Minimally required heat doses for various tumour sizes in induction heating cancer therapy determined by computer simulation using experimental data

Abstract

Purpose: Although induction heating cancer therapy (IHCT) using magnetic nanoparticles can be a promising approach to treatment-less multi-nodular cancers, the objective requirement for successful clinical application has not clearly been elucidated. We intended to define objective heat doses suitable for IHCT, especially focusing on the sizes of liver cancer nodules.

Materials and methods: Alternating magnetic fields were applied to three human pancreatic cancer cell lines, the intercellular space of those cell pellets were filled with magnetic nanoparticles, and confirmed the cytotoxic effect of IHCT. Subsequently, the temperatures of liver cancer nodules in IHCT were simulated using a computer software program and the required heat dose for various sized tumours were determined.

Results: Heating the cancer cells up to 50°C for 10 min was sufficient for complete cell killing and the heat dose of 1.7 W/g_tumour is required for 10 mm tumour. Larger tumours require a smaller heat dose, e.g. 20 mm and 40 mm tumours require 0.7 W/g_tumour and 0.6 W/g_tumour, respectively, whereas smaller tumours require large amounts of heat, e.g. 5 mm and 1 mm tumours require 5.1 W/g_tumour and 105 W/g_tumour, respectively.

Conclusions: Integrating the presently available technologies, including high-quality magnetic nanoparticles (1000 W/g_material) and effective drug delivery systems (1–2 mg_material/g_tumour), treatment of a 10 mm tumour seems possible. Since treatment of smaller tumours less than 5 mm require substantial heat dose, researchers involved in IHCT should target cancer nodules of 10 mm or more, and develop a heat delivery system providing a minimum of 1.7 W/g_tumour.

• induction heating cancer therapy (IHCT)
• magnetic nanoparticle
• liver metastasis
• pancreatic cancer
• specific absorption rate (SAR)

Introduction

Multiple liver metastases, especially those from notorious pancreatic cancer, have been awaiting an advent of new treatment strategies [1–3]. Thermal ablation, which involves heating the target cancer nodules to more than 46°C that results in irreversible cellular damage known as necrosis [4], has been developed as one of the less invasive cancer treatment strategies [5]. In order to deliver heat to cancer nodules, piercing needles wired to radiofrequency [6] and microwave [7] systems are widely used, mainly for liver tumours [6]. Due to the technical difficulties of needle puncture [8], [9], however, this approach is not suitable in the case of patients with advanced-stage cancers, including multiple and/or micro-disseminated lesions. In order to overcome these limitations, the development of induction heating using magnetic nanoparticles has recently attracted attention [10–12]. Magnetic nanoparticles selectively distributed to the cancer nodules generate heat when an external alternating magnetic field (AMF) is applied [12]. This induction heating cancer therapy (IHCT), however, has not been clinically employed, probably because the exact goals have not been clearly defined.

In the clinical setting the temperature of target cancer nodules is determined by the balance between the amount of applied heat dose (W/g_tumour) and heat loss to the surrounding tissue [13]. The reason for past incomplete IHCT development may be explained mainly by the insufficient administered heat dose against heat loss, resulting in the entire target cancer tumours not being heated up to tissue lethal temperature. The heat dose administered in IHCT takes into account two factors: the heating power of magnetic material (W/g_material) that is represented by the specific absorption rate (SAR) [10], and the amount of magnetic nanoparticles accumulated in the cancer nodule, which is represented by the weight of particles per unit weight of target tumour tissue (g_material/g_tumour). The main issue that we have to address should be to set the objective heat dose values which overcome the amount of heat loss.

Heat loss is basically mediated by static thermal diffusion, however, the cooling effect of blood flow should also be taken into consideration in a clinical setting [14–16]. It is true that the presence of blood flow acts as a heat radiator and disrupts heating the cancer nodules, we eliminate blood flow issue from our estimation since this obstacle may be overcome by employing a surgical technique known as Pringle's manoeuvre [17] which temporally occludes hepatic vascular inflow. The efficacy of Pringle's manoeuvre in reducing heat loss has been clinically shown in radio-frequency ablation treatment [18], [19]. We therefore focused only on static thermal diffusion loss to surrounding tissues as a heat loss factor. Since the size of liver tumours are known to vary in the clinical field, physical condition required for IHCT should be different according to the tumour sizes.

We addressed here the principal question of how much heat dose is required for successful IHCT in liver metastases of various sizes. The lethal temperatures of three human pancreatic cancer cell lines of different heat sensitivity were experimentally defined using magnetic nanoparticles and a previously developed AMF generator [20]. We then calculated the heat doses required for IHCT, especially focusing on the sizes of liver cancer nodules, by employing a computer-controlled heat simulator. Possibilities of achieving the estimated heat dose by integrating presently available technologies are discussed.

Materials and methods

AMF generator

An AMF was generated by using a portable induction heating device developed at Kanazawa University, Japan [20]. The maximum strength of the AMF is 150 Oe (15 mT) with a frequency of 114 kHz.

Magnetic nanoparticles

Ferucarbotran particles (Resovist®; Bayer Schering Pharma, Berlin) have been used as magnetic nanoparticles [21]. The concentration of Resovist® is 27.9 mg Fe/mL or 0.5 mol Fe/L or 40 mg γ-Fe₂O₃/mL. In this study, we used a double-concentrated ferucarbotran (80 mg γ-Fe₂O₃/mL) solution that was provided by Meito Sangyo (Aichi, Japan), who is the supplier of ferucarbotran to Bayer Schering Pharma.

Mammalian cancer cell lines

We used three human pancreatic cancer cell lines (SUIT-2, BxPC-3, and AsPC-1) as representative of the pancreatic cancer that causes typical experimental liver metastasis [22]. The SUIT-2 cells were generously provided by Dr. Takeshi Iwamura (Miyazaki Medical College, Miyazaki, Japan) [23]. The BxPC-3 and AsPC-1 cell lines were obtained from the American Type Culture Collection (Bethesda, MD).

Measurement of heating potential of ferucarbotran represented by SAR

The heating potential of each material is physically represented by SAR and is calculated using the following equation:where C is the specific heat capacity of the sample (J/g/°C) and ΔT (°C)/Δt (s) is the initial 30 s slope of the temperature versus time curve [10]. The specific heat capacity is unique for each material, for example, C_water = 4.185 J/g/°C and C_{ferucarbotran} =3.64 J/g/°C. Vs is the sample volume and m is the mass of iron oxide. Since the value of ΔTemp/Δtime of the ferucarbotran solution at 150 Oe, 114 kHz was 0.71°C/s, SAR value of the ferucarbotran was calculated as 32.3 W/g_material.

Induction heating of cell pellet with intercellular spaces filled with ferucarbotran

Considering the in vivo features of cancer nodules with distributed magnetic nanoparticles, we employed an in vitro tumour model of a cell pellet whose intercellular spaces were filled with five different concentrations of ferucarbotran. A total of 20 µL cell suspension containing 5 × 10⁶ cells and 70 µL of five different concentrations of ferucarbotran (20, 27, 40, 60, and 80 mg γ-Fe₂O₃/mL) were mixed and centrifuged to form a cell pellet. The temperature of the cell pellets and irradiated AMF, was monitored with an optical fibre thermo sensor (FL-100, Anritsu Meter, Tokyo, Japan). The mean temperature of three independent experiments attained after 300 s of exposure to the magnetic field was defined as the equilibrium temperature.

Heat doses administered to heat a cell pellet in vitro to various equilibrium temperatures

In order to determine the actual heat doses administered to the in vitro tumour model we measured the amount of γ-Fe₂O₃ by our original method [24]. Briefly, since the magnetic moment of γ-Fe₂O₃ per unit is constant (0.49/mg emu), the amount of γ-Fe₂O₃ surrounding intercellular space can be measured by detecting the magnetic moment by using a superconducting quantum interference device (SQUID) magnetometer. The values of the magnetic moments of γ-Fe₂O₃ were substituted into the following equation:

Cytotoxic effect of heat at different temperatures, generated by induction heating

We confirmed the cytotoxic effect of induction heating by using ferucarbotran; an AMF (100–150 Oe, 114 kHz) was applied to cell pellets from three different cell lines (SUIT-2, BxPC-3, and AsPC-1). Cell pellets were heated up to the target temperatures (39°C, 42°C, 46°C, 48°C, 51°C, and 60–65°C) and maintained at each temperature for 10 min. Each heated cell was plated in a 60-mm cell culture dish at the concentration of 1 × 10⁵ cells/dish and cultured for 7 days. The control growth curve was determined by using the ferucarbotran-containing cells that were not subjected to an AMF. Viable cells, determined by the trypan blue dye exclusion method, were counted on days 1, 3, and 7. The data values and bars represent the mean and SD of three independent experiments.

Computer simulations of tempo-spatial change in temperature

All the simulations were performed using a finite element method software program, COMSOL Multiphysics ver. 3.5 (COMSOL; Burlington, MA). The density, thermal conductivity and specific heat at constant pressure of the magnetic particles were assumed to be equal to those of magnetite at 37°C and constant in spite of changes in temperature. Those for cells and dextran were assumed to be equal to those of pure water, since almost all contents of cells are water and dextran is highly hydrated in water. All calculations were executed under the assumption that the magnetic particles were distributed homogeneously in a tumour and cell pellet. The density, thermal conductivity and specific heat at constant pressure of the tumour and pellet containing the magnetic particles were calculated assuming that the values were ‘additive’ of those of water and magnetite at 37°C. Though those temperature dependent properties of water are known to show relatively small diversity at the heat range of 30°C to 70°C, internal database of COMSOL enables provision of much precise simulation for a tumour and cell pellet without magnetic particles by automatically adapting appropriate values at each target temperature.

The tempo-spatial change in temperature in cell pellets and a human liver containing a tumour with magnetic particles was calculated with COMSOL. The governing equation is as follows.where ρ is the density (kg/m³), C_p the molar specific heat at constant pressure (J/kg/°C), T the temperature (°C), t the time (s), κ the thermal conductivity (W/m/°C), Q the heat generation rate (W/m³), and ∇ means Laplacian.

A mesh consisting of triangular elements was generated automatically and optimally by COMSOL at a resolution as fine as was permitted by the computer's memory (approximately 16 GB). For every calculation we confirmed that there was less than 5% difference in the obtained value between the result obtained with the finest mesh and that with a one-step coarser mesh. The UMFPACK direct solver and adequate conditions needed for each calculation were automatically selected by COMSOL.

Simulation of small cell pellet in vitro

The tempo-spatial change in temperature of a 20 µl cell pellet in a centrifuge microtube was simulated at five different heat doses (0.7, 1.5, 2.1, 7.3, and 9.5 W/g_tumour). In this case, the 2-dimentional axisymmetrical model was implemented following the actual shape of the microtube. A 100-µm thick polypropylene wall with a thermal conductivity of 0.12 W/m/°C and a 100-µm thick external air layer with 0.025 W/m/°C around the pellet were assumed. The fineness of mesh in COMSOL, i.e. total mesh number of the triangle elements, is represented by the degree of freedom as previously reported by Salloum et al. [25]. The total numbers of the triangle elements automatically and optimally generated by COMSOL and degree of freedom were about 7,000 and 13,000, respectively. At t = 0, all parts of the model were at 37°C and the outer side of the air layer and the top of the microtube were fixed at 25°C.

Simulation of liver tumours in vivo

The tempo-spatial change in temperature of in vivo tumours with two different sizes (10 mm and 5 mm in diameter) was calculated at a heat dose of 1.7 W/g_tumour. The assumption made in these calculations was that the human liver was 1200 mL in volume and had the shape of a triangular prism, with a rectangular base with short and long sides of 16.65 cm and 28.84 cm, respectively, and a height of 5 cm. The total number of the triangle elements automatically and optimally generated by COMSOL and degree of freedom were about 65,000 and 360,000, respectively [25]. At t = 0, all parts of the model were at 37°C and the outer surface of the liver was fixed at 37°C.

Heat dose required for liver tumours of various diameters.

Generalized correlations between the size of liver tumours and the heat dose required for achieving the target temperature in the IHCT were calculated using COMSOL. The model and boundary conditions were the same as described above. We simulated the heat dose that can heat tumours 0.5, 1, 2, 4, 5, 10, 20, and 40 mm in diameter up to 42°C, 46°C, and 50°C at the periphery after AMF exposure for 300 s.

Results

Increase in the temperature of SUIT-2 cell pellet containing ferucarbotran in the intercellular spaces and subjected to an AMF.

The increase in the temperature of the SUIT-2 cell pellet filled with five different concentrations of ferucarbotran (20, 27, 40, 60, and 80 mg γ-Fe₂O₃/ml initial ferucarbotran concentration) and subjected to an AMF of 150 Oe at 114 kHz is shown in Figure 1A. Equilibrium temperatures for these concentrations were 38.3°, 46.5°, 51.6°, 64.3° and 69.7°C, respectively. The same experiment was conducted for different types of cell pellets (BxPC-3 and AsPC-1) and similar results were obtained (data not shown).

Figure 1. Temperature of a cell pellet by induction heating. Cell pellets filling the intercellular space with five different concentrations of ferucarbotran were applied for an AMF. The equilibrium temperatures; 38.3°, 46.5°, 51.6°, 64.3°, and 69.7°C were obtained for the five different concentrations of 20♦, 27▾, 40▴, 60•, and 80▪ mg γ-Fe₂O₃/mL initial ferucarbotran concentration, respectively (A). The value between the equilibrium temperature and applied heat dose was plotted for three different cancer cell lines (SUIT-2▪, BxPC-3•, and AsPC-1▴) (B). Heat dose of 0.7, 1.5, 2.1, 7.3, and 9.5 W/g_tumour, resulted in equilibrium temperatures of 38.3°, 46.5°, 51.6°, 64.3°, and 69.7°C, respectively.

Heat doses used to heat the cell pellets in vitro to various equilibrium temperatures.

In the representative cell line SUIT-2, the amounts of γ-Fe₂O₃ in cell pellets containing five different concentrations of ferucarbotran were 21, 48, 64, 227, and 295 mg γ-Fe₂O₃/g_tumour, respectively. Since the SAR of γ-Fe₂O₃ is 32.3 W/g_material, 21 mg γ-Fe₂O₃/g_tumour corresponds to an applied heat dose of 0.7 (SD 0.1) W/g_tumour resulting in an equilibrium temperature of 38.3°C. Similarly, 48, 64, 227, and 295 mg γ-Fe₂O₃/g_tumour correspond to applied heat dose of 1.5 (SD 0.2), 2.1 (SD 0.04), 7.3 (SD 0.8), and 9.5 (SD 2.2) W/g_tumour, respectively, providing 46.5°, 51.6°, 64.3°, and 69.7°C equilibrium temperature, respectively. The relation between the heat doses used to heat SUIT-2 (▪), BxPC-3(•), and AsPC-1 (▴) cell pellets in vitro to various equilibrium temperatures is shown in Figure 1B. Further, the heat dose required to increase the temperature of an in vitro tumour model surrounded by air up to 50°C is in the range 1.5–2.0 W/g_tumour.

Simulation of thermal gradient in in vitro cell pellets

Thermal gradient simulations of 20 µL cell pellets are shown in Figure 2A. When a heat dose of 9.5 W/g_tumour was administered to a cell pellet the temperature at the centre of the cell pellet increased to 73.3°C and the temperature at the periphery of the pellet gradually decreased to 62.5°C. Although the entire cell pellet was subjected to a homogenous AMF, we observed a temperature gradient between the centre and the periphery of the cell pellet. The time-dependent changes in the temperature at the centre and the periphery of the cell pellet are shown in Figures 2B and 2C. The equilibrium temperature at the centre of samples that were heated with doses of 0.7, 1.5, 2.1, 7.3, and 9.5 W/g_tumour was 38.9°, 43.4°, 51.4°, 62.7°, and 73.3°C, respectively. These simulation data were quite comparable to actual experimental data (Figure 1A), indicating the validity of the COMSOL Multiphysics simulation results. The equilibrium temperatures at the periphery of the cell pellet were 36.0°, 39.5°, 45.7°, 54.5°, and 62.5°C, respectively.

Figure 2. Computer simulation of thermal gradient in a small in vitro cell pellet surrounded by air. Thermal gradients of the 20 µL cell pellet, which was heated with five different heat doses (0.7, 1.5, 2.1, 7.3, and 9.5 W/g_tumour) for 300 s are shown (A). The time-dependent change in the temperature at the centre (B) and periphery of pellet (C). Equilibrium temperatures at the centre of the tumour on administration of the above-mentioned heat doses were 38.9°, 43.4°, 51.4°, 62.7°, and 73.3°C, respectively. Those at the periphery were 36.0°, 39.5°, 45.7°, 54.5°, and 62.5°C, respectively.

Cytotoxic effect of heat generated by induction heating at different temperatures

The number of viable cancer cells 1, 3, and 7 days after exposure to six different temperatures is shown in Figure 3. The growth curves indicated the difference in heat sensitivity among the three cell lines. The BxPC-3 cells were relatively ‘sensitive cells’ because exposure to a temperature of 42°C induces obvious cellular damage and 46°C is more than enough to kill cells. In contrast, SUIT-2 and AsPC-1 cells are ‘heat tolerant cells’ because exposure to 46°C is not sufficient to kill them; more than half the number of cells that were considered in the control case were viable on day 7.

Figure 3. Cytotoxic effect of heat, generated by induction heating. An AMF (100–150 Oe, 114 kHz) was applied to three different cell pellets (SUIT-2, BxPC-3, and AsPC-1) containing ferucarbotran. After 10-min exposure to various temperatures (39°C, 42°C, 46°C, 48°C, 51°C, and 60–65°C), each cell pellet was cultured for 7 days. The numbers of viable cells 1, 3, and 7 days after incubation were counted. The values and bars are the mean and SD of three independent experiments.

Temperature simulation of a liver tumour in vivo

The spatiotemporal change in the temperature of liver tumours of different sizes (10 mm and 5 mm in diameter) is shown in Figure 4. The image of the entire liver and an enlarged image of the tumour portion are shown in 4A and 4B. Time-dependent changes in the temperature at the centre and periphery of the tumour are shown in 4C and 4D. The temperatures at the centre and periphery of the 10 mm tumour were 61°C and 50°C (4A, 4C), respectively. In contrast, the temperatures at the centre and periphery of the 5 mm tumour were 44°C and 41°C (4B, 4D), respectively.

Figure 4. Computer simulation of the thermal gradient in in vivo liver tumour of different sizes. The temperature changes in the 10 mm (A, C) and 5 mm tumours (B, D) with a heat dose of 1.7 W/g_tumour for 300 s were simulated. Images of the entire liver and an enlarged image of a part of the tumours (A, B). Time-dependent change in the temperatures at the centre and periphery of the 10 mm (C) and 5 mm (D) tumours. In the simulation of the 10-mm-diameter tumour, the centre and periphery of the 10-mm tumour were heated to 61°C and 50°C, respectively, however, those of the 5-mm tumour were heated only to 44°C and 41°C, respectively.

Heat dose required for liver tumours of various diameters

Generalized correlations between the size of liver tumours and the heat dose required for heating tumours up to 50°C, 46°C, and 42°C are shown in Figure 5. To increase the temperature of the periphery of the tumour up to 50°C, the heat doses required for tumours with diameters of 40, 20, 10, 5 and 1 mm were 0.6, 0.7, 1.7, 5.1 and 105 W/g_tumour, respectively.

Figure 5. Required heat dose for liver tumours with various diameters. The relationship between the tumour size and the heat dose administered for 300 s to heat the tumours to 42°C (▴), 46°C (•), and 50°C (▪) at their periphery was simulated. In order to increase the temperature of the tumour periphery up to 50°C, tumours with diameters 40, 20, 10, 5, and 1 mm require heat doses of 0.6, 0.7, 1.7, 5.1, and 105 W/g_tumour, respectively.

Discussion and conclusion

The biomedical significance of our study is that it presents minimal heat dose that should be considered for the successful implementation of IHCT. Large liver tumours, more than 10 mm in diameter, may be treated by applying a 1.5–2 W/g_tumour heat dose, which can be achieved by integrating present technologies; however, treatment of smaller tumours require substantial heat dose.

Defining the required temperature for cancer cell killing is the first issue we have to fix in starting development of thermal cancer therapy in liver metastases. Since heat sensitivity of clinical cancers is known to be variable, we addressed the lethal temperature of three pancreatic cancer cells that are representative of notorious liver metastasis-producing cancer. We settled the treatment time at 10 min, since long irradiation of AMF to living body tissue causes adverse events [26] and application of temporary blood flow interrupting surgical technique (Pringle's manoeuvre) is usually applicable for 10-15 min [17]. Our results demonstrated that maintaining a temperature of 46°C for 10 min was insufficient and resulted in the reproliferation of cancer cells, while a temperature of 50°C maintained for 10 min resulted in complete cell death regardless of the heat sensitivity of each cell type (Figure 3). A standard value which should be employed here is the equivalent minute of 43°C (EM₄₃) [27] which is intended to equate various experimental conditions to 43°C exposure. When EM₄₃ exceeds 240 min, cytotoxic effects are known to be sufficient [28]. Our deduced parameter, 50°C for 10 min, corresponds to EM₄₃ = 1280 min, and 46°C for 10 min corresponds only to EM₄₃ = 80 min, reconfirming the legitimacy of the value. We are confident, therefore, that exposing the entire tumour from the centre to the periphery to a temperature of 50°C for 10 min is a necessary and sufficient condition for IHCT.

Before using the software COMSOL for present heat simulation, we confirmed its reliability by comparing the data obtained by using it with the experimental data. The value of the heat dose is the basic input parameter for COMSOL. Although we added the same concentration of ferucarbotran for the case of the three cell lines, the final concentration of ferucarbotran was different. SUIT-2 was used as the representative cell line to examine the amount of γ-Fe₂O₃ (see result) that provides a heat dose of 0.7, 1.5, 2.1, 7.1, and 9.5 W/g_tumour (Figure 1B) for an AMF of 150 Oe (at 114 kHz). When we entered these values into COMSOL, the simulated temperatures at the centres of the cell pellets (Figure 2B) were observed to be well correlated with those detected experimentally (Figure 1A). This result indicates that COMSOL can be used in future studies for simulation of temperatures in vivo.

A major factor that affects static heat loss is the ratio of the relative surface area of the tumour to the tumour volume. The liver tumour simulations (Figure 4) indicated that a large tumour (10 mm) was sufficiently heated both at the centre (61°C) and periphery (50°C), however, a small tumour (5 mm) was not sufficiently heated, even at the centre (44°C), and periphery (41°C). A small sphere possesses a large surface area per unit volume, resulting in increased heat loss to the surrounding tissue. This phenomenon has already been validated by Rabin et al., addressing whether or not intercellular hyperthermia using magnetic nanoparticles is possible using physical equations [29–31]. They demonstrated that when single cells (10–100 µm in diameter) containing nanoparticles are heated by radiating AMF, they would never be heated as long as they are surrounded by a large cellular structure free of nanoparticles. Assuming the diameter of cells become larger than 1 mm, they could reach the threshold for hyperthermic conditions [29]. In addition to Rabin's findings that smaller tumours (less than 1 mm in diameter) are impossibly heated, we indicate a concrete heat dose value which is required for IHCT.

Our findings may be condensed into Figure 5, which demonstrates generalized correlations between the size of liver tumours and the heat dose required for increasing the temperature of the tumours to 50°C. Though a 10-mm liver tumour requires 1.7 W/g_tumour, larger tumours require a smaller heat dose, e.g. 20 mm and 40 mm tumours require 0.7 W/g_tumour and 0.6 W/g_tumour, respectively. In contrast, small tumours require large amounts of heat, e.g. 5 mm and 1 mm tumours require 5.1 W/g_tumour and 105 W/g_tumour, respectively. We then addressed whether a heat dose in the range of 0.6–105W/g_tumour can be provided using present technologies.

The heat dose administered in IHCT depends on two parameters: the heating potential of each nanoparticle (represented by SAR) and the concentration of nanoparticles accumulated at target sites. For example, in order to provide a heat dose of 1.7 W/g_tumour for targeting a 10-mm tumour, the accumulation of 52.6 mg ferucarbotran, the SAR of which is 32.3 W/g_material, is required (1.7 W/32.3 W/g_material = 0.0526 g_material). Since a dose equivalent to 52.6 mg ferucarbotran is contained in 1.3 mL commercially distributed Resovist® solution, it is not realistic to accumulate 52.6 mg ferucarbotran in 1 g of tumour by any drug delivery system. We conclude that successful clinical implementation of IHCT is difficult as long as nanoparticles with a low SAR such as Resovist® are used.

Researchers from the field of applied physics should contribute to IHCT development by providing high heat power magnetic nanoparticles. The SAR values of magnetic fluids should be improved by increasing the amplitude of the AMF, increasing the frequency of the AMF, and/or modifying the material properties of magnetic nanoparticles [10]. Obtaining high value SAR by applying a high-frequency AMF was shown by Levy et al. who obtained a SAR value of 950 W/g_material for γ-Fe₂O₃ at 339 Oe and 700 kHz [32]. However, the guidelines of the International Commission on Non-Ionizing Radiation Protection state that exposure to electromagnetic fields at frequencies above about 100 kHz causes significant increase in the temperature even in organs or tissues with no magnetic materials [33]. Since the maximum strength of the AMF that can be applied to animals and humans is around 1300 Oe × 150 kHz (reported by Ivkov et al. [26]), the development of materials that show high SAR within this AMF strength is desirable. Although the heat dose of 32.3 W/g_material (at 150 Oe and 114 kHz, our experiment) and the SAR of 123 W/g_material (at 88 Oe and 63 kHz, reported by Wang et al. [34]) were achieved in the safe range of the AMF strength, it seems to be difficult to achieve SAR values as high as 950 W/g_material within the range by using γ-Fe₂O₃. Therefore, using non-ferucarbotran materials, for example ferromagnetic materials, is another option to obtain high SAR values [35]. Since heat generation by ferromagnetic materials is mainly influenced by the strength of the magnetic field rather than its frequency, ferromagnetic materials have the potential to show a high SAR at clinically applicable low-frequency AMFs. We have been developing new ferromagnetic materials for achieving a heat dose of 450 W/g_material for a low-frequency AMF with a moderate strength (440 Oe, 120 kHz) (unpublished data). We assumed that the combination of newly developed magnetic nanoparticles and a clinically adapted AMF generator would be able to provide 800–1000 W/g_material, and this could be considered as the goal value of SAR in IHCT development.

Another factor requiring detailed study is the method of increasing the concentration of magnetic particles in the target cancerous tissue; this topic should be solved by researchers in the biomedical field. Nanoparticles or macromolecules larger than 10–100 nm are known to be predominantly precipitated in the cancerous tissues due to a unique physiological mechanism called enhanced permeability and retention effect [36]. The precipitation of macromolecules was enhanced eight times more (8% injection dose/g_tumour) than that of micromolecules due to this effect [37]. Although attempts to increase the concentration of accumulated nanoparticles by conjugating them with cancer-targeting antibodies have resulted in an increase by a factor of 1.5–2 (13.7 ± 2.1% injection dose/g_tissue), the amount accumulated is only 0.2 mg_material/g_tumour [12]. Since antibody conjugation has limited effect on the nanoparticles concentration [38] it is clear that drug delivery systems that can precipitate at most 1–2 mg_{magnetic nanoparticle}/g_tumour should be achieved using the currently available techniques.

The main theoretical merit of IHCT may be to control micro-disseminated multiple cancer nodules, which cannot be treated with needle-puncture ablation systems. However, smaller tumours (less than 1 mm in diameter) are revealed to be impossibly heated by IHCT as path-breaker's report [29]. Our data have added simple and concrete heat dose value which require for IHCT, demonstrating that treating small (1–5 mm in diameter) cancer nodules with IHCT is unrealistic since the required heat dose of 5.1–105 W/g_tumour cannot be provided to date. For the time being, researchers involved in IHCT should target cancer nodules with a diameter of 10 mm or more, and develop heat delivery systems capable of providing a heat dose of 1.7 W/g_tumour at least. It should be noted here that this 1.7 W/g_tumour value is the minimal estimate without considering cooling effect of blood flow, and two to three times larger heat dose would be required in a clinical setting if blood flow interruption technique has not been incorporated [16], [39]. To achieve this goal of 1.7 W/g_tumour, researchers in applied physics should develop magnetic nanoparticle systems capable of delivering 1000 W/g_material under conditions safe to humans, while researchers in the biomedical field should work on establishing a drug delivery system that can accumulate 1–2 mg of magnetic nanoparticles per gram of tumour.

Acknowledgements

The authors are grateful to Dr. Osamu Matsui and Dr. Shigeyuki Takamatsu (Kanazawa University) for valuable discussions, and to Dr. Takeshi Iwamura (Miyazaki Medical College) for providing the SUIT-2 cells.

Declaration of interest: This work was supported in part by a grant-in-aid for Cancer Research (21 TokubetuShitei-1) from the Ministry of Health, Labour and Welfare, and in part by a Grant-in-aid for Scientific Research (KAKENHI, 21591743) from the Ministry of Education, Culture, Sports, Science and Technology of Japan. The authors report no conflicts of interest. The authors alone are responsible for the content and writing of the paper.