TY - JOUR

T1 - Gaussian approximation in the theory of MR signal formation in the presence of structure-specific magnetic field inhomogeneities

AU - Sukstanskii, Alexander L.

AU - Yablonskiy, Dmitriy A.

N1 - Funding Information:
The authors are grateful to Professors Mark S. Conradi and Joseph J.H. Ackerman for substantial and helpful comments. This work is supported in part by NIH Grant R01 NS4519-01A1.

PY - 2003/8

Y1 - 2003/8

N2 - A detailed theoretical analysis of the free induction decay (FID) and spin echo (SE) MR signal formation in the presence of mesoscopic structure-specific magnetic field inhomogeneities is developed in the framework of the Gaussian phase distribution approximation. The theory takes into account diffusion of nuclear spins in inhomogeneous magnetic fields created by arbitrarily shaped magnetized objects with permeable boundaries. In the short-time limit the FID signal decays quadratically with time and depends on the objects' geometry only through the volume fraction, whereas the SE signal decays as 5/2 power of time with the coefficient depending on both the volume fraction of the magnetized objects and their surface-to-volume ratio. In the motional narrowing regime, the FID and SE signals for objects of finite size decay mono-exponentially; a simple general expression is obtained for the relaxation rate constant ΔR2. In the case of infinitely long cylinders in the motional narrowing regime the theory predicts non-exponential signal decay ln S ∼ -t ln t in accordance with previous results. For specific geometries of the objects (spheres and infinitely long cylinders) exact analytical expressions for the FID and SE signals are given. The theory can be applied, for instance, to biological systems where mesoscopic magnetic field inhomogeneities are induced by deoxygenated red blood cells, capillary network, contrast agents, etc.

AB - A detailed theoretical analysis of the free induction decay (FID) and spin echo (SE) MR signal formation in the presence of mesoscopic structure-specific magnetic field inhomogeneities is developed in the framework of the Gaussian phase distribution approximation. The theory takes into account diffusion of nuclear spins in inhomogeneous magnetic fields created by arbitrarily shaped magnetized objects with permeable boundaries. In the short-time limit the FID signal decays quadratically with time and depends on the objects' geometry only through the volume fraction, whereas the SE signal decays as 5/2 power of time with the coefficient depending on both the volume fraction of the magnetized objects and their surface-to-volume ratio. In the motional narrowing regime, the FID and SE signals for objects of finite size decay mono-exponentially; a simple general expression is obtained for the relaxation rate constant ΔR2. In the case of infinitely long cylinders in the motional narrowing regime the theory predicts non-exponential signal decay ln S ∼ -t ln t in accordance with previous results. For specific geometries of the objects (spheres and infinitely long cylinders) exact analytical expressions for the FID and SE signals are given. The theory can be applied, for instance, to biological systems where mesoscopic magnetic field inhomogeneities are induced by deoxygenated red blood cells, capillary network, contrast agents, etc.

KW - FMRI

KW - Magnetic resonance

KW - Relaxation effects

UR - http://www.scopus.com/inward/record.url?scp=0042030792&partnerID=8YFLogxK

U2 - 10.1016/S1090-7807(03)00131-9

DO - 10.1016/S1090-7807(03)00131-9

M3 - Article

C2 - 12914839

AN - SCOPUS:0042030792

SN - 1090-7807

VL - 163

SP - 236

EP - 247

JO - Journal of Magnetic Resonance

JF - Journal of Magnetic Resonance

IS - 2

ER -