Applying thermomechanical analogy to predict the arterial residual stress state

The prediction of the arterial zero-stress state is as of yet an unresolved problem in the field of modelling the mechanical response of patientspecific arteries. This is because the configuration associated with arterial zero-stress state is impossible to obtain experimentally. However, the zero-stress configuration (or, equivalently, the residual stresses related to this configuration) represents the crucial data of any numerical analysis. In this study, the mechanical response of a pre-stressed, pressurised, hyperelastic tube (representing the artery) is determined without knowing the initial zero-stress configuration of the artery. Instead, to predict the arterial residual (bending and stretching) stresses, a corresponding thermomechanical analogy is used. As shown in the paper, the arterial residual stress state can equally be obtained by thermally loading a properly defined closed tube. Thus, based on the loaded state of the corresponding thermomechanical model, the arterial residual stress sate is constructed, from where the arterial loaded state can be obtained. The initial configuration of the thermomechanical model is defined on the basis of the arterial loaded configuration. The methodology is validated by predicting the zero-stress state of the artery. The predicted equilibrium state of the artery, when cut longitudinally and transversally, has the form of an opened-up tube with a relatively low stress state in comparison to the arterial residual stresses. The results thus demonstrate that arterial residual stresses that are predicted with the corresponding thermomechanical model exhibited the bending distribution, which proves the methodology to be adequate. Določitev breznapetostnega stanja arterij predstavlja še vedno nerazrešen problem na področju numeričnega modeliranja mehanskega odziva realnih arterij. Breznapetostno stanje arterije, ki ima v splošnem obliko krožnega sektorja, je namreč eksperimentalno nemogoče določiti. Oblika breznapetostnega stanja (oziroma temu pripadajoče zaostalo napetostno stanje) pa je pomembno zato, ker predstavlja začetno stanje in tako ključen podatek sleherne numerične analize. Arterije se za karakterizacijo njihovega mehanskega odziva običajno obravnava kot idealno krožne cevi, to pomeni idealno krožne in ravne. Takšna poenostavitev omogoča določitev zaostalih napetosti arterije brez poznavanja njihovega breznapetostnega stanja. Prisotnost zaostalih napetosti je posledica homogenizacije odziva arterij in vivo. Napetostno stanje arterije in vivo bi bilo namreč izrazito nehomogeno z velikim transmuralnim gradientom brez upoštevanja zaostalih napetosti. Zaradi njihove porazdelitve skozi debelino žilne stene se jih običajno asociira z upogibnimi napetostmi. Na notranji površini kolobarja so zaostale napetosti tlačne, medtem ko so na zunanji površini natezne.