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Derivation and Validation of Metrics for Breast Cancer
Diagnosis from Diffuse Optical Tomography Imaging Data
Derivation and Validation of Metrics for Breast Cancer
Diagnosis from Diffuse Optical Tomography Imaging Data
Randall L. Barbour, Ph.D.
SUNY Downstate Medical CenterBrooklyn, New York
2
Corrosion Cast of Tumor Vasculature. ‘tp’, = tumor periphery, ‘st’ = surrounding tissue. (M. Molls and P. Vaupel, Eds. Blood Perfusion and Microenvironment of Human Tumors: Implications for Clinical Radiooncology. Springer-Verlag, New York 2000.)
Corrosion Cast of Tumor Vasculature
3
Basic Features of Tumor Vasculature
• Leaky vessels – Increased interstitial pressure
• Poorly developed vessels– altered/absence of normal control mechanisms
• Relative state of hypoxemia
• Dynamic optical studies should prove sensitive to multiple features of tumor biology.
4
Motivation For Dynamic Studies
• Functional Parameters Associated with Blood Delivery to Tissue– Tissue Oxygen Demand– Vascular Compliance– Autoregulation (e.g., reactive hyperemia)– Autonomic Control (modulation of blood delivery)
– Varying metabolic demand influences tissue-vascular coupling• Response to provocation• Influence of disease• Effects of drugs
– Technical Benefits • Multiple features• High intrinsic contrast• No need for injection
• Why Optical?– Simultaneous assessment of metabolic demand and vascular dynamics.
5
Dual Breast Imaging Result
-4.0E-05
-2.0E-05
0.0E+00
2.0E-05
4.0E-05
6.0E-05
8.0E-05
1.0E-04
1.2E-04
1.4E-04
2500 2550 2600 2650 2700 2750 2800 2850 2900 2950 3000
Imaging Frames
Estim
ate
d
D Hb
red
[m
ol/l]
1 2 3 4 5 6 7
1.5e-8
0
-9.3e-9
2.1e-8
0
-1.2e-8
Left
(tum
or)
1 2 3 4 5 6 7Rig
ht (
heal
thy)
D H
bred
[m
ol/l]
Imaging frames
6
Strategies for Data Analysis
Large dimensional
data sets.
Time Series Measures
Inherently information rich
To Obtain Useful Information: Consider the big picture
7
Dual Breast Imager
Phantom SpheresGantry
withOpening
Fiberoptics
Measuring Cup Adjusters (Tilt, Lift, Pitch/Yaw)
Approx. Breast Positions
8
Instrumentation
11a 11b
10a 10b
9b9a
6b6a
8Power Supply
Motor Controller
(4,5)b(4,5)a
12
11a 11b
10a 10b
9b9a
6b6a
8Power Supply
Motor Controller
(4,5)b(4,5)a
12
6a 6b
(4,5)a (4,5)b
9a 9b12
10a 10b
11a 11b
8
11a 11b
10a 10b
9b9a
6b6a
8Power Supply
Motor Controller
(4,5)b(4,5)a
12
Power Supply
Motor Controller
Detection Unit
Stepper Motor Controller
PC
Fiber optic
s
Measuring Heads
Support rods
Adjustable arcsStrain
reliefes
Steppermotors
Support rods
Adjustable arcsStrain
reliefes
Steppermotors
9
Approach
• Simple Idea:
– Define utility of scalar metrics of amplitude, variance and spatial coordination of low frequency hemodynamics obtained from baseline measures
– Amplitude response to a simple provocation
– Simultaneous Measures: Paired difference
10
Power Spectrum of Hb Signal
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9-3
-2
-1
0
1
2
3
4
5
6x 10
-9
Frequency (Hz)
Gro
up
-ave
rag
e In
ter-
bre
ast A
mp
litu
de
Diff
ere
nce
Spatial Mean Result, Hbtotal
Cancer Healthy
11
Dimension Reduction: Temporal Spatial Averaging
Time
Position (IV)
Spatial map of temporal standard
deviation (SD)
(III)Baseline temporal mean is 0, by
definition
temporal integration
drop position information
sorted parameter value
100
0
Hbdeoxy
Hboxy
(II)
spatial integration
mean SD
scalar quantities
(I)
12
Spatial Temporal Averaging
Time
Position (IV)
spatial integration
(II)
(I)
Time series of spatial mean → O2 demand / metabolic responsiveness
Time series of spatial SD → Spatial heterogeneity
temporal integration
Temporal mean of spatial mean time series: 0, by definition
Temporal SD of spatial mean time series
Temporal mean of spatial SD time series
Temporal SD of spatial SD time series
scalar quantities
13
1. Starting point is reconstructed image time series (IV)
2. Use (complex Morlet) wavelet transform as a time-domain bandpass filter operation
A. Output is an image time series (IV) of amplitude vs. time vs. spatial position, for the frequency band of interest
B. Filtered time series can be obtained for more than one frequency band
3. Recompute previously considered, but starting with the wavelet amplitude time series
Method 2: Time-frequency (wavelet) analysis
time
f1
f2
14
Vasomotor Coordination
Time (s)
FE
M m
esh
no
de
100 200 300 400 500 600 700
0
500
1000
1500
2000
0.5
1
1.5
2
2.5
Time (s)
FE
M m
esh
no
de
100 200 300 400 500 600 700
0
500
1000
1500
2000
0.5
1
1.5
2
2.5
Healthy Breast Tumor Breast
15
Method 3: Provocation Analysis: Healthy Subject
Left breast (blue curve) and right breast (red curve)
17
Scalar Metrics Explored
ExperimentalCondition
Tumor-AssociatedPhenotype
Scalar Metric
Re
sting
Sta
te
Hypoxia
SpatialCoordination
EvokedResponse
Angiogenesis
2
22. , t vt
SSDTSD x t N SMTSD N rr
23. , , v v tt
TMSSD x t x t N N N r rr r
24. , v tt
TSDSM x t N N rr
22
5. , , v v ttTSDSSD x t x t N N TMSSD N r r
r r
2
, , , ,
, , ,
6. 100 , , , ,
where:
, , , (Complex Morlet wavelet decomposition),
(Normalize to unit mean value, in, , , , , ,
the frequency bands of inter
l h t l h l h t l ht t t
l h t l h l ht
SC f N u t f u t f N u t f
x t M t f
U t f N M t f M t f
r r
r r r
, ,
,est)
, , , (Average over the image volume).l h l h vu t f U t f N rr
2
1
2 1 2 1 1 2 2 1 2 17.t
t
A y t y t y t t t y t t y t t t t t
1 21 2
8. max mint t tt t t
R y t y t
21. , t vt
SMTSD x t N N rr
18
Subject Population
Subject Group Breast Pathology Status NAge (yr)
[mean ± SD]BMI (kg-m2)[mean ± SD]
Tumor Size[largest dimension]
Clinical Description
Retrospective
Active CA 14 47.9 ± 12.3 28.7 ± 5.310 ≤ 3 cm4 > 3 cm
10 ductal carcinoma1 ductal & lobular carcinoma
1 mucinous carcinoma1 metastatic CA
1 inflammatory CA
Prior CA 3 50.7 ± 9.4 30.4 ± 0.5 —All had lumpectomies 2-3 yr
prior to NIRS study
Pre-CA 0 — — — —
Non-CA Pathology 11 45.7 ± 5.628.7 ± 5.5
(N = 7)—
3 fibrocystic disease4 breast cyst
1 axillary cyst2 benign breast lumps
1 breast reduction surgery
No Historyof Breast Pathology
9 41.6 ± 10.0 30.3 ± 7.2 — —
19
Subject Population
Prospective
Active CA 14 51.4 ± 10.9 30.4 ± 4.55 ≤ 3 cm9 > 3 cm(a
13 ductal carcinoma1 axillary adenocarcinoma with
mammary duct ectasiaand hyperplasia
Prior CA 4 60.8 ± 9.3 25.5 ± 1.7 —
3 prior ductal carcinoma1 prior mucinous carcinomaAll had lumpectomies 2-6 yr
prior to NIRS study
Pre-CA 4 53.5 ± 3.429.0 ± 4.1
(N = 3)—
2 DCIS1 atypical ductal hyperplasia
1 extremely dense breasts
Non-CA Pathology 6 43.7 ± 8.426.6 ± 4.9
(N = 4)—
1 cystic disease2 fibrocystic changes
1 fibrosis1 benign breast lump
1 breast reduction surgery
No Historyof Breast Pathology
8 44.0 ± 6.8 30.5 ± 8.9 — —
20
Patient Demographics
Age (years) BMI (kg-m-2) n1 Mean SD Range n2 Mean SD Range
(1) Retrospective / Training Group
14 47.9 12.3 29-70 14 28.7 5.3 21.6-43.9 Cancer (CA)
Subjects (2) Prospective / Validation Group
14 51.4 10.9 37-71 14 30.4 4.5 22.7-38.1
(3) Retrospective / Training Group
23 44.7 8.6 26-62 19(b 30.1 6.1 18.4-44.4 Non-CA Subjects (4) Prospective /
Validation Group 22(a 48.7 10.0 30-69 18(b 28.2 6.6 21.2-48.5
p-value(a
Comparison Age BMI
(1) vs. (3) 0.39 0.51 (2) vs. (4) 0.47 0.33 (1) vs. (2) 0.45 0.38 (3) vs. (4) 0.17 0.40
21
Logistic Regression Applied
Metrics
Pro
babi
lity
Metrics calculated and selected based on t-tests & ROC curves
Metrics used as inputs into logistic regression model
Logistic regression model calculates i for each metric (Xi)
Using i, a predicted probability distribution can be created
New patient’s Xi used to generate probability of cancer in patient
X1 = .43; X2 = -.05New Patient’s Values
Linear Model: P(cancer) = 0.75
Logistic Regression: P(cancer) = 0.90
22
Scalar Metrics Examined
Hypothesis Driven
Metrics Data Driven
Metrics Data Categories
1 1 2 3 1,2 1,2 1,2 1,2 1,3 2,3 2,3 1,2,3 1,2,3 1 2 3 3 1,2 1,2 2,3 1, [3]
1,2, [3]
Multiparameter Metric
Scalar Parameters
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22
SMTSDoxy X X X X SSDTSDoxy X X X X X TMSSDoxy X X X X X X X TSDSMoxy TSDSSDoxy X X SMTSDdeoxy X X X SSDTSDdeoxy X X X TMSSDdeoxy X X X TSDSMdeoxy X X X X X X TSDSSDdeoxy X X X X X SMTSDtot X X X X X SSDTSDtot X X TMSSDtot X X X X X TSDSMtot X X
Hyp
oxia
(1
)
TSDSSDtot X X WLoxy X X X X X X
WHoxy
WLdeoxy X X X X X X X X
Syn
chro
ny(2
)
WHdeoxy X X X X X X X X X
VMAoxy X X
VMAdeoxy X
VMRoxy X X X X X X X
Para
met
er C
ateg
ory
Ang
ioge
nesi
s (3
)
VMRdeoxy X X X X X
23
Multivariate Predictor Performance
Multivariate Predictor 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22
R 85.7 90 90 80 80 78.6 64.3 71.4 85.7 100 80 80 50 50 57.1 90 80 78 100 90 80 80 Sn
P 57.1 57.1 64.3 78.6 71.4 64.3 78.6 57.1 78.6 78.6 71.4 71.4 85.7 64.3 57.1 71.4 71.4 85.7 78.6 57.1 64.3 71.4 R 95 81.8 90.9 90.9 100 90 95 90 95 90 90.9 90.9 90 80 95 90.9 90.9 80 95 90.9 81.8 90.9
Sp P 86.7 84.6 76.9 92.3 92.3 60 86.7 93.3 100 100 84.6 92.3 93.3 93.3 100 84.6 84.6 100 93.3 61.5 84.6 69.2
24
Performance of Multivariate Predictor Averages
Retrospective Group
Sensitivity (%) Specificity (%)
Per
cent
age
of P
redi
ctor
Agg
rega
tes
4050
6070
8090
4050
6070
8090
0
5
10
15
20
25
Sensitivity (%)Specificity (%)
Perc
enta
ge o
f Pr
edic
tor A
ggre
gate
s
4050
6070
8090
4050
6070
8090
0
5
10
15
20
25
(Two views of the same histogram.)
(This one has the same orientation as the ones in Figures 2 and 3.)
(This one is rotated 90°, so that all the bars are visible.)
25
No
Path
olog
y
Non
-Can
cer
Path
olog
y
Prio
r C
ance
r
Can
cer
Subjects, by Category
0 10 20 30 40 50
Com
pute
d B
reas
t Can
cer
Pro
babi
lity
(Mea
n +
/- S
D)
0.0
0.2
0.4
0.6
0.8
1.0Retrospective Group
26C
ance
r
Pre
-Can
cer
Pri
or C
ance
r
Non
-Can
cer
Pat
holo
gy
No
Pat
holo
gy
Subjects, by Category
0 10 20 30 40 50
Com
pute
d B
reas
t Can
cer
Pro
babi
lity
(Mea
n +
/- S
D)
0.0
0.2
0.4
0.6
0.8
1.0Prospective Group
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