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Numerical simulation of magnetic drug targeting to a tumor in the simplified model of the human lung
Accepted Manuscript
Numerical Simulation of Magnetic Drug Targeting to a Tumor in the Simplified Model of the Human Lung M. Sabz , R. Kamali , S. Ahmadizade PII: DOI: Reference:
S0169-2607(18)31604-3 https://doi.org/10.1016/j.cmpb.2019.02.001 COMM 4842
To appear in:
Computer Methods and Programs in Biomedicine
Received date: Revised date: Accepted date:
7 November 2018 30 January 2019 1 February 2019
Please cite this article as: M. Sabz , R. Kamali , S. Ahmadizade , Numerical Simulation of Magnetic Drug Targeting to a Tumor in the Simplified Model of the Human Lung, Computer Methods and Programs in Biomedicine (2019), doi: https://doi.org/10.1016/j.cmpb.2019.02.001
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Highlights The presence of magnetic field, increases DE on tumor surface greatly. The best positions for magnetic source are found under the bifurcations in this study. DE on tumors reduces by enhancement the mass flow rate for I= 10 (A) and I=15 (A)
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Numerical Simulation of Magnetic Drug Targeting to a Tumor in the Simplified Model of the Human Lung
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M. Sabz, R. Kamali*, S. Ahmadizade School of Mechanical Engineering, Shiraz University, Shiraz, Iran *Corresponding author: R. Kamali/ E-mail address: [email protected]
Abstract
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Background: Magnetic Drug Targeting improves effectiveness of medicine application and reduces its side effects. In this method, drugs with magnetic core are released in the lung and they are steered towards the tumor by applying an external magnetic field. A number of researchers utilized numerical methods to study particle deposition in the lung, but magnetic drug delivery to the tumors in the human lung has not been addressed yet. Method: In the present study, Weibel model is used for human airway geometry from generation G0 to G3. Moreover, a tumor is considered in the lung, which is located in G2. Particles are made of iron oxide magnetic cores and poly lactic coglycolic acid shells. Fluid flow is assumed laminar and particles are coupled with the fluid by one-way method. The magnetic field is produced by a coil with law current intensities instead of a wire with high current intensities. Influences of various parameters such as particle diameter, magnetic source position, current intensity, and inlet mass flow rate and tumor size on the deposition efficiency on the tumor surface are reported. Results: Results show that magnetic drug targeting enhances deposition efficiency on the tumor surface Furthermore, when the current intensity rises from 10 (A) to 20 (A), tumor enlarging, and increasing particle diameter, lead to deposition efficiency enhancement, but efficiency decreases by increasing mass flow rate. However, when current intensity is 20 (A), deposition efficiency decreases in two situations. The first situation is when mass flow rate is 7 (L/min) and particle diameter is 9 (μm), and the second one is in 10 (L/min) mass flow rate and 9 (μm) diameter. Conclusion: The results demonstrated that magnetic drug targeting is applicable and suitable for all tumors specially for small tumors(r/R=0.5 in this case) that efficiency increase from 0% in the absence of magnetic field to more than 2% in the presence of magnetic field. Keywords: Magnetic Drug Targeting (MDT), 3-D simulation, Airway model, Hemispherical tumor, Particle deposition, Non-uniform magnetic field
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1. Introduction
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To improve the accumulation of drugs in tumor, an external magnetic field acts as an external force, which steers particles and diffuses them near the tumor. Magnetic drug targeting has a wide range of advantages including[1]: 1) Less amount of drug is consumed. 2) The drug remains a longer time in the target site and the absorption rate of the drug increases. 3) The drug-induced mucous irritation is prevented. 4) Drug side effects are reduced. 5) The absorption of the drug into the healthy cells and tissues decreases. 6) Elimination of surgery. Numerical simulation is employed to model the transposition, the diffusion and the deposition of the micro-particles throughout the human lungs. Zhang et al. [2] simulated the measurable effects of a carinal tumor on 3-D airflow. Farkas et al. [3] reported the effects of local obstructions and blockage on airflow and aerosol deposition in central human airways. Their results confirmed that large particles had higher DE compared with nano-particles. Ally et al. [4] investigated an in-vitro model to study the feasibility of the deposition of the suspended particles in the air by using a magnetic field. The purpose of their research was utilizing this method in the treatment of lung cancer. Martin et al. [5] proposed a novel method based on using aspheric magnetic particles and uniform magnetic field in the process of magnetic drug delivery. They employed an experimental model (in-vitro) of pulmonary branches. They exerted magnetic torque to steer particles instead of a magnetic force. Kannan et al. used CFD to investigate particle deposition in the human lung. they validated their results by using computational Euler Lagrangian method [6]. In the other study, they used Wind-Kessel algorithm for an oral delivery. In this method, the particles exiting the system were assume reenter to system during exhalation, thereby giving an upper bound for the deposition in the truncated lung model [7]. Dames et al. [8] suggested that magnetic particles can be useful for drug delivery to localized lung disease. They showed that targeted drug delivery to the lung could be achieved by magnetic particles in combination of magnetic gradient field. Dahmani et al. [9] employed a dynamic magnetic field that was inactive during the inhalation and was active during the expiration process. They increased the amounts of deposited particles in target areas, located in the depth of the lung to treat lung cancer. Dahmani et al. [10] also generated a magnetic field with a variable current coil and observed that creating the electrical eddy currents causes undesirable changes in the magnetic field and increasing the temperature dramatically. To resolve this problem, a set of permanent magnets were used. Xie et al. [11] studied the particle deposition in the presence of wedge-shaped permanent magnets for an experimental model (in-vitro) and in depth of mice’s lung (in-vivo). Results were presented for different mass flow rates, concentration of particles, and the pipe’s diameter. Redman et al. [12] investigated deposition of aspheric particles in the presence of uniform magnetic field in rabbit’s lung. Xi et al. [13] used numerical simulation of magnetic drug delivery to the olfactory of the nasal cavity in the upper respiratory system of
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human. The flow regime was laminar and magnetic field was produced by permanent magnets. They presented an optimized model for magnetic drug delivery. Their results confirmed an increasing particle deposition in the olfactory area and reducing particle deposition in other parts of respiratory system. Pourmehran et al. [14] investigated the application of magnetic drug targeting in a realistic geometry of the human respiratory system. They reported the influence of particle diameter, magnetic source position, magnetic field strength, and inhalation condition on particle transport pattern and DE in a realistic model through generation G0 to G2. Moreover, Pourmehran et al. [15] studied the effect of previous variants on DE in a new model comprising oral cavity, larynx, pharynx and trachea along with six generation of the lung based on CT scan images. Kenjeres et al. [16] investigated the effect of magnetic field on drug delivery in an realistic geometry of human lung from the mouth inlet to the eighth generation of the human lung and the transitional RANS approach was used. This study confirmed that magnetic drug targeting technique is a good method for treatment of respiratory diseases. There are other numerical studies in magnetic drug targeting in the arteries and in the human respiratory system [17-21]. Magnetic particles are widely used in biomedical technology applications and cancer therapy [22-
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26], lung cancer therapy and pulmonary disease [27-32] and diagnostic imaging, biological sensing, drug, cell, and gene delivery and cell tracking[33] , cell manipulation [34] and biological applications [35]. In the present study, particle deposition in a human lung with a tumor is investigated numerically. The geometry of the lung consists of two different models; Mitsakou [36] model is utilized in the first part of the lung (from mouth inlet to G0), and Weibel [37] model is used for G0 to G3. Mitsakou et al. developed nonCFD-based model to calculate deposition of particles along the oral rout. This model is a simplified geometry based on conducting ducts from mouth to throat region. Particles with different sizes are used in this study (1-17 µm ) and a good agreement with the available experimental study obtained.
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The magnetic field is produced by a coil. Influences of various parameters such as particle diameter, magnetic source position, current intensity, inlet mass flow rate and tumor size on the DE on the tumor surface are reported.
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2. Material and methods In this study, investigating of magnetic field and fluid flow physics are prerequisites for particle depositions. Finite element and finite volume methods are appropriate methods for this study. COMSOL software which is based on finite element method is used for modeling and analyzing. In the first step, magnetic field physics is modeled in a stationary study and then in the second step, magnetic field gradient is calculated. In the third step fluid flow under the influence of magnetic field is studied in a time dependent study. in the last step, particle tracing is analyzed
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based on the results of previous physics in a time dependent study from t= 0 s to t= 1 s and 0.005 s for particle time step size. In order to pass information from one physics to next physics and the results of one physics affect another physics fully coupled method is used. Algebraic Multigrid Solver for fluid flow physics, FGMRES for magnetic field and GMRES solver for particle tracing are selected. Magnetic field gradient is calculated by a direct solver (MUMPS). Solid Works software is used to model the geometry. The first part of the lung (from mouth inlet to G0) is described by Mitsakou model and Weibel model is used for generation G0 to G3 (see figure 1). The density of materials, boundary conditions and other properties are represented in table 1. Constant mass flow rate in the inlet of mouth in the inhalation process (without exhalation) and zero partial pressure in the outlets of the geometry are assumed as boundary conditions. The pressure difference between the intake air and the output air from branches is negligible, so the zero pressure in outlet branches is acceptable. For all solid boundaries, no-slip condition is applied. Particles are released continuously from plane A (see figure 2), with random distribution and their velocity are determined by the air velocity at the same point. Total number of particles in this study is 10000 and particles diameter are changed from 3 to 9 (μm) and their density is assumed 3415 (Kg/m3). The interactions between particles are negligible, because volume fraction of particles is less than 0.1 %. Stick boundary condition is considered for particles that collide to the walls and freezing boundary condition for the outlets.
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3.Theory
In order to investigate MDT numerically, magnetic field, fluid flow, and particle transportation equations should be solved. These equations are described as follows:
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3.1. Magnetic field
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Four laws define the magnetic field which are known as Maxwell’s Equations [38]. These equations are: 3.1.1 Gauss’s law for electric fields Two kinds of electric fields are in Maxwell’s Equations. Electrostatic field produced by electric charge and the induced electric field produced by a changing magnetic field. The integral form of Gauss’s law for electric field is:
q
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Left side of above equation is electric flux – the number of electric field lines – passing through a closed surface S. The right side is the total amount of charge contained within that surface divided by a constant called the permittivity of free space. The differential form of Gauss’s law is:
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. 0 E E
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This law also written in the differential form that is:
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3.1.2 Gauss’s law for magnetic fields Gauss’s law for magnetic fields has many similarities to the law for electric fields in form. However, it has some differences in content. The integral form of Gauss’s law for magnetic flux passing through a closed surface S is: (3)
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3.1.3 Faraday’s law When magnetic flux is altered in an enclosed circuit, an electric current may be induced in it. Faraday’s law describes this phenomenon as:
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3.1.4 The Ampere–Maxwell law A circulating magnetic field is generated around any path that bounds a surface by changing electric flux through the surface or an electric current. Ampere–Maxwell law explains such situation which the integral form of the law is: (7)
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The differential form of Ampere–Maxwell law is:
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3.2. Fluid flow Fluid flow through the lung is assumed laminar, and continuity and Navier-Stokes (momentum) equations are employed to find velocity and pressure fields. Continuity and momentum equations are: (9) .V 0
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3.3. Particle transportation
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Spherical magnetic particle is used with a magnetic core and a shell, which contains the drug. The magnetic core is made from iron oxide and the shell made from PLGA (Poly LacticCoglycolic Acid)[39]. The equation of motion of particles in the fluid flow is:
dup
Fi dt Particle velocity ( u p ) is: up
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mp
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Where Fi is total force that can act on particles which includes: drag, gravity, buoyancy,
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Suffman’s lift, Faxen, virtual mass, pressure gradient, Basset, and magnetic forces. These forces are defined as below. 3.3.1 Drag force: (13) mpf FD (u f u p ) p
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p
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To calculate f , various methods are used as below: f 1 If Re p 1 Zhang et al. If
Cohen stuart[40]
1 Re p 400
f Re p 0.354
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f 1 0.15Re0.687 0.0175(1 4.25 104 Rep1.16 ) p
1 Re p 3 105
If
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Morsi & Alexander[41] Re p f (1 2 3 2 ) 24 Re p Re p
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In equation (15), C c is Cunningham slip correction factor and in this study, is 1[42-44] and f 1 because Re p 1
3.3.2 Gravity and buoyancy force
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Fg b m p g (1
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The gravity force is important at the lower airways(from generation G9 on)[2]. 3.3.3 Suffman’s lift force
f d p 2 du f dy
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The Suffman’s lift force is not considered in this study due to it is negligibly small compared to drag force.
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3.3.4 Faxen force d 3 F Faxen f p 2 u f 8 Faxen force relative to drag force is weak and negligible. 3.3.5 Virtual mass force V D(u f u p ) F Virtualmass f p 2 Dt Since the density of particles is larger than that of the fluid, virtual mass force is negligible.
(24)
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3.3.6 Pressure gradient force F P. grad Vp f
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The pressure gradient force is not important in this study because the ratio of fluid density to particle density is too small.
F Basset
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3.3.7 Basset force
Du f u p t 3 2 Dt t dt ) d p f f ( 2 t t 0
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3.3.8 Magnetic force (27) 1 Fm d mp 3V p 0 X m H 2 2 Where d mp is the ratio of magnetic core diameter to particle diameter, V p is particle volume, 0 is permeability of vacuum, X m is particle susceptibility and H is magnetic intensity. According
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to the literature, magnetic and drag forces have the most effects in comparison to other one, so in the present study force balance is considered: (28) du
3.4 Particle deposition efficiency
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The deposition efficiency is determined by the percentage of the number of particles that is deposited on the tumor surface to the total number of particles. (29) DE =
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3.5 Mnp number
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0.84 in this study, dp, µ0, Msat, N, I, µf, UT and L are the particle diameter, the permeability of
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free space, saturation magnetization, number of coil turns, current intensity, dynamic viscosity of fluid (air), characteristic velocity and the length of the coil, respectively.
4. Results
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4.1. Model Validation
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In order to verify the numerical method, results of magnetic particle targeting in a simplified artery are compared to the data that reported by Haverkort [45] and Cohesn stuart [40]. A schematic of the geometry is shown in figure 3, and boundary conditions, fluid properties, and particle properties are given in table 2. As illustrated in figure 4, airflow velocity profiles are compared in three deflection planes (0°, 45°, and 90°). Moreover, DE for these models are studied and results are compared in figure 5. According to these figures, the results of present numerical method have presented acceptable accuracy. Consequently, the independence of the results from grids should be investigated. In order to achieve to this purpose, four different grid numbers are tested in the selected geometry. The fluid velocity at a given point in figure 6a and particle deposition on the tumor are compared for these grids. Results confirm that less than 1% differences in velocity between 305420 and 421624 grids and less than 2% between 305420 and 521852 grids (see figure 6b) are existed. The results in figure 6c reveals less than 1% difference in particle deposition efficiency between 305420 and 421624 grids and also between 305420 and 521852 grids. Therefore, 305420 grid number is used in this study. 4.2. Particle Transport and Deposition
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Figures 7 and 8 show air velocity contours for Q=7 (L/min). According to these figures tumor plays a significant role in changing velocity field through the lung. Moreover, it produces nonsymmetry in the secondary velocity. Figure 9 represents the effects of three parameters; tumor size, mass flow rate, and particle diameter on DE without any magnetic field. According to this figure, DE rises by increasing the inhalation mass flow rate and particle diameter except for tumor with r/R=0.5 that DE is zero for all cases. In lower mass flow rates, particle deposition near the wall is greater, but the particle inertia is lower because of low particle velocity. In this case, the Stokes number (St) - the tendency of particles to attend to the flow lines - is also small. Therefore, particles do not have enough inertia to get out of their path, and only the deposition of particles near the wall dominant their deposition. Increasing particle diameter (or increasing St Number) causes enhancement of particle deposition. When mass flow rate grows, fluid flow turbulences increases, so particles tend to leave their paths and collide to the walls, which is lead to increment of the DE.
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In addition, according to the figure 9, by enlarging tumor size, contact surface with flow rate increases that is lead to DE enhancement. However, increasing tumor size causes decreasing flow rate and particle numbers through the tumor branch, so DE reduces for larger tumors and DE is in its highest point for tumor with r/R=1 in this study. In addition to tumors, external magnetic fields also affect particle DE. In the first place, the most efficient position for the coil is determined. Figure 10 shows the effect of distance between the magnetic source and tumor on DE when Q = 7 (L/min), I = 10 (A), dp = 9 (μm). Six different positions for magnetic source are considered to find the best position of the coil (z = 1, 2, 3, 4, 5, 6 cm relative to reference plane (z = 0 cm), see figure 2). Regarding to results, the maximum efficiency occurs in z = 2 cm. This position is exactly under the first bifurcation and the second pick is z = 5 cm. This position is also under the second bifurcation. Consequently, the best positions for coil is under the bifurcations. Moreover, minimum efficiency occurs in z = 6 cm. This position is accurately under the tumor; it seems reasonable because of more distance between the coil and bifurcations, large number of particles pass through the upper branches and do not reach to tumor. On the other hand, when the coil is close to bifurcations, magnetic field attracts particles to the lower branches and the chance of particle deposition on tumor surface would be increased. Figures 11a, 12a, 13a indicate the effects of three parameters; mass flow rates, particle diameters, tumor size in three different current intensities (10 (A), 15 (A), 20 (A)). These three figures report following results: 1) DE on tumors decrease by enhancement the mass flow rate for all particle diameters that causes increasing fluid velocity and magnetic field has less time to impress and attract particles and consequently the chance of particle deposition on tumor surface would be decreased. This result is totally different to result in previous section in the absence of magnetic field; owing to in the presence of magnetic field dominant force is magnetic force and the effect of drag force is much less. So in this section the effective of magnetic force on particle deposition is determinative.
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2) DE enhances for all three tumors by particle diameter growth for constant mass flow rate, because by increasing particle diameter, the magnetic force that is applied on the particles increases and more particles pass thorough tumor branch.
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3) Magnetic field causes more deposition on the larger tumor (r/R=1.5 in this study) which is mainly because by increasing tumor size, mass flow rate in tumor branch would be dropped and as mentioned above (number 1), DE rises. On the other hand, by growth in tumor size, there is more space for particle deposition by magnetic field. 4)DE enhances by increasing current intensity. According to figure 13a, by increasing current intensity from 15 (A) to 20 (A), DE decreases in two situations when particle diameter is 9 (μm), current intensity is 20 (A) and mass flow rates
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are 7 (L/min) and 10 (L/min). In these two cases, DE curve has been dropped so much in the range of tumor with r/R = 1.5. The low mass flow rate, large particles, and high magnetic field strength are the main results of such phenomena and particles deposit before reaching the tumor as shown in figure 14. Additionally, figure 15 depicts the effect of current intensity on particle deposition patterns and magnetic field strength (T) for mass flow rate Q = 12 (L/min). Figures 11b, 12b, and 13b depict the effect of Mnp number on DE in the mentioned currents. According to definition of Mnp and numerical data that were acquired in this study for each current intensity and also each size of tumor, a DE equation versus to Mnp were approximated. Based on these equations DE would be determined for every particle diameter and flow rate. So we could find the appropriate conditions to reach to the best efficiencies.
5. Discussion
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The inhalation of drug aerosols is used for the treatment of many lung diseases such as asthma, infection and lung cancers. Magnetic drug targeting can improve therapeutic efficiency and decrease unwanted side effects. Dames et al. [8] investigated target drug delivery to the mice’s lung by computer aid simulation and experimentally for the first time. Price et al.[32] evaluated in-vivo and in-vitro magnetic drug targeting of inhaled Nano in moicroparticles in a healthy mice. Pourmehran et al.[14, 15] studied magnetic drug targeting in the human lung and reported the effect of particle diameter, magnetic source position and magnetic field strength on deposition efficiency and magnetic field was produced by a high current intensity wire. Despite dramatic progress in magnetic drug delivery, magnetic drug targeting to the tumors in the branches of human lung has not been adequately achieved to date numerically. In the present study, a tumor with three different sizes is modeled in the generation G2 of the human lung and the effect of tumor size, magnetic field strength, particle diameter, mass flow rate and magnetic field position on the particle deposition efficiency on the tumor surface are investigated. A coil with low current intensities is used to produce magnetic field and appropriate position is acquired exactly under the first bifurcation for the coil. Our results proved that employing magnetic field is totally necessary to drug delivery to the lung tumors especially for smaller tumors that were not covered by drug in the absence of magnetic field in this study.
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6. Conclusion
Present study investigates magnetic drug targeting to a lung tumor. A coil is used to produce the required magnetic field and steer the particles to the tumor. The air flow is laminar, unsteady, incompressible, and Newtonian. Several conclusions may be drawn from this study: 1) In the absence of magnetic field, increasing the mass flow rate and particle diameter lead to DE enhancement on tumor surface and maximum efficiency is related to tumor with r/R = 1.
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2) DE increase with particle diameter growth and decreases with mass flow rate growth when current intensity changes from 10 (A) to 20(A). Also, increasing tumor size and current intensity lead to DE enhancement except for two situations (Q=7 (L/min), d = 9 (μm), I = 20 (A) and Q = 10 (L/min), d = 9 (μm), I = 20 (A)). 3) The presence of magnetic field, enhances DE on tumor surface greatly and using this method is an efficient way for drug delivery to small tumors because of their small surfaces. 4) The position of magnetic source plays an important role in drug targeting to the tumors. In this study, the best positions are found under the bifurcations. 5) According to Mnp results, maximum DE occurs in the range of 3 to 9 (μm) in particle diameter and 7 to 12 (L/min) in mass flow rate for tumors with r/R = 1 and r/R = 1.5. Maximum DE for tumor with r/R=1.5 is 5.8 and it occurs when Mnp = 80.58 for 15 (A) current intensity and the highest DE for tumor with r/R=1 is 4.86 when Mnp = 67.375 and current intensity is 20 (A). For tumor with r/R=0.5, the highest efficiency is not in these ranges, and Mnp should increase to 210 for 15 (A) current intensity and in these condition, the DE reaches 2.48. To increase Mnp, mass flow rate should be reduced from 7 (L/min) or particle diameter should be enhanced to more than 9 (μm). To maintain such conditions in the proper range and preserve the one-way assumption, it is necessary to change the flow rate and diameter simultaneously.
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The authors made no disclosures.
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implementation of the Wind–Kessel algorithm for an oral delivery. International journal for numerical methods in biomedical engineering, 2016. 32(6): p. e02746. Dames, P., et al., Targeted delivery of magnetic aerosol droplets to the lung. Nature nanotechnology, 2007. 2(8): p. 495. Dahmani, C., et al. Respiration triggered magnetic drug targeting in the lungs. in Engineering in Medicine and Biology Society, 2009. EMBC 2009. Annual International Conference of the IEEE. 2009. IEEE. Dahmani, C., et al. An innovative rotational magnetic system to enhance cell transfection with magnetic nanoparticles. in World Congress on Medical Physics and Biomedical Engineering, September 7-12, 2009, Munich, Germany. 2009. Springer. Xie, Y., et al., In vitro and in vivo lung deposition of coated magnetic aerosol particles. Journal of pharmaceutical sciences, 2010. 99(11): p. 4658-4668. Redman, G.E., et al., Pilot study of inhaled aerosols targeted via magnetic alignment of high aspect ratio particles in rabbits. Journal of Nanomaterials, 2011. 2011: p. 2. Xi, J., et al., Optimization of magnetophoretic-guided drug delivery to the olfactory region in a human nose model. Biomechanics and modeling in mechanobiology, 2016. 15(4): p. 877-891. Pourmehran, O., et al., Simulation of magnetic drug targeting through tracheobronchial airways in the presence of an external non-uniform magnetic field using Lagrangian magnetic particle tracking. Journal of Magnetism and Magnetic Materials, 2015. 393: p. 380-393. Pourmehran, O., T.B. Gorji, and M. Gorji-Bandpy, Magnetic drug targeting through a realistic model of human tracheobronchial airways using computational fluid and particle dynamics. Biomechanics and modeling in mechanobiology, 2016. 15(5): p. 1355-1374. Kenjereš, S. and J.L. Tjin, Numerical simulations of targeted delivery of magnetic drug aerosols in the human upper and central respiratory system: a validation study. Royal Society open science, 2017. 4(12): p. 170873. Haverkort, J., S. Kenjereš, and C. Kleijn, Computational simulations of magnetic particle capture in arterial flows. Annals of biomedical engineering, 2009. 37(12): p. 2436. Haverkort, J., S. Kenjereš, and C. Kleijn, Magnetic particle motion in a Poiseuille flow. Physical review E, 2009. 80(1): p. 016302. Stuart, D.C., C. Kleijn, and S. Kenjereš, An efficient and robust method for Lagrangian magnetic particle tracking in fluid flow simulations on unstructured grids. Computers & Fluids, 2011. 40(1): p. 188-194. Nikookar, H., et al., Enhancing drug delivery to human trachea through oral airway using magnetophoretic steering of microsphere carriers composed of aggregated superparamagnetic nanoparticles and nanomedicine: A numerical study. Journal of Aerosol Science, 2019. 127: p. 63-92. Manshadi, M.K., et al., Delivery of magnetic micro/nanoparticles and magnetic-based drug/cargo into arterial flow for targeted therapy. Drug delivery, 2018. 25(1): p. 1963-1973. Wang, C., et al., Multifunctional theranostic red blood cells for magnetic‐field‐enhanced in vivo combination therapy of cancer. Advanced Materials, 2014. 26(28): p. 4794-4802. Gobbo, O.L., et al., Magnetic nanoparticles in cancer theranostics. Theranostics, 2015. 5(11): p. 1249. Tietze, R., et al., Magnetic nanoparticle-based drug delivery for cancer therapy. Biochemical and biophysical research communications, 2015. 468(3): p. 463-470. Al-Jamal, K.T., et al., Magnetic drug targeting: preclinical in vivo studies, mathematical modeling, and extrapolation to humans. Nano letters, 2016. 16(9): p. 5652-5660. Rodzinski, A., et al., Targeted and controlled anticancer drug delivery and release with magnetoelectric nanoparticles. Scientific reports, 2016. 6: p. 20867. Abdelaziz, H.M., et al., Inhalable particulate drug delivery systems for lung cancer therapy: Nanoparticles, microparticles, nanocomposites and nanoaggregates. Journal of controlled release, 2017.
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Stocke, N.A., et al., Formulation and characterization of inhalable magnetic nanocomposite microparticles (MnMs) for targeted pulmonary delivery via spray drying. International journal of pharmaceutics, 2015. 479(2): p. 320-328. Omlor, A.J., et al., Nanotechnology in respiratory medicine. Respiratory research, 2015. 16(1): p. 64. Munaweera, I., et al., Chemoradiotherapeutic magnetic nanoparticles for targeted treatment of nonsmall cell lung cancer. Molecular pharmaceutics, 2015. 12(10): p. 3588-3596. El-Sherbiny, I.M., et al., Magnetic nanoparticles-based drug and gene delivery systems for the treatment of pulmonary diseases. Nanomedicine, 2017. 12(4): p. 387-402. Price, D.N., et al., In vivo pulmonary delivery and magnetic-targeting of dry powder nano-inmicroparticles. Molecular pharmaceutics, 2017. 14(12): p. 4741-4750. Ling, D., N. Lee, and T. Hyeon, Chemical synthesis and assembly of uniformly sized iron oxide nanoparticles for medical applications. Accounts of chemical research, 2015. 48(5): p. 12761285. Abedini-Nassab, R. and M. Eslamian, Recent patents and advances on applications of magnetic nanoparticles and thin films in cell manipulation. Recent patents on nanotechnology, 2014. 8(3): p. 157-164. Colombo, M., et al., Biological applications of magnetic nanoparticles. Chemical Society Reviews, 2012. 41(11): p. 4306-4334. Mitsakou, C., et al., A simple mechanistic model of deposition of water-soluble aerosol particles in the mouth and throat. Journal of Aerosol Medicine, 2007. 20(4): p. 519-529. Weibel, E.R., Geometry and dimensions of airways of conductive and transitory zones. 1963: Springer. Fleisch, D., A Student's guide to Maxwell's equations. 2008: Cambridge University Press. Tjin, J.L., Magnetic Drug Targeting in Human Airway Geometry. 2014, TU Delft, Delft University of Technology. Cohen Stuart, D., The development of a discrete particle model for 3D unstructured grids: application to magnetic drug targeting. 2009, MSc thesis, Delft University of Technology. Morsi, S. and A. Alexander, An investigation of particle trajectories in two-phase flow systems. Journal of Fluid Mechanics, 1972. 55(02): p. 193-208. Moshfegh, A., et al., A novel slip correction factor for spherical aerosol particles. World Academy of Science, Engineering and Technology, 2009. 27: p. 709-715. Gussman, R.A., On the aerosol particle slip correction factor. Journal of Applied Meteorology, 1969. 8(6): p. 999-1001. Cunningham, E., On the velocity of steady fall of spherical particles through fluid medium. Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character, 1910. 83(563): p. 357-365. Haverkort, J., Analytical and computational analysis of magnetic drug targeting in simplified and realistic arterial geometries. 2008, MSc Thesis, Delft University of Technology.
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Figure 1. Airway model from mouth inlet to G3; a schematic of the geometry of the mouth inlet to trachea from Mitsakou model and specifications, b schematic of the trachea G3 from Weibel model,inlet c the Figure 1. Airway model from mouth inlet to G3; a schematic of thetogeometry of the mouth to geometry trachea from specification of Weibel model Mitsakou model and specifications, b schematic of the trachea to G3 from Weibel model, c the geometry specification of Weibel model
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Figure 2. Figure 2. different different positions positions of of coil coil center center (green (green points points at at xx = = -24 -24 cm cm and and yy = = 00 cm cm and and zz = = 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 66 cm) cm) relative to reference plane (z = 0 cm) relative to reference plane (z = 0 cm)
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Figure 3. Figure 3. Schematic Schematic of of the the geometry geometry and and the the parameters parameters of of construction construction for for model model validation validation
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Figure 4. 4. Velocity plane, bb45? 45◦deflection deflectionplane, plane,c c90? 90◦deflection deflection plane Figure Velocitymagnitude magnitudeprofiles profilesin ina: a: aa 0◦ 0? deflection deflection plane, plane forfor model validation model validation
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Figure 5. DE as a function of the particle diameter for model validation
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Figure 6. a Test point A for grid independency test for Q=7 (L/min), I=10 (A), d p =9 ( m) , b velocity magnitude in point A, c DE on tumor surface with r/R=1.5
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Figure 7. Air8.velocity contours at plane 1 of geometry; a position of plane 1, b Axial and radial air velocity contours Figure Air velocity contours at plane 1 of geometry; a position of plane 1, b Axial and radial air velocity at plane 1 contours at plane 1
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Figure 8. Air8.velocity contours at plane 2 of 2geometry; a position of plane 2, b 2, Axial and radial air velocity contours Figure Air velocity contours at plane of geometry; a position of plane b Axial and radial air velocity at plane 2 contours at plane 2
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Figure 9. Effect of three parameters; particle diameter (μm), inlet mass flow rate (L/min), tumor size (r/R (r/R = = 0.5, 0.5, 1, 1, 1.5) 1.5) on on DE DE in in the the absence absence of of magnetic magnetic field field size
FigureFigure 10. Effect magnetic source source position (x = -24 y =cm, 0xm, = 1, 2, cm) DE on forDE Q=7(L/min), 10. of Effect of magnetic position (xcm, = -24 y =z0xm, z =3,1,4,2,5,3,6 4, 5, on 6 cm) for I=10 (A), and dp=9 (μm) Q=7(L/min), I=10 (A), and dp=9 (μm)
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Figure 11. 11. Effect Effect of; of; aa three three parameters; parameters; particle particle diameter diameter (μm), (μm), inlet inlet mass mass flow flow rate rate (L/min), (L/min), tumor tumor Figure size (r/R = 0.5, 1, 1.5), b Mnp, on DE for I=10 (A) size (r/R = 0.5, 1, 1.5), b Mnp, on DE for I=10 (A)
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Figure 12. Effect of; a three parameters; particle diameter (μm), inlet mass flow rate (L/min), tumor size (r/R = 0.5, Figure 12. Effect of; a three parameters; particle diameter (μm), inlet mass flow rate (L/min), tumor size (r/R = 1, 1.5), b Mnp, on DE for I=15(A) 0.5, 1, 1.5), b Mnp, on DE for I=15(A)
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Figure 13. Effect of; a three parameters; particle diameter (μm), inlet mass flow rate (L/min), tumor size (r/R = 0.5, Figure 13. Effect of; a three parameters; particle diameter (μm), inlet mass flow rate (L/min), tumor size (r/R = 0.5, 1, 1.5), b Mnp, on DE for I=20(A) 1, 1.5), b Mnp, on DE for I=20(A)
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Figure 14. Particle deposition pattern for I=20(A) and dp =9 (μm); a Q=7 (L/min), b Q=10 (L/min)
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Figure 15. intensity on particle deposition patterns and magnetic flux density for (T) for Q=12 Figure 15.Effect Effectofofcurrent current intensity on particle deposition patterns and magnetic field (T) strength (L/min), d =9 (μm);a I=10 (A), b I=15 (A), c I=20 (A) Q=12 (L/min), dp =9p(μm);a I=10 (A), b I=15 (A), c I=20 (A)
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Fluid boundary condition Inlet = constant mass flow rate Q= 7 (Lit/min) Q= 10(Lit/min) Q=12(Lit/min)
Particle boundary condition Inlet = Up=fluid velocity Outlet= freeze Wall= stick
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Table1. Boundary conditions and properties of particles, fluid, and tumor in this study
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Table 2. Overview of the parameters used in the 90° bent tube simulation for model validation
Numerical Simulation of Magnetic Drug Targeting to a Tumor in the Simplified Model of the Human Lung M. Sabz , R. Kamali , S. Ahmadizade PII: DOI: Reference:
S0169-2607(18)31604-3 https://doi.org/10.1016/j.cmpb.2019.02.001 COMM 4842
To appear in:
Computer Methods and Programs in Biomedicine
Received date: Revised date: Accepted date:
7 November 2018 30 January 2019 1 February 2019
Please cite this article as: M. Sabz , R. Kamali , S. Ahmadizade , Numerical Simulation of Magnetic Drug Targeting to a Tumor in the Simplified Model of the Human Lung, Computer Methods and Programs in Biomedicine (2019), doi: https://doi.org/10.1016/j.cmpb.2019.02.001
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Highlights The presence of magnetic field, increases DE on tumor surface greatly. The best positions for magnetic source are found under the bifurcations in this study. DE on tumors reduces by enhancement the mass flow rate for I= 10 (A) and I=15 (A)
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Numerical Simulation of Magnetic Drug Targeting to a Tumor in the Simplified Model of the Human Lung
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M. Sabz, R. Kamali*, S. Ahmadizade School of Mechanical Engineering, Shiraz University, Shiraz, Iran *Corresponding author: R. Kamali/ E-mail address: [email protected]
Abstract
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Background: Magnetic Drug Targeting improves effectiveness of medicine application and reduces its side effects. In this method, drugs with magnetic core are released in the lung and they are steered towards the tumor by applying an external magnetic field. A number of researchers utilized numerical methods to study particle deposition in the lung, but magnetic drug delivery to the tumors in the human lung has not been addressed yet. Method: In the present study, Weibel model is used for human airway geometry from generation G0 to G3. Moreover, a tumor is considered in the lung, which is located in G2. Particles are made of iron oxide magnetic cores and poly lactic coglycolic acid shells. Fluid flow is assumed laminar and particles are coupled with the fluid by one-way method. The magnetic field is produced by a coil with law current intensities instead of a wire with high current intensities. Influences of various parameters such as particle diameter, magnetic source position, current intensity, and inlet mass flow rate and tumor size on the deposition efficiency on the tumor surface are reported. Results: Results show that magnetic drug targeting enhances deposition efficiency on the tumor surface Furthermore, when the current intensity rises from 10 (A) to 20 (A), tumor enlarging, and increasing particle diameter, lead to deposition efficiency enhancement, but efficiency decreases by increasing mass flow rate. However, when current intensity is 20 (A), deposition efficiency decreases in two situations. The first situation is when mass flow rate is 7 (L/min) and particle diameter is 9 (μm), and the second one is in 10 (L/min) mass flow rate and 9 (μm) diameter. Conclusion: The results demonstrated that magnetic drug targeting is applicable and suitable for all tumors specially for small tumors(r/R=0.5 in this case) that efficiency increase from 0% in the absence of magnetic field to more than 2% in the presence of magnetic field. Keywords: Magnetic Drug Targeting (MDT), 3-D simulation, Airway model, Hemispherical tumor, Particle deposition, Non-uniform magnetic field
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1. Introduction
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To improve the accumulation of drugs in tumor, an external magnetic field acts as an external force, which steers particles and diffuses them near the tumor. Magnetic drug targeting has a wide range of advantages including[1]: 1) Less amount of drug is consumed. 2) The drug remains a longer time in the target site and the absorption rate of the drug increases. 3) The drug-induced mucous irritation is prevented. 4) Drug side effects are reduced. 5) The absorption of the drug into the healthy cells and tissues decreases. 6) Elimination of surgery. Numerical simulation is employed to model the transposition, the diffusion and the deposition of the micro-particles throughout the human lungs. Zhang et al. [2] simulated the measurable effects of a carinal tumor on 3-D airflow. Farkas et al. [3] reported the effects of local obstructions and blockage on airflow and aerosol deposition in central human airways. Their results confirmed that large particles had higher DE compared with nano-particles. Ally et al. [4] investigated an in-vitro model to study the feasibility of the deposition of the suspended particles in the air by using a magnetic field. The purpose of their research was utilizing this method in the treatment of lung cancer. Martin et al. [5] proposed a novel method based on using aspheric magnetic particles and uniform magnetic field in the process of magnetic drug delivery. They employed an experimental model (in-vitro) of pulmonary branches. They exerted magnetic torque to steer particles instead of a magnetic force. Kannan et al. used CFD to investigate particle deposition in the human lung. they validated their results by using computational Euler Lagrangian method [6]. In the other study, they used Wind-Kessel algorithm for an oral delivery. In this method, the particles exiting the system were assume reenter to system during exhalation, thereby giving an upper bound for the deposition in the truncated lung model [7]. Dames et al. [8] suggested that magnetic particles can be useful for drug delivery to localized lung disease. They showed that targeted drug delivery to the lung could be achieved by magnetic particles in combination of magnetic gradient field. Dahmani et al. [9] employed a dynamic magnetic field that was inactive during the inhalation and was active during the expiration process. They increased the amounts of deposited particles in target areas, located in the depth of the lung to treat lung cancer. Dahmani et al. [10] also generated a magnetic field with a variable current coil and observed that creating the electrical eddy currents causes undesirable changes in the magnetic field and increasing the temperature dramatically. To resolve this problem, a set of permanent magnets were used. Xie et al. [11] studied the particle deposition in the presence of wedge-shaped permanent magnets for an experimental model (in-vitro) and in depth of mice’s lung (in-vivo). Results were presented for different mass flow rates, concentration of particles, and the pipe’s diameter. Redman et al. [12] investigated deposition of aspheric particles in the presence of uniform magnetic field in rabbit’s lung. Xi et al. [13] used numerical simulation of magnetic drug delivery to the olfactory of the nasal cavity in the upper respiratory system of
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human. The flow regime was laminar and magnetic field was produced by permanent magnets. They presented an optimized model for magnetic drug delivery. Their results confirmed an increasing particle deposition in the olfactory area and reducing particle deposition in other parts of respiratory system. Pourmehran et al. [14] investigated the application of magnetic drug targeting in a realistic geometry of the human respiratory system. They reported the influence of particle diameter, magnetic source position, magnetic field strength, and inhalation condition on particle transport pattern and DE in a realistic model through generation G0 to G2. Moreover, Pourmehran et al. [15] studied the effect of previous variants on DE in a new model comprising oral cavity, larynx, pharynx and trachea along with six generation of the lung based on CT scan images. Kenjeres et al. [16] investigated the effect of magnetic field on drug delivery in an realistic geometry of human lung from the mouth inlet to the eighth generation of the human lung and the transitional RANS approach was used. This study confirmed that magnetic drug targeting technique is a good method for treatment of respiratory diseases. There are other numerical studies in magnetic drug targeting in the arteries and in the human respiratory system [17-21]. Magnetic particles are widely used in biomedical technology applications and cancer therapy [22-
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26], lung cancer therapy and pulmonary disease [27-32] and diagnostic imaging, biological sensing, drug, cell, and gene delivery and cell tracking[33] , cell manipulation [34] and biological applications [35]. In the present study, particle deposition in a human lung with a tumor is investigated numerically. The geometry of the lung consists of two different models; Mitsakou [36] model is utilized in the first part of the lung (from mouth inlet to G0), and Weibel [37] model is used for G0 to G3. Mitsakou et al. developed nonCFD-based model to calculate deposition of particles along the oral rout. This model is a simplified geometry based on conducting ducts from mouth to throat region. Particles with different sizes are used in this study (1-17 µm ) and a good agreement with the available experimental study obtained.
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The magnetic field is produced by a coil. Influences of various parameters such as particle diameter, magnetic source position, current intensity, inlet mass flow rate and tumor size on the DE on the tumor surface are reported.
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2. Material and methods In this study, investigating of magnetic field and fluid flow physics are prerequisites for particle depositions. Finite element and finite volume methods are appropriate methods for this study. COMSOL software which is based on finite element method is used for modeling and analyzing. In the first step, magnetic field physics is modeled in a stationary study and then in the second step, magnetic field gradient is calculated. In the third step fluid flow under the influence of magnetic field is studied in a time dependent study. in the last step, particle tracing is analyzed
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based on the results of previous physics in a time dependent study from t= 0 s to t= 1 s and 0.005 s for particle time step size. In order to pass information from one physics to next physics and the results of one physics affect another physics fully coupled method is used. Algebraic Multigrid Solver for fluid flow physics, FGMRES for magnetic field and GMRES solver for particle tracing are selected. Magnetic field gradient is calculated by a direct solver (MUMPS). Solid Works software is used to model the geometry. The first part of the lung (from mouth inlet to G0) is described by Mitsakou model and Weibel model is used for generation G0 to G3 (see figure 1). The density of materials, boundary conditions and other properties are represented in table 1. Constant mass flow rate in the inlet of mouth in the inhalation process (without exhalation) and zero partial pressure in the outlets of the geometry are assumed as boundary conditions. The pressure difference between the intake air and the output air from branches is negligible, so the zero pressure in outlet branches is acceptable. For all solid boundaries, no-slip condition is applied. Particles are released continuously from plane A (see figure 2), with random distribution and their velocity are determined by the air velocity at the same point. Total number of particles in this study is 10000 and particles diameter are changed from 3 to 9 (μm) and their density is assumed 3415 (Kg/m3). The interactions between particles are negligible, because volume fraction of particles is less than 0.1 %. Stick boundary condition is considered for particles that collide to the walls and freezing boundary condition for the outlets.
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In order to investigate MDT numerically, magnetic field, fluid flow, and particle transportation equations should be solved. These equations are described as follows:
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4. Results
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In order to verify the numerical method, results of magnetic particle targeting in a simplified artery are compared to the data that reported by Haverkort [45] and Cohesn stuart [40]. A schematic of the geometry is shown in figure 3, and boundary conditions, fluid properties, and particle properties are given in table 2. As illustrated in figure 4, airflow velocity profiles are compared in three deflection planes (0°, 45°, and 90°). Moreover, DE for these models are studied and results are compared in figure 5. According to these figures, the results of present numerical method have presented acceptable accuracy. Consequently, the independence of the results from grids should be investigated. In order to achieve to this purpose, four different grid numbers are tested in the selected geometry. The fluid velocity at a given point in figure 6a and particle deposition on the tumor are compared for these grids. Results confirm that less than 1% differences in velocity between 305420 and 421624 grids and less than 2% between 305420 and 521852 grids (see figure 6b) are existed. The results in figure 6c reveals less than 1% difference in particle deposition efficiency between 305420 and 421624 grids and also between 305420 and 521852 grids. Therefore, 305420 grid number is used in this study. 4.2. Particle Transport and Deposition
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Figures 7 and 8 show air velocity contours for Q=7 (L/min). According to these figures tumor plays a significant role in changing velocity field through the lung. Moreover, it produces nonsymmetry in the secondary velocity. Figure 9 represents the effects of three parameters; tumor size, mass flow rate, and particle diameter on DE without any magnetic field. According to this figure, DE rises by increasing the inhalation mass flow rate and particle diameter except for tumor with r/R=0.5 that DE is zero for all cases. In lower mass flow rates, particle deposition near the wall is greater, but the particle inertia is lower because of low particle velocity. In this case, the Stokes number (St) - the tendency of particles to attend to the flow lines - is also small. Therefore, particles do not have enough inertia to get out of their path, and only the deposition of particles near the wall dominant their deposition. Increasing particle diameter (or increasing St Number) causes enhancement of particle deposition. When mass flow rate grows, fluid flow turbulences increases, so particles tend to leave their paths and collide to the walls, which is lead to increment of the DE.
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In addition, according to the figure 9, by enlarging tumor size, contact surface with flow rate increases that is lead to DE enhancement. However, increasing tumor size causes decreasing flow rate and particle numbers through the tumor branch, so DE reduces for larger tumors and DE is in its highest point for tumor with r/R=1 in this study. In addition to tumors, external magnetic fields also affect particle DE. In the first place, the most efficient position for the coil is determined. Figure 10 shows the effect of distance between the magnetic source and tumor on DE when Q = 7 (L/min), I = 10 (A), dp = 9 (μm). Six different positions for magnetic source are considered to find the best position of the coil (z = 1, 2, 3, 4, 5, 6 cm relative to reference plane (z = 0 cm), see figure 2). Regarding to results, the maximum efficiency occurs in z = 2 cm. This position is exactly under the first bifurcation and the second pick is z = 5 cm. This position is also under the second bifurcation. Consequently, the best positions for coil is under the bifurcations. Moreover, minimum efficiency occurs in z = 6 cm. This position is accurately under the tumor; it seems reasonable because of more distance between the coil and bifurcations, large number of particles pass through the upper branches and do not reach to tumor. On the other hand, when the coil is close to bifurcations, magnetic field attracts particles to the lower branches and the chance of particle deposition on tumor surface would be increased. Figures 11a, 12a, 13a indicate the effects of three parameters; mass flow rates, particle diameters, tumor size in three different current intensities (10 (A), 15 (A), 20 (A)). These three figures report following results: 1) DE on tumors decrease by enhancement the mass flow rate for all particle diameters that causes increasing fluid velocity and magnetic field has less time to impress and attract particles and consequently the chance of particle deposition on tumor surface would be decreased. This result is totally different to result in previous section in the absence of magnetic field; owing to in the presence of magnetic field dominant force is magnetic force and the effect of drag force is much less. So in this section the effective of magnetic force on particle deposition is determinative.
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2) DE enhances for all three tumors by particle diameter growth for constant mass flow rate, because by increasing particle diameter, the magnetic force that is applied on the particles increases and more particles pass thorough tumor branch.
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3) Magnetic field causes more deposition on the larger tumor (r/R=1.5 in this study) which is mainly because by increasing tumor size, mass flow rate in tumor branch would be dropped and as mentioned above (number 1), DE rises. On the other hand, by growth in tumor size, there is more space for particle deposition by magnetic field. 4)DE enhances by increasing current intensity. According to figure 13a, by increasing current intensity from 15 (A) to 20 (A), DE decreases in two situations when particle diameter is 9 (μm), current intensity is 20 (A) and mass flow rates
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are 7 (L/min) and 10 (L/min). In these two cases, DE curve has been dropped so much in the range of tumor with r/R = 1.5. The low mass flow rate, large particles, and high magnetic field strength are the main results of such phenomena and particles deposit before reaching the tumor as shown in figure 14. Additionally, figure 15 depicts the effect of current intensity on particle deposition patterns and magnetic field strength (T) for mass flow rate Q = 12 (L/min). Figures 11b, 12b, and 13b depict the effect of Mnp number on DE in the mentioned currents. According to definition of Mnp and numerical data that were acquired in this study for each current intensity and also each size of tumor, a DE equation versus to Mnp were approximated. Based on these equations DE would be determined for every particle diameter and flow rate. So we could find the appropriate conditions to reach to the best efficiencies.
5. Discussion
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The inhalation of drug aerosols is used for the treatment of many lung diseases such as asthma, infection and lung cancers. Magnetic drug targeting can improve therapeutic efficiency and decrease unwanted side effects. Dames et al. [8] investigated target drug delivery to the mice’s lung by computer aid simulation and experimentally for the first time. Price et al.[32] evaluated in-vivo and in-vitro magnetic drug targeting of inhaled Nano in moicroparticles in a healthy mice. Pourmehran et al.[14, 15] studied magnetic drug targeting in the human lung and reported the effect of particle diameter, magnetic source position and magnetic field strength on deposition efficiency and magnetic field was produced by a high current intensity wire. Despite dramatic progress in magnetic drug delivery, magnetic drug targeting to the tumors in the branches of human lung has not been adequately achieved to date numerically. In the present study, a tumor with three different sizes is modeled in the generation G2 of the human lung and the effect of tumor size, magnetic field strength, particle diameter, mass flow rate and magnetic field position on the particle deposition efficiency on the tumor surface are investigated. A coil with low current intensities is used to produce magnetic field and appropriate position is acquired exactly under the first bifurcation for the coil. Our results proved that employing magnetic field is totally necessary to drug delivery to the lung tumors especially for smaller tumors that were not covered by drug in the absence of magnetic field in this study.
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Present study investigates magnetic drug targeting to a lung tumor. A coil is used to produce the required magnetic field and steer the particles to the tumor. The air flow is laminar, unsteady, incompressible, and Newtonian. Several conclusions may be drawn from this study: 1) In the absence of magnetic field, increasing the mass flow rate and particle diameter lead to DE enhancement on tumor surface and maximum efficiency is related to tumor with r/R = 1.
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2) DE increase with particle diameter growth and decreases with mass flow rate growth when current intensity changes from 10 (A) to 20(A). Also, increasing tumor size and current intensity lead to DE enhancement except for two situations (Q=7 (L/min), d = 9 (μm), I = 20 (A) and Q = 10 (L/min), d = 9 (μm), I = 20 (A)). 3) The presence of magnetic field, enhances DE on tumor surface greatly and using this method is an efficient way for drug delivery to small tumors because of their small surfaces. 4) The position of magnetic source plays an important role in drug targeting to the tumors. In this study, the best positions are found under the bifurcations. 5) According to Mnp results, maximum DE occurs in the range of 3 to 9 (μm) in particle diameter and 7 to 12 (L/min) in mass flow rate for tumors with r/R = 1 and r/R = 1.5. Maximum DE for tumor with r/R=1.5 is 5.8 and it occurs when Mnp = 80.58 for 15 (A) current intensity and the highest DE for tumor with r/R=1 is 4.86 when Mnp = 67.375 and current intensity is 20 (A). For tumor with r/R=0.5, the highest efficiency is not in these ranges, and Mnp should increase to 210 for 15 (A) current intensity and in these condition, the DE reaches 2.48. To increase Mnp, mass flow rate should be reduced from 7 (L/min) or particle diameter should be enhanced to more than 9 (μm). To maintain such conditions in the proper range and preserve the one-way assumption, it is necessary to change the flow rate and diameter simultaneously.
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The authors made no disclosures.
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Figure 1. Airway model from mouth inlet to G3; a schematic of the geometry of the mouth inlet to trachea from Mitsakou model and specifications, b schematic of the trachea G3 from Weibel model,inlet c the Figure 1. Airway model from mouth inlet to G3; a schematic of thetogeometry of the mouth to geometry trachea from specification of Weibel model Mitsakou model and specifications, b schematic of the trachea to G3 from Weibel model, c the geometry specification of Weibel model
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Figure 2. Figure 2. different different positions positions of of coil coil center center (green (green points points at at xx = = -24 -24 cm cm and and yy = = 00 cm cm and and zz = = 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 66 cm) cm) relative to reference plane (z = 0 cm) relative to reference plane (z = 0 cm)
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Figure 3. Figure 3. Schematic Schematic of of the the geometry geometry and and the the parameters parameters of of construction construction for for model model validation validation
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Figure 4. 4. Velocity plane, bb45? 45◦deflection deflectionplane, plane,c c90? 90◦deflection deflection plane Figure Velocitymagnitude magnitudeprofiles profilesin ina: a: aa 0◦ 0? deflection deflection plane, plane forfor model validation model validation
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Figure 5. DE as a function of the particle diameter for model validation
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Figure 6. a Test point A for grid independency test for Q=7 (L/min), I=10 (A), d p =9 ( m) , b velocity magnitude in point A, c DE on tumor surface with r/R=1.5
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Figure 7. Air8.velocity contours at plane 1 of geometry; a position of plane 1, b Axial and radial air velocity contours Figure Air velocity contours at plane 1 of geometry; a position of plane 1, b Axial and radial air velocity at plane 1 contours at plane 1
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Figure 8. Air8.velocity contours at plane 2 of 2geometry; a position of plane 2, b 2, Axial and radial air velocity contours Figure Air velocity contours at plane of geometry; a position of plane b Axial and radial air velocity at plane 2 contours at plane 2
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Figure 9. Effect of three parameters; particle diameter (μm), inlet mass flow rate (L/min), tumor size (r/R (r/R = = 0.5, 0.5, 1, 1, 1.5) 1.5) on on DE DE in in the the absence absence of of magnetic magnetic field field size
FigureFigure 10. Effect magnetic source source position (x = -24 y =cm, 0xm, = 1, 2, cm) DE on forDE Q=7(L/min), 10. of Effect of magnetic position (xcm, = -24 y =z0xm, z =3,1,4,2,5,3,6 4, 5, on 6 cm) for I=10 (A), and dp=9 (μm) Q=7(L/min), I=10 (A), and dp=9 (μm)
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Figure 11. 11. Effect Effect of; of; aa three three parameters; parameters; particle particle diameter diameter (μm), (μm), inlet inlet mass mass flow flow rate rate (L/min), (L/min), tumor tumor Figure size (r/R = 0.5, 1, 1.5), b Mnp, on DE for I=10 (A) size (r/R = 0.5, 1, 1.5), b Mnp, on DE for I=10 (A)
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Figure 12. Effect of; a three parameters; particle diameter (μm), inlet mass flow rate (L/min), tumor size (r/R = 0.5, Figure 12. Effect of; a three parameters; particle diameter (μm), inlet mass flow rate (L/min), tumor size (r/R = 1, 1.5), b Mnp, on DE for I=15(A) 0.5, 1, 1.5), b Mnp, on DE for I=15(A)
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Figure 13. Effect of; a three parameters; particle diameter (μm), inlet mass flow rate (L/min), tumor size (r/R = 0.5, Figure 13. Effect of; a three parameters; particle diameter (μm), inlet mass flow rate (L/min), tumor size (r/R = 0.5, 1, 1.5), b Mnp, on DE for I=20(A) 1, 1.5), b Mnp, on DE for I=20(A)
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Figure 14. Particle deposition pattern for I=20(A) and dp =9 (μm); a Q=7 (L/min), b Q=10 (L/min)
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Figure 15. intensity on particle deposition patterns and magnetic flux density for (T) for Q=12 Figure 15.Effect Effectofofcurrent current intensity on particle deposition patterns and magnetic field (T) strength (L/min), d =9 (μm);a I=10 (A), b I=15 (A), c I=20 (A) Q=12 (L/min), dp =9p(μm);a I=10 (A), b I=15 (A), c I=20 (A)
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Fluid boundary condition Inlet = constant mass flow rate Q= 7 (Lit/min) Q= 10(Lit/min) Q=12(Lit/min)
Particle boundary condition Inlet = Up=fluid velocity Outlet= freeze Wall= stick
Wall = no slip properties ρ (kg/m3) = 1.185 μ (Pa.s) = 1.82 ×10-5
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Table1. Boundary conditions and properties of particles, fluid, and tumor in this study
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Fluid properties Density Dynamic viscosity
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Particle properties Density Diameter St Electrical current
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Table 2. Overview of the parameters used in the 90° bent tube simulation for model validation