Determination of human arterial wall parameters from clinical data

Abstract

This study suggests a method to compute the material parameters for arteries in vivo from clinically registered pressure-radius signals. The artery is modelled as a hyperelastic, incompressible, thin-walled cylinder and the membrane stresses are computed using a strain energy. The material parameters are determined in a minimisation process by tuning the membrane stress to the stress obtained by enforcing global equilibrium. In addition to the mechanical model, the study also suggests a preconditioning of the pressure-radius signal. The preconditioning computes an average pressure-radius cycle from all consecutive cycles in the registration and removes, or reduces, undesirable disturbances. The effect is a robust parameter identification that gives a unique solution. The proposed method is tested on clinical data from three human abdominal aortas and the results show that the material parameters from the proposed method do not differ significantly (p < 0.01) from the corresponding parameters obtained by averaging the result from consecutive cycles.

Constitutive modelling of arteries

“…A method for determining the parameters in this model on the basis of clinically registered pressure-radius signals was discussed by Stålhand (2009), who treated the artery as a singlelayered membrane. The method developed was shown to be robust and yielded unique values of the material parameters.…”

Determination of the layer-specific distributed collagen fibre orientations in human thoracic and abdominal aortas and common iliac arteries

“…Available evidence suggests that intimal thickening is owing to specific mechanical stresses [2], atherosclerosis may be related to increased arterial wall stiffness [3], aortic disease may be linked to differences in the tissue organization and content in the proximal and distal regions of the aorta [4], and enlargement of intracranial aneurysms may result from growth and rearrangement of collagen owing to stress (increasing the risk of rupture with a related mortality rate of 35-50%) [5]. Ageing processes such as stiffening of the vessel wall [6][7][8] are related to an increase in collagen content relative to elastin [9,10], fibrosis and continuous depositions of amorphous substances for the elastin, and increased cross-linking of collagen; all of which lead to reduced mobility of the arterial wall constituents [11]. Additionally, for the human abdominal aorta, sex-dependent differences in the degrees of stiffening have been reported [7], and generally, the interaction of the structural vessel wall components with the different constituents of the extracellular matrix is believed to be a key factor in understanding diseases [11].…”

The fiber orientation in the coronary arterial wall at physiological loading evaluated with a two-fiber constitutive model

“…Other studies adopted a patient-specific modeling approach to assess the elastic modulus or distensibility from a clinically obtained pressure-radius relation (Hansen et al 1995;Vavuranakis et al 1999). More recently, constitutive models, which take the microstructure into account, were fitted to patient data (Masson et al 2008;Stålhand 2009;Danpinid et al 2010). This had the advantage that pathologies could be related to the parameters associated with different tissue components.…”

“…Stålhand and Klarbring (2005) incorporated it as a loose constraint into the estimation procedure in combination with a thick-walled, Fung type, material model and successfully validated it on data from a human aorta obtained in-vivo. Furthermore, making use of a methodology that was first proposed and successfully applied by Schulze-Bauer and Holzapfel (2003), Stålhand (2009) was even able to fit a more microstructurally based, thin-walled, two-fiber constitutive model (Holzapfel et al 2000), to clinical data from human aortas. Besides the pressure-invariant axial force constraint, this methodology comprises a second constraint, which prescribes the ratio of axial to circumferential stress at a certain characteristic pressure.…”

“…Taking into account that the results should be applicable to clinical data, a constitutive model with a limited number of parameters is preferable. Therefore, a thick-walled, 1D, single-layered, fiber-reinforced model, of which the constitutive equations were developed by Holzapfel et al (2000) and used for parameter estimation from clinical data (Stålhand et al 2004;Stålhand 2009), was used in this study. Residual stresses were incorporated into the model by minimizing the circumferential stress gradients at physiological pressure by introducing a stress-free geometry with an opening angle (Chuong and Fung 1986;Takamizawa and Hayashi 1987).…”