# GPU tractography: What can we learn from half a trillion streamlines?

Yanis Aeschlimann, Samuel Deslauriers-Gauthier, Romain Veltz

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## To cite this version:

Yanis Aeschlimann, Samuel Deslauriers-Gauthier, Romain Veltz. GPU tractography: What can we learn from half a trillion streamlines?. International Society for Tractography Conference - IST 2025, Oct 2025, Bordeaux (France), France. hal-05272265

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Submitted on 22 Sep 2025

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# GPU tractography: What can we learn from half a trillion streamlines?

Yanis Aeschlimann¹, Samuel Deslauriers-Gauthier¹, and Romain Veltz¹

¹Université Côte d'Azur, Inria, France

**Introduction:** Probabilistic fiber tractography is a stochastic process whose outcomes can be used to estimate the probability of connection between two brain regions. The most commonly used estimator for the probability of connection between regions *i* and *j* is given by $c_{ij}^{(n)}/n$, where *n* represents the total number of seeds and $c_{ij}^{(n)}$ denotes the number of streamlines connecting the two regions. Despite its widespread use, the variance of this estimator is often overlooked. In this study, we leveraged a GPU-accelerated implementation of probabilistic tractography to generate a connectivity matrix from 500,000,000,000 streamlines. Using this large-scale dataset, we computed rigorous bounds on the confidence interval of the connection probability estimator.

**Methods:** When a streamline count connectivity matrix is normalized by the number of seeds, the entry in row *i* and column *j* can be interpreted as the probability of connecting regions *i* and *j* when generating a single streamline randomly. Each entry therefore follows a binomial distribution with parameters *n* and $p_{ij} \in [0, 1]$ which corresponds to the true (unknown) probability of connection of the tractography process (distinct from the strength of brain connectivity [1]). The quantity $\hat{p}_{ij}^{(n)} = c_{ij}^{(n)}/n$ is an unbiased estimator of $p_{ij}$ whose variance is $\hat{\sigma}^2 = \hat{p}_{ij}^{(n)} (1 - \hat{p}_{ij}^{(n)})/n$. Using the Clopper-Pearson method, the 95% confidence interval for the parameter $p_{ij}$ is computed. Probabilistic fiber tractography (step size 0.25 mm, maximum angle 30°) was performed on fiber orientation distribution function computed from the diffusion MRI data from subject 100206 of the Human Connectome Project. Our GPU accelerated implementation allowed us to generate a connectivity matrix from the Schaefer atlas [3] (400 regions) using $n = 0.5 \times 10^{12}$ streamlines and computed extremely precise bounds on the connection probability $p_{ij}$. For comparison, we also generated a connectivity matrix from the typically recommended $n = 2 \times 10^7$ streamlines.

**Results:** Figure 1 illustrates the ratio of the size of the confidence interval over the estimated probability and the histogram of the connection probabilities. For $n = 2 \times 10^7$, 33% of the values are above 1 (red region in the histogram), meaning that the uncertainty is at least as large as the estimate. This value drops to 1% (red and blue regions in the histogram) for $n = 0.5 \times 10^{12}$. The intra-hemispheric median ratios are 0.72 and 0.02 for $n = 2 \times 10^7$ and $n = 0.5 \times 10^{12}$, respectively. It highlights the high uncertainty of the estimated connectivity for $n = 2 \times 10^7$. In the histogram, the probabilities are in agreement only when the confidence interval is small compared to the estimated probability (in the red region).

**Conclusion:** GPU acceleration of tractography allows the generation of a large number of streamlines in a reasonable time. Our results show that many connectivity matrix entries are inaccurate with the current recommendation of $2 \times 10^7$ streamlines. Our conclusion differ from previous ones [2] because we focus on the accuracy of individuals probability of connection, rather than the global process of tractography. Our Python implementation is open-source and publicly available (https://gitlab.inria.fr/cronos/software/tractography).

**Acknowledgment:** We are grateful for the infrastructure of Slices RI (https://www.slices-ri.eu/) used in this study.

<figure><img src="image_3.png" /><figcaption>Figure 1: Ratio of the size of the confidence interval over the estimated probability $\hat{p}_{ij}^{(n)}$ for $n = 2 \times 10^7$ and $n = 0.5 \times 10^{12}$ streamlines. The histogram of the probabilities for 1/2 trillion and 20 million streamlines. The probabilities are reliable in the red regions for both estimates and only for $n = 0.5 \times 10^{12}$ in the blue region.</figcaption></figure>

## References

[1] Fernando Calamante. “The Seven Deadly Sins of Measuring Brain Structural Connectivity Using Diffusion MRI Streamlines Fibre-Tracking”. In: *Diagnostics* (2019).

[2] Daniel C. Moyer, Paul Thompson, and Greg Ver Steeg. “Measures of Tractography Convergence”. In: *Computational Diffusion MRI*. 2019.

[3] Alexander Schaefer et al. “Local-Global Parcellation of the Human Cerebral Cortex from Intrinsic Functional Connectivity MRI”. In: *Cerebral Cortex* 28 (2018).