An engineering tool to estimate eigenstresses in three-dimensional patient-specific arteries

Identification of residual stresses in multi-layered arterial wall tissues using a variational framework

“…Among these, we highlight the contributions of [1] with the first in-depth proposal of this idea, [5,7] accounting for the different behaviors presented for each constituent layer, and [18,19] displaying strategies to incorporate data obtained using experimental techniques into patientspecific geometries. It is also worthwhile to mention two different approaches explored in the literature, i) incorporating RSs through growth processes, considering that each mechanically relevant component is synthesized and deposited in the tissue with a predefined deformation (and consequently stress) level [20,21]; and ii) introducing RSs to achieve a uniform transmural distribution of stresses in physiological conditions [22]. The past decade has seen a rapid development of data assimilation techniques in the field of cardiovascular modeling.…”

Modeling of Anisotropic Growth and Residual Stresses in Arterial Walls

“…Being associated with a reduction of stress gradients in loaded states, residual stresses need to be included in numerical simulations to obtain a predictive stress distribution. Computational methods to reduce stress gradients by incorporating residual stresses are proposed in the literature [2][3][4][5]. These methods are however rather engineering approaches, as no biological processes are included to obtain the residual stresses.…”

A combined growth and remodeling framework for the approximation of residual stresses in arterial walls

“…Engineering approaches focusing on the consequence of residual stresses instead of their cause as means for their estimation have been proposed by Polzer et al [33] or Schröder and Brinkhues [40] and Schröder and von Hoegen. [41] Applying a linearly distributed isotropic growth deformation with vanishing average volume change, a minimization of stress gradients over the wall thickness was realized in [33]. In [40] and [41], an arterial segment was divided radially and circumferentially into sectors and the deviation between a stress measure at each local point and its sectorial volume average was applied as residual stress.…”

“…[41] Applying a linearly distributed isotropic growth deformation with vanishing average volume change, a minimization of stress gradients over the wall thickness was realized in [33]. In [40] and [41], an arterial segment was divided radially and circumferentially into sectors and the deviation between a stress measure at each local point and its sectorial volume average was applied as residual stress. This method is applicable for arterial walls with arbitrary geometry and can thus be used for patient-specific simulations.…”