Cochlear implants (CIs) are devices that restore the sense of hearing in people with severe sensorineural hearing loss. An electrode array inserted in the cochlea bypasses the natural transducer mechanism that transforms mechanical sound waves into neural activity by artificially stimulating the auditory nerve fibers with electrical pulses. The perception of sounds is possible because the brain extracts features from this neural activity, and loudness is among the most fundamental perceptual features. A computational model that uses a three-dimensional (3D) representation of the peripheral auditory system of CI users was developed to predict categorical loudness from the simulated peripheral neural activity. In contrast, current state-of-the-art computational loudness models predict loudness from the electrical pulses with minimal parametrization of the electrode-nerve interface. In the proposed model, the spikes produced in a population of auditory nerve fibers were grouped by cochlear places, a physiological representation of the auditory filters in psychoacoustics, to be transformed into loudness contribution. Then, a loudness index was obtained with a spatiotemporal integration over this loudness contribution. This index served to define the simulated threshold of hearing (THL) and most comfortable loudness (MCL) levels resembling the growth function in CI users. The performance of real CI users in loudness summation experiments was also used to validate the computational model. These experiments studied the effect of stimulation rate, electrode separation and amplitude modulation. The proposed model provides a new set of perceptual features that can be used in computational frameworks for CIs and narrows the gap between simulations and the human peripheral neural activity.