Application of Virtual Fields Method for the mechanical characterization of atherosclerotic plaques

Abstract

Atherosclerosis is a lipid-driven inflammatory disease of the arteries. It causes
increased thickness of the intima layer of an artery, due to build-up of, among
others, lipid deposits. Eventually, this could cause rupture of the blood vessel’s
wall, leading to thrombus forming and possibly to clinical events. Clinically, the
degree of stenosis (degree of narrowing of the lumen) is used as a metric for risk
assessment. However, narrow arteries do not necessarily rupture, while wide arteries can still rupture. Since rupture is a mechanical event, (mechanical) stress
in the arteries could be a better metric to assess rupture. Stress could be calculated
through a chosen constitutive model. However, these constitutive models require
patient-specific constitutive parameters, which presently are challenging to obtain.
To retrieve the patient-specific constitutive parameter(s), the Virtual Fields
Method (VFM) could be used. This is a method based on the principle of virtual
work. By minimizing the difference between the internal and external virtual work,
the constitutive parameter(s) can be calculated. In this study, five atherosclerotic
plaques were modeled with a neo-Hookean material model, subjected to intraluminal pressure in a Finite Element (FE) environment. The nodal deformations were
used to apply the VFM in MATLAB. This was done at three levels: level 1 assumed
that, for each model, a single constitutive parameter dictated the stress behavior
of the entire atherosclerotic model. At level 2, the models were divided into four
mechanically relevant components: intima, wall, calcified tissue, and lipid component. The ground truth for the constitutive parameter of each component was
unique (120 kPa, 250 kPa, 5 kPa, and 423 kPa for intima, wall, lipid, and calcified tissue component respectively). For each of the components, a constitutive
parameter was calculated. At the last level, the nodes provided by the FE model
were used to create four-noded quadrilateral elements. For each element separately,
a constitutive parameter was calculated. This level presents two sublevels: at the
first sublevel (level 3a), the ground truth for the constitutive parameter of all elements was set at 100 kPa. At the second sublevel (level 3b), the ground truth for
the constitutive parameter of an element depended on the component the element
belonged to; the elements that belonged to the intima, wall, lipid, or calcified tissue
component had a ground truth value for their constitutive parameter of 120 kPa,
250 kPa, 5 kPa, or 423 kPa, respectively.
The results showed how for the first level, the VFM was able to calculate the
constitutive parameter within 0:2% of the ground truth. For level 2, some of the
atherosclerotic arteries’ components were calculated very accurately (within 2% of
their ground truth), while others differed greatly (by more than 20% of their ground
truth). For level 3a, it was shown how a good initial guess for the minimization
algorithm could produce very accurate results. For level 3b, a good initial guess
was lacking and the minimization algorithm was not capable of finding results that
were in close proximity to the ground truth.
Clinically, the application of the VFM can be an interesting approach for assisting clinicians to decide on intervening. However, this still requires some improvements from the current work. The current study serves as a foundation upon
which to build.