Design of silica-core gold-shell nanoparticles for photothermal breast tumor therapy: a two-arm comparison of surface cooling with nanoparticle self-attenuation

We assemble a three-layer forward model for gold nanoshell photothermal therapy, core-shell Mie absorption, Pennes bioheat transport, and an Arrhenius thermal dose, each benchmarked against an external reference, and use it to maximize necrosis depth subject to a skin-temperature cap. The design variables are core radius, shell thickness, and irradiance at 808 nm; number density is derived per geometry from a fixed delivered gold mass anchored to a measured in vivo loading. The Beer-Lambert source deposits heat from both nanoparticle and native tissue absorption and includes self-attenuation, so the deposition shape depends on the design; at fixed geometry, the rise is exact in the source amplitude, so envelope inversion pins the safety cap in closed form. The search is a two-arm comparison differing only in the skin boundary condition. For near-surface loading under a common skin-temperature constraint, the no-cooling control admits no viable therapy (necrosis 0), while contact cooling reaches 15.6 mm at a 15 ◦C skin surface. As a secondary, boundary-dependent observation, at each arm's own safety limit the cooled optimum is 3.6 mm deeper than a control that reaches depth only by heating the skin to about 83 ◦C. The control becomes viable only once a nanoparticle-free skin cap exceeds about 5.6 mm, its surface still at the 45 ◦C cap; cooling remains the deeper arm at every cap thickness tested. Methodologically, omitting self-attenuation makes the necrosis objective appear geometry-independent, whereas resolving it makes particle geometry a design lever comparable to cooling, though the favored geometry is a model-dependent trend rather than a located optimum. The headline depths derive from a homogeneous constant-perfusion model with a ubiquitous nanoparticle distribution rather than a tumor-localized one; the cap sweep relaxes that distribution but not the constant perfusion. All depths are theoretical upper bounds, not clinical predictions.