Acoustic output¶

sonosk.safety computes the acoustic output quantities that are reported for diagnostic ultrasound systems and compares them with the limits in the FDA guidance (February 2023). The definitions follow IEC 62359 and the same guidance. Inputs are values measured, or simulated, in water on the beam axis.

Derating¶

Tissue attenuation is modelled by a fixed 0.3 dB/(cm MHz). A derated pressure, marked with the subscript “.3”, is

\[ p_{.3}(z) = p(z)\,10^{-0.3 f z / 20} \]

and a derated intensity or pulse intensity integral is

\[ I_{.3}(z) = I(z)\,10^{-0.3 f z / 10} \]

with \(f\) in MHz and \(z\) in cm.

from sonosk import safety

safety.derate(2.0, f_mhz=5.0, z_cm=3.0)
safety.derate_intensity(1.0, f_mhz=5.0, z_cm=3.0)

Pulse quantities¶

For a pressure waveform \(p(t)\) in a medium of density \(\rho\) and sound speed \(c\):

\[ \mathrm{PII} = \frac{1}{\rho c}\int p^2(t)\,dt \]

The pulse duration PD is 1.25 times the time between the points where the running integral of \(p^2\) reaches 10 % and 90 % of its final value. Then

\[ I_\mathrm{SPPA} = \frac{\mathrm{PII}}{\mathrm{PD}}, \qquad I_\mathrm{SPTA} = \mathrm{PII}\cdot\mathrm{PRF} \]

where the second form holds for an unscanned beam with pulse repetition frequency PRF.

pii = safety.pulse_intensity_integral(p, dt, rho=1000.0, c=1500.0)   # J/m^2
pd = safety.pulse_duration(p, dt)                                    # s
i_ppa = safety.isppa(p, dt)                                          # W/m^2
i_pta = safety.ispta(pii, prf=4000.0)                                # W/m^2
safety.w_m2_to_mw_cm2(i_pta)

Mechanical index¶

\[ \mathrm{MI} = \frac{p_{r.3}(z_{sp})}{\sqrt{f_c}} \]

with \(p_{r.3}\) the derated peak rarefactional pressure in MPa and \(f_c\) the centre frequency in MHz. The depth \(z_{sp}\) is the point on the beam axis where the derated pulse intensity integral is largest. When the PII along the axis is not given, mechanical_index uses \(p_r^2\) in its place, which assumes the pulse shape does not change with depth.

mi, z_sp = safety.mechanical_index(z_cm, pr_mpa, f_mhz=3.0, pii=pii_axis)

Limits¶

check_limits uses the Track 3 global maximum values:

Application	ISPTA.3 [mW/cm²]	MI	ISPPA.3 [W/cm²]	TI
general	720	1.9	190
ophthalmic	50	0.23		1.0

For general use the guidance asks for MI ≤ 1.9 or ISPPA.3 ≤ 190 W/cm², so the check passes if either one is within its limit.

r = safety.check_limits(mi=1.2, ispta3=430.0)
r["ok"]                       # True
r["mi"]                       # (1.2, 1.9, True)

safety.check_limits(mi=0.2, ispta3=40.0, ti=0.8, application="ophthalmic")

The thermal indices (TIS, TIB, TIC) are defined in IEC 62359 and are not in this release.

References¶

IEC 62359:2010+A1:2017. Ultrasonics. Field characterization. Test methods for the determination of thermal and mechanical indices related to medical diagnostic ultrasonic fields.

FDA. Marketing Clearance of Diagnostic Ultrasound Systems and Transducers. Guidance for Industry and Food and Drug Administration Staff, February 2023. Docket FDA-2017-D-5372.