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The giant extinct marsupial Diprotodon optatum has unusual skull morphology for an animal of its size, consisting of very thin bone and large cranial sinuses that occupy most of the internal cranial space. The function of these sinuses is unknown as there are no living marsupial analogues. The finite element method was applied to identify areas of high and low stress, and estimate the bite force of Diprotodon to test hypotheses on the function of the extensive cranial sinuses. Detailed three-dimensional models of the cranium, mandible and jaw adductor muscles were produced. In addition, manipulations to the Diprotodon cranial model were performed to investigate changes in skull and sinus structure, including a model with no sinuses (sinuses 'filled' with bone) and a model with a midsagittal crest. Results indicate that the cranial sinuses in Diprotodon significantly lighten the skull while still providing structural support, a high bite force and low stress, indicating the cranium may have been able to withstand higher loads than those generated during feeding. Data from this study support the hypothesis that pneumatisation is driven by biomechanical loads and occurs in areas of low stress. The presence of sinuses is likely to be a byproduct of the separation of the outer surface of the skull from the braincase due to the demands of soft tissue including the brain and the large jaw adductor musculature, especially the temporalis. In very large species, such as Diprotodon, this separation is more pronounced, resulting in extensive cranial sinuses due to a relatively small brain compared with the size of the skull. [ABSTRACT FROM AUTHOR]