Applied Measurment Tecniques

Ultrasounds

1. Ultrasound for diagnostic

I. General aspects and physics

Ultrasound radiation are commonly used in bioimaging, they are acoustic waves that require a means to be transmitted and are harmful and non-traumatic. US are waves with a frequency >20 KHz but if we consider an instrument for diagnostic tool, the range of frequency is: 1: 20 MHz. US are extremely well suited to detect the different muscle structures or the organ fibers even if they are moving, they are harmless, and allow to measure the flow velocity by means Doppler analysis.

US are:

• Low penetration
• Low intensity I = W/S

To be noted that US technique is based on reflection of waves due to tissues, for this reason the transmitter and receiver are at the same part, in fact, generally the transmitter and the receiver are made by the same transducer.

Every US systems in medicine work in a band of frequency surrounding the nominal frequency f 0, according to the diagnostic aim the optimal probe is chosen to work in a certain range:

• 1÷6 MHz: abdominal or cardiac exams
• 6÷15 MHz: special exams (e.g. thyroid, thorax…)

Also it is important to consider the two effects occur when frequency is increased: higher is the frequency, higher is the resolution power and higher is the attenuation (due to tissue energy absorption).

Physics of ultrasound

• Reflection and acoustic impedance - the acoustic impedance of a medium can be related to the “resistance” opposed by the medium to the passage of the acoustic wave; it is defined as the ρ product between the medium density and the propagation velocity c: = ∙

Acoustic impedances do not depend on the geometry of the mediums, but they can provide information on the density of a certain material. The echoes required to obtain images instead, are influenced both from Z and geometry. Here is shown some important acoustic impedances and velocity.

To be noted in air this velocity is lower than other materials, in fact it will shown that coupling the generator and target material requires a means that in general is water.

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Considering a wave propagation across two different means, part of the incidental wave is transmitted toward the second medium, and a part of the same incidental wave is reflected, as shown in the follow schema: Reflection coefficient Transmission coefficient.

To be noted that if medium 1 and medium 2 are the same material the reflection is 0, thus the wave energy is completely transmitted across the interface. Considering the pressure waves traveling across the two medium, it is possible to obtain the same information but from a different point of view. In fact when an incident plane wave, with amplitude p, which is traveling across a medium i with acoustic impedance Z hits a boundary with a second material of impedance Z at normal 1, 2 incidence, there is in general both a reflected wave p and a transmitted wave p: r t.

• → 0 Small reflection is bad. p / p r i Useful images occur only where there is a difference in acoustic impedance. Tissues with strikingly different properties in other respects may have similar acoustic impedances.
• → ±1 High reflection is bad. p / p r i If difference in acoustic impedance is too high, then virtually all the incident ultrasound will be reflected. This means that the boundary is opaque to ultrasound. The organ in question will show up very brightly, but there is an inability to see through it to find out what is underneath.

Impedance matching: In order to respect the maximum energy transfer theorem, it is required to couple the impedance of the transducer (which generates and receives US) and the impedance of the soft tissues. This is because energy losses are unwanted (at least from transducer and first layer of soft tissue), so in order to optimize the energy transfer, it is used a water gel for impedance adapting. An impedance matching is made also inside the probe: the internal matching layer allows the PZT crystal to be adapted (in impedance) with a constructive interference. Theoretically, the acoustic impedance of the matching layer should be: = √ ∙ λ/4.

If the matching material has a thickness equal to or to an odd multiple of quarter wavelength of the free oscillation frequency of the crystal, the interference between the transmitted and the reflected waves is constructive, so that the transfer energy is increased in both the directions.

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• Refraction - is the effect of waves when they travel in different media, with different features. In this case the difference for an acoustic wave is the acoustic impedance. The Snell law works for optics, electromagnetics, and other physical waves. If we do not impinge the material perpendicularly but θ θ we have and angle, the angle of incidence and the one of the outcoming wave are related i t ϱ cZ = through the velocities of the two medium, so basically on the acoustic impedance because.

By the Snell law it’s possible to define these relation: So when we launch US not perpendicularly to our surface, but laterally it will not go back with the incidence angle, but instead deviated: we must take care of that in the design of our probe. The ratio of the acoustic impedance is proportional in this case is given by the ratio of the sinus of incidence angle divided by the transmission one.

• Scattering - when the target/obstacle is very small, there will be reflection all around the scattering. The wavelength of the wave is very important: the smaller is the wavelength the higher will be the effect of that. In fact, in this case one loses information because for obstacles dimension comparable with the wavelength there is a massive deviation and diffraction of the wave, which will diffuse in all the surroundings, not coming back to the echo transducer. Since scattering phenomena have different types of diffusion. Scattering put in relation the frequency, so the wavelength, and the dimension of the impinging target: it is possible to have reflections and deviation if the obstacles have dimension comparable with the wavelength, while there is no scattering due to reduced dimensions. Scattering is bad because for example considering red blood cells, if the wavelength is comparable with these cells, scattering will be combined with diffusion, degrading the quality of the image in terms of resolution.

In order to guarantee a good quality of the images is required to find a wavelength (thus a frequency) that reduces the scattering phenomenon as much as possible and, at the same time, respects the deepness required from the diagnostic task.

• Absorption - Part of the energy stored in the US beam is dissipated by tissues absorption, thus transformed in heat. Absorbing energy, there are changes in tissues such as molecular excitations and chemical changes. It is difficult to measure the proportion of energy loss which occurs by scattering and the proportion lost by absorption. A model to evaluate the energy loss uses an approach similar to electromagnetic waves. The general equation of the power loss (in terms of intensity) is: −2( + () = (0) ∙ )0 0.

Thus the decay is exponentially proportional to the double of the deepness.

The deepness for which the intensity is half of its starting value, is called half value. This value depends both on the medium properties (absorption coefficient) and on the frequency f of the sound wave. It corresponds to an attenuation of 3 dB.

Example: the attenuation produced by a 1 cm thickness of bones is differences with the two frequencies 0.8 MHz and 1.6MHz. The first frequency allow the penetration of the 17% of the wave instead the second one allow the penetration of just 1% of the original wave.

• Diffraction - when the ultrasound passes through an aperture, each point on that aperture is like a source of secondary wavelets; interference between these wavelets gives rise to diffraction effects. Diffraction becomes significant when the apparatus dimensions and object examined become the radiation wavelength (acoustic wavelength, close to 0.1mm, are “bad” comparable with for the investigation because in the body there are lot of anatomically part of the same dimension).

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We can conclude that higher is the frequency and lower is the penetration and, at the same time, higher is the frequency and higher is the attenuation US are not very much suited to explore in deep the body. Confusing our echo there are: scattering, small particles that diffuses in all direction the pulsed wave instead to reflect in a precise direction; is deviated (Snell’s law). refraction, the transmission of the beam Diffraction, due to little fissures, they create new point sources which is giving new echoes, without knowing whether the energy is coming from my source or from diffraction point.

Transducer and probe

The transducer is a part of the probe, which is the object used to conduct the measurement. Typically there is an array of transducers receiving the echo from the probes, and the surface of the probe boundary can be: linear, convex, localized.

The backing material is used to stop the oscillation of the piezo, in the inner part of the probe. It is a big damper, capable to absorb the wave. US source and transducer are the same element: generates the wave and hear if this impinge back, so it is very important to have a good damper that stops the crystal after the generation of the pulse in order to be sensitive to the echo which is coming back from the tissue. The transducer is made by a PZT crystal with a high dielectric constant, and high electric impedance that is necessary to low dissipation in current. If the atomic structure of the crystal is very ordinated, with thousands of volts there is a reorganization of the structure, varying in dimensions. With an applied force, a small quantity of the crystal become available with small current, that is detectable. In general a series of pulses are launched, the advantage of this repetitive pulse is that for each echoing signal, if the probe detects the same measurement for each sent pulse, the system is quite sure that this values come from the same obstacle and not for instance by diffusion phenomena or diffraction.

Way to control that the recording signal is effectively produced by the impinging of the wave with the obstacle; the duration of the pulse is PD, pulse direction: is the period of the emitted wave by the number of pulse needed to launch and nothing could be recorded.

1 = ∙

Another quantity important is PRP, is the period that the system is operational in hearing the echo. The PRP determines the deepness of investigation with US. In electronics, the concept of PD is very close to the duty cycle: for any given period, the duty cycle is the ratio between the interval whereby the wave assumes the high value and the period itself. Duty cycle is fundamental in PWM in which square waves are modulated in frequency, making vary the duty cycle proportionally with the quantity to be encoded in binary logic. 2RPRP =max c.

The higher is the deepness, the higher is PRP. Generally PD is expressed as a percentage with PRP, being 1% of PRP (“little talking, lot of listening”) respect to.

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Spatial pulse length: is related to the PRP, the length and time are linked by the velocity (value known and constant for soft tissues). The distance that a pulse occupies in space, the distance from the start to the end of one pulse. So PD and SPL are directly proportional by the velocity of propagation, so that: = ∙ = ∙ =.

Axial resolution: is the minimum distance (in mm) between two reflecting surfaces placed along the beam direction, guaranteeing the formation of two distinct echoes. Therefore, being the wavelength of the single pulse equal to SPL = l X n, it is possible to act on these two parameters Usually n is reduced to the minimum due to the damping effect caused by the backing block of the probe. A good compromise is the band: 2 10 MHz.÷⇒ ⇒ ⇒ ⇒ Maximising f small l minimizing SPL high axial resolution low penetration deepness ≥ It is given by: 2.

For example a 5 MHz transducer generates US waves that travel 0.3 mm per cycle (wavelength = 0.3 mm). The spatial pulse length (SPL) is 0.9 mm and it is the distance traveled by one echo (n=3). The axial resolution is sufficient to distinguish the 2 target objects as separate because the incident wave hits target # 1 (brown) before hitting target # 2 (green).

A 2.5 MHz transducer (wavelength = 0.6 mm and spatial pulse length = 1.8 mm with n=3), the axial resolution is no longer adequate. Both target # 1(brown) and target # 2 (green) are hit by the same wave, both target objects are seen as one.

Lateral resolution: is defined as the capacity to detect two adjacent object placed on a plane perpendicular to the propagation direction of the US beam.

The lateral resolution is equal to the beam width. The less the beam width, the higher the side resolution. The best lateral resolution occurs at the focus distance.

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Focusing

It is possible to divide the US field in two parts:

• Z < NFL 1. Near Field 2 =
• Z > NFL 2. Far Field

The aim is to have the near field as long as possible, the NFL can be increased increasing the frequency but also the radius of the crystal (r).

The beamwidth can be reduced mainly in three ways:

• Acoustic mirrors (external focusing)
• Acoustic lenses (external focusing)
• Crystal with shaped profiles (internal focusing, not for frequency higher than 5 MHz)

Those used are the last two for US biomedical instrumentation. To be noted, the conformation obtained by focusing it is not a point but, generally, it is a surface or a volume if it is considered the focal zone. Considering a surface, it is required to work on the azimuthal angle and on the elevation angle to ensure an optimal focusing.

As we can see in the picture above, it is possible to distinguish parameters:

• The focal length: the distance between the lens and the area at which the focus diameter is equal to d
• The focal region: the zone that is between two areas of focal diameter equal to 2d.

Fundamental equations

Two formulas are important in order to obtain a good signal analysis:

• 1. Is useful to understand the distance between the probe and the target C: propagation velocity in the medium = = T: period of the wave
• 2. The second equation describes the relates of the intensity of the received signal to the intensity of the transmitted one S(t): intensity of the received signal; T(t): the intensity of the transmitted signal; β(t): the transducer properties of the medium; β(t) η(t) S(t) = T(t) * * A(t) * A(t): the distance between the transducer and echo element; η(t): the intensity of the diffused beam.

Where * indicates the time convolution.

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II. Probe

Mechanical scanners can be considered as the past technology used for diagnostic US system. It scans with a defined number of view line the medium, an important parameter is the frame rate which is c is the propagation velocity into the medium; = R is the depth of the medium that is analyzed; I is the number of view lines; v.

The multiplier 2 is due to the fact that the wave is sent and after received. The FR characterizes the resolution of the mechanical scanner, a way to increase this value is to reduce as much as possible the I and the R, instead it is not possible work on c value because depends on the medium. v.

Scanner array

• Sequential and linear array - In linear array (like in the other new types) nothing is mechanically moved. The scansion is sequential (sequential probe). It is composed by 128-512 elements (PZT crystal), this probe is more versatile than the mechanical scanning transductor.

It analyse a rectangular sector, whose width depend on the transducers used. The more recent models, called Linear Phased Array, are provided with a sophisticated electronic. That allow to create delayed signals which will give to the operator the possibility to steer the beam and to change the focal point (focal lens are no more necessary). Linear arrays require high sensitivity, high signal-to-noise ratio, good spatial resolution, no artefact. Array elements must have wide angular response in the steering direction, low losses due to the transverse coupling, electrical impedance adapted with the transmitter one.

It is composed by support (backing) material, the PZT crystals having rectangular shape, each one connected with two cables. These cables transmits voltage signals in both direction: when the transducer is used as a transmitter, a generator sends the signals toward the crystal in order to generate the US waves. In the hearing phase, the reflected signal travels from tissues to the crystal, than in the cables, at the end the signal is amplified by the Op.Amp. So each array element normally has a separated connection with his transmitter and its electronic receiver, that means a lot of cable that make hard to produce the probe. To solve that problem the ground is in common for all the crystals, that “trick” simplify a lot the realization of the device.

As already said, in the linear phased array the focusing is obtained with delayed electrical signal, in the figure below is shown a qualitative description of the phenomenon:

The main benefit is that thank to positive interference is possible to modify the focus whenever we want, instead with the physical lens that’s not possible. In facts the beam produced by a single crystal will diverge very rapidly resulting in a really poor lateral resolution. To solve that problem 8 to 16 PZT fire simultaneously (so to have a large diameter, long focus zone and long NFL), the