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Spatiotemporal Measurement of Concentration-Dependent Diffusion Coefficient
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  • Adib Ahmadzadegan,
  • Jiacheng Zhang,
  • Arezoo Ardekani,
  • Pavlos P Vlachos
Adib Ahmadzadegan
Purdue University

Corresponding Author:[email protected]

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Jiacheng Zhang
Purdue University
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Arezoo Ardekani
Purdue University
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Pavlos P Vlachos
Purdue University System
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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.
May 2022Published in Physics of Fluids volume 34 issue 5 on pages 051910. 10.1063/5.0094620