diffusion physics

Diffusion Physics

H2O in the body is always in random motion due to thermal agitation

B.M. Ellingson, Ph.D., Dept. of Radiological Sciences, David Geffen School of Medicine at UCLA, 2010

- Diffusion Coefficient is dependent on Temperature and Viscosity of Tissue

Diffusion Coefficient (rate of motion)

Temperature

Size of MoleculeViscosity

Diffusion Physics


-The “rate” of water motion is determine by a diffusion coefficient, “D”.

-Mean displacement of water molecules is related to “D” by Einstein’s equation:

TimeDiffusionCoefficient

MeanDisplacement

Diffusion Physics


Detecting Diffusion with MRI - Intravoxel Incoherent Motion

Ellingson et al., Concepts in MR, 2008

B.M. Ellingson, Ph.D., Dept. of Radiological Sciences, David Geffen School of Medicine at UCLA, 2010 From: Ellingson, Concepts in MR, 2008

Detecting Diffusion with MRI - Intravoxel Incoherent Motion

Detected DWI Signal

MRI Signal w/o Diffusion Sensitivity

Variability inPhase of “Tagged” H2O Level of Diffusion Weighting

Diffusion Coefficient


Intravoxel Incoherent vs Coherent Motion


Diffusion Effects (Incoherent)

Flow Effects (Coherent) -- Phase Contrast (PC)-MRI

d = /3 radians Velocity

Proton on H2O

Image Voxel = t1

= t2

= t3

MR

I Sig

nal

Diffusion Time (or level of diffusion weighting)


Factors that affect diffusion coefficient, D

Diffusion Time, t -Physical time between gradients used to “tag” H2O



Size of Compartment(s)- If we set a limit for r, then we observe an apparent diffusion coefficient, ADC


Physical Compartment Size

Expected Compartment Size


Tortuosity of the Compartments- More tortuous paths look like slow diffusion


Tortuosity

Actual Path

Expected Path


Viscosity and Temperature


Diffusion Coefficient (rate of motion) Temperature

Viscosity

Pure H2O CSF Infection (WBCs) Lymphoma


-Diffusion Time, t -Physical time between gradients used to “tag” H2O

-Size of Compartment(s)- If we set a limit for r, then we observe an apparent diffusion coefficient, ADC

-Tortuosity of the Compartments- More tortuous paths look like slow diffusion

-Temperature

-Viscosity

*** We can only measure “ADC” because of all the factors that change “D”! ***


Steps in Performing DWI

• DWI (isotropic):– Collect a DWI (b = 1000 or 500 s/mm2) dataset by applying motion probing gradients

in the x, y, and z-direction.• Make sure TE is low and TR is long to increase SNR• For higher resolution scans, use a lower b-value

– Collect a T2w dataset (b = 0 s/mm2)

– Collect a low b-value, flow nulled dataset (b = 50 s/mm2)

– Average DWIs from 3 directions

– Calculate ADC


For b-values < 1000

DWI vs. ADC

• DWI– Images collected during application of a “diffusion sensitizing gradient”

– Contains T1, T2, and ADC effects

– “Restricted diffusion”, long T2, and short T1 all influence DWIs


b = 1000

From: Taouli, Radiology, 2010

b = 750

DWI vs. ADC

• DWI– Influence of T2 in DWIs is known as “T2 shine through”



b = 500 ADC Map

DWI vs. ADC

• ADC– Quantitative

– Calculated from DWI and T2w (b = 0 or low b-value)



DWI vs. ADC

• ADC– Reflects diffusion magnitude

– Eliminates long T2 and short T1 effects



DWI vs. ADC

• DWI– Influence of T2 in DWIs is known as “T2 shine through”



b = 500 ADC Map

Diffusion Tensor Imaging (DTI)

Isotropic Diffusion Anisotropic Diffusion

From: Ellingson, Concepts in MR, 2008




Directional Encoding

6 directions (min) 15 directions

25 directions 41 directions



The Diffusion Tensor:



Isotropic Diffusion

1 = 2 = 3

Anisotropic Diffusion

1 > 2, 3

From Ellingson, Concepts in MR, 2008

Fractional Anisotropy (FA)

Isotropic Anisotropic

FA = 0 FA = 1


DTI Tractography

• In the CNS and MSK, lADC is parallel to axon orientation


DTI Tractography

• In the CNS, lADC is parallel to axon orientation


DTI Tractography

• In the MSK, lADC is parallel to muscle fiber orientation

QuickTime™ and a decompressor

are needed to see this picture.

From: University of Rochester


DTI Tractography

• In the heart, lADC is also parallel to muscle fiber orientation

From: University of Oxford






From: Eindhoven University of Technology

DTI Tractography

• Spinal Cord Injury


From Ellingson, Neurosurgery:Spine, 2010

Steps in Performing DTI

• DTI (6 directions):– Collect a DWI (b = 1000 or 500 s/mm2) along 6 non-collinear directions

– Collect a T2w dataset (b = 0 s/mm2)

– Calculate Diffusion Tensor:

• Calculate D in 6 different directions

• Set up the encoding matrix

• Define Tensors

• Solve Tensor Equations


Applications of Diffusion MRIin the Abdomen


Diffusion MR Imagingof the Liver




• Common pulse sequences– Single-shot spin-echo (SE) echoplanar with fat saturation

• With breathhold (20-30 seconds; sensitivity for lesion detection = 84.3%Parikh, 2008)– Need thicker slices (8-10 mm) for good SNR and good liver coverage

• Resp. gated (3-6 min; sensitivity for lesion detection = 93.7%Parikh, 2008)– Thinner slices can be used (5 mm)

– Better image quality, SNR and ADC quantificationTaouli, 2009







• Common b-values– b = 0 image (no diffusion weighting…essentially a “poor man’s” T2w image)







• Common b-values– b = 0 image (baseline with no diffusion weighting…essentially a “poor man’s” T2w

image

– Low b-value (b < 150 s/mm2) “Flow Nulled”• Nulls the intrahepatic vascular signal

• Allows for better detection of focal liver lesions(van den Bos, 2008; Parikh, 2008; Okada, 1998; Hussain, 2005)

~2% change in ADC







• Common b-values– b = 0 image (baseline with no diffusion weighting…essentially a “poor man’s” T2w

image

– Low b-value (b < 150 s/mm2) “Flow Nulled”• Nulls the intrahepatic vascular signal

• Allows for better detection of focal liver lesions(van den Bos, 2008; Parikh, 2008; Okada, 1998; Hussain, 2005)

– High b-value (500 < b < 1000 s/mm2)• Useful for focal liver lesion characterization (Taouli, 2003; Kim, 1999)



• Visual liver lesion characterization with DWI






b = 500 ADC

From: Xu, J Comput Assist Tomogr, 2010




From: Xu, J Comput Assist Tomogr, 2010

- DWI has higher specificity than CE



From: Colagrande, Radiol Med, 2006

Cirrhotic Liver -- ADCLiver Cysts -- ADCAngioma -- ADCFNH -- ADCHepatocarcimoma -- ADC (mixed results)Metastasis -- ADC (mixed results)

Diffusion MR Imagingof the Kidneys


Directionality -- DTI?



Directionality -- DTI?

From: Kido, Acta Radiol, 2010

Fractional Anisotropy (DTI)



From: Colagrande, Radiol Med, 2006

b = 0

b = 500

ADC

From: Kido, Acta Radiol, 2010

From: Kilickesmez, J Comput Assist Tomogr, 2009



Renal Fibrosis

Animal Model -- From: Togao, Radiology, 2010



Renal Cell Carcinoma


Contrast-Enhanced T1 b = 1000 ADC

Summary• Diffusion MRI is an MR technique that can quantify the magnitude of H20

diffusivity within tissues– Microstructural information

• ADC calculated from diffusion MR images is influenced by: – Cellularity– Tissue viscosity and temperature– Diffusion Time– Compartment Size (cell size and shape)– Tortuosity of environment

• DTI is useful for directionality of diffusion restrictions– CNS, MSK, Kidney

• DWI/ADC maps can be used to characterize many pathologies of the abdomen– Liver and Kidney pathologies are most common abdominal diffusion MR studies


diffusion physics

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radiological sciences

apparent diffusion coefficient

level of diffusion weightingb

diffusion physics h2o

ddiffusion time

t physical time

dsize of compartments

h2osize of compartments