In MRI, sequences with long echo times are prone to image artifacts due to magnetic field inhomogeneities. Commonly, static inhomogeneities are removed by the application of countering shim fields or accounted for at the reconstruction stage. However, typically these strategies target only static inhomogeneity. Although mostly much weaker in amplitude, dynamic changes of the B₀ field caused, e.g., by respiration or magnet drift, can introduce inconsistencies in acquired data and lead to image artifacts¹. A number of methods, including corrections based on navigators² or respiratory belts³ as well as feedback field control⁴ have been introduced to counter such problems. In this work we present a novel method for modeling spatiotemporal B₀ evolutions in a target volume, guided by external field probes. An underlying B₀ atlas is created by training with time-resolved B₀ maps and concurrent field probe readouts. During actual imaging the atlas is then used to infer current B₀ maps based on probe information only. The reliability of this approach is demonstrated by validation experiments. As a first application we demonstrate atlas-based real-time field control.

Atlas Generation: Generation and application of the atlas are summarized in figure 1. First, a series of (fast) phase images is acquired. After subtraction of a reference image, the series reflects the spatiotemporal evolution of B₀ in every pixel. The field evolution is also reflected in the probe data p, measured concurrently with image acquisition. A principal component analysis of the probe data extracts the spatial characteristics of this field evolution. A lower-dimensional representation of the spatiotemporal B₀-manifold is found by identifying spatial basis functions, evolving with the same temporal-evolution (w) as the principal components (PC) of the probe data. Doing so, each PC is paired with a corresponding B₀-pattern, all significant B₀-patterns forming a basis set Y. For the application of the atlas, the measured probe values p’ are transformed into the PC-basis. This operation yields the coefficients used to construct the B₀-estimate from Y. Atlases can be constructed for the entire imaging volume or for a sub-volume of interest.

Data Acquisition : For the atlas calibration we used low-resolution, single-shot EPI’s (2x2x2.5mm EPI, SENSE 3, TE 11.9ms, slice TR 56ms). Such images can be shot at high repetition times, capturing the entire manifold of breathing fields within a few respiration cycles. The magnetic field evolution was recorded concurrently with a ¹⁹F NMR field probe setup⁵ .

Application to Real Time Shim Feedback: Real-time spatiotemporal field stabilization with shim feedback⁴ allows to correct for dynamic field changes. A PI-controller dynamically actuates the shim-system during the image acquisition. It minimizes the difference between a constant target value and continuously measured field probe values. This way, the field distribution in the enclosed volume is stabilized over time. However, especially in the lower brain regions, respiratory field-disturbances are often of high spatial order and are counteracted only insufficiently. The introduction of an atlas-based shim-feedback can partly resolve this limitation. Based on a local model, it allows the feedback to be optimal for a specific target region, resulting in a more accurate compensation of local fluctuations as compared to whole volume stabilization.

Atlas-Validation: Data sets consisting of a phase image time series (same as above) paired with concurrent field measurements were acquired for validation. The field evolution predicted by the atlas was compared to the actually measured field evolution. Figure 2A shows the situation for a ROI selected in the primary visual cortex. The atlas-based prediction can reproduce the field distribution in the ROI with a precision below 1Hz (0.4Hz average over total scan duration). The situation is more accentuated in lower regions, as shown in figure 2B.

Shim Feedback: Atlas-based shim-feedback was applied to T2*-weigthed imaging of the brainstem (0.3x0.3x1.3mm, TE 25 ms, TR 700ms). Figure 3 shows the image obtained with atlas-feedback, in comparison with standard spherical harmonics feedback and without any correction. The advantage of the atlas-based correction can be appreciated especially in the lower region.

The presented B₀-atlas method has been shown to provide reliable predictions of the spatiotemporal field evolution in a region of interest. Further optimization of the field probe positions could allow the method to even better differentiate spatial characteristics of disturbing fields, potentially increasing the accuracy of B₀ prediction. The approach has likely much to gain also from higher-level models that may be inspired by manifold learning, a rapidly growing area in computer science. Besides the shown application in real-time field control, the method holds promise also for image reconstruction based on dynamic B₀ information.