Experimental and theoretical investigation of directional permeability of human vertebral cancellous bone for cement infiltration

The use of acrylic polymers in infiltrating the porous bone structure is an emerging procedure for the augmentation of osteoporotic vertebrae. Although this procedure is employed frequently, it is performed based on empirical knowledge, and therefore, does not take into consideration the porosity-dependent permeability of human vertebral cancellous bone. The purpose of this study was to: (a) experimentally and theoretically investigate interdependence of the vertebral cancellous bone permeability and porosity, and (b) examine if the bone permeability of spinal cancellous bone can be predicted using bone mineral density measurements. If these relations can be established, they can be useful in optimizing the injection conditions for predicable cement infiltration. To determine the porosity-dependent and directional permeability, 34 bone cores—20 samples in the superior–inferior (SI) direction and 14 in the anterior–posterior (AP) direction—were cut from 20 lumbar vertebrae and infiltrated with silicone oil with a viscosity matching that of PMMA. The permeability of the cores was determined based on Darcyʹs law. The mean permeability of SI and AP cores was 4.45±1.72×10−8 and 3.44±1.26×10−8 m2, respectively. An interesting finding of this study was that the permeability of the AP cores was approximately 78% of that of SI cores, though the porosity of the SI and AP cores taken from the same vertebra was approximately equal. In addition, we provided a theoretical model for the porosity-dependent permeability that accurately described non-linear dependency of the bone permeability and porosity in both directions. Although the relation of the bone permeability and porosity was established, bone mineral density was a weak predictor of the bone permeability. The experimental and theoretical results of this study can be used to understand polymer flow in cement infiltration procedures.