Spatial Information in DW- and DCE-MRI Parametric Maps in Breast Cancer Research

1. Spatial Information in DW- and DCE-MRI Parametric Maps in Breast Cancer Research • Hakmook Kang • Department of Biostatistics • Center for Quantitative Sciences • Vanderbilt University

2. Joint Work • Allison Hainline in Biostatistics • Xia (Lisa) Li Ph.D at VUIIS • Lori Arlinghaus, Ph.D at VUIIS • Tom Yankeelov, Ph.D at VUIIS

3. Table of Contents • Spatial & Temporal Correlation • Motivation • DW- & DCE-MRI • Spatial Information • Redundancy Analysis & Penalized Regression • Data Analysis

4. Spatial & Temporal Correlation • Temporal correlation: Any measure at a time point is correlated with measures from neighboring time points, e.g., longitudinal data • Spatial correlation: Any measure at a voxel is correlated with measures from its neighbors, e.g., ADC, Ktrans....

5. Spatial Correlation Radioactive Contamination Elevation

6. Medical Imaging Data • Structural & functional MRI data, e.g., brain fMRI, breast DW- & DCE-MRI • CT scans, etc • Imaging data consist of lots of measures at many pixels/voxels • Not reasonable to assume independence

7. Motivation • Intrinsic spatial correlation in medical imaging data • Ignoring the underlying dependence • Oversimplifying the underlying dependence • Overly optimistic if positive spatial/temporal correlation is ignored

8. Mathematics • Cov(X, Y) = 2, positively correlated • Var(X+Y) = Var(X) + Var(Y) + 2Cov(X,Y) • Var(X+Y) = Var(X) + Var(Y) if assume X⊥Y, always smaller by 2Cov(X,Y) • Variance is smaller than what it should be if correlations among voxels are ignored.

9. Motivation • DW- & DCE-MRI data from 33 patients with stage II/III breast cancer • Typical ROI-level analysis: define one region of interest (ROI) per patient and take the average of values (e.g., ADC) within ROI • Build models to predict who will response to NAC • Need a tool to fully use the given information to improve prediction

10. MRI – Derived Parameters

11. DW- and DCE-MRI • DW-MRI: water motion • DCE-MRI: tumor-related physiological parameters

12. MRI-derived Parameters • ADC: apparent diffusion coefficient • Ktrans: tumor perfusion and permeability • kep: efflux rate constant • ve: extravascular extracellular volume fraction • vp: blood plasma volume fraction

13. MRI-derived Parameters ADC Ktrans kep ve vp

14. Using Spatial Information Radioactive Contamination Kep & ADC http://www.neimagazine.com/features/featuresoil-contamination-in-belarus-25-years-later/featuresoil-contamination-in-belarus-25-years-later-5.html

15. Spatial Information • Model change in mortality by looking at the average contamination over time • Model Pr(pCR=1) using ROI-level Kep and/or ADC maps, pCR = pathological complete response • Oversimplification

16. How to use the given spatial information? • Variable selection + penalization • Ridge • LASSO (Least Absolute Shrinkage and Selection Operator) • Elastic Net

17. Redundancy Analysis • A method to select variables which are most unlikely to be predicted by other variables • X1, X2, ..., X21 • Fit Xj ~ X(-j), if R2 is high, then remove Xj • We can also use backward elimination, Y ~ X1 + ... + X21 + e

18. Redundancy Analysis • First, compute 0,5,...,100 percentiles of Kep and ADC for each patient • X1= min, X2=5 percentile,..., X20 = 95 percentile, and X21 = max • Apply redundancy analysis: choose which percentiles uniquely define the distribution of Kep (or ADC) • Apply backward elimination

19. vs. mean = 0.284

20. Penalized Regression • LASSO: L1 penalty • Ridge: L2 penalty • Elastic Net: L1 + L2 penalty

21. Penalized Regression • The penalty terms control the amount of shrinkage • The larger the amount of shrinkage, the greater the robustness to collinearity • 10-fold CV to estimate the penalty terms (default in R)

22. Approaches 1) Var Selection + Penalization (ridge) - Variable selection either by redundancy analysis or by backward elimination - Combined with ridge logistic regression 2) Ridge (No variable selection) 3) Lasso 4) Elastic Net

23. Models Voxel-Level Voxel-Level + ROI + Clinical

24. Conventional Method • ROI-level analysis • ROI + clinical variables (i.e., age and tumor grade)

25. Data Analysis

26. Description of Data • 33 patients with grade II/III breast cancer • Three MRI examinations MRI t2 MRI t1 1st NAC NACs MRI t3 Surgery

27. Objective: Using MRI data (Kep & ADC only) at t1 and t2, we want to predict if a patient will response to the first cycle of NAC.

29. Responder Non-Responder

30. Correction for Overfitting • Bootstrap based overfitting penalization • Overfitting-corrected AUC = AUC (apparent) – optimism (using bootstrap)

31. Results

34. Results • Penalizing overly optimistic results • Redundancy + Ridge with clinical variables is better than the others • AUC = 0.92, 5% improvement over ROI + clinical model • ACC = 0.84, 10% improvement over ROI + clinical model

35. Summary • Compared to ROI-level analysis (i.e., average ADC & Kep), we are fully using available information (voxel-level information) • We partially take into account the underlying spatial correlation • Reliable & early prediction -> better treatment options before surgery

36. Future Research:Spatial Correlation • Modeling the underlying spatial correlation in imaging data • Parametric function: 1) Exponential Cov function 2) Matern’s family • Need to relax isotropic assumption