Certain assays at certain times, the differences between the results for the two automatic edge detection methods can be very large with M(72) 68:9 for the barrier assay with 30,000 cells according to the ImageJ results whereas M(72) 82:0 for the same assay according to the automatic MATLAB method. Title Loaded From File Profiles in Fig. 2C and Fig. 2D show how M(t) varies with time according to the results obtained from the manual edge detection method applied to the images from the barrier assays initialized with 10,000 and 30,000 cells, respectively. Figure 2C and Fig. 2D each contain two sets of results corresponding to the average estimate of M(t) calculated using the low S threshold, and the average estimate of M(t) calculated using the high S threshold. The differences between the low and high threshold results in Fig. 2C is 14:2 , 25:0 and 25:7 for t 24, 48 and 72 hours, respectively. The difference between the low and high threshold results in Fig. 2D (30,000 cells) is 17:0 , 17:0 and 24:5 for t 24, 48 and 72 hours, respectively. These results indicate that estimates of cell migration using equation (1) are very sensitive to the details of the edge detection technique and that this sensitivity increases with time.the cell spreading process. For each barrier assay experiment, we solve equation (2) using the appropriate boundary and initial conditions (section 0.3) and previous estimates of the cell diffusivity [17]. The solution profiles in Fig. 3A and Fig. 3D, show the predicted cell density near the leading edge of the spreading cell populations in the barrier assay at t 24, 48 and 72 hours. The difference between the two initial cell densities in the barrier assays is shown in these profiles since we have c0 0:22 in the center of the barriers for the assays initialized with 10,000 cells (Fig. 3A) whereas we have c0 0:66 in the center of the barriers for the assays initialized with 30,000 cells (Fig. 3D). To determine a physical relationship between the threshold value S and the cell density at the corresponding detected edge, we compare our manual edge detection results to solutions of equation (2). For each set of averaged edge detection results, we scale the threshold values to match the corresponding solution of equation (2). The scaling is given by. Sscaled cmin z 23148522 max {cmin ?S{Smin , Smax {Smin ??0.6 A Physical Interpretation of the Leading EdgePreviously, we used three different edge detection techniques to determine the location of the leading edge of spreading cell populations in several barrier assays. Although these techniques Title Loaded From File produce visually reasonable approximations to the position of the leading edges, the techniques do not give us any physical measure, or definition, of the leading edge. To address this, we now interpret our edge detection results using a mathematical model of Table 2. Quantifying the cell migration rate using equation (1).where cmin and cmax are the minimum and maximum contours of the solution of equation (2), c(r,t), which enclose the same average area detected by the manual edge detection method applied with the minimum and maximum thresholds, Smin and Smax , respectively. Profiles in Fig. 3B and Fig. 3E compare the scaled edge detection results to corresponding solutions of equation (2) at t 24, 48 and 72 hours for barrier assays with 10,000 and 30,000 cells, respectively. For both initial density experiments at all time points, the shape of the c(r,t) density profiles matches the shape of the ed.Certain assays at certain times, the differences between the results for the two automatic edge detection methods can be very large with M(72) 68:9 for the barrier assay with 30,000 cells according to the ImageJ results whereas M(72) 82:0 for the same assay according to the automatic MATLAB method. Profiles in Fig. 2C and Fig. 2D show how M(t) varies with time according to the results obtained from the manual edge detection method applied to the images from the barrier assays initialized with 10,000 and 30,000 cells, respectively. Figure 2C and Fig. 2D each contain two sets of results corresponding to the average estimate of M(t) calculated using the low S threshold, and the average estimate of M(t) calculated using the high S threshold. The differences between the low and high threshold results in Fig. 2C is 14:2 , 25:0 and 25:7 for t 24, 48 and 72 hours, respectively. The difference between the low and high threshold results in Fig. 2D (30,000 cells) is 17:0 , 17:0 and 24:5 for t 24, 48 and 72 hours, respectively. These results indicate that estimates of cell migration using equation (1) are very sensitive to the details of the edge detection technique and that this sensitivity increases with time.the cell spreading process. For each barrier assay experiment, we solve equation (2) using the appropriate boundary and initial conditions (section 0.3) and previous estimates of the cell diffusivity [17]. The solution profiles in Fig. 3A and Fig. 3D, show the predicted cell density near the leading edge of the spreading cell populations in the barrier assay at t 24, 48 and 72 hours. The difference between the two initial cell densities in the barrier assays is shown in these profiles since we have c0 0:22 in the center of the barriers for the assays initialized with 10,000 cells (Fig. 3A) whereas we have c0 0:66 in the center of the barriers for the assays initialized with 30,000 cells (Fig. 3D). To determine a physical relationship between the threshold value S and the cell density at the corresponding detected edge, we compare our manual edge detection results to solutions of equation (2). For each set of averaged edge detection results, we scale the threshold values to match the corresponding solution of equation (2). The scaling is given by. Sscaled cmin z 23148522 max {cmin ?S{Smin , Smax {Smin ??0.6 A Physical Interpretation of the Leading EdgePreviously, we used three different edge detection techniques to determine the location of the leading edge of spreading cell populations in several barrier assays. Although these techniques produce visually reasonable approximations to the position of the leading edges, the techniques do not give us any physical measure, or definition, of the leading edge. To address this, we now interpret our edge detection results using a mathematical model of Table 2. Quantifying the cell migration rate using equation (1).where cmin and cmax are the minimum and maximum contours of the solution of equation (2), c(r,t), which enclose the same average area detected by the manual edge detection method applied with the minimum and maximum thresholds, Smin and Smax , respectively. Profiles in Fig. 3B and Fig. 3E compare the scaled edge detection results to corresponding solutions of equation (2) at t 24, 48 and 72 hours for barrier assays with 10,000 and 30,000 cells, respectively. For both initial density experiments at all time points, the shape of the c(r,t) density profiles matches the shape of the ed.