THE RELATIONSHIP BETWEEN THE SCALING PARAMETER AND RELAXATION TIME FOR NON-EXPONENTIAL RELAXATION IN DISORDERED SYSTEMS

2002 ◽  
Author(s):  
YA. E. RYABOV ◽  
YU. FELDMAN
Keyword(s):  
Relaxation Time ◽  
Disordered Systems ◽  
Scaling Parameter ◽  
Exponential Relaxation ◽  
The Relationship

THE RELATIONSHIP BETWEEN THE SCALING PARAMETER AND RELAXATION TIME FOR NON-EXPONENTIAL RELAXATION IN DISORDERED SYSTEMS

Fractals ◽  
2003 ◽  
Vol 11 (supp01) ◽  
pp. 173-183 ◽  
Author(s):  
YA. E. RYABOV ◽  
YU. FELDMAN
Keyword(s):  
Relaxation Time ◽  
Disordered Systems ◽  
Memory Function ◽  
Transition Process ◽  
Geometrical Properties ◽  
Self Diffusion ◽  
Nylon 6,6 ◽  
Exponential Relaxation ◽  
The Relationship ◽  
Composite Samples

A memory function equation and scaling relationships were used for the physical interpretation of the Cole-Cole exponent. The correspondence between the relaxation time, the geometrical properties, the self-diffusion coefficient and the Cole-Cole exponent was established. Using this approach the dielectric relaxation spectra of the polymer-water mixtures and the glass transition process in the nylon 6,6 quenched, crystalline and micro-composite samples were analyzed.

DIFFUSION UNDER CROSSED LOCAL AND GLOBAL BIASES IN DISORDERED SYSTEMS

2000 ◽  
Vol 11 (07) ◽  
pp. 1357-1369 ◽  
Author(s):  
SITANGSHU BIKAS SANTRA ◽  
WILLIAM A. SEITZ
Keyword(s):  
Relaxation Time ◽  
Disordered Systems ◽  
Maximum Rate ◽  
Rate Of Change ◽  
Square Lattice ◽  
Site Percolation ◽  
Local Bias ◽  
Random Walker ◽  
Percolation Clusters ◽  
Global Bias

Diffusion on 2D site percolation clusters at p = 0.7, 0.8, and 0.9 above pc on the square lattice in the presence of two crossed bias fields, a local bias B and a global bias E, has been investigated. The global bias E is applied in a fixed global direction whereas the local bias B imposes a rotational constraint on the motion of the diffusing particle. The rms displacement Rt ~ tk in the presence of both biases is studied. Depending on the strength of E and B, the behavior of the random walker changes from diffusion to drift to no-drift or trapping. There is always diffusion for finite B with no global bias. A crossover from drift to no-drift at a critical global bias Ec is observed in the presence of local bias B for all disordered lattices. At the crossover, value of the rms exponent changes from k = 1 to k < 1, the drift velocity vt changes from constant in time t to decreasing power law nature, and the "relaxation" time τ has a maximum rate of change with respect to the global bias E. The value of critical bias Ec depends on the disorder p as well as on the strength of local bias B. Phase diagrams for diffusion, drift, and no-drift are obtained as a function of bias fields E and B for these systems.

Method Dependence of Proton Spin-Lattice Relaxation Analysis in Biologic Tissues

1989 ◽  
Vol 30 (1) ◽  
pp. 97-100 ◽  
Author(s):  
M. Komu ◽  
A. Alanen ◽  
H. Määttänen ◽  
M. Kormano
Keyword(s):  
Relaxation Time ◽  
Spin Echo ◽  
Weighted Average ◽  
Proton Spin ◽  
Point Method ◽  
Spin Lattice Relaxation ◽  
Proton Relaxation ◽  
Spin Lattice ◽  
Exponential Relaxation ◽  
Data Point

Spin-lattice proton relaxation times (T1) in several biologic and phantom samples have been measured and analysed by using standard inversion recovery (IR) and spin echo (SE) sequences at 0.02 T. The average T1 of the sample was measured with the two-data point method. In the case of bi-exponential relaxation the value of a single T1 is strongly dependent on the T1 and TR selected. With short TI the T1 value obtained by using the two point method is approximately equal to the weighted average of the two relaxation time components (T1s and T1l), while at long inversion times TI the single T1 is more dependent on the long component T1l. The more the true short and long relaxation time components T1s and T1l of the bi-exponential relaxation differ from each other, the greater is the potential error, provided that the weights ws and wl do not differ very much. When two-data point analyzing method is used, the possible multi-exponential behaviour of the relaxation in tissues will be missed. For more reliable T1 values a series of images with as many values of TI as possible should be taken. Knowledge of true multi-exponential relaxation parameters helps in optimizing the sequence parameters and the image contrast between the various tissues.

MTR and T1 provide complementary information in MS NAWM, but not in lesions

2000 ◽  
Vol 6 (5) ◽  
pp. 327-331 ◽  
Author(s):  
C M Griffin ◽  
G JM Parker ◽  
G J Barker ◽  
A J Thompson ◽  
D H Miller
Keyword(s):  
Relaxation Time ◽  
White Matter ◽  
Mixed Model ◽  
Relaxation Times ◽  
Tissue Type ◽  
Tissue Characterisation ◽  
Complementary Information ◽  
T1 Relaxation Time ◽  
T1 Relaxation ◽  
The Relationship

MTR and T1 relaxation times are abnormal in MS lesions and NAWM, and may reflect tissue damage such as demyelination and axonal loss. Their relationship and potential to provide complementary information in tissue characterisation is explored. The aim of this study was to document the relationship between magnetisation transfer ratio (MTR) and T1 relaxation time in Multiple Sclerosis (MS) lesions and normal appearing white matter (NAWM) in order to determine whether the combination provides a more comprehensive tissue characterisation than either parameter in isolation. Ten patients with relapsing remitting MS and 10 age matched healthy controls underwent imaging using a protocol which included the measurement of both MTR and T1 relaxation times. The MTR and T1 values were compared statistically using a commonly adopted correlation approach and a mixed-model regression approach. There was a strong correlation between MTR and T1 in MS lesions (r=0.74). The correlation was seen equally in T1 hypointense and isointense lesions. The relationship was much weaker in MS NAWM (r=0.24) and no correlation was found in control white matter (r=0.06). Mixed-model regression analysis confirmed that the relationship between T1 and MTR is strongly dependent upon tissue type (MS lesion, MS NAWM, or control white matter). The relationship between MTR and T1 relaxation time measurements varies markedly between pathological and normal tissue types. In MS, the complementary information obtained from MTR and T1 is most apparent in NAWM. The results emphasise the potential for combinations of MR parameters to improve tissue characterisation, which in turn should improve understanding of disease pathology and treatment monitoring.

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