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New simulation approach using classical formalism to water nuclear magnetic relaxation dispersions in presence of superparamagnetic particles used as MRI contrast agents
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10.1063/1.4751442
/content/aip/journal/jcp/137/11/10.1063/1.4751442
http://aip.metastore.ingenta.com/content/aip/journal/jcp/137/11/10.1063/1.4751442

Figures

Image of FIG. 1.
FIG. 1.

Proton diffusion in the dipolar magnetic field produced by a superparamagnetic particle. The proton magnetic moment rotates around a local magnetic field composed of the static field B 0 and the dipolar field B 1.

Image of FIG. 2.
FIG. 2.

NMRDs obtained from the isotropic model for SPM radii of 5, 20, and 230 nm.

Image of FIG. 3.
FIG. 3.

Positions of the second inflection point obtained from simulated NMRDs at different radii (isotropic model). Two regimes can be distinguished and can be expressed by Eqs. (31) and (32).

Image of FIG. 4.
FIG. 4.

Influence of the SPM radius on the longitudinal and transverse relaxation rates at different B 0 fields (10−1, 10−3, and 10−6 T) for the isotropic model. Theoretical lines are traced with Eqs. (16) and (17), points corresponding to large radii are fitted with a law.

Image of FIG. 5.
FIG. 5.

Influence of SPM magnetization on relaxation rates at different B 0 fields and for a SPM radius of 20 nm. Longitudinal and transverse relaxation rates are equal at a B 0 = 10−6 T. The points corresponding to low magnetization are fitted by a ax b law (solid lines): b is equal to 1.71 for full squares, 1.75 for empty squares, and 1.95 for full circles. Dashed lines are linear fits of higher magnetization points.

Image of FIG. 6.
FIG. 6.

NMRDs obtained from the weak anisotropy model for SPM radii of 5 nm and 230 nm. Theoretical curves (for R S of 5 nm) are obtained with Eqs. (21) and (22). For comparison, data (dashed lines) are included from simulations of the isotropic model, Eqs. (16) and (17), for particles of 5 nm and 230 nm, respectively. R 1 and R 2 * curves of a same model can be distinguished knowing that R 2 * always saturate at high fields while R 1 tends to zero.

Image of FIG. 7.
FIG. 7.

Influence of SPM magnetization on relaxation rates for different B 0 fields (10−6, 10−3, 1 T) and for an SPM radius of 20 nm in the WA model. Longitudinal and transverse relaxation rates are equal at a B 0 = 10−6 T. The points corresponding to low magnetization are fitted by an ax 2 law (dashed lines). Solid line corresponds to the static model (7).

Image of FIG. 8.
FIG. 8.

NMRDs obtained from the SA model for SPM radii of 5 nm and 230 nm. SA theoretical curves are obtained with Eqs. (23) and (24) (solid lines) and WA theoretical curves from (21) and (22) for R S = 5 nm. For SPM radius of 230 nm, points from simulations of the WA models are also shown for comparison. R 1 and R 2 * curves of a same model can be distinguished knowing that R 2 * always saturate at high fields while R 1 tends to zero.

Image of FIG. 9.
FIG. 9.

Dependence of the longitudinal and transverse relaxation rates on the SPM radius in the SA model at different B 0 fields (10−3, 10−6, and 1 T). Solid line is obtained with Eq. (23). Dashed lines were obtained by fitting an law to the data.

Image of FIG. 10.
FIG. 10.

Influence of the SPM magnetization on the relaxation rates for a particle with 20 nm-radius in the SA model. Dashed lines are square law fit of the low magnetization points. Solid line is obtained from equation (7).

Tables

Generic image for table
Table I.

The different equations used in this work and their corresponding limitations.

Generic image for table
Table II.

Short summary of the observations made on the three simulated models.

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/content/aip/journal/jcp/137/11/10.1063/1.4751442
2012-09-20
2014-04-21
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: New simulation approach using classical formalism to water nuclear magnetic relaxation dispersions in presence of superparamagnetic particles used as MRI contrast agents
http://aip.metastore.ingenta.com/content/aip/journal/jcp/137/11/10.1063/1.4751442
10.1063/1.4751442
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