The choice of a constitutive formulation for modeling limb flexion-induced deformations and stresses in the human femoropopliteal arteries of different ages

Abstract

Open and endovascular treatments for Peripheral Arterial Disease are notorious for high failure rates. Severe mechanical deformations experienced by the femoropopliteal artery (FPA) during limb flexion and interactions between the artery and repair materials play important roles and may contribute to poor clinical outcomes. Computational modeling can help optimize FPA repair, but these simulations heavily depend on the choice of constitutive model describing the arterial behavior. In this study Finite Element model of the FPA in the standing (straight) and gardening (acutely bent) postures was built using Computed Tomography data, longitudinal pre-stretch and biaxially determined mechanical properties. Springs and dashpots were used to represent surrounding tissue forces associated with limb flexion-induced deformations. These forces were then used with age-specific longitudinal pre-stretch and mechanical properties to obtain deformed FPA configurations for seven age groups. Four commonly used invariant-based constitutive models were compared to determine the accuracy of capturing deformations and stresses in each age group. The four-fiber FPA model most accurately portrayed arterial behavior in all ages, but in subjects younger than 40 years, the performance of all constitutive formulations was similar. In older subjects, Demiray (Delfino) and classic two-fiber Holzapfel-Gasser-Ogden formulations were better than the Neo-Hookean model for predicting deformations due to limb flexion, but both significantly overestimated principal stresses compared to the FPA or Neo-Hookean models.

Limb flexion-induced axial compression and bending in human femoropopliteal artery segments

“…First and foremost, we have used lightly embalmed human cadavers which may have different arterial properties compared to living humans. Living humans, particularly young and healthy, have significant longitudinal pre-stretch in their arteries that may reduce limb flexion-induced deformations 16,22,26 . However, old and diseased arteries that require reconstruction typically have very little (if any) longitudinal pre-stretch, making them similar to those arteries studied here 27–29 .…”

Cross-sectional pinching in human femoropopliteal arteries due to limb flexion, and stent design optimization for maximum cross-sectional opening and minimum intramural stresses

“…Axial loading was not simulated because during limb flexion FPAs undergo axial compression [7] that releases most of the axial tension [29]. A two-fibre family Holzapfel-Gasser-Ogden constitutive model [35] with C 0 ¼ 23:3 kPa, C col 1 ¼ 12:04 kPa, C col 2 ¼ 18:2, g ¼ 45:22 parameters corresponding to a 60 -70 year old artery [32,36] were used to describe the mechanical behaviour of the arterial wall. Compressibility was simulated by setting the ratio of the initial bulk modulus to the shear modulus at K 0 =C 0 ¼ 20, and arterial density was assumed to be 1 g cm 23 .…”

Limb flexion-induced twist and associated intramural stresses in the human femoropopliteal artery

“…Unlike twist, mechanical stresses in the distal FPA did increase with age in some postures, possibly reflecting stiffening of the FPA. Age-associated stiffening has previously been related to the degradation and fragmentation of longitudinal elastin and accumulation of collagen [22,25], both resulting in higher limb flexion-induced mechanical stresses in the FPA as demonstrated by computational modelling [28]. High mechanical stress can damage the arterial wall, initiating a cascade of remodelling responses that involve migration and proliferation of cells and exacerbating FPA pathology [10,34].…”

“…The model assumed incompressibility and was based on the expanded HGO formulation [26] adjusted to FPA histological structure [22,25,27] accounting for the passive elastic contributions of amorphous ground substance (W gr ), longitudinally oriented elastic fibres (W el ), circumferential smooth muscle cells (W smc ) and two symmetrical families of collagen fibres (W col1,2 ) oriented at an angle +w to the longitudinal axis. This model was demonstrated to accurately portray the experimental response of the human FPA [25,28]. The strain energy density function was therefore:…”