Spatiotemporal measurement of concentration-dependent diffusion coefficient
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Spatiotemporal measurement of concentration-dependent diffusion coefficient

With advancements in biotechnology, the production of highly concentrated antibody formulations for subcutaneous injections is becoming common in the biopharmaceutical industry. Measurement of transport and more importantly diffusion of proteins in tissues is essential in drug development.

There is evidence suggesting that the assumption of the constant diffusion coefficient is not valid for high-concentration protein suspensions, and protein diffusion is, in fact, a function of the concentration of the proteins. However, there is no reliable method for measuring the concentration-dependent diffusion coefficient.

We introduce a novel image analysis method to measure the concentration-dependent diffusion coefficient.  We utilized both temporal and spatial changes of the concentration field from the sequence of images and numerically solves the general form of Fick’s second law using radial basis functions (RBF). We termed this method the Concentration Image Diffusimetry (CID).

This methodology works for low and high molecule concentrations and different sizes, such as proteins, quantum dots, particles, etc. We assessed CID’s performance using synthetically generated images and show it achieves less than 2% error. We validated CID with FRAP experimental images and showed that CID agrees with established FRAP algorithms for samples with a constant diffusion coefficient. Finally, we demonstrate the application of CID to experimental datasets of a concentration gradient-driven protein diffusion into a tissue replicate.

Figure1. CID’s flow chart. CID utilizes the spatial and temporal information in a sequence of concentration images and numerically solves the general form of Fick’s second law using radial basis functions (RBF) to report the concentration-dependent diffusion coefficient. CID makes no assumptions about the sink and source size and the diffusion dependence on concentration. 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 a bootstrapping approach, improving the reliability of the diffusion measurement
Figure 2 (a) FRAP experiment for validation using a circular bleach pattern. (b) FRAP experiments for validation using a P-bleach pattern. (c) Comparison of CID with constant diffusion solver and FRAP for fluorescein diffusion in a mixture of PBS and glycerol with circular and P-bleach patterns. (d) Demonstration experiment using images of concentration gradient driven diffusion of BSA in HA; (e) the raw and preprocessed intensity maps across the dashed line shown in (d); (f) the measured diffusion coefficient as a function of concentration using CID, FRAP, and the constant D solver. Shadows and error bars show the standard deviation for five replicates.

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