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In this work, a preliminary study in the application of a laser trap for ionization of living carcinoma cells is presented. The study was conducted using BT20 breast carcinoma cells cultured and harvested in our laboratory. Each cell, for a total of 50 cells, was trapped and ionized by a high intensity infrared laser at 1064 nm. The threshold radiation dose and the resultant charge from the ionization for each cell were determined. With the laser trap serving as a radiation source, the cell underwent dielectric breakdown of the membrane. When this process occurs, the cell becomes highly charged and its dielectric susceptibility changes. The charge creates an increasing electrostatic force while the changing dielectric susceptibility diminishes the strength of the trapping force. Consequently, at some instant of time the cell gets ejected from the trap. The time inside the trap while the cell is being ionized, the intensity of the radiation, and the post ionization trajectory of the cell were used to determine the threshold radiation dose and the charge for each cell. The measurement of the charge vs ionization radiation dose at single cell level could be useful in the accuracy of radiotherapy as the individual charges can collectively create a strong enough electrical interaction to cause dielectric breakdown in other cells in a tumor.
© 2016 Optical Society of America
1. Introduction
In medicine, radiotherapy, or radiation, is a mainstay treatment for cancer. Approximately 50% of cancer patients receive radiotherapy during the course of treatment. Radiotherapy also remains a cost effective treatment as well as it only accounts for 5% of the total cost of care [1]. Medicinally, radiotherapy is used largely to eradicate cancerous tissue by killing cancer cells. This is achieved largely by damaging the DNA sequence of the cancer cell, which either directly kills the cell by eliminating its ability to function or inhibits the cell’s production ability, that is, sterilization [2]. However, radiation also has the same effect on the healthy cells that surround the cancerous tumor. This is termed radiation-induced tissue toxicity. Radiation-induced tissue toxicity can consist of acute effects, or the more detrimental, late effects, such as ischemia, necrosis, and tissue fibrosis [2,3]. Thus, it is important to the patient’s recovery that the damage done to healthy cells be minimized. The balance of enough radiation to effectively kill the cancerous cells and with limitations to prevent the ill effects of radiotoxicity to the healthy cells is called the therapeutic ratio [2]. Normal cells proliferate much slower than cancer cells, meaning that they have more time to repair damage due to radiation before replicating. This is why traditionally, radiation doses are fractionated. The current formula used is the linear-quadratic model that factors the time-dose factors for both cancerous and normal cells [1]. Historically, the accepted tolerable doses of radiation have been derived empirically and are based on retrospective data and unpublished clinical observations [3]. A more accurate therapeutic ratio, based on the cellular level, could help eliminate radiation-induced tissue toxicity and improve the sterilization of the cancerous cells.
Laser trapping has long been used to manipulate biological samples at the micron level [4,5]. However, to the best of our knowledge, it has never been used to study the ionization of a live cell in application of measuring the threshold radiation dose. In our previous studies, we have used a high power laser trap to measure therapeutic efficacies in sickle cell anemia (SCA) disorder treatments [5]. During this process it was observed that a high power laser trap could ionize the human blood cells, effectively killing them, and eject them from the trap [6]. The hypothesis of this research project is that in the same fashion, the laser trap can be used to measure the threshold radiation dose that ionizes and kills carcinoma cells. While the cell is being ionized from the absorbed radiation, it becomes increasingly charged. The magnitude of this charge in the individual cells could be small and its standalone effect may not be significant. However, in a real a tumor, the collective charge of the individual cells can produce a strong enough electrical field to cause similar ionization effect on other cells, like incident radiation. Measurement of the magnitude of the charge vs radiation dose per cell and factoring its chain effect in the radiodosimetry could reduce the amount of radiation dose that is prescribed in the treatment of cancer. Therefore, such an approach could be valuable in improving the accuracy of radiotherapy. The formulation of an accurate radiation dosage that will kill a tumor while limiting damage to the surrounding healthy tissue is critical to the remission of the cancer.
In this paper, we are presenting a study introducing the measurement of radiation dose vs charge at the single cell level based on laser trapping technique. The study uses BT20 breast carcinoma cells cultured and harvested in our laboratory. One cell at a time, for a total of 50 cells, was trapped using a high intensity gradient infrared laser at 1064 nm. With the infrared laser as a source of radiation, the radiation dose and the resulting charge were determined for each cell. We begin, in section 1, with the discussion of the methods and procedures used for culturing, harvesting, and trapping the cells. In section 3, we present a theoretical explanation of how a cell undergoes dielectric breakdown and becomes ionized by the laser trap. The analyses of the experimental data to determine the radiation dose vs charge will be carried out in section 4. Finally, in section 5, we summarize and conclude the main results of the study.
2. Methods
2.1 Culturing of cells
The biological sample used was human breast carcinoma cells BT20. The BT20 cells were obtained from American Type Culture Collection (ATCC) and grown in the growth media RPMI-1640, supplemented with 10% fetal bovine serum (FBS) and 100 U/mL penicillin/streptomycin. The cells were incubated in a humidified atmosphere with 5% CO2 at 37°C, and cells with a passage number 5-10 were used for the following assays. The cells were harvested from the culturing vessel by using 1X trypsin-EDTA solution, and resuspended in the growth media at an intensity of 2 × 104 cells/mL.
2.2 The laser trap
The design for the complete set-up of the experiment is shown Fig. 1. The main elements of this experimental set-up are a high power infrared laser lasing at 1064 nm, an inverted microscope equipped with a high numerical aperture, and a computer-controlled digital camera. The laser was a linearly polarized infrared diode laser (LS) with a maximum power of 8 watts. The original beam size was 4 mm: this was expanded using a 20 × beam expander (BE). The beam was then again resized to approximately 2 cm using a pair of two lenses (L1 and L2), with focal lengths of 20 cm and 5 cm. Four optical mirrors (M1-4) were used to direct the beam into the dichroic mirror (DM) at the laser port of the inverted microscope (IX 71-Olympus). The dichroic mirror is angled at 45° such that the reflected light makes an angle normal to the incident light. The aligned beam would then be reflected into the back of the objective lens (OL) that has a 100 × magnification and a 1.25 numerical aperture. Two lenses (L3 and L4) are positioned such that the laser trap is on the focal plane of the microscope.
Fig. 1 Laser trap experimental set up: laser (LS), λ/2-wave plate (W), polarizer (P), dichroic mirror (DM), optical lens (OL), and digital camera (CCD) [5]
The power of the laser was controlled by a λ/2-wave plate (W) and a polarizer (P). At the location of the trap there was 19% efficiency with respect to the power measured before the fourth lens, L4. The power before L4 was measured near the focal point of L3 using a high power meter calibrated at 1064 nm wavelength. We then measured power at the trap location, using the same power meter placed on top of the microscope stage with head covering the tip of the objective lens. This efficiency was used to keep the power the same at the trap location where for each cells trapped and ionized in this study.
2.3 Experimental procedure
A sample of the BT20 cells was placed on a well slide that was then mounted on a mechanical microstage. An image was captured of the cell before the laser port to the microscope was opened. The port was then opened: the cell was consequentially levitated and trapped. During this time, successive images were taken until the cell had been fully ejected. To ensure focused images for later analysis, the microscope was focused to the plane of the laser trap. Additionally, to avoid interference due to contact with the bottom of the slide, the cell was raised by elevating the objective lenses.
The process for ionizing breast cancer cells was carried out successfully for 50 cells. For standardization, only three cells were ionized per slide. This was done to both reduce the potential for a Coulombic interaction due to the ionized cells remaining on the slide and to minimize the time a particular slide was radiated. When trapping the second and third cell precaution was taken to move in the direction away from the recently ionized cell.
3. Theory-cell membrane dielectric breakdown
A basic model of a cell is a spherical shell that contains a solution of dissolved ions [6]. The spherical shell, or membrane, itself is a phospholipid bilayer, meaning that it is two phospholipid molecules thick. The phosphate end is hydrophilic and the lipid end is hydrophobic. Thus the cell is in its lowest energy state when the lipid end is joined together with the other layer’s lipid end and the phosphate ends are on the outside barriers. Since there are no free ions in the membrane, it also serves as a good insulator. The conductance per area of the membrane is on the order of 10−13 Ω−1 m−2 for pure phospholipid bilayers. For biological membranes, this value is several magnitudes greater as there exist ionic channels in the membrane which allows more current to flow [8].
The principle types of ions contained inside the membrane include Na+, K+, Ca2+, and Cl−. Different concentrations of these ions can cause a gradient inside the cell [9]. In other words, due to the accumulation of mobile charge carriers at the inner surface of the membrane, there is an electrical potential, or voltage across the cell.
A simple model of a cell is an insulating, or dielectric, spherical shell made up of a two phospholipids that envelopes an ionic fluid. Though the phospholipid bilayer membrane does not contain free charges, it does contain bound charges. Under a strong applied electric field, these bound charges can become extremely polarized. The force of an external electric field, Eo, causes the dipoles in the material to align with the electric field. This is because as any dipole, that is out of line with the applied electric field, experiences a torque that tends to align the dipole with the applied electric field. The alignment of the dipoles decreases the external electric field to E = Eo / ɛr, where ɛr is the dielectric constant of the medium defined (the cell membrane). The dielectric constant of the membrane is approximately 5 [10]. This means that inside the membrane the applied electric field is reduced by a factor of 5.
Furthermore, in the case of a dynamic electric field, such as electromagnetic waves, at a certain frequency of oscillation of electric field, the charges can no longer respond in time to the applied external field. This means that the torque being applied to the individual dipoles does not have enough time to realign the dipoles before the electric field reverses again. Physically, in this strong external electric field the cell’s conductance and permeability increases rapidly [11]. At a certain strength of electric field, the cell will undergo irreversible dielectric breakdown of the membrane. This process mechanically ruptures the cell [12]. Therefore, the cell’s ionic solution is no longer contained and under the applied electric field, the cell becomes ionized due to the attraction and repulsion of the free charges.
Due to the electric field of the laser, the cell is subject to an electrostatic force, as a charge, q, is developed due to this dielectric breakdown. During the course of the dielectric breakdown, the cell builds up a greater and greater charge. Consequently, the electrostatic force on the cell is growing stronger and stronger. When the electrostatic force is greater than the intensity gradient trapping force of the laser trap, the cell will be pushed out or ejected from the laser trap. At this point the charge on the cell is constant.
4. Data analysis and results
4.1 Preemptive analysis
Using the software ImagePro, a conversion factor was found for pixels to meters by measuring silicon beads that had a known diameter. This value was 7.27 × 10−8 meters per pixel. Using the captured images of the cells before they were trapped, the diameter of the cell was measured. A spherical cell was assumed; therefore, the cross-sectional area was found as well as the volume. The mass of each cell was found by using the widely accepted density of cancer cells of 1000 kg/m3 [13]. Using the average volume 5.835 × 10−16 m3 calculated using the measured cross-sectional area the average mass of the cells was found to be 5.835 × 10−13 kg.
To find the average amplitude of the electric field, Eo, the Poynting vector of the laser beam, S = Eo Bo/µo, was used in conjunction with the recorded power, P, at the trap location. It can be easily shown that the peak magnitude of the Poynting vector is proportional to Eo2 and the laser beam area, A. Thus the amplitude of the electric field at the trap location can be expressed as
where v is the speed of light in in the medium that the cells are suspended in. The power of the trap used was recorded at the location of the trap for each cell. On average the power was 744 mW. For v we used the speed of light in water, v = 2.3 × 108 m/s and µo = 4π × 10−7 H·m−1. The beam size is estimated, following the method by Lian et al. [14], using w = (d0 cos(2αmax) + z0) tan(αmax), that depends on the size of the cell (d0), position of the trap (z0) as measured from the tip of the objective lens, and the maximum angular position of the incident ray with respect to the beam axis (αmax). αmax is determined by the numerical aperture (NA) of the objective lens and the refractive index of the surrounding medium (nwater), such that NA = nwater sin(αmax). For our trap, NA = 1.25 and nwater = 1.3 which gives αmax = 78°. Thus with d0 = 10.13μm and z0 = 100μm (the thickness of the coverslip), the beam size is estimated to be 426μm.The absorbed radiation energy was determined for each cell by the measured power for the incident beam at the location of the trap. A video was compiled of the images captured for each cell. A conversion factor was created between the time elapsed in the images using the time stamp and the length of the video. In the video analysis software, LoggerPro, the displacement versus time can be collected as sets of data points. In order to ensure that the displacement versus time measurements are synchronized for all the cells, the time will be reset to zero at the instant that the cell is first ejected from the trap. Figure 2 displays sample images of the trajectory a BT20 cell as it being ejected and receding away from the trap.
For the theoretical model, we considered three forces acting on the cell with mass m ejected from the trap at a distance r from the center of the trap, at a given time t. These forces were the electrostatic force, FE, the drag force, FD, and trapping force of the laser, FT. The electrical force and the trap force depend on the electric field strength at the position of the cell r measured from the center of the trap. Since the laser beam is Gaussian, one can assume an electric field at a distance r,
where ω0 is the beam waist of the laser. The electrical force that depends on the charge developed on the ejected cell is directly proportional to the electric field. The drag force due to the viscosity of the medium is equivalent towhere Stokes’ law was used to describe the drag coefficient, such that β = 6πµR, as the cells were assumed to be spherical with radius R in a fluid with viscosity µ. The viscosity of the growth media RPMI-1640 was approximated to be on the same order of water, which at room temperature is 1.0 × 10−3 Ns / m2. The trapping force is proportional to the gradient of the electric field in Eq. (2) squared and it can be found using the Lorentz force, assuming an electric dipole approximation for the cell. Thus the net forces acting on the cell just after it ejected from the trap can be written aswhere α is a constant that depends on the relative dielectric susceptibility of the ionized cell with respect to the medium and also its size. It is important to note that the electrical susceptibility that the cell has during the post ionization period should be significantly lower than its natural electrical susceptibility. This should be expected because while the cell was in the trap, it was undergoing dielectric breakdown and continually developed charge due to the incident radiation from the trap.In order to solve the differential equation in Eq. (4) we had to make physically reasonable approximation. We assumed the electrical force does not vary significantly over the range of the distance r in which we measured and analyzed. Similarly, over this range of distance, the trapping force is approximated like a spring force. The approximation for the trapping force was made by making a series expansion for the electric field and keeping terms up to the first in r. This yields
The first term represents the electrostatic force due to the charge, q, developed on cell due to the ionization by the radiation at the instant it got ejected from the trap. The second term is the damping force due to the viscosity of the fluid in which the cell is suspended. The last term in Eq. (5) is the trapping force that constantly keeps trying to suck the cell back to the center of the trap. The constant k is the trapping force constant that depends on the magnitude of the induced polarization in the ionized ejected cell. It also depends on the dielectric susceptibility of the ionized cell and the amplitude of the electric field of the trap. This constant varies from one cell to another. It is important to note that even though each cell carries a net charge due to the ionization by the radiation while it was trapped, it also has a smaller induced electrical polarization as it recedes away from the center of the trap. This induced polarization is primarily due the electric field of the laser trap, which could be amplified or diminished by the net charge developed on each cell. It could also vary from one cell to another depending on the size of the cells and on the level of the radiation damage on the cell.Equation (5) is an equation for a damped harmonic oscillator of mass m and charge q driven by a uniform electric field E0. The solution was found to be to
Equation (6) is an equation governing the displacement of the cells as measured from the center of the laser trap based on the forces acting upon them. The boundary conditions are set so that just before the cell is ejected from the trap, it is considered to be at rest at the center of the trap. The numerical model fitting function NonlinearModelFit in Mathematica was used to fit this model of displacement versus time data for each cell, where the mass, m, drag coefficient, β, and electric field, E0, were known for each cell. Equation (5) is an equation of an electrically driven damped harmonic oscillator. Our experimental data indicated that each cell, after being driven out of the trap, quickly loses its momentum as it recedes away from the center of the trap. Thus the motion of the cell must be an overdamped electrically driven harmonic oscillator. This requires the solution in Eq. (6) must remain hyperbolic and should not become trigonometric. A trigonometric solution would predict underdamped oscillatory motion for the cells that is contrary to the evidence provided by our experimental data. Consequently, we must choose β2≥4km. Physically, this means that after the cell is ionized and ejected from the trap, the force due to the induced polarization of the cell that was constantly trying to suck cell back to the trap, must be smaller than the drag force. This could certainly prove that, while the cell was in the trap, it had gone through an irreparable dielectric breakdown due to the high dose of radiation it absorbed that most likely lead to its death.The maximum value for k was approximately 0.005 for each cell. This was found by solving for k from β2-4km = 0 using the average mass and drag coefficient of each cell. Therefore, the NonlinearModelFit function started looking for k at several orders of magnitude below this value. The average k value was 6.705 × 10−8 N/m. There were slight variances in the trapping coefficient k for each cell. As previously stated, k is proportional to the cell’s polarization that is significantly diminished by the damage due to the absorbed radiation while the cell was in the trap. This weak remnant polarization also depends on the cell size and the polarizing electric field. The effect of the electric field diminishes as the cells receding from the center of the trap due to the Gaussian nature and the reduced beam waist of the laser beam by the microscope objective lens.
The function found the unknown constants of the charge on the cell, q, and the trapping coefficient, k, within a confidence interval of 0.99. The determination of agreeance value, R2, was extremely high for all 50 cells, with the lowest value being 0.989. The mean R2 value was 0.998. Thus, theoretical model had extremely high agreeance with the experimental data. Thus, the small variances in the k values should be expected. It is possible that the fitting of k could have an effect on the value of q, as both were fitted simultaneously. However, with such high determination of agreeance values coinciding with a tight distribution of k values, there is great confidence in the accuracy of the q values. For illustration purpose, the fitting of the solution described by Eq. (6) (described by the solid black lines) to the experimental data for four cells is displayed in Fig. 3. The curves fitted to the experimental data of these four cells had R2 values of: a = 0.996, b = 0.995, c = 0.998, and d = 0.999 that indeed shows extremely high agreeance values.
Fig. 3 Theoretical model solution (block solid lines) and the experimental data (symbols colored green (a), red (b), magenta (c), and blue (d)) for four cells.
4.2 Experimental results
Figure 4 shows the displacement of the 50 BT20 cells measured from the center of the laser trap as a function of time. Though there is great correlation in the trajectories of the cells, there are some discrepancies.
Fig. 4 Displacement for all ejected 50 BT20 breast cancer cells as measured from the center of the trap as a function of time.
As previously mentioned, the NonlinearModelFit function was used to find the unknown constants of the trapping coefficient and the charge developed on each cell. Figure 5(a) is a histogram of the amount of charge developed on each of the 50 ionized cells. It is customary to express the magnitude of charge in ionized microscopic compounds or charged molecules, such as Hemoglobin (Hb), in units of the magnitude of the charge of an electron (e = 1.602 × 10−19 C) known as the Z number [15]. Following this approach, the charge is expressed in units of e (the Z number). The distribution of the charge in Fig. 5(a) shows that the charge developed varies from 8.52e ( = 1.36 × 10−18 C) to 307.99e ( = 4.93 × 10−17 C) with an average of 83+/−65 e ( = (5.18+/−1.04) × 10−17 C). The big standard deviation in the charge could be due to the variation in the size of the cells. As we have discussed earlier, the sizes of the cells were taken into account when we determined the amplitude of the electric field of the beam acting on each cell. The size of the cells studied ranges from a 9.86 μm to 13.71μm with an average diameter of 10.13+/−1.56 μm. However, if we focus on the cells with sizes of statistical significance, comparing cumulative probability graph in Fig. 5(c) (black) with the histogram in Fig. 5(a), we note that nearly 90% of cells developed a charge that is less than 148e ( = 2.37 × 10−17 C) with an average of 88+/−32 e ( = 1.4+/0.5 × 10−17 C).
Fig. 5 Distribution of (a) the charge measured in units of e (magnitude of the charge of the electron) per BT20 breast cancer cell with bins width is 50e and (b) the incident ionization energy per cell in mJ (red) and per unit mass in J/μg (blue) with same bin size of 0.2mJ (J/μg). The color coded graphs in (c) displays the corresponding cumulative probabilities. The total number of cells is 50.
Using the cross-sectional area of the cell, the incident power at the location of the trap, and the time that the cell was in the trap, the total incident energy was also found for each cell. This is the energy required to ionize the cell and therefore render it irreparably damaged. The distribution of the incident energy, which we referred to as ionization energy, measured in milijoules (mJ) per cell is displayed in the histogram labeled red in Fig. 5(b). The result shows that the ionization energy varies from a minimal of 0.025 mJ to a 0.76 mJ maximal with an average of 0.22+/−0.16 mJ. Once again, focusing only on the bins that have statistical significance, from the cumulative probability graph shown in red in Fig. 5(a) with the histogram labeled red in Fig. 5(b) it can be seen that nearly 90% of the cells can be ionized by less than 0.4 mJ of incident radiation energy. For these cells the minimum is 0.025mJ and the maximum is 0.396 mJ with an average of 0.17+/−0.11 mJ.
We have also studied the distribution for the ionization radiation energy per unit mass. It is measured in joules per microgram (J/μg). The result is shown by the blue histogram in Fig. 5(b). The energy per mass of the individual cell varies from 0.055 to1.79 J/μg with an average value of 0.38+/−0.28 J/μg. This maximum value is not shown in the histogram as this bin consist of one cell with twice more than the value for the cells in the last bin (0.89 J/μg) shown in the Fig. 5(b) (blue). Here also it can be seen that 90% of the cells, the energy per unit mass is 0.055-0.584 J/μg with an average of 0.31+/−0.16J/μg to ionize.
The variation of the charge developed as a function the size and the ionization energy per unit mass has also be analyzed. The results are presented in Fig. 6. For all cells, (a), there does seem be a slight correlation between the cell’s diameter and the charge developed. In (b) it is evident that an increasing diameter leads to an increasing charge as can be seen from the cumulative average of the charge distribution for 100% (blue), 90% (red), and about 60% (wine). This positive correlation is similar to that of the relationship between the ionization energy and the charge (c). In (d) again there is found the cumulative averages for the charge distribution, that though more scattered, do show a positive relationship.
Fig. 6 This graph describes the charge as a function of the diameter of the cells (a & b) and as a function of ionization energy (c & d). (c) and (d) represent the results cumulative average of the charge distribution for 100% (blue), 90% (red), and about 60% (wine).
5. Conclusion
The charge to ionization energy was found as well as the ionization energy per unit mass for BT20 breast cancer cells. This was done by creating a theoretical model based on Newtonian mechanics. The net force acting upon the cell as it was ejected from the trap was used to find the equation of motion for the cell. These forces included the electrostatic force from the laser, the trapping force due to the gradient of the electric field squared, and the drag force due to the viscosity of the medium through which the cell traveled. This resultant differential equation was solved after linearizing the terms using a series expansion. The solution gave an accurate model of the displacement of the cell as it was ejected from the laser trap. Parameters, such as the mass, electric field, and the drag coefficient, were known for each cell. Thus, theoretical model was evaluated for each of the 50 cells using its specific mass, drag coefficient, and electric field. The charge developed was found specifically for each cell by using a numerical nonlinear model fitting function.
The relationship between the cell’s diameter and the charge had a positive correlation. In other words, larger cells had greater charges. If we again consider a cell to be a membrane full of ionic fluid, it is not surprising that a larger cell developed a greater charge as it contained a greater amount of charges (ions) initially. There was also a positive correlation between the ionization energy and charge. This can be explained by the process of dielectric breakdown. The longer the cell was radiated in the trap, thus having a greater total ionization energy, greater was the amount ions that were forced out of the cell by the electric field. This yielded a cell with an overall greater net charge. However, there seems to be more complexity to this positive relationship. This could be accounted for by size of the cell and by the strength of the electric field causing the dielectric breakdown. More study needs to be done to confirm this. Moreover, a more precise value could be found by accounting for factors such as the age of the cells and how long the cell had been out of the incubator. It was noted during the experiment that the time between harvesting the cells had direct correlation with the time taken to ionize the cell; the longer the incubation time of the cells, the shorter the ionization time. This was noted during the experiment, so an established incubation time of 3 days was established. A larger study varying the incubation time could verify if indeed the cell’s time out of the incubator was the deterministic factor in the energy required to ionize.
Overall, though laser traps have been used as a tool in the field of biophysics, never before has the technique been used to study the ionization of cancerous cells in this way, specifically at the cellular level. The ultimate objective of this experiment was to find a way to understand the ionization of a single BT20 cell and perhaps more importantly, to see if a laser trap could effectively and accurately be used for this. This experiment demonstrated that this technique for studying cancerous cells using a laser trap is indeed promising; yet the technique needs further research before it can be fully understood and implemented.
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