Quantitative Analysis of Viscoelastic Properties of Red Blood Cells Using Optical Tweezers and Defocusing Microscopy

This methodology allows to explore the mechanical behavior of erythrocytes, characterizing their viscoelastic parameters and soft glassy features for several physiological and pathological conditions. Our single-cell based method verifies video references by using the metal values for the form factor that relates forces and displacements, the stresses and scrapes in the erythrocyte surface. Begin by pouring silicone grease over the rubber ring surface in a way that covers the entire perimeter.

Next, place the rubber ring on the coverslip with the grease side facing the coverslip. Wait for five minutes for proper attachment, and the sample holders are then ready to receive the cell culture. Next, with the solution of cells previously prepared following the written protocol, seed the cells in the sample holder.

Add 0.2 microliters of a 10%volume by volume polystyrene sphere solution to the sample. Place the second coverslip above the rubber ring. Close the setup and finish the sample preparation.

Finally, move the entire sample to the microscope. To start with the experimentation, use the OT system, trap the sphere with the OT laser, and then attach it to the coverslip, close to the cell. Then, trap another sphere and repeat the same attachment procedure by pressing the sphere against the cell surface, near the top surface and close to the cell edge.

Add a sinusoidal function of amplitude and varying frequencies. Next, press the start"button, using the piezoelectric stage to allow the piezoelectric displacement. Keep the RBC sphere in the trap and submit the sample to a cycle of movements using the previously set sinusoidal function.

For analysis, open the ImageJ software and import the entire movie obtained during the sinusoidal movements. Click on adjust, and then select option threshold. Adjust the threshold with both scroll bars, and select the reference sphere by clicking on file, followed by rectangle.

Then in the analyze tab, click on set measurements"and select the center of mass"option. Click again on the analyze tab and select analyze particles. A new window containing a table with xy coordinates for the center of the mass will appear.

Repeat the procedure for the other sphere attached to the RBC surface. Open the analysis software and import the txt files previously obtained. Generate a plot with the centers of mass on the y-axis and time on the x-axis.

Plot the results on a graph using the x-axis for loss constant, denoted by K double prime, and the y-axis for storage constant, denoted by K prime. First, for video acquisition, move the piezoelectric stage in the xy direction, using the software to search for an isolated cell attached to the coverslip. Trap and attach a polystyrene sphere of known diameter to the RBC surface.

Next, using the piezoelectric stage, move the trapped bead attached to the RBC surface to deform the cell, and then attach the bead to the coverlip. Now, change the z-axis position to find the focused image. After fixing the position, use the camera software to create a movie of the entire cell.

Then, move the z-axis position two micrometers down or up to obtain a defocused image for the chosen cell. Finally, without changing the z-axis position, search for a region without cells to repeat the same procedure, and create a movie of the image background. For contrast image acquisition, first find the value of N zero, click on the polygon selection icon, then click on the analyze tab and select measure.

Next, use the contrast equation to determine N image minus N zero, and execute this by selecting math"under process, followed by subtract. Later, divide the result by N zero minus B.Finally, find the contrast for the focused and defocused images. Now, use the Hartley transform to obtain the RBC thickness.

In ImageJ, click on process, followed by FFT"and FFT options, and then choose FHT. Then perform the inverse transform FHT by selecting process, followed by FFT"and FFT. Use the resulting image to obtain the height profile.

After finding the image that contains the RBC height profile use the two micrometers defocused contrast to create a set of two images in ImageJ. To find the form factor, use an ImageJ customized macro to analyze the stack. The macro will deliver a table with the edge's position, the perimeter, the inverse of the perimeter, and an image of the analyzed cell.

Check whether the edges of this image are similar to the edges of the reference figure. Otherwise, repeat the procedure, and use the sum of the inverse of the perimeter to find the form factor. Start by organizing the experimental data in a table.

Create a new table in the analysis software by clicking on the file tab. Determine 10 different columns for the parameters. To plot the curve G prime and G double prime in the analysis software, use the data from the previous table and click on the plot"button.

To obtain parameters Gamma and GM, click on the curve fit tab and select fit1"to open a new window. Select the square, click on the define button, and type the equation. Click on the okay"button in both the windows, and the fitting will appear.

Next, create two other plots, namely G prime and G double prime as a function of omega. Place the error bars only on the y-axis, as previously demonstrated. Repeat the curve fitting procedure, select G"option.

Click curve definition"under general fit, and then write the concerned equation. Finally, click on okay, and a curve fitting will appear along with the values for Alpha and G zero. Again, perform another curve fitting procedure.

Select G"option, click curve definition"under general fit, and then write the concerned equation. Finally, click on okay, and a curve fitting will appear. The figure shows the storage elastic constant as a function of the loss elastic constant.

The linear dependence observed demonstrates that the RBC surface can be considered a soft glassy material. By applying the values for overall cell form factor and RBC surface thickness, the values for the exponent Alpha can be determined. This technique may provide the basis for novel diagnostic methods that correlates changes in erythrocytes'viscoelastic properties with modifications in blood flow of individuals with different pathologies.