NMR Vorlesung SS 2013 3

8/10/2019 NMR Vorlesung SS 2013 3

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3. NMR Relaxation Times T1and T2

Brain Tumor in NMR images:

T1-weighted T2-weighted T1-weighted with

(long T1 long T2 appears paramagnetic

appears brighter contrast agent

darkerMRI of the brain showing

plaques in multiple

sclerosis disease


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3. NMR Relaxation Times T1and T2

Reminder 1:

Spin-Lattice Relaxation Time (longitudinal relaxation time) T1:

Recovery of z-magnetization into thermal equilibrium by energy

exchange between the (magnetic) spin system and the environment

(lattice)


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Reminder 2:

Spin-Spin Relaxation Time (transversal relaxation time) T2:

Decay of x,y-magnetization to zero (into thermal equilibrium) by

energy exchange within the (magnetic) spin system

Problem:

What are the physics mechanisms behind those relaxation

processes?


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Introduction

In a quantum mechanical two-level system exist two possible

transition mechanisms:

- Spontaneous transitions

- Stimulated transitions

Spontaneous emissions occur without prior absorption of a photon.

Stimulated transitions occur by absorption or emission of radiation.The probability of stimulated transition is higher at lower energy gaps.

NMR is the area of stimulated transition.

It follows:

NMR transitions can be stimulated due to oscillating (magnetic) fields

of the correct resonance frequency and due to magnetic oscillations

in the environment


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T1relaxation describes the change of z-magnetization.

The whole energy E of the spin system in a magnetic field B ist:

E = MB = MzB

During T1relaxation the total energy E is changed

T2relaxation describes the coherent transitions between energy

states without energy loss.

Two examples:

- Different local magnetic fields give different resonance

frequencies and therefore induce a phase distribution of the spins

in the rotating frame

- Other spins precess in the neighborhood at the correct resonancefrequency but at different phases, which stimulates transitions

In (almost) all cases: T1 T2


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Basic Physics of NMR Relaxation

- Magnetic dipole-dipole interactions between spins

- Thermal motion of molecules (and spins)

The motion is described using a characteristic correlation time c

cis the mean time for a molecule to travel the distance of its diameter

(translation), or fully rotate around itself (rotation)

A few examples:

c of a water molecule:

free in bulk water: 10-12s

in hydrate shell: 10-8s

in solid state (ice): 10-6

s

Isotropic statistic motion:

Autocorrelation function G(t):

(Means: after a few cthere is no more information about the initial states)


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After Fourier transformation, we get the

frequency distribution J() of the molecular motion:

Solid state

Viscous media

Liquid state

NMR resonance frequency


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Depending on the NMR resonance frequency

(or magnetic field strength):

At solid state:

There are almost no (motional) frequency components in the region

of the NMR resonance frequencyAt liquid state:

There are always (motional) frequency components in the region of

the NMR resonance frequency


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If cis long and is low, the spins are for a longer time interval

in direct (magnetic) contact, which leads to a shorter T2value

(more spin dephasing).

Schematic diagram:

Liquid state

Solid state


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T1is shortest, when the motional frequency is comparable to the

NMR resonance frequency (stimulated transition due to lattice

vibrations)

Schematic diagram:

Liquid

state

Solid state

0


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The full theory is described in the BPP-Theory

(Bloch-Purcell-Pound)

with:

and is theNMR resonance

frequency


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A few results:

In the gas phase: very long T1and T2values (several hours or days!)

(due to large distances of the spins: r6dependence!)

In the solid state: long T1and very short T2values (large difference!)

In the liquid state: long T1and long T2values (small differences!)

In viscous media: medium long T1and T2values (small and large

differences depending on resonance frequency)

T2is (almost) not dependent on the field strength

T1increases with increasing magnetic field strength

Differences in T1values are smaller in high magnetic field strength,

especially in viscous media


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Typical values of 1H NMR signals of water and lipid molecules in

biological tissue:

T1: 50 ms5000 ms

T2

: 1 ms1000 ms


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Additional NMR relaxation mechanisms:

1. Anisotropic chemical shift:electronic shell in the molecules introduce additional

inhomogeneous magnetic fields, resulting in NMR line

broadening: 1/T1,2~ B02

2. Paramagnetic relaxation:Single electrons (transition metal complexes or radicals)have a 1000-times higher magnetic dipole moment

compared to nuclei and with 1/T1,2~ 2have a 106-times

more efficient dipole-dipole-interaction.

Paramagnetic substances shorten especially T1(e.g.: O2, Cu, Mn, Gd, Eu, .)Used as NMR imaging contrast media


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3. Magnetic particles:

Induce additional magnetic field inhomogeneities and

reduce especially T2Used as NMR imaging contrast media

4. Quadrupolar relaxation:

Nuclei having a spin I > have an additional electrical

quadrupolar moment which interact with oscillating

electrical field gradients

Those nuclei (e.g. 23Na, etc.) have short T1,2

values


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NMR relaxation times in biological tissue

(1H NMR signal of water and fat)

Large differences of T1and T2in soft tissue

(gives the basis of soft tissue contrast in NMR imaging)

Very short T2values in hard tissue (bones, tendons, )

(bones, etc. not visible in NMR imaging)

NMR relaxation times are changed in diseases (infarct, tumor,

inflamation, )NMR relaxation times can be changed using NMR contrast media

(magnetic nanoparticles, paramagnetic substances)

The quantitative interpretation of NMR relaxation times in biologicaltissue remains difficult and is unsolved at the moment

Interesting area of research !


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For practical NMR experiments:

T1should be as short as possible: Why?

T2should be as long as possible: Why?

There exists another relaxation time:

The effective T2: T2*This is the time constant describing the relaxation of the free

induction decay (The NMR-signal!).

T2* is always shorter than T2and influenced by the magneticfield inhomogeneity B, with:

1T2 =

1T2 + B


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1H NMR relaxation times of water in biological tissue:

Water is distributed between different phases (i)

(free, bound water and water in hydration shells)having different c and different T1,2,i

If the exchange rate of water is slow,

multiexponentialrelaxation behaviour will be detected

(with Pi: number of water molecules in different phases i):

M t = Pi e ,,

i

If the exchange rate is fast, a monoexponential relaxation is observed

with the weighted relaxation rate:

1T,2 =

PiT,2,ii


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NMR Vorlesung SS 2013 3