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The growth process of He bubbles in W is investigated using molecular dynamics and parallel replica dynamics for growth rates spanning 6 orders of magnitude. Fast and slow growth regimes are defined relative to typical diffusion hopping times of W interstitials around the He bubble. Slow growth rates allow the diffusion of interstitials around the bubble, favoring the biased growth of the bubble towards the surface. In contrast, at fast growth rates interstitials do not have time to diffuse around the bubble, leading to a more isotropic growth and increasing the surface damage.