Mathematical model of the post-ablation enhancement zone as a tissue-level oedematic response.

PURPOSE: A hyperdense rim is commonly observed at the periphery of ablation zones during post-ablation imaging (e.g. ultrasound) in tumours. A mathematical model has been developed here to investigate the occurrence of this enhanced rim, caused by the ablated cells, giving an indication of the location of the final ablation region.

MATERIALS AND METHODS: The enhanced rim has been assumed here to be due to a tissue-level oedematic response of viable cells, which necessitated coupling multiple modelling elements in a spatially distributed system: thermal cell death, tissue-state dependent ion concentration dynamics, ion transport in the extracellular space, and osmotic cell volume regulation.

RESULTS: In response to the imposed temperature function, an ablation zone was predicted, distinguishing the tissue state between 'dead' and 'alive'. A disturbance in intracellular/extracellular ion concentrations was induced due to ion redistribution, which acted as an osmotic stress and contributed to significant cell swelling in a thin rim at the periphery of the ablation zone. It was also found that the rim size only changed slightly with varying lesion size, in response to different temperature profiles.

CONCLUSIONS: The study presents a novel mathematical model to understand the enhanced rim surrounding the ablation zone by assuming tissue-level cell oedema as the primary potential cause. The model links the direct response to thermal injury to an observable secondary response, which could be of clinical value in that the location of this bright ring could potentially be used for more accurate determination of the extent of the ablation zone.