--\x3e\n
So, the product of sympletcic matrixes was also a symplectic matrix.
\nTheorem 2.5 Suppose a Householder matrix H was
\nSo, H is a symplectic unitary matrix.
Proof:
\nIn order to prove that the matrix H was symplectic matrix, we only needed to prove H*JH = J.
\nwhere
Plugging Eq. (2.8) into Eq. (2.7), we had:
\n∴ H is a symplectic matrix.
\n∴ H is also a unitary matrix.
\n∴ The Householder matrix H is a symplectic unitary matrix.
\nIn the real calculation, the above householder matrix H could be constructed from a time series according to Theorem 2.6.
\nTheorem 2.6 Suppose x and y were two unequal n dimension vectors, and
For a non-zero n dimension vector x = (x1, x2, ⋯, xn)T we could note
Then
It was easy to testify that the elementary reflective array H was symmetry matrix (HT = H), orthogonal matrix (HTH = 1) and involution matrix (H2 = 1).
\n\nFor a time series x, the covariance matrix A of the matrix X (see Eq. (2.2)) could first be given as follows:
\nWhere
For Hamilton matrix M (2n × 2n), its eigenvalues could be obtained by symplectic similar transform, such as symplectic QR decomposition. At present, there had been some algorithms for symplectic QR decomposition [28–34, 43]. Here, we could use symplectic Householder transform instead of the matrix Q to decompose the matrix M:
\nwhere Q is a Householder matrix, that is, a symplectic unitary matrix (the eigenvector matrix). R is an upper triangular matrix. It was easy to prove that the Householder matrix Q was a symplectic unitary matrix according to Theorem 2.5.
\nIn theory, for a Hamiltonian matrix
Thus, the primary 2n-dimension space could be transformed into n-dimension space to resolve. The symplectic eigenvalues (μ = {μ1, μ2, ⋯, μ2d}) of the matrix M could be composed of those (λ(A) = {μ1, μ2, ⋯, μd}) of the matrix A. The symplectic eigenvectors of the Householder matrix H could consist of those of the matrix P corresponding to the symplectic eigenvalues of the matrix A. These eigenvalues were given by descending order as following:
\nThe above symplectic eigenvalue method could be used to analyse the principal components of a system, called symplectic principal component analysis (SPCA) [40].
\nFor the above Hamiltonian matrix M, its symplectic eigenvalues μ = {μ1, μ2, ⋯, μ2d} could be got by using symplectic QR decomposition in Section 2.4. According to Eq. 2.17, the dominant symplectic eigenvalues μi (i = 1, …, l) of A could be obtained, that is
\nwhen μi >> μi+1. The lower symplectic eigenvalues μi, (i =l+1, …, d) got into a noise floor. Consequently, noise could be reduced from the data x by eliminating the lower eigenvalue components μi, (i =l+1, …, d). Corresponding to the dominant components μi, (i = 1, …, l), the truncation matrix W could be got from the Householder matrix H. The new data
Reconstruct the trajectory matrix X from the raw data x in terms of Eq. (2.2);
Build the real d × d symmetry matrix A (see Eq. (2.13));
Calculate the matrix P of the Householder matrix H from the matrix A [37]. Let A as follows:
First, suppose
Then, the elementary reflective matrix P(1) is computed by:
where
So, A is changed to a matrix A(2):
where the first element of the first column is σ1. Other elements were zeros.
Then, the second column vector of A(2) is also given like the above way. Let
construct P(2) matrix:
where
Thus, the second column of A(2) is also changed to all zero vector except the first and second elements. A(3) is obtained:
By repeating above-mentioned method, the matrix P could be obtained until A(n) became an upper triangle matrix:
It was easy to show that P was a symmetrical, orthogonal and involution matrix.
Use the matrix P to transform the matrix A into the upper triangular matrix T. The absolute values of the diagonal components Tii by descending order were called as the symplectic eigenvalues of the matrix A (see Eq. (2.17));
Corresponding to the dominant symplectic principal component values μi, (i= 1,…, l), let the first l column vectors of W as those of P. Corresponding to the lower eigenvalues μi, (i=l+1,…,d), the other vectors of W were zeros;
Construct the symplectic transform matrix Q and the Hamiltonian matrix S, i.e.
where X is given by Eq. (2.2).
Use the Q project S into Y,
Reestimate the
The reduced-noise data could be given by the first row of the matrix
For the heavily noisy time series, the first estimation of data was usually not good. Here, one could repeat the above steps 7 and 8 several times. Generally, the second or third reconstructed data would be better than the first reconstructed data.
\nThis chapter employed the three typical chaotic equations [41].
\nLorenz equation
where σ = 10, b = 8/3, and γ = 28.
Duffing equation
where ε=1, c=0.4, A=0.4, and ω=1.
Chua’s equation
where α = 15.6, β = 28.58, a = -8/7, and b = -5/7.
A measurement noise e was used because all the real measurements were polluted by noise. Here, the Gaussian white noise e as a measure noise was added to the clean signal x generated from the above chaotic equations. The contaminated data xn is obtained as follows:
\nThe signal-to-noise ratio was defined by the following:
\nwhere σx and σn are the standard deviation of the clean signal x and the noise e, respectively. The more details of noise notions were referred to the literature [44–46]. Here, SNR is 10 dB.
\nAs for a practical example of noise reduction, we chose the sunspot number data obtained from monthly observations. Sunspot number series were short, highly non-linear and noisy [49]. It was hard to predict accurately the sunspot period, although Wolf had reported the well-known 11-year cycle.
\nSPCA, like PCA, could not only represent the original data by capturing the relationship between the variables but also reduce the contribution of errors in the original data. Here, the performance evaluation of SPCA was first given based on the analysis of Lorenz chaotic time series [39].
\nSince the real systems were usually unknown, it was necessary to study the influence of sampling time, data length, and noise on the representation analysis based on the SPCA approach. For a clean chaotic time series, the root mean square error (RMSE) as a measure was employed in order to estimate the difference between the clean original data and the SPCA-filtered data:
\nwhere x(i) and
In order to analyse noisy data, the percentage of principal components (PCs) was defined to study the occupancy rate of each PC in order to reduce noise as follows:
\nwhere d is the embedding dimension and μi is the ith principal component value.
\nRMSE versus sampling time curves for the SPCA and PCA.
Here, we took the Lorenz system as an example. The dimension of the Lorenz system was 3, then, the embedding dimension d of the matrix A was chosen as 8. For the clean Lorenz time series generated by Eq. (4.1) (i.e., no noise e = 0 in Eq. (4.4)), when k = d, the estimated data were obtained by SPCA and PCA with k=d, respectively. For the different sampling time Ts, the RMSE values are calculated in Figure 1 by Eq. (5.1). The RMSE values of SPCA were lower than 10−14 for the different sampling time (see Figure 1). The results showed that the SPCA method was better than the PCA. Figure 2 shows the RMSE values of the different data lengths for SPCA and PCA, respectively. For the different data lengths, the RMSE values of SPCA were also lower than 10−14 (see Figure 2). From the Figures 1 and 2, we could see that the sampling time and the data length had less effect on SPCA method in the case of free noise.
\nRMSE versus data length curves for the SPCA and PCA.
The percentage of PCs for the SPCA and PCA.
From Figure 3, all of the principal components were given by Equation. (5.2) for the clean Lorenz time series according to the SPCA and PCA methods, respectively. We could see that the first largest symplectic principal component (SPC) of the SPCA was a little larger than that of the PCA. For the SPCA method, the first largest SPC was almost possessed of all the proportion of the SPCs. Next, the reduced space spanned by a few largest SPCs was explored to estimate the chaotic Lorenz time series without noise. For the different data length, we gave the RMSE values between the original data and the data estimated from the first seven largest SPCs and PCs, respectively, that is, in the case of k = 7 (see Figure 4). The sampling time is 0.1. The result showed that the data length had less effect on the SPCA than the PCA. Figure 5 shows the effect of sampling time on different number of PCs for the SPCA and the PCA methods, respectively. When the PCs number k =1 and k =7, respectively, the change of RMSE values with the sampling time is given in Figure 5. We could see that the RMSE values of the SPCA were smaller than those of the PCA. The sampling time had also less impact on the SPCA than the PCA.
\nThe RMSE versus the data length for the SPCA and PCA, where k =7. The sampling time is 0.1.
The RMSE values versus the sampling time for the SPCA and PCA, where (a) the PCs number k =7; (b) k =1.
Furthermore, the estimated data based on the first three largest SPCs are calculated in Figure 6, where the original data x are given with a sampling time of 0.01 from chaotic Lorenz system. The average error between the original data and the estimated data was −6.55e-16. The corresponding standard deviation was 1.03e-2. The estimated data were very close to the original data not only in time domain (see Figure 6a) but also in phase space (see Figure 6b).
\nChaotic signal reconstructed by the proposed SPCA algorithm with k=3, where (a) the time series of the original Lorenz data x without noise and the estimated data; (b) phase diagrams with L = 11 for the original Lorenz data x without noise and the estimated data. The sampling time Ts = 0.01.
To sum up, we could see that the SPCA method preserved the essential dynamical character of the primary time series generated from chaotic continuous systems. These indicated that the SPCA could reflect intrinsic non-linear characteristics of the original time series. The SPCA could elucidate the dominant features in the observed data. It was feasible for the SPCA to study the principal component analysis (PCA) of time series. Moreover, the SPCA would help to retrieve dominant patterns from the noisy data.
\nFor the performance evaluation on noise reduction, the SPCA method was further studied by dealing with the noisy Lorenz data x with Gaussian white noise of zero mean and one variance. The phase diagrams of the noisy and clean data are given in Figure 7a and b. The clean data x were obtained by the sampling time 0.01 from the chaotic Lorenz system with noise-free. The noisy data were the chaotic Lorenz data x with Gaussian white noise of zero mean and one variance (Eqs. (4.1) and (4.4)). The time delay L is 11 in Figure 7. It was obvious that noise is very strong (see Figure 7a). Here, we first built an attractor X with the embedding dimension of 8. Then, the transform matrix W was constructed when k=1. The first denoised data are generated according to Section 3 (see Figure 7c and d). In Figure 7c, the first denoised data are compared with the noisy Lorenz data x from the view of time field. Figure 7d shows the corresponding phase diagram of the first denoised data. Compared with Figure 7a, the first denoised data could basically give the structure of the original system. In order to obtain better results, these denoised data were reduced noise again by the step (8). For the second noise reduction, the results were greatly improved in Figure 7e and f. Comparing by Figure 7c, d, e and f, the curves of the second denoised data were better than those of the first denoised data whether in time domain or in phase space. Figure 7g shows that the PCA technique gave the first denoised result. Like Figure 7e, the second denoised data are obtained by the PCA (see Figure 7h). Although some of noise had been further reduced in Figure 7h, the curve of PCA was not better than that of SPCA in Figure 7e. The reason was that the PCA was a linear method indeed. When non-linear structures had to be considered, it could be misleading, especially in the case of a large sampling time (see Figure 8). The used program code of the PCA came from the TISEAN tools (http://www.mpipks– dresden.mpg.de/~tisean).
\nThe noise reduction analysis of the proposed SPCA algorithm and PCA for the noisy Lorenz time series, where L=11. (a) Phase diagram for noisy data, (b) phase diagram for the clean data, (c) Lorenz time series, (d) phase diagram for the SPCA, (e) phase diagram for the SPCA, (f) the second denoised data, (g) phase diagram of the first denoised data for PCA and (h) phase diagram of the second denoised data for PCA.
In order to evaluate the effectiveness of noise reduction, the correlation dimension D2 was estimated by the Grassberger-Procaccia’s algorithm [47–48] because it manifested non-linear properties of chaotic systems. The variations of correlation dimension D2 with embedding dimension d were given for the clean, noisy, and denoised Lorenz data (see Figure 8). The sampling time was 0.1. The results showed that, for the clean and SPCA denoised data, the trend of the curves had a platform and tended to smooth in the vicinity of 2. For the noisy data, the trend of the curve was constantly increasing and had no platform. For the PCA denoised data, the trend of the curve was also increasing and trended to a platform with 2. However, this platform was smaller than that of SPCA. The PCA algorithm was less effective than the SPCA algorithm. The result indicated that it was difficult for the PCA to describe the non-linear structure of a system.
\n(Colour online) D2 versus embedding dimension d.
Besides, it was necessary to show that the method of the locally projective non-linear noise reduction (NNR) in the TISEAN package (http://www.mpipks-dresden.mpg.de/~tisean) could not give the better result than SPCA and PCA [41].
\nIn the noise level SNR = 10 dB, the noisy Duffing chaotic data (see Figure 9a) and the noisy Chua’s chaotic data (see Figure 9c) show reduced noise by applying the SPCA. Embedding dimension d=8 had been used with the time delay k=1. The reduced noise results of SPCA are shown in Figure 9. The third denoised data of the noisy Duffing chaotic data are shown in Figure 9b. For the noisy Chua’s chaotic data, the third denoised data are given in Figure 9d. Obviously, a lot of noise had been removed from the noisy time series. Here, the number of dominant components was chosen as one according to the curves of SPCs in Figures 10 and 11.
\nThe noise reduction for the noisy Duffing chaotic data and the noisy Chua\'s chaotic data based on the SPCA. (a) Duffing chaotic data with SNR=10 dB, (b)The third denoised data for Duffing data, (c)Chua\'s chaotic data with SNR=10 dB and (d) The third denoised data for Chua\'s data.
The symplectic principal component analysis of the noisy Duffing chaotic data x.
The symplectic principal component analysis of the noisy Chua’s chaotic data x.
The noise reduction analysis of the monthly sunspot number based on the SPCA. (a) The monthly sunspot number, (b) the second denoised data, (c) phase diagram for SPCA, (d) the yearly sunspot data and the denoised monthly sunspot data.
The SPCA method was also applied to reduce noise from the monthly sunspot data (see Figure 12a). The time range was from January 1850 to February 2004. There was a lot of noise in the monthly data. According to our SPCA noise reduction algorithm, the resultant data were given by reducing noise twice when d =8, k=1 (see Figure 12b). It could be seen that plenty of noise had been removed from the monthly sunspot numbers. Its attractor in phase space was clearly shown with L=12 in Figure 12c. It was obvious that the sunspot cycle could be explained neither by regular periodicity nor by a sequence of random process. The sunspot numbers contained non-linear characteristics [49]. Furthermore, we compared the denoised monthly data and the yearly data in Figure 12d. The denoised monthly data were very close to the yearly data. The results showed that SPCA could effectively remove the noise from the monthly sunspot data.
\nHere, the first symplectic principal component was chosen to reduce the noise in the monthly sunspot numbers x referring to Figure 13.
\nhe symplectic principal component analysis of the monthly sunspot numbers x.
This chapter had proposed the symplectic principal component analysis method (SPCA) and the noise reduction method based on SPCA. In theory, the SPCA method was intrinsically non-linear, which could reflect non-linear structure of non-linear dynamical systems very well. Therefore, the clean chaotic Lorenz data were used to study the performance of the SPCA method by calculating RMSE, percentage, correlation dimension, and phase space diagrams. The results showed that the SPCA method could yield more reliable results for chaotic time series under the different data lengths and sampling times, especially with short data length and undersampled sampling time, than the classic PCA. With regard to noise reduction, SPCA algorithm was also more effective than PCA and NNR. It could reduce more noise than the other two methods. And for the SPCA noise reduction, the denoised data could catch the non-linear structure of the systems. The SPCA method was used to remove noise from the noisy Lorenz data, Duffing data, Chua’s data, and sunspot data. The results showed that the SPCA algorithm had a good effect of noise reduction. It was suitable for the SPCA method to analyse the non-linear time series and deal with the noisy data.
\nThis work was supported by the Science Fund for Creative Research Groups of the National Natural Science Foundation of China (Grant No. 51421092), the National Natural Science Foundation of China (Grant No. 10872125), Research Fund of State Key Laboratory of Mechanical System and Vibration (Grant No. MSV-MS-2010-08), Research Fund from Shanghai Jiao Tong University for medical and engineering science. (Grant No. YG2013MS74), Key Laboratory of Hand Reconstruction, Ministry of Health, Shanghai, People’s Republic of China, Shanghai Key Laboratory of Peripheral Nerve and Microsurgery, Shanghai, People’s Republic of China.
\nIn 1893, Paul Jules Tillaux described a painful crepitus sign (Aïe crépitant de Tillaux)—tenosynovitis of the adductor and the short extensor of the thumb. In 1894, Fritz de Quervain, a Swiss surgeon, first described tenosynovitis on December 18, 1894, in Mrs. D., a 35-year-old woman who had severe pain in the extensor muscle region of the thumb, excluding tuberculosis.
“It is a condition affecting the tendon sheaths of the abductor pollicis longus, and the extensor pollicis brevis. It has definite symptoms and signs. The condition may affect other extensor tendons at the wrist” [1].
\nPatients with DQT have difficulty gripping objects and performing their daily activities. De Quervain’s tendinopathy affects the abductor pollicis longus (APL) and extensor pollicis brevis (EPB) tendons in the first extensor compartment at the styloid process of the radius. It is characterized by pain or tenderness at the radial side of the wrist. Although de Quervain’s tendinopathy is often attributed to overuse or repetitive movements of the wrist or thumb, the cause is generally unknown.
\nDe Quervain’s tenosynovitis (DQT) is a common cause of wrist pain in adults and is the second most common entrapment tendinopathy in the hand following trigger finger. It usually occurs in middle-aged individuals and is around 3× more common in women (~80% of cases). It is most common among women between the ages of 30 and 50 years of age, including a small subset of women in the postpartum period [2]. These women tend to develop symptoms about 4–6 weeks after delivery. In a large analysis of a young active population of military personnel, women again had a significantly higher rate of de Quervain’s tenosynovitis at 2.8 cases per 1000 person-years, compared to men at 0.6 per 1000 person-years (almost 5×). Age greater than 40 was also a significant risk factor, with this age category showing a rate of 2.0 per 1000 person-years compared to 0.6 per 1000 in personnel under 20 years. There was also a racial difference, with blacks affected at 1.3 per 1000 person-years compared to whites at 0.8, in this population [3].
\nWith regard to work, Stahl found that in 189 patients surgically treated for DQT vs. 198 patients with wrist ganglia (WG) (controls), there was no significant difference between DQT vs. WG found after subgrouping professional activities (manual labor: 18 vs. 26%, respectively, p = 0.23). In addition, there was no asymmetric distribution of comorbidities, wrist trauma, forceful or repetitive manual work, or medication observed, and it was concluded that neither heavy manual labor nor trauma could be shown to be predisposing risk factors for DQT (Figure 1). Most cases of DQT, however, are associated with overuse, and, local trauma can also precipitate the condition [4].
\nDe Quervain’s tenosynovitis (DQT) is one of the most common work-related upper limb musculoskeletal disorders especially in the age of smartphones, tablets and laptop devices.
The etiology of de Quervain’s tenosynovitis (DQT) is not well understood. In the past, it was frequently attributed to occupational or repetitive activities involving postures that maintain the thumb in extension and abduction. As an example, it has been thought that new mothers are at risk postpartum due to repetitive motion of hands required to lift and hold newborns. Hormonal causes and fluid retention are another plausible explanation. The evidence to support etiologic hypotheses is limited and is largely based on observational data. The histopathology does not demonstrate inflammation but rather myxoid degeneration (disorganized collagen and increased cellular matrix) in patients referred for surgery [5].
\nDQT affects both the abductor pollicis longus (APL) and the extensor pollicis brevis (EPB) at the point where they pass through a fibro-osseous tunnel (the first dorsal compartment) from the forearm into the hand. These tendons are responsible for bringing the thumb away from the hand as it lies flat in the plane of the palm (i.e., radial abduction). Similar to trigger finger (or stenosing flexor tenosynovitis), this disease involves a noninflammatory thickening of both the tendons and the tunnel (or sheath) through which they pass. The APL and EPB tendons are tightly secured against the radial styloid by the overlying extensor retinaculum which creates a fibro-osseous tunnel. Thickening of the retinaculum and tendons from acute or repetitive trauma restrains normal gliding within the sheath. This causes inflammation and further edematous thickening of the tendon exacerbating the local stenosing effect. Microscopically, there are inflammatory cells found within the tendon sheath.
In ~10% of patients, there is an intertendinous septum between APL and EPB. The absence of a septum is associated with very high rates (almost 100%) of complete symptom resolution with conservative management. Presence of an intertendinous septum increases the likelihood that surgical management will be required.
\nStahl et al. [6] reviewed in a meta-analysis of 80 articles of an association between DQT and (1) repetitive, (2) forceful, or (3) ergonomically stressful manual work suggesting an odds ratio of 2.89 (95% CI, 1.4–5.97; p = 0.004). The analysis, however, found no evidence to support the Bradford Hill criteria for a causal relationship between de Quervain’s tenosynovitis and occupational risk factors.
\nWhile there have been several multidisciplinary treatment guidelines published [7], they are consensus-based rather than evidence-based. This review seeks to address this issue and identify any gaps in research for the investigation and treatment of DQT.
\nSystematic search of MEDLINE, CINAHL and EMBASE for articles published from September 2014 to August 2018, and the Cochrane Database of Systematic Reviews (most recent issue searched—Issue 2, 2018). Randomized controlled trials, meta-analyses, and reviews of all aspects of diagnoses and treatment for DQT among participants were limited to those aged 18 years.
\nAll studies were reviewed independently by the author, who recorded individual study results, and an assessment of study quality and treatment conclusions was made according to evidence-based protocols.
\nOut of a total of 72 articles from PUBMED for DQT diagnosis, we found 10 articles satisfying the research criteria. There were no suitable Cochrane review articles.
\nOut of a total of 95 articles from PUBMED for DQT treatment, we found 20 articles satisfying the criteria. There were no suitable Cochrane review articles.
\nThe Finkelstein test (Figure 2) is named after Harry Finkelstein (1865–1939), an American surgeon who first described it in 1930. It is a clinical test used to assess the presence of DQT in people with wrist pain. It is performed by grasping the patients thumb and deviating the hand in the ulnar direction. If a sharp pain occurs along the distal radius, this is considered to make DQT likely.
\nFinkelstein’s maneuver as described in 1930: the examiner pulls the thumb in ulnar deviation and longitudinal traction to exacerbate the symptoms of de Quervain’s disease.
Eichhoff’s test (Figure 3) is often wrongly named as Finkelstein’s test. Eichhoff’s test consists of grasping the thumb in the palm of the hand while the wrist is ulnar deviated, and the test is positive in the presence of pain over the radial styloid process during lunar deviation of the wrist.
\nEichhoff’s maneuver described in 1927, commonly confused with Finkelstein’s test described in 1930.
The wrist hyperflexion and abduction of the thumb (WHAT) test (Figure 4) revealed greater sensitivity (0.99) and an improved specificity (0.29) together with a slightly better positive predictive value (0.95) and an improved negative predictive value (0.67) compared with Eichhoff’s test in one study [8]. Moreover, the study showed that the wrist hyperflexion and abduction of the thumb test was very valuable in diagnosing dynamic instability after successful decompression of the first extensor compartment.
\nWHAT test: active testing by shearing the tendons of the first extensor compartment against the palmar distal edge of the pulley.
Plain radiographs are nondiagnostic of the condition but may show nonspecific signs and can help exclude other causes of pain such as fracture, carpometacarpal arthritis, and osteomyelitis. Signs include [9]:
Soft-tissue swelling over the radial styloid
Focal abnormalities of the radial styloid including cortical erosion, sclerosis, or periosteal reaction
Ultrasound is very often diagnostic. Findings include:
Edematous tendon thickening of APL and EPB at the level of the radial styloid (compare with the contralateral side)
Increased fluid within the first extensor tendon compartment tendon sheath
Thickening of overlying retinaculum and the synovial sheath
Peritendinous subcutaneous edema resulting in a hypoechoic halo sign
Peritendinous subcutaneous hyperemia on Doppler imaging
It is important to assess for an intertendinous septum which can usually be identified if present. Ultrasound is often used to guide corticosteroid injections into the tendon compartment to treat the condition [10].
Using B-mode ultrasound as standard, shear wave elastography (SWE) as diagnosis of de Quervain’s tenosynovitis has 95% specificity and 85% sensitivity in diagnosing DQT.
In addition, ultrasonic characteristics including a cutoff value of the extensor retinaculum for diagnosing DQT was 0.45 mm (sensitivity 96.3%, specificity 93.3%). Bony crests on the radial styloid were found in all cases of the presence of the intracompartmental septum [11].
MRI is very sensitive and specific and useful for detecting mild disease where ultrasound may be equivocal. The presence or absence of intertendinous septum can be assessed. Findings include:
Tenosynovitis
Increased fluid within tendon sheath (high T2, low-intermediate T1)
Debris within sheath (intermediate T1 signal)
Thickened edematous retinaculum
Peritendinous subcutaneous edema
Peritendinous subcutaneous contrast enhancement
Tendinosis
Tendon enlargement maximal at radial styloid and often greater at the medial aspect of the tendon
Slightly increased intratendinous T1 and T2 signal compared to other tendons
Striated appearance of tendons due to multiple enlarged slips
Longitudinal tendon tear
Linear high T2 signal due to fluid within the split
More common in APL
When comparing ultrasound and clinical characteristics of the operated and nonoperated wrists, it was found that patients with a high baseline visual analogue scale, with all positive clinical tests and with a persistent intracompartmental septum, had a significantly higher risk of failure following conservative treatment [12].
\nA recent review article by Huisstede et al. [13] found (1) moderate evidence for the effect of corticosteroid injection on the very short term for DQT and (2) moderate evidence that a thumb splint as additive to a corticosteroid injection seems to be effective in the short term and midterm.
\nOne prospective study of 35 patients found that ultrasound-guided partial release and simultaneous corticosteroid injection using a 21-gauge needle was feasible in current practice, with minimal complications [14].
\nProspectively randomized patients treated with either corticosteroid injection (CSI) alone were compared with CSI with immobilization [15]. Radial-sided wrist pain, first dorsal compartment tenderness, and positive Finkelstein test were used to define DQT. Pain score of 4 or higher on a visual analogue scale (VAS) was utilized for inclusion. Followed at 3 weeks and 6 months for further evaluation, resolution of symptoms and improvements in VAS and Disabilities of the Arm, Shoulder, and Hand (DASH) scores were assessed to evaluate treatment success. This small prospective controlled study (on 20 patients) found that immobilization of 3 weeks following injection increased costs, may hinder activities of daily living, and did not contribute to improved patient outcomes in this study.
\nContrasting this, Awan et al. [16] found in a randomized controlled trial of 30 patients with established DQT that the use of therapeutic ultrasound and spica splint together is more effective than using therapeutic ultrasound alone in the conservative management over 6 months.
\nHowever, Cavaleri et al. [17] in an earlier review of six studies confirmed combined orthosis/corticosteroid injection approaches are more effective than either intervention alone. It was found that significantly more participants were treated successfully when combined orthosis/corticosteroid injection approaches were compared to (i) orthoses (RR 0.53, 95% CI 0.35–0.80) and (ii) injections alone (RR 0.76, 95% CI 0.64–0.89).
A follow up of 89 patients who underwent surgical treatment with the Le Viet technique with a follow-up of 9.5 years, were favorable, with total regression of functional impairment in 85% of cases and a satisfaction rate of 97.5%, with no cases of tendon dislocation, neuroma, or recurrence [18].
\nDe Quervain’s tenosynovitis (DQT) is one of the most common forms of stenosing tenosynovitis and is a common workplace injury. Diagnosis is usually clinical using either the Finkelstein’s test, Eichhoff’s test, and/or the wrist hyperflexion and abduction of the thumb (WHAT) test. If required, the single most useful and accurate investigation is a high-resolution ultrasound scan. This evidence-based review identified a clear approach to treatment of DQT including nonsurgical (therapeutic ultrasound with or without orthoses) and surgical approaches. However, we found that more high-quality RCTs are still needed to further stimulate evidence-based practice, especially related to work-related disorders.
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