Abstract
Summary Statement
The structure of bone inside a porous bone graft substitute can be quantified and compared by using a combination of novel measurements of surface area and connectivity. This allows for a numerical representation of the bone structure to be calculated.
Introduction
Variation in absolute bone volume as a function of bone graft porosity has been well documented. However quantification of the 3D shape of bone and it's connectivity has always been difficult to assess let alone quantify. By use of novel computational methods the shape and connectivity of the bone can be characterised giving more insight to the relative quality of the bone ingrowth within the different porous grafts.
Materials & Methods
Cylindrical monoliths of hydroxyapatite (HA) of varying total porosities (60, 70 and 80% total) were implanted into a lapin model (subchondral distal femur) and the implants removed and XMT (resolution ∼30μm) scans taken at 3, 6, 12 and 24 weeks. The regions of bone and HA were defined using a modified tri-axial histogram with multiple boundaries. The volume and surface area was then collected for the bone in each of the samples, a controlled virtual multi centre degradation was also carried out to calculate the connectivity of the bone.
A non-dimensional linear measurement of the surface to volume ratio Kcube value was calculated, which is the number of thousand equal cubes which have the same volume to surface area ratio as the bone. A bone connectivity index is also calculated where a low value indicates the presence of an open interconnected bone structure within the graft. While a high value indicates the presence of bone within the graft as distinct islands distributed throughout the porosity.
Results
The change in volume, surface area, Kcube value and bone connectivity index against time for the samples. The volume and surface area values are of limited use when quantifying the shape of the bone, as the surface area generally increases with the volume regardless of surface area to volume ratio. The Kcube values shows that the largest change in shape for the bone occurs between 3 and 6 weeks which fits with the change between woven and lamella structure of the bone. Both the 80 and 60% drop in relative surface area at 6 weeks while the 70% increases. The 70 and 80% show a general increase in surface area while the 60% decreases. The bone connectivity index shows that the 80% has a more open structure than the 60% and they both open up with time. The 70% is close to the structure of the 80% with the exception of 6 weeks which as with the Kcube value is the exception, showing a closing of the bone structure.
Discussion/Conclusion
The using the Kcube and bone connectivity index values the structure of the bone in the differing bone graft substitutes can be meaningfully compared and quantified. In the case of the HA samples the significant different between the more closed, lower surface area bone produced by the 60% implant can be easily compared to the much higher surface area, open structures of the bone growing in the 70 and 80% HA.
