Synopsis

Numerous reports have shown that fiber tractography suffers from a difficult sensitivity-specificity tradeoff. We present an approach that leverages knowledge about certain well studied tracts (anchor tracts) in a tractogram to quantitatively assess and score the remaining tracts (candidate tracts) according to their plausibility in conjunction with this context information. We show that our approach has the potential for greatly reducing the number of false positive tracts in fiber tractography while maintaining high sensitivities.

Introduction

The problem of false positives in tractography is one of the grand challenges in diffusion MRI research. Due to the fundamental ill-posedness of tractography, there exist huge numbers of theoretically possible candidate tracts especially in bottleneck situations¹. Only a fraction of these candidates corresponds to the true fiber configuration, which results in a difficult sensitivity-specificity tradeoff. Current methods address this issue either by focusing exclusively on well-known tracts using prior knowledge^2,3 or by using filtering techniques based on tract morphology and the image signal^4,5. To date, the link between purely data driven and prior knowledge based approaches is missing.

We propose a novel concept that rigorously exploits information about the existence of certain tracts (anchor tracts) to reduce the degrees of freedom of a filtering of the candidates. This is based on the hypothesis that information about the presence or absence of each anchor influences the plausibility of the candidates and thereby reduces the ambiguities in the problem. We demonstrate the potential of this concept to greatly improve the sensitivity-specificity tradeoff of tractography in a series of phantom experiments.

Methods

Essentially, our method scores the candidate tracts by assessing their contribution to the signal, subject to constraints imposed by the anchor tracts. The process consists of four steps: (1) The input tractogram is filtered using a gray matter mask to discard streamlines that terminate inside the white matter. (2) Based on prior knowledge, anchor tracts are identified and extracted from the filtered tractogram. (3) The remaining streamlines are then clustered using QuickBundles⁶ to obtain the candidate tracts. (4) It is now assessed which parts of the image can be explained by the anchor tracts using the SIFT2 methodology⁷. The residual image only contains parts of the signal that cannot be explained by the anchor tracts. By then applying SIFT2 to the candidate tracts and the residual image, a score for each candidate is obtained that is defined as the difference in RMSE with and without the respective tract. This score is interpreted as the “importance” or “plausibility” of the respective candidate for explaining the image signal under consideration of boundary conditions in form of prior knowledge. The procedure follows the intuition that a candidate tract is likely to exist if it is the only tract that can explain parts of the signal that is not explained by any known tracts.

Experiment 1: Figure 1 illustrates the principle on a toy example consisting of two crossing fibers simulated with Fiberfox⁸. The experiment was performed once with each ground truth tract as anchor tract. The Invalid Bundle Ratio (IVR) was 3.8 (the invalid tracts outnumbered the valid tracts by a factor of 3.8).

Experiment 2: For this experiment we employed a simulated replication of the FiberCup phantom⁸. It was repeated five times with four out of seven randomly selected anchor tracts (IVR 1.9).

Experiment 3: Our main experiment is based on the brain-like phantom used in the ISMRM Tractography Challenge 2015^1,9. It was repeated fifty times with 50% of the ground truth bundles extracted from the tractogram randomly selected as anchor tracts in each repetition (IVR 7.7). For comparison, another fifty repetitions were performed completely without anchor tracts. Additional benchmarks were obtained using a volume-based ranking of the candidate tracts, as well as a streamline-weight-based ranking obtained with LiFE⁵.

All test-tractograms were obtained with probabilistic CSD tractography^10,11. Since the ground truth is known, the anchor tracts were extracted by using a simple overlap criterion with the binary mask of the respective ground truth. In vivo, this step could be replaced by an atlas-based tract selection or similar techniques^2,3,12.

Results

In Experiment 1, the highest ranked candidate in both configurations of the toy example was the correct tract corresponding to the ground truth. In Experiment 2, the proposed method ranked the three true candidate tracts highest in all repetitions (see Figure 2). Experiment 3 resulted in the ROC curves shown in Figure 3. The proposed method ($$$AUC=0.91$$$) performed significantly better than the benchmarks without anchor tracts ($$$AUC=0.78$$$, t-test: $$$p=1.7^{-25}$$$) and with volume-based scoring ($$$AUC=0.7$$$, t-test: $$$p=1.5^{-29}$$$). The LiFE scoring performed similar to random guessing ($$$AUC=0.5$$$).

Discussion

We proposed a novel concept that enables the quantification of the plausibility of fiber tracts by exploiting knowledge about known anchor tracts. Our results show that this approach has the potential to greatly improve the sensitivity-specificity tradeoff in tractography, which is a central issue of current tractography pipelines¹. All methods will be published in the open-source Medical Imaging Interaction Toolkit (MITK)¹³. Future work will concentrate on analyzing the performance of the method in vivo as well as the optimal number and nature of the chosen anchor tracts.

Acknowledgements

References

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