Tissue heating during RF/microwave hyperthermia and ablation is governed by the Pennes bioheat equation: heat diffuses through tissue, is deposited by the applicator, and is carried away by blood perfusion, a distributed heat sink.
∂T/∂t = α∇²T − ω(x)(T − T_a) + q(x)
α — thermal diffusivity of tissue
ω — perfusion (heat-sink) coefficient — small in bulk
tissue, much larger in the ring of cells around
a real blood vessel (fast blood clamps nearby
tissue close to arterial temperature T_a)
T_a — arterial blood temperature, 37°C
q — power deposited by the applicator (Gaussian, centered)
The heatmap is the actual solved grid, viewed top-down — every cell's colour is its temperature, with no 3D flattening involved. It is stepped every frame with an explicit finite-difference Laplacian for diffusion, plus a backward-Euler (implicit) update for the perfusion term. That implicit step matters: this simulator's own numbers show that treating perfusion explicitly — as a naive port of the equation would — lets the vessel's sink term blow the whole grid up to ±10⁴⁸°C the moment blood flow and vessel diameter are both pushed high, because its own stability bound only ever checked the diffusion term. Handling perfusion implicitly keeps the scheme stable at any blood-flow setting, the way a real bioheat solver has to.
- Heating power — strength of the applicator's Gaussian heat source at the target center.
- Blood flow (vessel cooling) — how strongly the vessel clamps nearby tissue toward 37°C; 0 removes the vessel's effect entirely, 1 is a large, fast-flowing vessel.
- Vessel distance / diameter — geometry of the vessel relative to the treatment target; closer and wider vessels cut a bigger cold streak through the coverage.
- Cross-section panel — a live slice through z = 0, showing the actual dip below the 43°C threshold next to the vessel.
- Coverage history panel — the ≥43°C target-zone coverage percentage traced over the last ~20 seconds, so you can see it settle (or collapse) as you move a slider.
- Drag / scroll on the heatmap — pan and zoom the temperature field itself.