diffusion physics - thermal agitation - in steady state, the motion of water is dominated by thermal...

Diffusion Physics - Thermal Agitation

- In steady state, the motion of water is dominated by thermal agitation.

-This causes “random” motion of water within a compartment.

Diffusion Physics - Thermal Agitation

-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:

Detecting Diffusion with MRI - Intravoxel Incoherent Motion

From Ellingson, Concepts in MR, 2008

Detecting Diffusion with MRI - Intravoxel Incoherent Motion

Detected DWI Signal

MRI Signal w/o Diffusion Sensitivity

Phase of “Tagged” H2O Function of Diffusion Gradients

Diffusion Coefficient

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

-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”! ***

Diffusion Tensor Imaging (DTI)• Diffusion anisotropy can occur when compartments are not symmetric

• Diffusion may be higher in different directions

• To determine diffusion anisotropy, we use Diffusion Tensor Imaging (DTI)

• DTI uses diffusion sensitizing gradients to determine ADC in different directions

• From these measurements we construct the mathematical tensor

• In this way, DTI more accurately models the geometry of tissues

Isotropic Diffusion Anisotropic Diffusion

Diffusion Tensor Imaging (DTI)The Diffusion Tensor:

Isotropic Diffusion

1 = 2 = 3

Anisotropic Diffusion

1 > 2, 3


Davidoff, A., Handbook of the Spinal Cord

• MR constraints largely limit ADC measurement to the extracellular compartment.

• Diffusion in the spinal cord is highly anisotropic for both gray matter and white matter

Diffusion MR Characteristics of theCentral Nervous System

From A.Todd, Univ. GlascowFrom Ellingson, Concepts in MR, 2008

• Transverse ADC (tADC) is dependent on (Schwartz, 2005)

Axon Counts = tADC Extracellular Volume = tADC Myelin Volume = tADC

• Longitudinal ADC (lADC) is dependent on (Song, 2003; 2002; Sun, 2006; Ellingson, 2008)

– Structural and Functional Integrity of Axons

– Microfilament & Neurofilament Density

– Axonal Transport System Integrity



DTI Tractography

• In the CNS, lADC > tADC & 1 is parallel to axon orientation

• ADC is consistent across pulse sequences (Ellingson, AJNR, 2008)

Ellingson, 2008


• Anisotropy is preserved across surrogates (Ellingson, Concepts in MR, 2008)


• ADC changes across the length of the spinal cord (Ellingson, AJNR, 2008; Ellingson, JMRI, 2008)

Human

Rat

Rostral Caudal

Pathology & DTI in Spinal Trauma

Pathology of Acute SCI• Mechanical Injury:

– Stretching and tearing of axons immediate death of all damaged cells.

• Hypoxia and Ischemia:

– Blood flow to injury is restricted.

– Anaerobic metabolic processes in viable tissue, other tissues become necrotic.

• Hemorrhage & Vasogenic Edema:

– In contusion injury, hemorrhages start in central gray matter and spread radially.

– Early vasogenic edema forms due to blood constituents leaving vasculature.

• Damage to Axon Transport Systems:

– Microtubules and neurofilaments begin to degrade.

Normal Mechanical Injury

Vasogenic Edema


DTI in Acute SCI• Mechanical Injury:

– Overall ADC at lesion site due to lack of boundaries to diffusion

• Hypoxia and Ischemia:

– Cause ADC

• Hemorrhage & Edema:

– Causes ADC at lesion site due to lack of boundaries to diffusion

• Damage to Axon Transport Systems:

– Causes lADC

Rat - Ex Vivo

(Ellingson, JMRI, 2008b)

lADCtADC


Pathology of Subacute SCI• Reactive Cells:

– Active microglia increase in density

– Active Astrocytes hypertropy and line the cavity wall

• Anterograde and Retrograde Degeneration:

– Axons form retraction bulbs at proximal ends

– Demyelination occurs

– Proximal axons begin to swell

– Distal axons are dissolved

• Gray Matter Morphological Changes:

– Damaged axon nuclei move to eccentric locations within the cell body.

– Neurons begin to hypotrophy and dendrites retract

• Cytotoxic Edema– Axons and soma swell, the

extracellular space decreases

Normal Reactive Cells

Cytotoxic Edema


DTI in Subacute SCI• Reactive Cells:

– Glial scar changes 1 orientation

(Schwartz, 2005)

– High density microglia ADC

– Tortuosity from activated astrocytes causes ADC

• Anterograde and Retrograde Degeneration:

– tADC during demyelination

– lADC due to axon transport damage

– ADC due to axon swelling

• Gray Matter Morphological Changes:

• Vasogenic Edema

– Axons and soma swell, the extracellular space decreases

– This causes ADC

Rat - Ex Vivo


lADCtADC


Pathology of Chronic SCI• Long-term Axon Degeneration

– Progressive demyelination

– Loss of large diameter axons

– Widespread spreading of cysts

– Retrograde & Transneuronal degeneration damages whole spinal tracts

• Gray Matter Morphology Changes

– Chromatolysis

– Nuclear Changes

• Spinal Cord Atrophy

Normal Atrophy

+ Axon Loss

Normal MNs Chronic SCI MNsFrom Ellingson, Concepts in MR, 2008

DTI in Chronic SCI

Cavity Formation

Remote Changes

Rat - Ex Vivo


DTI in Chronic SCIRat - Ex Vivo


DTI in Chronic SCIChronic Human SCI

(Ellingson, AJNR, 2008b)

C5 Complete Injury

Rostral-Caudal Asymmetry at Lesion Epicenter

Functional Correlates of DTI

Axonal Damage (Song, 2003; 2002; Nair, 2005; Sun, 2006)

↓ Longitudinal ADC (lADC)

Myelin Damage (Song, 2003; 2002; Nair, 2005; Sun, 2006)

↑ Transverse ADC (tADC)


Normal SCI

No temporalCoherence

Loss ofAmplitude


C-fiber input to LSTT

(Valeriani, 2007; Li, 1991; Latash, 1988)

A-fiber input to MSTT

(Valeriani, 2007; Latash, 1988)

Ellingson, J Neurotrauma, 2008, In Press

Functional Correlates of DTIFrom Ellingson, Biomed Sci Instrum, 2008 & Congress Neurological Surgeons, 2008

Conclusions

• DTI is highly sensitive to the structural integrity of the spinal cord.

• DTI can be used to monitor the progression of SCI from acute through chronic stages

• DTI may also be sensitive to the functional integrity of the spinal cord.

• Future studies will be aimed at determining if DTI can predict long-term functional recovery in incomplete SCI

Thank You• Brian Schmit, Ph.D., Dept. of Biomedical Eng., Marquette University• Shekar Kurpad, M.D., Ph.D., Dept. of Neurosurgery, MCW• John Ulmer, M.D., Dept. of Radiology, MCW• Maria Crowe, Ph.D., Dept. of Neurosurgery, MCW• Kathleen Schmainda, Ph.D., Dept. Radiology & Biophysics, MCW• Kristina Ropella, Ph.D., Dept. Biomed. Eng., Marquette University

• Funding: – NIH R21, Brian Schmit (PI)– Falk Foundation– Marquette University– VA Medical Center, Milwaukee, WI– Bryon Riesch Paralysis Foundation

diffusion physics - thermal agitation - in steady state, the motion of water is dominated by thermal...

Documents

symmetric diffusion

apparent diffusion coefficient

d diffusion time

slow diffusion temperature

spinal trauma slide

axon orientation slide

spinal cord ellingson

surrogates ellingson