A one-dimensional arterial network model for bypass graft assessment.

We propose an arterial network model based on one-dimensional hemodynamic equations to study the behavior of different vascular surgical bypass grafts in the case of an arterial occlusive pathology: a stenosis of the Right Iliac artery. We investigate the performances of three different bypass grafts (Aorto-Femoral, Axillo-Femoral and cross-over Femoral) depending on the degree of obstruction of the stenosis. Numerical simulations show that all bypass grafts are efficient since we retrieve in each case the healthy hemodynamics downstream of the stenosed region while ensuring at the same time a global healthy circulation. We analyze in detail the behavior of the Axillo-Femoral bypass graft by performing hundreds of simulations where we vary the values of its Young's modulus [0.1-50 MPa] and radius [0.01-5 cm]. Our analysis shows that Young's modulus and radius of commercial bypass grafts are optimal in terms of hemodynamic considerations. Our numerical findings prove that this model approach can be used to optimize or plan patient-specific surgeries, to numerically assess the viability of bypass grafts and to perform parametric analysis and error propagation evaluations by running extensive simulations.

Implementing boundary conditions in simulations of arterial flows.

Computational hemodynamic models of the cardiovascular system are often limited to finite segments of the system and therefore need well-controlled inlet and outlet boundary conditions. Classical boundary conditions are measured total pressure or flow rate imposed at the inlet and impedances of RLR, RLC, or LR filters at the outlet. We present a new approach based on an unidirectional propagative approach (UPA) to model the inlet/outlet boundary conditions on the axisymmetric Navier-Stokes equations. This condition is equivalent to a nonreflecting boundary condition in a fluid-structure interaction model of an axisymmetric artery. First we compare the UPA to the best impedance filter (RLC). Second, we apply this approach to a physiological situation, i.e., the presence of a stented segment into a coronary artery. In that case a reflection index is defined which quantifies the amount of pressure waves reflected upon the singularity.

[Digital simulation of venous and lymphatic edema and the effects of compression]. / Simulation numérique de l'œdème veinolymphatique et des effets de la compression.

OBJECTIVE: Compression therapy for venous and lymphatic edema of the lower limbs raises a major challenge concerning the optimal pressure ensuring both efficacy and patient compliance. We present a mathematical model of tissue fluid transfers which is aimed at determining the lowest pressure required to prevent edema. METHODS: The model is based on a set of equations, derived from published experimental data, which describe the fluid and solute transfers between blood, interstitium and lymphatics, and the mechanical properties of interstitial compartment. It enables us to compute the changes in tissue volume, at the ankle level, resulting from increases of capillary pressure in case of venous insufficiency, and from an impairment of lymph drainage; as well as the effect of various external pressures upon this volume. RESULTS: An increase of capillary pressure to 40 and 50 mmHg results in an ankle edema which is completely prevented by an external pressure of 10 mmHg. This result is in keeping with the observation by Partsch that vesperal leg swelling is reduced by low compression stockings. The dose effect reported in this study is also found by simulation. The complete blockade of lymphatic return leads to an edema, the prevention of which requires a counterpressure of at least 30 mmHg. When an increase of venous pressure to 60 mmHg, and a reduction by 2/3 of lymphatic drainage are combined, simulating chronic venous insufficiency, the resulting edema is prevented by a 25 mmHg counterpressure. CONCLUSION: These first results of simulation are in reasonable agreement with clinical experience. As nearly every combination of disturbances may be simulated, the computer model could help to understand and treat edemas, as long as their cause can be identified.

The venous return simulator: an effective tool for investigating the effects of external compression on the venous hemodynamics--first results after thigh compression.

BACKGROUND: To present a virtual model, the venous return simulator (VRS), designed to compute venous hemodynamic variations when compression is applied to the leg. METHODS: The VRS defines a numerical network of the lower extremity and computes the dynamic variables (flow rate, venous diameter and internal pressure) for a defined external pressure. The VRS was based on physiological data from the literature and clinical studies on healthy subjects. Clinical correlations were required to confirm its validity; for this purpose, we carried out experiments simulating the conditions of a clinical trial, in which the diameter of superficial and deep veins was measured while increasing pressures (20, 40 and 60 mmHg.) were applied to the thighs of patients enduring deep valvular insufficiency and venous ulcers. The diameters and flow rates calculated using our VRS model were compared with the experimental data obtained at the same thigh compression levels. RESULTS: The numerical results of VRS are in good agreement with the clinical data obtained by Duplex, (R2 = 0.96). In accordance with the in vivo measurement the computed results show that only a pressure greater than 40 mmHg is able to reduce the venous diameter at thigh-level, both in the great saphenous vein and in the femoral vein. CONCLUSION: The venous return simulator computes lower limb hemodynamic parameters under static conditions. The good correlation existing between the VRS and the data obtained in a previous clinical study shows that this numerical approach could provide a useful means of predicting the hemodynamic consequences of compression therapy.