Nanowarming 2D: Radial Heat Profile & SAR Curve

Rewarming Mode

Magnetic Nanoparticles

Fe concentration 40 mg/mL

AMF frequency 300 kHz

AMF field amplitude 20 kA/m

Bath / body temperature 37 °C

Organ radius 30 mm

Radius change applies on next Reset — organ size is fixed while rewarming runs.

Live Readouts

Vitrified — holding at −150 °C

Core temp

−150.0 °C

Surface temp

−150.0 °C

Max radial gradient

0.0 °C/mm

Elapsed (sim.)

0 s

Time spent in ice-nucleation band (−123…−90 °C, whole organ)

0.0 s

How it works

2D companion to the 3D nanowarming model: the same radial heat-equation physics, read off four flat panels instead of a rendered 3D organ.

Per-particle heating (linear-response theory):
  SAR(f,H) = A · f·H² / (1 + (f/f₀)²)      [W/g Fe]
Volumetric source:
  q = SAR · C                               [W/m³], C = Fe concentration
Radial heat equation (spherical symmetry):
  ρc ∂T/∂t = k(∂²T/∂r² + (2/r)∂T/∂r) + q
Surface boundary:
  −k ∂T/∂r|ᵣ = h·(T_surface − T_bath)

Cross-section (top-left) — a flat radial slice of the organ, shaded by local temperature; nanoparticle dots (nano mode only) become denser as Fe concentration rises.
Radial profile (top-right) — temperature from center to surface right now; watch the curve flatten in nano mode versus staying steep (core lagging) in convective-only mode.
SAR heating curve (bottom-left) — specific absorption rate vs. AMF frequency at the current field amplitude, with the live operating point marked. This is the formula that sets the volumetric source q — it is the same curve driving every other panel.
Core / surface vs. time (bottom-right) — both temperatures through the run, with the ice-nucleation danger band shaded; the gap between the two traces is the thermal-stress risk convective-only warming can't avoid.
Organ radius — larger organs make the core-vs-surface lag of convective-only warming dramatically worse (conduction path length grows, but nanowarming's volumetric heating barely notices) — this is the central real-world argument for nanowarming at whole-organ scale. Takes effect on the next Reset.

This mirrors real nanowarming research (Etheridge/Bischof-style protocols): magnetite nanoparticles plus radiofrequency fields rewarm large vitrified tissue at 100s of °C/min, fast enough to avoid devitrification where slow convective baths cannot.