Three-dimensional mechanisms of macro-to-micro-scale transport and absorption enhancement by gut villi motions

We evaluate the potential for physiological control of intestinal absorption by the generation of “micromixing layers” (MMLs) induced by coordinated motions of mucosal villi coupled with lumen-scale “macro” eddying motions generated by gut motility. To this end, we apply a three-dimensional (3D) multigrid lattice-Boltzmann model of a lid-driven macroscale cavity flow with microscale fingerlike protuberances at the lower surface. Integrated with a previous 2D study of leaflike villi, we generalize to 3D the 2D mechanisms found there to enhance nutrient absorption by controlled villi motility. In three dimensions, increased lateral spacing within villi within groups that move axially with the macroeddy reduces MML strength and absorptive enhancement relative to two dimensions. However, lateral villi motions create helical 3D particle trajectories that enhance absorption rate to the level of axially moving 2D leaflike villi. The 3D enhancements are associated with interesting fundamental adjustments to 2D micro-macro-motility coordination mechanisms and imply a refined potential for physiological or pharmaceutical control of intestinal absorption.

Figure 1

The 3D model lid-driven cavity flow used to model macro-micro-scale interactions in the small intestines with (a) axial villus motion (in lid direction), and (b) lateral villus motion. Panels (a) and (b) show the groupings of villi as well as isocontours of concentration advectively driven by the macroeddy with its source at the moving upper lid (red and blue are highest and lowest concentrations, respectively). Panel (c) illustrates the specification of villus geometry and motion: $({\delta }_x,{\delta }_y)=\mathrm{distance}$ between villi in $(x,y)$ within groups; ${\delta }_g=$ distance between groups; $R=$ villus radius. In (a) and (b) ${\delta }_x/R={\delta }_y/R=4$. In all simulations ${\delta }_g/R=8$.

Figure 2

Cavity flow with fixed lid is shown in (a) with instantaneous streamlines and (b) with time-averaged streamlines. The same cavity flow with moving lid is shown in (c) with instantaneous streamlines and (d) with time-averaged streamlines. Time averaging is over a single period in the stationary state; time-averaged particle paths coincide with time-averaged streamlines. The perspective in (d) focuses on the 3D structure of the time-averaged surface streamlines within vs above the villi. Streamlines are colored with scalar concentration ($\mathrm{dark}\mathrm{red}=\mathrm{local}\mathrm{maximum}$; $\mathrm{dark}\mathrm{blue}=\mathrm{zero}$). ${\delta }_x/R={\delta }_y/R=4$.

Figure 3

Variables averaged over a period in the stationary state. Panel (a) shows the time-averaged streamline (and particle path) pattern over the cavity [Fig. 2 shows a blown-up view at the villi], and (b) shows the time-averaged concentration field. Panels (c) and (d) show contributions to the vertical concentration flux balance: (c) shows advective flux $-\overline{u_z\varphi }$ and (d) shows diffusive flux $\overline{D_m\partial \varphi /\phantom{\partial \varphi \partial z}\partial z}$, where $\varphi$ is the concentration field and $z$ is the vertical coordinate. The insets show isosurfaces at fixed flux values, illustrating the quasi-2D nature of the scalar field and flow field above the villi groups. Colors: in (b) $\mathrm{red}=1$, $\mathrm{blue}=0$; in (c) the red and blue isocontours show maximum local time-averaged flux toward the villi $(-z)$ and towards the lid $(+z)$, respectively ($\pm 1\times {10}^{-4}\mathrm{m}/\mathrm{s}$, $\mathrm{green}\approx \mathrm{zero}$); in (d) all diffusive flux is towards the villi: $\mathrm{red}=2\times {10}^{-5}\mathrm{m}/\mathrm{s}$, $\mathrm{blue}=2\times {10}^{-6}\mathrm{m}/\mathrm{s}$. $\overline{\beta }\Rightarrow \mathrm{time}$ averaged $\beta$. ${\delta }_x/R={\delta }_y/R=4$.

Figure 4

Space-time averaged (a) scalar concentration, (b) diffusive flux, and (c) advective flux as a function of lateral villi spacing ${\delta }_y$. Panel (d) shows absorption rate as a function of ${\delta }_y/R$; $q_0=\mathrm{net}\mathrm{flux}$ without villi. The 2D result [6] is given at ${\delta }_y/R=2$. $\langle \rangle \Rightarrow \mathrm{average}$ on $z$ planes. $\varphi$ is unitless. In all simulations ${\delta }_x/R=4$.

Figure 5

Time-averaged flow fields with transverse villus motion with moving cavity lid. (a) 3D streamlines (and time-averaged particle paths); (b) isocontours and a single isosurface ($\overline{\varphi }=0.2$) of concentration; panels (c)–(f) show the following on the lateral plane midway in the cavity $(x=L_c/2)$: (c) projected streamlines colored by concentration, (d) isocontours of concentration ($\mathrm{red}=1$, $\mathrm{dark}\mathrm{blue}=0$), (e) vertical concentration flux by advection (where red is max upwards and dark blue is max downwards flux), and (f) flux by diffusion (where red is maximum downwards and blue is ≈ zero). ${\delta }_x/R={\delta }_y/R=4$.

Figure 6

Time-averaged 3D streamline and particle path patterns displaying the three-layer structure of the three-dimensional MML when villi groups move laterally to the macroeddy flow, displayed. (a) Perspective view; (b) side view. The streamlines are colored by scalar concentration consistent with the colors in Figs. 5 and 5.

Figure 7

Comparison of MMLs generated by lateral (red, solid curves) vs axial (blue, dashed curves) villus motion. (a) Space-time-averaged vertical scalar flux by advection and diffusion (as indicated). (b), (c) Axial distributions of time-averaged (b) vertical velocity and (c) scalar concentration along axially drawn lines at $z=0.35\mathrm{mm}$. With axial motion these are along arbitrary lines in $x$ [see Fig. 1]. With lateral villi motion these are over villi group centers and over gaps in between the villi groups, as indicated [see Fig. 1]. ${\delta }_x/R={\delta }_y/R=4$.