Spatial Information in DW- and DCE-MRI Parametric Maps in

Breast Cancer Research

Hakmook KangDepartment of Biostatistics

Center for Quantitative SciencesVanderbilt University

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

Table of Contents•Spatial & Temporal Correlation

•Motivation

•DW- & DCE-MRI

•Spatial Information

•Redundancy Analysis & Penalized Regression

•Data Analysis

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....

Spatial Correlation

Radioactive Contamination

Elevation

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

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

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.

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

MRI – Derived Parameters

DW- and DCE-MRI

•DW-MRI: water motion

•DCE-MRI: tumor-related physiological parameters

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

MRI-derived Parameters

ADC Ktrans kep ve vp

Using Spatial Information

Radioactive Contamination

http://www.neimagazine.com/features/featuresoil-contamination-in-belarus-25-years-later/featuresoil-contamination-in-belarus-25-years-later-5.html

Kep & ADC

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

How to use the given spatial information?

1. Variable selection + penalization

2. Ridge

3. LASSO (Least Absolute Shrinkage and Selection Operator)

1. Elastic Net

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

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

vs. mean = 0.284

Penalized Regression

•LASSO: L1 penalty

•Ridge: L2 penalty

•Elastic Net: L1 + L2 penalty

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)

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

ModelsVoxel-Level

Voxel-Level + ROI + Clinical

Conventional Method

•ROI-level analysis

•ROI + clinical variables (i.e., age and tumor grade)

Data Analysis

Description of Data•33 patients with grade II/III breast

cancer

•Three MRI examinations

MRI t1

1st NAC NACs MRI t3

MRI t2

Surgery

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.

Responder Non-Responder

Correction for Overfitting

•Bootstrap based overfitting penalization

•Overfitting-corrected AUC = AUC (apparent) – optimism (using bootstrap)

Results

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

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

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