Estimation of the mass density of biological matter from refractive index measurements

The quantification of physical properties of biological matter gives rise to novel ways of understanding functional mechanisms by utilizing models that explicitly depend on physical observables. One of the basic biophysical properties is the mass density (MD), which determines the degree of crowdedness. It impacts the dynamics in sub-cellular compartments and further plays a major role in defining the opto-acoustical properties of cells and tissues. As such, the MD can be connected to the refractive index (RI) via the well known Lorentz-Lorenz relation, which takes into account the polarizability of matter. However, computing the MD based on RI measurements poses a challenge as it requires detailed knowledge of the biochemical composition of the sample. Here we propose a methodology on how to account for a priori and a posteriori assumptions about the biochemical composition of the sample as well as respective RI measurements. To that aim, we employ the Biot mixing rule of RIs alongside the assumption of volume additivity to find an approximate relation of MD and RI. We use Monte-Carlo simulations as well as Gaussian propagation of uncertainty to obtain approximate analytical solutions for the respective uncertainties of MD and RI. We validate this approach by applying it to a set of well characterized complex mixtures given by bovine milk and intralipid emulsion. Further, we employ it to estimate the mass density of trunk tissue of living zebrafish (Danio rerio) larvae. Our results enable quantifying changes of mass density estimates based on variations in the a priori assumptions. This illustrates the importance of implementing this methodology not only for MD estimations but for many other related biophysical problems, such as mechanical measurements using Brillouin microscopy and transient optical coherence elastography.