**Nanomedicine,
Volume I: Basic Capabilities**

**©
1999 Robert A. Freitas Jr. All Rights
Reserved.**

Robert A. Freitas Jr., Nanomedicine, Volume I: Basic Capabilities, Landes Bioscience, Georgetown, TX, 1999

**4.9.1.3 Respiratory
Audition****
**

The variation of mechanical pressure over a complete respiratory cycle is ~0.003 atm in the pleura, ~0.002 atm at the alveoli, detectable by nanomedical pressure sensors positioned in the vicinity of the respiratory organs. Holding a deep breath further stretches the pulmonary elastic tissue, up to 0.02 atm.

However, turbulent flows at Reynolds
number N_{R} > 2300 in the trachea, main bronchus and lobar bronchus
produce a whooshing noise that may be the loudest noncardiac sound in the human
torso during conventional auscultation. The energy dissipation for turbulent
flow in a tube is

where P_{lam} is the dissipation for laminar (Poiseuillean)
flow in a long circular cylindrical tube of length L, v is the mean flow velocity,
and turbulence factor Z = 0.005 (N_{R}^{3/4} - (2300)^{3/4}),
a well-known empirical formula.^{363}
For h_{air} = 1.83 x 10^{-5} kg/m-sec
for room-temperature air (20°C), P_{turb} = 0.87 milliwatts for the
trachea (L = 0.12 m, v = 3.93 m/sec and N_{R} = 4350 at 1 liter/sec
volume flow; Table
8.7); P_{turb} = 0.66 milliwatts for the main bronchus (L = 0.167
m, v = 4.27 m/sec and N_{R} = 3210); and P_{turb} = 0.09 milliwatts
for the lobar bronchus (L = 0.186 m, v = 4.62 m/sec and N_{R} = 2390),
totalling ~1.6 milliwatts acoustic emission from a ~120 cm^{3} upper
tracheobroncheal volume. This is a power density of 13 watts/m^{3} corresponding
to a pressure of 4 x 10^{-5} atm assuming a 300 millisecond measurement
window at the maximum respiration rate.

The amplitude of an acoustic plane wave propagating through tissue attenuates exponentially with distance due to absorption, scattering and reflection. The amplitude is given approximately by

where A_{0 }is the initial wave amplitude in atm,
A_{x} is the amplitude a distance x from the source, and a
is the amplitude absorption coefficient. The function F expresses the frequency
dependence of the attenuation. For pure liquids, F = F_{liq} = n^{2}
(Hz^{2}); for example, a_{liq} =
2.5 x 10^{-14} sec^{2}/m for water at room temperature. However,
for soft tissues, F = F_{tiss} ~ n (Hz).^{505}*
Values for a_{tiss} (in sec/m) are in Table
4.2; the value for diamond was estimated from the acoustic line discussion
in Section 7.2.5.3. Assuming <10 KHz bronchial
turbulence noise of initial amplitude A_{0} = 4 x 10^{-5} atm,
A_{x} ~ 3.7 x 10^{5} atm through 1 meter of typical soft tissue;
A_{x} ~ 3.4 x 10^{-5} atm even if 0.1 meter of bone is interposed
in the acoustic path. Either A_{x} is reliably detected from anywhere
in the body using a >(210 nm)^{3} pressure sensor (Eqn
4.29).

* Most medical ultrasound textbooks assume
a ~n dependency of attenuation in soft tissues; apparently,
the actual dependency is ~n^{1.1}.^{730}

Last updated on 17 February 2003