Solving MRI Spin Relaxometry Problem using PJ

1
Solving MRI Spin Relaxometry Problem (using PJ)

• DATE October 22nd, 2007
• STUDENT
• HARDIK J. PARIKH (hjp0608)
• COMMITTEE
• CHAIR PROF. ALAN KAMINSKY
• READER PROF. PAUL TYMANN
• OBSERVER PROF. FEREYDOUN KAZEMIAN

2
Agenda

• Introduction and Background
• Project Scope
• Project Design and Architecture
• Results
• Lessons Learned
• Future Work
• Questions

3
Introduction

• MRI
• an imaging technique without using x-rays.
• MRI Spin Relaxometry
• recovering the spin density spectrum from the
  time samples of the spin signal
• Problem
• Noisy MRI Signal ?derive spin spectrum generated
  by signal
• Is an inverse problem (final output ? original
  input)
• Pixels signal s at given time t is given as
• S(t) ?(1 2e-xt)
• ? spins density
• x spins relaxation rate ( sec-1).
• t time at which image was taken

4
Introduction

• Input files
• Times file
• Contains timing at which the signals were taken.
• Image file
• Contains pixel values for image taken at a
  particular time.
• Mask file
• For reducing the pixels to compute
• 0 Pixel value is not to be analyzed.
• 1 Pixel value needs to be analyzed.

5
Background Previous Work

• Andrew P. Bak, Joseph P. Hornak, and Nan C.
  Schaller. From impractical to practical Solving
  an MRI problem using parallelism.
• Modified CONTIN (a program to solve MRI spin
  relaxometry inverse problem)
• Multiple CONTIN sequential algorithms ran in
  parallel.
• Prof. Alan Kaminsky and Luke McOmber Solving an
  MRI spin relaxometry problem with parallel
  computing
• Implemented in Java using MPI.

6
Introduction

• Why Parallel Computing ?
• Substantial Computation
• Sequential -- 6600 sec. in Java.
• Independent pixel calculations.
• Embarrassingly parallel
• Types of Parallel Computing
• SMP vs. Clusters
• SMP (paragon, parasite, paradise)
• Clusters (paranoia)
• We implemented algorithm on Clusters

7
Project Scope

• Algorithm Implementations
• Linear Regularization (PJ (Java) and MPI (C))
• Non-Linear Least Squares (PJ (Java) and MPI (C))
• Measurements
• Time taken
• Speed-up
• Efficiency

8
Project Scope

• User Interfaces
• Histogram (Linear Regularization)
• Distribution/Density plots (Non-Linear Least
  Squares)
• Comparisons
• Linear Regularization vs. Non-Linear Least
  Squares
• Java vs. C

9
Architectural Overview
MRI Input Data Set
Linear Regularization Analysis Program (parallel,
C/MPI)
Linear Regularization Analysis Program (parallel,
Java/PJ)
Non-Linear Least Squares Analysis Program
(parallel, C/MPI)
Non-Linear Least Squares Analysis Program
(parallel, Java/PJ)
Non-Linear Least Squares Output Dataset
Linear Regularization Output Dataset
Non-Linear Least Squares Visualization Program
(Non-parallel, Java)
Linear Regularization Visualization Program
(Non-parallel, Java)
Architectural Overview of Implementation
10
Design Specifications

• Implementation on Clusters
• Each node
• gets same input
• executes algorithm
• produces output
• Load balancing (differs by 1 pixel on nodes)
• Analysis programs ? Parallel
• Visualization programs ? Non-parallel

11
Results

• Timing Measurements (Linear Regularization)

• Timing average of 5 runs.
• Sequential programs benchmark for speed-up and
  efficiency

12
Results

• Speedup/Efficiency (Linear Regularization -
  Java)

• Speed-up within 20 of ideal speed-up
• Efficiency within 15 of ideal efficiency.

13
Results

• Histogram (Linear Regularization)

14
Results

• Concentration area 0.5 0.7
• Random measurement errors clustered at end. (1.98
  2.0)
• Maximum count between 0.561 0.58

15
Results

• Timing Measurements (Non-Linear Least Squares)

• Timing average of 5 runs.
• Sequential programs benchmark for speed-up and
  efficiency

16
Results

• Speedup/Efficiency (Non-Linear Least Squares -
  Java)

• Speed-up within 25 of ideal speed-up
• Efficiency within 25 of ideal efficiency.

17
Results

• Distribution plot (Non-Linear Least Squares)

• The values are (x1, 1/N), (x2, 2/N), (x3,
  3/N)(xN,1/N)
• Steepness of slope between x 0.55 and x
  0.65

Spin relaxation rates vs. Calculated y value
18
Results

• Density plot (Non-Linear Least Squares)

• Count values between (xi ?) and (xi ?).
• where ? is window parameter
• Maximum peak between x 0.55 and x 0.65
• Measurement errors in the initial portion.
• ? 0.08 used to generate plots.

Spin relaxation rates vs. Total Count
19
Results

• Comparison of Algorithms
• Non-Linear Least Squares faster than Linear
  Regularization
• For Java codes ?

20
Results

• Comparison of Visualization Programs
• Histogram
• Concentration area 0.5 0.7
• Highest Peak 0.561 058
• Distribution/Density Plots
• Concentration area 0.55 0.65

21
Results

• Comparison of Java and C
• Linear Regularization
• Java programs approximately 40 slower than C
  programs
• Non-Linear Least Squares
• Java programs approximately 20 slower than C
  programs
• Why Java slow than C ?
• Java programs ? byte codes ? machine language.
• C programs ? machine language binaries.

22
Lessons Learned

• Efficiency increases with Parallel Computing
• Java slow vs. C
• Programming in MPI (specifically C)
• Dug into previous code, so a good learning curve.
• Experience with Software Development Life Cycle.

23
Future Work

• Construction of covariance matrices
• Used to create confidence bounds on parameters of
  solution vector.
• Proper balancing for Non-Linear Least Squares
• Input signal not symmetric around 0 ? improper
  rates and amplitudes.
• Possible solution add additional parameter to
  solution.
• Testing with other images.
• Master-Worker load balancing

24
Questions

• ?