Intestinal villi and crypt density robustly maximizes nutrient absorption
The villi and crypts of the gastrointestinal tract increase the effective surface area of the intestinal mucosa, potentially enhancing nutrient absorption. It is commonly assumed that this is their primary function, and that a higher villi density necessarily leads to improved absorption. However, when villi are packed too closely together, diffusion can be hindered, potentially offsetting this benefit. In this work, we investigate quantitatively the relationship between the density of these structures and the overall efficiency of absorption. In three different simplified geometries, approximating leaf-like villi, finger-like villi, and colonic crypts, we calculate analytically the concentration profile and the absorption flux, assuming that there is only diffusion between these structures while the lumen is well mixed. When plotting the absorption flux per unit of gut length as a function of the structures' density, we observe that there is a density maximizing absorption. We study numerically this optimum. We find that it is robust to the nutrient absorption properties: a geometry optimal for one nutrient is close to optimum for another nutrient. Physiological data from various animal species fall within this predicted optimal range, consistent with the hypothesis that structure density is shaped by selection for efficient nutrient uptake.