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Evaluating the accuracy of diffusion MRI models in white matter.

Rokem A, Yeatman JD, Pestilli F, Kay KN, Mezer A, van der Walt S, Wandell BA - PLoS ONE (2015)

Bottom Line: This is the first evaluation of model-accuracy of these models.In most of the white matter the DTM predicts the data more accurately than test-retest reliability; SFM model-accuracy is higher than test-retest reliability and also higher than the DTM model-accuracy, particularly for measurements with (a) a b-value above 1000 in locations containing fiber crossings, and (b) in the regions of the brain surrounding the optic radiations.The SFM also has better parameter-validity: it more accurately estimates the fiber orientation distribution function (fODF) in each voxel, which is useful for fiber tracking.

View Article: PubMed Central - PubMed

Affiliation: Department of Psychology, Stanford, Stanford, California, United States of America.

ABSTRACT
Models of diffusion MRI within a voxel are useful for making inferences about the properties of the tissue and inferring fiber orientation distribution used by tractography algorithms. A useful model must fit the data accurately. However, evaluations of model-accuracy of commonly used models have not been published before. Here, we evaluate model-accuracy of the two main classes of diffusion MRI models. The diffusion tensor model (DTM) summarizes diffusion as a 3-dimensional Gaussian distribution. Sparse fascicle models (SFM) summarize the signal as a sum of signals originating from a collection of fascicles oriented in different directions. We use cross-validation to assess model-accuracy at different gradient amplitudes (b-values) throughout the white matter. Specifically, we fit each model to all the white matter voxels in one data set and then use the model to predict a second, independent data set. This is the first evaluation of model-accuracy of these models. In most of the white matter the DTM predicts the data more accurately than test-retest reliability; SFM model-accuracy is higher than test-retest reliability and also higher than the DTM model-accuracy, particularly for measurements with (a) a b-value above 1000 in locations containing fiber crossings, and (b) in the regions of the brain surrounding the optic radiations. The SFM also has better parameter-validity: it more accurately estimates the fiber orientation distribution function (fODF) in each voxel, which is useful for fiber tracking.

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Local extrema in the diffusion signal attenuation do not cross-validate well.The two middle columns are independent measurements of the same voxel from the centrum semiovale. The three rows show measurements of this voxel obtained at b = 1000, 2000, and 4000. Notice that local minima and maxima differ between replications (arrows). The DTM (left column) and SFM (right column) predictions generally cross-validate well and are much smoother than the data. This particular voxel was chosen to illustrate a case where there are likely to be crossing fascicles. At this location and at b = 4000, the rRMSE of the DTM is greater than 1, while the rRMSE of the SFM is less than 1.
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pone.0123272.g008: Local extrema in the diffusion signal attenuation do not cross-validate well.The two middle columns are independent measurements of the same voxel from the centrum semiovale. The three rows show measurements of this voxel obtained at b = 1000, 2000, and 4000. Notice that local minima and maxima differ between replications (arrows). The DTM (left column) and SFM (right column) predictions generally cross-validate well and are much smoother than the data. This particular voxel was chosen to illustrate a case where there are likely to be crossing fascicles. At this location and at b = 4000, the rRMSE of the DTM is greater than 1, while the rRMSE of the SFM is less than 1.

Mentions: To understand why the SFM improves the fit, we examined the signal in voxels that are substantially better fit by the SFM than the DTM. We illustrate a typical case using a voxel in centrum semiovale. Measured with a b-value of 4000, the DTM rRMSE is 1.2 and the SFM rRMSE is 0.8. We show the interpolated diffusion signal surface in Fig 8. At low b-value (1000) the two measurements of the surface are grossly the same and the noise appears as small modulations of that surface. The signal varies slowly with angle, while the noise varies relatively rapidly with angle. At higher b-values (2000, 4000) the signal is smaller and the noise is approximately the same (Fig 1). Even so, at higher b-values the signal angular resolution is higher, and reliable features of the angular distribution emerge. For example, two reliable ‘dimples’ appear in the signal profiles of both measurements (Fig 8), indicating two fascicles crossing through this voxel. These ‘dimples’ cannot be captured by the DTM, but they are accurately captured by the SFM. Hence, the SFM outperforms the DTM for this voxel.


Evaluating the accuracy of diffusion MRI models in white matter.

Rokem A, Yeatman JD, Pestilli F, Kay KN, Mezer A, van der Walt S, Wandell BA - PLoS ONE (2015)

Local extrema in the diffusion signal attenuation do not cross-validate well.The two middle columns are independent measurements of the same voxel from the centrum semiovale. The three rows show measurements of this voxel obtained at b = 1000, 2000, and 4000. Notice that local minima and maxima differ between replications (arrows). The DTM (left column) and SFM (right column) predictions generally cross-validate well and are much smoother than the data. This particular voxel was chosen to illustrate a case where there are likely to be crossing fascicles. At this location and at b = 4000, the rRMSE of the DTM is greater than 1, while the rRMSE of the SFM is less than 1.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4400066&req=5

pone.0123272.g008: Local extrema in the diffusion signal attenuation do not cross-validate well.The two middle columns are independent measurements of the same voxel from the centrum semiovale. The three rows show measurements of this voxel obtained at b = 1000, 2000, and 4000. Notice that local minima and maxima differ between replications (arrows). The DTM (left column) and SFM (right column) predictions generally cross-validate well and are much smoother than the data. This particular voxel was chosen to illustrate a case where there are likely to be crossing fascicles. At this location and at b = 4000, the rRMSE of the DTM is greater than 1, while the rRMSE of the SFM is less than 1.
Mentions: To understand why the SFM improves the fit, we examined the signal in voxels that are substantially better fit by the SFM than the DTM. We illustrate a typical case using a voxel in centrum semiovale. Measured with a b-value of 4000, the DTM rRMSE is 1.2 and the SFM rRMSE is 0.8. We show the interpolated diffusion signal surface in Fig 8. At low b-value (1000) the two measurements of the surface are grossly the same and the noise appears as small modulations of that surface. The signal varies slowly with angle, while the noise varies relatively rapidly with angle. At higher b-values (2000, 4000) the signal is smaller and the noise is approximately the same (Fig 1). Even so, at higher b-values the signal angular resolution is higher, and reliable features of the angular distribution emerge. For example, two reliable ‘dimples’ appear in the signal profiles of both measurements (Fig 8), indicating two fascicles crossing through this voxel. These ‘dimples’ cannot be captured by the DTM, but they are accurately captured by the SFM. Hence, the SFM outperforms the DTM for this voxel.

Bottom Line: This is the first evaluation of model-accuracy of these models.In most of the white matter the DTM predicts the data more accurately than test-retest reliability; SFM model-accuracy is higher than test-retest reliability and also higher than the DTM model-accuracy, particularly for measurements with (a) a b-value above 1000 in locations containing fiber crossings, and (b) in the regions of the brain surrounding the optic radiations.The SFM also has better parameter-validity: it more accurately estimates the fiber orientation distribution function (fODF) in each voxel, which is useful for fiber tracking.

View Article: PubMed Central - PubMed

Affiliation: Department of Psychology, Stanford, Stanford, California, United States of America.

ABSTRACT
Models of diffusion MRI within a voxel are useful for making inferences about the properties of the tissue and inferring fiber orientation distribution used by tractography algorithms. A useful model must fit the data accurately. However, evaluations of model-accuracy of commonly used models have not been published before. Here, we evaluate model-accuracy of the two main classes of diffusion MRI models. The diffusion tensor model (DTM) summarizes diffusion as a 3-dimensional Gaussian distribution. Sparse fascicle models (SFM) summarize the signal as a sum of signals originating from a collection of fascicles oriented in different directions. We use cross-validation to assess model-accuracy at different gradient amplitudes (b-values) throughout the white matter. Specifically, we fit each model to all the white matter voxels in one data set and then use the model to predict a second, independent data set. This is the first evaluation of model-accuracy of these models. In most of the white matter the DTM predicts the data more accurately than test-retest reliability; SFM model-accuracy is higher than test-retest reliability and also higher than the DTM model-accuracy, particularly for measurements with (a) a b-value above 1000 in locations containing fiber crossings, and (b) in the regions of the brain surrounding the optic radiations. The SFM also has better parameter-validity: it more accurately estimates the fiber orientation distribution function (fODF) in each voxel, which is useful for fiber tracking.

Show MeSH