A multiscale analysis of liver lobule fibrosis and its impact on drug propagation and metabolism - a DLA approach

Employing DLA methods, this paper explores the self-assembly of collagen fibers and resulting fibrosis at three scales up to the scale of regular lobule models. This allows a mechanistic exploration of the effects of collagen on drug transport (flow and diffusion) and metabolism. In addition, this method permits an analysis of fiber growth characteristics. First, variations of the DLA method of Parkinson et al (1994) will be used to generate multiple explicit collagen microfibril self-assembly using DLA particles in one dimension using cubic grid blocks of (4 mm)3 in a 240 x 20 x 20 grid model. The second stage will be to assess the consequences of various densities of these fibers in three dimensions on flow reductions at a higher scale. Here we utilize DLA methods in cubic grid blocks of (80 nm)3 to mimic 3D collagen self-assembly of fibrils. We then apply a pressure gradient or specified flow rates across a spatially gridded version of these models to quantify flow effects. This region represents a local zone of liver tissue affected by fibrosis. Analytic models of fibrotic effects on flow are employed for comparison. A third stage explores the implications of fibrosis in a liver lobule model using multiple grid blocks of size 3200 mm to represent the lobule tissue. Here, a continuum model of fiber density is employed, based on the previous two scales. The model also includes the effects of additional grid blocks representing sinusoidal flow paths found in the lobule. We contrast and quantify drug propagation and metabolism of molecular dissolved versus nanoparticle delivery vehicles in fibrotic media, achieved by upscaling explicit collagen distributions to appropriate average values.