Triple-energy photon-counting x-ray imaging for bone-strontium estimation: A simulation study

Strontium quantification in bone is clinically relevant but typically requires specialized stand-alone systems. Photon-counting detectors offer energy-resolved imaging that may enable low-dose estimation of both strontium concentration and bone mineral density in a single acquisition.

To evaluate the feasibility of triple-energy photon-counting x-ray imaging for low-dose quantification of strontium in bone, using a simulation framework that accounts for energy bin sensitivity, detector noise, and anatomical geometry.

A forward model of a photon-counting detector was used to simulate energy-resolved x-ray measurements through a simplified model of the human finger, incorporating cortical bone, trabecular bone, and soft tissue. Strontium uptake was modeled as a mass concentration relative to bone. A generalized least-squares estimator was used to compute the strontium-to-bone concentration from energy-resolved measurements. We optimized tube voltage and energy thresholds for three clinically relevant anode/filter combinations and three levels of electronic noise (5, 10, and 15 keV), with the goal of minimizing the limit of quantification (LOQ) and absorbed dose. A Fisher information analysis was conducted to assess the relative contribution of each energy bin to estimation precision.

Optimal tube voltages and thresholds depended strongly on electronic noise but only modestly on anode/filter choice. At a 5 keV noise floor, an LOQ of 100 ppm could be achieved with an absorbed dose of $\sim$ 13  $\mu \mathrm{Gy}$ , whereas 10 and 15 keV noise levels required $\sim$ 100  $\mu \mathrm{Gy}$ and >175  $\mu \mathrm{Gy}$ , respectively. At a fixed dose of 20  $\mu \mathrm{Gy}$ , reliable detection (SNR > 1) was possible at concentrations as low as 50 ppm for 5  and 10 keV noise floors. The mid-energy bin consistently contributed the most to estimation precision across all scenarios. At low noise, the high-energy bin was second most informative; at higher noise levels, the low-energy bin overtook it due to shifting energy thresholds that placed the strontium K-edge ( $\sim$ 16 keV) in the lower bins.

Triple-energy photon-counting x-ray imaging offers a promising strategy for low-dose quantification of strontium in bone. Its performance is primarily limited by electronic noise, while spectral shaping through anode and filter selection plays a secondary role when acquisition parameters are optimized.