Method Of Tendon Stress Measurement Using Ultrasound Computer Science Essay


Tendons are flexible fibrous tissues that are subject to stress and strain during effort and movement. Some tendons are more injury prone than others, especially those with low blood levels such as the Achilles tendon. This makes evaluating the stress and strain levels of such tendons particularly important in diagnosing current and preventing possible future injuries by using appropriate treatments and taking suitable precautionary measures.

This project deals with the prospect of developing a novel non-invasive technique in which the stress and strain levels of a tendon can be experimentally evaluated. In achieving so, the velocity of ultrasonic waves transmitted and received along the main axis of the tendon is measured. As the velocity is found to vary with the tendon stress, it can be used as an indicative measure of the extent of the tendon injury and assist in the treatment and rehabilitation phase of the injury.

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This report details the development of the technique, deals with the various associated technical issues and discusses the results obtained and the possible future work. The project has successfully developed the hardware required to drive the ultrasonic transducers and appropriately condition the received signals. It has also succeeded in accurately measuring the time of flight (TOF) of the ultrasound signals (a parameter of crucial significance in calculating the US velocity) using both low and high frequency ultrasound in mediums such as air, steel and aluminium. Some preliminary results of measuring TOF of the US waves travelling through a tendon are also given and discussed.


2. Introduction

Tendon injuries can occur in many physical activities in which excessive tension is applied to a tendon structure connecting muscle and bone. Sudden eccentric stretching for instance could result in partial or full Achilles tendon ruptures which require lengthy and painful recovery programmes [1].

Tendon recovery programmes form a particularly important part of many sportspersons' careers. This is mainly owing to the fact that a tendon injury, depending on its severity, can require a lengthy healing period, an intensive physiotherapy programme, a surgical procedure and/or a painful recovery time. Of the many tendons vulnerable to injuries such as hand, finger and wrist tendons, Achilles tendon is the most consistently injured. This is largely because it has one of the lowest blood supplies of any tendon and therefore is prone to chronic injury and difficult tendon recovery [2]. In fact, as many as 232,000 Achilles tendon sports injuries are reported in the U.S.A alone annually, preventing nearly 50% of participating in future sport commitments [3].

In a statistical study, researchers investigated the factors and aftereffects of Achilles tendon ruptures among NFL players to establish the impact of these injuries on their performance. Researchers collected data and figures on NFL games and injuries and identified players who had sustained a complete Achilles tendon rupture. For those players, data collected both before and after the injury was combined with information on their position, age, how long they played in the NFL to complie performance related statistics.

With surgery being the sole effective treatment for a complete Achilles tendon rupture, the researchers found that the lengthy recovery period results in nearly 36 percent of players who had suffered a complete rupture in never returning to play in the NFL, and those who did return were never able to meet their pre-injury levels of performance. The injured players who did return to active play averaged a 50% reduction in their power ratings.

In general, tendon injuries are found to be widespread among the general adult population. People with occupations or athletic activities that require rhythmic motion of the shoulder, knee, elbow, or ankle joints suffer more Injuries to the tendons than those with less demanding physical professions. For instance, shoulder tendon injuries often occur among baseball players, violinists, dancers and some assembly line workers. Rowers are at increased threat for injuries to the forearm tendons. The repetitive stress exerted by particular types of movement such as those of classical ballet, running, and jogging may cause damage to the Achilles tendon. Five percent of American adults over the age of 30 are thought to be affected by injuries to the so-called tennis elbow. This type of injury is very common among construction workers, highway crews, maintenance workers, and baggage handlers as well as professional golfers and tennis players.

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Diagnosing a tendon injury can involve an invasive medical procedure. This is true for most types of tendon injuries except raptures, a type of injury that can be verified using X-ray or MRI scanning. For instance, inspection of partial cuts of tendons occurring as a result of glass or knife accidents often require exploring the wound by cutting it further as a part of a regional or, in some cases, general anaesthetic procedure[4].

Having an effective means to non-invasively inspect a particular tendon injury can serve as an important alternative to most of the surgical and other invasive medical procedures currently in use. Furthermore, early inspection of tendon stress and strain levels can prevent possible future tendon ruptures by preventing the exposure to further physical stress and taking other suitable precautionary measures. Of those means currently being investigated, is the use of ultrasonic signals to observe the stress and strain levels of a tendon. Being a function of the stress level of a tendon, the velocity of a travelling ultrasonic wave along the axis of an inspected tendon can be measured to serve as an indication of the type and severity of the injury and indeed assist in the follow-up medical procedure and recovery programme.

The velocity of the US signals can be estimated using (at least) two transducers, one acting as a transmitter and the other as a receiver. With the distance separating the transducers known, the velocity can be calculated by finding the time of flight of the US waves using an oscilloscope [2], [5].

To follow, the principles of the technique are explained and a discussion of the progress of the project is given detailing the work that has been done and outlining future work.

3. Mechanical Properties of Tendons

Tendons are fibrous connective tissue structures that connect muscles to bones. They are crucial parts of the skeletal muscular system as without them the two parts providing framework and power to the body (bones and muscles) would fail to function. Furthermore, the human body consists of thousands of tendons, each serving as a primary means to generate contractile forces necessary to facilitate different types of movement.

Contrary to the intuitive thought, muscles cannot contract in isolation; rather, tendons must participate by providing the necessary connection to muscles to generate and then transmit contractile forces. The mechanism of muscle - tendon interaction and the elastic properties of the tendon govern the type and quality of movement. In almost all movements, when the muscle contracts, the tendon will lengthen before it shortens, independent of any change in muscle length. This property of recoil enables elastic energy to be stored and released, thereby increasing the efficiency of the muscular contraction. Thus, movement is a combination of two factors within the muscle - tendon complex (MTC):

Muscle forces transmitted through the tendon to the joint.

Elastic energy recoil of the tendon.

Each tendon has its own mechanical properties such as stiffness, toughness, ultimate stress and ultimate strain and is subject to different levels of loading forces. The two key properties of tendons of relevance to the performance of the muscle-tendon complex are: stiffness and hysteresis. Both of which can be altered with training.

Tendon stiffness is a mechanical property describing the relationship between the force applied to the muscle-tendon complex and the change in the length of the unit. It has no direct relation to flexibility, or range of motion. The exact equation is:

Thus, if a greater degree of force is needed to produce a given amount of stretch, it can be said the muscle-tendon complex is stiffer. Correspondingly, the exertion of less force to produce the stretch means the muscle-tendon complex is more compliant.

A tendon injury occurs when an excessive force is applied across the cross sectional area of the tendon than it can physically stand. Effects can cause the stress and strain levels of the tendon to increase leading to tendon stretching, inflammation and eventually raptures. Consequently, during the diagnosis phase of an injury, an examination of the tendon's stress and strain levels (particularly during effort) can reveal significant information about the extent of the injury and assist in the recovery programme.

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A typical tensile testing of a tendon can characterises most of the mechanical properties of the tendon and relate them to its stress levels. Figure-2 shows a typical force-deformation diagram

FIGURE-NUMBER: A view of the Achilles tendon and other associated connective muscles and tissues. The soleus and is a powerful muscle in the back part of the lower leg that runs from just below the knee to the heel. The gastrocnemius is similar superficial muscle that is involved in standing, walking, running and jumping

deduced from a tendon tensile testing experiment. The diagram can be divided to four key regions. Loads within region I elongate the tendon but they do not cause further fiber stretching. Forces operating within this region do not top the tendon elastic limit; as the tendon's initial length is restored upon unloading. Subsequent elongation however, brings the tendon into region II, in which linearity dictates that the stiffness remains constant as a function of elongation. At the end point of this region, some fibers start to fail reducing the tendon stiffness and resulting in unrecoverable tendon elongation upon unloading. Unpredictable fiber failures start to occur for elongation past the linear region (i.e. within region III). Region IV represent subsequent elongation where complete tendon failure normally arises [6].



Figure-2: Typical tendon Deformation-Force diagram. Key mechanical properties of the tendon can be deduced from the diagram such as stiffness (slope) and energy (area) [reproduced from [6]].

This is why tendon strain and injury can be very debilitating, particularly when it's a major tendon such as the Achilles tendon.

4. History of Ultrasound Development in Medicine

The use of ultrasound in medical applications has evolved significantly throughout the 19th and 20th century, from simple pulse-echo detection techniques to complex 2D and 3D image scanning systems.

The development of medical ultrasound started with the publication of "the Theory of Sound" in 1877 by English physicist Lord Rayleigh, in which he described acoustics phenomena such as ultrasound transmission and refraction in mathematical form, forming the foundation of future work in ultrasound. Practical experiments followed by utilising ultrasound to measure distance under water albeit with limited success.

Following the discovery of high frequency ultrasound by Italian biologist Lazzaro Spallanzani, a breakthrough in the development of echo-sounding techniques came when the discovery of piezoelectricity exhibited by certain crystals was made by the Curie brothers in Paris, France in 1880. The generation of electric potential as a result of mechanical pressure exerted on a crystal and the reciprocal behaviour of gaining mechanical stress in response to a potential difference made the transmission of reception of acoustic waves in the frequency of megahertz possible.

The progress of naval pulse-echo sonar took a giant step forward when the first patent for an underwater echo ranging sonar was filed by English meteorologist Lewis Richardson. By the mid 1930s, many ships were equipped with some form of underwater echo-sounding range display systems. In the 1930's, other parallel and equally significant advances in ultrasonics in the metal flaw detection industry were made. The integrity of the metal parts of ships and vessels and the armour plates of battle tanks was made possible to check through the development of pulse-echo ultrasonic metal flaw detectors.

Development of medical ultrasound applications took advantage of the advances made in the naval and metal industry when the first successful application was recorded in 1947. Practical work started with the detection of gallbladder stones by using A mode metal flaw detectors on animal tissues. Ultrasonic energy was also extensively used in physical and rehabilitation medicine. In the early 1950s, ultrasound was successfully utilised for the first time in locating brain tumors. A through-transmission technique with a pair of 1.2 MHz transducers placed on either side of the head generating echo images of the ventricles of the brain enabled the detection of foreign cells and tissues in the brain such as tumours. The technique relied on reflections within the skull and its attenuation patterns to contribute to the attenuation pattern and thus produce an echo image. The introduction of newer uni-directional pulse-echo A-mode scanners soon followed to enable developments in medical diagnosis scientists around the world.

The increase in the research and application of ultrasound in Obstetrics and Gynaecology appeared to boom soon after, as dedicated studies in the application of ultrasound diagnosis in this specialty became popular in Europe and Japan. A- and B- mode equipment were both in use including the first 'fast B-scanner', developed at the Wilhelm University in Münster, Germany.

From the mid sixties onwards, the advent of commercially available systems allowed the wider distribution of the art. Rapid technological advances in electronics and piezoelectric materials provided further improvements from bi-stable to greyscale images and from still images to real-time moving images. The technical advances at this time led to a rapid growth in the applications to which ultrasound could be put. The development of Doppler ultrasound had been progressing alongside the imaging technology but the fusing of the two technologies in Duplex scanning and the subsequent development of colour Doppler imaging provided even more scope for investigating the circulation and blood supply to organs, tumours etc. The advent of the microchip in the seventies and subsequent exponential increases in processing power have allowed faster and more powerful systems incorporating digital beam-forming, more enhancement of the signal and new ways of interpreting and displaying data , such as power Doppler and 3d imaging.

Using the first B-mode images obtained; images that static, without gray-scale information in simple black and white and compound technique, scientists succeeded in acquiring the first scan of heart activity. Continuous development in obstetric and gynaecologic ultrasound research led to study pregnancy and diagnose possible complications.

In the 1970's, gray scale imaging became available and with progress of computer techniques, ultrasonic imaging became better and faster. The continuous work carried out in 1980's to further improve current ultrasonic imaging techniques led to the development a fast real-time B-mode gray-scale imaging. Electronic focusing and duplex flow measurements became popular and a wider range of applications were possible.

Further research led to the development of high resolution scanners with digital beam-forming, high transducer frequencies, multi-channel focus and broad-band transducer technology. Optimized tissue contrast and improved diagnostic accuracy lead to an important role in cancer detection. Colour Doppler and Duplex became available and sensitivity for low flow was continuously improved. Further technological advances enabled the invention of machines with advanced ultrasound system performance that are equipped with real-time compound imaging, tissue harmonic imaging, contrast harmonic imaging, vascular assessment, matrix array transducers, pulse inversion imaging, and 3D/4D ultrasound with panoramic view.

With regards to musculoskeletal ultrasound, images obtained from imaging systems provide pictures of muscles, tendons, ligaments, joints and soft tissue throughout the body. This enabled detection of various types of injures and structures such as:

Tendon tears, such as tears of the rotator cuff in the shoulder or Achilles tendon in the ankle.

Abnormalities of the muscles, such as tears and soft-tissue masses.

Bleeding or other fluid collections within the muscles, bursae and joints.

Small benign and malignant soft tissue tumors.

Early changes of rheumatoid arthritis.

In a musculoskeletal ultrasound examination, a transducer both sends the sound waves and records the echoing waves. When the transducer is pressed against the skin, it directs small pulses of inaudible, high-frequency sound waves into the body. As the sound waves bounce off of internal organs, fluids and tissues, the sensitive microphone in the transducer records tiny changes in the sound's pitch and direction. These signature waves are instantly measured and displayed by a computer, which in turn creates a real-time picture on the monitor. One or more frames of the moving pictures are typically captured as still images.

A clear water-based gel is applied to the area of the body being studied to help the transducer make secure contact with the body and eliminate air pockets between the transducer and the skin. The sonographer (ultrasound technologist) or radiologist then presses the transducer firmly against the skin and sweeps it over the area of interest.

Ultrasound typically suffers difficulty penetrating bone and therefore can only see the outer surface of bony structures and not what lies within. For visualizing internal structure of bones or certain joints, other imaging modalities such as MRI are typically used. However, the case is different with tendons, as ultrasound may have advantages over MRI in seeing the tendon structure.

Current technologies in tendon imaging enable medical assessment of dislocations, degenerative changes and tendon tears, including intra-substance tears, longitudinal splits, partial and complete ruptures, inflammatory conditions and tendon tumors.

5. Technical Approach

Tendon stress and strain levels during effort can be indicative of the type of injury a tendon has sustained (e.g. a tendon strain or sprain), thus assisting in both the diagnosis and follow up recovery phases. C. Roux et al. and P. Pourcelot et al. [2], [5] have developed a technique in which the stress level of a tendon can be quantitatively established through the measurement of the velocity of US waves transmitted axially along the tendon fibers axis. The velocity is found to increase with the level of effort a tendon is subject to. However, for a damaged tendon, the velocity is lower than that for a healthy tendon.

To measure the velocity, one ultrasonic transmitter (emitting probe) and five receivers are used. As reported by [2], the use of multiple receivers can help eliminate the effect of the skin and probes' complex transfer functions. Upon the use of appropriate high and low frequency noise flittering, the time of flight can then be estimated by analysing the cross correlation of the signals obtained from the neighbouring receivers.

The velocity is then given by:

Where is the distance separating the first and the last receivers, and is the sum of adjacent receivers' approximated delays.

When transmitted, the US waves suffer reflections from various surfaces and boundaries such as the skin, the skin-tendon interface and parts of the inner tendon medium (Figure-2). Thus, it is necessary to ensure that the US probes are inclined with an angle to ensure the generation of a lateral wave. This lateral wave is a head wave representing the longitudinal wave propagating along the tendon surface and radiating through the critical angle at the receivers. It is the lateral wave's velocity that is found to vary with the celerity of the tendon.

The resonant frequency of the transducers used in such an application is usually higher than 1 MHz. This is the case for most medical and non-destructive testing applications since higher frequencies guarantee the required resolution needed in medical imaging devices and are conventionally used for this purpose. Additionally, a frequency of around 1.5 MHz transducer is used for convenience in this application since the wavelength of the US waves in this case matches that the tendon fascicule (a small bundle or cluster of the tendon fibers that are associated functionally [7]). The researchers have had their probers manufactured (by Vermon [NUMBER]) from a costume design dedicated to suit the application. [2][5].

The study consisted of devising a number of muscular exercises designed to exercise the Achilles tendon and was carried on a number of test subjects. The exercises ensured that isometric contractions are applied to the tendon muscle complex; hence guarantying that the measured force is essentially related to Achilles tendon force [3]. Throughout a ten seconds period, the subject develops a decreasing effort from maximal voluntary contraction to relaxation.

Tendon head wave

Skin head wave




Tendon lateral wave

Skin lateral wave


Figure-2: An illustration of the device used to generate and detect the US waves (only three receivers shown) and the various reflections generated upon incidence. The tendon head wave is the source of the lateral wave necessary to detect and analyse [reproduced from [5]].

During signal analysis, only the first echoes in the RF signals are used in the correlation and lead to US waves velocity estimation (Figure-Number). Figure-Number shows the force-velocity data gathered from on test subject. As the figure illustrates, the results demonstrate the capability of the technique in detecting tendon injuries and the force the tendon is subject to. The results show the force-velocity data for both a healthy tendon (blue) and a distended tendon (red). As expected, velocity is directly proportional to the level of effort. However, it can be observed that that in the abnormal tendon the velocity is lower for the same level of effort.

While the findings only represent preliminary results, the technique has a great potential in detecting tendon injuries and estimating tendon stress levels non-invasively. Further tests and experiments can grant the necessary data needed to provide normalised values of stress levels against particular US velocity points recorded for a certain effort level. With such data available, the technique can be used as a diagnosis measure of various excessive tendon stress injuries and help prescribing the suitable recovery programme.

6. System Implementation and Experimental Setup

6.1 Overview

Implementing the experimental setup discussed in the previous section begins with choosing the appropriate transducers to generate and receive the US waves. The first phase of practical work consequently involves using the transducers as a tape measure (i.e. to estimate small distances). Initial experiments are carried out using transmission media other than a tendon, such as air, wood or steel. Having established the time of flight through a different medium, the concept can then be extended to include propagating the waves through a tendon such as the Achilles tendon, and using the TOF parameter to estimate the tendon stress during effort.

Both low and high frequency ultrasound were investigated to measure the time of flight through various media. To follow, the details of the experimental setup design for both HF and LF ultrasound will be given along with a discussion of some important technical and design related parameters.

6.2 Transducer Selection and Availability

Unlike their high frequency counterparts, a large range of low frequency transducers is commercially available for relatively cheap prices. This is because they are commonly used in everyday electronics in a variety of applications such as tape measures and motion detection. Frequencies usually range between 20 KHz to 200 KHz and the transducers are usually made of ceramic PZT materials.

As for high frequency transducers (higher than 0.5 MHz), Very few are commercially available. Although some transducers used industrially in non destructive testing of metals are available through specialist companies such as (Olympus), their prohibitive cost (prices start from £270 for an individual 25 mm contact transducer to thousands of pounds for a transducer with a custom design [8]) makes acquiring them a difficulty.

Furthermore, while the use of high frequency ultrasound is very common in medical applications, commercially available medical transducers are rare and expensive. Transducers in this case come as medical probes to be connected with an ultrasound scanning device and are typically manufactured (by companies such as Vermon) following a custom design.

Liquid atomising transducers are usually the only high frequency transducers cheaply available. As their main application, they are commonly used in Inhalation and disinfecting equipment as they utilise US waves to atomize, fog and spray liquid samples.

Two 1.65 MHz ultrasonic liquid atomisers [9] were purchased to be tested for suitability for the application intended. Together with two 2 MHz PZT transducers acquired from the university, the liquid atomisers make up the high frequency ultrasonic elements intended for the generation and reception of US signals.

When selecting a HF or LF transducer for an application a number of parameters have to be considered:

Transducer size: transducers come in various shapes and sizes. While the transducer shape is usually circular, the size tend to vary, and is given in terms of the diameter of transducer. Typical LF transducers diameters of 12, 15 and 20 mm are common choices with the 15 mm long diameter being the most commonly available. Size can be an important design factor in such applications whereby the transducers are integrated in a PCB and in cases where maximising ultrasound reception is crucial. However, for initial TOF experiments the size is of a relatively small significance.

Transducer sensitivity: the sensitivity is a parameter that indicates the ability of the transducer to detect reflectors and objects at a given distance away from the transducer. Datasheets usually provide figures for the sensitivity in units of dB/V/µBar against a range of operating frequencies and temperatures. The sensitivity is an important design factor since it governs how much detail (such as defects and discontinuities) the ultrasonic system can detect in the test material.

Transducer beam angle profile: The beam angle profile is an indicator of the radiation pattern of the ultrasonic sensor. It describes the relative sensitivity of the sensor as a function of spatial angle. The radiation patterns of the transducers are influenced by such factors as the size and shape of the transducer and the operating frequency. Beam patterns vary vastly from one transducer to another, from multi-directional to very narrow beams. For a transducer with a circular radiating and receptive surface, the narrowness of the radiation profile is determined by such parameters as the transducer diameter and the wavelength of sound at the operating frequency, according to the ratio D/λ. As the transducer diameter increases relative to the acoustic wavelength, a narrower beam profile is acquired.

A transducer beam angle pattern usually consists of a main beam and secondary side lobes where the sensitivity of the transducers sequentially decreases with respect to adjacent lobes (Figure-NUMBER). The beam angle is defined as the measurement of the total angle where the sound pressure level of the main beam has been reduced by 3 dB on both sides of the on-axis peak. Such 2D radiation patterns as those illustrated by Figure-NUMBER are usually provided by the manufacturer and apply for both the transmitter and receiver. For instance, according to the figure, the total (main) beam angle of the transducer is 30° since the off-peak 3 dB points are located at angles 15° and 345° (i.e. -15°), producing a main beam angle of 30°. The value of the side lobes beam angle can be calculated in the same manner by taking the peak point of the side lobes as a reference.

Choosing a transducer with a narrow beam angle can be of crucial importance. This applies to both selecting a transducer with a small total beam angle and a minimum sensitivity side lobes. This is because a narrow radiating profile minimises any unneeded reflections of unwanted objects and prevent the introduction of redundant echoes.

Due to the lack of HF transducer availability, no choices were available to assist in evaluating the best transducer for the application.

6.3 Transducer Testing and Characterization

Testing the transducers involves exciting (driving) one with a square-wave like signal and observing the response of another nearby transducer through an oscilloscope. The driving signal usually takes the form of an ON-OFF square or sinusoidal signal whose ON frequency is equal to the resonant frequency of the transducers (Figure-3). Such signal is obtainable from a signal generator by configuring it to modulate a square wave of a low frequency (e.g. 10 KHz) with a sinusoid of a frequency equal to that of the resonant frequency of the transducer.

By connecting another transducer (the receiver) to an oscilloscope, the response can be viewed and used to calculate the time of flight of the US signals. The time interval between the start of the transmitter signal and the start of the received signal (echo) conveys the TOF parameter of interest.

The distance between the transducers is usually only a few centimetres (in order to get sufficiently large signal amplitude without needing amplification). While testing, various propagation media are tested to find out the most suitable medium of transmission for a particular transducer. Media such as air, metal and wood are typical testing media.

OFF Phase

ON Phase


Figure-3: The driving signal used to excite the transducers. f = 1/T is the transducer's resonant frequency.

A battery powered driving circuit (Figure-5) was designed to provide the drive signal for the transducers. The circuit is based on two CMOS multivibrators [10] generating two square waves with different frequencies, one is the transducer's resonant frequency and other is a lower frequency representing the OFF phase cycle. One chip then triggers the other generating the required form of the driving signal. The circuit is powered by a nine volts battery and a combination of a resistor and a capacitor determine the frequency generated by each chip.

In order to have a non symmetric duty cycle for the ON and OFF phases, a 555 chip is used in place of the triggering CMOS multivibrator since the latter only provides a 50% duty cycle. A non symmetric duty cycle driving signal is needed since the ON phase needs to be much shorter than the OFF phase. This allows the transmitter excitation to be brief, hence allowing the receiver to detect the transmitted echo and its reflections before another US signal is transmitted. Usually ten cycles of the transmitter's resonance frequency are sufficient to provide the required transmitter excitation, while an OFF phase of frequency of tens of kilo hertz is deemed practical for short distance echo detection.

Figure-5: Circuit diagram of the battery powered circuitry used to drive the transducers.

6.4 Signal Conditioning and Amplification

LF Ultrasound

An op-amp circuit to amplify the receiver signal was designed and constructed. The circuit serves as a means of making small amplitude echoes reflected from surfaces at a distance from the receiver detectable on the oscilloscope screen. The amplifier designed is a non-inverting op-amp (powered by a nine volts battery) with an amplification factor of 110. Figure-NUMBER shows a frequency response simulation of the amplifier.

HF Ultrasound

Since a piezoelectric transducer outputs a high impendence charge signal, the signal is very sensitive to noise from the surrounding environment. Such noise introducing elements are cables, whose capacitances at high frequencies, and other stray capacitances become significant. The introduction of signal noise from these capacitances affect the quality of the received signal and in some cases prevents the reception of detectable echo signals altogether.

As such, the effect of stray capacitance must be minimised through, for example, the use of special low noise coaxial cables for appropriate experimental measurements. A more practical technique however, is the use of a charge amplifier. The amplifier (FIGURE-NUMBER) converts the charge signal at the output of the PZT sensor to a proportional low impendence voltage signal. Through the low impedance voltage signal, and the high insulation resistance of the MOSFET transistor at the input, the capacitive feedback amplifier provides an output signal less receptive to noise and more suitable for measurement purposes.

Neglecting the effects Rt and Ri, the resulting output voltage, Vo, becomes:

For sufficiently high open-loop gain, the cable and sensor capacitance can be neglected, leaving the output voltage dependent only on the input charge and the range capacitance:

Besides generating the required output voltage, the feedback capacitor dictates, with the feedback resistor, the transient response (the time constant) of the circuit. The time constant is given by the product of the two elements, and the feedback resistor is usually taken to be in orders of Mohms as it act as a means of providing the necessary bias current.

6.5 Test Medium Properties

Acoustic Impedance: The (specific) acoustic impedance () of a material is a parameter relating the material density () to its acoustic velocity (). The impedance affects the mechanism of which sound pressure travels through a material, and thus depends on material attributes such as atoms distribution and elasticity.

While the (specific) acoustic impedance of a material is usually a property of the material and does not depend on its dimensions (also referred to as the specific or characteristic acoustic impedance), it can also be defined in terms of the material size and dimensions via the relation:


Is the acoustic impedance.

Is the sound pressure level.

Is the material surface area.

Is the acoustic velocity in the material.

The acoustic impedance is important in the determination of acoustic transmission and reflection at the boundary of two materials having different acoustic impedances. A big acoustic impedance mismatch between the two materials at the boundary results in most of the acoustic energy reflecting off the edge of the boundary rather than transmitting trough the medium.

The percentage of energy reflected at an interface between any two materials can be calculated via:

Where and are the acoustic impedances of the materials on either side of the boundary.

The acoustic impedance plays a major role in the design of ultrasonic transducers, to ensure that the transducer is optimised for transmission in a particular medium by matching the impedances of the transducer to that of the medium.

6.6 Transducer Frequency Response

A transducer frequency response analysis can be carried out to reveal the transducer resonant frequency (usually varies slightly from that given by the manufacturer) and its response to other frequencies in range. To do so, the transmitter transducer is excited by a driving signal of a variant ON cycle frequency and the corresponding amplitude of the receiver transducer signal is recoded (FIGURE-NUMBER).

7 Results and Discussion:

7.1 Overview

Measurement of the time of flight parameter was carried out using both low and high frequency ultrasound propagation. The first phase of the project concentrated on using HF US transmission (as detailed in the progress report). However, due to the difficulties encountered in accurately obtaining TOF readings, it was decided to investigate LF ultrasound for the purpose. Having succeeded in measuring TOF with LF ultrasound, the HF ultrasound technique was revised and improved, which allowed acquiring accurate time of flight measurements in the HF domain as well.

7.2 Low Frequency Measurements

The use of low frequency transducers to estimate small distances is simpler than utilizing high frequency ultrasound for the same purpose. This is due to the fact that low frequency ultrasonics do not suffer to the same extent as their HF counterparts from crucial shortcomings such as attenuation and noise. This makes them prime candidates for ultrasound Inspection of high attenuation materials such as concrete and wood.

Experiments on time of flight measurement were carried out using a pair of 40 KHz ceramic PZT transducers ([NUMBER]). The transducers are designed for ultrasound transmission through air as they provide a good mechanical impedance match with air. This ensures that most of the acoustic energy is transmitted through the transducer-air boundary rather than reflected back.

By driving the transducers with a square-like wave of the resonant frequency and providing a reflective surface of low acoustic attenuation, the reflected low frequency echoes were detected by the receiver (Figure-NUMBER). The time of flight was consequently calculated by measuring the time separation between the transmitted and received signals on the oscilloscope. The values were checked by using:


Is the measured time of flight (The factor of two is necessary to compensate for the double journey suffered by the ultrasonic waves).

Is the distance separating the transducer and the reflective surface vertically.

Is the speed of sound in medium of propagation (= 341 m/s, though it can vary with temperature and humidity according to the formula)

Rx transducer

Tx transducer

Reflective surfaceD:\Documents and Settings\M.Tabib\OrCAD 9.1\Desktop\1-1.jpg

Figure [NUMBER]: The experimental setup used to measure TOF using low frequency ultrasound.

Figure [NUMBERS] show some of the results obtained. Figure-Number demonstrates the response of the receiver transducer (blue trace) to the transmitted signal (orange trace). The receiver responds to the acoustic echo by resonating at a frequency of 41 KHz after a time period of 840 us from generating the transmitted acoustic signal, which accords well with the prediction of equation NUMBER. Variation of the distance separating the transducer and the reflective surface vertically results in a relative change in the measured time of flight according to the same equation, as the Figures illustrate.

Furthermore, shortening the period of the ON cycle of the transmitted acoustic signal allows the detection of multiple echoes by various reflective objects. FIGURE-9 shows the detection of three distinct echoes, the first of which is the shortest allowed path the acoustic signals can travel to reach the receiver. Further echoes are a consequence of reflections at other angles with other surfaces and boundaries.

Furthermore, the integration of the op-amp circuit to the receiver transducer also allows the detection of further echoes rendered otherwise undetectable due to the long distance separating the target surface and the receiver (FIGURE-NUMBER). These small amplitude echoes are amplified by the op-amp, and analysis of their time of flight readings indicate that their presence is originated from reflections off long distance objects such as the room ceiling.

While the results show the ability of the technique to obtain accurate time of light measurements, the LF transducers used suffer from a few drawbacks. The wide angle beam profile of the transducers limits their applicability to be used in the tendon stress measurement application. This is due to the application requiring a narrow angle beam profile transducers (with the transducer inclined by 35 - 40 degrees for Achilles tendon stress evaluation) to guarantee the generation and detection of a lateral wave. The wide beam profile would result in the generation of multiple rays taking different paths and thus producing multiple reflections and echoes off various surfaces and boundaries such as the skin-tendon and tendon-muscle boundary. Consequently, where these multiple echoes superimpose together, the detection of a lateral wave and the interpretation of the acoustic echoes would be rendered difficult or impossible.

Another technical issue affecting the applicability of the transducers is the mechanical impedance. While the transducers have been optimised for acoustic transmission through air, the generation of ultrasonic waves by the transducers through mediums such as tendons is

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difficult. The mechanical impedance mismatch would result in most of the acoustic energy reflecting back from the transducer-skin boundary rather than transmitting through. In fact, since The transducers are made from ceramic PZT, the percentage of acoustic energy reflecting off the transducers-skin boundary would be 97.3%. Hence, without matching the mechanical impedance of the transducers to that of the skin, no acoustic signals would be propagated or detected.

7.3 High Frequency Measurements

The use of HF ultrasound in measuring the time of flight of acoustic waves has a few similarities and differences to that of the LF ultrasound technique. While the same experimental procedure is used in driving the transducers and calculating the time of flight, other issues differ such as the transmission medium used and the interpretation of acoustic echoes.

Metals such as iron, steel and aluminium offer medium properties better suited for high frequency ultrasound propagation than other mediums such as air. The lower attenuation coefficient values of metals allow the transmission of attenuation-prone high frequency waves without considerable energy loss. As such, time of flight experiments were carried out using a pair of US liquid atomising transducers, and a NUMBER cm stainless steel rod. The transmitting and receiving transducers are set up to face one another at each end of the rod (FIGURE-NUMBER). With such configuration, the formula used to predict the time of flight of the acoustic waves differ slightly since the waves suffer no 'double journey' between the transmitter and receiver:

Where the symbols indicate the same meaning as explained above. However, with the speed of sound in metal being considerably higher than in air (5980 m/s in stainless steel), the time of flight values expected for small propagation distances such as the steel rod length are much less than those obtained for LF ultrasound for similar distances.

FIGURE [NUMBERS] show some of the results for TOF measurements obtained from various experimental settings. FIGURE-Number illustrates the reception of multiple echoes after the transmission of a short ultrasonic burst. The distinct echoes are found to be odd multiples of the shortest possible time of flight of acoustic waves between the transmitter and the receiver (= 59.4 us). These echoes are a result of the ultrasonic waves reflecting back and forth from one end of the rod to the other. Although further echoes representing acoustic waves taking longer paths are theoretically detectable, no such distinct echoes can be observed from the figure.

Steel rod

Rx transducer

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Figure [NUMBER]: The experimental setup used to measure TOF using high frequency ultrasound.

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While there is the possibility that the transducers exhibit a very narrow beam angle profile, thus eliminating the presence of any longer routes waves, the possibility is unlikely as such narrow beam transducers are practically difficult to make and a limited number at least of rays suffering longer paths are expected to be present.

A more precise explanation as to why such reflections are unobservable from the figure is that upon suffering each extra surface reflection, the acoustic wave dissipates some of its energy, making the signal amplitude small enough to prevent its detection from noise. This can be proven by the integration of the charge amplifier at the receiver end. With the amplifier

reducing the effect of such noise as that introduced by cable and stray capacitance, the presence of those smaller amplitude echoes travelling longer distances to reach the receiver can now be more clearly distinguished (FIGURE-NUMBER).

A technical issue of significance encountered, is the affect of transducer coupling. During the measurement procedure, the transducers must be firmly coupled to the end of the rod to prevent the presence of air gaps between the face of the transducer and the rod. The presence of air space would create a PZT-air boundary where most of the acoustic energy would be wasted (due to the mechanical impedance mismatch) before propagating through the metal. To overcome this issue, an ultrasonic gel was used in all HF experiments to ensure the existence of good acoustic coupling between the transducer and steel rod. The ultrasonic gel [NUMBER] is widely used in medicine in such applications as ultrasonic imaging of body organs to provide good US probe coupling and mechanical impedance match.

To obtain further results for HF time of flight measurements, the same experimental procedure was carried out on an Aluminium rod. Figure-NUMBER shows that for the 14 cm long rod, a time of flight reading of NUMBER m/s is recorded, which is in agreement with the value equation (NUMBER) predicts for a speed of sound in aluminium of 4877 m/s.

7.4 Tendon TOF Measurements

Time of flight of ultrasonic waves travelling through a tendon, can be measured by adopting a similar technique to that used in the HF TOF evaluation through solids. However, a number of important technical issues in this method differ from that dealt with in the previous techniques. For instance, type of reflections and refractions suffered by ultrasonic waves and caused by the transducer-skin and skin-tendon boundaries vary from those encountered in the previous techniques. In particular, the detection of a lateral wave caused by the reflection of US waves off the back of the tendon is of crucial importance since it is its time of flight that determines the tendon celerity.

Incident US wave


Lateral wave


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