Lipid domain coarsening and fluidity in multicomponent lipid vesicles: A continuum based model and its experimental validation.

Liposomes that achieve a heterogeneous and spatially organized surface through phase separation have been recognized to be a promising platform for delivery purposes. However, their design and optimization through experimentation can be expensive and time-consuming. To assist with the design and reduce the associated cost, we propose a computational platform for modeling membrane coarsening dynamics based on the principles of continuum mechanics and thermodynamics. This model couples phase separation to lateral flow and accounts for different membrane fluidity within the different phases, which is known to affect the coarsening dynamics on lipid membranes. The simulation results are in agreement with the experimental data in terms of liquid ordered domains area fraction, total domains perimeter over time, and total number of domains over time for two different membrane compositions (DOPC:DPPC with a 1:1 M ratio with 15% Chol and DOPC:DPPC with a 1:2 M ratio with 25% Chol) that yield opposite and nearly inverse phase behavior. This quantitative validation shows that the developed platform can be a valuable tool in complementing experimental practice.

Experimental validation of a phase-field model to predict coarsening dynamics of lipid domains in multicomponent membranes.

Membrane phase-separation is a mechanism that biological membranes often use to locally concentrate specific lipid species in order to organize diverse membrane processes. Phase separation has also been explored as a tool for the design of liposomes with heterogeneous and spatially organized surfaces. These "patchy" liposomes are promising platforms for delivery purposes, however their design and optimization through experimentation can be expensive and time-consuming. We developed a computationally efficient method based on the surface Cahn-Hilliard phase-field model to complement experimental investigations in the design of patchy liposomes. The method relies on thermodynamic considerations to set the initial state for numerical simulations. We show that our computational approach delivers not only qualitative pictures, but also accurate quantitative information about the dynamics of the membrane organization. In particular, the computational and experimental results are in excellent agreement in terms of lipid domain area fraction, total lipid domain perimeter over time and total number of lipid domains over time for two different membrane compositions (DOPC:DPPC with a 2:1 M ratio with 20% Chol and DOPC:DPPC with a 3:1 M ratio with 20% Chol). Thus, the computational phase-field model informed by experiments has a considerable potential to assist in the design of liposomes with spatially organized surfaces, thereby containing the cost and time required by the design process.

Validation of an open source framework for the simulation of blood flow in rigid and deformable vessels.

We discuss in this paper the validation of an open source framework for the solution of problems arising in hemodynamics. The proposed framework is assessed through experimental data for fluid flow in an idealized medical device with rigid boundaries and a numerical benchmark for flow in compliant vessels. The core of the framework is an open source parallel finite element library that features several algorithms to solve both fluid and fluid-structure interaction problems. The numerical results for the flow in the idealized medical device (consisting of a conical convergent, a narrow throat, and a sudden expansion) are in good quantitative agreement with the measured axial components of the velocity and pressures for three different flow rates corresponding to laminar, transitional, and turbulent regimes. We emphasize the crucial role played by the accuracy in performing numerical integration, mesh, and time step to match the measurements. The numerical fluid-structure interaction benchmark deals with the propagation of a pressure wave in a fluid-filled elastic tube. The computed pressure wave speed and frequency of oscillations, and the axial velocity of the fluid on the tube axis are close to the values predicted by the analytical solution associated with the benchmark. A detailed account of the methods used for both benchmarks is provided.

Validation of a 3D computational fluid-structure interaction model simulating flow through an elastic aperture.

This work presents a validation of a fluid-structure interaction computational model simulating the flow conditions in an in vitro mock heart chamber modeling mitral valve regurgitation during the ejection phase during which the trans-valvular pressure drop and valve displacement are not as large. The mock heart chamber was developed to study the use of 2D and 3D color Doppler techniques in imaging the clinically relevant complex intra-cardiac flow events associated with mitral regurgitation. Computational models are expected to play an important role in supporting, refining, and reinforcing the emerging 3D echocardiographic applications. We have developed a 3D computational fluid-structure interaction algorithm based on a semi-implicit, monolithic method, combined with an arbitrary Lagrangian-Eulerian approach to capture the fluid domain motion. The mock regurgitant mitral valve corresponding to an elastic plate with a geometric orifice, was modeled using 3D elasticity, while the blood flow was modeled using the 3D Navier-Stokes equations for an incompressible, viscous fluid. The two are coupled via the kinematic and dynamic conditions describing the two-way coupling. The pressure, the flow rate, and orifice plate displacement were measured and compared with numerical simulation results. In-line flow meter was used to measure the flow, pressure transducers were used to measure the pressure, and a Doppler method developed by one of the authors was used to measure the axial displacement of the orifice plate. The maximum recorded difference between experiment and numerical simulation for the flow rate was 4%, the pressure 3.6%, and for the orifice displacement 15%, showing excellent agreement between the two.