Early detection and treatment of cancerous tumours significantly improve the lives of cancer patients, as well as increase their chance of surviving and reduce treatment cost. A novel study has utilised the human adipose (fat) tissue as a propagation channel for radio frequency communication within the human body. A notable application of this technology is the continuous monitoring of the growth of perturbants, such as tumours, in the channel. This paper addresses the privacy issues associated with the deployment of this monitoring technology. Our work departs from previous studies in that we consider the privacy of the sensing process itself, rather than the privacy of sensed data. We study the information leakage associated with the deployment of this technology and propose and evaluate a set of privacy-enhancing techniques that reduces information leakage. Finally, we propose and evaluate an approach that combines these techniques and, thereby, protects patient's privacy.