<i>GACELLE:</i> GPU-accelerated tools for model parameter estimation and image reconstruction.

Quantitative MRI (qMRI) offers tissue-specific biomarkers that can be tracked over time or compared across populations; however, its adoption in clinical research is hindered by significant computational demands of parameter estimation. Images acquired at high spatial resolution and/or requiring fitting for multiple parameters often require lengthy processing time, constraining their use in routine pipelines and slowing methodological innovation and clinical translation. We present <i>GACELLE</i>, an open source, GPU-accelerated framework for high-throughput qMRI analysis. <i>GACELLE</i> unifies a stochastic gradient descent optimiser (<i>askadam.m</i>) and a stochastic sampler (<i>mcmc.m</i>) under a common interface in MATLAB, enabling fast parameter mapping, improved estimation robustness via spatial regularisation, and uncertainty quantification. <i>GACELLE</i> prioritises accessibility and ease of integration: users only need to provide a forward signal model, while <i>GACELLE</i>'s backend manages computational parallelisation, automatic parameter updates, and memory-efficient batching. The stochastic solver performs fully vectorised Markov chain Monte Carlo with identical likelihoods on CPU and GPU, ensuring reproducibility across hardware. Benchmarking demonstrates up to 451-fold acceleration for the stochastic gradient descent solver and 14,380-fold acceleration for stochastic sampling compared to CPU-based estimation, without compromising quantitative accuracy. We demonstrate <i>GACELLE</i>'s versatility on three representative qMRI models and on an image reconstruction task. Across these applications, <i>GACELLE</i> improves parameter precision, enhances test-retest reproducibility, and reduces noise in quantitative maps. By combining speed, usability and flexibility, <i>GACELLE</i> provides a generalisable optimisation framework for medical image analysis. It lowers the computational barrier for advanced qMRI, paving the way for reproducible biomarker development, large-scale imaging studies, and clinical translation.