Conformal Transformation–Based Mechanical Modeling for Continuous Blood Pressure Monitoring

Abstract Continuous blood pressure monitoring is essential for individuals, particularly those with cardiovascular diseases. Numerous studies have focused on the continuous measurement of blood pressure using versatile, flexible wearable sensors. However, the analytical relationship among blood pressure, arterial properties, and the pressure sensed by these flexible sensors remains unclear, leading to potential misdiagnoses or missed early warnings. This paper presents a mechanical model that establishes the relationship between blood pressure and the pressure sensed by flexible sensors for continuous blood pressure monitoring, utilizing the conformal transformation method. The blood artery and surrounding tissues are modeled as an elastic half-plane with a circular cavity, subjected to uniform radial pressure at the cavity's inner boundary. By combining conformal transformation and inverse conformal transformation techniques, explicit expressions for stress and displacement are derived in the tissues surrounding the blood vessel and on the skin surface. These findings are validated through finite element analysis and experimental results obtained using digital image correlation methods. Additionally, a simple scaling law relating the normalized pressure perceived by the sensor to the normalized artery depth and radius is established. The mechanical model established in this paper provides an analytical relationship among the pressure perceived by the sensor, blood pressure, and artery parameters, paving the way for analytically extracting accurate blood pressure values from the output electrical signals of flexible wearable sensors.