Profs. Brooks and DiMarzio Northeastern University Spring 2004

1 / 26

# Profs. Brooks and DiMarzio Northeastern University Spring 2004 - PowerPoint PPT Presentation

ECEU692 Subsurface Imaging Course Notes Part 12: Imaging with Light (4): Diffusive Optical Tomography. Profs. Brooks and DiMarzio Northeastern University Spring 2004. Topic Outline. Goal: “Find the Matrix Elements” A Bit of Radiometry Terminology and Units Radiative Transport

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## PowerPoint Slideshow about ' Profs. Brooks and DiMarzio Northeastern University Spring 2004' - urbain

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

### ECEU692Subsurface ImagingCourse NotesPart 12: Imaging with Light (4):Diffusive Optical Tomography

Profs. Brooks and DiMarzio

Northeastern University

Spring 2004

Chuck DiMarzio, Northeastern University

Topic Outline
• Goal: “Find the Matrix Elements”
• Terminology and Units
• Approximation to Radiative Transport Equation
• Diffusion Approximation
• Wave Solution
• Generating the Diffusive Waves
• Examples
• Solving for the Matrix Elements

Chuck DiMarzio, Northeastern University

P

P

t

t

The Matrix Elements

DC

AC Amplitude

AC Phase

Chuck DiMarzio, Northeastern University

Chuck DiMarzio, Northeastern University

M, Flux/Proj. Area

Notes: Spectral x=dx/dn or dx/dl: Add subscript n or w, divide units by Hz or mm.

F, Flux

Watts

Luminous Flux

Lumens

Watts/m2

Luminous Exitance

Lumens/m2=Lux

1 W is 683 L at 555 nm.

Watts/m2/sr

Luminance

Lumens/m2/sr

1 Lambert=

(1L/cm2/sr)/p

I, Flux/W

L,Flux/AW

Watts/sr

Luminous Intensity

Lumens/sr

E, Flux/Area Rcd.

Watts/m2

Illuminance

Lumens/m2=Lux

1 ftLambert= (1L/ft2/sr)/p

1mLambert= (1L/m2/sr)/p

1 Ft Candle=1L/ft2

1 Candela=1cd=1L/sr

Chuck DiMarzio, Northeastern University

L+dL

dW

dW

L

ds

Chuck DiMarzio, Northeastern University

Solutions to RTE
• Monte-Carlo
• Low Scattering
• High Scattering
• Diffusion Approximation
• Usually Valid in Tissue, Except...
• Certain Tissue Types
• Certain Imaging Modalities (eg. Confocal, OCT)
• Close to Source or to Rapid Changes in Parameters

Chuck DiMarzio, Northeastern University

Resolution Limits (M-C)

Tissue Parameters

ma = 0.03 /cm

ms = 200 /cm

g = 0.95

d = 1 cm

• Approach
• Monte-Carlo
• Reciprocity
• Fourier Transform
• Parameters
• Depth 1 cm.
• Thickness 2 cm.
• Transillumination

MTF

125

150

200-ps Gate

Spatial Frequency, /cm

Dunn, Andrew, and Charles A. DiMarzio, “Efficient Computation of Time--Resolved Transfer Functions for Imaging in Turbid Media,” Journal of the Optical Society of America A 13, No. 1, January 1996. Pp. 65--70.

Chuck DiMarzio, Northeastern University

Photon Diffusion Approximation
• Taylor Series: f is Fluence Rate, J is Flux
• Result

Chuck DiMarzio, Northeastern University

Fluence Rate?
• Fluence is Energy/Area
• Fluence Rate is Energy/Area/Time
• =Power/Area
• Units Like E or M, but Different Meaning
• Relation to Absorbed Power/Volume
• A=fma
• Used to Determine f in Monte-Carlo

Chuck DiMarzio, Northeastern University

F

(

)

Ñ

·

D

Ñ

F

-

-

a

F

=

0

Dispersion Equation
• The Diffusion Equation
• Wave Solution

t

k

• k2

Im

=0

Re

Chuck DiMarzio, Northeastern University

Dispersion Results

Chuck DiMarzio, Northeastern University

Spherical Waves

Chuck DiMarzio, Northeastern University

8

10

Light

(Real)

6

10

-1

4

10

DPDW

Sound

), Wavenumber, m

(Imag)

(Imag)

2

10

p

(Real)

0

k/(2

10

-2

10

-4

10

0

5

10

15

20

10

10

10

10

10

f, Frequency, Hz.

Different Types of Waves

1mm

1mm

1m

1km

10059_1

Chuck DiMarzio, Northeastern University

Physical Reason for Dispersion

Imaginary part

of k increases

with frequency

Easy to understand in terms of multiple paths.

m100574a.m

Chuck DiMarzio, Northeastern University

20 Photon Tracks

20,000 Photon Tracks

Pabs=0.1

Pext=0.3

Watch the Photons Migrate!

90

80

70

60

Photons in Box

50

40

30

20

10

0

0

20

40

60

80

100

Time Step

Chuck DiMarzio, Northeastern University

How Diffuisve Waves Begin?

Tissue

Extrapolated

Boundary

• Generation
• From Light Wave
• Wave Behavior
• Absorption
• Reflection
• Refraction
• Diffraction
• Interference
• Scattering

Detector

Image

Source

Image

Source

Effective

Source

Input

Chuck DiMarzio, Northeastern University

Noise Issues

Noise proportional

to square root of

DC signal.

m100574a.m

Chuck DiMarzio, Northeastern University

DOT Instrumentation at MGH Imaging Center
• TECHNOLOGY
• Near-infrared light
• Fiber optics
• Computed Tomography
• Optical contrast
• Portable - bedside, ambulance
• Continuous
• Inexpensive
• Resolution
• Depth penetration

From David A. Boas - MGH NMR Center

Chuck DiMarzio, Northeastern University

Detectors

Sources

Functional Imaging of a Neonate

6 cm

Mid-line

4 cm

Passive movement of

right arm

Passive movement of

right arm

At Rest

Data Set I - 98-05-14

From David A. Boas - MGH NMR Center

Chuck DiMarzio, Northeastern University

0

-1

Z axis

-2

-3

-4

6

-5

5

4

6

3

5

2

4

3

1

2

1

0

0

X axis

Y axis

0.15

0

-1

0.1

0.05

-2

0

0

0.14

-3

0.05

0.12

0.04

-1

-1

-4

Reconstruction with

Reflection only

(Top Sources)

0.1

-5

0

0.03

-2

-2

0

2

4

6

0.08

-3

-3

0.06

0.02

0.04

-4

-4

Reflection and

Transmission

(All Sources)

0.01

0.02

-5

-5

0

1

2

3

4

5

6

0

0

1

2

3

4

5

6

Keeping the Matrix Rank Up

Source

z

y=4

Detector

Object

x

• DiMarzio, et. al., Presented at Photonics West, Jan 1999

Chuck DiMarzio, Northeastern University

API Virtual Source

Ultrasound

Beam

Optical

Source

Optical

Source

Optical

Source

Optical

Optical

Optical

Ultrasound

Focal Point

Light from Source to Receiver through Ultrasound Focus

All Light from

Source Fiber

Chuck DiMarzio, Northeastern University

Solving the Wave Equation (1)

Chuck DiMarzio, Northeastern University

Solving the Wave Equation (2)

Chuck DiMarzio, Northeastern University

The First Born Approximation

Chuck DiMarzio, Northeastern University

Why Do We Want a Model?
• Applications
• Forward Model
• Will it work?
• Inverse Algorithms
• How Much Does k Change?
• ie. Is there a Tumor?
• And Where?
• Understanding
• What is k?
• See Panel to Right.

Chuck DiMarzio, Northeastern University