Quantitative Susceptibility Mapping (QSM) calculates the relative magnetic susceptibility (χ) of tissues from the MRI phase data. In standard gradient-echo sequences there is no phase signal for air, teeth and bone. However, due to the non-local relationship between χ and phase, the phase generated from these regions extends into adjacent regions with MR signal. This phase information can be exploited to provide information about the χ of regions with no phase signal. Here we assess an iterative phase replacement (IPR) method proposed by Buch et. al. [1] using a numerical head phantom in which we attempt to calculate the χ distribution in the air-filled sinuses and teeth in order to segment these regions.We applied the IPR method [1] to a numerical χ phantom (figure 1a) modified from that provided by Buch et al. by downsampling and removing χ variation within soft tissue. The phantom consisted of 3 classes: air (+9 ppm), soft tissue (+0.09 ppm) and teeth (-3 ppm) [2]. The phase was calculated using the forward model [3] with TE= 2.5 ms and B₀ = 3 T, setting the dipole kernel to 0 at k=0. The matrix size was 256³, zero-padded to 512³ and the voxels were isotropic (1x1x1 mm³). B₀ was set along the inferior-posterior direction. The phase in teeth and air was nulled to simulate the real case and IPR was applied as in [1]. As we found the change in χ to increase between successive iterations in some regions, 8 iterations were used rather than a stopping criterion based on the change in mean χ falling below an appropriate level in a chosen Region of Interest (ROI). Final χ maps (figures 1b-c) were calculated using threshold-based k-space division (TKD) [4], with a threshold of 0.1 [1]; 0.4 and $$$\frac{2}{3}$$$ were also investigated. The mean and standard deviation (SD) of χ were recorded in several ROIs. The ROIs were the air and teeth regions in the head as defined in the initial χ map and single-slice sinus regions as shown in figures 1d-f. To assess the ability of IPR to improve the segmentation of the regions with no phase signal into air, teeth and tissue, Otsu’s method was performed after each iteration to find a χ threshold between air and teeth [5], as tissue had previously been identified by thresholding the magnitude image.Results from the IPR method over successive iterations are shown for the air, teeth and sinus ROIs. The final χ map for TKD threshold 0.1 is shown in figures 1b-c. Figures 2, 3 and 4 show that in the teeth the mean χ decreases and in the air/sinus regions the mean χ increases over iterations, however the χ the iteration converges towards is different for each region and each TKD threshold. The SD behaves differently depending on the region and TKD threshold. Figure 5 demonstrates the performance of the segmentation algorithm on the χ map (TKD threshold 0.1) at the end of each iteration.In common with the findings of Buch et. al [1], the first iteration of IPR produced the largest change in χ. However, convergence was not achieved within a small number of iterations meaning the stopping criterion was not applicable [1]. Calculated χ distributions were highly dependent on ROI geometry as can be seen from the different results obtained for three sinus regions, despite identical initial χ values. The SD did not behave uniformly across regions and TKD thresholds, and increased in some regions, suggesting that the repeated use of the regularized inverse calculation leads to an increase in error. Mean χ values decreased as the TKD threshold increased as expected due to systematic underestimation which could be corrected as described in [6]. Despite inaccurate χ distributions, this method showed promise in aiding automatic segmentation of air and teeth as shown in figure 5 where the first few iterations improve the segmentation. There were, however, regions which were misclassified, for example the pharynx, potentially due to alignment with the B₀ field or adjacency with the image edge.As it failed to converge on the correct χ value, IPR may not be suitable for calculating accurate χ distributions in regions that have no phase signal. However, IPR was found to aid a simple segmentation method in distinguishing between air and teeth. Due to dependence on geometry, complex regions such as the mastoid sinus which contains a mixture of air and bone may be particularly difficult to segment. Work is ongoing to investigate alternative inverse problem solutions for the susceptibility calculation.