**3.2 Spatial resolution**

Spatial resolution represents the system's ability to distinguish point nearby objects under high contrast conditions.

The spatial resolution can be evaluated with first-level quality controls using phantoms or test objects in which point targets are placed at gradually decreasing and known distances, horizontal or vertical respectively, (e.g. 4, 3, 2, 1, 0,5 mm) and evaluated at what level the points no longer appear distinguishable in the image (first level visual inspection). These checks can be carried out at different depths and at different lateral positions with respect to the axis of symmetry of the image.

The second level of controls involves the processing of the digital image of a pointlike object in an area of the field of view identified by selecting the depth and lateral position with respect to the axis of symmetry of the image. The full width at half maximum (FWHM) of the object's two-dimensional point spread function in the axial and transverse directions is the absolute numerical estimate of the spatial resolution.

In ultrasound imaging, the spatial resolution can be axial (parallel to the direction of propagation of the beam, generally better especially for linear probes) or lateral (perpendicular to the direction of propagation, generally worse especially for convex probes). There is also a third resolution, called "elevation resolution", which represents the possibility of separating two adjacent layers in a direction perpendicular to the displayed plane.

Axial spatial resolution is defined as the ability to distinguish two adjacent objects along the direction of propagation of the ultrasound beam. This parameter, from a physical point of view, is determined primarily by the emission frequency of the transducer. In fact, it is evident that it is impossible to resolve objects having dimensions smaller than one wavelength. For pulsed beams the axial resolution depends on the bandwidth of the ultrasound pulse: this depends on the Q factor of the transducer. The quality factor Q of the transducer is defined as the ratio between the central frequency of the transducer and its band. In particular, in two-dimensional echo imaging, transducers with low Q values are used to have a better spatial resolution, short echoes = wide band. High Q values give a very narrow band whilst low Q gives a wide band. In diagnostics it is necessary to have a wide band, in fact, this means having short spatial pulses (SPL) which allow to resolve objects very close to each other.). It must be kept in mind that ultrasound undergoes attenuation in the tissues and that this attenuation is a function of frequency, i.e. high frequencies are attenuated more, this implies a narrowing of the frequency band of the spectrum, therefore, a reduction in resolution axial as the depth of penetration into the tissue increases.

So, axial (also called longitudinal) resolution is the minimum distance that can be differentiated between two reflectors located parallel to the direction of the ultrasound beam.

$$\text{Axial resolution} = \mathbb{M} \times \text{spatial pulse length.} \tag{1}$$

The spatial pulse length is determined by the wavelength of the beam and the number of cycles (periods) within a pulse. Axial resolution is high when the spatial pulse length is short. Spatial pulse length is the product of the number of cycles in a pulse of ultrasound and the wavelength. Most pulses consist of two or three cycles, the number of which is determined by the damping of piezoelectric elements after excitation: high damping reduces the number of cycles in a pulse and hence shortens spatial pulse length. The wavelength of a pulse is determined by the operating frequency of the transducer; transducers of high frequency have thin piezoelectric elements that generate pulses of short wavelengths.

Supposing three cycles per pulse and using the equation *c* = λν, you obtain the wavelengths and the consequent theoretical maximal axial resolution values reported in the following **Table 1**:

*Perspective Chapter: Quality Assurance in Diagnostic Ultrasound DOI: http://dx.doi.org/10.5772/intechopen.114115*


**Table 1.**

*Wavelength and theoretical maximal axial resolution supposing three cycles per pulse at different frequencies.*

AAPM (American Association of Physicists in Medicine) suggests the following tolerance limits on axial resolution:


The axial resolution should remain constant over time. If changes occur, the intervention of the technical assistance service is advisable.

Generally, in commercially available phantoms the pins for axial resolution are slightly moved horizontally with respect to each other in order to reduce acoustic shadow effects. Also, this test is very simple to perform but the results are very variable, depending on the depth, the position of the pins and the quality of the scanner. For example, we found resolutions close to 0,3 mm for superficial pins at 10 MHz for high-quality scanners, and significantly higher values for low-quality ones.

#### **3.3 Lateral spatial resolution**

Lateral spatial resolution is defined as the ability of the instrument to resolve two adjacent point objects (pin in the phantom) arranged perpendicular to the beam axis. It is known that in ultrasound imaging the lateral spatial resolution is worse than the axial spatial resolution. The diameter of the beam is a quantity that crucially determines the lateral resolution: in fact, a single object smaller than the width of the beam produces an echo signal during scanning for the entire time it is inside the beam, therefore the object appears as if its size were equal to the width of the beam itself at that depth, so the lateral resolution of fixed focus transducers varies greatly with depth and frequency. However, systems with multiple focal zones or dynamic focus can produce more uniform lateral resolution over a wider range of depths. The lateral resolution can also deteriorate significantly due to side lobes and grating lobes and type of probe (best with linear, less with convex, sector).

As regards the lateral resolution values and their tolerance limit, there is considerable uncertainty regarding the solution that can be proposed for routine checks. In this regard, it is useful to refer to the −20 dB pulse echo focal length, W20 proposed by AAPM and proportional to the wavelength at the centre frequency and to the pulseecho focal length and inversely proportional to the diameter of the active element (transducer).


**Table 2.**

*Theoretical lateral resolution for different depths and frequencies.*


#### **Table 3.**

*Desired axial and lateral resolution for different frequencies in real conditions.*

In general, it is suggested by AAPM that the measured lateral resolutions respect the specifications reported in **Table 2**.

In real conditions (not mathematical), the optimization of spatial resolution will be obtained with the values proposed in **Table 3** for a medium-quality scanner.

#### **3.4 Contrast resolution**

The contrast in the object determines a modulation of the reflected echo that returns to the probe and produces a contrast in the grey scale of the image. Contrast resolution represents the smallest contrast in the object that determines a contrast detectable by the human eye in the image, in conditions that do not have problems related to spatial resolution.

Various test objects are available with circular areas of decreasing and known contrast (scatter relative to the background). **Figure 4** can be reproduced in the image. It is therefore possible to evaluate the response curve of the system (contrast in the image as a function of contrast in the object) and consequently the contrast resolution. First- and second-level checks can also be carried out for this parameter. In the first case, a visual inspection and the first insert not visible can give such an indication. In the second a plot with the grey scale contrast of the object in the image as a function of the actual one in the phantom can give a numerical assessment (contrast drop to zero). In our experience, the max contrast resolution is of the order of magnitude of 10 dB. No particular problems were found in performing this test.

#### **3.5 Uniformity**

Uniformity describes the ability of the ultrasound system to obtain a uniform image of a homogeneous object, i.e., to show echoes of the same amplitude and depth with equal brightness on the screen. Factors that influence uniformity are tissue attenuation and focus.

The attenuation of the beam in-depth, and therefore the underestimation of the echoes coming from the deeper layers, is corrected by the operator's adjustment of the time gain compensation (TGC), which determines the amplification curve of the signals as a function of their time of delay (and therefore depending on the depth of origin of the echo itself).

By using a phantom or a test object with a homogeneous tissue texture, i.e., made up of a homogeneous set of diffusers smaller than the wavelength of the beam and correct by means of an appropriate adjustment of the TGC, a "homogeneous" image is obtained and used to calculate parameters numbers that characterise uniformity. A first-level check is only a visual inspection and, if possible. A profile of the grey level as a function of depth. One way of the second level is to select a region of interest (ROI) which is moved deeper and deeper to be able to calculate the average and standard deviation of the grey levels of the pixels as a function of the depth itself. Ideally, ultrasound images are characterised by an irregular background (texture), in which, however, the average value of the grey levels calculated in areas of interest of dimensions much larger than the "grain" of the image, should not vary either with the depth nor with the angle of displacement from the centre of the image. In reality, however, there may be areas of the image with an average grey level value different from the rest. These can manifest themselves in the form of dark vertical and/or horizontal bands: these non-uniformities can be explained in different ways. Horizontal bands may arise due to multiple focusing. In some multiple focusing systems there may be a gap between some focal zones, this can cause the beam to be wider in this zone and therefore there is a reduction in the amplitude of the echoes, this "strip" of different values of the grey is therefore completely normal because it is associated with the technological "limits" of the equipment. The presence of vertical bands in the image, however, can be caused by a damaged transducer element, but it can also be due to a defect in the transmission circuit connected to a certain element of the transducer. Vertical bands due to these electrical causes appear in the upper part of the image.

However, the absence of vertical bands in the image is not sufficient to ensure that all elements of the probe are functioning; if there is only one non-functioning element, it is very difficult to realise this in the case of phased array probes that use all their elements to create each line of the image. In this case, the absence of a single transducer in a transmission line causes a weak effect that has repercussions in all lines of sight of the image. However, it is easier to recognise such a defect in the case of vector, convex and linear array probes. In these, in fact, it manifests itself in the form of small vertical bands.

An image grey scale histogram is normally used to quantify the uniformity.

As regards the reference limits, the AAPM recommends notifying the technical assistance service if significant non-uniformities occur. The term significant is, however, subjective; each user can identify an appropriate threshold; however, a reference value of 4 dB is suggested. No particular problems were found in performing this test.

#### **3.6 Dead zone**

By dead zone, we mean the distance along the direction of propagation of the beam between the front surface of the probe and the first reflector that produces a detectable echo on the image. This region, where no information can be collected, exists because the transducer cannot emit and receive ultrasonic pulses at the same time. This depends on the instrument and is the result of both the reverberations coming from the probe-object interface under examination and the length of the pulse train. As the frequency increases, keeping the other parameters constant, the length of the pulse decreases and consequently the depth of the dead zone.

The extension of the dead zone is controlled since its variations are linked to variations in the performance of the probe and therefore of the ultrasound equipment. For example, an increase in the extension of the dead zone can be caused by a long-lasting ultrasonic pulse (caused by the fracture of a crystal), the incorrect functioning of damping materials, or the breakage of a lens. However, it must be emphasised that the reverberations observed in phantoms can differ significantly from those in patients, especially when the impedance of the phantom surface is very different from that of the skin.

Several test objects and phantoms are available for first-level dead zone control (visual inspection). If the trough between the initial pulse wave and the first echo wave is 6 dB lower than the peak of the first echo wave, then we can distinguish them and this distance is the dead zone (second level). In our experience, the dead zone ranges from 0,5 to 1,5 mm. No particular problems were found in performing this test.

#### **3.7 Focus**

The focal point of the transducer is the point of the ultrasound beam at a given depth in the medium crossed, where the intensity is maximum and the width of the beam is minimum. By focal zone, we mean the region surrounding the focal point in which the intensity of the ultrasound beam is within 3 dB of the maximum. This area is clearly the region where lateral resolution is best.

The focusing can be fixed (in mechanical sector probes) or electronic (in all others); electronic focusing can also be dynamic (multiple focal zones at the same time).

Focusing control consists of verifying the correspondence between the focal zone selected by the operator and the actual one. It is possible to verify the position of the focal zone by evaluating that of the best lateral resolution (see spatial resolution) or by using special test objects that allow direct visualisation of the shape of the beam.

Focus control can be a first-level control or a second, measuring the FWHM of the pin in the position of focus selected. We found different results depending on the frequency and quality of the scanner.

#### **3.8 Sensitivity (or depth of maximum penetration)**

Sensitivity represents the system's ability to detect the weakest ultrasound signal that can be clearly visualised, originating from small interfaces located at a given depth in an attenuating medium. In practical terms, sensitivity represents the maximum display depth of the system under certain reproducible conditions. The weak signal in question is detected in the presence of noise, and its detectability is an indication of the signal-to-noise ratio. The factors that can influence the sensitivity are the frequency and intensity of the excitation pulse; the gain; the TGC; the focusing; the attenuation of the medium; the depth; the composition and geometry of the reflecting element; and finally, the noise due to the system electronics. The signal/ noise ratio is maximum within the focal area and decreases on the sides of it.

By carrying out this type of check, it is necessary to be able to distinguish the echoes diffused from the background from those generated by electronic noise. The former, by keeping the transducer stationary on the phantom, will appear stationary, whilst the latter will present fluctuations.

For this parameter, it is possible to carry out first and second-level assessments. In the first case, a vertical inspection of the pin in the phantom is performed and the depth of the last visible pin is measured. In the second a rectangular ROI around the pins is acquired and its profile analysed. No particular problems were found in performing this test. The depth of penetration (sensitivity) is generally limited to approximately 200 wavelengths, corresponding to a depth of 30 cm for a 1 MHz transducer, 12 cm for 2.5 MHz transducer, and 6 cm for a 5 MHz transducer.

#### **3.9 Dynamic range**

The dynamic range of an ultrasound scanner is defined as the ratio, expressed in dB, between the intensity of the largest echo and that of the smallest echo, which can be displayed simultaneously. The smallest echo is the one that is barely distinguishable from the system noise, whilst the largest is the one just below the saturation level. Therefore, the dynamic range provides a measure of the intensity (or amplitude) that the system can handle. All elements of the equipment, from the probe to the screen, influence the dynamic range. The dynamics of the signals reaching the probe are normally much wider than that which can be represented with a normal screen; a non-linear compression (usually logarithmic) of the intensity of the echoes is therefore necessary. In particular, most of the grey level range is reserved for weak signals, compressing very intense signals more.

The dynamic range can be evaluated with first and second-level controls with phantoms or test objects similar to those used for contrast resolution. No particular problems were found in performing this test. The typical value we found can reach 100 dB.

#### **3.10 Size, shape and filling of pseudo-cysts**

Cysts are fluid-filled, hypoechoic and normally poorly attenuating structures. The shape, size and consistency of the cyst must be represented correctly.

The first level of control of these parameters allows you to evaluate any changes in the system output, an incorrect selection of the TGC curve, an incorrect insonation non-uniformity, an incorrect focusing or an insufficient quantity of number of lines of sight in the image.

Various phantoms suitable for this purpose are available for the evaluation of the circular shape of the circular insert in the phantom. No limits are suggested.

No particular problems were found in performing this test.

#### **3.11 Size, shape and shadowing of solid pseudo-masses**

Solid masses are generally echogenic and normally with high attenuation. The shape, size and consistency of solid masses must be represented correctly.

The first level of control of these parameters allows you to evaluate any changes in the system output, an incorrect selection of the TGC curve that leads to an incorrect uniformity of the image, an incorrect focusing or an insufficient quantity of number of lines of sight in the image.

The result of the test is correct if all the scanner parameters are optimised and particular attention to the angles is taken.
