Spatiotemporal measurement of concentration-dependent diffusion coefficient

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. Most approaches such as Fluorescence Recovery After Photobleaching (FRAP), assume the diffusion coefficient is constant. Hence, they cannot capture the concentration dependence of the diffusion coefficient. Other approaches measure the concentration-dependent diffusion from an instantaneous concentration profile and lose the temporal information. These methods make unrealistic assumptions and lead to 100% error. <p>We introduce a framework that utilizes spatial and temporal information in a sequence of images and numerically solves the general form of Fick's second law using Radial Basis Functions to measure the concentration-dependent diffusion coefficient. We term this approach Concentration Image Diffusimetry (CID).</p> <p>Our method 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 bootstrapping.</p> <p>We assessed CID's performance using synthetic images. Our analysis suggests that CID accurately measures the diffusion coefficient with less than 2% error for most cases. We validated CID with FRAP images and showed agreement with established FRAP algorithms for samples with a constant diffusion.</p> <p>Finally, we demonstrate the application of CID to experimental datasets of protein diffusion into tissue. In conclusion, this work presents the first of its kind image-based methodology that uses the spatial and temporal changes of concentration fields to measure the concentration-dependent diffusion coefficient.

Concentration‐dependent diffusion of unlabeled protein within an in vitro hyaluronic acid matrix

“…The images captured by the complementary metal–oxide–semiconductor sensor in each of the scanners were converted from scanner format to image format (tiff) (Figure 1b) using Bioformat (Linkert et al, 2010) in MATLAB R2021a (MathWorks) (Ahmadzadegan et al, 2022; dos Santos et al, 2022). The corresponding numerical files consisted of pixel values (PVs) that represented light intensity in each of the ~116,000 pixels that make up the region of interest (ROI) as illustrated in Figure 1c,d.…”

“…The pixels corresponding to PV ≤ 2.35 × 10 3 were set to zero across the entire matrix leaving the circles in Figure 1b that represented BSA, in this example. The PV associated with the background (i.e., 2.35 × 10 3 ) is due to the combined autofluorescence of the quartz bottom, HA matrix, and quartz lid within the ROI (green dashed line in Figure 1c) (Ahmadzadegan et al, 2022; dos Santos et al, 2022).…”

“…The accuracy of the measurements was evaluated through mass closure that averaged between 95%–105% for BSA and 94%–109% for bIgG. The resulting concentration maps were analyzed using spatiotemporal measurement of diffusion coefficients with the computational solution (Equation 1 and Table 2) for concentration‐dependent diffusion resulting in the curves shown in Figure 2 (Ahmadzadegan et al, 2022). …”

“…We have recently reported an in vitro S ubcutaneous M atrix (ISM) system that enables direct measurement of unlabeled proteins within an in vitro matrix representing the electrostatic character of the SC tissue environment (dos Santos et al, 2022). Concurrently, Ahmadzadegan et al (2022) developed a method for the direct calculation of concentration‐dependent diffusion from images of protein movement within an HA matrix. The combination of the two methods enables the diffusion of unlabeled proteins within an HA matrix to be determined.…”

“…The internal standards were used to account for any fluctuations in response from the scanner, protein, and device. The 20 μL sample volumes were relevant to facilitating testing when only small amounts of proteins would be available at the early stages of drug development (dosSantos et al, 2022).The images captured by the complementary metal-oxidesemiconductor sensor in each of the scanners were converted from scanner format to image format (tiff) (Figure1b) using Bioformat(Linkert et al, 2010) in MATLAB R2021a (MathWorks)(Ahmadzadegan et al, 2022;dos Santos et al, 2022). The corresponding numerical files consisted of pixel values (PVs) that represented light intensity in each of the ~116,000 pixels that make up the region of interest (ROI) as illustrated in Figure1c,d.…”