#### Description of the Volume-Clamp Method of Blood Pressure Measurements Using the Mathematical Model of the Lamé Problem

Marek Żyliński1, Wiktor Niewiadomski2, Gerard Cybulski3, Anna Gąsiorowska2
1Warsaw University of Technology, 2Mossakowski Medical Research Centre PAS, Warsaw, Poland, 3Department of Mechatronics, WUT

#### Abstract

The volume-clamp method allows non-invasive continuous blood pressure monitoring from a finger, despite its utility clamp method lacking a solid model that can describe its principle of operation. This paper proposes a simple model of the phenomena during continuous non-invasive blood pressure measurement from the finger cuff. Employed was a thick-walled cylinder loaded with inner (blood pressure) and external (cuff pressure) pressures – the Lamé cylinder. During measurement in the volume-clamp method, an artery wall is loaded with two pressures: inner blood pressure and external cuff pressure. The most straightforward description of artery geometry is a thick-walled cylinder – the inner radius works as the diameter of the artery, the external radius corresponds to finger diameter. To calculate stress and distortions, we use Lamé's equation for a thick cylinder. The simulation of method calibration (finding the correct pressure set-point) and blood pressure measurement was performed. It was found that in this model, wall stress is not neglected, even when blood pressure equals cuff pressure. The elastic properties of the artery wall are crucial to finding the correct set-point. Maximum volume oscillation occurs when transmural pressure fits the minimum of Young's modulus. For a constant modulus, calibration of the method is impossible. The reverse situation occurs for blood pressure simulation: for constant modulus, a linear characteristic was found. Young's modulus describes how the exponential transmural pressure relationship between blood pressure and cuff pressure, for given set-points, is disturbed. This result may explain blood pressure measurements with the volume-clamp method – finger properties, especially artery elasticity, can disturb measurement even when transmural pressure is 0. However, observations are constrained to the limitation of the model: the finger is not homogeneous, and Young's modulus for a real finger may be significantly different from the values used in this simulation.