Intensity of Pulsed Waves chapter 5

Definition and Understanding of Intensity

Intensity is defined as the beam's power divided by its area. This metric is crucial in various applications, including ultrasound and other fields that utilize wave propagation and measurement.

Key Relations to Intensity of Pulsed Waves

1. Spatial Distance

  • Spatial Intensity Variations: The intensity of the ultrasound (US) beam does not remain constant at different locations in space. This variation is primarily due to the geometrical spreading of the beam.

    • Peak Intensity (Isp): This is the maximum value of intensity measured at a specific point in space within the beam.

    • Average Intensity (Isa): This denotes the mean intensity averaged over the entire cross-sectional area of the beam. It is essential to note that the peak intensity is always greater than the average intensity because it reflects the maximum concentration of energy at that location.

2. Temporal Considerations

  • Temporal Variability: The ultrasound beam does not maintain a steady intensity throughout the duration of the pulse.

    • Temporal Peak Intensity (Lip): This represents the intensity at the instant when the ultrasound beam reaches its maximum value.

    • Average Intensity During Most Intense Half-Cycle (Imax): This reflects the average intensity within the peak half of the pulse duration.

    • Pulse Average Intensity (Ipa): This is the average intensity during the entire pulse duration when the ultrasound is transmitting.

    • Temporal Average Intensity (Ita): This is averaged over the entire pulse repetition period, including both transmitted and received signals.

    • Hierarchical Intensity Values: From highest to lowest, the temporal intensities can be arranged in the following order: $Ip > I{max} > I{pa} > I{ta}$.

Combining Spatial and Temporal Factors

  • When describing the intensity of sound, we must consider both spatial and temporal factors:

    • Isptp: Measured at the location where intensity is maximized at the moment the most powerful part of the pulse passes. It reflects the peak intensity at a spatial location at a given instant.

    • Ispp: This designation is measured at the location where intensity peaks, averaged over the transmit time.

    • Ispta: Represents intensity measured at maximum, averaged over all time (including both transmit and receive periods).

    • Isata: Indicates the average intensity measured over the entire cross-section of the sound beam, averaged over all time.

Definition and Understanding of Intensity Intensity is defined as the beam's power divided by its area. This metric is crucial in various applications, including ultrasound and other fields that utilize wave propagation and measurement.

Key Relations to Intensity of Pulsed Waves

  1. Spatial Distance

    • Spatial Intensity Variations: The intensity of the ultrasound (US) beam does not remain constant at different locations in space. This variation is primarily due to the geometrical spreading of the beam.

    • Peak Intensity (I_{sp}): This is the maximum value of intensity measured at a specific point in space within the beam.

    • Average Intensity (I_{sa}): This denotes the mean intensity averaged over the entire cross-sectional area of the beam. It is essential to note that the peak intensity is always greater than the average intensity because it reflects the maximum concentration of energy at that location.

  2. Temporal Considerations

    • Temporal Variability: The ultrasound beam does not maintain a steady intensity throughout the duration of the pulse.

    • Temporal Peak Intensity (I_{tp}): This represents the intensity at the instant when the ultrasound beam reaches its maximum value.

    • Average Intensity During Most Intense Half-Cycle (I{max} or I{m}): This reflects the average intensity within the peak half of the pulse duration.

    • Pulse Average Intensity (I_{pa}): This is the average intensity during the entire pulse duration when the ultrasound is transmitting.

    • Temporal Average Intensity (I_{ta}): This is averaged over the entire pulse repetition period, including both transmitted and received signals.

    • Hierarchical Intensity Values: From highest to lowest, the temporal intensities can be arranged in the following order.

Combining Spatial and Temporal Factors

When describing the intensity of sound, we must consider both spatial and temporal factors:

  • I_{sptp}: Measured at the location where intensity is maximized at the moment the most powerful part of the pulse passes. It reflects the peak intensity at a spatial location at a given instant.

  • I_{sppa}: This designation is measured at the location where intensity peaks, averaged over the transmit time (pulse duration).

  • I_{spta}: Represents intensity measured at maximum, averaged over all time pulses (including both transmit and receive periods). This is the most relevant intensity regarding tissue heating and bioeffects.

  • I_{sata}: Indicates the average intensity measured over the entire cross-section of the sound beam, averaged over all time.

The "10 Commandments" of Intensity in Ultrasound

  1. Intensities may be reported in various ways with respect to time and space.

  2. The different measurements of intensity are important in the study of bioeffects. I_{spta} is the most relevant intensity with respect to tissue heating.

  3. The units for all intensities are Watts per square centimeter (W/cm^2).

  4. Because peak intensity is higher than average intensity, I{sptp} has the highest value, and I{sata} has the lowest value.

  5. A number called the Beam Uniformity Coefficient (also called SP/SA factor) describes the spread of a beam in space. The SP/SA factor is unitless, with a value of 1 or greater.

  6. The Duty Factor describes the relationship of beam intensities with respect to time. The duty factor is a unitless number with a value between 0 and 1.

  7. For continuous wave (CW) ultrasound, the beam is always "on." Therefore, the pulse average and temporal average intensities are the same. Specifically, I{spta} = I{sppa} and I{sata} = I{sapa}.

  8. When pulsed and continuous wave beams have the same SPTP intensities, the continuous wave beam has the higher SPTA intensity.

  9. When pulsed and continuous wave beams have the same SATP intensities, the continuous wave beam has the higher SATA intensity.

  10. Temporal and Spatial Considerations:

    • Temporal Considerations: Includes I{tp} (Temporal Peak), I{m} (Maximum), I{pa} (Pulse Average), and I{ta} (Temporal Average).

    • Spatial Considerations: Includes I{sp} (Spatial Peak) and I{sa} (Spatial Average).