Prescribed boundary conditions.

(a) Inlet pressure boundary condition, inlet velocity boundary condition, and gravity. (b) Pulsed-wave function.</p

Effect of valve lesion on venous valve cycle: A modified immersed finite element modeling - Fig 8

(a) Velocity distributions at the orifice. (b) Flow rate at the inlet, orifice, and outlet.</p

Material properties of the bileaflet valves with mechanical lesion.

Material properties of the bileaflet valves with mechanical lesion.</p

Venous volume and the related time of different valves for one cycle.

Venous volume and the related time of different valves for one cycle.</p

Effect of valve lesion on venous valve cycle: A modified immersed finite element modeling

The present study aimed to understand the effect of venous valve lesion on the valve cycle. A modified immersed finite element method was used to model the blood–tissue interactions in the pathological vein. The contact process between leaflets or between leaflet and sinus was evaluated using an adhesive contact method. The venous valve modeling was validated by comparing the results of the healthy valve with those of experiments and other simulations. Four valve lesions induced by the abnormal elasticity variation were considered for the unhealthy valve: fibrosis, atrophy, incomplete fibrosis, and incomplete atrophy. The opening orifice area was inversely proportional to the structural stiffness of the valve, while the transvalvular flow velocity was proportional to the structural stiffness of the valve. The stiffening of the fibrotic leaflet led to a decrease in the orifice area and a stronger jet. The leaflet and blood wall shear stress (WSS) in fibrosis was the highest. The softening of the atrophic leaflet resulted in overly soft behavior. The venous incompetence and reflux were observed in atrophy. Also, the atrophic leaflet in incomplete atrophy exhibited weak resistance to the hemodynamic action, and the valve was reluctant to be closed owing to the large rotation of the healthy leaflet. Low blood WSS and maximum leaflet WSS existed in all the cases. A less biologically favorable condition was found especially in the fibrotic leaflet, involving a higher mechanical cost. This study provided an insight into the venous valve lesion, which might help understand the valve mechanism of the diseased vein. These findings will be more useful when the biology is also understood. Thus, more biological studies are needed.</div

Effect of valve lesion on venous valve cycle: A modified immersed finite element modeling - Fig 15

Blood and leaflet WSSs (a) at 0.30s and (b) at 1.0 s for the IAV.</p

Effect of valve lesion on venous valve cycle: A modified immersed finite element modeling - Fig 7

(a) Time variations of the venous behavior: A, opening phase, 0.05–0.20 s; B, equilibrium phase, 0.20–0.39 s; C, closing phase, 0.39–0.68 s; and D, closed phase, 0.68–1.05 s. Δd’wa is the displacement of the marked position on the anterior wall, Δd’wp is the displacement of the marked position on the posterior wall, and Δd’s is the displacement of the sinus. (b) Time variation of the geometric orifice area AGOA.</p

Various valve configurations and flow streamlines in a normal valve cycle.

(a) In the opening phase, 0.08 s. (b) In the equilibrium phase, 0.30 s. (c) In the closing phase, 0.51 s. (d) In the closed phase, 0.8 s. (e) In the closed phase, 1.0 s.</p

Dimensional parameters of the vein model.

Dimensional parameters of the vein model.</p

Effect of valve lesion on venous valve cycle: A modified immersed finite element modeling - Fig 16

(a) Blood and leaflet WSSs in the closed phase for the CFV. (b) Mechanical cost of the valve for different cases. (c) SWSS and (d) FWSS at the leaflet backside.</p