Histotripsy: Overcoming Technical Limitations of Treatment Target Size—A Mathematical Framework for Palliative Debulking

Source abstract

ABSTRACT Objective To address technical limitations of histotripsy in treating hepatic tumours larger than 3 cm by developing a mathematical framework to optimize treatment coverage while minimizing unsafe overlap. Methodology A theoretical model was constructed using sphere packing and covering principles to estimate the number of smaller treatment zones required to cover a larger tumour volume and applied to a clinical case of a 6 × 6 cm hepatic tumour. Volume ratios were calculated and adjusted using random close packing density (~64%). Results Our model predicted 2.16–4.94 treatment zones for a 6 cm tumour; three overlapping treatments were performed to ensure adequate coverage. Our model suggests that the number of required treatments may increase exponentially with tumour size. Conclusions This framework provides a practical tool for preoperative planning. As tumour size increases, challenges include prolonged procedures, increased anaesthesia exposure and greater resource utilization, especially for tumours exceeding 7 cm. Overlapping treatments may increase risks such as acute kidney injury and vascular thrombosis, necessitating careful patient selection and thorough risk–benefit discussion. Importantly, safety‐limited overlap makes untreated voids within tumours mathematically unavoidable. Thus, our model should not be interpreted as achieving curative intent but can be interpreted as a method for palliative debulking.