Abstract
We introduce a new method to measure the concentration-dependent
diffusion coefficient from a sequence of images of molecules diffusion
from a source towards a sink. Generally, approaches measuring the
diffusion coefficient, such as Fluorescence Recovery After
Photobleaching (FRAP), assume that the diffusion coefficient is
constant. Hence, these methods cannot capture the concentration
dependence of the diffusion coefficient if present. Other approaches
measure the concentration-dependent diffusion coefficient from an
instantaneous concentration profile and lose the temporal information.
These methods make unrealistic assumptions and lead to 100% error. We
introduce a novel image analysis framework that utilizes spatial and
temporal information in a sequence of concentration images and
numerically solves the general form of Fick’s law using Radial Basis
Functions (RBF) to measure the concentration-dependent diffusion
coefficient. We term this approach as Concentration Image Diffusimetry
(CID). Our method makes no assumptions about the sink and source size.
CID is superior to existing methods in estimating spatiotemporal changes
and concentration-dependent diffusion. CID also provides a statistical
uncertainty quantification on the measurements using bootstrapping,
improving the reliability of the diffusion measurement. We assessed
CID’s performance using synthetically generated images. Our analysis
suggests that CID measures the diffusion coefficient with less than 2%
error for most cases. We validated CID with FRAP experimental images and
showed that CID agrees with established FRAP algorithms for constant
diffusion coefficient. Finally, we demonstrate the application of CID to
experimental datasets of a concentration gradient-driven protein
diffusion into a tissue replicate.