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More on image quality or resolution.  We have touched upon axial resolution (ability to differentiate objects that are located along the imaging beam axis) when we discussed spatial pulse length.  The smaller the axial resolution length, the better the system is and it can resolve structures that are closer together.  Thus the shorter the pulse length, the better picture quality.  Current transducers are designed with the minimum number of cycle per pulse to optimize image quality. The primary determinant of axial resolution is the transducer frequency.  Axial resolution (mm) = 0.77 x # cycles / frequency (MHz).  One must remember that attenuation is also dependent on the transducer frequency, thus a tradeoff must be reached.  Lateral resolution is the minimum distance that can be imaged between two objects that are located side to side or perpendicular to the beam axis.  Again, the smaller the number the more accurate is the image.  Since the beam diameter varies with depth, the lateral resolution will vary with depth as well.  The lateral resolution is best at the beam focus (near zone length) as will discuss later when will talk about the transducers.  Lateral resolution is usually worse than axial resolution because the pulse length is usually smaller compared to the pulse width.  Temporal resolution implies how fast the frame rate is. FR = 77000/(# cycles/sector x depth).  Thus frame rate is limited by the frequency of ultrasound and the imaging depth.  The larger the depth, the slower the FR is and worse temporal resolution.  The higher the frequency is, the higher is the FR and the temporal resolution improves.  Sonographer can do several things to improve the temporal resolution: images at shallow depth, decrease the #cycles by using multifocusing, decrease the sector size, lower the line density.  However one can realize quickly that some of these manipulations will degrade image quality.  And this is in fact correct: improving temporal resolution often degrades image quality.  M-mode is still the highest temporal resolution modality within ultrasound imaging to date.   
More on image quality or resolution.  We have touched upon axial resolution (ability to differentiate objects that are located along the imaging beam axis) when we discussed spatial pulse length.  The smaller the axial resolution length, the better the system is and it can resolve structures that are closer together.  Thus the shorter the pulse length, the better picture quality.  Current transducers are designed with the minimum number of cycle per pulse to optimize image quality. The primary determinant of axial resolution is the transducer frequency.  Axial resolution (mm) = 0.77 x # cycles / frequency (MHz).  One must remember that attenuation is also dependent on the transducer frequency, thus a tradeoff must be reached.   
 
[[File:PhysicsUltrasound_Fig20.svg|thumb|left|300px| Fig. 20]]
{{clr}}
 
Lateral resolution is the minimum distance that can be imaged between two objects that are located side to side or perpendicular to the beam axis.  Again, the smaller the number the more accurate is the image.  Since the beam diameter varies with depth, the lateral resolution will vary with depth as well.  The lateral resolution is best at the beam focus (near zone length) as will discuss later when will talk about the transducers.  Lateral resolution is usually worse than axial resolution because the pulse length is usually smaller compared to the pulse width.   
 
[[File:PhysicsUltrasound_Fig21.svg|thumb|left|300px| Fig. 21]]
{{clr}}
 
 
Temporal resolution implies how fast the frame rate is. FR = 77000/(# cycles/sector x depth).  Thus frame rate is limited by the frequency of ultrasound and the imaging depth.  The larger the depth, the slower the FR is and worse temporal resolution.  The higher the frequency is, the higher is the FR and the temporal resolution improves.  Sonographer can do several things to improve the temporal resolution: images at shallow depth, decrease the #cycles by using multifocusing, decrease the sector size, lower the line density.  However one can realize quickly that some of these manipulations will degrade image quality.  And this is in fact correct: improving temporal resolution often degrades image quality.  M-mode is still the highest temporal resolution modality within ultrasound imaging to date.   
 
Before we talk about '''Doppler Effect''', let us discuss the ultrasound transducer architecture and function.  The current transducers became available after the discovery that some materials can change shape very quickly or vibrate with the application of direct current.  As important is the fact that these materials can in turn produce electricity as they change shape from an external energy input (i.e., from the reflected ultrasound beam).  This effect of vibration form an application of alternative current is called a piezoelectric effect (PZT). 
 
[[File:PhysicsUltrasound_Fig22.svg|thumb|left|350px| Fig. 22]]
{{clr}}
 
Many materials exist in nature that exhibit piezoelectric effect.  Ccommercial transducers employ ceramics like barium titanate or lead zirconate titanate.  The transducer usually consists of many PZT crystals that are arranged next to each other and are connected electronically.  The frequency of the transducer depends on the thickness of these crystals, in medical imaging it ranges 2-8 MHz.  An ultrasound pulse is created by applying alternative current to these crystals for a short time period.  Afterwards, the system “listens” and generates voltage from the crystal vibrations that come from the returning ultrasound.  An important part of the transducer is the backing material that is placed behind the PZT, it is designed to maximally shorten the time the PZT crystal vibrates after the current input is gone also known as ringing response.  By decreasing the ringdown time, one decreases the pulse length and improves the axial resolution.  In addition, the backing material decreases the amount of ultrasound energy that is directed backwards and laterally.
 
[[File:PhysicsUltrasound_Fig23.svg|thumb|left|350px| Fig. 23]]
{{clr}}
 
 
In front of the PZT, several matching layers are placed to decrease the difference in the impedance between the PZT and the patient’s skin.  This increases in efficiency of ultrasound transfer and decrease the amount of energy that is reflected from the patient.
Let us talk about the shape of the ultrasound beam.  Since there are many PZT crystals that are connected electronically, the beam shape can be adjusted to optimize image resolution.  The beam is cylindrical in shape as it exits the transducer, eventually it diverges and becomes more conical.  The cylindrical (or proximal) part of the beam is referred to as near filed or Freznel zone.  The image quality and resolution is best at the focal depth that can be determined by Focal depth = (Transducer Diameter)^2 x frequency /4.  When the ultrasound beam diverges, it is called the far field. 
 
[[File:PhysicsUltrasound_Fig24.svg|thumb|left|400px| Fig. 24]]
{{clr}}
 
 
One would state that the best images are acquired using a large diameter transducer with high frequency.  However, as we have learned, high frequency transducers have significant attenuation issues.  In addition, larger diameter transducers are impractical to use because the imaging windows are small.  The way around these problems is electronic focusing with either an acoustic lens or by arranging the PZT crystals in a concave shape. 
 
[[File:PhysicsUltrasound_Fig25.svg|thumb|left|400px| Fig. 25]]
{{clr}}
 
In clinical imaging, the ultrasound beam is electronically focused as well as it is steered.  This became possible after phased array technology was invented.  By applying electrical current in a differential manner and adjusting the timing of individual PZT excitation, the beam can travel in an arch producing a two-dimensional image.  If one applies electricity in a differential manner from outside inward to the center of the transducer, differential focusing can be produced resulting in a dynamic transmit focusing process. 
 
[[File:PhysicsUltrasound_Fig26.svg|thumb|left|400px| Fig. 26]]
{{clr}}


Before we talk about '''Doppler Effect''', let us discuss the ultrasound transducer architecture and function.  The current transducers became available after the discovery that some materials can change shape very quickly or vibrate with the application of direct current.  As important is the fact that these materials can in turn produce electricity as they change shape from an external energy input (i.e., from the reflected ultrasound beam).  This effect of vibration form an application of alternative current is called a piezoelectric effect (PZT).  Many materials exist in nature that exhibit piezoelectric effect.  Ccommercial transducers employ ceramics like barium titanate or lead zirconate titanate.  The transducer usually consists of many PZT crystals that are arranged next to each other and are connected electronically.  The frequency of the transducer depends on the thickness of these crystals, in medical imaging it ranges 2-8 MHz.  An ultrasound pulse is created by applying alternative current to these crystals for a short time period.  Afterwards, the system “listens” and generates voltage from the crystal vibrations that come from the returning ultrasound.  An important part of the transducer is the backing material that is placed behind the PZT, it is designed to maximally shorten the time the PZT crystal vibrates after the current input is gone also known as ringing response.  By decreasing the ringdown time, one decreases the pulse length and improves the axial resolution.  In addition, the backing material decreases the amount of ultrasound energy that is directed backwards and laterally.  In front of the PZT, several matching layers are placed to decrease the difference in the impedance between the PZT and the patient’s skin.  This increases in efficiency of ultrasound transfer and decrease the amount of energy that is reflected from the patient.
Let us talk about the shape of the ultrasound beam.  Since there are many PZT crystals that are connected electronically, the beam shape can be adjusted to optimize image resolution.  The beam is cylindrical in shape as it exits the transducer, eventually it diverges and becomes more conical.  The cylindrical (or proximal) part of the beam is referred to as near filed or Freznel zone.  The image quality and resolution is best at the focal depth that can be determined by Focal depth = (Transducer Diameter)^2 x frequency /4.  When the ultrasound beam diverges, it is called the far field.  One would state that the best images are acquired using a large diameter transducer with high frequency.  However, as we have learned, high frequency transducers have significant attenuation issues.  In addition, larger diameter transducers are impractical to use because the imaging windows are small.  The way around these problems is electronic focusing with either an acoustic lens or by arranging the PZT crystals in a concave shape.  In clinical imaging, the ultrasound beam is electronically focused as well as it is steered.  This became possible after phased array technology was invented.  By applying electrical current in a differential manner and adjusting the timing of individual PZT excitation, the beam can travel in an arch producing a two-dimensional image.  If one applies electricity in a differential manner from outside inward to the center of the transducer, differential focusing can be produced resulting in a dynamic transmit focusing process. 


Briefly, I would like to touch upon '''real time 3D imaging'''.  In order to accomplish this, the PZT elements need to be arranged in a 2D matrix.  Each PZT element represents a scan line, by combining all the data, a 3D set is reconstructed.  For example, if we have a matrix of 128 by 128 PZT elements, one can generate over 16 thousand scan lines.  With careful timing for individual excitation, a pyramidal volumetric data set is created.  When imaged several times per minute (>20), a real time image is achieved.   
Briefly, I would like to touch upon '''real time 3D imaging'''.  In order to accomplish this, the PZT elements need to be arranged in a 2D matrix.  Each PZT element represents a scan line, by combining all the data, a 3D set is reconstructed.  For example, if we have a matrix of 128 by 128 PZT elements, one can generate over 16 thousand scan lines.  With careful timing for individual excitation, a pyramidal volumetric data set is created.  When imaged several times per minute (>20), a real time image is achieved.   
[[File:PhysicsUltrasound_Fig27.svg|thumb|left|600px| Fig. 27]]
{{clr}}
Image production is a complex process.  Echo instrumentation must generate and transmit the ultrasound and receive the data.  Then the data needs to be amplified, filtered and processed.  Eventually the final result needs to be displayed for the clinician to view the ultrasound information.  As the first step in data processing, the returning ultrasound signals need to be converted to voltage.  Since their amplitude is usually low, they need to be amplified.  The ultrasound signal usually is out of phase so it needs to be realigned in time.  At this point one has the raw frequency (RF) data, which is usually high frequency with larger variability in amplitudes and it has background noise.  The next step is filtering and mathematical manipulations (logarithmic compression, etc) to render this data for further processing.  At this stage one has sinusoidal data in polar coordinates with distance and an angle attached to each data point.  This information needs to be converted to Cartesian coordinate data using fast Fourier transform functions.  Once at this stage, the ultrasound data can be converted to analog signal for video display and interpretation.   
Image production is a complex process.  Echo instrumentation must generate and transmit the ultrasound and receive the data.  Then the data needs to be amplified, filtered and processed.  Eventually the final result needs to be displayed for the clinician to view the ultrasound information.  As the first step in data processing, the returning ultrasound signals need to be converted to voltage.  Since their amplitude is usually low, they need to be amplified.  The ultrasound signal usually is out of phase so it needs to be realigned in time.  At this point one has the raw frequency (RF) data, which is usually high frequency with larger variability in amplitudes and it has background noise.  The next step is filtering and mathematical manipulations (logarithmic compression, etc) to render this data for further processing.  At this stage one has sinusoidal data in polar coordinates with distance and an angle attached to each data point.  This information needs to be converted to Cartesian coordinate data using fast Fourier transform functions.  Once at this stage, the ultrasound data can be converted to analog signal for video display and interpretation.   
Image display has evolved substantially in clinical ultrasound.  Currently, 2D and real time 3D display of ultrasound date is utilized.  Without going into complexities of physics that are involved in translating RF data into what we see every day when one reads echo, the following section will provide the basic knowledge of image display.  If one can imagine a rod that is imaged and displayed on an oscilloscope, it would look like a bright spot.  Displaying it as a function of amplitude (how high is the return signal) is called A-mode.  If one converts the amplitude signal into brightness (the higher the amplitude the brighter the dot is), then this imaging display is called B-mode.  Using B mode data, once can scan the rod multiple times and then display the intensity and the location of the rod with respect to time.  This is called M-mode display.  Using B-mode scanning in a sector created a 2D representation of anatomical structures in motion.   
Image display has evolved substantially in clinical ultrasound.  Currently, 2D and real time 3D display of ultrasound date is utilized.  Without going into complexities of physics that are involved in translating RF data into what we see every day when one reads echo, the following section will provide the basic knowledge of image display.  If one can imagine a rod that is imaged and displayed on an oscilloscope, it would look like a bright spot.  Displaying it as a function of amplitude (how high is the return signal) is called A-mode.  If one converts the amplitude signal into brightness (the higher the amplitude the brighter the dot is), then this imaging display is called B-mode.   


'''Second Harmonic''' is an important concept that is used today for image production. The basis for this is that fact that as ultrasound travels through tissue, it has a non-linear behavior and some of its energy is converted to frequency that is doubled (or second harmonic) from the initial frequency that is used (or fundamental frequency).  There are several parameters that make second harmonic imaging preferential.  Since it is produced by the tissue, the deeper the target the more second harmonic frequency is returned.  As the ultrasound beam travels through tissue, new frequencies appear that can be interrogated.  Second harmonic data gets less distortion, thus it produces better picture.  Also, the second harmonic is strongest in the center of the beam, thus it has less side lobe artifacts.  At the chest wall the fundamental frequency gets the worst hit due to issues that we have discussed (reflection, attenuation) – if one can eliminate the fundamental frequency data then these artifacts will not be processed.  One concept of eliminating fundamental frequency data is called pulse inversion technology.  The transducer sends out 2 fundamental frequency pulses of the same amplitude but of different phase.  As these pulses are reflected back to the transducer, because of the different phase they cancel each other out (destructive interference) and what is left is the second harmonic frequency data which is selectively amplified and used to generate an image.
[[File:PhysicsUltrasound_Fig28.svg|thumb|left|400px| Fig. 28]]
{{clr}}


'''Doppler Effect''' is change in frequency of sound as a result of motion between the source of ultrasound and the receiver.  Greater velocity creates a larger shift in ultrasound frequency.  An example of a moving object in cardiac ultrasound is red blood cells.  Typical values for Doppler shift is 20 Hz to 20 kHz, thus comparing to the fundamental frequency, the Doppler shift is small.  Since it “rides” on top of the much larger frequency (i.e., 5 MHz), the process of extracting this data is termed demodulation.  Doppler shift = (2 x reflector speed x incident frequency x cosine (angle)) / propagation speed.  There are two important concepts that must be emphasized.  First, the Doppler shift is highly angle dependent.  Since cosine (90) = 0 and cosine (0) = 1, then the most true velocity will be measured when the ultrasound beam is parallel to the axis of motion of the reflector.  At perpendicular axis, the measured shift should be 0, however usually some velocity would be measured since not all red blood cells would be moving at 90 degree angle.  The other concept is the direction of the motion of the reflector.  When the reflector is moving away from the source of the ultrasound, the shift is negative, and when the reflector is moving towards the source of ultrasound the shift is positive.   
 
Using B mode data, once can scan the rod multiple times and then display the intensity and the location of the rod with respect to time.  This is called M-mode display.  Using B-mode scanning in a sector created a 2D representation of anatomical structures in motion.   
 
[[File:PhysicsUltrasound_Fig28b.svg|thumb|left|600px| Fig. 28 (All 3 modes of display are depicted: A, B, and M)]]
{{clr}}
 
[[File:PhysicsUltrasound_Fig29.svg|thumb|left|250px| Fig. 29]]
{{clr}}
 
 
 
'''Second Harmonic''' is an important concept that is used today for image production.  The basis for this is that fact that as ultrasound travels through tissue, it has a non-linear behavior and some of its energy is converted to frequency that is doubled (or second harmonic) from the initial frequency that is used (or fundamental frequency). 
 
[[File:PhysicsUltrasound_Fig30.svg|thumb|left|400px| Fig. 30]]
{{clr}}
 
 
There are several parameters that make second harmonic imaging preferential.  Since it is produced by the tissue, the deeper the target the more second harmonic frequency is returned.  As the ultrasound beam travels through tissue, new frequencies appear that can be interrogated.  Second harmonic data gets less distortion, thus it produces better picture.  Also, the second harmonic is strongest in the center of the beam, thus it has less side lobe artifacts.  At the chest wall the fundamental frequency gets the worst hit due to issues that we have discussed (reflection, attenuation) – if one can eliminate the fundamental frequency data then these artifacts will not be processed.  One concept of eliminating fundamental frequency data is called pulse inversion technology.  The transducer sends out 2 fundamental frequency pulses of the same amplitude but of different phase.  As these pulses are reflected back to the transducer, because of the different phase they cancel each other out (destructive interference) and what is left is the second harmonic frequency data which is selectively amplified and used to generate an image.
 
[[File:PhysicsUltrasound_Fig31.svg|thumb|left|600px| Fig. 31]]
{{clr}}
 
 
'''Doppler Effect''' is change in frequency of sound as a result of motion between the source of ultrasound and the receiver.  Greater velocity creates a larger shift in ultrasound frequency.   
 
[[File:PhysicsUltrasound_Fig32.svg|thumb|left|600px| Fig. 32]]
{{clr}}
 
 
An example of a moving object in cardiac ultrasound is red blood cells.  Typical values for Doppler shift is 20 Hz to 20 kHz, thus comparing to the fundamental frequency, the Doppler shift is small.  Since it “rides” on top of the much larger frequency (i.e., 5 MHz), the process of extracting this data is termed demodulation.  Doppler shift = (2 x reflector speed x incident frequency x cosine (angle)) / propagation speed.  There are two important concepts that must be emphasized.  First, the Doppler shift is highly angle dependent.  Since cosine (90) = 0 and cosine (0) = 1, then the most true velocity will be measured when the ultrasound beam is parallel to the axis of motion of the reflector.  At perpendicular axis, the measured shift should be 0, however usually some velocity would be measured since not all red blood cells would be moving at 90 degree angle.   
 
[[File:PhysicsUltrasound_Fig33.svg|thumb|left|200px| Fig. 33]]
{{clr}}
 
 
The other concept is the direction of the motion of the reflector.  When the reflector is moving away from the source of the ultrasound, the shift is negative, and when the reflector is moving towards the source of ultrasound the shift is positive.   
Continuous wave (CW) Doppler required 2 separate crystals, one that constantly transmits, and one that constantly receives data.  There is no damping using this mode of imaging.  One can measure very high velocities (i.e., velocities of aortic stenosis or mitral regurgitation).  The advantage of CW is high sensitivity and ease of detecting very small Doppler shifts.  The disadvantage of CW is the fact that echos arise from the entire length of the beam and they overlap between transmit and receive beams.  Thus one cannot determine where in the body the highest velocity is coming from – range ambiguity.
Continuous wave (CW) Doppler required 2 separate crystals, one that constantly transmits, and one that constantly receives data.  There is no damping using this mode of imaging.  One can measure very high velocities (i.e., velocities of aortic stenosis or mitral regurgitation).  The advantage of CW is high sensitivity and ease of detecting very small Doppler shifts.  The disadvantage of CW is the fact that echos arise from the entire length of the beam and they overlap between transmit and receive beams.  Thus one cannot determine where in the body the highest velocity is coming from – range ambiguity.
{| border="0"
|+
|-
| align="center" width="150" | [[File:PhysicsUltrasound_Fig33a.svg | 200px]]
| align="center" width="150" | [[File:PhysicsUltrasound_Fig33b.jpg | 260px]]
|-
|}
Fig. 33
{{clr}}


'''Pulsed wave''' (PW) Doppler requires only one crystal.  It alternates between transmitting and receiving data.  The transducer “listens” for the data at a certain time only, since the sampling volume is coming from the location that is selected by the sonographer (i.e., the velocity at the LVOT or at the tips of the mitral valve).  This is called range resolution.  The major disadvantage of PW Doppler is aliasing.  In PW mode, the transducer has to sample a certain frequency at least twice to resolve it with certainty.  This put a limit on the max velocity that it can resolve with accuracy.  2 x Doppler frequency (Nyquist) = PRF.  If the velocity is greater than the sampling rate / 2, aliasing is produced.  The following maneuvers can be performed to eliminate aliasing: change the Nyquist limit (change the scale), select a lower frequency transducer, select a view with a shallower sample volume.  
'''Pulsed wave''' (PW) Doppler requires only one crystal.  It alternates between transmitting and receiving data.  The transducer “listens” for the data at a certain time only, since the sampling volume is coming from the location that is selected by the sonographer (i.e., the velocity at the LVOT or at the tips of the mitral valve).  This is called range resolution.  The major disadvantage of PW Doppler is aliasing.  In PW mode, the transducer has to sample a certain frequency at least twice to resolve it with certainty.  This put a limit on the max velocity that it can resolve with accuracy.  2 x Doppler frequency (Nyquist) = PRF.  If the velocity is greater than the sampling rate / 2, aliasing is produced.  The following maneuvers can be performed to eliminate aliasing: change the Nyquist limit (change the scale), select a lower frequency transducer, select a view with a shallower sample volume.  
{| border="0"
|+
|-
| align="center" width="150" | [[File:PhysicsUltrasound_Fig34a.svg | 200px]]
| align="center" width="150" | [[File:PhysicsUltrasound_Fig34b.jpg | 300px]]
|-
|}
Fig. 34
{{clr}}
Imaging and PW Doppler can be achieved with a single crystal transducer (both are created using pulsed ultrasound).  With 2D imaging, one uses high frequencies and the incidence is usually at 90 degrees.  With PW Doppler, one uses lower frequency and the incidence is usually at 0 degrees for optimal data.  
Imaging and PW Doppler can be achieved with a single crystal transducer (both are created using pulsed ultrasound).  With 2D imaging, one uses high frequencies and the incidence is usually at 90 degrees.  With PW Doppler, one uses lower frequency and the incidence is usually at 0 degrees for optimal data.  


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