Single-cell ionization
A total of 80, 80, and 76 BT20 cells from the untreated, 2-hrs, and 24-hrs treated groups were analyzed, respectively. Table 1 shows the basic statistical parameters for each group, such as mean diameter (D), ionization time (T), cross-sectional area (Ac), volume (Vc), mass (Mc), TIE, and TRD. The average ionization time is calculated and tabulated in Table 1. We calculated the average cross-sectional area and the volume by assuming a spherical model.
No significant differences were observed in their values, which resulted in similar values for average masses in the three groups. A similar closeness was observed with 4T1, and the variations in response to radiation for the three groups were attributed to the inherent biochemical structure differences caused by the dose and period of treatment of DMDD [22]. As the treatment period increases, the ionization time decreases. The absorbed threshold energy is calculated from the ionization time, each cell and beam area ratio, and the power transmitted (\({P}_{t}\)),
Table 1
Key calculated and measured statistics for diameter, mass, TIE, and TRD.
Quantities | Mean | ST.Dev | Min | Median | Max |
Untreated BT20 control group (80 cells) |
D (µm) | 13.3 | 2.2 | 8.3 | 13.5 | 21.3 |
AC (µm2) | 572.8 | 188.7 | 214.9 | 576.1 | 1425.2 |
VC (µm3) | 1339.2 | 691.5 | 296.1 | 1300.1 | 5059.3 |
T(sec) | 405.8 | 210.3 | 30.0 | 393.0 | 921.0 |
MC (ng) | 1.3 | 0.6 | 0.2 | 1.3 | 5.1 |
TIE (mJ) | 76.7 | 39.8 | 5.7 | 74.3 | 174.1 |
TRD (J/µg) | 63.7 | 39.4 | 9.8 | 53.6 | 244.2 |
2-hrs treated group (80 cells) |
D (µm) | 12.9 | 2.1 | 8.8 | 12.5 | 19.9 |
AC (µm2) | 539.7 | 180.4 | 243.1 | 489.6 | 1242.9 |
VC (µm3) | 1226.4 | 629.9 | 356.5 | 1018.8 | 4120.7 |
TI (sec) | 190.0 | 65.2 | 78.0 | 170.0 | 379.0 |
MC (ng) | 1.23 | 0.6 | 0.4 | 1.0 | 4.12 |
TIE (mJ) | 41.6 | 25.8 | 9.9 | 31.1 | 119.2 |
TRD (J/µg) | 33.4 | 9.0 | 15.9 | 32.3 | 55.8 |
24-hrs treated group (76-cells) |
D (µm) | 12.4 | 2.3 | 6.6 | 11.9 | 19.2 |
AC (µm2) | 495.7 | 184.3 | 135.7 | 443.4 | 1152.2 |
VC (µm3) | 1089.2 | 627.6 | 148.6 | 877.9 | 3677.6 |
TI (sec) | 97.1 | 52.6 | 8 | 94 | 216 |
MC (ng) | 1.1 | 0.6 | 0.2 | 0.9 | 3.7 |
TIE (mJ) | 20.8 | 18.3 | 0.9 | 15.9 | 93.7 |
TRD (J/µg) | 16.9 | 7.6 | 1.6 | 17.0 | 35.8 |
$$\text{T}\text{I}\text{E}=\frac{{\text{A}}_{\text{c}}}{{\text{A}}_{\text{b}}}{\text{P}}_{\text{t}}\text{T}$$
4
.
The average absorbed threshold ionization energy for each group, were found to be TIE = 76.71 ± 39.75 mJ, 41.64 ± 25.83 mJ, and 20.85 ± 18.31 mJ respectively. The higher standard deviation is due to the wide range of cell size, one of the factors that affects the magnitude of the ionization energy.
The statistical distributions for TIE for all cells in each group are displayed using a bar graph, box plot, and histograms in Fig. 3(a–c). In each graph, the data coded red represents the untreated group, green denotes the 2-hrs treated group, and blue denotes the 24-hrs treated BT20 cells. From these distribution graphs and the calculated average values, we observe that the TIE for the treated groups is less than that of the untreated group. This effect is amplified with an increase in the duration of treatment, as observed from the lower TIE for the 24-hrs treated group compared to the 2-hrs treated group, as shown in Fig. 3(b). The bar graph in Fig. 3(a) shows that the TIE for untreated BT20 cells makes up 77% of the Bar, whereas the 2-hrs and 24-hrs treated BT20 cells cover 42% and 21%, respectively.
In each group, there were different numbers of cells. TIE per unit mass is used to calculate the absorbed TRD for each cell in each group. Figure 3(d–f) shows the results for each group in the same color coding. We found the average absorbed TRD for the untreated, the 2-hrs treated, and 24-hrs treated groups to be TRD = 63.66 ± 39.44J/µg, 33.38 ± 9.04J/µg, and 16.93 ± 7.62J/µg, with 64%, 33%, and 17% respectively as shown in the bar graph in Fig. 3(d). This Figure also shows lower radiation doses in the BT20 cells treated with DMDD than the untreated group. DMDD treatment of BT20 cells results in lower radiation doses than untreated cells. Figure 3(e) shows that this effect also increases with the length of the treatment period.
The results’ validity for TIE and TRD was confirmed by statistical analysis. In this case, Fcrit(2,15) = 3.68 at 0.05. Since F = 43.4 > 3.68, the results are significant; the p-value for this test is almost zero (see Table 2). Thus, we can conclude that there is strong evidence that the expected values in the three groups are different.
Table 2
Hypothesis of one-way ANOVA
Homogeneity variance test for untreated, 2hrs and 24hrs treated groups |
| TIE | TRD |
| DF | SS | MS | F-Value | Prob. >F | DF | SS | MS | F-Value | Prob. >F |
Model | 2 | 13342.8 | 6671.4 | 21.4 | 2.9343E-9 | 2 | 23704.9 | 11852.5 | 43.4 | 1.1E-16 |
Error | 233 | 72635.3 | 311.7 | | | 233 | 63591.1 | 272.9 | | |
Mean comparison for untreated (1), 2hrs treated (2) and 24hrs treated (3) groups |
| MD | SEM | q-v | Prob. | α | Sign | LCL | UCL | MD | SEM | q-v | Prob. | α | LCL | UCL |
1 vs. 2 | 55.9 | 4.7 | 16.7 | 0 | 0.05 | 1 | 67.1 | 44.7 | 30.3 | 3.78 | 11.3 | 0 | 0 | 39.2 | 21.3 |
1 vs. 3 | 35.1 | 4.7 | 10.6 | 0 | 0.05 | 1 | 46.1 | 24.1 | 46.2 | 3.83 | 17.2 | 0 | 0 | 55.8 | 37.7 |
2 vs. 3 | 20.8 | 4.7 | 6.2 | 4.8E-5 | 0.05 | 1 | 9.6 | 31.9 | 16.5 | 3.83 | 6.1 | 7.8E-5 | 0 | 25.5 | 7.4 |
BT20 cells were analyzed using TIE and TRD as functions of mass to investigate the relationship between ionization radiation energy and mass. In Fig. 4(a–f), we are displaying the TIE and TRD versus mass for untreated (red), 2-hourly(green), and 24-hourly treated (blue)BT20 cells. Using Origin software, we established a statistically valid relationship between TIE, TRD, and cell mass. Figure 4(a, b) displays the reduced data for the TIE, while Fig. 4(d, e) shows that for the TRD. The statistical reduction method from our studies [22–29] was followed by sorting each data by TIE or TRD in ascending order. Thus, the reduced data obtained is shown in Fig. 4(a) for the TIE and in Fig. 4(d) for the TRD.
An additional reduction was made by subgrouping the data in Fig. 4(b–e) with an incremental mass of 0.19 ng; the average mass, TIE, and TRD for each subgroup were calculated. The respective results for TIE and TRD, are displayed in Fig. 4. The results in Fig. 4(a) match our previous results for 4T1 cancers [22]. It shows that the TIE increases with cell mass for all three groups and confirms that BT20 cells treated for 24 hours had the lowest TIE among the treated cells. On TRD vs. mass in Fig. 4(d) confirms that the treated cells had a low TRD but predicts, in all three groups, that the TRD and mass of BT20 cells would be inversely related.
Multiple Cell Ionization
Until the cell was fully ionized and trapped, we kept it isolated from the others for the single-cell study. Compared to other small cells, such as RBCs, cancer cells have a longer ionization period which makes the procedure somewhat challenging [22–29]. The strong gradient force attracts the nearby cells, which causes them to enter the trap at different times. This results in multiple cells in the trap. However, all the cells eject at the same time after ionization.
The goal was to calculate the TIE and TRD for multiple cells for the untreated control, 2-hrs, and 24-hrs treated groups. Here investigated whether the TIE and TRD change as cells are added to the trap as the first cell experience membrane breakdown as charge builds up from radiation exposure.
As a result, we formed five subgroups (1-cell, 2-cells, 3-cells, 4-cells, and 5-cells) based on the number of cells present in the trap during the ionization period in each untreated control group, the 2-hour treated group and the 24-hour treated group. In multiple-cell ionization, the cells may enter the trap at different times, but all cells leave the trap simultaneously. As such, we calculated the ionization period (T) for all the various subgroups from the image of the cell as it enters to when they simultaneously leave the trap. The TIE, which is the energy absorbed, is calculated using Eq. (2), using the same procedure for single-cell ionization. From Eq. (1), we determine the cell's mass in the trap during multiple ionization phases. We assume the same density such that we replaced Vc by the Vsum (the sum of the volume of the individual cells in the subgroups) so that Eq. (1) becomes Msubgroup = ρVsum.
We display the results using a histogram and the box-and-whisker plot of the TIE and TRD in Fig. 5 (the left histograms are for the TIE, and the right side is for the TRD). The control group is Fig. 5(a), 2 hours treated is Fig. 5(b), and 24 hours treated is Fig.(c). A one-cell subgroup, a two-cell subgroup, a three-cell subgroup, a four-cell subgroup, and a five-cell subgroup are represented by pink, yellow, orange, navy, and cyan, respectively, in each histogram. In the left side of Fig. 5(a–c), we observed the shift in the peak values to the right, which indicates that the TIE is increasing with the number of cells in the trap consistently for control, 2-hrs, and 24-hrs treated groups. The box-and-whisker plot displays this in Fig. 5(d).
The summary of the values for the basic statistical parameters for the TIE is given in Table 3. The average TIE for the five subgroups (1-cell to 5-cells) increases with the number of cells regardless of treatment. A quantitative comparison was made between the subgroups (1–5 cells) and the two groups by analyzing the relative TIE percentage increase. Concerning the single cell, we would expect 200–500% relative increases in the TIE for either of the three groups after removing the effects of intracellular electrical and thermal interactions resulting from the radiation field. Nevertheless, we found values were 3.8%, 12.8%, 18.3%, and 24.8% (untreated), 19.5%, 38.7%, 66.8%, and 78.9% (two-hours treated), and 15.8%, 54.8%, 96.1% and 134.8% (24-hours treated). The results of the TIE in multiple cell ionization indicate that intracellular electrical and thermal effects is resulted from the infrared radiation. For the multiple cells corresponding to the treated groups and the control group, relative comparisons showed 37.5%, 33.2%, 23.5%, and 22.1% in the 2-hour treated group, and 69.7%, 62.7%, and 54.9% in the 24-hour treated group. These values are lower than the corresponding values for the control group. Here, we confirm that the DMDD treatment activates the augmented cell's reactive response.
The corresponding TRD is displayed in the graphs with the same color coding on the right side of Fig. 5. We observed a shift to the left in the TRD distribution curves in all three groups–control (Fig. 5(a)), 2-hrs (Fig. 5 (b)), and 24-hrs (Fig. 5(c)) treated. This indicates a decrease in TRD as the number of cells in the trap increased. The box-and-whisker plot in Fig. 5(d) for control (red), 2-hrs (green), and 24-hrs treated (blue) displays this result. Table 3 summarizes the basic statistical parameters in the TRD. A consistent decrease in the TRD value can be observed as the number of cells in the trap increases from 1 to 5 cells: 63.66–10.74 J/µg for the control; 33.38–10.39 J/µg for the 2-hour treated; and 16.93–9.81 J/µg for the 24-hour treated.
Table 3
The descriptive statistics showing the parameters for the TIE, the mass, and TRD for the 5 subgroups in the untreated, 2-hrs treated and 24-hrs treated groups of BT20 cell-line.
Untreated BT20 group |
No | # of Cells | TIE (mJ) | Mass (ng) | TRD (J/µg) |
mean | SD | Min | max | mean | SD | Min | Max | Mean | SD | Min | Max |
1 | 80 | 76.7 | 39.8 | 5.7 | 74.3 | 1.3 | 0.7 | 0.3 | 1.3 | 63.7 | 39.4 | 9.8 | 53.6 |
2 | 80 | 79.6 | 58.0 | 3.7 | 70.7 | 1.9 | 0.9 | 0.6 | 1.9 | 37.6 | 17.6 | 4.2 | 36.9 |
3 | 80 | 86.5 | 58.9 | 5.1 | 78.9 | 3.4 | 1.2 | 1.2 | 3.3 | 24.4 | 11.3 | 2.9 | 23.7 |
4 | 80 | 90.7 | 58.2 | 6.5 | 82.7 | 5.6 | 1.7 | 2.5 | 5.6 | 15.4 | 7.1 | 1.9 | 14.9 |
5 | 80 | 95.7 | 58.6 | 7.9 | 88.5 | 8.8 | 2.3 | 4.4 | 8.8 | 10.7 | 4.8 | 1.4 | 10.1 |
2-hrs Treated BT20 group |
| TIE (mJ) | Mass (ng) | TRD (J/µg) |
1 | 80 | 41.6 | 25.8 | 9.9 | 31.1 | 1.2 | 0.6 | 0.4 | 1.0 | 33.4 | 9.0 | 15.9 | 32.3 |
2 | 80 | 49.8 | 38.5 | 6.2 | 38.3 | 1.5 | 0.7 | 0.5 | 1.3 | 31.1 | 16.7 | 4.7 | 26.1 |
3 | 80 | 57.8 | 41.3 | 9.5 | 46.4 | 2.2 | 0.9 | 0.9 | 1.9 | 24.7 | 12.4 | 4.9 | 20.9 |
4 | 80 | 69.4 | 46.6 | 13.6 | 57.3 | 3.3 | 1.2 | 1.5 | 2.9 | 20.1 | 9.7 | 4.6 | 16.9 |
5 | 80 | 74.5 | 46.2 | 17.8 | 62.7 | 4.9 | 1.6 | 2.4 | 4.4 | 10.4 | 6.7 | 4.1 | 12.4 |
24-hrs Treated BT20 group |
| TIE (mJ) | Mass (ng) | TRD (J/µg) |
1 | 76 | 20.9 | 18.3 | 0.9 | 15.9 | 1.1 | 0.6 | 0.2 | 0.6 | 16.9 | 7.6 | 1.6 | 35.8 |
2 | 76 | 24.2 | 19.4 | 2.3 | 19.2 | 1.4 | 0.7 | 0.2 | 4.3 | 16.1 | 6.3 | 0.2 | 31.9 |
3 | 76 | 32.3 | 22.9 | 4.8 | 26.7 | 2.0 | 0.9 | 0.5 | 5.7 | 14.8 | 5.0 | 4.3 | 27.5 |
4 | 76 | 40.9 | 24.8 | 8.7 | 35.2 | 3.1 | 1.2 | 0.9 | 7.8 | 12.3 | 3.6 | 0.9 | 21.5 |
5 | 76 | 48.9 | 25.6 | 13.4 | 43.5 | 4.8 | 1.6 | 1.7 | 10.8 | 9.8 | 2.4 | 4.9 | 15.9 |
According to the results of the study, the average TRD of multiple cells (2–5) decreased by 40.9% when untreated; 6.8%, 26.2%, 39.9%, and 68.9% when treated for 2 hours; and 4.7%, 12.8%, 27.2%, and 42.1% when treated for 24 hours. Compared to single cell ionization, multiple cell ionization (2–5 cells) shows a significant impact on radiation dosimetry, which can be applied to chemo and hyperthermia treatments together. Multiple cells (2–5 cells) entering the trap can be explained by the same statistical analysis as a single cell entering the trap. Figure 6 shows the results for the control ((a) and (b)), 2-hour ((c) and (d)) and 24-hour ((e) and (f)) treatments. These graphs illustrate the TIE and the TRD, respectively, on the left and right axes. A color scheme is also displayed in the TIE and TRD graphs for the number of cells in the trap: (two cells (yellow), three cells (orange), four cells (Navy), and five cells (Cyan)) with symbols corresponding to the color scheme for TIE.
In the bottom row (b), (d), and (f) we show all the calculated data for TIE and TRD vs. mass, while the top row (a), (c), and (e) show reduced data obtained from a similar linear fit procedure for single cells. According to the linear fit (solid for TIE and dotted for TRD) for the reduced data in Fig. 6(a, c, e) which agrees with the results for the single cell in Fig. 4, the TIE in multiple cell ionization increases with mass and the TRD decreases with mass. In multiple cell ionizations, a small TRD may be caused by slow charging and radiation-induced temperature rise caused by infrared radiation. Cancer cells are destroyed by radiation because their DNA is damaged. Radiation incident on cancer cells is enough to cause dielectric breakdown since it conveys enough ionization energy. A great deal of evidence supports that small amounts of energy (TIE) or radiation dose (TRD) can be altered by combining chemotherapy with hyperthermia [17].
When there is no radiation, the simplest model of a cell (e.g., a BT20 cell) is a dielectric sphere with various electric dipoles. The quickly oscillating electric field of laser radiation causes the dipoles to oscillate along the polarization direction of the radiation field [20]. Thus, a strong field causes the weaker dipoles to break, and the cell becomes charged.
Cells are comprised of distinctive sorts of atoms that have unique dipole strengths, which means that they also show different time-dependent vitalities and breaks. Subsequently, the charge buildup could be a progressive process depending on time. Besides, due to the Gaussian nature of the laser beam, diverse parts of the cell get distinctive electric field qualities (with the most intense at the center). This field strength to aids the progressive charge buildup within the cell, which may be a noteworthy effect on the threshold radiation dose due to multiple cell ionization as they enter the trap one by one. Radiation causes cell dielectric breakdown, which leads to the buildup of charges. The said free charges on the cell(s) result in significant damage in the ionization of cells. Subsequently, the TRD decreases as the cell number grows.
Bt-20 Verses 4t1 Cancer Cells
As we discussed in the mechanism of cell ionization, the radiation doses for two breast cancer cell samples (4T1 and BT20) differ in energy absorbed. This section presents the TIE and TRD versus mass values of single and multiple ionization using laser trapping.
A. Single Cell Ionization
In this section, we compare the TIE and TRD as a function of individual cell mass for 4T1 cancer cell lines [22, 23], which were not treated and then treated with Chinese herbal medicine for 24 hours, to that of the BT20 cell line, which originated from a human mammary tumor cell. A scatter plot was used to display the TIE and TRD versus the mass of the two-sample cells in Fig. 7. TIE scatter plots are on the left side of Fig. 1, while TRD scatter plots are on the right. The untreated (green) and 24-hour treated (cyan) 4T1 cancer cells groups, as well as the untreated (red) and 24-hour treated (blue), BT20 cancer cells groups, are shown on both the left and right sides of Fig. 7.
Using the data analyzed results of 4T1 cancer cell lines [22] and BT20 cancer cells, the mean TIE value for untreated and the 24-hrs treated 4T1 cells were found to be TIE = 81 ± 64 mJ and 24 ± 20 mJ, respectively, but for BT20 it was found to be 76 ± 39 mJ and 20 ± 18 mJ. The untreated cells in 4T1 cells and BT20 cells have a relative TIE value difference of about 6.17 percent, while the 24-hour treated one has about 16.67 percent. The mean TRD value for 4T1 cells of the untreated and the 24-hrs treated were found to be TRD = 33 ± 15 J/µg and 10 ± 6 J/µg respectively, but 64 ± 39 J/µg and 17 ± 7 J/µg for BT20.
B. Multiple Cells
This section will compare the TIE and TRD for BT20 and 4T1 cell lines in breast cancer cell samples when multiple cells are in the trap. As each cell enters the trap, undergoes membrane breakdown, and accumulates charges due to radiation damage, this study aims to distinguish between the two types of breast cancer cells. To achieve this goal, we selected five subgroups in the trap during the ionization process in each untreated and treated group from the two samples. The mass of the cells in the trap is also estimated using Eq. (1).
We obtained the sum of the masses of the individual cells in the trap with the same density. From this, we calculated the TRD for each subgroup in the untreated and 24-h treated groups. The results for the TIE and TRD for multiple cells are displayed in Fig. 8. The TIE and TRD vs number of cells in the trap are plotted on the left and right sides of Fig. 8 for both cell samples. The red color-coded and blue color-coded scatter plots illustrate the 4T1 and BT20 cell lines, respectively. Each data point values from the right in the linear fit to the left side of Fig. 8(a) indicates that the TIE increases consistently for both sample cells as the number of cells in the trap increases. Moreover, the TIE values for 4T1 and BT20 cell lines are not the same. This can be due to the difference in chemical and biological properties of the cell lines. For instance, some human mammary epithelial cells have larger quantities of polyunsaturated fatty acids than other types of cells, such as those found in the 4T1 cell line, which has a higher level than the BT20 cell line [39]. In Fig. 8b, similar plots and color coding are employed to depict the corresponding computed TRD for multiple cells in both cell samples. Unlike the TIE, the distribution curves in shift to the right, indicating a reduction in TRD as the number of cells in the trap increases (see Fig. 3). The difference in TRD values recorded in both cell lines might be attributed mostly to the capacity differential in the gradual charging of the cell and the higher temperature caused by the infrared ionization radiation.
The Comparison With N2a And 4t1 Cells Lines
Figure 9. Multiple cells mean versus number of cells in a trap comparison for the tree N2a, BT20 and 4T1 cancer cells. a) TIE. b) TRD. In each of these scattered line plats, the red color-coded data point represents 4T1 cancer cells with the same color-coded error bars, the blue color-coded data points denote the BT20 cancer Cells with same color-coded error bars and the black one is just N2a cell lines of a mouse neuroblasts with black color -coded error bars.
Radiation therapy exploits the fact that cancer cells accumulate gene mutations in DNA and, as a result, may lose DNA repair function compared to normal cells [46–49]. Furthermore, in radiotherapy, the therapeutic ratio is the maximum radiation dose that kills cancer cells locally. A low acute and late morbidity is associated with the minimum radiation dose in normal tissues [50]. To determine how much energy is required to kill a specific cell, single-cell ionization is used. Thus, the maximum ionization energy required for a single cancer cell is required for safe radiation dosing. In comparing TRD between single cells for BT20, 4T1, and N2a, we found that the TRD decreased with cell mass. The reduction observed in the TRD with increased cell mass is attributed to chain ionization (Fig. 9(b)) [22, 23, 29]. Our results indicate that, since tumors are clusters of single cells, we can adjust the amount of energy necessary to destroy a tumor based on its size and mass. This is done by knowing the maximum amount of energy required for single cell death.
From BT20 and 4T1 which both treated with oligostilbenes their TRDs were further reduce compared to these cells being untreated. This means that the chain ionization effect occurring in the presence of multiple cells and treatment of oligostilbenes will optimize the therapeutic ratio as demonstrated by the reduction in TRD in BT20, 4T1, and N2a. Figure 9 (b) demonstrate that there is a way forward in radiotherapy for more effective treatment plans, seen in the fact that the TRD decreases with the increase of cell mass for all three cancer lines. Furthermore, as our method enables very precise measurements of radiation energy, the possibility of a more effective therapeutic ratio based on the cellular level is confirmed here, which reduces tissue toxicity caused by radiation while promoting sterilization of the cancerous cells.