Analysis and development of a viscoelastic model of biological tissues to assess their nonlinear properties

The purpose of the research is to analyze existing viscoelastic models of biological tissues to develop a model that takes into account the nonlinearity of deformation processes during the propagation of transverse acoustic waves.

Methods. Acoustic elastography is a group of methods based on the analysis of the interaction of low-frequency transverse acoustic waves with biological tissues. The physical basis of such methods are viscoelastic models of biological fabrics that take into account changes in their deformation parameters when they are subjected to forces with variable amplitude and direction. Taking into account the nonlinearity of the processes of deformation of biological tissues during the propagation of transverse acoustic waves will allow us to introduce a new informative characteristic for analyzing the processes of their structural changes – a nonlinear parameter. Simultaneous consideration of linear and nonlinear properties of biological tissues will improve the quality of diagnosis of diseases occurring in the human body, including in the early stages. As part of the study, a two-element viscoelastic model of biological tissues was analyzed, allowing for both physical nonlinearity and linear characteristics. A model is also considered that allows taking into account the geometric nonlinearity of the deformation processes and the deformation process es of the models when changing the parameters of the acting force.

Results. We have proposed a viscoelastic model of biological tissues that accounts for both physical and geometric nonlinearity. The key mathematical expressions describing this model have been derived. Results have been obtained from mathematical modeling of deformation processes for the developed viscoelastic model under varying applied forces and for a model that accounts only for physical nonlinearity.

Conclusion. The proposed mathematical model allows for the deviation of biological tissue deformation processes from linear laws due to both physical and geometric nonlinearity. Application of this model will improve the accuracy of assessing the interaction of low-frequency acoustic radiation with biological tissue, which can be used to develop new, high-precision methods for assessing tissue changes during ongoing diseases, including in the early stages

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