[Ultrasound Physics] RESOLUTION

[Contents]

1. Resolution

2. Axial Resolution

3. Lateral Resolution

4. Slice Thickness/Elevational Resolution

5. Contrast Resolution

6. Spatial Resolution

7. Temporal Resolution

8. Frame Rate

1. Resolution [★]

1) The ability to separate closely spaced objects

 

2) Types of Resolution

- Detail resolution: relating to the transducer

: Axial Resolution

: Lateral resolution

: Elevational Resolution

- Contrast Resolution: relating to the instrument

- Spatial Resolution: relates to instrument

- Temporal Resolution: Relating to the instrument

2. Axial Resolution= Longitudinal, Axial, Range/Radial Depth (LARD) [★★]

 

 

1) Accuracy in imaging parallel to beams axis. 

- The ability to accurately distinguish two reflectors as two reflectors parallel to the beam

 

2) Is a Number

- Depicts minimum separation that can be resolved

: Lower number = more accurate image (better axial resolution)

: Space between 2 reflectors less than AR = unresolved

· Structures will not be shown as individual structures 

: Space between two reflectors greater than AR = resolved

· Structures will be shown as individual structures

- AR [mm] = SPL/2 (best axial resolution with given transducer)

: spatial pulse length (SPL, [mm]) = # of cycles in a pulse x wavelength

: λ = c/f (wavelength = Propagating speed / frequency)

- propagating speed: determined by medium

- frequency: determined by source

: f↑- λ↓ - SPL↓ - AR↓(better axial resolution)

: pulse duration ↓ (bandwidth ↑) → SPL ↓ → better axial resolution

 

3) Superior AR

- AR depends on [★★★★]

: frequency (wavelength) - f↑ → better AR

: pulse duration (bandwidth) – PD ↓ → better AR

: higher bandwidth, increased damping → better AR

: AR is determined chiefly by pulse duration

- Increased focusing → beam width ↓ → better LR but pulse length ↑ (poorer AR)

4) Best measure of resolution for modern-day ultrasound: axial resolution

- cf) worst measure of resolution: elevational resolution

3. Lateral Resolution = Lateral, Angular, Transverse, Azimuthal (LATA) [★★]

-

 

 

1) Accuracy in imaging perpendicular to beam axis

- The ability to separate two reflectors as two reflectors perpendicular to the beam axis

- The minimum separation of two structures positioned side by side

 

2) Is a Number

- Depicts minimum separation that can be resolved

: Lower number = more accurate image (better lateral resolution)

: Space between 2 reflectors less than LR = unresolved

· Structures will not be shown as individual structures

: Space between two reflectors greater than LR = resolved

· Structures will be shown as individual structures

- LR [mm] = Beam diameter (beam width) [mm]

: Narrow Beams = Better LR. 

: Best at beam’s focus (end of near zone) 

 

3) Superior LR

- 3 things affect LR [★★]

1) Beam Aperture (diameter): Narrow/small is better

2) Distance from the transducer (T): Beam diameter varies with depth

3) Frequency: Higher frequency (narrower beam) is better

- to improve LR in far field: ↑frequency pulses diverge less in far field    

- primary method of improving LR: focusing, dynamic aperture, ↑ line density [★★★★★]

               : increase the number of transmit focal zones and optimize their location

 

4) Axial resolution is better than Lateral resolution for imaging

- US pulses are shorter than they are wide

- Higher frequency improves both

4. Slice Thickness/Elevational Resolution

 

 

1) The third dimension of the imaging plane, section thickness

- It is not thin or uniform

- True reflectors lie above/below assumed imaging plane but displayed on image                                                                                                                                                                           

 

2) Related to dimension of the beam perpendicular to the imaging plane [★★]

- Elevational resolution is worst with one-dimensional linear array transducer

- Elevational resolution is most affected by mechanical focus on linear array transducer

 

3) Contributes to image Artifacts

- Thicker portions: worse ER (worse artifact of image)

- Thinner portions: better ER (less artifact of image)

 

4) If using poor elevational resolution

- inability to clearly demonstrate small cystic structures

5. Contrast Resolution [★★★★]

 

 

1) ability of gray scale display to distinguish echoes of slightly different amplitudes and intensities

- ability to differentiate between two regions at different depths having similar echogenicity

- Better Contrast Resolution = Better detail

- improper adjustment → operator will likely over-gain or under-gain the image

 

2) Digital Displays [shades of gray]

- Pixel = picture element

: Smallest building block of image

- Entire pixel = single shade of gray

: Shade of gray determined by bits

- The more bits per pixel, the more shades of gray = better CR

               : 8 bit system produces a maximum of 2⁸ (256) possible shades of gray

               : n bit system → 2ⁿ shades of gray

- Dynamic Range/Shades of Gray

               : ratio of the largest to the smallest signal that a system can handle

: Determines the extent a signal can vary and maintain accuracy

: Narrow dynamic range = fewer shades of gray (High contrast)

: Wide dynamic range = many shades of gray (Low contrast)

- contrast resolution is improved by changing the gray-scale map

 

3) to improve contrast resolution: use 2D or matrix array transducer

- 2D (matrix array) transducer

               : have both rows and columns of elements

               → electronic focusing in the out-of-plane dimension possible (slice thickness is thinner)

               : contrast resolution is improved due to decreased volume averaging

6. Spatial Resolution

 

 

1) The overall detail of an image

- Greater detail images =↑Spatial Resolution

 

2) Determining factors [★]

- Line density: More scan lines = Better SR

: High line density (Sound pulses are closely packed) = better SR

: Low line density (Wider gaps between sound pulses) = worse SR

- reduce beam width (better SR) by focusing

- Axial resolution

- Lateral resolution

 

3) Digital Displays (pixel density)

- Pixel density: #of pixels per inch

: High pixel density = ↑SR (better image detail)

- Smaller pixel size

: Low pixel density = ↓SR (worse image detail)

- Large pixel size

 

4) higher frequency → better spatial resolution but greater attenuation

- to gain penetration: use lower frequency, sacrifice some spatial resolution

- for improved spatial resolution: use higher frequency, sacrifice penetration

7. Temporal Resolution

 

 

1) The ability of the display to distinguish closely spaced events in time

- Accuracy of displaying structures as they pertain to time

- The ability to precisely position moving structures from instant to instant

 

2) Determined by frame rate

- Frame Rate: # of frames (still images) displayed per second [★]

: Frame Time x Frame Rate = 1

(FR = 1/FT)

- More frames per second (higher frame rates) = Improved TR

 

3) Determining Factors of frame rate / Temporal resolution [★★★★★]

- Number of Pulses per frame

: Greater Line Density = ↑Frame Time, ↓Frame Rate (Worse TR)

- Multi focus: ↑ pulses per scan line, ↑Frame Time, ↓Frame Rate (Worse TR)

a. ↓pulses ↑ Frame Rate (Improved TR)

b. ↑pulses↓Frame Rate (Worse TR)

: Increase PRF = faster frame rate (improved TR)

: sector width ↑ → ↓Frame Rate (Worse TR)

- Depth of image

: Time of flight/Frame Time is directly related to depth

: Shallower Imaging

- shorter go return time, shorter Frame Time, higher Frame Rate (Superior TR)

: Deeper Imaging

- Longer go return time, longer Frame time, Lower Frame Rate (Inferior TR)

8. Frame Rate

1) Frame rate [★]

- Image formation

: Many single images are displayed in 1 second to produce “motion”

- How many frames pass in front of you per second

- similar to motion picture, multiple still images flashed in a rapid succession

- US examinations requiring highest frame rate: cardiac

- Determined by two factors

: Sound’s speed in the medium

: Depth of the image

- System settings that affect frame rate [★★]

: Image depth

: Number of pulses per frame (proportional)

               - PRF ↑ → frame rate ↑

- if scanning depth ↑, system automatically decreases PRF to avoid range ambiguity

- sector width ↑ → frame rate ↓

               : system fires more scan lines for each imaging frame

               → increase the length of time it takes to create each frame

- Determines Temporal Resolution

: Accuracy of displaying structures as it pertains to time

: Ability to precisely position moving structures from instant to instant

: Excellent when a system produces many frames per second

: Substandard when displays few images per second

 

2) Relationship between FR and Time

- FR = 1/FT

 

* Multiple transmit focusing [★]

1) beam must be fired once for each zone on each line of sight → reduce frame rate

- other types of focusing do not affect frame rate

2) Parallel processing (co-processing)

- method for improving frame rates with multizone electronic focusing

               : simultaneously acquiring data for multiple acoustic scan lines

 

Reference

 

* Davies Ultrasound Physics review

* https://sites.google.com/site/lindadmsportfolio/ultrasound-physics/

* https://sites.google.com/site/nataljasultrasoundphysics/

* https://sites.google.com/site/ektasphysicseportfolio/doppler