# Conjecture on reflectionlessness of blood-vascular system as a wave-conducting medium

## TL;DR

This paper explores the hypothesis that the blood-vascular system acts as a nearly reflection-free wave-conducting medium, deriving equations for wave dynamics and analyzing PPG and LDF signals based on this conjecture.

## Contribution

It introduces a theoretical conjecture about the blood-vascular system's reflectionless wave propagation and derives governing equations for inhomogeneous parameters.

## Key findings

- Derived wave dynamics equations for inhomogeneous blood vessels
- Proposed the reflectionlessness condition for the vascular system
- Analyzed relationships between PPG and LDF signals based on the conjecture

## Abstract

Our research is related to the employment of photoplethysmography (PPG) and laser Doppler flowmetry (LDF) techniques (measuring the blood volume and flux, respectively) for the peripheral vascular system. We derive the governing equations of the wave dynamics for the case of extremely inhomogeneous parameters. We argue for the conjecture that the blood-vascular system as a wave-conducting medium should be nearly reflection-free. With the reflectionlessness condition, one can find the general solution to the governing equation and, on the basis of this solution, analyse the relationships between PPG- and LDF-signals.