Incorporating Magnetic Nanoparticle Aggregation Effects into Heat Generation and Temperature Profiles for Magnetic Hyperthermia Cancer Treatments
Holladay, Robert Tyler
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In treating cancer, a primary consideration is the target specificity of the treatment. This is a measure of the treatment dose that the cancerous (target) tissue receives compared to the dose that healthy tissue receives. Nanoparticle (NP) based treatments offer many advantages for target specificity compared to other forms of treatment due to their ability to selectively target tumors. One benefit of using magnetic NPs is their ability to release heat, which can both sensitize tumors to other forms of treatment as well as damage the tumor. The work here aims to incorporate a broad range of relevant physics into a comprehensive model. NP aggregation is known to be a large source of uncertainty in these treatments, thus a framework has been developed that can incorporate the effects of aggregation on NP diffusion, NP heat release, temperature rise, and overall thermal damage. To quanitify thermal damage in both healthy tissue and tumor tissue, the Cumulative Equivalent Minutes at 43 textcelsius~model is used. The Pennes bioheat equation is used as the governing equation for the temperature rise and included in it is a source heating term due to the NPs. NP diffusion and aggregation are simulated via a random walk process, with a probability of aggregation determining if nearest neighbor particles aggregate at each time step. Additionally, models are developed that attempt to incorporate aggregation effects into NP heat dissipation, though each proves to only be accurate when there is little aggregation occurring. In this work, verification analyses are done for each of the above areas and, at minimum, qualitatively accurate results have been achieved. Verification results of this work show that aggregation can be neglected at concentrations on the order of $100~nM$ or less. This however only serves as a rough estimation and further work is needed to gain a better quantitative understanding of the effects of NP concentration on aggregation. Using this concentration as a limitation, results are presented for a variety of tumor sizes and concentration distributions. Because this work incorporates a variety of physics and numerical methods into a single encompassing model, depth and physical accuracy in each area (bio-heat transfer, diffusion via random walk, NP energy dissipation, and aggregation) have been somewhat limited. This does however provide a framework in which each of the above areas can be further developed and their effects examined in the overall course of treatment.
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