In this report I will cover the fundamentals of Diagnostic Ultrasound and Elastography. The basic theory of Ultrasound such as tissue scattering, transducers, signal processing and display will be elaborated. Also the hazards, limitations, devices currently on the market and future applications will be covered.
Ultrasound has been in use as a medical imaging device for over thirty years, it was first promoted for therapeutic applications in the 1940s to treat a variety of conditions such as arthritis, gastric ulcers and eczema among others. However concern was expressed over the harmful tissue effects of ultrasound which curtailed the development of diagnostic ultrasound in the following years. The founding fathers of diagnostic ultrasound are Karl Theodore Dussik of Austria who published a paper on medical ultrasonics in 1942 and Professor Ian Donald of Scotland, who developed practical technology and diagnostic applications for ultrasound in the 1950's. Finally in the late 1960's the use of diagnostic ultrasound became widespread in hospitals across Europe the United and States and Japan for use in Obstetrics and Gynaecology. Unique characteristics such as low cost, temporal resolution, non ionizing radiation and portability have ensured that Ultrasound remains popular in its traditional guise. However, current developments such as Elastography have added to the quality and applications of diagnostic ultrasound imaging. In the early nineties Ophir et al.,  introduced elastography, which is defined as biological tissue elasticity imaging. Primary objectives of elastography were to complement B-mode ultrasound as a screening method to detect hard areas in the breast and to investigate prostate cancers, but future improvements in the technology promises to further enhance its value for clinical applications.
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Ultrasound is used in a range of clinical settings including gynaecology and obstetrics, cardiology and cancer detection. 
Obstetrics and Gynaecology
Measuring the size of the foetus to determine the due date.
Determining the position of the foetus.
Checking the position of the placenta to see if it is improperly developing over the opening to the uterus.
Seeing the number of foetuses in the uterus.
Checking the sex of the baby.
Checking the foetus's growth rate by making many measurements over time.
Diagnosing tumors of the ovary and breast
Looking the inside of the heart to identify abnormal structures or functions.
Measuring blood flow through the heart and major blood vessels
Measuring blood flow through the kidney.
Diagnosing kidney stones.
Detecting prostate cancer
Advantages of Ultrasound
Most ultrasound scanning is usually painless and is non-invasive.
It is widely available, easy-to-use and less expensive than other imaging methods.
Ultrasound does not use ionizing radiation making it especially useful for the diagnosing and monitoring of pregnant women and their babies.
Ultrasound provides a clear picture of soft tissues that would be poorly visible on x-ray images.
Ultrasound images are real-time, making it an ideal tool for guiding minimally invasive procedures such as needle biopsies and needle aspiration. 
Ultrasonic waves can be disrupted by air or gas; as a result it is not a suitable imaging technique for the bowel or organs obscured by the bowel. Magnetic Resonance Imaging or CT scanning would be more suitable imaging techniques for these areas. As sound waves pass deeper through tissue they become attenuated which makes it difficult to image larger patients. Finally, Ultrasound is not effective at penetrating bone and therefore can only see the outer surface or bony structures, not what lies within.
Hazards to Humans
The hazards associated with ultrasound are well documented. However, there have been no substantiated ill-effects of ultrasound documented in studies in and the risk to patients can be minimised if due precaution is taken by the operator. The main risk associated with ultrasound use is the thermal heating of tissue, which if uncontrolled can cause apoptosis. As sound energy is transmitted through tissue, some energy is reflected and some energy is lost from the ultrasonic wave as it passes through tissue which is largely due to viscoelastic absorption. This loss depends on the amplitude absorption coefficient of tissue, Î±, which quantifies the loss of wave amplitude with depth. Bones have the highest absorption coefficient, body fluids the lowest and soft tissues lie somewhere in between. Most of the acoustic energy deposited is converted to heat, raising the tissue temperature. The initial rate of temperature rise is equal to: , where (I) is the intensity of the wave and (C), is the specific heat capacity of the medium. The intensities and powers used in modern ultrasound machines are sufficient to raise the temperature of tissues by a few degrees Celsius. Heating caused by ultrasound tends to be highly localised to the region within or immediately adjacent to the ultrasound beam. The greatest increases in temperature occur at the surface of bone, in soft tissues conditions which could give rise to temperatures greater than 2 degrees Celsius. To minimise the risk of heating, the operator should not keep the transducer stationary for lengthy periods and also consider the risk of damaging tissue surrounding bone where temperatures will be higher.
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Another risk from ultrasound exposure is Acoustic Cavitation. This phenomenon occurs when a gas bubble in a liquid (blood) experiences the variations in pressure of an acoustic wave. The bubble will expand during the decreased pressure and contracts during the compressive half cycle of the wave.  The risk of acoustic cavitation is the mechanical forces that are exerted on the surrounding fluid. This could lead to capillary rupture and the leakage of blood contents into the surrounding extra-vascular space.  It is extremely improbable that acoustic cavitation occurs "iv-vivo" at diagnostic levels of ultrasound. However the risk does exist for patients with clots or those taking anti-clotting drugs such as the aspirin which the operator should be aware of.
Finally, the presence of gas within tissue gives rise to specific mechanical effects. Any gas/tissue interface reflects all the sound energy which causes the energy density at the interface to double and inverts the phase of the wave. The deposition of energy in such structure is likely to cause heating and also an acoustic cavitation like effect on any semi-free cavities. Lung capillary damage may be caused when ultrasound scanners are used at the upper end of the available pulse amplitudes. However, the risk from gas body effects is still not fully understood and more research needs to be undertaken in this area. 
Principle of Operation
A transducer transmits high frequency sound pulses into the body.
As the sound waves travel deeper into the body they hit a boundary between tissues.
Some sound waves are reflected back to the transducer while others travel further until they are reflected back by another boundary.
Reflected waves are sent back to the machines CPU.
The distance from the probe and the tissue or organ is calculated using the speed of sound in tissue(1,540 ms-1) and the time of each echoes return => d = ct/2.
This distances and intensities of the echoes is displayed on the screen, forming a 2D image as demonstrated in figure1 below:
Figure 1, Ultrasound image of human Foetus 
Sounds with a frequency above 20 KHz are ultrasonic since they cannot be heard by the human ear. When emitted in short bursts the sound travels through media with slow reflection coefficient and is reflected by obstacles. The detection of this reflection, or echo, of the ultrasonic wave localises the obstacle.
As an ultrasonic wave travels through tissue, the peak local pressure in the tissue increases. The oscillations of the particles result to harmonic pressure variations within the tissue and to a pressure wave that propagates through the medium as neighbouring particles move with respect to one another.
Tissues are composed of cells that serve as boundaries to a propagating wave. As the wave travels through these complex structures, waves are reflected and transmitted at any interface encountered dependant on the density, compressibility and absorption of tissue at that location. The groups of cells are known as scatterers as they scatter acoustic energy. The backscattered field picked up by the transducer is used to generate an ultrasound image. An example of an ultrasound image of prostate can be seen in figure 2 below.
Fig. 2, Sonogram of prostate and it corresponding anatomy at the same plane 
The outermost layer of the prostate is shown to have a strong echo, mainly between due to the impedance mismatch between the surrounding medium (gel) and the prostate. The grainy appearance is called speckle . It is produced by the destructive and constructive interference of the scattered signals from structures smaller than the wavelength; this causes the appearance of bright and dark light echoes. Therefore speckle does not necessarily relate to a particular structure in the tissue. The amplitude of speckle has been represented as having a Gaussian distribution with a certain mean and variance . Theses parameters may be used to indicate that the Signal to Noise Ratio of an ultrasound image is limited to 1.91. Previously, several attempts were made at speckle cancellation techniques in an effort to increase the image quality . However, speckle does have its advantages, despite being described solely by statistics it is not a random signal, it is coherent and preserves its characteristics when shifting from position to position.
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As a result motion elimination techniques that can be used to determine anything from blood flow to elasticity are possible in a technique known as speckle tracking.
Figure 3, 2D Echocardiographic Right Ventricular Strain Derived from Speckle Tracking. 
As an ultrasonic wave propagates through tissue it loses power directly proportional to the distance travelled in the tissue. This phenomenon is known as attenuation and can be attributed to a number of factors such as; divergence of the wave-front, reflection at planar interfaces, scattering from irregularities or point scatters and absorption of the wave energy . The absorption of wave energy leads to heat increase.
Ultrasound waves are generated using transducers. They typically use a piezoelectric material that transmits a pressure wave when an electrical potential is applied across it. This phenomenon is reversible, that is, a piezoelectric crystal will convert an impinging pressure wave to an electrical potential, thus allowing the same transducer to act as a receiver. Examples of piezoelectric materials are polyvinylidiene fluoride, quartz and lead zirconium titinate (PZT). A schematic of a single element ultrasound transducer is shown in figure 4 below.
Figure 4, typical construction of a single element transducer. 
The resonance frequency of the piezoelectric material can be given by fo = , with
respect to its thickness (t) and propagation speed (c).
The speed in the PZT material is around 4000ms-1, so for a 5MHz transducer, the thickness should be 0.4mm thick. The matching layer is usually coated onto the piezoelectric crystal in order to minimise the impedance mismatch between the crystal and skin surface. To overcome the impedance mismatch, the ideal impedance Zm and thickness dm of the matching layer are given by:
with Zt = transducing impedance, and Z = impedance of the medium.
The backing layers behind the piezoelectric crystal increase the bandwidth and energy output. If the backing layer contains air, then the air crystal interference yields a maximum reflection coefficient given the high impedance mismatch. Also, an air backed crystal element will have a crystal that is relatively un-damped, that is the signal transmitted will have a low bandwidth and a longer duration. The axial resolution of the transducer depends on the signal duration or pulse width transmitted. Consequently, there is a trade off between transmitted power and the resolution of an ultrasound system. Therefore the type of backing layer to be used depends on the application. Air backed transducers are used in continuous wave ultrasound applications while where high resolution images are required, heavily backed transducers can be used at the expense of reduced penetration and lower sensitivity.
Signal Processing and Display
Figure 5, Block diagram of a pulsed-wave system and resulting signal or image at three different steps
Figure 5 shows the different steps used in order to acquire process and display the signal from the tissue.
A pulse o set duration, frequency and bandwidth is transmitted with a trade off between penetration and resolution, therefore the frequency chosen will depend on the application. For deeper organs such as the heart, liver or the uterus, frequencies would be in the range of 3-5MHz. For more superficial structures such as the breast and thyroid or on children, a wider range of 4-10MHz is applied. Finally, for ocular applications a range of 7 to 15 MHz is set because of the low attenuation, depth and high resolution required.
The received signal needs to be initially amplified so as to ensure a good signal to noise ratio. The input of the amplifier should not have a high voltage pulse to protect the circuits while also maintaining its low noise with high gain. A typical dynamic range at the output would be 70-80db time gain compensation
As the ultrasound wave travels through the tissue attenuation occurs with increasing depth. As a result, the artificial darkening of deeper structures may occur, to avoid this, a voltage controlled attenuator can be used which manually adjusts the system gain accordingly after an initial scan. A mean attenuation level with depth is compensated for with a logarithmic voltage ramp . The dynamic range is further reduced to 40-50db.
Signals are usually to be displayed on a CRT screen where the dynamics range is typically only 20-30db, therefore as amplifier with a logarithmic response is used.
Since the image is in greyscale the envelope of the RF signal needs to be calculated, this is usually achieved by using Hilbert transforms. The resulting signal is called an A-scan or A-mode as can be seen in figure 5.
The A-Scans are spatially combined after acquisition using transducers and the Brightness (B-Mode) is created. This is the most widely used diagnostic ultrasound mode as it has a true image format. One of the greatest advantages of ultrasound imaging is real time scanning, which is possible due to the shallow depth of most tissues and the high speed of sound. Frame rates are usually in the order of 30-100MHz. The frame rate is limited to the number of A-Mode scans acquired (Na) and the Maximum depth.
Max Frame Rate, PRFF = 
Where tissue motion needs to be monitored and analysed, A-Scans can be displayed as a function of time. To achieve this, only one A-Scan from a particular tissue structure is displayed in B-Mode but followed in time depending on the pulse repetition frequency used. This method is known as the motion or M-Mode scan. A time depth display is then generated. A Typical application of M-Mode display would be in the examination of the heart valve motion.
Constant depth mode differs from aforementioned modes due to its distinct use of scanning. Instead of relying on echoes reflected from tissue, the pulse is transmitted from one side of the body by a transmitter and picked up on the other side by a separate transducer with a scanning motion perpendicular to the transmitter beam. Applications of the C-Mode are found in superficial tissues that are relatively homogenous so as to ensure travel of the echo through all the interfaces, for example in the female breast.
Diagnostic Ultrasound Machine Components
Figure 6, Basic components of Ultrasound machines 
As is demonstrated in figure 6 above, an ultrasound machine consists basically of the following components:
Transducer probe; sends and receives the sound waves.
Central Processing Unit (CPU); calculates and processes signals from transducer.
Transducer pulse controls; changes the amplitude, frequency and duration of the pulses emitted from the transducer probe.
Display; shows image from the CPU has processed from ultrasound data.
Keyboard; Data input and measurement capture.
Disk storage device; stores the acquired images.
Printer; prints the image from the displayed data.
Current State of the Art - Elastography
Elasticity imaging has emerged out of ultrasound imaging in the last decade that is based on the mechanical properties of tissue. Elastography can be defined as an imaging technique whereby local axial tissue strains are estimated from differential speckle displacements acquired from ultrasound frames. These displacements are generated by a weak, quasi-static stress field. The resultant strain image is called an elastogram.
The principle of operation of Elastography is based on two facts:
Firstly, the mechanical properties of several tissue components can be significantly different. Figure 7 shows the validity of this fact by showing the range of elastic moduli for several different normal and pathological human breast tissues. As can be seen the hardness of normal glandular tissue is different than tumerous tissue by up to one order of magnitude.
Figure 7, Elastic moduli of normal and tumorous breast tissues; DCa: ductal carcinoma, IDCa: invasive ductal carcinoma 
Secondly, that the information contained in the speckle is sufficient to depict these differences as a result of a quasi-static compression. Figure 8 shows the general concept behind Elastography, tissue is insonified (left) before and (right) after a small uniform compression. In harder tissues (encircled area) the echoes will be less distorted than in the surrounding tissues, denoting less strain.
Figure 8, the principle of elastography. 
The Radio-Frequency (RF) ultrasonic data before and after the applied compression are acquired and speckle tracking techniques are employed in order to calculate the resulting strain . The higher the strain estimated, the softer the material and vice versa. The resulting strain image is called an elastogram. Each pixel on an elastogram denotes the estimated amount of strain, Îµ, which the tissue experiences during applied compression, defined by:
Where and denote the estimates of tissue displacement, spaced by change in time, Î”t.
Elastogram Photograph Sonogram
Figure 9, canine prostate. Black and white denote highest and lowest strains respectively .
An example of an elastogram is shown in figure 9. Compared with the sonogram, complementary information based on the distinct mechanical responses and properties of several anatomical structures of the prostate such as the urethra and the peripheral zones is provided. The urethral crest undergoes the highest strain given the existence of the cavity and higher fluid content. This demonstrates the hoe the high contrast in strain results in more clearly defined tissue components compared to a sonogram.
Elastography is fast becoming an extremely useful technology in the diagnosis of certain cancers as strain images of soft tissues can be used to detect or classify tumours. According to an ongoing study of the Radiological Society of North America (RSNA), elastography is a technique that when added to breast ultrasound can tell cancerous breast lesions from benign ones .Traditionally if a mammogram resulted in questionable findings, a patient would usually be sent for a biopsy. However, the American Cancer Society states that more than 80 percent of breast biopsies turn out to be benign thereby putting patients under undue duress.
Prostate cancer is one of the leading cancer causes of men deaths. To improve patient survival chances, early detection is vital. Early detection of prostate cancer is essential to provide definitive treatment and improve patient survival. Figure x shows the results of initial clinical studies for the prostate cancer detection.
Figure 10, suspicious cancer regions obtained from elasticity imaging. 
Studying figure 10, several hard regions of prostate are identified using ultrasound elasticity imaging. Suspicious cancer regions obtained using elasticity imaging were confirmed as cancer through histological analysis 
Devices Currently on the Market
The major Ultrasound equipment manufacturers are starting to introduce Elastography on their premium products and as upgrade options on older machines.
Siemens ACUSON S2000 Ultrasound System
Figure 11, Siemens acuson s2000 
The Siemens Acuson S2000 features "eSie Touch" Elastography technology.
Elastograms are formed by computing relative tissue deformation globally and displaying the information within a user defined region of interest.
Axial detection pulses are continuously transmitted throughout the field of view to provide information about the state of tissue deformation along one axial line at a specific point in time. Using this technique, stiff and soft tissue may be differentiated even when the tissues appear isoechoic on the B-mode exam. The main features of the Siemens device are:
High resolution elastographic images may be visualised using a variety of grayscale and colour maps.
Shadow Measurements - Measurement calipers are automatically applied to both images in a side by side display for comparison of elastographic.
Transducer support; eSie Touch imaging is supported on linear, endocavity and curved array transducers .
Philips iU22 (Vision 2010 upgrade)
Figure 12, Philips iU22 
As part of an upgrade on their premium diagnostic ultrasound unit, Philips Medical has introduced elastography technology. The main features of this device are:
Highly sensitive strain based technology which obtains elastograms from internal patient movement (breathing, cardiac motion)
Distance and area measurements can be taken at the device.
Size comparisons are available to validate size and location of lesions on an elastograms.
Utilises anchoic imaging to enhance cystic structures of the elastograms.
Colour coded strain ratio parametric image display .
Real time Elastography
Currently in elastography, block matching algorithms are used to estimate the displacement and strain. Displacement estimators are based on a 2D cross-correlation method which requires a lot of multiplications. To efficiently implement a realtime 2D cross correlator, processors in parallelisation are required. Field Programmable Gate Arrays (FPGAs) with high capacity memory banks, have more resources compared to general purpose CPUs and digital signal processors (DSPs). Therefore implementing real time elasticity imaging in FPGAs is being proposed as a viable solution. In a paper entitled, "FPGA based real time ultrasound elasticity imaging system" , the hardware architecture required to implement a real time elasticity imaging system utilising FPGAs is designed and tested. The method proposed is to use normalised cross correlation with a 2D kernel and 2D search for integer level displacement estimates. The subpixel level displacement is calculated by parabolic interpolation in both lateral and axial directions. The target frame rate is at least 30 frames per second.
The Xilinx (XC4VSX55) FPGA with an operating frequency of 500 Mhz is used for implementation of the real time displacement estimator.
Figure 13, top level architecture for proposed FPGA based Elastography system 
Figure 13 shows the block diagram for a real time FPGA based displacement and strain estimator. Using 2-D (KL by KA) kernel and 2-D (SL by SA) search area, the normalised cross correlation engine requiring approximately (KLÃ-KAÃ-SLÃ-SA)Ã-2 multiplications per one output is needed. If one frame has (FLÃ-FA) samples, there are (FLÃ-FA)Ã-FR outputs per second where FR is the frame rate. Therefore, the amount of multiplications per second needed for real time elasticity imaging can be given by:
Using 5 by 31 kernel, 5 by 7 search range, 256 by 4096 for frame and 30 frames per second, 340 billion MAC operations per second will be needed. However, by optimizing the hardware architecture of the normalised cross correlation engine, the impact of KA can be removed. Therefore, MAC operations were reduced to around 11 billion per second. Furthermore, to improve the robustness and quality of the displacement estimates, two step (coarse and fine) search and autocorrelation based error correction method can be performed.
Within the given processing time for one line, 2D cross-correlation using envelope data for coarse search is performed first, and then the radiofrequency (RF) data is used for both fine search and displacement error correction. With this system the desired 30 frames per second was achieved .
Vascular Elastography- United States Patent Application 20070282202
Changes in vessel wall elasticity may be indicative of vessel pathologies. It is known that the presence of plaque stiffens the vascular wall and plaque may lead to thrombosis. It would seem Elastography would be a suitable technology to diagnose atherosclerosis, however, as tissue motion occurs radially within the vessel wall while the ultrasound beam propagates axially, motion parameters might be difficult to interpret. To compensate for this, conventional vascular elastography must be invasive; vascular tissue is compressed by applying a force from within the lumen. The compression can be induced by the normal cardiac pulsation or by using a compliant intravascular angioplasty balloon. A patent has been filed for a for Non-Invasive Vascular Elastography system .
The device aims to provide pre-tissue motion and post-tissue motion images in digital form of a vessel delimited by a vascular wall; the pre-tissue motion and post tissue motion images being representative of first and second time delayed configuration of the vessel. Portions of both the pre-tissue motion and post tissue motion images will be partitioned into corresponding data windows and using the trajectory for each data window to compute a strain tensor in each data window. The Von Mises coefficient is proposed as a new parameter to characterise the vessel wall. The Lagrangian speckle model estimator (LSME) is proposed to non-invasively characterise vascular tissues because it computes the full 2D strain tensor that is required to provide the Von Mises coefficient.
Figure 14, Non-invasive vascular elastography system 
The block diagram in figure 14 shows the components of the proposed elastography device (10). The ultrasound instrument (12) is provided with a scanhead (20) including an ultrasound transducer. The instrument (12) is coupled to an analogue to digital acquisition board (14) of a controller (16) via a radio frequency (RF) pre-amplifier (18). The ultrasound system (11) is configured with access to RF data so as to allow computing vascular elastograms of vessels. The ultrasound instrument (12) provides an RF output from which the received RF data is transferred to the pre-amplifier (18). The acquisition board (14) allows digitising of the pre-amplified signals from the preamplifier. The controller (16) is a PC including a CPU (22) which is provided with an output device (24) in the form of a display monitor coupled to the personal computer (16). The controller is provided with memory for storing the scan signals and/or storing elastograms information. The transducer (11) is applied on the skin over the region of interest and the arterial tissue is dilated by the cardiac pulsation or any other tissue dilation means.
Ultrasound has become an invaluable diagnostic tool since it was widely introduced in the late sixties and despite the fact that it is an older imaging technique, it continues to expand as a field and offer numerous applications. In the past decade, as faster processors have become available, new applications have emerged including contrast agents, complex transducer architecture and signal processing techniques. For the purpose of this report, Elastography was chosen as the state of the art device due to the vast impact that this technique could have on the imaging and characterisation of tissue based on their mechanical attributes. Evidence proves the accuracy of elastography at diagnosing malignant tumerous tissue without the need for biopsies, which averts the need for invasive surgery and undue patient duress. For the future of elastography, a variety of very promising methods have recently developed. Spanning from hand held and real time application of elastography to elastic modulus maps based on the wavelength of propagation through different tissues following an applied stimulus(transient elastography) and the use of internal radiation force resulting from the pressure of the beam itself to locally displace (remote palpation) or vibrate (ultrasound stimulated vibro-acoustography), to name a few.