TABLE I.

Example MR and Ultrasound Methods for Thermography and Thermometry.

Modality	Method	Temperature Dependence	Tissue Dependence	Sensitivity	Spatial Res	Temporal Res
MR	Proton Resonance Frequency	ω(θ) = γx0(1 − σ(θ))	Low	~0.01 ppm/°C	$\mathcal{O}\left(\text{mm}\right)$	$\mathcal{O}\left(1\mathrm{s}\right)$
MR	Spin-lattice Relaxation	$T_1~e^{-\frac{E_a(T_1)}{k\theta }}$	High	1-2%/°C	$\mathcal{O}\left(\text{mm}\right)$	$\mathcal{O}\left(1\mathrm{s}\right)$
MR	Water Diffusion Coefficient	$D~e^{-\frac{E_a(D)}{k\theta }}$	Medium	~2%/°C	$\mathcal{O}\left(\text{mm}\right)$	$\mathcal{O}\left(1\mathrm{s}\right)$
US	Mean Scatterer Resonance	$f(\theta )=\frac{c(\theta )}{2d_s(\theta )}$	High	~0.05%/°C	$\mathcal{O}\left(\text{mm}\right)$	$\mathcal{O}\left(\text{ms}\right)$
US	Echo Shift	Equation 5	High	~0.05%/°C	$\mathcal{O}\left(\text{mm}\right)$	$\mathcal{O}\left(\text{ms}\right)$
US	Backscatter Energy	Equation 4	High	0.3 dB/°C	$\mathcal{O}\left(1\text{cm}\right)$	$\mathcal{O}\left(1\mathrm{s}\right)$

Parameters: γ (gyromagnetic ratio), B₀ (static magnetic field), σ (shielding constant), E_a (activation energy), k (Boltzmann constant); c (speed of sound), d_s (mean scatterer spacing)