A Combined Linear Poroelastic Model With Diffusion Optics for Photoplethysmography Simulations of Skin Perfusion
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In the present work, we aim at simulating PhotoPlethysmoGraphy (PPG) signals and their relations to skin blood pressure. PPG is a well-known technique used, primarily, for evaluating heart rates and measuring oxygen saturation; see [1]. However, the relation between PPG signals and blood pressure is challenging from the complex interaction between tissue perfusion and light absorption. Our approach consists in combining two models for skin perfusion and light scattering and absorption, respectively. First, for skin perfusion, we consider a linear poroelastic model, based on the work performed in [2]. We focus on blood volume content varia- tion from appropriate initial and boundary conditions. We are specifically interested in evaluating the variation in the concentration of hemoglobin in the skin, subject to external blood pressure. Second, for light scattering and absorption, we consider a diffusion model (see [3]) with its absorption coefficients are deduced from the skin chromophores concentration, where hemoglobin plays a crucial role in light absorption; see [4]. In this talk, we will also delve into solving numerically our problem using, in particu- lar, finite elements and the Nitsche method to couple the fluid and solid phases at the boundary. We will compare our computed results against measured data at several light wavelengths, to illustrate the performance of our approach. References [1] John Allen. Photoplethysmography and its application in clinical physiological mea- surement. Physiological measurement, 28(3):R1, 2007. [2] Mathieu Barré, Céline Grandmont, and Philippe Moireau. Analysis of a linearized poromechanics model for incompressible and nearly incompressible materials. Evo- lution Equations and Control Theory, 12(3):846–906, 2023. [3] Akira Ishimaru. Wave propagation and scattering in random media, volume 1. Aca- demic Press, 1978. [4] Steven L Jacques. Optical properties of biological tissues: a review. Physics in Medicine & Biology, 58(11):R37, 2013.
