Determining a performance envelope for capture of kidney stones functionalized with superparamagnetic microparticles

Complete stone removal is important in upper tract stone surgery. Unfortunately, even with the latest technologic advances, current methods only achieve 50% to 80% complete clearance of upper tract stones at the time of primary treatment. Our group has explored the novel use of peptide-coated iron oxide superparamagnetic microparticles that bind to calcium stones, allowing for extraction of these stones with magnetic tools. We present analytic and numeric models that characterize stone attraction performance for feasible magnetic tool sizes and stone magnetization levels.

Magnetostatics equations are applied to a simplified, one-dimensional scenario of a spherical target coated with a variable amount of superparamagnetic particles, placed under the influence of a magnetic field aimed at vertical attraction (capture) of the target. Equations are parameterized in terms of (a) target size, ranging from 0.5 mm to 3 mm to represent stone sizes of interest, (b) effective magnetization per surface area delivered by the particle binding chemistry, and (c) distance to the field source.

Target capture is predicted to be effective in the low, single-digit millimeter distance range, favoring smaller stones and then up to a practical upper limit of 3 mm diameter. Higher iron loading chemistries have a direct improvement in magnetic force and therefore increase the viability of the technique, albeit along an asymptotic trendline.

We are able to characterize the potential for kidney stone capture via magnetic attraction. Computer-developed models show good correlation with experimental results using actual magnetized stone samples. Future research efforts can use the proposed techniques to estimate the performance impact of advanced magnetic tools and surface chemistries.