There are several causal explanations for dyslexia, drawing on distinctions between dyslexics and control groups at genetic, biological, or cognitive levels of description. However, few theories explicitly bridge these different levels of description. In this paper, we review a long-standing theory that some dyslexics' reading impairments are due to impairments in hemispheric transfer. We test this theory in a computational model of reading, implementing anatomical features of the visual system. We demonstrate that, when callosal transfer is impaired, the model reads nonwords as well as an unimpaired model, but reads exception words poorly: a pattern of behaviour similar to surface dyslexia. This computational modelling provides a causal link between brain-based theories of dyslexia to cognitive-level theories that refer specifically to phonological impairments within the reading system.