Computational Investigation of Magnetic Hyperthermia for Complex-Shaped Tumor using Finite Volume Immersed Boundary Method

Abstract

Magnetic nanoparticle hyperthermia therapy (MNPH) is an emerging cancer treatment modality owing to its advantage of minimal invasive as well as can target irregular deep-rooted and poorly accessible tumors. Hyperthermia utilizes heat to sensitize pathological (cancerous) tissues for chemo/radiation therapy or to directly kill the cancerous cell through thermal ablation. However, achieving precise control of the spatial thermal dose within the tumor region is challenging due to various factors. These include tissue physiology, the size and shape of tumors, the distribution of magnetic nano-particle (MNP) in the tissue and magnetic field parameters. Since the tumors can have any irregular shape, thus devising the treatment protocol for MNPH for complexly shaped tumor remains a challenging task. Application of computational methodology can assist to clinician to devise a suitable treatment protocol for hyperthermia therapy. Computational simulation of the bioheat models in the complex tissue is challenging and computationally intensive due to the unavoidable complexity associated with the body-fitted grid generation. The objective of the present study is to develop the Cartesian grid based finite volume immersed boundary method (FV-IBM) for the bioheat transfer equation. The developed FV-IBM framework is used to simulate and analyze intratumoral MNPH therapy in complex and real tumor models. Immersed boundary method (IBM) is employed to enforce the boundary effect on the non-body conformal Cartesian grid. The finite volume method (FVM) is used as a numerical technique to discretize the governing equations. The validation and verification of the FV-IB method have shown that the scheme is nearly second-order accurate. Furthermore, the numerical results in the spherical tumor model are in good agreement with previously reported results for steady and transient cases. Results for MNP-based hyperthermia investigation with two heat source (Gaussian and uniform) distribution patterns in the liver tumor are in good agreement with the numerical solution of COMSOL Multiphysics. Thus, a simple and robust FV-IBM based numerical scheme is proposed to solve the bioheat models in arbitrary tissue shapes. The developed FV-IBM framework is used to investigate the effects of tumor shape on magnetic nanoparticle hyperthermia (MNPH) using four categories (spherical, oblate, prolate, and egg-shape) of tumor models having different morphologies. These tumors have equal volume; however, due to the differences in their shapes, they have different surface area. The shape of tumors is quantified in terms of shape factor (ζ). Magnetic hyperthermia is applied (frequency 150 kHz, and magnetic field amplitude 20.5 kA⁄m) to all tumor models, for 1 hour, after injection of magnetic nanoparticles (MNP) at the respective tumor centroids. The distribution of MNP after injection is considered as Gaussian. Results show that the therapeutic effects of MNPH depend significantly on the shape of a tumor. Tumors with higher shape factors receive less therapeutic effects in comparison to the tumors having lower shape factors. An empirical thermal damage model is also developed to assess the MNPH efficacy in real complex-shaped tumors. Intratumoral multi-injection strategy enhances the efficacy of magnetic nanoparticle hyperthermia therapy (MNPH). Further a criterion for the selection of injections and their location depending on the tumor shape/geometry is also developed. Developed strategy is based on the thermal dosimetry results obtained on different invasive 3D tumor models during MNPH simulation. Primary and secondary injections are used to inject MNP, based on the invasiveness of the tumor. Optimizing strategy is devised based on the zone of influence of primary and secondary injections. Results indicate that the zone of influence of secondary injection lies between the 0.7 and 0.8 times the radial distance between the center of tumor core and the branch node point. This zone of influence of secondary injection produces minimum heterogeneity of temperature in the tumor model. Additionally, the multi-injection strategy is more effective when the protrusion volume exceeds 10% of the total volume. The developed criterion for the selection of multi- injection strategy and the location of the injection point can help in devising treatment protocol for magnetic nanoparticle hyperthermia therapy. Moreover, a supplementary study is also conducted to analyze the cooling effect caused by blood vessels on a MNPH. The MNPH is simulated on the physical models constructed from DICOM images using the open-source 3D-Slicer software. The physical model comprises cancerous tissue, blood vessels, and surrounding liver tissue. Intratumoral injection of magnetic nanoparticles (MNP) is used to deliver MNP at the center of the tumor volume. In order to perform the parametric study, the tumor's position with respect to the blood vessel is changed. The therapeutic effect is evaluated based on the percentage of tumor volume exceeding the therapeutic threshold temperature of 43°C. The results indicate that there is a significant increase in the cooling effect when the tumor is in close proximity to the blood vessel. Close proximity of blood vessel with respect to tumor reduces the effectiveness of MNPH. However, this cooling effects diminish when tumor is away from the major blood vessels.