Whenever a linear gradient is activated, concomitant magnetic fields with non-linear spatial dependence result. This is a consequence of Maxwell's equations, i.e., within the imaging volume the magnetic field must have zero divergence, and has negligible curl. The concomitant, or Maxwell field has been described in the MRI literature for over 10 years. In this paper, we theoretically and experimentally show the existence of two additional lowest-order terms in the concomitant field, which we call cross-terms. The concomitant gradient cross-terms only arise when the longitudinal gradient Gz is simultaneously active with a transverse gradient (Gx or Gy). The effect of all of the concomitant gradient terms on phase contrast imaging is examined in detail. Several methods for reducing or eliminating phase errors arising from the concomitant magnetic field are described. The feasibility of a joint pulse sequence-reconstruction method, which requires no increase in minimum TE, is demonstrated. Since the lowest-order terms of the concomitant field are proportional to G2/B0, the importance of concomitant gradient terms is expected to increase given the current interest in systems with stronger gradients and/or weaker main magnetic fields.

Accurate system modeling in tomographic image reconstruction has been shown to reduce the spatial variance of resolution and improve quantitative accuracy. System modeling can be improved through analytic calculations, Monte Carlo simulations, and physical measurements. The purpose of this work is to improve clinical fully-3-D reconstruction without substantially increasing computation time. We present a practical method for measuring the detector blurring component of a whole-body positron emission tomography (PET) system to form an approximate system model for use with fully-3-D reconstruction. We employ Monte Carlo simulations to show that a non-collimated point source is acceptable for modeling the radial blurring present in a PET tomograph and we justify the use of a Na22 point source for collecting these measurements. We measure the system response on a whole-body scanner, simplify it to a 2-D function, and incorporate a parameterized version of this response into a modified fully-3-D OSEM algorithm. Empirical testing of the signal versus noise benefits reveal roughly a 15% improvement in spatial resolution and 10% improvement in contrast at matched image noise levels. Convergence analysis demonstrates improved resolution and contrast versus noise properties can be achieved with the proposed method with similar computation time as the conventional approach. Comparison of the measured spatially variant and invariant reconstruction revealed similar performance with conventional image metrics. Edge artifacts, which are a common artifact of resolution-modeled reconstruction methods, were less apparent in the spatially variant method than in the invariant method. With the proposed and other resolution-modeled reconstruction methods, edge artifacts need to be studied in more detail to determine the optimal tradeoff of resolution/contrast enhancement and edge fidelity.

Purpose: To minimize respiratory motion artifacts, this work proposes quiescent period gating ͑QPG͒ methods that extract PET data from the end-expiration quiescent period and form a single PET frame with reduced motion and improved signal-to-noise properties. Methods: Two QPG methods are proposed and evaluated. Histogram-based quiescent period gating ͑H-QPG͒ extracts a fraction of PET data determined by a window of the respiratory displacement signal histogram. Cycle-based quiescent period gating ͑C-QPG͒ extracts data with a respiratory displacement signal below a specified threshold of the maximum amplitude of each individual respiratory cycle. Performances of both QPG methods were compared to ungated and five-bin phase-gated images across 21 FDG-PET/CT patient data sets containing 31 thorax and abdomen lesions as well as with computer simulations driven by 1295 different patient respiratory traces. Image quality was evaluated in terms of the lesion SUV max and the fraction of counts included in each gate as a surrogate for image noise. Results: For all the gating methods, image noise artifactually increases SUV max when the fraction of counts included in each gate is less than 50%. While simulation data show that H-QPG is superior to C-QPG, the H-QPG and C-QPG methods lead to similar quantification-noise tradeoffs in patient data. Compared to ungated images, both QPG methods yield significantly higher lesion SUV max . Compared to five-bin phase gating, the QPG methods yield significantly larger fraction of counts with similar SUV max improvement. Both QPG methods result in increased lesion SUV max for patients whose lesions have longer quiescent periods. Conclusions: Compared to ungated and phase-gated images, the QPG methods lead to images with less motion blurring and an improved compromise between SUV max and fraction of counts. The QPG methods for respiratory motion compensation could effectively improve tumor quantification with minimal noise increase.

Maxwell's equations imply that imaging gradients are accompanied by higher order spatially varying fields (concomitant fields) that can cause artifacts in MR imaging. The lowest order concomitant fields depend quadratically on the imaging gradient amplitude and inversely on the static field strength. Timevarying concomitant fields that accompany the readout gradients of spiral scans cause unwanted phase accumulation during the readout, resulting in spatially dependent blurring. Concomitant field phase errors are independent of echo time and, therefore, cannot be detected using Dixon-type field map measurements that are normally used to deblur spiral scan images. Data acquisition methods that reduce concomitant field blurring increase off-resonant spin blurring, and vice versa. Blurring caused by concomitant fields can be removed by variations of image reconstruction methods developed to correct for spatially dependent resonance offsets with nonrectangular k-space trajec-

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