^{1}, S. A. Sciuto

^{1}and A. Scorza

^{1,a)}

### Abstract

The aim of the present study is to develop and compare two different automatic methods for accuracy evaluation in ultrasound phantom measurements on B-mode images: both of them give as a result the relative error *e* between measured distances, performed by 14 brand new ultrasoundmedicalscanners, and nominal distances, among nylon wires embedded in a reference test object. The first method is based on a least squares estimation, while the second one applies the mean value of the same distance evaluated at different locations in ultrasoundimage (same distance method). Results for both of them are proposed and explained.

INTRODUCTION

METHOD OF ANALYSIS

Definitions

Limit of acceptance in distance measurement

Least square method (LSM)

Same distance method (SDM)

EXPERIMENTAL SETUP

RESULTS

CONCLUSIONS

### Key Topics

- Ultrasonography
- 90.0
- Image scanners
- 43.0
- Medical imaging
- 26.0
- Ultrasonics
- 15.0
- Error analysis
- 12.0

## Figures

Distance displaying on US images for ultrasound array probes with different scanning. A point reflector in (x, z) position from probe surface is displayed in (ξ, ζ) position on the scanner monitor, where ξ ≠ x and ζ ≠ z. Difference between real and displayed distances depends also on scanning geometry of the ultrasound probe and on difference between the effective acoustic velocities of the medium c_{m} and the acoustic velocity c_{t} used to calibrate the scanner.

Distance displaying on US images for ultrasound array probes with different scanning. A point reflector in (x, z) position from probe surface is displayed in (ξ, ζ) position on the scanner monitor, where ξ ≠ x and ζ ≠ z. Difference between real and displayed distances depends also on scanning geometry of the ultrasound probe and on difference between the effective acoustic velocities of the medium c_{m} and the acoustic velocity c_{t} used to calibrate the scanner.

On the left: a probe scanning an ultrasound phantom made by tissue-mimicking material. On the right: the corresponding ultrasound image, vertical and horizontal test objects are visible on the background. The LSM is performed on the known distances along vertical and horizontal distances: for each direction, firstly the distance error |Δ*d* _{ k } | = |*d* _{ k } − *d* _{ rk } | is evaluated between the measured value of distance *d* _{ k } and a reference value *d* _{ rk }, where *d* _{ rk } is the kth nominal distance between test objects within USPh (nominal distances are claimed in the USPh data sheet), then from Δ*d* _{ k } values of different distances the LSM calculates the relative error *e* by means of a last square fit on *(d* _{ rk } *,* Δ*d* _{ k } *)* points.

On the left: a probe scanning an ultrasound phantom made by tissue-mimicking material. On the right: the corresponding ultrasound image, vertical and horizontal test objects are visible on the background. The LSM is performed on the known distances along vertical and horizontal distances: for each direction, firstly the distance error |Δ*d* _{ k } | = |*d* _{ k } − *d* _{ rk } | is evaluated between the measured value of distance *d* _{ k } and a reference value *d* _{ rk }, where *d* _{ rk } is the kth nominal distance between test objects within USPh (nominal distances are claimed in the USPh data sheet), then from Δ*d* _{ k } values of different distances the LSM calculates the relative error *e* by means of a last square fit on *(d* _{ rk } *,* Δ*d* _{ k } *)* points.

Plot diagrams from LSM and SDM. Both methods are applied on the same ultrasound system. In (a) vertical and horizontal error in distance measurements Δ*d* evaluated with the LSM (the least squares fit is the solid line) versus nominal distance *d* _{ r }. In (b) vertical and horizontal error in distance measurements Δ*d* versus target position, evaluated with the SDM method for a 2 cm distance. For vertical distances *e* = 0.70 ± 0.11 mm/cm with LSM (z axis diagram in the (a) plot) and *e* = 0.66 ± 0.07 mm/cm with the SDM (z axis diagram in the (b) plot), while for horizontal distances *e* = 0.49 ± 0.14 mm/cm with the LSM (x axis diagram in the (a) plot) and *e* = 0.51 ± 0.07 mm/cm with the SDM (x axis diagram in the (b) plot). Evaluations by means of a CIRS54 ultrasound phantom (c_{m} = 1540 ± 3 m/s) at 4 MHz working frequency, 170 mm FoV, and 24 °C room temperature.

Plot diagrams from LSM and SDM. Both methods are applied on the same ultrasound system. In (a) vertical and horizontal error in distance measurements Δ*d* evaluated with the LSM (the least squares fit is the solid line) versus nominal distance *d* _{ r }. In (b) vertical and horizontal error in distance measurements Δ*d* versus target position, evaluated with the SDM method for a 2 cm distance. For vertical distances *e* = 0.70 ± 0.11 mm/cm with LSM (z axis diagram in the (a) plot) and *e* = 0.66 ± 0.07 mm/cm with the SDM (z axis diagram in the (b) plot), while for horizontal distances *e* = 0.49 ± 0.14 mm/cm with the LSM (x axis diagram in the (a) plot) and *e* = 0.51 ± 0.07 mm/cm with the SDM (x axis diagram in the (b) plot). Evaluations by means of a CIRS54 ultrasound phantom (c_{m} = 1540 ± 3 m/s) at 4 MHz working frequency, 170 mm FoV, and 24 °C room temperature.

Distance relative error *e* in vertical and horizontal measurements for different probes models and subgroups. Hatched bars and gray bars refer to LSM and SDM, respectively. (a) Vertical and (b) horizontal measurements for convex array probes. (c) Vertical and (d) horizontal measurements for phased array probes. (e) Vertical and (f) horizontal measurements for linear array probes. Each plot shows the mean values of *e* among the probes of the group both for LSM (continuous line, LSM_{MV}) and SDM (dotted line, SDM_{MV}). Suffixes “a” and “b” in each probe label refer to advanced and intermediate technology level, respectively.

Distance relative error *e* in vertical and horizontal measurements for different probes models and subgroups. Hatched bars and gray bars refer to LSM and SDM, respectively. (a) Vertical and (b) horizontal measurements for convex array probes. (c) Vertical and (d) horizontal measurements for phased array probes. (e) Vertical and (f) horizontal measurements for linear array probes. Each plot shows the mean values of *e* among the probes of the group both for LSM (continuous line, LSM_{MV}) and SDM (dotted line, SDM_{MV}). Suffixes “a” and “b” in each probe label refer to advanced and intermediate technology level, respectively.

Difference between nominal and measured vertical distances for a probe phased array. In (a), from the LSM plot a nonlinear behaviour of the diagnostic system can be noticed (R_{square} = 0.4533), while in (b) the SDM plot is shown for a 20 mm distance evaluated at different depths. (a) *e* = 0.08 ± 0.14 mm/cm and (b) *e* = 0.13 ± 0.11 mm/cm. As the image spatial resolution is about 0.39 mm/pixel, the peak in (b) is due to a 1 pixel variation on 2 cm distance measurement (about 2% difference from nominal length).

Difference between nominal and measured vertical distances for a probe phased array. In (a), from the LSM plot a nonlinear behaviour of the diagnostic system can be noticed (R_{square} = 0.4533), while in (b) the SDM plot is shown for a 20 mm distance evaluated at different depths. (a) *e* = 0.08 ± 0.14 mm/cm and (b) *e* = 0.13 ± 0.11 mm/cm. As the image spatial resolution is about 0.39 mm/pixel, the peak in (b) is due to a 1 pixel variation on 2 cm distance measurement (about 2% difference from nominal length).

## Tables

Speed of sound c_{m} for human tissues and percentage error referring to ultrasound scanner setting speed c_{t} = 1540 m/s. Adapted from Ref. 14.

Speed of sound c_{m} for human tissues and percentage error referring to ultrasound scanner setting speed c_{t} = 1540 m/s. Adapted from Ref. 14.

Experimental results on distance relative error *e* evaluation for four probes (LSM).

Experimental results on distance relative error *e* evaluation for four probes (LSM).

Experimental results on distance relative error evaluation for four probes (SDM).

Experimental results on distance relative error evaluation for four probes (SDM).

Ultrasound phantoms characteristic.

Ultrasound phantoms characteristic.

Experimental settings adopted in the present study. FOV: field of view, DR: dynamic range, FZN: focal zones number, FZD: focal zone depth, OG: overall gain, PP: post-processing, FZ: focal zone.

Experimental settings adopted in the present study. FOV: field of view, DR: dynamic range, FZN: focal zones number, FZD: focal zone depth, OG: overall gain, PP: post-processing, FZ: focal zone.

Test range of distances for LSM and SDM evaluation.

Test range of distances for LSM and SDM evaluation.

Averages on *e* values among three groups of probes.

Averages on *e* values among three groups of probes.

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