Systematic Evaluation of Linear and Nonlinear DTI Estimation Methods:

An Open Framework

 

Introduction

 

A basic premise of DTI is that the tensor formalism (e.g., assumption of Gaussian diffusion) meaningfully represents diffusion processes, and thus the derived contrasts are relevant. Yet, not all tensors represent physically possible processes (e.g., those with negative eigenvalues); typical log-linear mean squared error methods can result in these non-physical solutions. Various non-linear tensor estimation frameworks have been developed to prevent these problems (Tschumperlé and Deriche 2003; Cox and Glen 2006; Niethammer, Estepar et al. 2006), while regulation and robust tensor estimation methods employ spatial correlations to lessen the effects of noise (Mangin, Poupon et al. 2002; Chang, Jones et al. 2005). Despite the emergence of new methods, little evidence has been presented to provide equivalent experimental comparisons or enable well-informed selection of the appropriate tensor estimation method for a particular task.

 

Methods

 

            A high resolution, high SNR dataset (15 repetitions of 30 diffusion weighted, DW, + 5 scanner averaged minimally weighted, b0, images at 1.5T) was used as ground truth to assess the effects tensor estimation method; simulations were performed with modeled noise as previously described (Landman, Farrell et al. 2006). An axial slice at the level of the lateral ventricles was selected to be representative of human brain anatomy. SNR is reported with respect to the b0.

            For each method, fractional anisotropy (FA) and mean diffusivity (MD) were computed. To provide a single quantitative measure of the differences between tensor estimation methods, we computed the average root mean square (RMS) error over 25 dB to 40 dB. This interval was chosen to correspond to typical achievable range SNR in in vivo clinical DTI settings. To enable direct comparisons at arbitrary SNR, a sigmoid function was fit to the FA and MD RMS errors over the same SNR levels.

 

Results

 

Mean Tensor Estimation Error (25 to 40 dB) (FA: [FA]x1000. MD: um2/s x 1000)

 

RMS Error

Bias

Std. Dev.

CPU Time

Estimation Methods

FA

MD

FA

MD

FA

MD

Relative

LL-MMSE 1

63.19

45.08

37.20

-7.97

53.81

47.42

1

LL-MMSE (clip DWI) 1

63.16

45.03

37.20

-7.94

53.75

47.38

1

LL-MMSE (clip eigenvalues) 1

63.18

45.03

37.20

-7.94

53.76

47.38

1

Positive Definite MMSE 1

59.99

46.08

34.43

-14.74

51.53

46.64

7.5

 

 

Sigmoid Fit* to RMSE (25 to 40 dB) (FA: [FA]x1000. MD: um2/s x 1000)

 

FA [FA]

MD [x10-3 mm2/s]

Estimation Methods

a

b

c

d

a

b

c

d

LL-MMSE 1

6.49 x10-3

1.27 x103

9.18

6.51

9.96 x10-7

8.64 x102

-2.21

1.04 x101

LL-MMSE (clip DWI) 1

7.39 x10-3

1.40 x103

1.50 x101

6.24

1.06 x10-6

9.01 x102

-1.92

1.01 x101

LL-MMSE (clip eigenvalues) 1

7.95 x10-3

1.51 x103

2.01 x101

6.07

1.12 x10-6

9.39 x102

-1.59

9.88

Positive Definite MMSE 1

7.85x10-3

1.46 x103

2.31 x101

6.08

9.87 x10-7

1.35x103

-9.33 x10-1

9.39

* Definition of sigmoid functional form:

Reported by

1 Bennett Landman, April 2007 (AFNI 2006_06_30_1332. Linux 64 bit)

 

 

Publications

B. A. Landman, S. Mori, and J. L. Prince, Systematic Evaluation of Linear and Nonlinear DTI Estimation Methods: An Open Framework, International Society for Magnetic Resonance in Medicine, Berlin, Germany, May 2007

 

Download

 

High SNR DTI Data [download]

Single slice, 31 dynamics. 1st dynamic = b0 (minimally weighted), 2nd – 31st dynamic = g­1…g30

            .gzip’ed raw file. Floating point (32 bpp, IEEE Little Endian). Field of View: 240x240 mm 2.5 mm slice thickness

            dimensions: 256x256 pixels

 

Gradient Table [download]

            Text file: Three columns corresponding to x, y, z diffusion weighting gradient strengths with 30 rows (1 per direction).

 

Source Code [download]

            Tar.gz: See example.m. Tested on Matlab 7.0. (Configure AFNI installation path in TensorEstimatorAFNI.m).

         

Submit Evaluation of Tensor Error

 

Submissions of evaluations of other algorithms are encouraged and will be incorporated. Please contact Bennett Landman (landman@jhu.edu) for information on how to submit your analyses. Comments and suggestions are welcome and appreciated.

 

 

Last Updated: Tuesday May 27, 2008

© Copyright 2006, Bennett Landman. All rights reserved.