# Ravinder Reddy, PhD Professor of Radiology & Director of CMROI, Department of Radiology, University...

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04-Jan-2016Category

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Ravinder Reddy, PhDProfessor of Radiology & Director of CMROI, Department of Radiology, University of Pennsylvania School of Medicine, Philadelphia, PA

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Outline

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Thermal equilibrium?How is the thermal equilibrium established?

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T1 and T2

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T2 ProcessFluctuating fields (Hz) which perturb the energy levels of the spin states cause transverse magnetization to dephaseObserved line = 1/2 = 1/T2*1/T2* = 1/T2 + Bo/2

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Relaxation MechanismsMotion of nuclear magnetic moments generates fluctuating magnetic fieldsH= iHx +jHy+kHzM= iMx + jMy +kMz (magnetization vector)

Interaction between them(H x M)= i(HyMz-HzMy)+j(HzMx-Hx Mz) +k(HxMy-HyMx)Hx,y ----> T1 and T2 relaxationHz ----> T2 relaxation-----> T1>T2

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Fluctuating fields and spectral densitiesFluctuating fields have zero average: = 0Mean square fluctuating field 0

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Correlation time

If is small compared to the timescale of the fluctuations, then the values of the field at the two time points tend to be similar.

If is long, then the system loses its memory.

Comparison of field at any one time point t with its value at t+

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Fluctuating fieldsHow rapidly do the fields fluctuate?Autocorrelation function of the field (convolution of a function with itself) defined as: G(t) = 0It tells us how self similar a function is

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Autocorrelation function G(t)An exponential form is assumed:G(t)= exp(-|t|/tc)G(t) is large for small values of t, and tends to zero for large values of t.

c is known as correlation time of the fluctuations.It indicates how long it takes before the random field changes sign.

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Spectral density J()Spectral density function(SDF) is defined as the 2 FT of G(t):J() = 2 o G(t) exp{-i t}

For G(t)= exp(-|t|/c)

The spectral density is given J() = 2 c/(1+2 c 2) Normalized SDF: J(0) = c/(1+2 c 2) If tc is short then the SDF is broad and vice versa

Levitt, Spin dynamics

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Spectral densityAs the solution gets more viscous the number of molecules with high frequency components decreases.Viscosity of Tissues vary significantly.Biological tissues have different T1s.SDF also varies with temp.

oJ()log()

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Rotational Motion

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Dipole-dipole relaxationFor spins-1/2, the important relaxation mechanism is through space dipolar coupling:Rotational correlation time c1/T1= (3/10)b2{J(o)+ 4J(2o)}1/T2= (3/20)b2{3J(0)+ 5J(o)+ 2J(2o)}b= (oh2/4r3)J(o)= c/{1+ (oc)2}

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T1 and T2Variation of relaxation time of protons in water as a function of correlation time at a resonance frequency of 100 MHz (1/o = 10-8 s)o c < 1, T1=T2o c 1, T1>T2

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Frequency range probedT1 probes molecular motional processes in MHz rangeTo measure the processes in

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