Design and Assessment of a Novel Biconical Human-Sized Alternating Magnetic Field Coil for MNP Hyperthermia Treatment of Deep-Seated Cancer

Simple Summary A novel human-sized alternating magnetic field (AMF) coil is researched, designed and evaluated using numerical methods to achieve magnetic nanoparticle hyperthermia therapy in deep-seated tumors while avoiding damage to normal tissues. This is achieved by utilizing a circular current’s electric and magnetic field spatial distributions. The studies are done for pancreatic cancer. Computational electromagnetic and temperature distributions are presented for a full-body, 3D human model. The results showed that the proposed human-sized coil could provide clinically relevant AMF to cancerous regions while causing negligible Joule heating to normal tissue, compared to commonly used AMF coils. Abstract Magnetic nanoparticle (MNP) hyperthermia therapy is a treatment technique that can be used alone or as an adjunct to radiation and/or chemotherapies for killing cancer cells. During treatment, MNPs absorb a part of electromagnetic field (EMF) energy and generate localized heat when subjected to an alternating magnetic field (AMF). The MNP-absorbed EMF energy, which is characterized by a specific absorption rate (SAR), is directly proportional to AMF frequency and the magnitude of transmitting currents in the coil. Furthermore, the AMF penetrates inside tissue and induces eddy currents in electrically conducting tissues, which are proportional to the electric field (J = σE). The eddy currents produce Joule heating ( = 0.5·σ·E2) in the normal tissue, the rate of energy transfer to the charge carriers from the applied electric fields. This Joule heating contains only the electric field because the magnetic field is always perpendicular to the velocity of the conduction charges, i.e., it does not produce work on moving charge. Like the SAR due to MNP, the electric field produced by the AMF coil is directly proportional to AMF frequency and the magnitude of transmitting currents in the coil. As a result, the Joule heating is directly proportional to the square of the frequency and transmitter current magnitude. Due to the fast decay of magnetic fields from an AMF coil over distance, MNP hyperthermia treatment of deep-seated tumors requires high-magnitude transmitting currents in the coil for clinically achievable MNP distributions in the tumor. This inevitably produces significant Joule heating in the normal tissue and becomes more complicated for a standard MNP hyperthermia approach for deep-seated tumors, such as pancreatic, prostate, liver, lung, ovarian, kidney, and colorectal cancers. This paper presents a novel human-sized AMF coil and MNP hyperthermia system design for safely and effectively treating deep-seated cancers. The proposed design utilizes the spatial distribution of electric and magnetic fields of circular coils. Namely, it first minimizes the SAR due to eddy currents in the normal tissue by moving the conductors away from the tissue (i.e., increasing coils’ radii), and second, it increases the magnetic field at the targeted area (z = 0) due to elevated coils (|z| > 0) by increasing the radius of the elevated coils (|z| > 0). This approach is a promising alternative aimed at overcoming the limitation of standard MNP hyperthermia for deep-seated cancers by taking advantage of the transmitter coil’s electric and magnetic field distributions in the human body for maximizing AMF in tumor regions and avoiding damage to normal tissue. The human-sized coil’s AMF, MNP activation, and eddy current distribution characteristics are investigated for safe and effective treatment of deep-seated tumors using numerical models. Namely, computational results such as AMF, Joule heating SAR, and temperature distributions are presented for a full-body, 3D human model. The SAR and temperature distributions clearly show that the proposed human-sized AMF coil can provide clinically relevant AMF to the region occupied by deep-seated cancers for the application of MNP hyperthermia therapy while causing less Joule heating in the normal tissues than commonly used AMF techniques.

Ivkov et al. [13] demonstrated the enhancement of radiation therapy for pancreatic cancer when combined with MNP hyperthermia.
In order to translate these results in mice to a clinical setting, a few major obstacles related to the physics of low-frequency electromagnetic field absorption must be overcome. The rise of local temperature is directly related to the magnitude of the AMF in the tumor, which decays rapidly (as 1/R 2 , where R is the distance from a coil to the tumor) from a coil. As a result, for deeper targets, one would need to increase the transmitter current in the coil to achieve therapeutic magnetic field strength within the tumor. However, high transmitter currents activate not only MNPs in cancerous tissues but also produce a high electric field, E, and eddy currents, J, within normal tissue that cause non-specific Joule heating (<J·E>) in the normal tissues [15,25,26]. This significantly limits the applicability of MNP hyperthermia for deep-seated tumors, such as oral melanoma, head-neck, pancreatic, prostate, etc., and imposes limitations on the product of magnetic flux density and frequency (B·f) for MNP hyperthermia treatment [19,[27][28][29][30]. The B·f limitations that clinical test subjects were able to withstand for more than one hour without major complications have been reported in four independent studies [27][28][29][30]; the limit varies from 562.5 mT·kHz to 6250 mT·kHz) [30]. One way to address this issue is to develop an MNP which produces high SAR at low AMF strength for generating therapeutic temperature within tumors. Another way is to redesign the AMF coil to provide the desired AMF at the tumor while decreasing the Joule heat in the normal tissues as compared to a standard coil setup. Recently, a Dartmouth group has developed flower-like MNPs which exhibit high SAR at low (<20 mT) AMF strength [31]. However, to achieve a therapeutic effect in deep-seated tumors, such as lung, pancreatic, prostate, colorectal esophagus, and liver, it is desirable to develop a new coil for delivering AMF to deep-seated tumors while minimizing undesirable eddy current heating in normal tissues.
This paper introduces a human-sized AMF coil for MNP hyperthermia. The proposed AMF system is a coil with multiple turns of varying radii forming a biconical shape. It takes advantage of the circular coils' electric and magnetic field spatial distributions to minimize eddy currents and maximize AMF at the tumor. The system provides 15 mT magnetic flux density at the tumor for the 133 Ampere alternating transmitter current at 100 kHz frequency, i.e., the B·f = 1500 mT·kHz is well below the upper limit, and keeping the Joule heating temperature below the acceptable level in the normal tissues. The numerical results are given for a full-body, 3D virtual human model to illustrate the applicability of the proposed human-sized coil to AMF application for deep-seated tumors. The SAR and temperature distributions are presented for different size pancreatic cancers and for different MNP distributions to show proof of principle for the new human-sized coil.

Materials and Methods
This section summarizes numerical methods and MNP that are used in this study. Namely, first, the virtual human (VF) model [32,33] is introduced to assess the applicability of MNPH for deep-seated tumors in humans. Then, the Dartmouth MNP is described, and finally, electric and magnetic field integral equations and bio-heat equations are presented for calculations of electromagnetic fields and temperature distributions inside a VF model subjected to an AMF field produced by a human-sized biconical coil.

Virtual Human Model
A virtual human model is used to assess the applicability of the proposed humansize, biconical AMF coil for deep-seated tumors. Specifically, computational studies are done for pancreatic cancer. The electric field, magnetic field, non-specific Joule heating SAR, and temperature distributions are calculated for a virtual family (VF) human model Christ et al. [33]. The VF models consist of four highly detailed anatomically correct wholebody models of an adult male, an adult female, and two children. Figure 1 shows a cross-section of a 2 mm resolution VF-Duke model. The model consists of up to 84 different tissues and organs. The models are reconstructed as three-dimensional computer-aided design (CAD) objects with high-fidelity anatomical detail. The electromagnetic fields and temperature distributions in the whole body are calculated when the human model is exposed to the AMF produced by the human-sized coil. All subsequent results are presented for the adult male in Figure 1, called Duke in the VF model [33]. The computational domain is divided into Nx · Ny · Nz voxels of size 2 mm × 2 mm × 2 mm, in total 43,538,880 voxels (Nx = 304, Ny = 154, Nz = 930). The tissue electromagnetic and thermal properties, summarized in Table 1, are extracted from a tissue database [34] and assigned to each voxel.  The model consists of up to 84 different tissues and organs. The models are reconstructed as three-dimensional computer-aided design (CAD) objects with high-fidelity anatomical detail. The electromagnetic fields and temperature distributions in the whole body are calculated when the human model is exposed to the AMF produced by the humansized coil. All subsequent results are presented for the adult male in Figure 1, called Duke in the VF model [33]. The computational domain is divided into Nx · Ny · Nz voxels of size 2 mm × 2 mm × 2 mm, in total 43,538,880 voxels (Nx = 304, Ny = 154, Nz = 930). The tissue electromagnetic and thermal properties, summarized in Table 1, are extracted from a tissue database [34] and assigned to each voxel.

Magnetic Nanoparticles
Although all subsequent studies are done for the Dartmouth gamma-Fe 2 O 3 MNP, the presented results are applicable to other types of MNP. Dartmouth MNP consists of 2-5 nm crystals in 20-40 nm flower-like aggregates with a mean size of 27 nm and a standard deviation of 5.2 nm. The hydrodynamic diameter has a mean of 110 nm and a standard deviation of 0.33 nm, and the saturation magnetization, remanence, and coercivity are 1.1 emu/g, 0.007 emu/g, and 30 µT (0.3 G), respectively. More detailed information about Dartmouth MNP's shape, size, magnetic properties, and heating mechanism can be found in our previously published manuscripts [31,35,36]. These studies have shown that these particles produce therapeutic levels of SAR at low AMF strength, which makes them advantageous for deep-seated tumor MNP hyperthermia cancer therapy, where high field strengths are not practical using an external coil. For these studies, we selected 15 mT, for which the particles have an SAR of~55 W/g Fe 2 O 3 at 100 kHz [31].

Alternating Electromagnetic Fields Calculations
The alternating electromagnetic (E and B) fields that are produced by the human-sized coil are modeled using the E electric and magnetic B flux density integral equations, as where in Equations (1) and (2) Ie −ikR R d is the magnetic vector potential, I is current in the coil, R = |r − r | is the distance between observation r and r source points, d the differential length tangential vector at the r source point, µ = µ r µ o , ε = ε r ε o , µ r and ε r are relative magnetic and electric permeabilities of the medium, respectively, µ o = 4π·10 −7 [H/m] and ε o = 1 /µ 0 c 2 [F/m] are vacuum magnetic permeability and electric permittivity, respectively, c is the speed of light in vacuum, i = √ −1 is the unit complex number, ω is circular frequency, and k is wave number in a medium. For simplicity, the coils are modeled as infinitesimally thin wires. The total AMF (B) at the center (n c = 0) of a biconical coil, Figure 2, carrying I current, can be calculated as in [37].  : is the radius of the nc = 0 coil's radius, and α is a ha flare angle between the upper and lower cones.

AMF Coil Design
The most used AMF coils for MNPH consist of a main coil (or pair of coils), whic provides a magnetic field, and/or magnetic core, which focuses the AMF over a region interest (ROI). There are two major issues associated with the design coils, such as, firs the coils should provide a desirable AMF field at the ROI with minimal magnetic fie distributions in the surrounding areas, and second, the generation of eddy current (i.e nonspecific Joule heat) in healthy tissues.
To overcome these issues, an optimal AMF coil geometry was researched using a integral equation solver, which provides the relationship between the current and the r sultant electromagnetic field (see Section 2.3). For simplicity, first, the electric and ma netic fields were analyzed for a single circular current coil, Figure 3. Figure 4A,B sho electric and magnetic field distributions on the R-θ plane when ϕ = 0 (i.e., y = 0) for th circular coil with a 35 cm radius carrying I = 1 [A] current, respectively. The calculate results show that the magnitude of the electric field decreases as the R-distance decrease In addition, the electric field peak moves inside the a = 35 cm radius coil when R-observ tion is less than a. The magnetic field exhibits a similar but opposite trend, Figure  Namely, the magnitude of the magnetic flux density increases as the R-observation poi Figure 2. Human-sized coil; The system has a biconical shape and contains 1 + N c,1 + N c,2 turns/coils. ∆h is the separation between two nearby coils, a n c = R min + ∆h (|n c |) tan(α) is the radius of the n c -th coil, where n c ∈ [−N c,2 : N c,1 ]. a o = R min is the radius of the n c = 0 coil's radius, and α is a half flare angle between the upper and lower cones.

AMF Coil Design
The most used AMF coils for MNPH consist of a main coil (or pair of coils), which provides a magnetic field, and/or magnetic core, which focuses the AMF over a region of interest (ROI). There are two major issues associated with the design coils, such as, first, the coils should provide a desirable AMF field at the ROI with minimal magnetic field distributions in the surrounding areas, and second, the generation of eddy current (i.e., nonspecific Joule heat) in healthy tissues.
To overcome these issues, an optimal AMF coil geometry was researched using an integral equation solver, which provides the relationship between the current and the resultant electromagnetic field (see Section 2.3). For simplicity, first, the electric and magnetic fields were analyzed for a single circular current coil, Figure 3. Figure 4A,B show electric and magnetic field distributions on the R-θ plane when φ = 0 (i.e., y = 0) for the circular coil with a 35 cm radius carrying I = 1 [A] current, respectively. The calculated results show that the magnitude of the electric field decreases as the R-distance decreases. In addition, the electric field peak moves inside the a = 35 cm radius coil when R-observation is less than a. The magnetic field exhibits a similar but opposite trend, Figure 4. Namely, the magnitude of the magnetic flux density increases as the R-observation point moves toward the center. Using these results, one could achieve the desirable magnetic flux density around the axis of a current-carrying coil with acceptable electric field values by varying the α angle (α = 90 − θ) and the R-observation distance. Based on these results, we have decided to design and investigate a biconical shape coil α = 60 • degree half flare angle. The results were evaluated against Helmholtz and solenoidal coils for achieving therapeutic 15 mT AMF at the pancreas. moves toward the center. Using these results, one could achieve the desirable magnetic flux density around the axis of a current-carrying coil with acceptable electric field values by varying the α angle (α = 90 − θ) and the R-observation distance. Based on these results, we have decided to design and investigate a biconical shape coil α = 60° degree half flare angle. The results were evaluated against Helmholtz and solenoidal coils for achieving therapeutic 15 mT AMF at the pancreas.    Table 2 shows that a single-turn Helmholtz coil will require an impractical ~10 kA current to achieve 15 mT AMF at the pancreas center. The same impractical current value was reported for a single-turn Helmholtz coil by Attaluri et al. in [38]. The comparisons between the 164-turn standard solenoid and biconical coils, operating at 100 kHz, illustrate that the latter coil produces the desirable 15 mT AMF at the pancreas center and the smallest 42 W/kg Joule heating SARJoule in the normal tissues using the realistic 133 A current. Furthermore, this 42 W/kg Joule heating SARJoule, at 100 kHz AMF and 15 mT magnetic field flux density at the pancreas center, for the proposed biconical coil is much smaller than the SARJoule = 248 W/kg and SARJoule = 758 W/kg deposed in a cylindrical shape 0.5 S/m conductive (typical muscle tissue conductivity) homogeneous tissue model placed in the Johns Hopkins University (JHU) Maxwell [38] and in the MagForce MFH300F [39] coils, respectively. The SARJoule = 248 W/kg and SARJoule = 758 W/kg are calculated using empirical and analytical expressions provided by Attaluri et al. supplement materials [38]. moves toward the center. Using these results, one could achieve the desirable magnetic flux density around the axis of a current-carrying coil with acceptable electric field values by varying the α angle (α = 90 − θ) and the R-observation distance. Based on these results, we have decided to design and investigate a biconical shape coil α = 60° degree half flare angle. The results were evaluated against Helmholtz and solenoidal coils for achieving therapeutic 15 mT AMF at the pancreas.    Table 2 shows that a single-turn Helmholtz coil will require an impractical ~10 kA current to achieve 15 mT AMF at the pancreas center. The same impractical current value was reported for a single-turn Helmholtz coil by Attaluri et al. in [38]. The comparisons between the 164-turn standard solenoid and biconical coils, operating at 100 kHz, illustrate that the latter coil produces the desirable 15 mT AMF at the pancreas center and the smallest 42 W/kg Joule heating SARJoule in the normal tissues using the realistic 133 A current. Furthermore, this 42 W/kg Joule heating SARJoule, at 100 kHz AMF and 15 mT magnetic field flux density at the pancreas center, for the proposed biconical coil is much smaller than the SARJoule = 248 W/kg and SARJoule = 758 W/kg deposed in a cylindrical shape 0.5 S/m conductive (typical muscle tissue conductivity) homogeneous tissue model placed in the Johns Hopkins University (JHU) Maxwell [38] and in the MagForce MFH300F [39] coils, respectively. The SARJoule = 248 W/kg and SARJoule = 758 W/kg are calculated using empirical and analytical expressions provided by Attaluri et al. supplement materials [38].  Table 2 shows that a single-turn Helmholtz coil will require an impractical~10 kA current to achieve 15 mT AMF at the pancreas center. The same impractical current value was reported for a single-turn Helmholtz coil by Attaluri et al. in [38]. The comparisons between the 164-turn standard solenoid and biconical coils, operating at 100 kHz, illustrate that the latter coil produces the desirable 15 mT AMF at the pancreas center and the smallest 42 W/kg Joule heating SAR Joule in the normal tissues using the realistic 133 A current. Furthermore, this 42 W/kg Joule heating SAR Joule , at 100 kHz AMF and 15 mT magnetic field flux density at the pancreas center, for the proposed biconical coil is much smaller than the SAR Joule = 248 W/kg and SAR Joule = 758 W/kg deposed in a cylindrical shape 0.5 S/m conductive (typical muscle tissue conductivity) homogeneous tissue model placed in the Johns Hopkins University (JHU) Maxwell [38] and in the MagForce MFH300F [39] coils, respectively. The SAR Joule = 248 W/kg and SAR Joule = 758 W/kg are calculated using empirical and analytical expressions provided by Attaluri et al. supplement materials [38].

Bio-Heat Equation
For describing the MNP and non-specific Joule heats transfer in the tissues, Penne's [40] equation is solved using the finite difference technique [29,41], where ρ (kg/m 3 ) is the tissue density, C (J/kg·K) is the heat capacity, k (W/(m·K)) is the thermal conductivity, T (K) is transient temperature, Q b (W/m 3 ), and Q m (W/m 3 ) are heat dissipation due to the blood flow and metabolic heat, respectively.
where ρ b and C b are blood density and blood heat capacity, T a ( • C) and T ( • C) are arterial blood and tissue temperature, respectively, and ω b (m 3 /s/kg) is the heat transfer rate in blood. These parameters are summarized in Table 1. In Equation (4), the term Q joule is non-specific Joule heat (<j·E> = 0.5σE 2 ) due to the E electric field in the σ conducting tissue, and Q mnp is heat produced by the MNP in the tumor when subjected to an external AMF. The thermophysical and electromagnetic properties of the tissue are extracted from a tissue database [34] and summarized in Table 1. In all subsequent calculations, the convection boundary conditions are set between skin-air surface with the convection coefficient = 10 W/m 2 .

Results
In this section, we present electromagnetic fields, SAR, and temperature simulation results for the VF Duke model. All subsequent calculations are done for pancreatic cancer. First, AMF and Joule heating SAR Joule distributions are illustrated for the high (2 mm) resolution Duke model subjected to alternating electromagnetic (AEMF) produced by a single-turn Helmholtz coil. Then the temperature and Joule heating SAR Joule distributions are presented for the same VF-Duke model placed in AEMF generated by the novel biconical coil. Finally, the applicability of the combined human-sized biconical coil and MNPH is assessed for the treatment of deep-seated tumors.

Analysis of the Limitations of the Standard Approach
To illustrate the limitations of the standard approach for deep-seated tumors, we conducted numerical calculations of AMF distributions inside the 2 mm-resolution VF Duke model (Figure 1) at 100 kHz. The AEMFs are produced by 60 cm diameter Helmholtz coils in three configurations. In the first configuration Figure 5A), coils are placed front (centered at x = 28.6 cm, y = 47.2 cm, z = 123.6 cm) and back (centered at x = 28.6 cm, y = −13.8 cm, z = 123.6 cm), and in the second configuration Figure 5B), coils are placed left (centered at x = −1.4 cm, y = 17.2 cm, z = 123.6 cm) and back (centered at x = 58.6 cm, y = 17.2 cm, z = 123.6 cm). The coils centers are aligned to the pancreas center (x = 28.6 cm, y = 17.2 cm, z = 123.6 cm). Studies in [31] showed that for achieving therapeutic levels of heating at the pancreas, the Dartmouth MNPs, which provide high SAR due to MNP at low AMF strength [31], would require at least 15 mT. Figure 6 shows the Joule heating SAR Joule distributions inside the VF Duke model. The 10K ampere currents are required in the single-turn coils to achieve the required 15 mT magnetic field at the pancreas' center. The maximum SAR Joule = 22.5 KW/kg is observed in spinal cerebrospinal fluid. This high SAR Joule resulted in a temperature rise of 100-s • C in the normal tissues in less than 1 min. Similar results were observed for the Helmholtz coil placed symmetrically to the x-axis ((A) and (B), see Figure 5) and z-axis. = 17.2 cm, z = 123.6 cm). The coils centers are aligned to the pancreas center (x = 28.6 cm, y = 17.2 cm, z = 123.6 cm). Studies in [31] showed that for achieving therapeutic levels of heating at the pancreas, the Dartmouth MNPs, which provide high SAR due to MNP at low AMF strength [31], would require at least 15 mT. Figure 6 shows the Joule heating SARJoule distributions inside the VF Duke model. The 10K ampere currents are required in the single-turn coils to achieve the required 15 mT magnetic field at the pancreas' center. The maximum SARJoule = 22.5 KW/kg is observed in spinal cerebrospinal fluid. This high SARJoule resulted in a temperature rise of 100-s °C in the normal tissues in less than 1 min. Similar results were observed for the Helmholtz coil placed symmetrically to the x-axis ((A) and (B), see Figure 5) and z-axis.  Overall, these simulations clearly show that the standard approaches, which use single (or multi closely spaced) turn coils, are not applicable for deep-seated tumors, and an alternative approach that can supply sufficient field strength at the tumor with tolerable eddy current heating is needed.

Human-Sized Biconical Coil: SARJoule and Temperature Distributions
A series of electromagnetic and bio-heat-temperature calculations were conducted for human-sized biconical-shaped coils using the electromagnetic volume integral and bio-heat equations solvers developed by our group and validated against experimental Overall, these simulations clearly show that the standard approaches, which use single (or multi closely spaced) turn coils, are not applicable for deep-seated tumors, and an alternative approach that can supply sufficient field strength at the tumor with tolerable eddy current heating is needed.

Human-Sized Biconical Coil: SAR Joule and Temperature Distributions
A series of electromagnetic and bio-heat-temperature calculations were conducted for human-sized biconical-shaped coils using the electromagnetic volume integral and bio-heat equations solvers developed by our group and validated against experimental and analytical data [29,31,41]. Here, the main goal was to determine the human coil's optimal size and number of turns that will provide at least a 15 mT magnetic field at the pancreas for achieving therapeutic levels of MNP heating in the tumor while minimizing the Joule heating in the normal tissue. The simulations were done for the human-sized coil at 100 kHz frequency. Attention was given to temperature and SAR Joule distributions in and around the spine and the brain for two reasons. First, the spinal cord contains the most electrically conductive human tissue in the body and lacks significant temperature regulation, see Table 1. Second, although the brain has better temperature regulation but is highly sensitive to temperature elevation, it is reported that at temperatures between 42 and 43 • C, neurons can be damaged permanently [42]. After a series of calculations, the human-sized biconical coil that provides the desired AMF and SAR Joule distributions was determined to be a double-layer biconical coil, with the inner and outer layers radius of R min = 35 cm and R min = 37.5 cm, respectively. The separation between nearby coils was set to be ∆h = 2.5 cm, and the half flare angle α = 60 • ; between upper and low cones was determined to be α = 60 • for both coils. The number of turns was chosen to be N c,1 = 30; N c,2 = 51. Note that the ∆h = 2.5 cm is chosen to use for constructing a realistic size current carrying tube.
The steady-state temperature was calculated for the VF Duke model by dividing the entire computation volume into Nx · Ny · Nz = 43,538,880 voxels of size 2 mm × 2 mm × 2 (Nx = 304, Ny = 154, Nz = 930). We assumed that the VF Duke model was placed at room temperature, 22 • C. The simulations were run for 8 h to reach steady-state conditions to establish the baseline. The steady-state was then used as an initial temperature distribution to calculate the induced temperature due to Joule heating and MNP heading. Figure 7 shows the Joule heating, SAR Joule , distribution on a plane containing the maximum SAR Joule . As expected, the maximum SAR Joule is in the cerebrospinal fluid within the spine. Figure 7 shows the temperature distribution after 20 min in the same plane containing the maximum SAR Joule . The result shows that although the maximum SAR Joule is within the cerebrospinal fluid, the maximum temperature after 20 min is registered in arms, which are close to the coils. The temperature distribution after 20 min on the plane with maximum temperature due to the Joule heating, SAR Joule , is depicted in Figure 8. temperature, 22 °C. The simulations were run for 8 h to reach steady-state condition establish the baseline. The steady-state was then used as an initial temperature distri tion to calculate the induced temperature due to Joule heating and MNP heading. Fig  7 shows the Joule heating, SARJoule, distribution on a plane containing the maxim SARJoule. As expected, the maximum SARJoule is in the cerebrospinal fluid within the sp Figure 7 shows the temperature distribution after 20 min in the same plane containing maximum SARJoule. The result shows that although the maximum SARJoule is within cerebrospinal fluid, the maximum temperature after 20 min is registered in arms, wh are close to the coils. The temperature distribution after 20 min on the plane with ma mum temperature due to the Joule heating, SARJoule, is depicted in Figure 8.    The maximum induced Joule heating temperature reaches about 41.7 °C in the s der regions, which are close again to the coils. Although the temperature elevation i arms and shoulders is below 42 °C, one could utilize other techniques, such as repos ing the patient's arms or using surface cooling pads to further manage this tempera The maximum induced Joule heating temperature reaches about 41.7 • C in the shoulder regions, which are close again to the coils. Although the temperature elevation in the arms and shoulders is below 42 • C, one could utilize other techniques, such as repositioning the patient's arms or using surface cooling pads to further manage this temperature.
Furthermore, we calculated and analyzed the steady state and the Joule heat-induced temperature in the brain. The calculated temperatures are depicted in Figures 9 and 10 in the plane with the maximum T due to the Joule heating, SAR Joule . The studies illustrate that a maximum temperature rise (see Figures 9 and 10) is less than 1 • C in the brain after 20 min MNPH treatment. This is significantly below 42 • C, the acceptable maximum brain temperature for avoiding permanent damage to neurons [42].
Cancers 2023, 15, x FOR PEER REVIEW 13 Furthermore, we calculated and analyzed the steady state and the Joule heat-indu temperature in the brain. The calculated temperatures are depicted in Figures 9 and 1 the plane with the maximum T due to the Joule heating, SARJoule. The studies illust that a maximum temperature rise (see Figures 9 and 10) is less than 1 °C in the brain a 20 min MNPH treatment. This is significantly below 42 °C, the acceptable maximum b temperature for avoiding permanent damage to neurons [42].

Human-Sized Coil: Assessing MNPH Efficacy and Temperature Distributions
Finally, results are given to demonstrate the applicability of the human-sized coil MNPH therapy. Although all subsequent calculations are done for the flowerlike D mouth MNP with a concentration of 63.5 mgFe2O3/mL in 1 mL water, these results applicable to other types of MNPs as well. We assume that Dartmouth MNP is delive in the tumor via local injection and activated with the human-sized biconical AEMF Figure 10. 2D Temperature distribution after 20 min in the brain in the plane with maximum T due to the Joule heating, SARJoule.

Human-Sized Coil: Assessing MNPH Efficacy and Temperature Distributions
Finally, results are given to demonstrate the applicability of the human-sized coil for MNPH therapy. Although all subsequent calculations are done for the flowerlike Dartmouth MNP with a concentration of 63.5 mgFe 2 O 3 /mL in 1 mL water, these results are applicable to other types of MNPs as well. We assume that Dartmouth MNP is delivered in the tumor via local injection and activated with the human-sized biconical AEMF coil operating at a frequency of 100 kHz and providing a 15 mT magnetic field at the tumor. The SAR mnp = 55 W/g Fe 2 O 3 due to MNP was estimated from [31]. Three 1 cm 3 , 2 cm 3 , and 3 cm 3 size tumors are considered. Tumors are modeled as a rectangular parallelepiped. Studies are demonstrated for each size tumor receiving the equivalent of three 3 µL MNP per gram tumor, 5 µL MNP per gram tumor, and 10 µL MNP per gram tumor dose. Figure 11 shows the cross-section of the xy plane at the z = 123.6 slice containing the 1 cm 3 cubic shape tumor (black).  Figure  11 shows the cross-section of the xy plane at the z = 123.6 slice containing the 1 cm 3 cubic shape tumor (black). The 2 cm 3 tumor was modeled by adding 1 cm 3 volume to the 1 cm 3 cubic tumor (Figure 11), and the 3 cm 3 was modeled by adding 1 cm 3 volume above the 2 cm 3 tumor model along the z-axis. We assumed that the modeled tumors and healthy pancreases have the same mass density and thermal properties, see Table 1. Figures 12 and 13 show The 2 cm 3 tumor was modeled by adding 1 cm 3 volume to the 1 cm 3 cubic tumor (Figure 11), and the 3 cm 3 was modeled by adding 1 cm 3 volume above the 2 cm 3 tumor model along the z-axis. We assumed that the modeled tumors and healthy pancreases have the same mass density and thermal properties, see Table 1. Figures 12 and 13 show the calculated temperature versus distance for 1 cm 3 , 2 cm 3 and 3 cm 3 size pancreatic tumors before (steady state) and during MNPH treatment at times t = 1 min, 5 min, 10 min, and 20 min. The MNPH-induced temperature distributions are calculated for the human size biconical coil running 100 kHz and 134 A alternating current and producing a 15 mT field at the pancreas. Figure 12A,B and Figure 13A-D correspond to temperature distributions at different times for 1 µL, 3 µL and 5 µL Dartmouth MNP concentration per gram tumor, respectively. The results show that MNPH-induced temperature is localized in the area containing MNP and rises above the steady-state temperature and Joule heating-induced temperature levels in the normal tissues. Even though the MNPH-induced temperatures do not exceed 42 • C to achieve tumor cell apoptosis, the predicated temperature change could be used for localized drug release and mild hyperthermia.

Discussion
A new human-sized biconical shape coil in combination with Dartmouth magne nanoparticles (MNPs) is presented and assessed as a viable approach for deep-seated ca cer treatment. Numerical results using a 3D electromagnetic and bio-heat equations solv for a high-resolution virtual human model (VF Duke model) indicate that this approa can effectively produce therapeutic temperatures in pancreatic tumors while minimizi temperature rises in healthy tissues. This is achieved by taking advantage of the circu coil's electric and magnetic fields' spatial distributions. Namely, on the one hand, it m imizes magnitudes of the induced eddy currents in healthy tissues by increasing the co radii, and on the other hand, it increases the AMF due to nearby coils (|z| > 0) at targeted area (z = 0) by increasing off (|z| > 0) coils' radii gradually. Overall, this decrea the electric field and non-specific Joule heating in the human body while maintainin consistent magnetic field at the targeted area of the pancreas. As a result, our calculatio show that the proposed new human-sized biconical produces much smaller eddy curr SAR-s in healthy tissues than the Johns Hopkins University (JHU) Maxwell [38]

Discussion
A new human-sized biconical shape coil in combination with Dartmouth magnetic nanoparticles (MNPs) is presented and assessed as a viable approach for deep-seated cancer treatment. Numerical results using a 3D electromagnetic and bio-heat equations solver for a high-resolution virtual human model (VF Duke model) indicate that this approach can effectively produce therapeutic temperatures in pancreatic tumors while minimizing temperature rises in healthy tissues. This is achieved by taking advantage of the circular coil's electric and magnetic fields' spatial distributions. Namely, on the one hand, it minimizes magnitudes of the induced eddy currents in healthy tissues by increasing the coils' radii, and on the other hand, it increases the AMF due to nearby coils (|z| > 0) at the targeted area (z = 0) by increasing off (|z| > 0) coils' radii gradually. Overall, this decreases the electric field and non-specific Joule heating in the human body while maintaining a consistent magnetic field at the targeted area of the pancreas. As a result, our calculations show that the proposed new human-sized biconical produces much smaller eddy current SAR-s in healthy tissues than the Johns Hopkins University (JHU) Maxwell [38] and in the MagForce MFH300F [39] coils.
One way to realize a biconical coil is to build an LC resonant circuit using the biconical coil and a matching capacitor. At the resonant frequency f = 1/ 2π √ LC , the reactance of the inductor and the capacitor cancel each other out in the LC circuit, allowing the maximum current flow through the circuit. Constructing an LC circuit at the resonant f = 100 kHz frequency using the biconical coil requires a matching C capacitor with the desired capacitance value. To determine the capacitance, we modeled the human-sized biconical coil, Figure 17, connected to a capacitor and power source in series using the full 3D Maxwell equation solver software package called EMCoS studio [43]. After performing a set of calculations, the required capacitance value for the resonant f = 100 kHz frequency LC circuit was determined to be C = 0.625 nF. Figure 18 shows the calculated impedance (Ohm), current (A), and power(W) versus Frequency for the biconical coil connected to the external V = 312.5 V voltage source and C = 0.625 nF capacitor in series. These results show that the human-sized biconical coil can generate a desirable 133 A current and deliver 25 kW of power at a 100 kHz frequency. Figure 18. Impedance, current, and power vs. frequency for a biconical coil.
Ultimately, the greatest limitation of this technique will likely be the MNP biodistributions in non-cancerous tissues. Such as Prijic et al. [44] have reported that the majority of the intravenously injected, systemically delivered MNP is accumulated in the liver, spleen, and kidneys. Since these vital organs are close to the pancreas, they will be placed in the alternating magnetic field. Consequently, MNPs will produce undesirable heat in After performing a set of calculations, the required capacitance value for the resonant f = 100 kHz frequency LC circuit was determined to be C = 0.625 nF. Figure 18 shows the calculated impedance (Ohm), current (A), and power(W) versus Frequency for the biconical coil connected to the external V = 312.5 V voltage source and C = 0.625 nF capacitor in series. These results show that the human-sized biconical coil can generate a desirable 133 A current and deliver 25 kW of power at a 100 kHz frequency. After performing a set of calculations, the required capacitance value for the resonant f = 100 kHz frequency LC circuit was determined to be C = 0.625 nF. Figure 18 shows the calculated impedance (Ohm), current (A), and power(W) versus Frequency for the biconical coil connected to the external V = 312.5 V voltage source and C = 0.625 nF capacitor in series. These results show that the human-sized biconical coil can generate a desirable 133 A current and deliver 25 kW of power at a 100 kHz frequency. Figure 18. Impedance, current, and power vs. frequency for a biconical coil.
Ultimately, the greatest limitation of this technique will likely be the MNP biodistributions in non-cancerous tissues. Such as Prijic et al. [44] have reported that the majority of the intravenously injected, systemically delivered MNP is accumulated in the liver, spleen, and kidneys. Since these vital organs are close to the pancreas, they will be placed in the alternating magnetic field. Consequently, MNPs will produce undesirable heat in the liver, spleen, and kidneys. This lack of specificity of AMF distribution can limit treat- Ultimately, the greatest limitation of this technique will likely be the MNP biodistributions in non-cancerous tissues. Such as Prijic et al. [44] have reported that the majority of the intravenously injected, systemically delivered MNP is accumulated in the liver, spleen, and kidneys. Since these vital organs are close to the pancreas, they will be placed in the alternating magnetic field. Consequently, MNPs will produce undesirable heat in the liver, spleen, and kidneys. This lack of specificity of AMF distribution can limit treatment efficacy by limiting the maximum safe applied field strength, thus limiting MNP heating of the pancreatic tumor. One of the ways to overcome this limitation is to place a passive ferrite material, such as a low SAR ferrofluid or flexible ferrite material, next to the targeted tumor to focus and/or direct the alternating magnetic field. In addition, the proposed human-sized coil was not optimized for systemically delivered MNP; hence, these results warrant further study of human-sized coil design in combination with a magnetic field focusing and targeting approach when applied to specific deep-seated tumors with complex tissue geometry.

Conclusions
The novel biconical human-sized coil delivers the desirable 15 mT AMF at pancreatic cancer at a smaller alternating current (~133 A) than the Helmholtz (~10 KA current) and solenoidal (156 A) coils. The coil induces minimum non-specific Joule heating of the normal tissues and achieves the therapeutic temperature (>42 • C) level in tumors containing 10 µL Dartmouth MNPs per gram tumor concentration by utilizing the circular coil's electric and magnetic fields spatial distributions. It improves upon the performance of a simple Helmholtz, JHU Maxwell and the MagForce MFH300F by providing clinically acceptable non-specific temperature distributions in the human body while creating the desirable AMF at the target area. Overall, the presented numerical results illustrate an innovative way to deliver AMF and activate MNPs at a previously unachievable distance with clinically viable levels of Joule heating, potentially opening new opportunities to extend the use of MNPH to deep-seated cancers. As a next step before bringing the system into clinical settings, we plan to build a prototype system and conduct MNPH studies on large animals. Institutional Review Board Statement: The numerical study was conducted using a virtual family model.

Informed Consent Statement: Not applicable.
Data Availability Statement: The data supporting this study's findings are available on request from the corresponding author.