Ultrasonic Targeting of NK Cell in Vessel Bifurcation for Immunotherapy: Simulation and Experimental Validation

1. INTRODUCTION

Imposing an ultrasound field on a fluid with suspended particles induces acoustic scattering owing to the differences in sound speed and density between the particles and surrounding fluid, resulting in an acoustic radiation force (ARF) on the particles. This phenomenon, known as acoustophoresis, utilizes acoustophoretic force to manipulate particles, including cells, microorganisms, and microbubbles. Such manipulation is crucial for on-chip microparticle management and acoustic navigation of microparticles in complex fluid flows [1].

Over the past few decades, ultrasound has been widely studied for imaging and therapeutic purposes. For instance, high-intensity focused ultrasound has been employed in cancer therapy [2-4], while shock wave lithotripsy (SWL) is routinely used to disintegrate kidney stones [5-7]. Ultrasound has also been reported to enhance thrombolysis in deep vein thrombosis (DVT) [8] and increase drug permeability through the skin [9]. The development of multiarray transducers has spurred interest in using ultrasound for targeted drug delivery, particularly for the trapping and navigation/blocking of drug carriers, such as drug-loaded liposomes, microbubbles carrying drugs, and cytokine transfection [10-15].

Immune cell therapies, including CAR T-cell and NK cell therapies, have shown success in treating hematological malignancies, such as lymphomas and leukemias [16-20]. Notably, HLA-mismatched NK cells offer a viable treatment without the risk of graft-versus-host disease (GVHD), with extensive clinical use indicating safety and a minimal risk of cytokine release syndrome (CRS) [21,22]. However, navigating these cells within the cardiovascular system remains challenging because of their size, density, and compressibility.

This article introduces an acoustic manipulation system designed to direct natural killer (NK) cells into fluid flow and through vessel bifurcations. The system leverages hydrodynamic drag as the primary carrier force, supplemented by acoustic pressure, to guide the cells toward the target. Our simulations utilized a 30-transducer acoustic actuator operating at 1 MHz, capable of generating a focused beam at the center of the array, demonstrating a novel technique for NK cell delivery.

2. THEORY AND METHODS

2.1 Generation of focused US beam

The ultrasound navigation system was developed with 30 transducers, and each transducer signal was modulated using a custom control system. A Schematic of the US actuator is depicted in Fig. 1. To compute the acoustic field, we utilized a far-field piston source with single-frequency emissions controlled through acceleration. The complex acoustic pressure (P) generated by the entire array at a specific location result from the vector summation of 30 individual complex acoustic pressures (Pj) contributed by each piston source emitted at a single frequency. This phenomenon can be mathematically expressed as follows [26]:

$\[ P={\sum }_{j=1}^{30}{P}_j\left(r\right)=P_{0}A\frac{D_f\left(\theta \right)}{d}{e}^{i\left(\phi +kd\right)} \]$

(1)

$\[ D_f=\frac{2J_1\left(aksin\theta \right)}{aksin\theta } \]$

(2)

Fig. 1.

Schematic concept of acoustic navigation system for controlling micro/nano carriers for targeted drug delivery in the vessel bifurcations. (a) Schematic description of liver vessel bifurcations. (b) Absolute acoustic radiation pressure field with both zoomed ZY plane and top view. (c) Animated description of Y-shaped blood vessel bifurcation surrounded on the top of 30 UT array ultrasonic actuator. (d) ZY plane lateral view of ultrasonic actuator.

where P₀ denotes the transducer amplitude constant power and A denotes the peak-to-peak amplitude of the excitation signal. D_f represents a far-field directivity function based on the angle θ between the transducer normal and point r. Moreover, d denotes the propagation distance in free space, ϕ denotes the phase delay of the transducer, k = 2π/λ indicates the wavenumber, J₁ represents a first-order Bessel function, and a denotes the radius of the emitting source.

3. RESULTS AND DISCUSSIONS

3.1 Numerical Simulations

To assess the enhanced targeting efficiency of NK cells, we developed an idealized numerical model using the finite element software COMSOL Multiphysics. This model facilitates the coupled calculation of acoustic pressure fields, acoustic radiation force on NK cells, primary Bjerknes force on microbubbles (MB), and flow field along with particle trajectory analysis. The Y-shaped channel simulation featured inlet and outlet diameters of 3 mm and 1.5 mm, respectively, with average fluid velocity 'v' at the inlet serving as a tunable parameter that affects the intra-vessel velocity distribution. In this study, we modeled a non-pulsatile steady flow of a weakly compressible fluid, as detailed in Table 1.

Table 1.

Simulation parameters.

To streamline the simulation process, we introduced an ensemble of 100 microparticles at the inlet in four temporal batches of 25, each matching the initial velocity “v.” These particles, representing NK cells with diameters between 10–15 μm, had uniform acoustic properties, such as density and compressibility, throughout the simulation. A submerged transducer array positioned below the channel, as shown in Fig. 1, facilitates the tracking of these particles.

Neglecting the buoyancy and secondary radiation forces, we traced the time-dependent particle positions using the particle tracing module of COMSOL based on the equivalent force equation (Eq. 6). The focus of the ultrasound, which is crucial for applications in microscale robotics and biomedicine, was optimized by manually adjusting the focal point of the polystyrene particles, thereby enhancing the precision of particle movement within the vessel geometry.

Fig. 2(a)-(e) depict the particle behavior without an external acoustic pressure field, where the particles primarily followed the natural drag of the fluid, leading to their uniform distribution across the channel. Interestingly, particle tracking at both outlets was performed using the particle counting function of COSMOL, with 50 particles systematically reaching each outlet.

Fig. 2.

(a)-(e) Simulated particle trajectories and targeting efficiency in the absence of any external acoustic field exhibit a state of uniform particle distribution within both channels. The mean velocity and particle diameter of the fluid are established at 1 mm/s and 10 μm, respectively. (f)-(j) Simulated particle trajectories and targeting efficiency in the presence of any external acoustic field, 1 MPa and 1 μm/s fluid flow.

3.2 The effect of NK cell size on navigation

The NK cells, utilized for navigation within the described phantom model, typically measure between 10–15 μm in diameter, which was verified using confocal imaging, as shown in Fig. 4(a). In our model, the diameter of the NK cells was a critical consideration, given the significant impact of particle size on their dynamic response to acoustic radiation and drag forces. Ultimately, the response influences the mobility and precision of cells in navigating within a fluid medium. Smaller particles are more amenable to manipulation, enabling more accurate control and targeting. The simulations tracked the trajectories of uniformly distributed microparticles with diameters ranging from 10–15 μm, with subsequent calculation of navigation efficiency for each size group. Fig. 3 presents a comparative analysis of these results, indicating that the efficiency is positively correlated with the particle size. However, the inherent variability of NK cell size in practical scenarios precludes size control. Confocal imaging confirmed the presence of NK cells with sizes varying randomly within the 10–15 μm range in a fluid solution. Therefore, we incorporated cells with random diameters to reflect this variation. The recalculated targeting efficiencies, depicted in Fig. 3(d), are consistent with the experimental outcomes illustrated in Fig. 4(b).

Fig. 3.

Simulated target navigation efficiency dependence on the particle size. The acoustic radiation force becomes increasingly dominant as the size of NK cells increases.

Fig. 4.

(a) Confocal images of NK cells, with scale bar of 10 μm. (b) Graphs represent the experimental targeting efficiency of NK cells. (c) Phantom containing fluid channel suspended on top of the ultrasonic transducers with specified inlets and outlets.

3.3 The effect of Fluid velocity on navigation

Fluid dynamics in vessel bifurcations present a formidable challenge for intravascular navigation systems because of their complexity. The primary obstacle is the variable flow patterns found in living organisms, which complicate the precision of the control mechanisms. Fluctuations in the fluid velocity of blood vessels alter the drag forces, thereby affecting micro-particle navigation. Fig. 5 illustrates this dynamic, showing the alteration in the particle trajectories at different fluid velocities. At a velocity of 2 mm/s, the targeting efficiency of the vessels drops to 40–60% compared to that at 1 mm/s. This inefficiency can be addressed by increasing the acoustic pressure; however, it may affect the blood flow and cell distribution. By incrementally increasing the acoustic pressure to 1.5 MPa, we successfully directed 86 particles toward the target, with 16 particles entering the occluded area. Increasing the pressure to 2 MPa resulted in complete trajectory control, achieving 100% targeting efficiency. At a higher velocity of 3 mm/s, the particles outpaced the acoustic forces, as reflected in a targeting ratio of 48–52%. Increasing the acoustic pressure to 2 MPa enhanced the targeting efficiency by 85%. Escalating the pressure to 2.5 MPa yielded perfect efficiency. However, increasing the pressure further elevates the risk of NK cells adhering to vessel walls. Our simulations underscore the necessity of fine-tuning acoustic pressure to match specific fluid and particle conditions for successful navigation.

Fig. 5.

(a) Simulated trajectories of particles illustrating the change in navigation efficiency as the fluid velocity increases. For 2 mm/s, the vessel blockage ratio is reduced to 40–60. (b)-(d) The graphs represent the simulated targeting efficiency of NK cells increasing with the acoustic pressure. (e) Simulated trajectories of particles for a fluid velocity of 3 mm/s. The particles move too fast to be affected by acoustic force, resulting in a targeting ratio of 48–52. (f)-(h) The graphs represent the simulated targeting efficiency of NK cells increasing with the acoustic pressure.

4. CONCLUSIONS

In conclusion, this study demonstrated the capability of a focused ultrasound beam to direct the movement of NK cells at vessel bifurcations, a technique with potential applications in immunotherapy. Additionally, we successfully simulated the relationship between the targeting efficiency and variables, such as cell size and fluid velocity. We observed that the efficiency diminished with smaller cell sizes and higher fluid velocities. However, this reduction in efficiency could be mitigated by incrementally increasing the intensity of the acoustic pressure. Our simulation model was experimentally validated using a phantom vessel bifurcation model that closely replicated the physical characteristics of actual vessels.

Acknowledgments

This research was supported by a grant from the Korean Health Technology R&D Project through the Korea Health Industry Development Institute (KHIDI), funded by the Ministry of Health & Welfare, Republic of Korea (Grant number: RS-2023-00302148).

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