Strain Energy and Biomechanical Constituent Models in Blood Vessel Tissues

Objective: To show the analysis of mechanical constitutive models in blood vessel tissues with a continuous media approach based on strain energy, which serve as a reference for new mathematical modeling proposals in them. Theoretical Framework: The mechanics of blood vessels, describes the structural and functional behavior of blood vessels and can characterize various cardiovascular diseases. Harmful changes that alter the mechanical response of the walls of blood vessels produce severe alterations in the health of the circulatory system. Predicting the mechanical behavior of blood vessels based on physiological status using biomechanical models is paramount for diagnosis. Therefore, in the present work, an analysis of the constitutive models is carried out with a continuous media approach based on strain energy. Method: Bibliographic review that identifies, analyzes and synthesizes the existing scientific proposals on blood vessel tissue modeling based on the deformation energy theory. Results and Discussion: A bibliographic study of the biomechanical constitutive models of blood vessel walls, generated over time, is presented. The behavior of the vascular wall is analyzed from the deformation energy approach. The benefits, limitations and potentialities of the models are also exposed: a) Strain energy with a transversely isotropic and homogeneous matrix; b) Strain energy with axis-symmetric fiber constants; c) Strain energy with collagen fibers subject to dispersion; d) Strain energy of four families of fibers without dispersion; and e) Strain energy of two families of fibers with anisotropic elastin and fiber recruitment. Implications of the research: The conclusions and analyzes presented serve as a basis for future research and mathematical modeling of the phenomenon of degradation and deformation of blood vessels, which will facilitate the understanding of the phenomenon and the subsequent strengthening of alternative treatment strategies that combat the clinical conditions derived from the transformations of mechanical properties in the same blood vessels. Originality/Value: This study contributes by giving order to the multiple bibliographic information related to the subject. The relevance of this research is evidenced in the conclusions issued when analyzing models based on the theory of continuous media as a function of strain energy.