Magnetic Hyperthermia Simulator

Scientific tool, not a clinical device. This simulator provides model-based estimates. The calculated temperature, SAR, relaxation behavior, and heating rate depend strongly on assumptions regarding particle size, magnetic anisotropy, magnetic properties, thermal properties, suspension behavior, and experimental conditions. The model should be calibrated and validated against experimental measurements before scientific conclusions are drawn.

1 Experimental Data (optional)

2 Simulation Parameters

Initial Temperature T0 °C Sample temperature at t = 0. Time Interval Δt s Integration time step. Total Simulation Time t_end s Simulated duration. Viscosity η Pa·s Dynamic viscosity of the carrier fluid (water at 20 °C ≈ 0.001 Pa·s). Concentration C ppm Nanoparticle mass fraction (1 ppm = 1 mg/kg of suspension). Frequency f kHz AC magnetic field frequency. Magnetic Field H kA/m AC magnetic field amplitude.

3 Advanced Physical Parameters

Show Advanced Parameters

All default values below are MODEL ASSUMPTIONS (typical magnetite-like particles in water). They are not experimental results — replace them with measured values when available. Values left at the default are reported with source “Model Assumption”.

Particle (Core) Diameter d MODEL ASSUMPTION nm Magnetic core diameter (spherical, monodisperse). Hydrodynamic Diameter d_h MODEL ASSUMPTION nm Core + coating + solvation layer; must be ≥ core diameter. Saturation Magnetization Ms MODEL ASSUMPTION A/m Bulk-magnetite order of magnitude; nanoparticles are often lower. Anisotropy Constant K MODEL ASSUMPTION J/m³ Effective uniaxial anisotropy energy density. Attempt Time τ0 MODEL ASSUMPTION s Néel attempt time (typically 1e-10 – 1e-9 s). Sample Volume V_s MODEL ASSUMPTION mL Volume of the heated suspension. Specific Heat Capacity (fluid) c_p,f MODEL ASSUMPTION J/(kg·K) Water ≈ 4186 J/(kg·K). Density (fluid) ρ_f MODEL ASSUMPTION kg/m³ Carrier fluid / suspension density. Specific Heat Capacity (particle) c_p,p MODEL ASSUMPTION J/(kg·K) Magnetite ≈ 650 – 700 J/(kg·K). Density (particle) ρ_p MODEL ASSUMPTION kg/m³ Magnetite ≈ 5180 kg/m³. Heat Transfer Coefficient h_loss MODEL ASSUMPTION W/K Effective lumped heat-loss coefficient of the whole sample (0 = adiabatic). Ambient Temperature T_env MODEL ASSUMPTION °C Environment temperature for heat loss. Leave empty to use the initial temperature. Reference Frequency f_ref MODEL ASSUMPTION kHz Normalisation frequency of the factorised model. Reference Magnetic Field H_ref MODEL ASSUMPTION kA/m Normalisation field of the factorised model. Reference Concentration C_ref MODEL ASSUMPTION ppm Normalisation concentration (F_C = 1 at C = C_ref). Saturation Concentration C_sat MODEL ASSUMPTION ppm Concentration scale at which heating per particle starts to saturate (saturating model). Magnetic Heating Exponent n MODEL ASSUMPTION - Empirical field exponent; n = 2 corresponds to linear response theory. Frequency Exponent (Simplified) m MODEL ASSUMPTION - Empirical frequency exponent, used only in Simplified mode. Reference Heating Power (Simplified) P0 MODEL ASSUMPTION W Heating power at (f_ref, H_ref, C_ref), used only in Simplified mode. Calibration Factor α MODEL ASSUMPTION - Manual multiplier on P_mag (Experimental-Calibrated mode fits its own α on top). Concentration Model MODEL ASSUMPTION Saturating form prevents unbounded heating for C → ∞. Integration Method Euler: T_i+1 = T_i + (dT/dt)·Δt.

4 Simulation Mode

Simplified
Empirical heating model: P = α·P0·(f/f_ref)^m·(H/H_ref)ⁿ·F_C Relaxation-Based
τN, τB, τeff, ωτeff with linear-response loss x/(1+x²) Experimental-Calibrated
Model + least-squares fit of α to the uploaded experiment

Compare Simulations

Each scenario starts from the current form parameters and overrides frequency, field, concentration and viscosity. Maximum 10 scenarios.

Label	f (kHz)	H (kA/m)	C (ppm)	η (Pa·s)

Sensitivity Analysis

Parameter Values (comma separated, max 25)

Model Assumptions

Spherical nanoparticle geometry
Uniform (monodisperse) particle properties — no size distribution
Homogeneous, dilute suspension
Uniform temperature approximation (lumped thermal model)
No spatial temperature gradient
Simplified relaxation model (Debye-type x/(1+x²) response, linear response theory)
Zero-field Néel–Arrhenius relaxation (no field-dependent energy barrier)
Empirical magnetic field response (exponent n)
Empirical concentration response (linear or saturating)
Constant saturation magnetization, anisotropy and viscosity (no temperature dependence except through T in τN, τB, χ0)
Newtonian (linear) heat loss with constant effective coefficient h_loss
No explicit convection model
No radiation model
No aggregation / chain-formation model
No boiling / evaporation model
Effective heat capacity — not a calorimetric measurement
Advanced parameter defaults are MODEL ASSUMPTIONS, not experimental results

Model equations

Unit conversion	T[K] = T[°C] + 273.15; f[Hz] = f[kHz]·1000; H[A/m] = H[kA/m]·1000; C[kg/m³] = ppm·1e-6·ρ_fluid
Particle volumes	V = π d³ / 6; V_h = π d_h³ / 6
Néel relaxation	τN = τ0 · exp(K V / (kB T)) (exponent capped for numerical safety)
Brownian relaxation	τB = 3 η V_h / (kB T)
Effective relaxation	1/τeff = 1/τN + 1/τB
Relaxation response (simplified)	ω = 2πf; x = ω τeff; F_relax = x / (1 + x²) (Relaxation-Based mode only)
Frequency factor	Relaxation-Based: F_f = f / f_ref; Simplified: F_f = (f / f_ref)^m; F_f ≤ F_f,max
Field factor (empirical)	F_H = (H / H_ref)^n, F_H ≤ F_H,max
Concentration factor	saturating: F_C = (C/C_ref)·(C_ref + C_sat)/(C + C_sat); linear: F_C = C/C_ref (capped)
Equilibrium susceptibility	χ0 = μ0 φ Ms² V / (3 kB T), φ = C / ρ_particle
Reference power	Relaxation-Based: P_ref(T) = μ0 π χ0(φ_ref, T) H_ref² f_ref V_sample; Simplified: P_ref = P0
Magnetic heating power	P_mag = α · P_ref · F_f · F_H · F_C · F_relax
Heat capacity (effective)	C_total = m_fluid c_p,fluid + m_particle c_p,particle
Heat loss	P_loss = h_loss (T − T_env)
Energy balance	C_total dT/dt = P_mag − P_loss
Integration	Euler: T_{i+1} = T_i + (dT/dt)_i Δt; RK4 optional
Temperature rise	ΔT(t) = T(t) − T_initial
Local heating rate	HR_i = (T_i − T_{i−1}) / (t_i − t_{i−1}) [°C/s]; ×60 → °C/min
Calibration (Experimental-Calibrated)	T_cal = T_initial + α_fit (T_model − T_initial); α_fit = Σ ΔT_model ΔT_exp / Σ ΔT_model²
Goodness of fit	RMSE = √(Σ e²/N); MAE = Σ\|e\|/N; R² = 1 − SS_res/SS_tot
Estimated SAR (model)	SAR_est = P_mag(t=0) / m_particle [W/kg] — estimate, not a measurement
Estimated SAR (experimental initial slope)	SAR_est = C_total · (dT/dt)_initial / m_particle — uses assumed C_total, no heat-loss correction

Important Scientific Limitations

This simulator provides model-based estimates. The calculated temperature, SAR, relaxation behavior, and heating rate depend strongly on assumptions regarding particle size, magnetic anisotropy, magnetic properties, thermal properties, suspension behavior, and experimental conditions. The model should be calibrated and validated against experimental measurements before scientific conclusions are drawn.

Linear response theory is only quantitatively valid for Langevin parameter ξ = μ0 Ms V H/(kB T) < ~1.
Hysteresis losses of large/ferromagnetic particles are not modelled.
SAR values are labelled "Estimated SAR" and are not measured SAR values.
Experimental-Calibrated mode scales the predicted temperature rise; it does not identify individual physical parameters.
Results outside the validity range (e.g. above the boiling point) are not physically meaningful.

Magnetic Hyperthermia Simulator

1 Experimental Data (optional)

2 Simulation Parameters

3 Advanced Physical Parameters

4 Simulation Mode

Result

Simulation Summary

Experimental Calibration

Temperature vs Time

Delta Temperature vs Time

Heating Rate vs Time

Relaxation Parameters (log scale)

Magnetic Heating Power & Heat Loss

Model Calculation (audit trace)

Parameters Used

Compare Simulations

Sensitivity Analysis

Model Assumptions

Important Scientific Limitations