Study the effect of static magnetic field intensity on drug delivery by magnetic nanoparticles

Magnet therapy and the effect of static magnetic field intensity on the treatment of diseases are very controversial¹⁹. It has been reported that thrombolysis with magnetic nanoparticles carrying thrombolytic agents is more effective than administering the free drugs at the same dose¹⁵. The phenomenon of diffusion and mass transport process is effective in dissolving the clot with the thrombolytic drug²⁰. It is reported that one of the best strategies to enhance the thrombolysis without increasing the tPA concentration is improving the mass transport process during thrombolysis²⁰. Agitating the plasma or blood flow is one of mechanism to achieve this aim²¹. Researchers confirmed that creating a drop pressure on clot or rising blood flow resulting in heightening the permeation of plasmin activators to the thrombus²². A computer simulation of clot lysis process based on the reaction–diffusion–convection equations show that raising the pressure drop from 1 to 10 and 20 Pa heighten the lysis strongly. A higher pressure drops increase the penetration of tPA in the thrombus²³. When the clot is dense or the drop pressure is low, the clot lysis is controlled by diffusive process instead of permeation (however, solutions such as increased pressure are virtually impossible and can pose many risks)²². It is confirmed that in the absent of any permeations, the dominant mechanism is limited to diffusion equations²⁴. The effectiveness of thrombolytic therapy is determined by accessibility of thrombus compartments to plasminogen activators and, therefore, depends on permeability of thrombolytic molecules to clot macromolecules²⁵. Therefore, enhancing of mass transfer or accumulation of plasminogen activators during thrombolytic therapy play a significant role in thrombolytic efficiency²⁶.

As, it is confirmed that there is a direct relationship between the clot thrombolysis and the penetration of thrombolytic agent in the thrombus²², one of the best strategy to promote the thrombolysis efficacy, without increasing the drag concentration (or low SK concentration), is improving the diffusion during thrombolysis²⁰. The results (Fig. 6) confirm that there is a direct relationship between clot thrombolysis and magnetic field strengths. This may be due to the effect of the static magnetic field strengths on the magnetic nanoparticles carrying thrombolytic agents or other parameters, which is further studied below.

The two phenomena of mass transport process and diffusion can be effective in increasing the efficiency of the thrombolytic drugs. Because the drug is placed on magnetic nanoparticles, the motion of the nanoparticles and the forces acting on the nanoparticles affect the mass transfer of the drug. In addition, the diffusion phenomenon that follows Fick’s laws also affects the movement of drug molecules. When drug-carrying nanoparticles are exposed to a magnetic field in a fluid, they are affected by several forces, including magnetic force (F_m), gravity (F_g), viscous force (F_d) and buoyancy (F_m). While the force of gravity and magnetic force try to push the nanoparticles down, the buoyancy force (F_b) pushes up as shown Fig. 7.

where F_g and F_b are gravity and buoyancy, respectively and F_d and F_m is viscous force (drag) and magnetic force, respectively.

The magnetic force is given by:

where μ₀ = 4π × 10^–7 is the magnetic permeability of the vacuum, M_p is the magnetization of Fe₃O₄ in a given magnetic field B.

In addition, the drag force of viscosity on a small sphere moving through a viscous fluid is given by:

where ({F}_{d}) is the frictional force—known as Stokes’ drag—acting on the interface between the normal saline and the particles; μ is the dynamic viscosity; R is the radius of the spherical nanoparticle; (v) is the flow velocity relative to the nanoparticle.

The buoyancy force is given by:

And the gravity force is given by:

The excess force F_g due to the difference between the weight and buoyancy of the sphere (both caused by gravity) is given by:

With ({rho }_{P}) and ({rho }_{f}) the mass densities of the nanoparticle and fluid (normal saline), respectively, and g the gravitational acceleration.

Although the phenomenon of diffusion occurs in all cases (from free drug to drug delivery by magnetic nanoparticles), but in the case of free drug, streptokinase, the diffusion phenomenon dominates during the process. In case of drug delivery by nanoparticles, in the absence of magnetic force, gravity plays a major role in transporting the nanoparticles coated with drug molecules to the clot surface. When magnetic nanoparticles are under a magnetic field, the magnetic force governs the motion of particles (the magnetic force will be much larger than the gravity force).

Thrombolysis efficacy of free SK

Figure 6 shows that the thrombolysis efficacy of free SK is around 37%. In the case of the free drug—streptokinase—the penetration phenomenon is predominant. Based on first Fick’s law, SK molecules under random thermal motion tend to spread from a region of higher concentration (normal saline) to a region of lower concentration (clot) as follow²⁷:

where C is the concentration of the diffusing particles (C₂ − C₁ is the difference in concentration for the direction of flow (from C₁ to C₂), F is the diffusion flux (particles per square meter per second), X is the position (the dimension of which is length), and D is the diffusion constant, which has units of cm² per second.

According to first Fick’s law, the efficiency of clot lysis can be related to the concentration of the drug. Drug molecules (SK) break down the fibrins, the major constituents of blood thrombi, thereby dissolving clots. However, the mesh of cross-linked fibrin protein (the aggregated platelets and red blood cells) forming a biological barrier (especially on the surface of the clot) inhibiting the passage of drug molecules to the inner of the clot. In principle, the lysis of the clot by thrombolytic agents is a combination process of diffusion and chemical reaction. Two steps are involved in thrombolysis processes: firstly, is the diffusing of streptokinase molecules to the thrombus surface, secondly is activating plasminogen and converting into enzyme plasmin, which degrading the fibrin into a fibrin-hydrolyzed product.

Fick’s diffusion law, which states that the diffusion flux is proportional to the concentration gradient, employing a high concentration of thrombolytic agent leads to enhancing the rate of clot lysis. SK molecules tend to flow down a concentration gradient (from solvent to clot), this diffusion process leads to clot-dissolving. It has been reported that there is a direct relationship between the dosage of SK and thrombolysis. Administration of higher concentrations of streptokinase leads to increasing clot dissolution. Consequently, as the concentration of SK (in contact with the clot surface,), or diffusion constant being increased, the dissolving of the clot will be enhanced. So, attachment the drug molecules on the surface of the nanoparticles which are in contact with the clot surface will increase the concentration of the drug on the surface, meanwhile applying magnetic force enhances the diffusion constant and accelerate the thrombolysis process as mention below.

Thrombolysis efficacy of MNP@SiO₂ (without magnet)

As shown in Fig. 7, the efficacy of Fe₃O₄@SiO₂-SK + is around 20% more than administration-free SK, at the same drug dosage (62 mg/mL). In this case, the phenomenon of diffusion and the phenomenon of the mass transport process are done with the help of magnetic nanoparticles. In the absence of magnetic force, the force of gravity is the dominant force that tends to place nanoparticles on the surface of the clot, leading to an increase in the concentration of streptokinase in the clot surface over a shorter period of time. Therefore, improving the thrombolysis could be related to the increasing local SK concentrations on the surface of the clot due to gravity, which provides more effect on the diffusion of drug molecules and clot-dissolving. While in free SK, molecules of streptokinase are dissolved in normal saline above the clot which leads to the low concentration of drug molecules in the clot contact with clot surface and being less effective, in the case of MNP@SiO₂ + SK, magnetic nanoparticles (Fe₃O₄) fall on the surface of clot, due to gravity, and the more streptokinase molecules are in contact with the surface of the clot, therefore, the drug concentration will be higher at the surface of the clot (C_(MNP@SiO₂) > C_(Free SK)). The schematic of the effect of gravity on nanoparticles is shown in Fig. 7A. Micro-CT scan image (Fig. 8) shows that magnetic nanoparticles are located on the surface of the clot, which confirms the effect of gravity on drug-carrying nanoparticles.

Thrombolysis efficacy of MNP@SiO₂ + drug + magnet

In the case of MNP@SiO₂ + drug + magnet, there is a growth in thrombolysis efficiency compared to free SK and even non-magnetic magnetic nanoparticles as shown in Fig. 6. According to Eq. (2), this effect can be attributed to the effect of magnetic force. The schematic of gravity and magnetic force on nanoparticles is shown in Fig. 7B. The magnetic force, which is much larger than the force of gravity, causes the nanoparticles to move from the injection site to the surface of the clot. This causes the drug-carrying nanoparticles to be located on the surface of the clot and the drug concentration to increase on the clot surface, which leads to an increase in thrombolysis efficiency. In addition, the penetration of nanoparticles into the clot can be an explanation for increasing the efficiency of the clot by increasing the magnetic field, which is confirmed by micro-CT-scan images. Micro-CT-scan images (Figs. 8, 9, 10, and 11) also show that as the magnetic field increases, nanoparticles penetrate into the clot, and the rate of penetration into the clot rises with increasing magnetic field strength. These images also display that as the magnetic field intensifies, not only does the penetration depth of the nanoparticles increase, but also the number of nanoparticles penetrating into the clot.

The penetration of the drug into the clot allows the drugs to break down the fibrins inside the clot, which is not possible with the free drug. As the magnetic field intensifies, more fibrin inside the clot is exposed to the drug and broken down. Whereas a free drug or the drug is carrying by nanoparticles (without a magnetic field) is used, the drug molecules are only in contact with the fibrins on the surface and break down the fibrins on the surface of the clot, but when a magnetic field is used, the molecules of the drug can penetrate into the depth of clot and break the fibrins inside the clot. In fact, the magnetic force guides the thrombolytic agent into the clot by magnetic nanoparticles (like injecting a drug into a tissue with a needle).

In addition to the penetration of nanoparticles into the clot, the time of contact nanoparticles with the clot is also significant.

The magnetic field applies a force on magnetic nanoparticles that accelerate the movement of the nanoparticles towards the clot surface and the nanoparticles carrying a thrombolytic agent reach the surface of the clot in a shorter time, and the drug will be in contact with the clot longer. According to physic laws, the time of falling (moving from the injecting site of nanoparticles to the surface of clot) is given by:

L is the distance between injecting site and the surface of clot and m is the mass of nanoparticles.

Therefore, the nanoparticles carry the drug, increasing the contact time of the nanoparticles with the clot causes the drug molecules to be in contact with the fibrins longer and there is more time for a chemical reaction, which increases fibrin breakdown.

Meanwhile, nanoparticles fall to the surface of the clot in less time and, as a result, stay in contact with the clot surface for a longer time. Rapid placement of nanoparticles carrying thrombolytic agent on the surface of the clot leads to increasing the contacting time of nanoparticles with clot surface. Based on Fick’s second law reveals that, in diffusive processes, there is a fundamental relation between the contacted time and the square of the length over which diffusion takes place as below²⁸:

(varphi ) is the concentration in dimensions.

So, increasing the time of contacting drug molecules with clot surface leading to increasing the length of diffusion in the clot. As a result, the thrombolysis efficiency when streptokinase loaded on a nanoparticle is greater than is free SK (a greater number of SK molecules are in contact with clot surface compare with that of free SK that led to increasing thrombolysis efficacy).

According to Nernst–Planck equation, the magnetic field also affects the diffusion. In the static electromagnetic conditions, one obtains the steady-state Nernst–Planck equation²⁹:

where J is the diffusion flux density, t is time, D is the diffusivity of the chemical species, c is the concentration of the species, z is the valence of ionic species, k_B is the Boltzmann constant, T is the temperature, (c mu ) is velocity of fluid, M is the magnetic vector potential.

Besides, magnetic force enhances the diffusion constant based on the Nernst–Planck equation, which states that the addition of a magnetic field will increase the penetration phenomenon. Therefore, the increasing magnetic field not only makes the nanoparticles get more in contact with the clot surface faster (SK concentration increases faster) but also rises the diffusion constant which leads to increasing the thrombolysis efficacy as shown in Fig. 6.

The magnetic field causes the nanoparticles to not only penetrate the surface of the clot but also penetrate inside the clot. Because these nanoparticles carry drugs, the magnetic field increases the concentration of the drug and increases the contact of the drug molecules with the clotted fibrins. Other researchers have reported similar phenomena in other areas, such as the penetration of magnetic nanoparticles under a magnetic field into cancer cell³⁰. The penetration of magnetic nanoparticles under the magnetic field in the clot mesh increases the effect of thrombolytic drug. The clot, as shown in Fig. 13, has a mesh-like structure composed of fibrin, red blood cells and platelets. The drug-carrying nanoparticles can pass through these meshes due to magnetic force. In all micro-CT scan images, nanoparticles have penetrated in the middle of the clot, and this can be clearly seen in Fig. 12. As shown in Fig. 12, nanoparticles in a strong magnetic field (0.5 T) are funnel-shaped, which could be due to the shape of the magnetic field of the magnetic coil, which is stronger in the middle and weaker around it. However, by changing the position of the magnetic field or by rotating it, an equal distribution of nanoparticles can be created in the clot.