An integral is a mathematical object that can be interpreted as an area or a generalization of an area. A number computed by a limiting process in which the domain of a function, often an interval or planar region, is divided into arbitrarily small units, the value of the function at a point in each unit is multiplied by the linear or areal measurement of that unit, and all such products are summed (summation in the limit). In ultrasound imaging for example this mathematical function is used in the fast Fourier transformation.

(I) The intensity of a wave is the rate of power through a unit region perpendicular to the direction of propagation. The unit of intensity is watts per square meter (W/cm2).

Interference is the interplay of two or more waveforms. When two or more waves with equal frequency and wavelength interfere, a new wave is created whose amplitude at any point in time and space is the sum of the amplitudes of the original waves at the same point in time and space. Constructive interference occurs when two waves of equal frequency are in phase. The amplitudes will always be in the same direction, and the waves will combine to produce a stronger one. Two equally strong waves with the same amplitude that are 180° out of phase will cancel each other out.

See also Interference Artifact.

Interference artifacts occur if decreasing of the echo amplitude is not exponential with penetration depth caused by inhomogeneous tissue layers and fluid or air-filled regions. If ultrasound waves have opposite phases, i.e. if the phase difference is 180°, their amplitudes will always be in opposite directions and their sum is a weaker wave. This is destructive interference and artifacts occur.

Contrast microbubbles can be destroyed by intense ultrasound and the scattered signal level can increase abruptly for a short time during microbubble destruction, resulting in an acoustical flash (sudden increase in echogenicity).
Intermittent imaging with high acoustic output utilizes the properties of contrast microbubbles to improve blood-to-tissue image contrast by imaging intermittently at very low frame rates.
The frame rate is usually reduced to about one frame per second, or it is synchronized with cardiac cycles so that enough contrast microbubbles can flow into the imaging site where most microbubbles have been destroyed by the previous acoustic pulse. Because bubbles are destroyed by ultrasound, controlling the delay time between frames produces images whose contrast emphasizes regions with rapid blood flow rate or regions with high or low blood volume.