Approximate Fourier domain expression for Bloch–Siegert shift. Issue 1 (29th January 2014)

• Record Type: Journal Article
• Authors: Turk, Esra Abaci; Ider, Yusuf Ziya; Ergun, Arif Sanli; Atalar, Ergin
• Is Part Of: Magnetic resonance in medicine. Volume 73:Issue 1(2015:Jan.)
• Page Start: 117
• Page End: 125
• Publication Date: 2014-01-29
• Subjects: Nuclear magnetic resonance -- Periodicals; Electron paramagnetic resonance -- Periodicals; 616.07548
• DOI: 10.1002/mrm.25104
• Languages: English
• ISSNs: 0740-3194

Abstract

<abstract abstract-type="main"> <title> <x xml:space="preserve">Abstract</x> </title> <sec id="mrm25104-sec-0001" sec-type="section"> <title>Purpose</title> <p>In this study, a new simple Fourier domain‐based analytical expression for the Bloch–Siegert (BS) shift‐based <italic>B</italic><sub>1</sub> mapping method is proposed to obtain <inline-formula><alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgh2xqbwg3v" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math display="inline" altimg="urn:x-wiley::media:mrm25104:mrm25104-math-0001" overflow="scroll" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mo>|</mml:mo><mml:msubsup><mml:mi>B</mml:mi><mml:mn>1</mml:mn><mml:mo>+</mml:mo></mml:msubsup><mml:mo>|</mml:mo></mml:mrow></mml:math></alternatives></inline-formula> more accurately while using short BS pulse durations and small off‐resonance frequencies.</p> </sec> <sec id="mrm25104-sec-0002" sec-type="section"> <title>Theory and Methods</title> <p>A new simple analytical expression for the BS shift is derived by simplifying the Bloch equations. In this expression, the phase is calculated in terms of the Fourier transform of the radiofrequency pulse envelope, and thus making the off‐ and on‐resonance effects more easily understandable. To verify the accuracy of the proposed expression, Bloch simulations and MR experiments are performed for the hard, Fermi, and Shinner–Le Roux pulse shapes.</p> </sec> <sec id="mrm25104-sec-0003" sec-type="section"> <title>Results</title> <p>Analyses of the BS phase shift‐based <italic>B</italic><sub>1</sub> mapping method in terms of radiofrequency pulse shape, pulse duration, and off‐resonance frequency show that <inline-formula><alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgh2xqbwg29" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math display="inline" altimg="urn:x-wiley::media:mrm25104:mrm25104-math-0002" overflow="scroll" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mo>|</mml:mo><mml:msubsup><mml:mi>B</mml:mi><mml:mn>1</mml:mn><mml:mo>+</mml:mo></mml:msubsup><mml:mo>|</mml:mo></mml:mrow></mml:math></alternatives></inline-formula> can be obtained more accurately with the aid of this new expression.</p> </sec> <sec id="mrm25104-sec-0004" sec-type="section"> <title>Conclusions</title> <p>In this study, a new simple frequency domain analytical expression is proposed for the BS shift. Using this expression, <inline-formula><alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgh2xqbwg1r" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math display="inline" altimg="urn:x-wiley::media:mrm25104:mrm25104-math-0003" overflow="scroll" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mo>|</mml:mo><mml:msubsup><mml:mi>B</mml:mi><mml:mn>1</mml:mn><mml:mo>+</mml:mo></mml:msubsup><mml:mo>|</mml:mo></mml:mrow></mml:math></alternatives></inline-formula> values can be predicted from the phase data using the frequency spectrum of the radiofrequency pulse. This method works well even for short pulse durations and small offset frequencies. Magn Reson Med 73:117–125, 2015. © 2014 Wiley Periodicals, Inc.</p> </sec> </abstract>