional Models: A Comprehensive Development and Functional Applications to Predict Metabolic Alterations in Experimentally-Inaccessible Cells or Tissues

“…This paper is devoted to providing a physical-mathematical approach for the study of living matter. So, in order to continue our previous research approach in the network of NET [10,[19][20][21][22][23]36] and apply it to biological systems, in the next section we will formulate a dielectric fractional model based on NET.…”

“…In many cases, fractional models are more efficient than non-fractional models, as they better fit experimental data, and this efficiency becomes important when we want to study complex phenomena such as those occurring in the biological field. Our model is based on thermodynamic considerations, and therefore, it is more suited to the investigation of the evolution of the system under study [31][32][33][34][35][36]. We start by introducing a new fractional model in the final sections of this paper.…”

Thermodynamics Characterization of Lung Carcinoma, Entropic Study and Metabolic Correlations

“…This is due to both the indistinguishable characteristics of the first cancer cells, as well as the difficulty in coordinating non-invasive and low costs screening with diagnostic sensitivity. In recent years there has been a rising interest in dielectric spectroscopy, an investigation technique that can obtain information on the chemical-physical characteristics of biological materials starting from the dielectric properties [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23]. The response of biological tissues to an electric field is characterized by two intrinsic properties conductivity and relative permittivity, which are both dependent on frequency.…”