In-situ calibration for optimizing parameters for sorting cells

The theory explained in section 4.3 shows that it is possible to find the optimum set of parameters to achieve fractionation of binary colloidal samples if the sizes and

refractive indices of the particles to be fractionated are known. In principle the same theory can be extrapolated to achieve fractionation of cells. However the sizes and refractive indices of the cells to be sorted are unknown, which makes it practically difficult to optimize the system and to choose the right set of parameters to obtain fractionation of cells using optical landscape. The non-spherical shape of cells makes the task further complicated. Other unknown parameters are the viscosity and refractive index of the buffer medium where cells have to be suspended. With all these unknown parameters, the four parameter space of the tunable parameters makes it practically impossible to find the optimum set by a trial and error approach.

A solution to this would be to draw an analogy between a spherical colloidal particle with known size and refractive index and a particular species of cell. Fundamentally fractionation of micro-particle in an optical landscape is facilitated by the interplay between the optical radiation force and viscous drag force. If it is possible to find a spherical colloidal particle (eg. polystyrene bead) which interacts with the optical trap, while in a flow similar to that of a particular cell species which is to be fractionated, then it is possible to optimize the parameters for line trap based cell sorter based on the size and refractive index of the colloidal particle.

An in situ calibration may be performed to find the spherical colloidal particle whose interaction is similar to that of a cell in the flow-optical trapping system. A drag force method can be used to find a figure of merit which is directly related to the Q- value of the trap. The Q-value is a dimensionless number which relates to the efficiency of transfer of momentum from the optical beam to the particle which can be expressed as [85]: d m c Q F n P = (4.10)

Where, F is the drag force which may be required to remove the particle from the d

trap may be calculated from equation 4.6, for a given optical power P in a fluid of refractive indexn . Equation 4.10 shows that Q value depends on the refractive index m

and viscosity of the buffer medium which is unknown in this case. Hence it is not possible to measure Q value in this case. However it is possible to estimate the fluid

velocity at which the particle would escape from the trap, which is a parameter that directly related to the Q value.

The in situ calibration can be performed on a chip whose schematic is shown in Fig. 26. In this design, two parallel microfluidic channel are connected with a cross channel. One of the channel act as a sample loading channel and the other channel would be the channel for drag force measurement.

Fig. 26: Schematic diagram of the design of the chip for in situ calibration for finding spherical colloidal analogue to a cell for passive optical fractionation. (Diagram not drawn to the scale)

In order to perform the experiment, the microfluidic chip should be filled with the buffer solution which is used for suspending the cells. Spherical colloidal particles (eg. polystyrene micro-beads), suspended in the same buffer solution may be injected into the sample channel. A particle from the sample channel may be trapped using a single optical trap and brought to the measurement channel. While the trapped particle was in the measurement channel, the flow rate at the measurement channel should be increased till the particle escaped from the trap. This would give the escape velocity for a particle with a particular size and refractive index. Performing this measurement in a separate measurement channel helps to avoid interaction between other particles in the channel. The same process may be repeated to build up the statistics. By measuring the escape velocity for micro-beads with different sizes, it is possible to create a calibration graph of size vs. escape velocity. The escape velocity is a parameter that is directly related to the Q factor of the trap.

Fig. 27 shows a calibration plot for polystyrene micro-spheres with varying diameters. As can be seen from the graph, the graph does not follow a constant trend across the whole range of measurement. The curve tends to be linear for diameters higher than 3 µm. This is because the relationship between the size and radiation force undergo a transition from a third order dependency to a quadratic dependency in this region [86]. Such variation makes it complicated to fit a function to the data obtained for size vs. escape velocity. Hence the obtained data was interpolated to get a calibration curve.

Fig. 27: Calibration plot for escape velocities for polystyrene micro-beads with varying diameters. The solid curve is obtained by interpolating the escape velocities obtained for five different sizes of particles. The error bar at each point was the standard deviation of six escape velocity measure-

ments.

The procedure to find escape velocity can be repeated for cells to find an equivalent escape velocity for a particular cell. Using this information it is possible to find a polystyrene micro-sphere which is equivalent to the cell under consideration. Since both the calibration measurement and the measurements on cells are carried out on the same environment within the microfluidic channel, the obtained figure of merit would contain all other factors such as degradation of the trap stiffness due to optical aberrations and variation in the drag force due to boundary effects.

For cell samples, intra species variation in escape velocity might be expected due to the variation in size and shape of the cells at various stages of its cell cycle. If the standard deviation of the escape velocities obtained for two cell species are relatively large in such a way that they overlap, this gives an indication that it would not be possible to optically fractionate a binary mixture of these cell samples. Thus in situ calibration measurements can act as an experiment which can be used to determine the feasibility of optically fractionating two types of cell species. In some cases it would not be possible to obtain fractionated samples for performing the calibration experiment. In such cases the feasibility of fractionating such samples may be estimated from a relatively large (n~100) number of measurements of escape velocity of cells from the binary mixture. If the distribution of the obtained escape velocities shows a trend of grouping into two distinct values, it would give an indication that it is possible to fractionate them.

Once a micro-bead size which is equivalent to a cell species is identified the code shown in Fig. 25 can be used to find the optimum parameters for performing the experiment.

Further investigation is required with different cell samples to validate this procedure and implement this in experiments for passive optical fractionation of cells using optical landscapes.

4.5

Conclusion

Passive optical sorting of micro-particles using periodic optical landscape has been proven to be effective and highly sensitive for fractionating micro-particles or nano- particles [77]. Extending this technology further would be beneficial to develop devices to achieve passive optical fractionation of cells. Although passive sorting techniques would not be able to compete with already established active sorting techniques like FACS, the prospect of achieving label free fractionation of biological particles makes it a desirable technology. This could open up new opportunities which might have applications in the field of fundamental biology and biotechnology.

The research discussed in this chapter is a step towards developing such passive optical sorting technology based on periodic optical landscape. Such a device should be

a combination of an optical trapping system with a microfluidic platform. An optical trapping system, capable of creating a periodic optical landscape using time shared multiple optical trap was constructed. An acousto-optic deflector was used to obtain time-shared multiple optical traps. An interface was developed using LabVIEW in order to control this optical trapping system. This user friendly interface can be used to generate customized optical landscapes, suitable for optical fractionation experiments.

Although the theory of optical fractionation using periodic optical landscape is well studied, the theory is based on the assumption that the particle to be sorted is spherical in shape with known size and refractive index. When it comes to fractionation of cells, this theory becomes insufficient for cell samples since they generally are non-spherical and the refractive index and size of the samples are not known. A solution to this issue is proposed based on in situ calibration, where a spherical micro-particle, whose interaction with optical trap is similar in a flow when compared to that of a cell. A drag force measurement can be performed within the microfluidic channel in order to estimate the escape velocity of a particle from the optical trap. An interpolated calibration curve obtained from similar measurements for particles of different sizes can be used to find a spherical micro-bead equivalent to the cell. The results from these measurements may be used to assess the feasibility of fractionating two types of cells. If it is feasible, the optimum set of parameters for the device to achieve efficient fractionation may be obtained.

Further investigations are required for the validation of this technique with various cellular samples. Once the calibration procedure is completed and the optimum set of parameters for fractionation is identified, the DA-AOD based optical trapping system may be used to achieve fractionation of different types of cells flown through a microfluidic chip. It is also necessary to develop techniques to retrieve fractionated cells from microfluidic chip. Fractionation efficiency and viability of cells after fractionation should also be assessed using multi modal approaches.

Contributions

P. C. Ashok was trained on the DA-AOD based optical trapping technology by T. Cizmar. P. C. Ashok built the optical trapping system with the assistance of S. Kagitani. P. C. Ashok developed the LabVIEW based interface for optical trapping setup. S. Kagitani wrote the Mathematica code for optimizing the parameters for fractionation with the assistance of P. C. Ashok. P. C. Ashok developed the idea of in situ calibration for finding a spherical micro-particle equivalent for cells.