2.1 Estimation of optical trapping force

To estimate the trapping force of optical tweezers, a laser spot of power P was applied to a sample particle, as shown in Fig. 1(a). The sample stage was dragged to the right where a viscous drag force F_D was applied to the particle, as shown in Fig. 1(b). At the same time, a transverse trapping force F_L was applied to the particle by a fixed laser spot (shown by a circle with a cross) in the opposite direction [⁴].

When the particle is displaced from the equilibrium, the trapping force increases to a power-dependent maximum value called escape force, and then begins to decrease to zero [⁵]. When the viscous drag force F_D was smaller than the escape force, the particle was confined by optical tweezers; when F_D was equal to or slightly larger than the escape force, the particle began to be dragged out of the spot and escape the trap. The viscous drag force F_D applied to the dragged particle was determined by Stokes’ Law [⁶]:

where η denotes the viscosity coefficient of fluid, R denotes the radius of particle, and v the dragging speed of the stage. As the trapping force F_L was balanced with the viscous drag force F_D at equilibrium, Eq. (1) was used to evaluate the trapping force F_L of the optical tweezers.

According to the theory of optical tweezers [⁷]:

where n denotes the index of incident media, P is the power of source, and c the vacuum speed of light. Varying the optical power P applied to the particle, we measured the trapping force F_L and derived the curve of F_L(P) versus P. By using the relation curve, we determined the microscopic trapping force F_L directly for a given laser power P.

2.2 The interaction between red blood cells in coagulation

During the process of coagulation, an RBC is attracted by a coagulative interaction F_B from the right coagulated group, as shown in Fig. 2. In order to stop the cell from moving to this group, sufficient power was applied to a spot to make the trapping force F_L greater than the coagulative interaction F_B. With the power reduced to a critical value P, the cell began to escape the trap and was attracted to the right, as illustrated in Fig. 2. At this point, F_B was balanced with F_L. Using the relation curve of F_L versus P, the coagulative force F_B was derived by the minimum power P required to trap the coagulating RBC.

2.3 Apparatus and materials

A 1064 nm IR laser, an optical microscope and a 100 × oil lens were utilized to establish the optical tweezers system, as depicted in Fig. 3. A motorized X-Y stage was equipped to the system to induce viscous drag force, by which the trapping forces of the optical tweezers were determined. In the below coagulation experiments, samples were prepared by diluting 20 μl of blood in 1 ml of normal saline. Control samples were prepared without the addition of drug substances. In the other samples, 20 μl of 100 IU heparin and 20 μl of 3% tranexamic acid were added.

3.1 The evaluation of coagulating interaction

As stated previously, dragging experiments were performed to determine the trapping force F_L of the optical tweezers. The dependence of trapping force F_L on varying laser power P is summarized in Table 1 and Fig. 4, which are used accordingly to derive the interaction between coagulating RBCs.

The process used to evaluate coagulating interactions is illustrated in Fig. 5. In Fig. 5(a), the coagulating RBCs 1 and 3 were attracted to the blood group on the left. By applying higher laser power, RBC 1 was trapped and stopped moving to the left, as shown in Fig. 5(b). However, when the power was reduced to ~130 mW, cell 1 was released and was attracted to the blood group again, as shown in Fig. 5(c) and Fig. 5(d). According to the data shown in Table 1, the coagulating force F_B on RBC 1 was estimated to be ~1.64 pN.

3.2 The phases of blood coagulation

The blood samples were prepared on microscope slides and situated on the stage of optical tweezers for coagulation experiments, as shown in Fig. 6. Coagulation was initiated in blood solution located outside the edge of the coverslip, which exerted outward attractive forces on the remainder of the sample. As the coverslip and slide were bonded by a two-sided adhesive tape which served as a spacer as thick as 50~100 μm, the attracted RBCs could move outwards free of effects from the substrates. Based on the mobility of the RBCs and the strength of intercellular interactions, we observed three distinct coagulation phases. In the first phase, the RBCs vibrated around their equilibrium positions. In the second phase, individual RBCs began to shift outwards to the coagulated region, while the final phase featured intense group migration until the entire process was complete.

For blood samples with no additives, RBCs were randomly distributed inside or outside the coverslip at the beginning. After the coagulated region was formed, RBCs located on the inside exhibited attraction and began to shift individually and slowly outwards. After the process proceeded for roughly five minutes, extensive cell migration commenced, marking the third phase. Cellular interaction versus coagulation time is summarized in Fig. 7(a). In the second phase, interaction ranged from ~1.0 pN at beginning and increased to ~3.9 pN at around five minutes. In the third phase, the interaction was so intense that the 380 mW source power was insufficient to trap the rapidly-moving RBCs.

The blood sample containing heparin entered its first phase at the beginning. Heparin attenuated the inter-cellular interaction and prolonged the coagulation time. Figure 7(b) illustrates the time variation of cellular interaction in the blood samples. The addition of heparin extended the first phase by keeping the interaction at ~1.5 pN for four minutes. At around seven minutes, the samples proceeded to the second phase with a corresponding increase in force. The interaction increased to 3.9 pN at ten minutes at which point the third phase commenced. The addition of heparin postponed coagulation for about five minutes.

The sample containing tranexamic acid immediately entered the third phase at the beginning. The fast and intense group migration allowed the overall coagulation process to be completed within two minutes. Figure 7(c) shows the variation in cellular interactions of the samples. As illustrated, we found that the interaction increased towards and stabilized at 3.9 pN till the end of the process.

Time variations in the micro-interaction of the three samples are summarized in Fig. 7(d). The control sample entered the second phase at the beginning and the intensity of cellular interactions increased with time until the third phase began at five minutes. Heparin containing samples exhibited a prolonged first phase without group migration or net coagulation. Contrastingly, samples containing tranexamic acid proceeded immediately to the third phase and completed the coagulation within two minutes.