Comparison of solid and fluid constitutive models of bone marrow during trabecular bone compression

The mechanical environment and mechanobiology of bone marrow may play essential roles in bone adaptation, cancer metastasis, and immune cell regulation. However, the location of marrow within the trabecular pore space complicates experimental measurement of marrow mechanics. Computational models provide a means to assess the shear stress and pressure in the marrow during physiological loading, but they rely on accurate inputs for the marrow and the physics assumed for the interaction of bone and marrow. Elastic, viscoelastic, and fluid constitutive properties have all been reported from experimental measurements of marrow properties. It is unclear whether this ambiguity reflects the various length-scales, loading rates, and boundary conditions of the experiments, or if the material models are sufficiently similar as to be interchangeable. To address this question, we analyzed both the mean shear stress and its spatial distribution induced in marrow during compression of trabecular bone cubes when using linear elastic, neo-Hookean, viscoelastic, and power-law fluid constitutive models. Experimentally reported parameters were initially applied for all four constitutive models, resulting in poor agreement. The parameters of the soft solid models were calibrated by linear interpolation so that the volume averaged shear stress agreed with the fluid model for each, but this could only be accomplished on a specimen-by-specimen basis. Following calibration, the root-mean-squared (RMS) difference between the solid and fluid constitutive models was still greater than 26% even when the overall mean shear stress was in close agreement, indicating that the spatial distribution of stress is also sensitive to the constitutive model. As such, the choice of constitutive model should be backed by a strong rationale, and results should be interpreted with care.