Spatial Deconvolution of 3-D Diffuse Spatial Deconvolution of 3-D Diffuse Optical Tomographic Time Series: Optical Tomographic Time Series:

Influence of Background Medium Influence of Background Medium HeterogeneityHeterogeneity

Spatial Deconvolution of 3-D Diffuse Spatial Deconvolution of 3-D Diffuse Optical Tomographic Time Series: Optical Tomographic Time Series:

Influence of Background Medium Influence of Background Medium HeterogeneityHeterogeneity

Y. Xu, H. L. Graber, R. L. Barbour

SUNY Downstate Medical Center

Acknowledgements

• National Institutes of Health (NIH)–R21-HL67387–R21-DK63692–R41-CA96102–R41-NS050007–R43-NS49734

• U.S. Army–DAMD017-03-C-0018

Enhanced CW DOT Images

Origin of Low Resolution in DOT?

Medium Image

Reconstruction

1,

m

a D 2

,m

a D

,m

a ND

1,

r

a D 2

,r

a D

,r

a ND

ImageMedium

Reconstruction Filter

1,

m

a D 2

,m

a D

,m

a ND

1,

r

a D 2

,r

a D

,r

a ND

Spatial Deconvolution Approach

μa(t)1, D(t)1

μa(t)2, D(t)2

μa(r), D(r)t = t0+Δt: R(r) ,a Dr r

μa(r), D(r)t = t0:

Medium

R(r)

Detector Data

,a Dr r

Image

μa(r), D(r)t = t0+2Δt: R(r) ,a Dr r

μa(r), D(r)t = t0+3Δt: R(r) ,a Dr r

Spatial Deconvolution Approach

=

Medium Image

Deconvolution operator, or Filter

Spatial Deconvolution Result

Reconstruction time 10-2 s

Deconvolution time 10-3 s

Structural MRI-based Heterogeneity

32 64 96 128 160 192 224

32

64

96

128

160

192

224

256

Scalp

Skull

M. Temporalis

White Matter

CSFGray Matter

Complex Heterogeneous “Cylinder”

Scalp

Skull

Muscle

CSF

Gray Matter

White Matter

Source/Detector

Contrast

Static

Tumor: μa = 0.24 cm-1, μ′s = 10 cm-1

CSF: μa = 0.08 cm-1, μ′s = 10 cm-1

Scalp, Skull, Muscle, White matter:

μa = 0.08 cm-1, μ′s = 10 cm-1 (D = 0.0331 cm)

Static

Tumor: μa = 0.24 cm-1, μ′s = 10 cm-1

CSF: μa = 0.08 cm-1, μ′s = 10 cm-1;

μa = 0.04 cm-1, μ′s = 5 cm-1;

μa = 0.01 cm-1, μ′s = 1 cm-1;

μa = 0.005 cm-1, μ′s = 0.5 cm-1

Dynamic

Tumor: f = 0.06 Hz, m = 20%

Gray matter: f1 = 0.1 Hz, m = 10%; f2 = 1.0 Hz, m = 2%

gray matter

inclusion

Static

Tumor: μa = 0.24 cm-1, μ′s = 10 cm-1

CSF: μa = 0.08 cm-1, μ′s = 10 cm-1;

μa = 0.04 cm-1, μ′s = 5 cm-1

Static

Tumor: μa = 0.24 cm-1, μ′s = 10 cm-1

CSF: μa = 0.08 cm-1, μ′s = 10 cm-1;

μa = 0.04 cm-1, μ′s = 5 cm-1;

μa = 0.01 cm-1, μ′s = 1 cm-1

No Mismatch Overestimated CSF Optical Coefficients

Recovered Images

Underestimated CSF Optical Coefficients

Overestimated CSF Optical Coefficients

Impact of Noise in Data

Target Medium

Noise Level 1:

1% – 10%

Noise Level 2:

2% – 20%

Noise Level 3:

3% – 30%

Deconvolved Image (No Mismatch)

Deconvolution + Temporal LPF

Deconvolution + Temporal LPF +

Spatial LPF

What if We Don’t Have an MRI?

(I)

(II)

MRI

Homogeneous Medium

+

Baseline Data (Mean)

Reconstruct Update

What if We Don’t Have an MRI?

 Spatial Correlation

- +

  Homog.Recursive

UpdateMRI Homog.

RecursiveUpdate

MRI

Case 1 0.339 0.371 0.353 0.541 0.462 0.511

Case 2 0.345 0.379 0.363 0.498 0.485 0.527

Case 3 0.333 0.382 0.368 0.154 0.499 0.554

Case 4 0.324 0.381 0.368 0.021 0.480 0.549

 Temporal Correlation

- +

  Homog.Recursive

UpdateMRI Homog.

RecursiveUpdate

MRI

Case 1 0.938 0.948 0.958 0.961 0.925 0.980

Case 2 0.939 0.947 0.958 0.966 0.931 0.986

Case 3 0.909 0.917 0.934 -0.503 0.920 0.984

Case 4 0.849 0.870 0.891 -0.677 0.571 0.928

Conclusions

• Complex medium heterogeneity can have the effect of increasing the spatial and temporal accuracy of deconvolved reconstructed images

• Effect of errors in estimates of background optical coefficient values depends on the direction of the error– Overestimating the optical coefficients produces

image quality degradation– Underestimating them has minimal, or even

beneficial, effects

Conclusions

• Two effective methods for increasing confidence in accuracy of deconvolved images– Use structural images to design reference media– Use one nonlinear image reconstruction sequence to

produce a heterogeneous reference medium