Modeling tracer transport in an Osteon under cyclic loading

A mathematical model is developed to explain the fundamental conundrum as t o how during cyclic mechanical loading there can be net solute (e.g., nutri ent, tracer) transport in bone via the lacunar-canalicular porosity when th ere is no net fluid movement in the canaliculi over a loading cycle. Our hy pothesis is that the fluid space in an osteocytic lacuna facilitates a near ly instantaneous mixing process of bone quid that creates a difference in t racer concentration between the inward and outward canalicular flow and thu s ensures net tracer transport to the osteocytes during cyclic loading, as has been shown experimentally. The sequential spread of the tracer from the osteonal canal to the lacunae is investigated for an osteon experiencing s inusoidal loading. The fluid pressure in the canaliculi is calculated using poroelasticity theory and the mixing process in the lacunae is then simula ted computationally. The tracer concentration in lacunae extending radially from the osteonal canal to the cement line is calculated as a function of the loading frequency, loading magnitude, and number of loading cycles as w ell as the permeability of the lacunar-canalicular porosity. Our results sh ow that net tracer transport to the lacunae does occur for cyclic loading. Tracer transport is found to increase with higher loading magnitude and hig her permeability and to decrease with increasing loading frequency. This wo rk will be helpful in designing experimental studies of tracer movement and bone fluid flow, which will enhance our understanding of bone metabolism a s well as bone adaptation. (C) 2000 Biomedical Engineering Society. [S0090- 6964(00)00410-0].