Computational modelling of cancer nanomedicine: Integrating hyperthermia treatment into a multiphase porous-media tumour model

TL;DR

This work addresses the challenge of predicting temperature distributions during nanoparticle-mediated hyperthermia by embedding nanoparticle transport and heat generation into a fully coupled multiphase porous-media model of the tumour microenvironment. The authors develop two vascular representations (lumped Pennes-based and discrete microvasculature) and couple diffusion–advection transport with heat generation proportional to the specific absorption rate (SAR) of iron oxide nanoparticles. Key findings show that surrounding healthy tissue can experience substantial heating due to tissue conductivity, and that discretising blood perfusion cooling yields only modest temperature differences (e.g., ~0.75°C) compared with lumped models under certain conditions; microvasculature small vessels have limited cooling impact, while nanoparticle clustering can yield a small local temperature boost. The model provides a framework to optimize treatment parameters (NP accumulation, SAR, and perfusion representation) and is extensible to other local hyperthermia modalities, enabling more efficient and safer cancer therapy design.

Abstract

Heat-based cancer treatment, so-called hyperthermia, can be used to destroy tumour cells directly or to make them more susceptible to chemotherapy or radiation therapy. To apply heat locally, iron oxide nanoparticles are injected into the bloodstream and accumulate at the tumour site, where they generate heat when exposed to an alternating magnetic field. However, the temperature must be precisely controlled to achieve therapeutic benefits while avoiding damage to healthy tissue. We therefore present a computational model for nanoparticle-mediated hyperthermia treatment fully integrated into a multiphase porous-media model of the tumour and its microenvironment. We study how the temperature depends on the amount of nanoparticles accumulated in the tumour area and the specific absorption rate of the nanoparticles. Our results show that host tissue surrounding the tumour is also exposed to considerable doses of heat due to the high thermal conductivity of the tissue, which may cause pain or even unnecessary irreversible damage. Further, we include a lumped and a discrete model for the cooling effect of blood perfusion. Using a discrete model of a realistic microvasculature reveals that the small capillaries do not have a significant cooling effect during hyperthermia treatment and that the commonly used lumped model based on Pennes' bioheat equation overestimates the effect: within the specific conditions analysed, the difference between lumped and discrete approaches is approximatively 0.75°C, which could influence the therapeutic intervention outcome. Such a comprehensive computational model, as presented here, can provide insights into the optimal treatment parameters for nanoparticle-mediated hyperthermia and can be used to design more efficient treatment strategies.

Figures (4)

• Figure 1: (A) Porous medium with the pore space of the extracellular matrix (ECM) occupied by the tumour cells, host cells, and the interstitial fluid (IF), and the vasculature as an additional porous network. (B) At the microscale, the different phases can be distinguished (left), while at the macroscale, the phases are described by their volume fractions $\varepsilon^\alpha$ (right). Up-scaling based on the thermodynamically constrained averaging theory (TCAT) bridges the gap between the two scales.
• Figure 2: Idealised spherical tumour with lumped heat sink term. (A) Characteristic features of a solid tumour described by the saturation of tumour cells $S^t$, the pressure in the interstitial fluid (IF) $p^\ell$, and the volume fraction of the vasculature $\varepsilon^v$. The white dashed line indicates the tumour boundary in all plots. (B) Treatment protocol. (C) Mass fraction of nanoparticles in the IF $\omega^{\textsf{NP}\ell}$ after 5min, 20min, 40min, and 60min. (D) Temperature field after 40min. (E) Temperature curves for different values of injected nanoparticles $\omega^{\textsf{NP}v}_D$ and specific absorption rates ($SAR$). (F) Temperature curves for different specific absorption rates ($SAR$) and blood perfusion rates $w$.
• Figure 3: Tumour with a discrete microvascular network. (A) Saturation of tumour cells $S^t$. The white dashed line indicates the tumour boundary in all plots. (B) Mass fraction of nanoparticles in the interstitial fluid (IF) $\omega^{\textsf{NP}\ell}$ after 5min, 40min, and 60min. (C) Temperature field after 60min for a heat exchange coefficient $\beta_T = 2e-5W\per mm\squared\per K$. (D) Temperature field after 60min for a hypothetical heat exchange coefficient $\beta_T = 2e-3W\per mm\squared\per K$. (E) Comparison of the temperature curves at $y = 1.8mm$ after 60min for the discrete and the lumped model of the cooling effect of blood perfusion, including different values for the heat exchange coefficient $\beta_T$ or the blood perfusion rate $w$ and the case without blood perfusion.
• Figure 4: In vivo tumour in a mouse model. (A) Geometry of the tumour in the leg of the mouse taken from the experimental study of Cho et al. Cho2017 (B) Saturation of tumour cells $S^t$. The white dashed line indicates the tumour boundary in all plots. (C) Homogeneous distribution: Mass fraction of nanoparticles in the interstitial fluid (IF) $\omega^{\textsf{NP}\ell}_D$ and temperature field after 30min. (D) Clustered distribution: Mass fraction of nanoparticles in the IF $\omega^{\textsf{NP}\ell}_D$ and temperature field after 30min.