BASC PHYSICS OF ULTRASOUND: INTENSITY OF ULTRASOUND

To understand the meaning of intensity, we recall that an oscillating source of ultrasound in contact with tissue transfers its mechanical energy to the particles of the tissue medium, causing them to vibrate. The medium particles then possess energy by virtue of their motion. Intensity is a measure of this energy. It represents the vigour of mechanical vibrations of the medium particles. Different physical parameters may be used to express this vigour. These include particle displacement, particle velocity, particle acceleration, and particle pressure. Each of these parameters varies in time and in space within the medium, and so does the intensity. Intensity may be expressed either as an absolute measurement, or using a relative scale.?

ABSOLUTE MEASURE OF INTENSITY

On the absolute scale, intensity is expressed as the rate of flow or energy per unit area. Definition: The intensity of a beam of ultrasound at a point is the amount of energy passing through unit cross-sectional area perpendicularly to the beam per unit time at that point. Units: The following units are commonly used to specify absolute intensities in clinical ultrasound.

Joule (J) for energy, Seconds (s) for time Square centimetre (cm2 ) for area.??

Using these units, intensity is expressed in joules/second/square centimetre. joule/second represents the rate of flow of energy and is given the special name watt.

1 watt (W) = 1 J/s

Therefore intensity can be specified as watts/square centimetre (W /cm2 )

The power in a beam of ultrasound is the total energy passing over the whole cross-sectional area of the beam per unit time. If the intensity is uniform over the plane of interest, then

Power = intensity (W /cm2 ) x area (cm2?)

When the intensity is not uniform, then the spatial variations within the beam must be taken into account.?

The units of power are joules/second, or watts.

Knowledge of the absolute intensity of ultrasound is required for two reasons.

(i) the output intensity of an ultrasound instrument affects its sensitivity, and hence signal Sizes.

(ii) when one wish to assess the potential biological consequences of exposure to ultrasonic energy, one must have knowledge of the amounts of energy actually dissipated in tissue.

It is common for manufacturers to provide information on the output powers of ultrasound instruments. However, the time variations of intensity complicate the power specification. In particular, the temporal differences between pulsed wave and continuous wave applications makes it necessary to quote different quantities such as the peak power and the time averaged power. For example, the peak power for a pulsed wave instrument could be as high as a thousand times the time averaged power. Fortunately, the peak power is applied over very short durations during the total exposure.?

RELATIVE INTENSITY?

On the relative scale, the intensity at a point of interest is compared to that at some defined reference point, and expressed in units called decibels (dB).

Definition: The intensity, I, relative to a reference intensity I0, is defined as:??

Relative intensity (dB) = 10log10 (I/I0)?

The dB values will be positive if the intensity of interest, I, is larger than the reference intensity, I0, and negative if I is less than I0. The choice of the reference intensity is arbitrary, but must be defined. For example, I could be the intensity at some point of interest in tissue, and I0 the intensity on the skin surface.?

The logarithmic scale used in the definition has the inherent mathematical characteristic of compressing the intensity scale such that a very wide range of intensities on the absolute scale can be accommodated on a much smaller range on the dB scale.?

The dB notation is useful practically because the levels of intensity used in diagnostic imaging are very low and therefore difficult to measure absolutely. The determination of the ratio of one intensity relative to another is easier, since neither of the two has to be measured absolutely.?

THE 3dB CHANGE

A change of relative intensity by 3 dB is of special significance. For every 3 dB change, there is a change in absolute intensity by a factor of two.

For those who are familiar with logarithms, consideration of the following special cases will make this clear.

By definition, intensity in dB = 10 log 10 (I/I0)

case 1: Intensity at point of interest equals the reference intensity.?

When I = 10, decibel level = 10 loglO (I)?

= l0x0 dB?

= 0 dB?

The decibel level at the reference point is equal to zero.?

Case 2: Intensity at point of interest equals half the reference intensity.

When I = 1/2I0, decibel level = 10log10 (0.5)?

= 10 x (-0.301) dB?

= - 3.01 dB

Reducing the intensity to a half corresponds to a 3 dB reduction in relative intensity.?

Case 3. Intensity at point of interest equals twice the reference intensity.??

When I = 2 I0, decibel level = 10log10 (2)

= 10 x (+ 3.01) dB

= + 3.01 dB?

Doubling the intensity corresponds to a 3 dB increase in relative intensity.??

These calculations illustrate that a change in intensity by a factor of 2, be it an increase or a decrease, results in a corresponding change of 3 dB on the relative scale. In the previous article, the HVT of a beam of ultrasound was defined. It can now be inferred that every HVT in a medium reduces the relative intensity by 3 dB.?

Table 1 represents data that show this relationship:

The reference level in these data has been arbitrarily assigned the absolute intensity value of 1,600 mW/cm2 . Note the compressing effect of the logarithmic dB scale, a thousand-fold reduction in absolute intensity from 1,600 mW/cm2 to 1.6 mW/cm2 corresponds to a dynamic range of only 30 dB on the relative scale. Any other choice of reference intensity, in place of the 1,600 mW/cm2 , would give the same result.?