Hemodynamic Changes following Aortic Valve Bypass: A Mathematical Approach

Aortic valve bypass (AVB) has been shown to be a viable solution for patients with severe aortic stenosis (AS). Under this circumstance, the left ventricle (LV) has a double outlet. The objective was to develop a mathematical model capable of evaluating the hemodynamic performance following the AVB surgery. A mathematical model that captures the interaction between LV, AS, arterial system, and AVB was developed. This model uses a limited number of parameters that all can be non-invasively measured using patient data. The model was validated using in vivo data from the literature. The model was used to determine the effect of different AVB and AS configurations on flow proportion and pressure of the aortic valve and the AVB. Results showed that the AVB leads to a significant reduction in transvalvular pressure gradient. The percentage of flow through the AVB can range from 55.47% to 69.43% following AVB with a severe AS. LV stroke work was also significantly reduced following the AVB surgery and reached a value of around 1.2 J for several AS severities. Findings of this study suggest: 1) the AVB leads to a significant reduction in transvalvular pressure gradients; 2) flow distribution between the AS and the AVB is significantly affected by the conduit valve size; 3) the AVB leads to a significant reduction in LV stroke work; and 4) hemodynamic performance variations can be estimated using the model.Fonds quebecois de la recherche sur la nature et les technologies (176048

Shape optimization of stress concentration-free lattice for self-expandable Nitinol stent-grafts

In a mechanical component, stress-concentration is one of the factors contributing to reduce fatigue life. This paper presents a design methodology based on shape optimization to improve the fatigue safety factor and increase the radial stiffness of Nitinol self-expandable stent-grafts. A planar lattice free of stress concentrators is proposed for the synthesis of a stent with smooth cell shapes. Design optimization is systematically applied to minimize the curvature and reduce the bending strain of the elements defining the lattice cells. A novel cell geometry with improved fatigue life and radial supportive force is introduced for Nitinol self-expandable stent-grafts used for treating abdominal aortic aneurism. A parametric study comparing the optimized stent-graft to recent stent designs demonstrates that the former exhibits a superior anchoring performance and a reduction of the risk of fatigue failure

Summarized cardiovascular parameters used to simulate all cases.

<p>*Maximum error in computed ratio between AS and AVB flow rates from sensitivity analysis in response to independent variation (±30%) in each parameter</p><p>Summarized cardiovascular parameters used to simulate all cases.</p

Simulated left ventricle and aorta pressures and flow distribution.

<p>(A) Severe AS (EOA = 0.7 cm²) & AVB (conduit valve size: 19 mm, conduit size: 18mm), (B) severe AS (EOA = 0.7 cm²) & AVB (conduit valve size: 19 mm, conduit size: 26mm). Stroke volume, heart rate and cardiac output are 75 ml, 70 beats/min and 5.2 l/min, respectively.</p

Schematic diagrams.

<p>(A) Electrical representation, (B) schematic representation of the lumped parameter model used to simulate left-sided heart in presence of aortic stenosis and/or apico-aortic conduit (please see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0123000#pone.0123000.t001" target="_blank">Table 1</a> for all other parameters used in the lumped parameter model).</p

Simulated LV stroke work.

<p>(A) Pre-AVB surgery for a severe AS (EOA = 0.7 cm²), (B) post-AVB surgery with a conduit valve size of 19 mm and a conduit size of 18mm, (C) LV stroke work variations with and without AVB for different AS severities. The values are averaged over the all configurations for AVB in terms of conduit and valves sizes simulated in this study.</p

Simulated left ventricle and aorta pressures.

<p>(A) Healthy (No AS & No AVB), (B) severe AS (EOA = 0.7 cm²) & No AVB. Stroke volume, heart rate and cardiac output are 75 ml, 70 beats/min and 5.2 l/min, respectively.</p

Computed AS and AVB flow rate ratio in the presence of fixed severe AS (EOA = 0.7 cm2).

<p>*Relative error in computed flow rates through native valve with EOA of 0.7 cm² and AVB with combinations of 18–19, 20–21 and 22–23, compared to the results reported by Stauffer et al. (2011) are 4.49%, 2.34% and 0.11%, respectively. AV: aortic valve; AVB: aortic valve bypass</p><p>Stroke volume, heart rate and cardiac output are 75 ml, 70 beats/min and 5.2 l/min, respectively. AV: aortic valve, AVB: aortic valve bypass</p><p>Computed AS and AVB flow rate ratio in the presence of fixed severe AS (EOA = 0.7 cm2).</p