Proof of Stake (PoS) models are energy-efficient and require limited computational power. These features are critical in telemedicine environments, where resource-constrained devices must handle sensitive data securely. The growing need for auditable and privacy-preserving data storage in telemedicine underscores the importance of PoS models optimized for lightweight devices while complying with strict regulatory requirements, such as the Health Insurance Portability and Accountability Act (HIPAA).This study was guided by two research questions: (i) Which PoS models are lightweight and suitable for telemedicine? and (ii) What features make lightweight PoS models effective for privacy and efficiency in telemedicine? To address these questions, a systematic literature review (SLR) guided by the PICOC framework was conducted to investigate lightweight PoS models that can enhance privacy in telemedicine systems. Out of 2,394 papers studies screened, 55 were included in the analysis. The findings identified Algorand, Ouroboros Praos, Tendermint, Nxt, and Casper CBC as promising candidates. Key enabling features included lightweight voting mechanisms, such as Byzantine Agreement protocols and Verifiable Random Functions, as well as cryptographic techniques like symmetric encryption and multiparty computation. Performance metrics evaluated included latency, throughput, energy efficiency, and battery consumption, with Grey Relational Analysis ranking Algorand highest due to its low latency, high throughput, and minimal energy consumption.