Hierarchical modeling of diffusive transport through nanochannels by coupling molecular dynamics with finite element method

Multiscale Modeling of Molecular Diffusion in Tissue

“…The Force Field (FF) represents a functional form of behavior of chemical structures and is evaluated from potential energy function, intra inter E E E , of CHARMM FF [6] which is used in our MD models. MD simulations for calculating diffusion coefficients in nanochannels were carried out [1], [7] using NAMD 2.6 [8] with a TIP3P water model [9] and NVT (fixed number of particles N, pressure P, volume V) ensembles. CHARMM compatible amorphous silica force field [10] was employed to model the silica nanochannel, which is 59 modeled by charged hydrophilic amorphous silica phase to match the silica properties after the fabrication process.…”

“…An ideal scenario is to properly transfer MD information to macroscopic models. Hierarchical (multiscale) modeling approach, introduced in [1] and which couples MD and Finite Element Method (FEM), offer this possibility.…”

“…Our method relies on the fundamental condition of the equivalency of mass-release kinetics between the continuum and microstructural models for a given region of space and over a prescribed concentration range. The continuum model is based on constitutive parameters, which include equivalent "bulk" diffusion coefficients (characterizing free, or Fickian, diffusion within the solvent) and equivalent distances from an imaginary surface (describing surface effects within the microstructure, [1]). Constitutive parameters, depending only on the structural geometry and the material properties of the diffusing constituents, are evaluated for three orthogonal coordinate directions -enabling modeling of general 3D diffusion conditions.…”

EMBnet.journal 19 Suppl. B

“…A model is considered to be multi-scale if it spans two or more different spatial scales and/or includes processes that occur at two or more temporal scales. It is considered to be multi-physics if it involves multiple physical models or multiple simultaneous physical phenomena For what concerns (1), consider the angiogenesis (Ziemys et al, 2011), a significant transforming phase in tumour growth. Drugs delivered to tissues will not only change the behaviour of melanoma cells (secretion of cytokines, proliferation, differentiation, apoptosis, or migration) in the intracellular drug-triggered cell division process, but also inhibit the development of new capillary sprouts by preventing sprouts from receiving vascular endothelial growth factors.…”

A mechanical picture of fractional-order Darcy equation

“…Indeed the time evolution of the concentration and velocity profile predicted by Fick or Darcy is described by exponential-type solution and, several deviations from experimental results have been found in scientific literature regarding fluid flows in biological tissues [4,5] usually referred to long-tails of the diffusion processes as well as through biological membranes [6,7]. The difference among Fick prediction and experimental results have been captured, recently, considering particle transport at nanometric scale by means of molecular dynamics simulations [8][9][10][11].…”