SHARP edges: Recovering cortical phase contrast through harmonic extension

Purpose: To recover local phase contrast at the edges of the brain (e.g., cortex), where it is otherwise unavailable with the conventional form of the technique sophisticated harmonic artifact reduction for phase data (SHARP). Methods: A harmonic potential field, such as the magnetic "background" field, is an analytic field and can thus be represented by a convergent power series. Using SHARP to obtain an initial estimate of the harmonic background field over a reduced inner portion of the brain, a three-dimensional Taylor expansion was performed to extend field coverage to the brain edges. The method, called Extended-SHARP, was quantitatively assessed through a numerical field-forward simulation and qualitatively demonstrated in vivo. Results: Using a typical spherical kernel (6 mm radius), Extended-SHARP recovered on average 26% more in vivo brain volume than SHARP. When applied to the numerical model, local field contrast around an otherwise lost edge source was recovered, with the resulting error comparable to that of conventional SHARP. Conclusion: The lost field values near the edges of the brain can be recovered through an easily implemented adaptation to conventional SHARP.