Therapeutic Ultrasound 2D: Tissue Cross-Section Heating Model

Applicator Settings

Frequency 1 MHz

Spatial-average intensity 1.5 W/cm²

Duty cycle Continuous (100%)

Applicator position 0.0 cm

Tissue perfusion (blood flow) Normal

Live Readouts

Peak tissue temp

37.0 °C

Half-value depth

–

Treatment time elapsed

0:00

How it works

An ultrasound applicator radiates acoustic energy that is absorbed by tissue as it travels deeper, converting to heat. Intensity falls off with depth by the tissue's absorption coefficient, which scales with frequency:

I(d) = I₀ · 10^(−α·f·d / 10)      [one-way attenuation, α in dB/cm/MHz]
I(r) = I(d) · exp(−r² / 2σ²)      [Gaussian beam profile, r = lateral offset]
dT/dt = 2·α_np·I / (ρc) − k(T − T_body)   [local heating minus perfusion washout]

α (skin ≈0.5, fat ≈0.25, muscle ≈0.6 dB/cm/MHz) means higher frequency deposits energy faster and shallower, while 1 MHz reaches deep muscle with a gentler gradient — the reason clinicians pick 3 MHz for a superficial tendon and 1 MHz for a deep hip muscle.

Frequency — sets α·f, i.e. how fast the beam is absorbed with depth (penetration ∝ 1/f).
Intensity — scales I₀, the total acoustic power delivered per cm².
Duty cycle — pulsed mode (20% on-time) delivers the same peak intensity but a fifth of the average heating, used when only non-thermal effects (micromassage) are wanted.
Applicator position — moves the beam laterally, exactly like sweeping a soundhead by hand to avoid a periosteal hot spot.
Tissue perfusion — the −k(T−T_body) washout term: better-perfused tissue (e.g. muscle at rest vs. a poorly vascularised tendon) carries heat away faster, which is why temperature plateaus instead of climbing forever, and why the plateau sits lower with higher blood flow.
Cross-section view — drag to pan, scroll/pinch to zoom; this only changes what you see, not the physics.

drag to pan · scroll to zoom

Skin (0–0.2 cm) Fat (0.2–1.5 cm) Muscle (1.5–6 cm)

37°C45°C+