Trabecular bone imaging has a high clinical significance for predicting fracture risk in patients with osteoporosis [1-5]. Quantitative susceptibility mapping (QSM) has been recently emerging for mapping diamagnetic and paramagnetic substances [6]. Recent reports attempted to use QSM combined with ultra-short echo time imaging for mapping the susceptibility of cortical bone [7,8]. However, it remains unknown whether QSM is feasible for measuring bone volume density in trabecular bone, where the bone density is much lower than cortical bone. The purpose of the present work is to study the feasibility of QSM for trabecular bone density mapping, using numerical simulations, specimen measurements and preliminary in vivo measurements.

Simulations

From a micro CT dataset of a healthy vertebral body a bone mask was derived by cropping out a cube containing only trabecular bone structure and applying a simple threshold for segmentation (Figure 1). Assigning the susceptibility of bone and water [5] inside and outside the mask respectively yielded an estimate on the susceptibility map of the bone cube. To match the simulation to the in vitro scan the bone cube was isotropically surrounded by water. Next an object-based fieldmap was computed in a forward simulation comparable to [9,10]. The resulting fieldmap was used to simulate a complex 6-echo signal at 3T with TE1=2ms and ΔTE=1ms. Since this signal had the high resolution of the original micro CT image (0.055mm isotropic) the data was down-sampled to a MR achievable resolution of 0.5mm isotropic. Afterwards a fieldmap was fitted to the phase of the down-sampled signal, which was passed to the MEDI QSM algorithm [12-15] that computed a susceptibility map for the MR-like signal. The averaged susceptibility in the QSM image inside and outside the bone cube was then put into relation with the bone volume to total volume ratio (BV/TV) of the original bone mask. The processing chain was repeated multiple times, where, before simulating the object-based fieldmap, the chimap was eroded with standard image processing tools to simulate the degeneration of trabecular bone as it happens in osteoporosis. In the first row of Figure 2 three object-based chimaps are depicted that differ by approximately 10% in BV/TV. The bottom row shows the resulting QSM chimaps with their average susceptibility differences plotted in Figure 5.

In Vitro Measurements

A cubic bone specimen from a human femur with roughly the same size and shape as the numerical phantom was scanned in a 3 T scanner (Ingenia, Philips Healthcare) with a 12-echo gradient-echo sequence at 0.5 mm isotropic resolution using the wrist coil with TE1=3.37ms and ΔTE=1.74ms. The same QSM method was applied to the fieldmap resulting from a water-fat separation separation [11]. No BV/TV values could be obtained, but the resulting averaged susceptibility differences between the inside of the bone cube and the outside water environment was -0.33ppm (Figure 3).

In Vivo Measurements

The knee of a healthy volunteer was also scanned using a knee coil. A 12-echo gradient-echo sequence with TE1=3.37ms, ΔTE=1.83ms was used for QSM (voxel size=0.9x0.9x0.9 mm³) and a high-resolution balanced SSFP sequence (with 2 phase cycles) was performed for high-resolution trabecular bone imaging (voxel size=0.3x0.3x0.45mm³). The resulting data was passed through a water-fat separation algorithm [7] that estimates the fieldmap, which was processed again with the MEDI algorithm [12-15]. For one slice in the high resolution scan (see Figure 4) two ROIs covering the trabecular bone in the femur (red) and the patella (green) were defined. With a 50% threshold on the ROIs in the high resolution image the BV/TV in the trabecular bone regions were estimated resulting in a BV/TV of approximately 34% in the femur and 65% in the patella. In the QSM result (Figure 4) of the low resolution scan the averaged susceptibility in ROIs inside the femur (blue) and the patella (orange) are referenced to a fat only region (pink). $$$\Delta \chi$$$ in the patella was around -0.14ppm, whereas the femur showed a difference of 0.18ppm. Figure 5 also summarizes the findings of the in vivo measurements.

The present simulations show that magnetic susceptibility in trabecular bone regions lies in the range between 0 and 0.3ppm, and the in vitro and in vivo measurements show that trabecular bone QSM was able to give reasonable results for trabecular bone density mapping at 3T. Further work is needed in order to overcome problems with background field removal and the presence of fat. However, the present work demonstrates the feasibility of QSM for trabecular bone density mapping.