Peridynamics-Lattice Boltzmann Coupling and Application to Biological Systems

Within the cardiovascular system, in the veins and heart, are soft valves which control the blood by preventing retrograde flow. Valves are comprised of two or three leaflets (or cusps) which attach to vein walls and interact in the centre of the lumen (the blood-carrying cavity inside vessels). Over time, these valves are subject to wear and illness, leading to malfunction. Valves which are not operating correctly may not open sufficiently, or create an effective seal to prevent backflow, allowing pooling in veins. This stagnation of the flow can lead to snaking varicose veins, blood coagulation and clotting, and loss of oxygen to tissue. Degradation and illness in the cardiovascular system is challenging to investigate in vivo due to small scales and impracticality of invasive techniques. Non-invasive techniques are certainly useful, however, it is necessary to simulate conditions to fully understand phenomena – the fluid behaviour, dynamics of the valves, and the interaction between the two. From this more detailed understanding, we can draw conclusions on the causes and effects of different illnesses, and improve treatment methods, such as the development of replacement valves from synthetic materials.

This investigation models bicuspid (2-leaflet) soft-material valves using peridynamics, coupled with the surrounding fluid (Cascaded Lattice Boltzmann Method) via a strong coupling (using the Immersed Boundary Method). The method used for this study has been shown to capture the interaction of solids and liquids effectively, considering both the case of beams bending and oscillating due to an applied flow velocity [1]. The vein is simulated as a 2D rigid channel containing attached arc-shaped beams of peridynamic material to represent the valve leaflets. The fluid motion is driven by an oscillating force density, mimicking the pulsing nature of the blood flow. Whilst the operation of biological valves has long been a topic of interest, this study presents a novel investigation utilising the damage and fracture propagation capabilities of peridynamics.

First, effects of various parameters on valve operation and flow field will be presented, confirming that the method used captures the expected dynamics. These include the effects of increasing pressure (more rapid valve opening and leaflet direction inversion during reverse flow), increasing the elastic modulus of the leaflet material (greater resistance to opening but improved closing characteristics), and altering the frequency with which the flow oscillates (an increased frequency leads to improved closing and seal but reduced pulse volume). The model is then extended to allow for naturally developing and a priori enforced damage. This presentation will cover this analysis – how the weakness of valve material can affect their operation.