We experimentally demonstrate a 20-fold improvement in acquisition time in projection reconstruction (PR) magnetic particle imaging (MPI) relative to the state-of-the-art PR MPI imaging results. We achieve this acceleration in our imaging system by introducing an additional Helmholtz electromagnet pair, which creates a slow shift (focus) field. Because of magnetostimulation limits in humans, we show that scan time with three-dimensional (3D) PR MPI is theoretically within the same order of magnitude as 3D MPI with a field free point; however, PR MPI has an order of magnitude signal-to-noise ratio gain.
J.J. Konkle and P.W. Goodwill contributed equally to this work. This work was supported in part by the CIRM Tools and Technology Grant RT2-01893, the University of California Discovery Grant, the NIH National Institute of Biomedical Imaging and Bioengineering grant 1R01EB013689, and the National Science Foundation Graduate Research Fellowship grant DGE 1106400. The contents of this publication are solely the responsibility of the authors and do not necessarily represent the official views of CIRM or any other agency of the State of California, the National Institute of Biomedical Imaging and Bioengineering, or the National Institutes of Health.
Appendix 1 Projection reconstruction SNR gain calculation
We calculate the SNR gain of 3D PR with an FFL as compared to 3D imaging with an FFP with equal imaging time. Here, we assume that the two systems have identical noise characteristics, pulse sequence, resolution, and gradient strength. In a simulation study, Weizenecker et al.  noted that the SNR of a 3D PR image is approximately proportional to
where σ0 is the standard deviation of noise per pixel assuming Gaussian random noise, k is spatial frequency, G(k) is the filter frequency response, φ is the angle in radians, and Kmax is the maximum radial spatial frequency of the acquired image (i.e., the total extent is 2Kmax). Similar calculations have been done in CT . Note that filtering takes place after discretization of the acquired projection images. Hence, the spatial-frequency domain is “normalized” such that the maximum frequency is one-half cycle per pixel, i.e., 2Kmax=1. For a ramp filter G(k)=k, the noise variance becomes
We then calculate the SNR for a PR image after FBP with a ramp filter:
where μ is the signal mean or expected value. Similarly, the noise variance in an image acquired with an FFP can be calculated:
Again, we used 2Kmax=1. Thus,
Finally, we find
In general, the exact value of the constant multiplier before
Appendix 2 MPI acquisition time calculation
We can calculate the optimum imaging time based on specific absorption rate (SAR) and magnetostimulation (dB/dt) limits, the two primary safety concerns when imaging human subjects using time-varying magnetic fields. Owing to the frequency range in which MPI operates, magnetostimulation (and not SAR) is the dominant limitation for scanning speed in MPI [11, 35]. For human-sized MPI scanners, magnetostimulation will restrict the amplitude of both the excitation (drive) field and the slow shift (focus) fields.
The drive field in MPI is typically a ~25 kHz frequency sinusoidal field. Between 5 and 50 kHz, the magnetostimulation threshold in the human torso is extrapolated as approximately Bth=7 mT . With a G=10 T/m gradient strength, which will produce 1 mm native (i.e., no deconvolution) resolution with Resovist [11–13, 16], the FOV can be calculated as FOV=2Bth/G=1.4 mm.
To address the limited FOV coverage of the drive subsystem, slow shift magnets  or focus field magnets  are used. These slow shift magnets slowly raster the mean position of the FFP or FFL (see Figure 8), expanding the FOV beyond what is covered by the drive field alone. In a system with slow shift magnets, the space covered solely by the drive field (with the slow shift field disabled) is termed a “partial FOV” (pFOV)  or “imaging station” with multistation reconstruction . Slow shift fields also limit the acquisition time for an MPI system owing to magnetostimulation limits. The ICNIRP define a maximal magnetic field slew rate of 20 T/s for pulse durations longer than a couple of milliseconds . As we determine below, the slew rate causes the slow shift fields to become binding constraints on imaging time in addition to the drive field.
Generally, the total imaging time, T [s], in MPI can be calculated as
where D [m] is the total distance traveled by the field free region and vs [m/s] is the slow shift field scanning rate. The total distance traveled depends on the type of drive field and slow shift field pulse sequences. Commonly, a linear or Lissajous trajectory is used for the drive field. These trajectories provide near ideal spatial coverage and are easy to calculate [32, 39].
The total distance traveled by the mean position of the field free region dominates the total imaging time assuming that (1) the time to cover the pFOV is nearly instantaneous, (2) magnetostimulation thresholds from the drive field and the slow shift fields do not affect each other, and (3) the pFOV is small relative to the total FOV (see Figure 8). The total distance is then calculated as
Here, 2D refers to a single slice in FFP imaging or a single projection using an FFL, and 3D refers to imaging using an FFP. FOVi is the size of the field of view along axis i, pFOVi is the size of the partial FOV along i, pi is the number of pFOVs along i, and β is a factor (>1) determining the overlap extent of the pFOVs required for baseline recovery . We can calculate the maximal size of the pFOV using the simple relation pFOV=2Bth/G [m]. Accordingly, the imaging time can be estimated as
where Smax=20 T/s is the maximum slew rate as described above and μ0Gab [T/m] is the partial derivative of the magnetic field in the a direction with respect to b.
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