SUNY Downstate Medical Center Derivation and Validation of Metrics for Breast Cancer Diagnosis from Diffuse Optical Tomography Imaging Data Randall L. Barbour, Ph.D. SUNY Downstate Medical Center Brooklyn, New York

Corrosion Cast of Tumor Vasculature 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.)

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.

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.

Dual Breast Imaging Result -9.3e-9 2.1e-8 -1.2e-8 Left (tumor) 1 2 3 4 5 6 7 Right (healthy) D Hbred [mol/l] Imaging frames 1 2 3 4 5 6 7

Strategies for Data Analysis Time Series Measures Inherently information rich Large dimensional data sets. To Obtain Useful Information: Consider the big picture

Dual Breast Imager Approx. Breast Positions Phantom Spheres Gantry with Opening Fiberoptics Measuring Cup Adjusters (Tilt, Lift, Pitch/Yaw) Approx. Breast Positions

Instrumentation Measuring Heads Stepper Motor Controller Fiber optics 8 Power Supply Motor Controller (4,5)b (4,5)a 12 Detection Unit Stepper Motor Controller PC Fiber optics Measuring Heads

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

Power Spectrum of Hb Signal

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 Hbdeoxy Hboxy (II) spatial integration mean SD scalar quantities (I)

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

Method 2: Time-frequency (wavelet) analysis Starting point is reconstructed image time series (IV) Use (complex Morlet) wavelet transform as a time-domain bandpass filter operation Output is an image time series (IV) of amplitude vs. time vs. spatial position, for the frequency band of interest Filtered time series can be obtained for more than one frequency band Recompute previously considered, but starting with the wavelet amplitude time series time f1 f2

Vasomotor Coordination Healthy Breast Tumor Breast

Method 3: Provocation Analysis: Healthy Subject Left breast (blue curve) and right breast (red curve)

Provocation Analysis: Cancer case

Scalar Metrics Explored Experimental Condition Tumor-Associated Phenotype Scalar Metric Resting State Hypoxia Spatial Coordination Evoked Response Angiogenesis

Breast Pathology Status Subject Population Subject Group Breast Pathology Status N Age (yr) [mean ± SD] BMI (kg-m2) Tumor Size [largest dimension] Clinical Description Retrospective Active CA 14 47.9 ± 12.3 28.7 ± 5.3 10 ≤ 3 cm 4 > 3 cm 10 ductal carcinoma 1 ductal & lobular carcinoma 1 mucinous carcinoma 1 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 Non-CA Pathology 11 45.7 ± 5.6 28.7 ± 5.5 (N = 7) 3 fibrocystic disease 4 breast cyst 1 axillary cyst 2 benign breast lumps 1 breast reduction surgery No History of Breast Pathology 9 41.6 ± 10.0 30.3 ± 7.2

Subject Population Prospective Active CA 14 51.4 ± 10.9 30.4 ± 4.5 51.4 ± 10.9 30.4 ± 4.5 5 ≤ 3 cm 9 > 3 cm(a 13 ductal carcinoma 1 axillary adenocarcinoma with mammary duct ectasia and hyperplasia Prior CA 4 60.8 ± 9.3 25.5 ± 1.7 — 3 prior ductal carcinoma 1 prior mucinous carcinoma All had lumpectomies 2-6 yr prior to NIRS study Pre-CA 53.5 ± 3.4 29.0 ± 4.1 (N = 3) 2 DCIS 1 atypical ductal hyperplasia 1 extremely dense breasts Non-CA Pathology 6 43.7 ± 8.4 26.6 ± 4.9 (N = 4) 1 cystic disease 2 fibrocystic changes 1 fibrosis 1 benign breast lump 1 breast reduction surgery No History of Breast Pathology 8 44.0 ± 6.8 30.5 ± 8.9

Patient Demographics

Logistic Regression Applied Metrics calculated and selected based on t-tests & ROC curves Metrics used as inputs into logistic regression model Probability Logistic regression model calculates i for each metric (Xi) Using i, a predicted probability distribution can be created Metrics X1 = .43; X2 = -.05 New Patient’s Values New patient’s Xi used to generate probability of cancer in patient Linear Model: P(cancer) = 0.75 Logistic Regression: P(cancer) = 0.90

Scalar Metrics Examined

Multivariate Predictor Performance

Performance of Multivariate Predictor Averages (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.)

Summary: The amplitude and spatial coordination of the Hb signal is notable altered in tumor bearing breasts. Multivariate metrics derived from simple scalar quantities derived from resting and provoked responses yield predictors having high discriminatory values.