BME355 Lab Listing: Ultrasound
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Ultrasound


Preparation

Lab Outline

Procedure

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Preparation

Ultrasound Measurement

In medical acoustics and ultrasound, we deal with sound propagation in liquids (like blood and soft tissue). All experiments we do in this lab will therefore be done in a liquid medium such as water. We will use two types of acoustic transducers in these exercises: speakers and microphones. A speaker converts an electrical signal into mechanical motion, which then excites the surrounding air, creating an acoustic wave. A microphone does just the opposite, turning acoustic energy into mechanical energy and then into an electrical signal.

Emission Transducer

The emission transducer will act as our "speaker''. It is constructed of a thin disk of PZT material. A PZT or piezoelectric material is a special kind of crystal which expands or contracts in response to an applied voltage. The disk shaped PZT in our emission transducer has a resonance frequency at 3.35 MHz (3.35 million cycles per second), meaning that it couples the electrical input to mechanical motion most efficiently at this frequency.

We will use an electrical signal from the function generator to drive the emission transducer. The emission transducer requires a good deal of power to produce any acoustic output (PZT transducers are generally very inefficient). The function generator cannot provide this power by itself, so we must use an amplifier. The amplifier is an ENI A150, which is especially designed for operation at very high frequencies. The amplifier is rated to provide a fixed voltage gain of roughly 55dB which translates to increasing the input voltage 562 times.

Thus, an input to the amplifier as low as 50 mV will produce an output that is  50 × 562 = 28.1 V. 50-150mV is high enough to drive the transducer. 50 mV is the lowest output amplitude of the function generator.

Hydrophone

We will use a special kind of "microphone'' called a hydrophone. As you can figure out from its name, a hydrophone is an underwater microphone. The hydrophone you will use is a needle hydrophone. The tip of the hydrophone contains a PZT element, and responds well at ultrasonic frequencies. The output of the hydrophone is extremely low, and we therefore must use a pre-amplifier to amplify the signal before we view it on the scope. The amplifier requires 15 volts DC from a power supply.

Measuring sound propagation speed

Sound waves can propagate in media besides air. In medical acoustics, we are typically concerned sound propagation in liquids (i.e., water, blood, or soft tissue). We use frequencies much greater than audible sound waves in air ( < 20kHz). The reason for this will become apparent in a later exercise. Different propagation media have different acoustic properties. For example, in air, sound propagates at 343 meters per second. In water, this propagation speed is very different and the purpose of the first exercise is to determine this speed. Both water and air are dispersionless media, meaning that sound propagates at the same speed regardless of frequency. We therefore only need to measure the sound speed at one frequency.

Measuring wavelength

The wavelength  is defined as the distance traveled by sound during one cycle of vibration. Therefore: 

(1)


As you can see, for a fixed frequency,f, the wavelength grows as the speed of sound does. The wavelength increasesis because in one cycle, the sound propagates a longer distance.

Principal of superposition

In order to better understand the radiated field of an acoustic source, we can consider it to be composed of many smaller "simple" sources. A simple source is an infinitesimal source which radiates equally in all directions, with a pressure amplitude falling off as 1/r. To determine the acoustic field at any point in space, we may add up the contributions from all the simple sources comprising the more complex source. Most transducers used in medicine are either planar or concave focused.

At any given point in time, every point on the transducer has the same displacement. It can be said that every element is vibrating "in phase". However, since the ray paths from the transducer to the observation point may differ in length, the phases of the contributions from each point may differ.

Focussed Transducer

The transducer you will use is concave in order to provide a more focussed field. For a focussed transducer, the rays will maximally add up at the radius corresponding to the curved segment. Away from the focus,there will be cancellation.

Planar Transducer

Consider a point along the axis of a plane piston transducer. The acoustic field at that point will be composed of contributions from the points at the center of the transducer, at the edge, and everywhere in between. It is important to note that the acoustic path lengths from the different points to the observation point differ. In this case, the shortest path is from the center of the transducer to the observation point, and the longest originates from the edge of the transducer.

Understanding far field behavior

We can understand the azimuthal behavior of the far field once again by considering the superposition of the many rays coming from the transducer.

 
Figure 1: Observation point in the far field at an angle $\theta$ off axis for a planar transducer.
 
Figure 2: Close-up shot of planar transducer face with rays headed towards observation point in far field. Path length difference between adjacent rays is shown.

Figure 1 shows the transducer and an observation point in the far field located at an angle  $\theta$ off the transducer axis, along with many acoustic rays. Figure 2 is a zoom shot near the transducer. Notice that up close it appears that all the rays are nearly parallel. We can then approximate the path length difference between adjacent rays by the distance  $\Delta l$, which from basic trigonometry: 

(2)


where d is the distance between the adjacent rays along the transducer face. Consider the uppermost ray in the diagram and the ray coming from the center of the transducer. If the path length difference between these two is an odd number of half wavelengths, then complete cancellation will occur. If this is the case, the second ray from the top and the first ray below the center ray will also have the same path length difference and cancel each other. The result is that each pair will cancel so that we have complete cancellation. Mathematically, this condition is 

(3)


 
Figure 3: In the far field, we can relate off axis angle to distance.
 
Figure 4: Theoretical far field pressure distribution for a planar transducer. Here $z=9\mathrm{cm}$$f=3.35\mathrm{MHz}$$a=6\mathrm{mm}$

Our system does not directly scan as a function of angle, but instead just scans a plane perpendicular to the transducer axis. Looking at figure 3 we see that in the far field we can relate the position in the measurement plane to angle by 
\begin{equation}y = z \tan \theta \approx z \theta\end{equation}

(4)


We might therefore expect to see the first minimum in transducer response near $y=z \lambda/2 a$.

We will have complete cancellation if the path length difference between each pair of adjacent rays is equal to an odd number of half wavelengths 

(5)


A theoretical plot of the azimuthal variation of the pressure field for a planar transducer is shown in figure 4.

Approximations

In our qualitative analysis of the wave cancellation of this transducer in the far field, we have ignored the circular shape of the transducer and considered only its projection onto a line. We then considered each ray to be of the same strength (which would be exact if we had a square transducer). In the case of a circular transducer, we would need to consider the elements near the center of the line to be stronger than those at the edge. Still, the differences are small and this reasoning should provide a good estimate as to where the first minimum lies.

Also note that when sound scatters off an inhomogeneity in a tissue, energy may be returned not only from the main lobe signal, but also from side lobe signals. Thus, there can be some ambiguity in the information returned to the transducer and thus the image created from scattered acoustic waves. Therefore, transducer design often attempts to minimize these sidelobes. This can be accomplished by using a many element array, and phasing as well as tapering (giving different strength signals to the elements).

Principles of ultrasonic imaging

A typical imaging transducer has the capability of both sending and receiving acoustic signals. Consider the case where a short acoustic pulse is emitted from an imaging transducer. The pulse travels until it encounters an object. A portion of the pulse is reflected straight back and is received by the transducer. The pulse travels a total distance 2d , where d is the distance from the transducer to the object. If the sound propagation speed c is known, then the distance can be found from the time delay t between the sent and received pulses: 
  \begin{equation}d = c\, \frac{t}{2}\,.\end{equation}

(1)


Most ultrasound imaging systems assume a sound speed of 1540 meters/second. The actual sound speed in the body is relatively constant, usually varying by less than 5% [Kremkau, Diagnostic Ultrasound, page 16].

Now consider several objects lying along the propagation path of the transducer. When the pulse hits the first object, some of it will be reflected back towards the transducer, while some will continue and reflect off of further objects. Even though one pulse is initially sent out, the received signal may be a train of many pulses, each one corresponding to the reflection from a particular object.

If the transducer was always fixed in one position only objects lying along one line could be imaged. The imaging transducers of the Sonos 100CF feature a motorized transducer element which sweeps back and forth through an angle. In this way, a pie-shaped 2-D region can be swept out.

The strength of an acoustic reflection from an object depends on the object's density and sound speed relative to the surrounding material. We can define a pressure reflection coefficient R with tells us how much of the incident sound pressure is reflected. 
$P_r = P_i\left(\frac{\rho' c'-\rho c}{\rho' c'+\rho c}\right)=P_i R$

(2)


where Pr is the reflected pressure amplitude, Pi is the incident pressure amplitude,  $\rho'$ and $\rho$ are the densities of the object and surrounding medium, and c' and c are the sound speeds of the object and surrounding medium.

Image resolution

As you will notice, ultrasonic imaging does not necessarily provide a crystal clear picture of what you are trying to image! There are many factors that limit resolution, and lead to image artifacts. When talking about resolution, we will deal with both axial and lateral resolution. Axial resolution is the minimum spatial detail which can be resolved in the direction of rays radiating from the transducer, while lateral resolution is the minimum spatial detail in the direction perpendicular to this.

Axial resolution

The primary factor determining axial resolution is the pulse length of the outgoing signal. The transducer element is constructed out of a piezoelectric ceramic which has its own characteristic resonant frequency. When a short voltage pulse is applied to the ceramic, it will "ring" at this frequency and quickly die away (analogous to the ringing of a bell), producing a short acoustic pulse.

Consider a pulse of temporal pulse length tp . Now consider two point objects in a single line separated by less than half of the spatial pulse length lp:
\begin{equation}l_p = c t_p\,.\end{equation}

(3)


After being reflected from both objects, there appears to be only one return pulse. If the objects are separated by more than half of the spatial pulse length (tp/ 2), two distinct return pulses can still be seen. If they are closer together than that, the reflections will merge into one single pulse. Therefore, there is a lower limit on axial resolution determined by the pulse width alone: 
$\mathrm{Axial\ resolution}=\frac{l_p}{2}=c\frac{t_p}{2}\,.$
(4)


Clearly, the shorter the pulse, the better the axial resolution. A short pulse width requires a transducer with high damping (to make the "ring" as short as possible), but this high damping will compromise the acoustical efficiency of the transducer as well. Note that although this gives us a nominal lower limit in resolution, in reality the actual resolution will be somewhat lower.
    
Lateral Resolution

One of the chief factors determining lateral resolution is the beam width of the transducer. Ideally, we would have a transducer with a perfectly narrow beam which travels straight ahead with little divergence. The elements in the transducers of the Sonos 100CF are slightly curved, which creates a beam profile with a maximum intensity at the geometrical focus. The beam is narrowest at the focus, and becomes wider as you move further away from it. The lateral resolution is approximately the same as the beam width. Transducers can be designed with various depths of focus. With a sharp focus, the lateral resolution will be excellent at the focal depth, but will deteriorate rapidly away from it. Most transducers have a broader focus, which slightly compromises the resolution at the focus but gives better overall resolution over a greater depth range. Most imaging systems have better axial resolution than lateral resolution.
 
 

Introduction to Doppler Imaging

Consider a flow of liquid with constant velocity v containing scattering inhomogeneities (i.e. blood cell flow in a vessel). As a sound wave travels into the moving fluid, the disturbance is carried along by the velocity of the fluid. Let the wavelength of the original sound wave be . By the time that one full wavelength has entered the moving fluid, the wavefront has moved a distance 
doppler equations
where  theta is the angle between the direction of flow and the direction of the ultrasound beam, v is the velocity of fluid flow, T is the period of the sound wave, f is the frequency of the sound wave, and c is the sound propagation speed of the medium (assumed to be the same both inside and outside of the flow).

The spatial wavelength will therefore be longer inside the vessel. Next, the sound wave will be scattered by inhomogeneities (i.e. red blood cells), and some will be scattered back in the same direction as the incident wave. This wave will begin propagating back towards the transducer at a speed c-vcostheta. Once the scattered wave reaches the vessel wall, one full wavelength will propagate into the still medium in a time: 

doppler equations

If we make the assumption that  v<<c (which is always the case in blood flow), we can rewrite the new frequency to first order as

   doppler equations

Clearly the received frequency is lowered when flow is moving away from the transducer, and raised when moving towards the transducer. The frequency shifts can be small, but are maximized when the flow and transducer axes are parallel.


SONOS 100CF specifications

The following specifications are taken from the SONOS 100CF manual.

Table 1: 
  2.5 MHz 5.0 MHz
Center Frequency (imaging mode) 2.43 MHz 4.85 MHz
Pulse duration 0.761 $\mathrm{\mu s}$ 0.507 $\mathrm{\mu s}$
Pulse repetition rate 2446 Hz 2446 Hz
Axial resolution 1.5 mm 0.8 mm
Lateral resolution 2.5 mm 1.2 mm
  

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