DWI and ADC map

Diagnostic Imaging Practice in the Oral and Maxillofacial Region

H.Nishiyama / Div. of Oral and Maxillofacial Radiology; Niigata-univ.

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• Possibility of understanding

the condition of soft tissue

• To image the tissue water

• Amount of water

• Water status

• Tissue structure

• Micro circulation

• Metabolism

• Molecular imaging

• etc…

State and dynamics of water observable by MRI

Proton Density

Water Diffusion

direction and amount

Perfusion

T2WI

DWI

T2 map

T1WI

FLAIR

T2 value T1 value

ADC map

MRS

Body circulation

Arteriovenous

MRA

MTC

Proton exchange

CEST, APT

T1ρ

UTE

IVIM, QSI, DKI

Imaging other than

(water) proton

Functional MRI

Fat

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About flow imaging of MRI • blood flow

• Flow of relatively thick blood vessels

• Mainly displayed by MRA (MR Angiography)

• perfusion • Peripheral circulation (capillary blood flow)

• Images are treated as a model combining multiple compartments, such as the arterial system, the venous system, and the capillary system.

• diffusion • Physical definition: A phenomenon in which energy and

matter flow from high concentration to low concentration, leading to a uniform steady state.

• In the case of water molecules, random molecular motion (thermal motion). However, due to the structure of the tissue, the degree or direction of movement is suppressed.

• In diffusion-weighted images, factors of perfusion in voxels are included. → IVIM (intra voxel incoherent motion)

Fast

Slow

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Imaging of "flow" (Diffusion and perfusion)

• Perfusion • It is used for evaluation of peripheral circulation including

exchange between microcirculation such as capillary system and interstitial fluid.

• There are three compartment models of inflow system, tissue system and outflow system, and more complicated models.

• Diffusion • Movement of water molecules along internal structures (eg, fiber

side). Brown movement etc.

• In the nervous system including the cerebrospinal cord, the direction of dispersion may be tracked with a tensor (a set of three-dimensional vectors with directionality) in order to see the relationship with the pathological condition.

• An imaging method called DWIBS renders the lesion of the trunk in 3D as if it were FDG-PET. However, the signal strength is affected by the T2 value, and needs to be confirmed in a reference image called an ADC (apparent diffusion coefficient) map.

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Diffusion basics • Inter-diffusion coefficient

• Diffusion coefficient when molecules in the fluid diffuse while exchanging positions with different kinds of molecules

• Self diffusion coefficient • Diffusion coefficient in case of

diffusion while exchanging position with homogeneous molecule

• Water molecules in MRI • Water molecules with

positional information are mixed with surrounding water molecules.

x

** Steady state diffusion

𝐽 = −𝐷𝜕𝐶(𝑥,𝑡)

𝜕𝑥 --- Fick’s first law

J: Diffuse flux, an amount of a property that passes

through a unit area per unit time.

D: Diffusion coefficient

Diffusion flux at any position is proportional to

concentration gradient.

** Non steady state diffusion 𝜕𝐶(𝑥,𝑡)

𝜕𝑡= 𝐷

𝜕2𝐶(𝑥,𝑡)

𝜕𝑥2 --- Fick’s second law

There are several solutions depending on the initial

conditions and the boundary conditions.

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S(b=0) image of SE sequence※

T2 weighted image itself

ω0

ω0-β

ω0+α

180°

ω0

ω0-β

ω0+α ω0-β

ω0+α

※ Usually, high-speed imaging such as EPI or SSFSE is used, but the principle can be sufficiently explained by the SE method

When α/γ and -β/γ are regarded as ±Blocal

RF plus

90° 180° Echo signal TE/2 TE/2

B0±Blocal B0±Blocal

Dispersion of phase due to local

magnetic field inhomogeneity

Phase convergence with 180°

reverse pulse

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Stejskal Tanner Method※

Influence of the static spin

※Stejskal EO, Tanner JE: Spin diffusion measurements: spin echoes in the

presence if a time dependent field gradient. J Chem Phys 42: 228-292, 1965.

δ Δ δ

G

MPG MPG

RF plus

90° 180° Echo signal TE/2 TE/2

+MPG +MPG

b=γ2G2δ2(Δ-δ/3)

B0±Blocal B0±Blocal

＋

Add to dispersion

＋

Add to convergence

Dispersion of phase due to local

magnetic field inhomogeneity

Phase convergence with 180°

reverse pulse

A set of MPG pulses both only temporarily

speed up the dispersion and convergence

of the stationary spin phase. Therefore,

theoretically, the echo signal itself is not

affected. It converges with a 180 degree

pulse because it is equivalent to the static

local magnetic field in T2 / T2 * relaxation.

MPG: Motion Probing Gradient

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MPG (gradient magnetic field) first half

(static spin)

Center of the gradient field.

Center of phase dispersion.

Larmor precession is early.

Phase dispersion in the

positive direction.

Larmor precession is early.

Phase dispersion in the

negative direction.

B2 B0

B3

＋ －

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Static spin after 180 degree pulse

Inverted 180 degrees

without phase dispersion.

Inverted 180 degrees with

phase dispersed in the

positive direction.

Inverted 180 degrees with

phase dispersed in the

negative direction.

B0

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MPG (gradient magnetic field) latter half

(static spin)

Center of the gradient field.

Center of phase dispersion.

Movement of the phase by

dispersion and convergence

matches.

Larmor precession is early.

The phase converges in the

positive direction.

Movement of the phase by

dispersion and convergence

matches.

Larmor precession is early.

The phase converges in the

negative direction.

Movement of the phase by

dispersion and convergence

matches.

B2 B0

B3

＋ －

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The phases are aligned

High signal (T2 weighted image itself)

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Stejskal Tanner Method※

Influence of the moving spin

δ Δ δ

G

MPG MPG

※Stejskal EO, Tanner JE: Spin diffusion measurements: spin echoes in the

presence if a time dependent field gradient. J Chem Phys 42: 228-292, 1965.

RF plus

90° 180° Echo signal TE/2 TE/2

+MPG +MPG

One set of MPG pulses provides irreversible

dispersion to the phase of moving spins and

degrades the echo signal. As MPG

becomes stronger, the degree of phase

dispersion due to diffusion becomes

stronger. A relatively strong signal is emitted

from the weak diffusion area.

Dispersion of

phase by diffusion

B0±Blocal

B0±Blocal

b=γ2G2δ2(Δ-δ/3)

Dispersion of phase due to local

magnetic field inhomogeneity

Phase convergence with 180°

reverse pulse

MPG: Motion Probing Gradient

Rabbit and turtle omitted

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MPG (gradient magnetic field) first half

(moving spin)

B2 B0

B3

For ease of understanding, it does not move until before 180 pulse application.

＋ －

Center of the gradient field.

Center of phase dispersion.

Larmor precession is early.

Phase dispersion in the

positive direction.

Larmor precession is early.

Phase dispersion in the

negative direction.

Rabbit and turtle omitted

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Moving spin after 180 degree pulse

B0

Rabbit and turtle omitted

Inverted 180 degrees

without phase dispersion.

Inverted 180 degrees with

phase dispersed in the

positive direction.

Inverted 180 degrees with

phase dispersed in the

negative direction.

For ease of understanding, it does not move until before 180 pulse application.

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MPG (gradient magnetic field) latter half

(moving spin)

Molecular motion Molecular motion Molecular motion

B0

Rabbit and turtle omitted

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MPG (gradient magnetic field) latter half

(moving spin)

B2 B0

B3

Center of the gradient field.

The phase was supposed to

converge, but not in the

original place, so it could not

converge.

Larmor precession is early.

The phase was supposed to

converge in the positive

direction, but not in the

original place, so it could not

converge.

Larmor precession is early.

The phase was supposed to

converge in the negative

direction, but not in the

original place, so it could not

converge.

＋ －

Rabbit and turtle omitted

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The phases are not aligned

Low signal (the degree of diffusion changes the signal strength)

Since the magnetization vectors in the horizontal plane in the

voxel are combined to take out a signal as a macroscopic

magnetization vector, they are influenced by the proton

density and the T2 value (T2 relaxation rate).

Rabbit and turtle omitted

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Equation of spin echo

and diffusion weighted images

2TTEePDkSI

DbTTETTR eeePDkSI 21/1 DbTTE eePDkSI 2

21/1 TTETTR eePDkSI

Signal strength equation in spin echo method Ideal equation for a T2-weighted

Equation including

diffusion term

b = 0 (does not emphasize diffusion)

or D = 0 (zero diffusion)

e-bD→1

TR→∞

TR→∞

（1-e-TR/T1）→1

（1-e-TR/T1）→1 Diffusion-weighted equation in spin echo method Equation of

T2-weighted X diffusion-weighted

Equation including

diffusion term

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b value and apparent diffusion coefficient:

relationship with ADC and signal strength

• b=γ2G2δ2(Δ-δ/3) • unit：s/mm2

• γ： Magnetic rotation ratio (MHz)

• G：MPG strength (mT/m)

• δ：MPG application time (msec)

• Δ：Pair of MPG intervals (msec)

• τd=(Δ-δ/3)： diffusion time

• MPG（motion probing gradient）pulse： Gradient magnetic field pulse • In the NMR, PFG（Pulsed-field Gradient）

• Signal strength when MPG is not applied ：S(0)

• Signal strength when applying MPG ：S(b)

• D：Here same as ADC

FFSS DbSDbSbS

b

SbSD

DbSbS

DbSbS

exp0exp0

lchangeexponentiabi

0ln

0ln

exp0

lchangeexponentiamono

b (s/mm2)

ln(Sb/S0)

0

-4 0 6000

mono-

exponential

change (ideal)

bi-

exponential

change

δ Δ δ

G

MPG MPG

The value of D is estimated by changing the

b-value and shooting multiple times.

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0

1

2

3

4 20

40

60

80

100

0

50

100

150

200

250

300

350

400

SI

D[x10 -3mm 2

/sec] T2[msec

]

SI=k×PD×exp(-TE/T2)×exp(-bD)

b=1000sec/mm2, TE=100msecPD=1000, k=1, (TR→∞)

0-50 50-100

100-150 150-200

200-250 250-300

300-350 350-400

Hard to diffuse water molecules

At D = 0 (zero diffusion), the T2

weighted image itself

Easy to diffuse water

→ low signal T2 decay

Fast (low signal)

T2 decay

Slow (high signal)

Influence on signal strength when

D is changed from 0 to 4 and T2

is changed from 20 to 100

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b=1000, DWI T2= 25 50 75 100

D=

0.5

1.0

1.5

2.0

b=0, T2WI T2= 25 50 75 100

D=

0.5

1.0

1.5

2.0

DbT

TE

eePDkSI

2

Hard to diffuse

water molecules

high signal

Easy to diffuse

water molecules

low signal Affected not only by diffusion but

also by T2 weighted images

b or D is zero, then e-bD=1

And T2 weighted image itself

When TR can be considered infinite

T2 decay

Fast

T2 decay

Slow

T2 decay

Fast

T2 decay

Slow

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b=1000, DWI T2= 25 50 75 100

D=

0.5

1.0

1.5

2.0

b=0, T2WI T2= 25 50 75 100

D=

0.5

1.0

1.5

2.0

D=

0.5

1.0

1.5

2.0

T2= 25 50 75 100 ADC map (shows ADC high value as high signal)

Distribution of "apparent diffusion coefficient"

D=

0.5

1.0

1.5

2.0

T2= 25 50 75 100 Inverted ADC map.

Easy to understand in terms of signal strength

ADC is a value that

eliminates the effects

of T2 relaxation.

Sometimes we use

Exponential ADC image.

Si = exp(-ADC) Emphasize small ADC values.

Signal strength of three images

is related by multiplication and

division

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参考図書・参考資料 • 青木茂樹、阿部 修、増谷佳孝 編集：「新版これで

わかる拡散MRI」、秀潤社、2005年10月1日、第2版

• 荒木 力：「拡散MRI」 ブラウン運動、拡散テンソルからq空間へ、秀潤社、2006年8月31日、第1版

• 日本電子株式会社(www.jeol.co.jp) • PFG-NMR法による拡散測定を始める時のために (独)

産業技術総合研究所 早水紀久子 • 定期刊行物・日本電子 news（日本語版）

https://m.jeol.co.jp/publication/ バックナンバー https://m.jeol.co.jp/publication/ja/ Vol.38, 2006

• 「PFG-NMR 法による拡散現象測定の手引書 (第三版) 」 • NMRによる拡散測定と電解質のイオン拡散現象観測

http://diffusion-nmr.jp/ http://diffusion-nmr.jp/wordpress/wp-content/uploads/2014/07/a0884a65911fac1bf006ddac937e4bff.pdf

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参考資料

• MRIの基本 パワーテキスト第2版―基礎理論から最新撮像法まで、 Ray H. Hashemi (原著), Christopher J. Lisanti (原著), William G.,Jr. Bradley (原著),メディカル・サイエンス・インターナショナル、6,500円（税別）

• MRI「超」講義―Q&Aで学ぶ原理と臨床応用、 Allen D. Elster (原著), Jonathan H. Burdette (原著)、メディカル・サイエンス・インターナショナル、5,800円（税別）

• MRIデータブック、MEDICAL VIEW、6,000円（税別）

• NMRハンドブック 、Ray Freeman (著)、共立出版、8,400円

• パルスおよびフーリェ変換NMR―理論および方法への入門 (現代科学)、Thomas C. Farrar (著), Edwin D. Becker (著)、吉岡書店

• 生体系の水、上平 恒 、 逢坂 昭 (著) 、講談社

• 細胞の中の水、パスカル マントレ (著), 辻 繁, 落合 正宏, 中西 節子, 大岡 忠一 (翻訳) 、東京大学出版会、5,200円（税別）

• MRI応用自在（第３版）、高原太郎（監修）、高橋光幸、堀江朋彦、中村理宣、北川 久（編集）、MedicalView、7,500円（税別）