### Diffusion MRI Ch1: Introduction to Diffusion Magnetic Resonance

**A. What is diffusion **

Diffusion is a mass transport process arising in nature. It results in molecular or particle mixing without requiring bulk motion.

Fick’s laws of diffusion describes the diffusion phenomenon that explain mixing. (Adolf Fick 1855)

J= -D∇C

J is the net diffusion flux vector

D is the diffusion coefficient (intrinsic property of medium, determined by size and temp)

C is the particle concentration

On a molecular level diffusive mixing results from collisions of atoms and molecules in l or g state. Fick’s law embodies the notion that particles flow from regions of high to low concentration. However, diffusive efflux also occurs in states of thermodynamic eq. In this case, microscopic motions still persist; there is diffusion but there is no net molecular flux in eq.

Brownian motion explains this: particles move randomly without apparent cause.

Seeking evidence of the existence of atoms, Einstein developed a probabilistic framework linking Fick’s law with Brownian motion.

His displacement distribution described diffusion in a cohesive fashion; it quantifies the fraction of particles that will traverse a certain distance within a particular time frame.

x^2 = 2DΔ where x is mean squared displacement.

**B. MR and Diffusion
**

Magnetic resonance provides a unique opportunity to quantify the diffusional characteristics of a specimen. In a biological samples, diffusion is influenced by the geometric structure of the enviroment. These structural bounderies of such structures are so small that they cannot be resolved using conventional MRI.

NMR is a property that magnetic nuclei have in a magnetic field and applied electromagnetic (EM) pulse or pulses, which cause the nuclei to absorb energy from the EM pulse and radiate this energy back out. The energy radiated back out is at a specific resonance frequency which depends on the strength of the magnetic field and other factors. This allows the observation of specific quantum mechanical magnetic properties of an atomic nucleus. Scientific techniques exploit NMR phenomena to study molecular physics, crystals and non-crystalline materials through NMR spectroscopy.

**Typical NMR scan
**Begin with the excitation of nuclei at a 90 degree radiofrequency (rf) pulse. This tilts that magnetization vector into the plane whose normal is along the main magnetic field. The spins then start to precess around the magnetic field. Larmor precession describes this.

Precession is the regular motion of a spinning body such as a spinning top or a planet, in which the axis of rotation describes a cone.

Larmor precession is the precession of the magnetic moments of electrons, atomic nuclei, and atoms about an external magnetic field. the Angular frequency of this precession is bound the equation:

ω = γ B, where ω is angular frequency of precession, B is the magnetic field that is exposed to the spin, and γ is the gyromangetic ratio: a constant specific to the nucleus under study.

Problems, coherent spins might dephase due to (1) magnetic field inhomogeneity and (2) Dipolar interactions. This leads to a decay in the voltage signal in the reciever. To correct this dephasing, the application of a revrese 180 degree rf pulse reproduces a coherent spin and a signal recieved by the MR antenna or coil receiver. This is termed a “spin echo” experiment.

t is an rf pulse. TE is the time two rf pulses.

Spin-echo pulse sequence.

A 90 degree pulse is first applied to the spin system. The 90 degree pulse rotates the magnetization down into the X’Y’ plane. The transverse magnetization begins to dephase. At some point in time after the 90 degree pulse, a 180 degree pulse is applied. This pulse rotates the magnetization by 180 degree about the X’ axis. The 180o pulse causes the magnetization to at least partially rephase and to produce a signal called an echo.

To acquire MR images, a carefully devised sequence of rf pulses is set with external magnetic field gradients linearly changing in space.

1950: Hahn recognized the sensitivity of spin echo in molecular diffusion. Spin echo causes a reduction in signal due to dephasing of the spin as a result of translation diffusion within an inhomogeneous field. he proposed that the diffusion coefficient (D) of the solution containing spin labeled molecules can be measured.

Effects of Diffusion on free precession in NMR experiemnts

1954: Carr and Purcell devised a complete mathematical and physical framework to measure the diffusion coefficient using the spin echo sequence. The idea is that the echo magnitude could be sensitized solely to the effects of random molecular spreading caused by diffusion in a way that permits direct measurement. This is very similar to the current diffusion weighted MRI method.

1. A spins frequency is determined by the local magnetic field. ω = γ B

2. If a magnetic field gradient is applied, spins at different locations experience different magnetic fields. This means that they precess at different angular frequencies. (Linear main field or another coil to create another main field on top of the homogenous field of the scanner).

3. With time, the spins will acquire a different phase shift bound by location. A particle is assumed to spend a short time t’ at a point before moving on to another location. the particle will suffer a phase shift as a result of the larmor precession at the field modified by the constant gradient. This means that the net phase shift that infleunces the MR signal is related to the motional history of the particle. This way the diffusion coefficient can be obtained allowing NMR to be used in measuring molecular diffusion. Others (Torrey, stejskal, tanner) introduced innovations on the mathematical framework.

4. Stronger gradients will lead to sharper phase changes in the specimen yielding to higher sensitivity on diffusion. a b-value is used to describe this level of sensitivity of diffusion.

While carr and Purcell used a linear gradient to measure the diffusion coefficient, Stejskal and Torry introduced a Pulse gradient spin echo sequence (PGSE). This shorter pulse allowed a clearer distinction between the encoding time (pulse duration) and the diffusion time (separation of pulses).

PGSE is complex and littered with mathematical equations. I will revisit it in due time.

**1965: Sedjkal used PGSE spin echoe equations to study anisotropic diffusion and flow. He used a tensor or a 3×3 matrix that represents the natural orientation of anisotropic diffusion with respect to the reference frame. Diffusion tensor imaging was developed by Basser in 1994 to measure the entire diffusion tensor in each voxel (diagonal and off diagonal elements) within the frame of reference. **

In a normal “isotropic” sample, the optical properties are the same in all directions. Anisotropy refers to the directional-dependent optical properties of a material.The optical properties of a material depend on the

underlying atomic or molecular structure. If this basic building block has a non-symmetric ‘shape’ and a longrange order throughout the material, then the material can be anisotropic. For example, an electronic transition may occur at different resonant energies depending on the spacing between atoms in a non-cubic crystal. This would lead to different values across the spectrum.

Due to the need for both non-symmetric “shape” and long-range order, anisotropic materials tend to be of a couple types: non-cubic crystals and ordered organics. Included in the first type are such materials as rutile (with tetragonal symmetry) and sapphire with its hexagonal crystal structure. A few anisotropic organics include liquid crystal films and PET.

**C. Diffusion in Neural Tissue**

Water is incessantly moving is bound by restrictions to

1. Cell membranes

2. Cytoskeleton

3. Macromolecules

By using our understanding of the micro-structural features causing the process of diffusion, we can obtain valuable information about the biological microstructure simply by observing the motion of water molecules. This is undeniably important in brain science and has great implications for acquiring anatomical information of its complex structure.

Attenuation is the opposite of Amplification

An important application of using gradients in spin echo NMR experiments is Attenuation correction (pdf on correction in myocardial MRI). Accounting for attenuation effects is important because a reduced signal amplitude can affect the quality of the image produced. Attenuation correction is aimed at providing improved quantification of tomographic brain images. Utilizing attenuation information, one can adjust the input signal amplitude to compensate for any loss of energy at the desired imaging depth or resolution. Attenuation correction reduces the artifactual decrease in activity caused by attenuation, so that the image appearance more accurately represents actual activity. Thus, attenuation correction leads to improved quantitation, improved image quality, and may lead to improved specificity.

In diffusion MRI, attenuation enhacement with the application of spin echo gradients introduces a contrast mechanism better than relaxation weighted MRI. These are called diffusion weighted images and have been used extensively in neuroimaging. In ischemic stroke diffusion weighted MRI allows detection earlier than conventional T1/T2 weighted MRI.

The CNS is a comprised of axonal transmission wires that are intricately connected. Water molecules tend to diffuse freely across the direction of these axonal fibers. Analyzing the orientation of diffusional flow of water across these fibers may allow us image these axons.

**Grey matter is isotropic**: measured apparent diffusivity is largely independent of the orientation of the tissue at the voxel length scale. Diffusion characteristics can be measured with a single apparent diffusion coefficient (ADC).

**White matter is anisotropic**: measured diffusivity is dependent on the orientation of the tissue. ADC is not sufficient in characterzing the orientation dependent water mobility. Scalar ADC is replaced with a symmetric effective or appraent diffusion tensor of water D.

What is a tensor? Good article here.

The anatomical determinant of diffusion anisotropy in the neural cells have not been fully elucidated, but it is thought that ordered heterogeneous structures including extra/intra-cellular macromolecular, super-molecular structures, organelles and membranes. Myelin has been shown to be correlated with increased diffusion anisotropy. Nonetheless, other structures must be significantly involved since the degree of diffusion anisotropy has been shown to not be a quantitative measure or stain of myelin content.

D. Conclusion

As water diffuses it encounters barriers. MR permits the probing of different tissue structures at different length scales. The mean squared displacement of water is on the order of microns. The molecular motions are ensemble-averaged within a voxel, which are then assembled into multislice or 3D images of tissue and organs.

Finally, this emerging imaging modality permits the PHOTOGRAPHY of complex structural features (macromolecular to macroscopic) without using exogenous contrast agents.

Complied by A.S.K.

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**One Response to “Diffusion MRI Ch1: Introduction to Diffusion Magnetic Resonance”**

it easy to understand.