Quality assurance of small dose fields shaped with a multileaf collimator is crucial in x-ray radiotherapy. Tissue-equivalent scintillating fibers (SciFi) can measure a sinogram of the dose field at the detector plane sampled with a few angles and open up the possibility of real-time quality assurance. We investigate the use of such detectors for estimating dose fields obtained with multileaf collimators (MLC). We propose a forward model of the tomographic projection based on geometrical parameters of the MLC and the beam dose. A least squares minimization is then used to identify these parameters. We validate our approach on real data acquired with a prototype SciFi detector measuring six projections of a field generated with a 6 MeV linear accelerator and shaped by nine pairs of leaves. We observe a good fit with the reference gafchromic film.