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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
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Acknowledgements
• National Institutes of Health (NIH)–R21-HL67387–R21-DK63692–R41-CA96102–R41-NS050007–R43-NS49734
• U.S. Army–DAMD017-03-C-0018
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Enhanced CW DOT Images
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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
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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
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Spatial Deconvolution Approach
=
Medium Image
Deconvolution operator, or Filter
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Spatial Deconvolution Result
Reconstruction time 10-2 s
Deconvolution time 10-3 s
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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
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Complex Heterogeneous “Cylinder”
Scalp
Skull
Muscle
CSF
Gray Matter
White Matter
Source/Detector
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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
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No Mismatch Overestimated CSF Optical Coefficients
Recovered Images
Underestimated CSF Optical Coefficients
Overestimated CSF Optical Coefficients
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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
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What if We Don’t Have an MRI?
(I)
(II)
MRI
Homogeneous Medium
+
Baseline Data (Mean)
Reconstruct Update
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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
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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
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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