Basic Math Concepts for Ultrasound Physics

Graphs

• Graphs are used to display data on an ultrasound machine.
• Graphs may display numeric data or qualitative data.
• Doppler data and M-Mode data are displayed on graphs.

Axes

• Lines that provide context.
  • Horizontal axis (X)
    • Runs side to side.
    • X axis represents time.
  • Vertical axis (Y)
    • Runs up and down.
    • Y axis may represent amplitude, speed, velocity.

Relational Terms

• UNRELATED
  • The items are not associated at all.
  • There is no relationship.
• RELATED
  • The items are associated.
  • The relationship is not specific.

Relational Terms Continued

• DIRECTLY RELATED/ DIRECTLY PROPORTIONAL
  • When one increases, the other increases.
  • When one decreases, the other decreases.
  • Graph extends from lower left to upper right.
• INVERSELY RELATED/ INVERSELY PROPORTIONAL
  • When one increases, the other decreases.
  • Graph extends from upper left to lower right.

Reciprocals

• Two numbers that are multiplied together equal 1.
• Type of inverse relationship.
  • When one increases the other decreases.
  • Example: 2 and 1/2

Units/ Unit Conversions

• Numbers must have units for context.
• A lone number is ambiguous.
• In ultrasound, we will work with units of:
  • Distance: cm, and mm.
  • Velocity: meters per second.
  • Volume: cm^3
  • Area: cm^2
• At times we may convert units such as CM to meters.

Powers of Ten

• Represents very large or very small numbers.
• Scientific or engineering notation.
• Positive exponent has value greater than 10.
• Negative exponent has value less than 1.
• Exponent of zero has a value between 1 and 10.
• To calculate, shift decimal point so number is between 1 and 10.
• Multiple by the appropriate power of ten.