# Presentation: 049882

## Global MR Diagnostic Tools Via Complexity/Information Measures

## The Challenge

- Large data sets from large number of magnetic resonance (MR) modalities are available (i.e. high dimensional feature space)
- structural images (standard MRI, DTI,...)
- functional images (fMRI, perfusion MRI,...)
- metabolite images (MRSI)
- Analysis is complex and hard to interpret

## 
Motivating Example
Use of intuitively plausible, physically based, summary variables for classification and longitudinal tracking of pathology 

- Motivating Example
- Use of intuitively plausible, physically based, summary variables for classification and longitudinal tracking of pathology

- The  Proposal: Use Complexity/Information Measures as Summary Variables

- Like HR diagram,
- i.e. a stellar diagnosis

## Complexity/Information Measures Used

- Metric Entropy – measures number, and uniformity of distribution over observed patterns
-  	_[Symbolic Dynamics of Noisy Chaos](http://www.santafe.edu/projects/CompMech/papers/SDoNCTitlePage.html)_
- 		J. P. Crutchfield and N. H. Packard
- 		Physica **7D** (1983) 201-223.
- Statistical Complexity – measures number and uniformity of restrictions in correlation of observed patterns
-  _[Inferring Statistical Complexity](http://www.santafe.edu/projects/CompMech/papers/ISCTitlePage.html)_
- 		J. P. Crutchfield and K. Young
-  	 	Physical Review Letters **63** (1989) 105-108.
- Excess Entropy – measures convergence rate of metric entropy
- _[Structural Information in Two-Dimensional Patterns: Entropy Convergence and Excess Entropy](http://www.santafe.edu/projects/CompMech/papers/2dnnn.html)_
- 		D. P. Feldman and J. P. Crutchfield
- 		Santa Fe Institute Working Paper 02-12-065

## Analysis of MR data via Complexity/Information Measures

- Fundamental Intuition:

- q1

- q2

- Basic question: How does P(q2|q1) vary
- as function of q1,q2, and shape ?

## Joint Histogram P(q2,q1)

- <footer>

**“****Future” Conditioned on “Past” - P(q2|q1)**

**“****Past” Conditioned on “future” - P(q1|q2)**

**Joint Histogram P(q2,q1)**

**q1**

**q2**

## Analysis Proceeds in 4 Stages

- Choice of appropriate Feature Space (e.g. co-registered MRI, DTI, MRSI data)
- Dimension Reduction of Feature Space (e.g. segmentation, PCA,...)
- Application of Information Measures for Generation of Summary Variables (Stay tuned)
- Classification Based on Summary Variables (e.g. supervised - CART, MARS,... or unsupervised)

## Stage I - Choice of Appropriate Feature Space

- Utilize prior information
- E.g. for AD studies might choose structural (MRI)+ functional (Perfusion) + metabolic (NAA, glutamate,... levels) information
- Feature space visualization useful for choosing appropriate variables (e.g. scatter plot matrices) - canonical case for use of Exploratory Data Analysis

## Stage I - Choice of Appropriate Feature Space

## Stage I - Choice of Appropriate Feature Space

## Stage I - Choice of Appropriate Feature Space

## Stage I - Choice of Appropriate Feature Space

## Stage I - Feature Space Point

## Stage I - Feature Space

## Stage II - Dimensional Reduction of Feature Space

- Currently use fuzzy clustering (fanny, fuzzy c-means algorithms)
- Some alternatives (usual unsupervised learning suspects)
- Generating Partitions (in dynamical systems)
- PCA
- Projection Pursuit
- Principal Curves
- Self Organized Maps
- Independent Component Analysis
- ...

## Stage II - Dimension Reduction In Feature SpaceVia Hard or Fuzzy Clustering

## Stage II - Map Reduced Variables Back To Original Image

**Voxel**
**Grid**

**A**

**C**

**B**

**A**

## Stage III - Use of Information Measures for Generation of Summary Variables

-  Generate joint distribution (fuzzy clustering or continuous reduced variables) or parse tree (hard clustering) by parsing labeled image
- Calculate information measures from joint distribution or parse tree

## Stage III - Parse Tree Generated By Parsing An Image

- Calculate Complexity/Information Measures
- from Parse Tree or Joint Distribution

## Stage IV - Classification Based on Summary Variables

-  Now have small set of summary variables (e.g. Metric Entropy and Statistical Complexity)
- Classification (via CART, MARS, SOM,... no “curse of dimensionality”) can be applied
-  Results easily interpreted and visualized

## A Trivial Example - Checkerboard

**Entropy = (log****2**** N) = 1**
**Statistical Complexity = log****2**** 2 = 1**

## Another Trivial Example – Random Pattern

**Entropy = (log****2**** N) = L**
**Statistical Complexity = log****2**** 1 =  0**

## Complexity/Entropy Plot for Trivial Examples

**L**

**Statistical Complexity**

**1**

## q1

- <footer>

**0**

**1**

**1**

**0**

- 25

- 25

- 75

- 75

**q1**

**q2**

**q1**

**q2**

**counts**

## Simulation 1 – Noisy Checkerboards

- Model 1 - Non-stationary checkerboard

## Simulation 1 – Noisy Checkerboards

- Model 1 - Non-stationary checkerboard

## Simulation 1 – Noisy Checkerboards

- Model 1 - Non-stationary checkerboard

## Simulation 1 – Noisy Checkerboards

## Simulation 1 – Noisy Checkerboards

## Simulation 1 – Noisy Checkerboards

## Simulation 1 – Noisy Checkerboards

## Simulation 1 – Noisy Checkerboards

## Simulation 1 – Noisy Checkerboards

## SC

- <footer>

- H

## Simulation 1 – Noisy Checkerboards

- Model 2 - Stationary checkerboard

## Simulation 1 – Noisy Checkerboards

- Model 2 - Stationary checkerboard

## SC

- <footer>

- H

## Simulation 2 - Reduced NAA in Gray Matter – 3 Features

**“****Truth”**

**Spectroscopy Resolution**

**20 %**
**Tissue**
**Mask**

**Masked Features**

- G
- M

- W
- M

- N
- A
- A

**x**

**=**

**GM %**

**WM %**

**NAA**

## Simulation 2 - Reduction of GM/WM NAA Ratio in Successive Steps

- ...

- ...

- 2/1

- 1.5/1

- 1/1

## Simulation 2 – Scatter Plot Matrices

- NAA – 2/1 in GM/WM

- NAA – 1/1 in GM/WM

**...**

## H

- SC

## Conclusion

- Use of Complexity/Information Measures Proved Sensitive/Specific on Simulated MR Data and Picked Up Subtle Global, Nonlinear Changes – Individual NAA Amplitude Changes Were Less Than Simulated Noise Amplitude But Were Clearly Distinguished
- Collaborators – Yue Chen, John Kornak, Gerald Matson, and Norbert Schuff