Generalized Lorentzian Tensor Approach (GLTA) as a biophysical background for quantitative susceptibility mapping. Issue 2 (26th November 2014)

• Record Type: Journal Article
• Authors: Yablonskiy, Dmitriy A.; Sukstanskii, Alexander L.
• Is Part Of: Magnetic resonance in medicine. Volume 73:Issue 2(2015:Feb.)
• Page Start: 757
• Page End: 764
• Publication Date: 2014-11-26
• Subjects: Nuclear magnetic resonance -- Periodicals; Electron paramagnetic resonance -- Periodicals; 616.07548
• DOI: 10.1002/mrm.25538
• Languages: English
• ISSNs: 0740-3194

Abstract

<abstract abstract-type="main"> <title> <x xml:space="preserve">Abstract</x> </title> <sec id="mrm25538-sec-0001" sec-type="section"> <title>Purpose</title> <p>Quantitative susceptibility mapping (QSM) is a potentially powerful technique for mapping tissue magnetic susceptibility from gradient recalled echo (GRE) MRI. Herein we aim to derive the relationships between GRE signal phase and the underlying tissue microstructure and magnetic susceptibility at the cellular level.</p> </sec> <sec id="mrm25538-sec-0002" sec-type="section"> <title>Methods</title> <p>We use Maxwell's equations and a statistical approach to derive the expression for the magnetic‐susceptibility‐induced MR signal frequency shift of the GRE signal in single‐ and multicompartment systems, in which inhomogeneous magnetic field is induced by the cellular constituents (proteins, lipids, iron, etc.) distributed in intra‐ and extracellular spaces.</p> </sec> <sec id="mrm25538-sec-0003" sec-type="section"> <title>Results</title> <p>We introduce the Generalized Lorentzian Tensor Approach (GLTA) that accounts for both types of anisotropy: the anisotropy of magnetic susceptibility and the structural tissue anisotropy. In the GLTA the frequency shift due to the local environment is characterized by the Lorentzian tensor <inline-formula><alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgh372znhtj" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math display="inline" altimg="urn:x-wiley:07403194:media:mrm25538:mrm25538-math-0001" overflow="scroll" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mover accent="true"><mml:mi mathvariant="bold">L</mml:mi><mml:mo>⁁</mml:mo></mml:mover></mml:math></alternatives></inline-formula> which has a substantially different structure than the susceptibility tensor <inline-formula><alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgh372znhs0" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math display="inline" altimg="urn:x-wiley:07403194:media:mrm25538:mrm25538-math-0002" overflow="scroll" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mover accent="true"><mml:mi mathvariant="bold">χ</mml:mi><mml:mo>⁁</mml:mo></mml:mover></mml:math></alternatives></inline-formula>. While components of <inline-formula><alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgh372znhrf" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math display="inline" altimg="urn:x-wiley:07403194:media:mrm25538:mrm25538-math-0003" overflow="scroll" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mover accent="true"><mml:mi mathvariant="bold">χ</mml:mi><mml:mo>⁁</mml:mo></mml:mover></mml:math></alternatives></inline-formula> are simply compartmental susceptibilities "weighted" by their relative volumes, the components of <inline-formula><alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgh372znhqw" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math display="inline" altimg="urn:x-wiley:07403194:media:mrm25538:mrm25538-math-0004" overflow="scroll" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mover accent="true"><mml:mi mathvariant="bold">L</mml:mi><mml:mo>⁁</mml:mo></mml:mover></mml:math></alternatives></inline-formula> are weighted by specific numerical factors depending on tissue micro‐symmetry and parameters related to the MR pulse sequence. We also provide equations bridging phenomenological and microscopic considerations.</p> </sec> <sec id="mrm25538-sec-0004" sec-type="section"> <title>Conclusion</title> <p>The GLTA provides a consistent background for deciphering phase data. <bold>Magn Reson Med 73:757–764, 2015. © 2014 Wiley Periodicals, Inc.</bold></p> </sec> </abstract>