Ultrasound Physics: Chapter 1-3 PDF

Ultrasound Physics  The Basics Chapter 1 Physics: The Basics  Graphs ◦ 2 axes  Horizontal axis, x-axis; runs side to side  Vertical axis, y-axis; runs up & down  Applying Graphs to Ultrasound This is a spectral Doppler tracing that is used to measure blood velo...

Ultrasound Physics  The Basics Chapter 1 Physics: The Basics  Graphs ◦ 2 axes  Horizontal axis, x-axis; runs side to side  Vertical axis, y-axis; runs up & down  Applying Graphs to Ultrasound This is a spectral Doppler tracing that is used to measure blood velocity. In this case: The x axis is time The Y axis represents velocity of blood  In m-mode ultrasound the x-axis represents time and the y axis represents the depth of reflectors M-mode is used to take fetal heart rate and is used in echocardiography Relationships In ultrasound physics, we often describe the relationships between two different parameters or variables. Two items are related or proportional when they are associated with each other such that when one changes, the other will also change in some way. No relationship or unrelated Two items that are not associated or have no bearing upon each other. Examples: Hair color is unrelated to intelligence Your income is unrelated to your eye color. Direct Relationships Two items are associated in a way that when one increases the other increases. When one decreases the other decreases. When one increases the other increases. Examples: Clothing size is directly proportional to the age of a child (older child/larger child) The age of a tree and its size are directly related  Indirect/Inverse Relationships Two items are associated with each other such that when one increases the other decreases. When one decreases the other increases. When one increases the other decreases. Examples: Golf scores are inversely related to skills A car’s gas mileage is indirectly proportional to its size Reciprocal Relationships A type of inverse relationship When two numbers are multiplied together the result is one. (1) Reciprocal Relationships When one increases the other proportionally decreases. Examples of reciprocals: 2 and ½ are reciprocals 1 and 1/10th are reciprocals 1/100,000th and 100,000 are reciprocals Reciprocals cont. Reciprocal relationships: if one factor changes the other changes proportionally So… If factor A is doubled, factor B will be halved If factor A is tripled, factor B will be 1/3 what it was If factor B is quartered, factor A will quadruple Let’s Practice Factor A and B are reciprocals. Factor A increases 8 times. What happens to factor B? Factors C and D are reciprocals. Factor D is doubled. What will happen to factor C? Units and Presentation All numerical values must have units Units give the numerical value meaning. Example: You state that you are 6 tall. You must give a unit to define 6 “what?” tall You could be stating that you are six inches tall or six feet, six miles etc.  Units and Presentation Unless a number is a percentage or it is directly stated that it is a “unitless” number, you MUST use units to define your number. You can use any unit that is technically correct. You can measure a mile in inches, you wouldn’t usually, but it would still be technically correct. 1 mile=63,360 inches You can measure your height in miles and it would still be technically correct!  Scientific Notation Scientific notation is used to define the numbers of a measurement that are in each unit. Very large or very small numbers are often expressed in scientific notation. This is a shorthand way to express these numbers. Example: 0.000000124 =1.24 x 10-7 1,000,000 = 1.0 x 106 Count the zeros! You can use scientific notation in converting units but there is an easier way! Using the Metric System In science, we use the metric system to express measurements. For Ultrasound and specifically for the physics registry, we MUST understand how to convert numbers within the metric system. Using the Metric System Mega (M) 106 = 1,000,000 kilo (k) 103 = 1,000 hecto (h) 102 = 100 deka (da) 101 = 10 no prefix 100 deci (d) 10-1 = 0.1 centi (c) 10-2 = 0.01 milli (m) 10-3 = 0.001 micro (µ) 10-6 = 0.000,001 Metric Units & Converting To remember the prefixes in order, you can use the following sentence: King Henry Doesn't [Usually] Drink Chocolate Milk kilo- hecto- deka- [unit] deci- centi- milli- Unit is meters, Hertz, Grams, Liters etc. Converting with Metrics (the easy way) Create a number line. M k h da d c m m 6_5 _4 _ 3_ 2_ 1_ 0 _-1 _-2 _-3 _ -4_-5_ -6 Figure out how many spaces are between the prefix that you have and the prefix that you need.  Converting with Metrics 8 m = ___ mm m = 100 mm= 10-3 Ask how many spaces are between meters (100) and mm (10-3) M k h da d c m m 6_5 _4 _ 3_ 2_ 1_ 0 _-1 _-2 _-3 _ -4_-5_ -6 3 spaces  our number is going to be moving towards the smaller prefixes. So we move the decimal to the right.  Converting with Metrics 5000 mHz = ___ kHz mHz = 10-3 kHz = 103 M k h da d c m m 6_5 _4 _ 3_ 2_ 1_ 0 _-1 _-2 _-3 _ -4_-5_ -6 6 spaces between the mHz and kHz We are going to a larger prefix so we move to the left! 5000.  0.0.0.5.0.0.0. 0.005 km in 5000 mm Converting with Metrics 0.003 km = ___ cm km= 103 cm= 10-2 M k h da d c m m 6_5 _4 _ 3_ 2_ 1_ 0 _-1 _-2 _-3 _ -4_-5_ -6 5 spaces between km and cm we are going to a smaller prefix so we move to the right  move the decimal point 5 spaces to the right 0.0.0.3.0.0. 300 cm 0.003 km = 300 cm  Lets practice a few of these! 5000 cL = _____________ L 8 cm = ____________ mm 0.002 m = ____________mm 0.05 ks = ____________ s 70000 cHz = ____________ MHz  Did you get them all?  5000 cL = 50 L  8 cm = 80 mm  0.002 m = 2 mm  0.05 ks = 50 s  70000 cHz = 0.0007 MHz Chapter 2: SOUND Waves waves carry energy from place to place. Many different types of waves exist: light, sound, heat, magnetic etc. Sound Sound is: a type of wave that carries ENERGY from place to place Sound does not carry matter or particles it only carries energy  Sound pulses travel through media and return to our machine to create an image Our machine creates images by sending short bursts of sound into the body Properties of Sound Sound MUST travel through a medium cannot travel through a vacuum Sound travels in a straight line Sound will travel in a straight line until it encounters something that will change the direction of the sound wave (like bumping into a wall) Sound waves are also called “acoustic waves” Types of Waves Transverse wave-particles move or vibrate in a perpendicular direction to the direction of the wave If the wave is moving right to left, the particles move up and down If the wave is moving toward toward the sky, the particles would move side to side. Waves Longitudinal wave- particles move or vibrate in the same direction as the wave If the wave moves right to left, the particles move right to left If the wave moves toward the sky, the particles move toward the sky then back towards the ground. Waves Mechanical wave - particles of a medium move (vibrate back and forth)  http://www.youtube.com/watch?v=Rbuhdo0AZ DU Know this! Sound is a mechanical, longitudinal wave  Sound waves are comprised of compressions and rarefactions Rarefactions-regions of lower particle density and lower pressure Compressions-regions of higher particle density and higher pressure  In physics we will diagram sound waves. While in reality, the wave actually looks like the image on the previous slide, we will diagram waves using a much simpler format.  Instead of looking at movement of energy through particles, we create a wave with peaks and troughs. The peaks are the compressions (or areas of high pressure and particle density) The troughs are the rarefactions (or low areas of pressure and density)  A “cycle” is one compression and one rarefaction or one peak and one trough. Acoustic Variables When a sound wave travels, certain properties or aspects of the particles in a medium will change. These changes are known as acoustic variables. Sound waves are identified by changes in acoustic variables. When one of these variables changes, we know that a sound wave is present.  The 3 acoustic variables are: Pressure density distance (particle motion) Acoustic Variables Pressure: concentration of force in an area Density: concentration of mass in a volume Distance: measure of particle motion When these change, we know that a sound wave is present. Acoustic Parameters After we are aware that a wave is a sound wave, it is important to describe its features and characteristics. 7 Acoustic parameters are used to describe sound waves: Period Frequency Amplitude Power Intensity Wavelength Propagation speed More on this in Chapter 3 The Acoustic Parameters Period - The time required to complete a single cycle-can also be described as the time from the start of a cycle to the start of the next cycle  Frequency - The number of cycles that occur in one second  Wavelength – the length or distance of a single cycle  Propagation Speed - the rate that sound travels through a medium. The Acoustic Parameters Power - the rate of energy transfer  Intensity – the concentration of energy in a sound beam  Amplitude - the difference between the average value and the maximum value of an acoustic variable Phase Relationships Waves can be either in phase or out of phase. In phase waves – waves that are synchronized. They peak at the same time. Out of phase waves- waves that are not synchronized. When one wave is at its peak, the other wave is at its trough or lowest point. Phase Relationships In Phase Out of Phase Phase Relationships Interference-when two waves overlap at the same location at the same time, they will combine to form one wave Constructive interference - occurs when the amplitude or size of the new wave is greater than the original wave Destructive interference - occurs when the amplitude or size of the new wave is less than that of the original waves Interference Waves of Different Frequencies Frequency – how often cycles occur in a wave When two waves with different frequencies interfere, at some moments the interference is constructive and at other moments the interference is destructive! So… When the frequencies of the waves differ, destructive and constructive interference occur!  Physics: Sound Biologic Effects/Bioeffects: pg. 11 The effects of the sound wave upon biologic tissue through which it passes. Acoustic Propagation Properties: The effects of the medium upon the sound wave.  Chapter 3: Describing Sound Waves  Acoustic Parameters describe the features of a sound wave. There are 7 parameters that we use to completely characterize a wave.  You must know the units for each parameter understand how the parameters are related to one another Whether or not we can change the parameter Sound source vs. Medium If you know whether a parameter is determined by the sound source or the medium, you can understand how the parameter relates to ultrasound physics. The sound source The ultrasound system and transducer. The quantity or level of some parameters is established by the ultrasound system. Some of these levels can be changed by turning a knob on the machine, others cannot. The medium The medium or material through which the sound travels In the case of diagnostic medical sonography, the medium is soft tissue. The speed of sound in soft tissue is 1540 m/s. This can also be expressed as 1.54 mm/µs and 1.54 km/s  It is important to understand whether you have the ability to change the value of a parameter while using a single transducer. We should also know the typical values of a parameter as it applies to diagnostic medical sonography. Describing Sound Waves Acoustic variables inform us which waves are sound waves  Acoustic parameters describe the features of a sound wave 3 Acoustic Variables Acoustic variables identify certain waves as sound waves-when an acoustic variable changes in time, a sound wave is present Pressure- concentration of force within an area (Pascals) Density-concentration of mass within a volume (kg/cm cubed) Distance-measure of particle motion (units of distance: feet, cm, miles) Describing sound waves Just as you may describe yourself as 5 feet, 5 inches tall, 150 lbs etc. you must also describe similar features of a sound wave. Parameters that describe sound waves Period Frequency Amplitude Power Intensity Speed Wavelength Period The time required to complete a single cycle can also be described as the time from the start of a cycle to the start of the next cycle Period Example: the cycle of the earth circling the sun is 365 days Units of time Typical values for ultrasound 0.1-.05 microseconds Determined by the sound source Can it be changed by the sonographer- no Period Period Which strip below has a longer period for each cycle? Frequency The number of events that occur in a duration of time Example: what is the frequency of your birthday? In ultrasound, frequency is the number of cycles that occur in one second Frequency Measured in hertz (cycles/second) Determined by the sound source Cannot be changed by the sonographer Frequency affects penetration and image quality Frequency One Cycle Cycle 1 – Cycle 2 - 1 second  Frequency The frequency of sound determines whether it is ultrasound, audible sound or infrasound Ultrasound-frequency exceeds 20,000 Hz or 20 kHz Audible sound is between 20 Hz and 20,000 Hz Infrasound is less that 20 Hz and is not audible  Physics: Describing Sound Waves Frequency Frequency Typical Ultrasound Values 2 MHz to 10Mhz What is the frequency of each strip if the time is 1 sec? What is the frequency of each strip if the time is 2 sec? What is the frequency of each strip if the time is 0.5 sec? The relationship between Frequency and Period Period and frequency have an inversere relationship. More specifically, they are reciprocals As frequency increases, period will decrease proportionally As period increase, frequency will decrease proportionally If period does not change, frequency does not change Remember Reciprocals What is the reciprocal of ½? What is the reciprocal of 0.5? What is the reciprocal of 2? What is the reciprocal of 3? What is the reciprocal of 0.25?  Since frequency and period are reciprocals what happens to each parameter in these situations? If frequency is doubled, period is ____. If period is doubled, frequency is ____. If period is tripled, frequency is ____. If frequency is quartered, period is ____. Frequency Frequency x period = 1  Remember: If a wave takes longer to complete, we must have fewer waves per second. If a wave completes a cycle more quickly, we will have more waves completed in each second. Which frequency is highest (each take place in 1 second)? A B C D Which frequency is lowest (each take place in 1 second)? A B C D  FREQUENCY (f) Formula: Frequency (MHz) = propagation speed (mm/µs) wavelength (mm) In soft tissue, what is the frequency of a wavelength measuring 1 mm?  FREQUENCY ANSWER: 1.54 MHz The “Bigness” Parameters Tell us how big or how strong a wave is Amplitude Power Intensity The “Bigness” Parameters: Amplitude Amplitude – the difference between the average value and the maximum or minimum value of an acoustic variable The “bigness” or height of a wave Amplitude Units are those of the acoustic variables (pressure - Pascals, density - cubic cm, particle motion) Typical values: 1MPa to 3 MPa (MegaPascals) Determined by sound source CAN be changed by the sonographer Amplitude decreases as sound propagates through the body Amplitude Displacement from the average Amplitude Amplitude Displacement from the average Peak to peak amplitude – the difference between the minimum amplitude and the maximum amplitude. Peak to peak amplitude The “Bigness” Parameters – Power Power-the rate of energy transfer Units are watts (W) Determined by the sound source Typical values: 0.004 – 0.09 watts (4- 90milliwatts) Power decreases as sound propagates through the body Power Power is proportional to the amplitude of the wave squared Power  amplitude2 With this equation: we will always calculate power when given an amplitude. Example A sonographer increases the amplitude of a wave by a factor of 3. How has the power changed? Remember our equation: Power  amplitude2 Simply plug in the change in amplitude. In this case it was increased by a factor of 3. Power  32 32 =3x3 SO Power would increase by 9! Example Example: The sonographer decreases the amplitude by ½. What is the change in power? Remember our equation: Power  amplitude2 Simply plug in the change in amplitude. Power  1/22 ½ x ½ = ¼ Power is ¼ of what it was. Your turn! Example: The sonographer decreases the amplitude by 1/5. What is the change in power? The sonographer doubles the amplitude. What is the change in power? The “Bigness” Parameters - Intensity Intensity - the concentration of energy in a sound beam Describes the bigness of a wave Relates to how the power in a beam is distributed in space. Intensity depends on the amount of power in a beam and the area of which the power is applied. Intensity Intensity(watts/cm2) Watts = power cm2 = beam area Intensity = power(watts)÷beam area (cm2) Determined by sound source Can be changed by the sonographer (since power can be changed so can intensity) Typical ultrasound values- 0.001-100watts/cm2  INTENSITY Sunlight does not normally ignite a fire When sunlight is focused, intensity increases, and ignition can occur How is intensity related to power and amplitude? Intensity is proportional to power So…if power is doubled, intensity is doubled If power is quartered, intensity is quartered If power proportional to intensity, what do we know about the relationship between intensity and amplitude? The reasoning behind it: If power  amplitude2 And… Power  intensity then… Intensity  amplitude2 Other Intensity related math Often you will be asked how intensity changes when another variable changes. Example: Power is doubled and beam area remains unchanged. How will intensity change?  Solve it: Power is doubled and beam area remains unchanged. How will intensity change? First, you will use the equation for intensity: Next, plug in the changes to the equation. Doubled = 2 Unchanged = 1 Halved = ½ So…. Intensity = and therefore intensity is doubled Lets try another: The power of a wave is doubled. If intensity remains the same, what must happen to beam area? Intensity = power/beam area In this case intensity =1, power =2 and beam area is unknown… 1= Beam area x 1 =2 Beam area = 2, so the beam area is doubled! Your Turn Power of a wave is quadrupled. The intensity is halved. What must happen to beam area? Wavelength The length or distance of a single complete cycle. Wavelength Units: meters or any unity of length Determined by sound source and medium through which it travels Cannot be changed by the sonographer Typical ultrasound values-0.1-0.8 mm (in soft tissue) Wavelength is the ONLY parameter determined by the source and medium Wavelength Wavelength - Which strip has cycles with the longer wavelength? Wavelength Wavelength is the only parameter determined by the source and the medium! The relationship between wavelength and frequency Wavelength and frequency are inversely related. As wavelength increases, frequency decreases. As wavelength decreases, frequency increases.  Higher frequency = shorter wavelength Lower frequency = longer wavelength The wavelength equation: propagation speed mm/ms l= __________________________ frequency (MHz) ( l is the symbol for wavelength, remember it because it looks like a wave!) Use your triangle trick here too!  When using the wavelength equation we have to make sure our units match the units in the equation. Wavelength should be in mm Propagation speed should be in mm/ms Frequency should be in MHz If you are given a value that is not in this format you have to convert! Ex: if frequency is in Hertz you have to convert to megahertz!  Physics: Describing Sound Waves Wavelength & Frequency  Inversely related (as long as the wave remains in one medium) As frequency increases, wavelength decreases. Ex: If a wave’s frequency is twice that of another, the wavelength will be half.  Physics: Describing Sound Waves Wavelength in Soft Tissue  In soft tissue, sound with a frequency of 1MHz has a wavelength of 1.54 mm.  Relationship between frequency & sound in soft tissue: Divide 1.54mm by the frequency in MHz.  wavelength = 1.54 mm/µs frequency (MHz) Shorter wavelength sound = higher resolution  WAVELENGTH (L) Formula: Wavelength (mm) = Propagation speed (mm/µs) Frequency (MHz)  WAVELENGTH What is the wavelength of a 10MHz transducer traveling through soft tissue? λ= = 0.154 mm With a constant propagation speed If wavelength increases, frequency decreases (inversely proportional). REFER TO PAGE 41 FOR EXAMPLES OF FREQUENCY AND WAVELENGTH  What is the wavelength of a sound wave with a frequency of 2 MHz in soft tissue?  l = = 0.77 l = 0.77 mm Important! In order to use 1.54 mm/ms as your speed of sound you must be informed that the medium is soft tissue!! If you are not provided with a speed of sound, and it is not indicated that your medium is soft tissue, you do not have enough information to solve the problem. If you are provided with a speed of sound, and frequency, simply ‘plug’ it into the equation. Why do we care about wavelength? Wavelength is important in image quality. Shorter wavelength sound produces higher quality images with greater detail. This is why high frequency transducers provide better resolution because high frequency is associated with shorter wavelength. Propagation Speed The rate that sound travels through a medium The distance that sound travels in 1 second Calculating propagation speed (2 ways) If you are given frequency and wavelength you can calculate propagation speed by using the wavelength equation You may also be asked to calculate propagation speed using distance traveled and time that it took.  Example: A sound wave travels 10 cm in 2 seconds. What is the propagation speed in this medium? Divide the distance by the time 10cm/2sec = 5 cm/sec (the units carry over!) Speed Units: meters per second or mm/ms Determined by: medium only All sound will travel through any given medium at the same speed regardless of frequency or any other parameter value. Equation for Propagation Speed Propagation Speed = frequency x wavelength Why? Wavelength is determined by the sound source and the medium. By knowing wavelength, and initial frequency of the sound, we can calculate propagation speed! What is interesting about this equation? it is the same equation that is used to calculate wavelength! It is Just arranged in a different way. Properties of Medium and Speed Speed of sound is related to stiffness and density of a medium Stiffness a medium’s ability to be moved Density related to a medium’s weight how closely packed the molecules in that medium are  Stiffness and Speed-directly related Density and Speed-indirectly related Stiffness has more of an impact on speed than density Bulk modulus is the same as stiffness General Rules Sound travels the fastest in a medium that is low density and high stiffness Sound travels slowest in a medium that is very dense and not very stiff. Speed of sound in various types of tissues/media Gas has the slowest speed of sound, liquid is in the middle, and solids have the fastest speed of sound. General rule: gas