In vivo blood viscosity estimation from microscopic images by solving an inverse incompressible Navier-Stokes problem

Reliable routines for assessing in vivo blood viscosity is an ongoing challenge. This limits bedside monitoring, cardiovascular risk stratification, and the parameterization of patient-specific computational hemodynamic models. While inverse modeling approaches have been explored in the biomedical field extensively, the feasibility of estimating effective blood viscosity remains insufficiently investigated, wherein many existing methods rely on simplified flow descriptions and have rarely been applied to real measurement data. In this work, we present a non-invasive framework that combines microvascular particle image velocimetry (micro-PIV) with computational fluid dynamics (CFD) to estimate the effective blood viscosity in vivo. Time-averaged velocity fields are reconstructed from high-speed microscopic image sequences of blood flow, using red blood cells as tracer particles. These velocity fields are incorporated into an inverse formulation of the incompressible Navier-Stokes equations for an either Newtonian or non-Newtonian fluid, which is solved using full CFD simulations. The proposed approach is validated using synthetic benchmark cases with varying noise intensity and vessel geometries, demonstrating robust recovery of power-law viscosity parameters. As a proof of concept, the framework is applied to in vivo microcirculatory data obtained from zebrafish embryos, yielding effective viscosity estimates consistent with values reported in the literature. The presented method establishes an image-based, physics-constrained framework for estimating blood rheology and provides a tool to improve the parameterization and validation of computational hemodynamic models.