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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.  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.   


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.  
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.   
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.   
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.  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.     
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'''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.  
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.  
Color Flow Doppler uses pulsed Doppler technique.  The velocity data is encoded in color, and it reports mean velocities.  Since it is a pulsed Doppler technique, it is subject to range resolution and aliasing.  Color data is extremely complex and consumes significant computational resources, thus several assumptions are made to speed up this process.  Returned echo frequencies are compared to a predetermined threshold to decide whether this is a 2D image vs Doppler shift.  Once the computer decides that the frequency is low enough to be a Doppler shift data, repetitive sampling determines the mean velocity and variance.  Then a color is assigned using a color look-up table rather than doing a discrete Fourier transform for each data point.  Velocities that move toward the transducer are encoded in red, velocities that move away are encoded in blue.  One must remember that the color jets on echo are not equal to the regurgitant flow for a number of reasons.  The regurgitant flow is a three dimensional structure with jet momentum being the primary determinant of jet size.  This parameter is effected by the jet velocity as well as flow rate.  Blood pressure will affect the velocity and thus the regurgitant flow.  Chamber constraints will have an effect on the appearance of the color jet, especially eccentric jets.  Lastly, the settings of the echo machine will have an effect on how the color flow jet appears on the screen.  
 
'''Color Flow Doppler uses pulsed Doppler technique.''' The velocity data is encoded in color, and it reports mean velocities.  Since it is a pulsed Doppler technique, it is subject to range resolution and aliasing.  Color data is extremely complex and consumes significant computational resources, thus several assumptions are made to speed up this process.  Returned echo frequencies are compared to a predetermined threshold to decide whether this is a 2D image vs Doppler shift.  Once the computer decides that the frequency is low enough to be a Doppler shift data, repetitive sampling determines the mean velocity and variance.  Then a color is assigned using a color look-up table rather than doing a discrete Fourier transform for each data point.  Velocities that move toward the transducer are encoded in red, velocities that move away are encoded in blue.  One must remember that the color jets on echo are not equal to the regurgitant flow for a number of reasons.  The regurgitant flow is a three dimensional structure with jet momentum being the primary determinant of jet size.  This parameter is effected by the jet velocity as well as flow rate.  Blood pressure will affect the velocity and thus the regurgitant flow.  Chamber constraints will have an effect on the appearance of the color jet, especially eccentric jets.  Lastly, the settings of the echo machine will have an effect on how the color flow jet appears on the screen.  


==Reference:==
==Reference:==
Feigenbaum's Echocardiography, 7th Edition
*Feigenbaum's Echocardiography, 7th Edition
Sidney K. Edelman, PhD.  Lecture notes from 2005 ASCeXAM Review course
*Sidney K. Edelman, PhD.  Lecture notes from 2005 ASCeXAM Review course
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