General Solution to the Mixing Problem: Application to Medical Research and Diagnostics

TL;DR

This paper presents a comprehensive solution to the classical mixing problem, tailored for biomedical applications involving fluid movement and sampling in difficult-to-access areas, enhancing understanding and measurement of biologic markers.

Contribution

It introduces a general solution to the mixing problem specifically adapted for physiological and biomedical contexts, including challenging sampling scenarios.

Findings

Provides a mathematical framework for fluid mixing in medical contexts.

Enhances sampling techniques for inaccessible bodily fluids.

Facilitates accurate measurement of biologic markers.

Abstract

The mixing problem is classically encountered in the study of differential equations applied to fluid dynamics. An understanding of fluid movement under constraints is particularly important in the field of medicine as many therapeutics and biologic molecules are dissolved in bodily fluids. Many areas of biomedical research and diagnostics also rely on fluid sampling to obtain accurate measurements of biologic markers. We present in this manuscript the general solution to the mixing problem in the context of studying physiological phenomena based on the movement of fluid acting as a carrier for medically relevant molecules/solutes. We also expanded the general solution to become more compatible with areas of biomedical research and diagnostics that seek to characterize bodily fluids located in areas that are difficult to sample.