Characterizing diffusion‐controlled release of small‐molecules using quantitative MRI in view of applications to orthopedic infection

Calcium sulfate is an established carrier for localized drug delivery, but a means to non-invasively measure drug release, which would improve our understanding of localized delivery, remains an unmet need. We aim to quantitatively estimate the diffusion-controlled release of small molecules loaded into a calcium sulfate carrier through a gadobutrol-based contrast agent, which acts as a surrogate small molecule. A central cylindrical core made of calcium sulfate, either alone or within a metal scaffold, is loaded with contrast agents that release into agar. Multi-echo scans are acquired at multiple time points over 4 weeks and processed into R2* and quantitative susceptibility mapping (QSM) maps. Mean R2* values are fit to a known drug delivery model, which are then compared with the decrease in core QSM. Fitting R2* measurements of calcium sulfate core while constraining constants to a drug release model results in an R²-value of 0.991, yielding a diffusion constant of 4.59 × 10^-11 m² s^-1. Incorporating the carrier within a metal scaffold results in a slower release. QSM shows the resulting loss of susceptibility in the non-metal core but is unreliable around metal. R2* characterizes the released gadobutrol, and QSM detects the resulting decrease in core susceptibility. The addition of a porous metal scaffold slows the release of gadobutrol, as expected.