Medical Engineering & Physics 33 (2011) 534–545
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Medical Engineering & Physics journal homepage: www.elsevier.com/locate/medengphy
Knee acoustic emission: A potential biomarker for quantitative assessment of joint ageing and degeneration L.-K. Shark a,∗ , H. Chen a , J. Goodacre b a b
Applied Digital Signal and Image Processing Research Centre, University of Central Lancashire, Preston, PR1 2HE, UK School of Health and Medicine, Lancaster University, Lancaster, LA1 4YD, UK
a r t i c l e
i n f o
Article history: Received 9 July 2010 Received in revised form 7 December 2010 Accepted 13 December 2010 Keywords: Acoustic emission Knee joint ageing and degeneration Osteoarthritis
a b s t r a c t Based on a single time-point study of 34 healthy and 19 osteoarthritic knees in three different age groups (early, middle and late adulthood), this paper reports the potential of knee acoustic emission as a biomarker to monitor joint ageing and degeneration. Measurements were made of short transient high frequency acoustic emission signals generated by knee joints under stress during repeated sit–stand–sit movements along with joint angle. A statistically significant feature profile was established using a fourphase model of sit–stand–sit movements and two waveform features. The four-phase movement model is derived from joint angle measurement during repeated sit–stand–sit movements, and it consists of the ascending-acceleration and ascending-deceleration phases in the sit-to-stand movement, followed by the descending-acceleration and descending-deceleration phases in the stand-to-sit movement. The two statistically significant waveform features are extracted from AE measurement during repeated sit–stand–sit movements, and they consist of the peak magnitude value and average signal level of each AE burst. In addition to the use of bilateral plots, statistical distributions and 2D colour histograms to visualise the differences and similarities among participants, use of principal component analysis showed not only distinct data clusters corresponding to participating groups, but also an age- and disease-related trajectory progressing from the early adulthood healthy group to the late adulthood healthy group followed by the middle adulthood osteoarthritic group to the late adulthood osteoarthritic group. Furthermore, this trajectory shows increasing areas for each data cluster, with a highly compact cluster for the early adulthood healthy group at one end and a widely spread cluster for the late adulthood osteoarthritic group at the other end. From these results, a strong basis is formed for further development of knee acoustic emission as a convenient and non-invasive biomarker for quantitative assessment of joint ageing and degeneration. © 2010 IPEM. Published by Elsevier Ltd. All rights reserved.
1. Introduction As one of the largest joints capable of withstanding several times body weight and one of the most complex musculoskeletal structures with movements involving interaction among various anatomical parts (bones, cartilage, muscles, tendons, and ligaments) [1], the human knee joint has been studied extensively. Typical changes in knees caused by the ageing process include increased stiffness of ligaments, reduced quality and quantity of synovial fluid, increased articular surface roughness, reduced cartilage thickness, and reduced muscle strength [2]. The incidence of knee osteoarthritis (OA) increases with age, and is associated with cartilage degeneration [3].
∗ Corresponding author at: University of Central Lancashire, School of Computing, Engineering & Physical Sciences, Computing & Technology Building, Fylde Road, Preston, Lancashire PR1 2HE, UK. Tel.: +44 1772 893253; fax: +44 1772 892915. E-mail address:
[email protected] (L.-K. Shark).
If markers of normal knees could be identified for different age groups, a baseline for identifying degenerative change out with the age-related norms could be established. This would enable not only the possibility of preventive measures for those at increased risk, but also the efficacy of early treatment programmes to be evaluated. Despite advances in medical imaging technology, there is currently no convenient and non-invasive biomarker for quantitative assessment of joint ageing and degeneration. While commonly used X-ray, magnetic resonance imaging (MRI) and ultrasound [4–8] are only able to provide a static snapshot of a knee joint in a particular pose, gait analysis of knee joint movements has the limitation of sensitivity [9]. Although dynamic MRI can be used to assess knee function with excellent measurement accuracy [10], it is not practical for use in clinic and home settings due to accessibility, costs and portability. This paper presents work to demonstrate the potential of using acoustic emission (AE) acquired from moving knee joints as a convenient and non-invasive biomarker for quantitative assessment of joint ageing and degeneration. AE is a natural phenomenon of
1350-4533/$ – see front matter © 2010 IPEM. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.medengphy.2010.12.009
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high frequency sound that can be generated by structure under loading or surface interaction. A normal knee with smooth and well-lubricated cartilage surfaces should move quietly, whereas an unhealthy knee covered by rough and poorly lubricated cartilage surface should move unevenly, producing acoustic signals. Previously, phonoarthrography [11,12], vibroarthrography [13–15] and a combination of both modalities [16] have been explored for musculoskeletal assessment. They sense low frequency vibration signals below 20 kHz which are emitted from joints and hips during movement by using microphones and accelerometers. In contrast, wide-band AE sensors are used by the authors to detect sound waves with frequencies from 20 kHz up to 200 kHz, as is widely used in non-destructive evaluation of engineering structures [17]. Since crack initiation and propagation are detectable by AE in engineering structures, others have studied acoustic signals from bone fractures and hips [18,19]. However, no work has been undertaken previously to investigate AE for detecting more subtle joint conditions like joint ageing and degeneration. The work presented in this paper builds on the previous findings reported by the authors, in which a significant difference in the amount of AE was discovered between young healthy and older OA knees representing two ends of the joint condition scale, as well as two natural clusters of AE characteristics for age-matched healthy and OA knees [20–22]. With the difference in the amount of AE between OA knees in old age and healthy knees in young age found to be larger than that between age-matched OA and healthy knees, it has led to a hypothesis of possible correlation between the knee AE profile and the progression of joint ageing and degeneration, and the study to investigate knee AE produced by different age groups with both healthy and OA knees. Through statistical analysis of the AE profiles among different knees at different ages and conditions, the work aims to establish an evidence base for using knee AE as a biomarker to monitor joint ageing and degeneration. 2. Participants The work is based on the study of knee AE acquired from 41 participants, among which are 27 healthy participants with ages from 22 to 83 years recruited from the student population at the University of Central Lancashire and the local population in Preston area, and 14 OA participants with ages from 52 to 82 years recruited from among patients referred for physiotherapy to the Blackpool, Fylde & Wyre NHS Foundation Trust. All participants were provided with an information sheet and written consent was obtained prior to knee AE measurement. The study was approved by the NHS local research ethics committee. Based on a self-completing questionnaire, 34 knees among the healthy participants (which may be left, right or both knees of each healthy participant) were classified as healthy knees with no previous treatment for an injury to knees and no symptoms of knee swelling, pain, stiffness or tenderness. Based on the Kellgren & Lawrence (K&L) X-ray scores [23], 19 knees among the OA participants (which may be left, right or both knees of each OA participant) were classified as OA knees. For the purpose of studying the changes in knee AE as a result of joint ageing and degeneration, age stratification was applied according to the three periods of the adulthood (namely, early, middle and late adulthood), thereby yielding the following five groups of knees based on age and knee condition: • Group H1 of the early adulthood consisting of 10 health knees from 8 healthy participants (involving both knees from 2 healthy participants and one left or right knee from each of the remaining healthy participants) aged between 22 and 40 years with an average age of 29.00 years and a standard deviation of 5.45 years. • Group H2 of the middle adulthood consisting of 11 health knees from 8 participants (involving both knees from 3 healthy par-
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ticipants and one left or right knee from each of the remaining healthy participants) aged between 42 and 58 years with an average age of 50.00 years and a standard deviation of 5.07 years. • Group H3 of the late adulthood consisting of 13 health knees from 11 participants (involving both knees from 2 healthy participants and one left or right knee from each of the remaining healthy participants) aged over 61 years with an average age of 71.27 years and a standard deviation of 6.99 years. • Group OA1 of the middle adulthood consisting of 7 OA knees from 6 OA participants (involving both knees from 1 OA participant and one left or right knee from each of the remaining OA participants) aged between 52 and 58 years with an average age of 55.00 years and a standard deviation of 1.90 years and • Group OA2 of the late adulthood consisting of 12 OA knees from 8 participants (involving both knees from 4 OA participants and one left or right knee from each of the remaining OA participants) aged over 61 years with an average age of 69.50 years and a standard deviation of 6.39 years.
3. Measurement system and protocol The measurement of knee AE was performed using the Joint Acoustic Analysis System (JAAS) developed by the authors [20]. Essentially, JAAS combines a traditional AE system for engineering structure integrity measurement with an electronic angle measurement system to provide joint angle based AE data. The traditional AE system is from Physical Acoustics that consists of two circular general purpose piezoelectric sensors (model S9204 with a frequency range of 50–200 kHz as well as a size of 23 mm in diameter and 15 mm in thickness) to attach to each knee joint, two pre-amplifiers to provide 40 dB gain for each sensor, an AE Acquisition Board with PCI connection, and a laptop computer running AEWin software for measurement control and signal processing [24]. The electronic angle measurement system is from Biometrics that consists of two electro-goniometers (model SG-150) and an amplification unit (model K800). The latter is also connected to the AE Acquisition Board and is driven by the same start trigger sent from the AEWin software to enable synchronised data acquisition. The anatomical site for AE sensor attachment is upon the medial compartment of the knee joint, inferior to the patella and anterior to the medial patella retinaculum (Fig. 1). This specific anatomical site has shown to provide good measurement sensitivity [20], because it is closest to the area of contact between bone surfaces moving against each other in the knee joint, and it offers a relative stable sensor position that is less affected by skin movement. The attachment of the AE sensor is through the use of a hypoallergenic medical adhesive tape with a size of 130 mm × 130 mm. To ensure consistent contact between the sensor surfaces and skin, a coupling gel is applied. For sensor attachment, each knee is supported in extension and the adhesive tape is applied in such a way so as to provide the highest possible elastic tension to hold down tightly each AE sensor on the anatomical site. This prevents AE sensor from sliding during joint movement as joint flexion will create a greater elastic tension to press down further the AE sensor on the anatomical site. A small hole is made in the middle of the tape to allow connection of the cable after sensor placement on the knee. The location and attachment of the two electro-goniometers are not critical and they are positioned laterally to each knee using double sided medical tape. For a knee to generate AE, it is required to move under loading. Based on the previous studies [20–22,25], repeated sit–stand–sit movements were used as the movement protocol for acquisition of joint angle based AE. Each sit–stand–sit movement consists of ascending from a standard height chair, with arms folded across the chest (in order to remove the influence of the movement strat-
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peak definition time (PDT) that is retriggered upon encountering each higher signal magnitude after the first threshold crossing was set to 200 s. In order to reduce the possibility of two separate AE hits being treated as one, the hit definition time (HDT) that is retriggered upon encountering each threshold crossing with the signal magnitude falling below the threshold for determination of the end of the hit at the last threshold crossing was set to 800 s and the hit lockout time (HLT) that is activated by the end of HDT was set to 1000 s during which data acquisition is inhibited. 4. Analysis of joint angle based knee acoustic emission 4.1. Statistics in four movement phases
Fig. 1. (a) JAAS system and sensor attachment, and (b) sensor location.
egy), reaching a fully erect standing position and then descending to return to a seated position. Movement was demonstrated to each participant, with each also being informed to move at a usual, comfortable speed. During measurement, each participant was asked to perform a total of 10 sit–stand–sit movements, through series of 5 consecutive movements with a 30 s to 1 min break between each series. While the angular output signals from the electro-goniometers are acquired at 100 Hz sampling frequency, the AE signals are acquired at 1 MHz sampling frequency. To minimise AE data volume, AE data acquisition is operated in a non-continuous recording mode. With AE signals characterised by short duration bursts, a burst signal is recognised and recorded as an AE event or AE hit only if the waveform characteristics of the burst signal satisfying a set of hit definition parameters [24] as shown in Fig. 2. The settings of these hit definition parameters were based on observation and analysis of typical AE waveforms acquired in the previous study [20]. For the joint angle based AE data presented in this paper, the magnitude threshold to trigger AE recording was set to 32 dB (around 40 V) in order for the acquisition system to be sufficiently sensitive to collect low magnitude AE signals observed at the initiation of joint movement. Furthermore, in order to provide adequate duration for detection of the highest peak in the waveform, the
An example of joint angle based AE acquired by JAAS from a participant for a set of five repeated sit–stand–sit movements is shown in Fig. 3, where the solid curve shows the joint angle signal and each dot superimposed on the joint angle signal corresponds to an AE event detected with its burst signal magnitude value above the defined threshold of 32 dB. There are five cycles in the joint angle signal corresponding to five repeated sit–stand–sit movements. The starting joint angle in each cycle corresponds to the knee flexion angle at the sitting position and the peak joint angle in each cycle corresponds to the knee extension angle at the standing position. The increase in the joint angle in each cycle corresponds to the ascending (sit-to-stand) phase and the decrease in the joint angle in each cycle corresponds to the descending (stand-to-sit) phase. There exists a variation in the starting flexion angle among the participants, as it is determined by the height of the chair and the height of the subject which could not be controlled. The times taken by participants to complete each sit–stand–sit movement cycle were within a range of 2.5–6.5 s. With sit–stand–sit forming the fundamental action in the movement protocol to create knee AE, each sit–stand–sit movement cycle performed by a participant can be considered as performing one individual test that gives a particular AE measurement outcome. With the action repeated several times, it is not unreasonable to assume some meaningful statistics to be contained in the multiple AE measurement outcomes generated by the repeated movement actions. This assumption leads to pre-processing of the joint angle signal to separate each sit–stand–sit movement cycle for statistical analysis of knee AE. If g(t) denotes the joint angle signal, and (t) = dg(t)/dt denotes the angular velocity, then the start and stop of each sit–stand–sit movement cycle can be identified by assigning a threshold value to |(t)|. In the implementation, the knee joint is assumed to be static when |(t)| < 0.1◦ /s and in motion when |(t)| ≥ 0.1◦ /s. For the same argument, each movement cycle can be divided further into its constituent phases for statistical analysis. Previously, a two-phase model, based on the ascending and descending movement phases, has been used to identify the statistical differences in AE between young healthy knees and old OA knees [20,21]; and a four-phase model, based on joint acceleration and deceleration in each of the ascending and descending movement phases, has been used to identify the statistical differences in AE between age matched healthy and OA knees [22]. The latter model is employed in this study, since it links more closely with the underlying bio-mechanical strategies of knee joint movement including the temporal sequences of segment movement, muscle activity, and joint moments [26]. By extracting each joint angle variation cycle based on the start and stop of each movement cycle and normalising the time scale of each extracted joint angle variation cycle to one, an example is shown in Fig. 4 with five joint angle variation cycles superimposed on each other for a set of five repeated sit–stand–sit movements, and their corresponding angular velocity variations. Based on the occurrence of the peak joint angle as well as
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the peak angular velocity, the four phases for the movement model are defined as:
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Based on the four-phase model of sit–stand–sit movements, the number of AE hits generated by participants with both knees healthy and OA were compared using bilateral plots with left knee versus right knee in each sit–stand–sit cycle. Four bilateral plots with one for each movement phase are shown in Fig. 5 for one participant in each group, where a point near to the diagonal line indicates a symmetrical pair of knees with the number of AE hits from its left knee similar to that from the right knee in a sit–stand–sit cycle. Although the number of participants with both knees selected for the study is small, some general observations can be made. For the early adulthood healthy group (H1), the participants are seen to generate particularly low, repeatable, and symmetrical numbers of AE hits from the left and right knees in all movement phases. With the increase in age, the participants in the middle and late adulthood healthy groups (H2 and H3) are seen to generate higher but still relatively repeatable numbers of AE hits with a certain loss of symmetry in some movement phases. As the knee condition changed from healthy to OA, the participants in the middle and late adulthood OA groups (OA1 and OA2) are seen to generate much higher numbers of AE hits with a wider spread and a certain hit asymmetry in some or all movement phases. To show the statistical differences between the five participating groups, some basic statistics (average, standard deviation, minimum and maximum) for the number of AE hits in each movement phase over ten repeated movements are illustrated using a box and whisker plot in Fig. 6. Although there are overlaps between the five
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groups in the number of AE hits as shown in Fig. 6 (with the DD phase showing minimum overlaps), the average number (shown by the middle of each box in Fig. 6), maximum number and minimum number (shown by the top and bottom whiskers in Fig. 6) of AE hits in each movement phase are seen to increase based on age and knee condition, increasing from the early adulthood healthy group (H1) to the late adulthood healthy group (H3) followed by the middle adulthood OA group (OA1) to the late adulthood OA group (OA2). In particular, using the average number of AE hits from group H1 as reference, the maximum increase is seen to occur in the AA phase (around 10 times increase from group H1 to group H3 and 28 times increase from group H1 to group OA2), and the minimum increase is seen to occur in the DA phase (around 5 times increase from group H1 to group H3 and 15 times increase from group H1 to group OA2). In addition to trends of increasing average, minimum, maximum values, there is a trend of increasing standard deviation related to age and knee condition (as shown by the length of box in Fig. 6) with the number of AE hits generated by the OA groups seen to be more variable than those of the healthy groups. These observations form a basic statistical basis for the use of knee AE for quantitative assessment of joint ageing and degeneration. 4.2. Statistical distributions in four movement phases Building on the basic statistics of the number of AE hits, detail analysis based on the statistical distributions of various AE waveform features was carried out to investigate further differences among the participating groups. The AE waveform features can be described in terms of amplitude (such as peak magnitude value
of the AE waveform, and average signal level (ASL) over the AE waveform duration), energy (such as sum of absolute or squared amplitude values in the AE waveform), frequency (such as peak frequency corresponding to the frequency of the peak waveform, and average frequency over the whole AE duration), and time (such as duration of the AE waveform above the detection threshold, and the rise time corresponding to the time interval between the start and the peak of the AE waveform). These features for a typical healthy knee AE waveform from a participant in group H1 and a typical OA knee AE waveform from a participant in group OA2 are illustrated in Fig. 7. Among various AE waveform features investigated based on statistical distribution, AE peak amplitude and ASL were found to stand out as two of the most significant statistical factors for discrimination of different groups, in terms of the statistical trends in their upper bounds and the rate of increase in their cumulative probabilities. The probability density function of AE peak magnitude values has been shown previously to exhibit an exponential form [20]. Using the exponential probability plot, the cumulative probability of the AE peak magnitude values (in dB) in four different movement phases is shown in Fig. 8 based on the AE hits acquired from each participating group performing 10 repeated sit–stand–sit movements. From Fig. 8, the five participating groups in all four different movement phases are seen to produce similar curve shapes for the cumulative probability of the AE peak magnitude values, with more than 99% of the AE peak magnitude values in each group forming a relatively straight curve in each movement phase. Although some highest AE peak magnitude values on the tail of the distribution are seen to deviate from the straight lines, they represent a very low
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Fig. 6. Statistical differences of AE hits between five groups in four movement phase (a) AA phase, (b) AD phase, (c) DA phase, and (d) DD phase.
probability of occurrence (less than 1%). With the straight lines of different slopes being produced as a result of using the exponential scale, it implies that the probability distributions of AE peak magnitude values for different participating groups in different movement phases can be modelled using an exponential function with different exponents. From Fig. 8, all participating groups are seen to have the same lower bound value of 32 dB for the AE peak magnitude values in all four different movement phases, which corresponds to the threshold set for detection of an AE hit. In addition, a very high percentage of overlap in the range of AE peak magnitude values among the different participating groups is seen in each movement phase. However, there are significant differences in the upper bounds of the AE peak magnitude values. For the three age groups of healthy knees from H1 to H3, the maximum AE peak magnitude values are seen to increase according to the increasing age groups in the ascending phase, and large differences between them are seen in the AD movement phase with the maximum peak magnitude values around 60, 70 and 80 dB for H1, H2 and H3, respectively. For the two age groups of OA knees, the maximum AE peak magnitude values are seen to decrease in the AA movement phase and increase in the AD movement phase with the increasing age groups. The differences between the two OA groups are seen to be the largest in the AA movement phase (more than 10 dB), with the
highest peak magnitude value at around 90 dB coming from group OA1. Furthermore, the upper bounds of the AE peak magnitude values for the two OA groups are higher than those for the three healthy groups in three out of four movement phases, namely, AD, DA and DD, with the largest difference seen in the DD movement phase. Another significant statistical factor for discrimination of different groups was found to be ASL, the probability density functions of ASL for the healthy and OA groups were found to show multiple peaks. To assess whether or not ASL follows approximately Gaussian distribution, the Gaussian probability plot is used to show the cumulative probability of the ASL values (in dB) in four different movement phases based on the AE hits acquired from each participating group performing 10 repeated sit–stand–sit movements. From the Gaussian probability plots of ASL shown in Fig. 9, although the curve shapes produced by different participating groups exhibit some similarities in all four movement phases, they are not straight implying non-Gaussian distributions. From Fig. 9, while all participating groups are seen to have the same lower bound value of 10 dB for ASL in all four movement phases, their cumulative probabilities are seen to increase at significantly different rates to significantly different upper bounds. For the three age groups of healthy knees from H1 to H3, the increase in age is seen to be accompanied by an increase in the maximum ASL
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ing age and knee condition in each movement phase, the statistical distributions shown in this section provide further support to the correlation based on two AE waveform features. The underlying statistical trends for the AE peak amplitude and ASL values are each shown to be increasing predominantly in most movement phases with knee ageing and degeneration. By combining these statistically significant features, it becomes possible to identify each age and knee condition class as shown in the next section.
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5. Feature based visualisation of knee acoustic emission
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The volume of the joint angle based AE data set generated by each knee performing repeated movements is large. Although extraction of waveform features from AE hits has helped to reduce the data set to be processed to a more manageable level, it is not an easy matter to compare two different knees. A feature based representation method has been proposed previously [20,22], and is adopted to represent the discriminate AE features in different movement phases in a compact and concise format for visualisation of different knee AE profiles. With the peak magnitude and ASL values of AE hits providing good statistical differences between the five participating groups as shown in the previous section, an AE hit waveform detected in the ith sit–stand–sit movement can be represented by a vector of three dimensions, Wi (peak, ASL, p), where peak and ASL denote the values of the two AE features, and p denotes the four movement phases of AA, AD, DA, and DD, respectively. If the range of peak and ASL is divided into U and V intervals, then the descriptor of each AE hit waveform becomes Wi (peakj , ASLk , p), where j = 1, 2, . . ., U and k = 1, 2, . . ., V yielding a total of U × V possible AE feature classes per each movement phase. For a set of M repeated sit–stand–sit movements performed by a participant, a statistically significant AE feature profile of the participant can be constructed based on the average number of AE hit waveforms for each possible feature class in each movement phase, denoted by Wi (peakj , ASLk , p). To provide a visual display of the AE feature profile, an image based representation is used with the AE feature profile in each movement phase shown as a 2D colour histogram in each quarter of the image. In particular, the image based representation is organised to show the AE feature profile of the ascending phase in the left half of the image, the AE feature profile of the descending phase in the right half of the image, the AE feature profile of the acceleration phase in the top half of the image, and the AE feature profile of the deceleration phase in the bottom half of the image. Within each quarter, ASLk is represented by the horizontal axis and peakj by the vertical axis. Furthermore, the directions of feature classes with increasing peak magnitude and ASL values are oriented outwards from the image centre to enable visualisation of pattern symmetry. Using five knees in different participating groups, the typical AE feature profiles of each participating group is shown in Fig. 10 with the average number of hits in each feature class per movement cycle shown not only in colour but also the corresponding numerical value. They are produced based on the AE peak magnitude and ASL values acquired over 10 repeated sit–stand–sit movements and falling in 7 peak magnitude intervals and in 9 ASL intervals. While the first six peak magnitude intervals are given by
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Fig. 7. AE waveform examples (a) from healthy knee in group H1; and (b) from OA knee in group OA2.
values in the first three of the four movement phases (AA, AD and DA) with differences of more than 10 dB shown in the AA and DA movement phases. For the two age groups of OA knees, the maximum ASL values are seen to increase again in the first three of the four movement phases and decrease in the DD movement phase with the increasing age group. The differences between the two OA groups are seen to be the largest in the AA movement phase (around 10 dB), with the highest ASL value at more than 50 dB coming from group OA2. Furthermore, the two OA cumulative probability curves are seen to crossover in all phases. Finally, the upper bounds of the ASL values for the two OA groups are consistently higher than those for the three healthy groups in all the movement phases with the largest difference seen in the DD movement phase. Following the statistical correlation established in the previous section to link the increase in the number of AE hits to the increas-
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and the last peak magnitude interval given by peak7 > 90 dB, the first eight ASL intervals are given by 10 + 5(k − 1) ≤ ASLk < 10 + 5k
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and the last ASL interval is given by ASL9 > 50 dB. The typical AE feature profiles of different participating groups shown in Fig. 10 reveal a visual trend related to joint ageing and
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Fig. 8. Exponential probability plots of AE peak magnitude for (a) AA phase, (b) AD phase, (c) DA phase, and (d) DD phase.
degeneration. A healthy knee joint in the early adulthood is seen from Fig. 10(a) to generate a small number of AE hits of lower peak magnitude and ASL values. As the age increases, the number of AE hits increases with increasing higher peak magnitude and ASL values as shown in Fig. 10(b) and (c). For knees with OA, they are seen from Fig. 10(d) and (e) to generate the highest number of AE hits with a wide range of peak magnitude and ASL values. Furthermore, there are visual differences in the AE feature profile between the two OA groups. A significant number of AE hits with high ASL and low peak magnitude (corresponding to relatively long duration and low magnitude waveforms) is seen to occur in the AA movement phase for group OA1 and in the DA movement phase for group OA2. 6. Biomarker identification by principal component analysis In order to assess the robustness and sensitivity of knee AE as a potential biomarker to monitor joint ageing and degeneration, multivariate statistical analysis is needed to separate the complete set of AE measurement data acquired from all the knees into a number of meaningful clusters without using the prior knowledge. One of the most widely used multivariate statistical analysis methods is principal component analysis (PCA) that is able to transform a large set of original measurement variables into a small set of new variables, known as principal components, in such a way as to highlight the differences and similarities among the measured subjects [27]. However, direct application of PCA to raw knee AE
data presents technical implementation issues. One is due to a very high dimensionality of each knee AE data set that contains a large number of AE waveforms with each AE waveform consisting of a large number of samples, and the other is due to highly irregular AE patterns with a large variation in the number and occurrence of AE waveforms from one knee to another. These issues are overcome by using the image based visual display of the knee AE profile presented in the previous section, which provides a compact and uniform AE data representation of each knee based on U × V × 4 AE feature classes. In the implementation of PCA, the image based AE profile display of each knee is converted from its matrix form of size 2U × 2V to a row feature vector of length of 4UV by row concatenation. The row feature vector of each knee is then merged into one data matrix. This results in the data matrix with a size of N × 4UV, where N is the number of knees, and the entry at the ith row and jth column corresponding to the ith knee with the number of AE hit waveforms in the jth AE feature class. If M denotes the data matrix, then its covariance matrix can be computed from C=
1 (M − M )T (M − M ) N−1
(3)
where M is the matrix of means of each column (feature class) in M. Applying PCA to the covariance matrix to obtain its eigenvectors denoted by V and eigenvalues denoted by i , the AE features can be represented in a different domain using eigenvectors as new basis
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Fig. 9. Gaussian probability plots of ASL for (a) AA phase, (b) AD phase, (c) DA phase, and (d) DD phase.
vectors, i.e. P = VM
(4)
By selecting a small number of eigenvectors associated with highest eigenvalues (called principal components), the whole set of knee AE profiles can be projected on a different basis formed by a small set of orthogonal and ordered principal component axes with the first few principal component axes capturing most of the variation present in the AE feature profile data. Based on a total of 63 AE feature classes with 7 peak magnitude intervals and 9 ASL intervals per each movement phase, the projection of the AE feature profiles from 53 knees is shown in Fig. 11(a) using the first three principal components capturing approximately 87.97% of the total variance in the data. By labelling each projected AE feature profile according to its age and knee condition group, there are five clusters in Fig. 11(a) corresponding to five groups with a trajectory related to knee age and degeneration, progressing from group H1 with the early adulthood healthy knees to group H3 with the late adulthood healthy knees, followed by group OA1 with the middle adulthood OA knees to group OA2 with the late adulthood OA knees. Furthermore, this trajectory shows increasing areas for each cluster. It starts from the smallest cluster for the early adulthood healthy knees in group H1 with significant overlapping of the projected AE feature profiles. With the increase in the age,
the cluster areas increase with longer distances among the projected AE feature profiles for the middle and late adulthood healthy knees in groups H2 and H3. As the knee condition changes from healthy to OA, the cluster areas are seen to spread even further with much longer distances shown among the projected AE feature profiles of the knees in group OA1 compared with those in group H3. At the end of the trajectory, group OA2 with the late adulthood OA knees is seen to produce the largest cluster area with the widest spread of the projected AE feature profiles. While the zoom-in view of the H2 and H3 clusters is shown in Fig. 11(b), the zoom-in view of the H1 cluster is shown in Fig. 11(c). The trend of increasing cluster area shown in Fig. 11(a) is in agreement with the trend of increasing standard deviation shown in Fig. 6. Investigation was also performed to see the sensitivity of PCA based projection of AE feature profiles to the change of the peak magnitude and ASL intervals, or “granularity”. Although using a different granularity will give a different result with a reduction in the distances among the projected points in the same group and between clusters, it does not change the trajectory and each cluster remains well defined by most of the projected points in the corresponding group. These results demonstrate the potential of using the projected AE feature profile in the PCA space as a biomarker for quantitative assessment of knee age and condition. By increasing the number of age groups with a large number
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Fig. 10. Typical AE feature profiles of a knee in each group.
of healthy and OA knees in each age group to establish the reference clusters and trajectory, a knee could be diagnosed based on the position of its projected AE feature profile along the trajectory and the distance of it with respect to the centre and boundary of the nearest two clusters, or ranked with respect to the statistical standard AE parameters corresponding to each age group. Use of knee AE to monitor the ageing process opens up the possibility to introduce preventive measures to knees whose projected AE fea-
ture profiles approach the boundary of their age group in the PCA space. In addition, the wide spread of the OA clusters observed in the PCA space suggests the possibility of further group clustering to define sub-domains based on different pathologies and severities for different OA patients (such as the level of cartilage degeneration which could be measured by using MRI [28]), thereby enabling better diagnosis, more personalised and therefore more effective treatment.
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H1 H2 H3 OA1 OA2
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Fig. 11. PCA of AE feature profiles with numbers corresponding to ages (a) all five groups, (b) zoom-in view of H2 and H3 groups, and (c) zoom-in view of H1 group.
7. Conclusions By dividing participants into five groups according to age and knee condition, this paper presents the work carried out to acquire joint angle based AE from 53 healthy and OA knees, and signal anal-
ysis based on the four-phase model of sit–stand–sit movements derived from joint movement angle and angular velocity. Basic statistical analysis of the number of AE hits showed a trend of increase with the increasing age group and a change of knee condition from healthy to OA in each movement phase, and the maximum increase
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was found to occur in the AA movement phase. This trend was further supported by statistical distributions of the AE waveform features with an increase in the upper bounds of the peak magnitude in the AD movement phase and in the ASL values in the first three of the four movement phases (AA, AD, and DA). Using an image based representation to show the AE feature profile in terms of AE peak magnitude and ASL values in each movement phase, the paper shows a visual trend of increasing higher peak magnitude and ASL values with the increasing age groups and the change of knee condition from healthy to OA. Application of PCA to the AE feature profiles of all knees yields an age and disease related trajectory with five clusters of increasing sizes and progressing from the youngest to the oldest healthy group followed by the younger to the older OA group. With all the trends from knee AE signal analysis showing a strong correlation with knee age and condition, there is significant prima facie evidence for knee AE as a biomarker for quantitative assessment of joint ageing and degeneration. With the advantages of simplicity and accessibility, a good prospect is viewed to be offered by knee AE as a rapid and non-invasive measurement tool for use in clinic and home settings for objective monitoring of condition change in knee joints. Acknowledgements The work was supported by the Arthritis Research Campaign (Grant Ref. No. 17542) and we thank the people participating in the study and Dr B. Mascaro for the technical input. Conflict of interest statement There are no financial and personal relationships with other people or organisations that could inappropriately influence (bias) our work. References [1] Gray H. Anatomy of the human body. New York: Bartleby.com; 2000. [2] Kauffman TL, Barr JO, Moran ML, editors. Geriatric rehabilitation manual. Elsevier; 2007. [3] Peat G, McCartney R, Croft P. Knee pain and osteoarthritis in older adults: a review of community burden and current use of primary health care. Ann Rheum Dis 2001;60:91–7. [4] Cooper C, Snow S, McAlindon TE, Kellingray S, Stuart B, Coggon D, et al. Risk factors for the incidence and progression of radiographic knee osteoarthritis. Arthritis Rheum 2001;43(5):995–1000. [5] Tehranzadeh J, Ashikyan O, Dascalos J. Magnetic resonance imaging in early detection of rheumatoid arthritis. Semin Musculoskeletal Radiol 2003;7:79–94.
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