Boundary-only mechanobiological modeling of thermoelastic tissue deformation during nanoparticle-mediated hyperthermia

Localized hyperthermia not only causes thermal injury to the tissues but also causes mechanical deformation of the tissues due to expansion of the tissues resulting from temperature changes, stress creation, and strain concentration. In this paper, an exclusive mechanobiological model for nanoparticle-enhanced hyperthermia is developed by modeling transient bioheat transfer, Arrhenius thermal damage, and thermoelastic responses of the tissues due to temperature change. It combines the transient Pennes bioheat transfer model, spatially heterogeneous nanoparticle-specific absorption rate-based heat sources, Arrhenius thermal damage kinetics, and linear isotropic thermoelasticity based on temperature-based eigenstrain. To circumvent the requirement for domain discretization to incorporate internal heat source, perfusion, and transient heat storage in the bioheat transfer model, a Dual Reciprocity Boundary Element Model is developed. Temperature histories are then used to assess the level of accumulated thermal damage and provide the inputs for thermoelastic boundary integral formulation, where displacements, strains, and stresses will be obtained. Through the correlation of nanoparticle-generated internal heat into mechanical deformations, the proposed methodology establishes the connection between thermal therapy, tissue reaction, and elastography. Numerical validation through manufactured solutions, comparison to the analytical steady state solution, and overall energy balance analysis reveals the first-order convergence and stability of transient simulation along with overall energy conservation up to 2.7% in the transient energy balance test. The simulations show that nanoparticle heating creates detectable thermoelastic displacements, which could be the early signs of treatment.