sensors Article

A Compressed Sensing-Based Wearable Sensor Network for Quantitative Assessment of Stroke Patients Lei Yu 1,2, *, Daxi Xiong 1 , Liquan Guo 1 and Jiping Wang 1 1

2

*

Jiangsu Key Laboratory of Medical Optics, Suzhou Institute of Biomedical Engineering and Technology, Chinese Academy of Sciences, No. 88, Keling Road, Suzhou, Jiangsu 215163, China; [email protected] (D.X.); [email protected] (L.G.); [email protected] (J.W.) University of Chinese Academy of Sciences, Beijing 100049, China Correspondence: [email protected]; Tel./Fax: +86-512-6958-8302

Academic Editor: Leonhard M. Reindl Received: 12 December 2015; Accepted: 3 February 2016; Published: 5 February 2016

Abstract: Clinical rehabilitation assessment is an important part of the therapy process because it is the premise for prescribing suitable rehabilitation interventions. However, the commonly used assessment scales have the following two drawbacks: (1) they are susceptible to subjective factors; (2) they only have several rating levels and are influenced by a ceiling effect, making it impossible to exactly detect any further improvement in the movement. Meanwhile, energy constraints are a primary design consideration in wearable sensor network systems since they are often battery-operated. Traditionally, for wearable sensor network systems that follow the Shannon/Nyquist sampling theorem, there are many data that need to be sampled and transmitted. This paper proposes a novel wearable sensor network system to monitor and quantitatively assess the upper limb motion function, based on compressed sensing technology. With the sparse representation model, less data is transmitted to the computer than with traditional systems. The experimental results show that the accelerometer signals of Bobath handshake and shoulder touch exercises can be compressed, and the length of the compressed signal is less than 1/3 of the raw signal length. More importantly, the reconstruction errors have no influence on the predictive accuracy of the Brunnstrom stage classification model. It also indicated that the proposed system can not only reduce the amount of data during the sampling and transmission processes, but also, the reconstructed accelerometer signals can be used for quantitative assessment without any loss of useful information. Keywords: compressed sensing; wearable sensor network; quantitative assessment; stroke; Brunnstrom stage classification

1. Introduction Stroke, also known as cerebrovascular insult (CVI), cerebrovascular accident (CVA), or brain attack, is when poor blood flow to the brain results in cell death. Between 1990 and 2010, the number of strokes which occurred each year decreased by approximately 10% in the developed world and increased by 10% in the developing world [1]. In 2013, stroke was the second most frequent cause of death after coronary artery disease, accounting for 6.4 million deaths (12% of the total) [2]. In China, stroke, with an annual mortality rate of approximately 157 per 100,000, has surpassed heart disease to become the leading cause of death and adult disability. In addition, China has 2.5 million new stroke cases each year and 7.5 million stroke survivors [3]. Considering the large population of stroke patients in China and the limited rehabilitation resources (rehabilitation centers, physicians, therapists), it is an inevitable trend for stroke patients to do rehabilitation

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training in home settings. Many previous research results have proven that, in comparison with inpatient care, home-based rehabilitation shows no difference in the effect on any of the outcomes [4,5]. Moreover, as there are fewer limitations on the time and space, patients can do rehabilitation training according to their own schedule in the home settings. However, due to the fact that there are no physicians or physiotherapists in these home settings to evaluate the motor function of stroke patients and adjust the prescribed training, how to precisely and automatically assess the motor function without the participation of physicians has become an important problem that needs to be resolved. Fortunately, the availability of wearable devices provides a potential approach to solve this problem. With the development of the Internet of Things (IoT), wearable devices have been widely applied in the healthcare area. Considering sensor types, inertial measurement sensors such as accelerometers, gyroscopes, and magnetometers are used individually or together to monitor and analyze the motor functions of stroke patients [6,7]. In addition, some studies combine inertial measurement sensors with physiological sensors, like ECG, sEMG, etc. [8,9]. Based on the application scenarios, the following four categories can be distinguished: fall detection [10,11], physical activity monitoring [12–14], movement recognition [15–17] and quantitative assessment [18–20]. Particularly in the area of quantitative assessment for stroke patients, many valuable research results have been published. Patel et al. [21] proposed a Random Forests-based algorithm to estimate Functional Ability Scale (FAS) scores by using the signals of six accelerometers placed on the affected arm and the trunk. Based on the same dataset, Din et al. [20] established a Random Forests model to predict the Fugl-Meyer Assessment (FMA) scores. Uswatte et al. [22] have shown that just two accelerometers are adequate for assessing whether rehabilitation has an effect on arm function outside the laboratory. Previous work by our research group found that accelerometer data can be used to automatically classify the clinical Brunnstrom stages and some quantitative assessment indexes were designed to evaluate the motor function of stroke patients [23–26]. However, in our previous works, the accelerometer data were wirelessly transmitted from wearable devices to a receiver using the ZigBee protocol. Because the wearable devices are battery-operated, the battery life is inversely proportional to the amount of data transmitted. Hence, in order to extend the battery life and reduce the amount of data during the sampling and transmission processes, this paper proposes a novel wearable sensor network system based on compressed sensing technology. The main aim of this paper is to investigate whether the accelerometer signals collected during the training process of stroke patients could be compressed and whether the reconstruction errors have any influence on the quantitative assessment models. This paper is organized as follows: in Section 2, the wearable sensor network, compressed sensing technology and experiment protocols will be described. The experimental results and corresponding discussion will be described in Section 3. Finally, the contributions of this work and future work will be presented in Section 4. 2. Materials and Methods 2.1. Compressed Sensing-Based Wearable Sensor Network As shown in Figure 1, the compressed sensing-based wearable sensor network consists of three parts: an accelerometer sensor node, ZigBee wireless receiver, and computer. Compared with traditional accelerometer sensor nodes based on the Nyquist sampling theorem, the sensor node proposed in this paper has the advantage of “compressed sampling”, through which the sampling rate was reduced and the power consumption during the sampling and transmission processes were much lower than with the traditional method. The ZigBee wireless receiver was connected to the computer through a USB port and sends the compressed data to the computer. On the computer side, firstly, the accelerometer signal was reconstructed from the compressed data; secondly, those features that can represent the motor function of stroke patients were extracted using the time and frequency domain method; finally, through mapping the features were related to the clinical assessment outcomes given by physicians, and a quantitative assessment model was built.

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Figure 1. 1. System of aa compressed compressed sensing-based sensing-based wearable wearable sensor sensor network. network. Figure System structure structure of

2.2. Signal Recovery Algorithms

novel signal signal compression compression method that depends on the the Compressed sensing (CS) [27–29] is aa novel sparsity of signals for compression and reconstruction. The The following following Equation Equation (1) describes the relationship of of aa fundamental fundamental noisy noisy model: model: relationship yy“= Φx Φx` +v

(1) (1)

ˆ1 In R Nℝˆ ×1 . isisaapart a raw accelerometer signal, y P RM data In this thispaper, paper,x P ∈ partofof a raw accelerometer signal, ∈ ℝ is× the is compressed the compressed that wirelessly transmitted to a remote receiver via the wireless protocol, and vand can be datawill thatbe will be wirelessly transmitted to a remote receiver viaZigBee the ZigBee wireless protocol, v Mˆ N pM ! ×Nq is a designed sensing matrix that linearly compresses x. Therefore, the omitted. Φ P R can be omitted. ∈ℝ ( ≪ ) is a designed sensing matrix that linearly compresses x. model usedthe in model this paper a noiseless expressed as: expressed as: Therefore, usedisin this papermodel, is a noiseless model,

yy“= Φx Φx

(2) (2) Assume the signal x was sparse under a certain orthogonal space Ψ P R N ˆ× N ; that is, x can be Assume the signal x was sparse under a certain orthogonal space ∈ℝ ; that is, x can be represented by the following form: represented by the following form: x “ Ψθ (3) (3) x = Ψθ where θ = [θ 1 , θ 2 , . . . θ N ]T was a K-sparse vector pK ! Nq, which means θ only has K where θ elements. = [θ1, θ2,…θN]T was a K-sparse vector ( ≪ ), which means θ only has K non-zero non-zero elements. In this paper, for ease of hardware implementation, the sparse Gaussian random matrix was In this paper, ease hardware the sparse into Gaussian random matrix was adopted, where the for value of of every elementimplementation, was previously embedded the microcontroller unit in adopted, where the value the form of a lookup table. of every element was previously embedded into the microcontroller unit in theBased formon of athe lookup table. proposed by Candes and Donoho [30], the principle of signal recovery framework Based the framework proposed by Candes and Donoho [30], the principle of signal recovery was to solveon the following l1 norm optimization problem: $ was to solve the following l1 norm optimization problem: & min||θ||1 θ (4) min θ1 % s.t.y “ ΦΨθ θ (4)  s.t. y focused = ΦΨθ on this problem and proposed a series of have In the past decades, many researchers  recovery algorithms, suchmany as matching pursuit (MP) [31], on orthogonal matching pursuit (OMP) [32], In the past decades, researchers have focused this problem and proposed a series of basis pursuit (BP) [33], sparse Bayesian learning (SBL) [34] and so on. Considering the signal generally recovery algorithms, such as matching pursuit (MP) [31], orthogonal matching pursuit (OMP) [32], has structure and there existslearning intra-block correlation elements within each basisblock/group pursuit (BP) [33], sparse Bayesian (SBL) [34] andamong so on.the Considering the signal block, Zhang et al. [35,36] proposed a new signal recovery framework called block SBL (BSBL) and generally has block/group structure and there exists intra-block correlation among the elements the results showed theetperformance was obviously better than that of other traditional methods. within each block, that Zhang al. [35,36] proposed a new signal recovery framework called block SBL

(BSBL) and the results showed that the performance was obviously better than that of other traditional methods. Hence, this paper chose the BSBL algorithm to reconstruct the accelerometer

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Hence, this paper chose the BSBL algorithm to reconstruct the accelerometer signal from compressed signal from compressed data. The basic principle of the BSBL framework is illustrated in the data. The basic principle of the BSBL framework is illustrated in the Appendix. Appendix. 2.3. Extreme Learning Machine 2.3. Extreme Learning Machine Extreme learning machine Huangetetal. al.[37], [37],who whoapplied applied it to Extreme learning machine(ELM) (ELM)was wasfirstly firstlyproposed proposed by by Huang it to thethe nonlinear mapping of a single layer feedforward network (SLFN). The SLFN structure is shown nonlinear mapping of a single layer feedforward network (SLFN). The SLFN structure is shown in in Figure 2. In thethe following the principle principleof ofELM. ELM. Figure 2. In followingsection, section,we wewill willbriefly briefly introduce introduce the

Figure2.2.Structure Structureof of single single layer layer feedforward Figure feedforwardnetwork. network. T

Assumethere thereare areN Nsamples samplestxi ,y where xixi“ rx xii11 ,, xxii22 ,, xii,uypii “i 1,  1,2,2,¨ ¨ N  , where ¨ ,,Nq, Assume ¨ ¨ ¨, x, inxin  sT∈PℝR×nˆ, 1 , yi “ ryi1 , yi2 , ¨ ¨ ¨ , yim sT PTRmˆ1 ,× m and n are the size of the input and output vector, respectively. y i   yi1 , yi 2 ,, yim  ∈ ℝ , m and n are the size of the input and output vector, respectively. Equation (5) is the mathematically expression of a standard single layer feedforward networks (SLFNs), Equation is the mathematically expression of a gstandard single layer feedforward networks which has L (5) hidden neurons with activation function pxq: (SLFNs), which has L hidden neurons with activation function g  x  : Hβ “ Y (5) Hβ = Y (5) where Y “ ry1 , ¨ ¨ ¨ , y N sT P R N ˆm , β “ rβ1 , ¨ ¨ ¨ , β L sT P R Lˆm and: where

T

Y   y1 ,  , y N  ∈ ℝ

×

,

T

β  β1 ,, β L¨ ∈ ℝ

˚ H pw1 , ¨ ¨ ¨ , w L , b1 , ¨ ¨ ¨ , bL , x1 , ¨ ¨ ¨ , x N q “ ˝

× ˛ and: g pw1 x1 ` b1 q . . . g pw L x1 ` b1 q ‹ . . . g  w 1 x..1  b1  . . g  w L x..1  b1   ‚ g pw1 xN ` b1 q  ¨ ¨ ¨ g pw L x N ` b1 q 

(6)

 H  w1 , , w L , b1 , , bL , x1 , , x N    (6)  g w x  b   g w x  b  where wi “ rwi1 , wi2 , ¨ ¨ ¨ , win sT is the weight vector connecting the input neurons 1 N 1 L N and 1 the  ith hidden

neuron, βi “ rβ i1 , β i2 , ¨ ¨ ¨ , β im sT Tis the weight vector connecting the output neurons and the ith hidden w i bi is wthe is the weight neuron. vector connecting the input neurons and the ith whereand  the neuron, threshold ith hidden i1 , w i 2 ,  , win of ˆ of T The training process of an SLFN is simply the equivalent to finding a least-squares solution β hidden neuron, βi   i1 , i 2 , , im  is the weight vector connecting the output neurons and the Equation (5): ith hidden neuron, and bi is the threshold of the ith hidden neuron. ˆ ´ Y|| “ min||H pw1 , ¨ ¨ ¨ , w L , b1 , ¨ ¨ ¨ , bL q β ´ Y|| (7) ||H pw1 , ¨ ¨ ¨ , w L , b1 , ¨ ¨ ¨ , bL q β  The training process of an SLFN is simply theβequivalent to finding a least-squares solution β to the least-squares regression theory, the best solution of the linear system is: of According Equation (5): ˆ “ β H` YH  w1 , , w L , b1 , , bL  β  Y (8) H  w1 ,, w L , b1 ,, bL  β  Y  min (7) β where H+ is the pseudo inverse of H. According to the least-squares regression theory, the best solution of the linear system is:

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Compared with traditional backpropagation neural networks, ELM does not have to iteratively adjust the connecting weights and bias, as it maps the training process to a problem of solving a group of linear equations. Besides, in reference [37], Huang et al. have proved that given any small positive value ε ą 0 and activation function g : R Ñ R which is infinitely differentiable in any interval, there r ď N such that for N arbitrary distinct samples, for any wi and bi randomly chosen, then with exists N probability one, ||Hβ ´ Y|| ă ε. In summary, the whole procedure of establishing an ELM model includes three steps, which are listed in Table 1. Table 1. Flow of the ELM algorithm. r Step 1: Generate random input weight wi and bias bi , i “ 1, ¨ ¨ ¨ , N. Step 2: Compute the output of neurons in hidden layer according to Equation (6). Step 3: Compute the output weight β according to Equation (8).

2.4. Experiment Protocols All the following experiments were approved by the Ethics Committee of Jiaxing 2nd Hospital, (Jiaxing, China). Twenty-three stroke patients and four physicians were selected to participate in these experiments. According to the Brunnstrom stage classification criteria, the 23 patients’ Brunnstrom stages ranged from II to V. However, considering that patients in stage I cannot move their upper limbs without extra assistance, patients in stage I were not selected for our experiments. Similarly, due to the fact that in China, the majority part of stage VI patients leave the hospital due to the high medical costs and limited rehabilitation resources, we used four physicians instead of stage VI patients to participate our experiments. Table 2 lists the general information of the 23 stroke patients, from which it can be clearly seen that there were 13 males and 10 females, with an age distribution range from 47 to 79. None of the patients had severe communication and cognitive problems. Before the data collection, all the experimental processes were demonstrated and the matters needing attention during the experiments were highlighted in advance by the physicians. Table 2. The general information of the 23 stroke patients.

Brunnstrom Stage Level

Patients

Sex (M/F)

Hemiplegic Side (Left/Right)

Limb Dominance (Left/Right)

II III IV V

2 10 4 7

0/2 5/5 3/1 5/2

2/0 6/4 3/1 2/5

0/2 2/8 0/4 1/6

The accelerometer sensors were placed on the geometric center of the arms, as shown in Figure 3. The distance between the accelerometer sensor on the forearm and dorsal stripes was 10 cm, while the distance between the accelerometer sensor on the upper arm and the epicondyus lateralis humeri was 8 cm.

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(a)

(b)

Figure sensor location. location. Figure 3. 3. General General view view of of (a) (a) the the accelerometer accelerometer sensors sensors and and (b) (b) the the accelerometer accelerometer sensor

Generally, motioncapturing capturing and monitoring applications, reconstruction performance is Generally, ininmotion and monitoring applications, reconstruction performance is often often evaluated by comparing the reconstructed signals withones raw through ones through the mean evaluated by comparing the reconstructed signals with raw the mean squaresquare error error (MSE). However, in thisthe paper, signal reconstruction thesofinal goal, so the (MSE). However, in this paper, signalthe reconstruction was not thewas finalnot goal, the reconstructed reconstructed accelerometer signals were further processed to establish an automatic Brunnstrom accelerometer signals were further processed to establish an automatic Brunnstrom stage classification stage classification model. Due to the infidelity of the MSE for structured signals, it is difficult to model. Due to the infidelity of the MSE for structured signals, it is difficult to analyze how the analyze how the predictive accuracy of the quantitative is affected by the predictive accuracy of the quantitative assessment model isassessment affected bymodel the reconstruction errors reconstruction errorsHence, measured MSE. Hence, it is necessary to compare the predictive accuracy of measured by MSE. it is by necessary to compare the predictive accuracy of Brunnstrom stage Brunnstrom stage classification models, which are built based on the reconstructed and raw classification models, which are built based on the reconstructed and raw accelerometer signals, accelerometer signals, respectively. Consequently, toof achieve our goal, all of the experimentsinwere respectively. Consequently, to achieve our goal, all the experiments were implemented two implemented in two actions: (1) Bobath handshake; (2) shoulder touch. actions: (1) Bobath handshake; (2) shoulder touch. 2.4.1. Bobath Handshake experiment is toisvalidate the reconstruction performance of the BSBL The purpose purposeofofthis this experiment to validate the reconstruction performance of algorithm the BSBL during the during Bobath the handshake Theexercise. whole process of theprocess Bobath handshake exercise can be algorithm Bobath exercise. handshake The whole of the Bobath handshake divided into thedivided following steps: exercise can be intothree the following three steps: (1) (2) (3)

(1) Sit down a chair, the hand and keep the thumb the hemiplegic side on top. Sit down on a on chair, crosscross the hand and keep the thumb of theofhemiplegic side on top. (2) Straighten the upper extremities, lift above the head and hold for 3 s. Straighten the upper extremities, lift above the head and hold for 3 s. (3) Move the hands toinitial the initial position. Move the hands backback to the position.

An additional movie file shows the Bobath handshake exercise in more detail (see An additional movie file shows the Bobath handshake exercise in more detail (see Supplementary File 1). Supplementary File 1). 2.4.2. 2.4.2. Shoulder Shoulder Touch Touch Our previous studies studies have found that that the the accelerometer accelerometer signals signals of of the the shoulder shoulder touch touch exercise exercise Our previous have found can be applied applied to to automatically automatically classify classify the the Brunnstrom Brunnstrom stage stage for for stroke stroke patients. patients. To investigate can be To investigate whether the reconstruction errors affect the predictive accuracy of the quantitative assessment whether the reconstruction errors affect the predictive accuracy of the quantitative assessment model, model, the shoulder touch was exercise was completed by every participant order collect the the shoulder touch exercise completed by every participant in order to in collect thetocompressed compressed accelerometer whole of the touch shoulder touchcan exercise can be into divided accelerometer signals. Thesignals. whole The process of process the shoulder exercise be divided the into the following four steps: following four steps: (1) Sit down on a chair, and naturally droop the upper limb of the hemiplegic side. Sit down on a chair, and naturally droop the upper limb of the hemiplegic side. (2) Raise the upper limb of the hemiplegic side to the horizontal position. Raise the upper limb of the hemiplegic side to the horizontal position. (3) Move horizontally to the healthy side shoulder and hold for 5 s. Move horizontally to the healthy side shoulder and hold for 5 s. (4) Move back to the initial droop position and take a short break. Move back to the initial droop position and take a short break. An additional movie file shows the shoulder touch exercise in more detail [see Supplementary An additional movie file shows the shoulder touch exercise in more detail [see Supplementary File 2]. File 2]. All patients were required to finish these exercises without extra assistance to reflect their true movement function. Before the data collection, they were asked to practice several times with the (1) (2) (3) (4)

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of 16 were required to finish these exercises without extra assistance to reflect their7 true movement function. Before the data collection, they were asked to practice several times with the guidance that they they were were familiar familiar with with the the whole whole process. process. During During the the experimental experimental guidance of of physicians physicians so so that processes, they were requested to repeat the shoulder touching exercise eight times. processes, they were requested to repeat the shoulder touching exercise eight times. The data sampling sampling and and management management were were implemented implemented by by using using the the Remote Remote Rehabilitation Rehabilitation The data Training and Assessment Software (RRTAS), which was developed by our group. The run Training and Assessment Software (RRTAS), which was developed by our group. The run environment environment of RRTAS is Windows 32 bit platform and .Net Framework 3.5 or above. An additional of RRTAS is Windows 32 bit platform and .Net Framework 3.5 or above. An additional document file document introduces in more detail (see Supplementary File 3). introduces file RRTAS in moreRRTAS detail (see Supplementary File 3).

3. Results Resultsand andDiscussion Discussion 3.1. Accelerometer Signals Compress and Recovery The raw accelerometer signal of the Bobath handshake exercise is shown in Figure 4, in which the axes X1, X1, Y1 Y1and andZ1 Z1are arethe thesignals signalsofofsensors sensorsplaced placed forearm, while axes onon thethe forearm, while thethe axes X2,X2, Y2 Y2 andand Z2 Z2 are signals of sensors placed onupper the upper arm. Figure From Figure 4, we that during the are the the signals of sensors placed on the arm. From 4, we can seecan thatsee during the Bobath Bobath handshake exercise, the axes from accelerometer sensorsshow showperiod period changes. changes. handshake exercise, all six all of six theofaxes from twotwo accelerometer sensors However, 5400 raw sampling data in each axis need to be transmitted to the computer through the ZigBee wireless protocol during all eight Bobath Bobath handshake handshake exercises. exercises. Raw Accelerometer Signal X1

1 0

Y1

-1 1 0

Z1

-1 1 0

X2

-1 1 0

Y2

-1 1 0

Z2

-1 1 0 -1

0

900

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2700 Time Point

3600

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Figure Figure 4. 4. Raw Raw accelerometer accelerometer signals. signals.

As mentioned above, by adjusting the dimension of sensing matrix Φ , the compression ratio As mentioned above, by adjusting the dimension of sensing matrix Φ, the compression ratio (CR) (CR) can be changed as follows: can be changed as follows: NN´ M M MM CR (9) CR“ N “ 1 ´ N (9) N N Here, we first set the CR to 0.7222 to validate the reconstruction performance of the BSBL Here, we first set the CR to 0.7222 to validate the reconstruction performance of the BSBL algorithm. This means that the raw accelerometer signal was compressed to 1500 sampling data. algorithm. This means that the raw accelerometer signal was compressed to 1500 sampling data. The The corresponding compressed signal is shown in Figure 5, where it can be seen that the compressed corresponding compressed signal is shown in Figure 5, where it can be seen that the compressed signal looks very different from the raw accelerometer signal due to the randomness of the sensing signal looks very different from the raw accelerometer signal due to the randomness of the sensing matrix Φ. This characteristic indicates that compressed sensing can not only compress the raw signal matrix Φ . This characteristic indicates that compressed sensing can not only compress the raw into a lower dimension compressed signal, but also can encrypt the raw signal so that the privacy of signal into a lower dimension compressed signal, but also can encrypt the raw signal so that the the patients is protected. privacy of the patients is protected.

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Z2

Z2

Y2 Y2

X2 X2

Z1

Z1

Y1 Y1

X1 X1

Compressed accelerometer signal 50 0 50 -50 00 0 -50 -200 0 -40 -20 0 40 -40 200 40 0 20 0 0 0 -200 -40 0 -20 0 -40 0 -200 -40 0 -20 0 -40 40 200 40 0 20 0 0 0

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Time Point Figure5.5.Compressed Compressed accelerometer signals. Figure accelerometer signals. Figure 5. Compressed accelerometer signals.

From Figure 4, it is obvious that the raw accelerometer signal is far from sparse and periodic. From Figure 4, it difficulty is obvious that the raw signal to is reconstruct far from sparse and This creates a huge CS accelerometer recoverysignal algorithms the raw From Figure 4, it is obvious for thattraditional the raw accelerometer is far from sparse and periodic. periodic. This creates a huge difficulty for traditional CS recovery algorithms to reconstruct the accelerometer Fortunately, the BSBL recovery framework proposed by Zhangthe [35,36] This creates a signals. huge difficulty for traditional CS recovery algorithms to reconstruct raw raw accelerometer signals. Fortunately, the BSBL recovery proposed by Zhang [35,36] significantly outperforms tradition CS thanksframework toframework its ability to explore exploit an accelerometer signals. Fortunately, thealgorithms BSBL recovery proposed by and Zhang [35,36] significantly outperforms tradition CS algorithms thanks to its ability to explore and exploit intra-block correlation signals. CS When the prior block partition significantly outperformsintradition algorithms thanks to its ability is to given, explorethe andwhole exploitraw anan intra-block correlation in signals. When the prior block partition is given, the whole raw accelerometer accelerometer signal is divided intoWhen 30 blocks equal sizepartition (each block containsthe5400/30 180 intra-block correlation in signals. the of prior block is given, whole= raw signal is divided into 30 blocks of equal size (each block contains 5400/30 = 180 sampling data). sampling data). The reconstructed accelerometer signals are shown in Figure 6. To validate the accelerometer signal is divided into 30 blocks of equal size (each block contains 5400/30 = 180 Thesampling reconstructed accelerometer signals are shown in Figure 6. To validate the recovery performance recovery performance of BSBL algorithm, we also reconstructed the compressed signals with BP data). The reconstructed accelerometer signals are shown in Figure 6. To validate the and OMP algorithms, and the correlation coefficients of the reconstructed and raw signals of each of BSBL algorithm, we also reconstructed the compressed signals with BP and OMP algorithms, and recovery performance of BSBL algorithm, we also reconstructed the compressed signals with BP algorithm all listedand inofTable 3. It is clear that the of BSBL theand correlation coefficients thecorrelation reconstructed andby raw signals eachalgorithm, algorithm arecorrelation alloflisted OMP are algorithms, the coefficients ofusing the reconstructed and raw the signals each in coefficients of all the reconstructed signals higherthe than with the other two methods, Table 3. It is clear that by using theand the using correlation coefficients of the reconstructed algorithm are listed in Table 3.BSBL It raw isalgorithm, clear thatwere by BSBL algorithm, the correlation which suggests thatreconstructed the BSBL algorithm isother very effective for accelerometer recovery. coefficients ofwere the andthe raw signals were higher thansuggests withsignal thethat other and raw signals higher than with two methods, which the two BSBLmethods, algorithm which suggestsfor that the BSBL algorithm is very effective for accelerometer signal recovery. is very effective accelerometer signal recovery. X1 X1 Y1 Y1 Z1 Z1 X2 X2 Y2 Y2 Z2 Z2

0.5

Reconstructed Accelerometer Signal

0 1 -1 0 1 -1 0 1 -1 0 1 -1 0 1

0 0.5 -0.5 0 0.5 -0.5 0 0.5 -0.5 0 0.5 -0.5 0 0.5

-1 0 1 -1 0 1

-0.5 0 0.5 -0.5 0 0.5

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Figure 6. Reconstructed accelerometer signals and absolute errors (AE). Figure6.6.Reconstructed Reconstructedaccelerometer accelerometer signals Figure signals and andabsolute absoluteerrors errors(AE). (AE).

AEZ2AE AEY2AE AEX2AE AEZ1AE AEY1 AEY1 AEX1AEX1 Z2 Y2 X2 Z1

Reconstructed Accelerometer Signal

1

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Table 3. Signal BPBP and OMP algorithms. Signalrecovery recoveryresults resultsofofBSBL, BSBL, and OMP algorithms. Correlation Coefficients between Reconstructed and Raw Signals Correlation Coefficients between Reconstructed and Raw Signals Methods Methods X1 Y1 Z1 X2 Y2 Z2 X1 Y1 Z1 X2 Y2 Z2 BSBL 0.9991 0.9957 0.9965 0.9991 0.9979 0.9969 BSBL 0.87620.9991 0.9957 0.9965 0.9991 0.9979 BP 0.8814 0.8729 0.8651 0.8964 0.99690.9015 BP 0.8762 0.8814 0.8729 0.8651 0.8964 0.9015 OMP 0.9356 0.9521 0.9188 0.9672 0.9248 0.9366 OMP 0.9356 0.9521 0.9188 0.9672 0.9248 0.9366

3.2. Effects of Block Size and CR on Recovery Performance 3.2. Effects of Block Size and CR on Recovery Performance In this section, we will discuss the effects of block size and compression ratio on the quality of In this section, we will discuss the effects of block and compression ratio ratio on the quality signals reconstructed from raw accelerometer signals. Here,size we chose the signal to noise (SNR) ofassignals reconstructed raw accelerometer signals. Here, chose the signal noiseinratio the evaluation index from to analyze the reconstruction error. The we definition of SNR is to shown Equation (10): (SNR) as the evaluation index to analyze the reconstruction error. The definition of SNR is shown in Equation (10): 2

x2 k x k222 SNR “ 20lg x  x^ 2 k x ´ x2 k2 SNR  20 lg

(10) (10)

^

where x and x are  the raw and reconstructed signals, respectively. A higher SNR means a smaller x x and where reconstruction error.are the raw and reconstructed signals, respectively. A higher SNR means a smaller error. Thereconstruction effects of block size on SNR are shown in Figure 7. It is clear that the trends of all six axes The effects of block size onsize SNRincreases, are shown in SNR Figure 7. Itincreases. is clear that trends ofwhen all sixthe axes are same; that is, as the block the also Inthe particular block are same; that is, as the block size increases, the SNR also increases. In particular when the block size size changes from 5 to 20, the corresponding SNR increases quickly. This is due to the fact that the changes from 5 to 20, the corresponding SNR increases quickly. This is due to the fact that the sampling rate of the raw accelerometer sensor is 50 Hz, and for stroke patients the duration of the sampling rate of the raw accelerometer sensor is 50 Hz, and for stroke patients the duration of the Bobath handshake exercise is about 12 s. Hence, if the block size is too small (for example, a block size Bobath handshake exercise is about 12 s. Hence, if the block size is too small (for example, a block less than 10), the signals in each block are almost unchanged because the duration of each block is very size less than 10), the signals in each block are almost unchanged because the duration of each block short. Consequently, all of the intra-block correlations of each block are close to 1 and the variances are is very short. Consequently, all of the intra-block correlations of each block are close to 1 and the close to 0. are close to 0. variances Although performanceisisaffected affectedbyby the block size in the block partition, Although the the reconstruction reconstruction performance the block size in the block partition, this this does not limit its application to the wearable sensor network. Figure 7 also shows that a wide range does not limit its application to the wearable sensor network. Figure 7 also shows that a wide range of the block sizesize (for(for example, from 2020 toto 40) can of the block example, from 40) canlead leadtotosatisfying satisfyingresults. results. Effects of the block size on SNR 160

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140 120 100 80 60

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Figure 7. Effects of the block size on SNR. Figure 7. Effects of the block size on SNR.

Figure88illustrates illustrates the which wewe cancan seesee thatthat when the the CR increases, Figure the effects effectsof ofCR CRon onSNR, SNR,from from which when CR increases, the SNR decreases, especially when the CR is higher than 0.75. That is to say, if the CR does not the SNR decreases, especially when the CR is higher than 0.75. That is to say, if the CR does not exceed

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Sensors 16, 202 10 of 16 0.75 (the2016, length of compressed signal cannot be less thanbe 1350), satisfactory reconstructed exceed 0.75 (the length of compressed signal cannot less athan 1350), a quality satisfactory quality signal can be achieved. reconstructed signal can be achieved. exceed 0.75 (the length of compressed signal cannot be less than 1350), a satisfactory quality reconstructed signal can be achieved. Effects of the compression ratio on SNR 180 Axis X1 Axis Y1 Axis Axis X1 Z1 Axis Axis Y1 X2 Axis Axis Z1 Y2 Axis Axis X2 Z2 Axis Y2 Axis Z2

Effects of the compression ratio on SNR 180 160

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Figure8.8.Effects Effectsof of the compression ratioon Figure onSNR. SNR. Figure 8. Effects of the compression ratio on SNR.

According compressedsensing sensingtheory, theory, the the relationship relationship between satisfy thethe According toto compressed betweenM Mand andNNshould should satisfy following inequality: following inequality: According to compressed sensing theory, the relationship between M and N should satisfy the ˆ N˙ following inequality: N   M K log (11)(11) M ą Klog  K  K   N M  K log   (11)  K  the where K the is the sparsityofofthe theraw rawsignal. signal. Now Now we we validate validate where K is sparsity the theoretical theoreticalCR CRofofthe theaccelerometer accelerometer signals. Figure9 9shows shows the sparsity sparsity discrete discrete cosine transform (DCT) coefficients ofofthetheraw signals. transform (DCT)CR coefficients raw where Figure K is the sparsity ofthe the raw signal. Now we validate the theoretical of the accelerometer accelerometer signal. Clearly, only a few DCT coefficients (K ≈ 600) have large amplitudes, while the accelerometer signal. Clearly, a few DCT coefficients (K « 600) (DCT) have large amplitudes, while signals. Figure 9 shows theonly sparsity discrete cosine transform coefficients of the rawthe majority of coefficients havesmall smallamplitudes. amplitudes. Hence, Hence, the the theoretical maximum CR should be: majority of coefficients have theoretical maximum CR should be: accelerometer signal. Clearly, only a few DCT coefficients (K ≈ 600) have large amplitudes, while the majority of coefficients have small amplitudes. Hence, theoretical maximum CR should be: 600  logthe / 600   5400 M CR  1M  min  1  600 ˆ log p5400{600q  0.7559 (12) CRmax “max1 ´ min « 1 ´600  log5400 « 0.7559 (12) N 5400 / 600   M N 5400 min CRmax  1   1  0.7559 (12) N 5400 Sparsity of Raw Signal 20 Sparsity of Raw Signal 20 10 10 0 DCT Coefficients DCT Coefficients

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Figure 9. Sparsity of raw Time accelerometer signal (axis X1). Points Figure 9. Sparsity of raw accelerometer signal (axis X1).

Figurethe 9. Sparsity raw accelerometer signal This result is essentially same as of Figure 8, which means that(axis the X1). more sparser the raw signal is, the higher CR can be achieved. This result is essentially the same as Figure 8, which means that the more sparser the raw signal This result is essentially the same as Figure 8, which means that the more sparser the raw signal is, the higher CR can be achieved. is, the higher CR can be achieved.

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Effects of Compressed Sensing Quantitative Model In3.3. the previous experiment, weonshowed thatAssessment the accelerometer signals of rehabilitation exercises can be compressed and precisely reconstructed. Another question is whether the reconstructed signals In the previous experiment, we showed that the accelerometer signals of rehabilitation exercises affect can the predictive accuracy of the quantitative assessment Toisanswer this, carried out the be compressed and precisely reconstructed. Anothermodel. question whether thewe reconstructed signals affect the predictive accuracy of the quantitative model. we to following experiment: as mentioned above, there are manyassessment assessment scalesToinanswer clinicalthis, settings carried out the following experiment: as mentioned above, there are many assessment scales in evaluate the movement function of stroke patients, such as the Fugl-Meyer assessment scale, Functional clinical settings to evaluate the movement function of stroke patients, such as the Fugl-Meyer ability scale, Brunnstrom stage classification, Action Research Arm Test, and so on. Compared with Functional ability scale, Brunnstrom stage classification, Action Research Arm other assessment assessmentscale, scales, the Brunnstrom stage classification tool only has six levels, hence it has the Test, and so on. Compared with other assessment scales, the Brunnstrom stage classification tool advantage of being easy to use and time saving. In our previous work [26], we have proven that the only has six levels, hence it has the advantage of being easy to use and time saving. In our previous Brunnstrom stage of stroke patients can be automatically classified through the shoulder touch exercise work [26], we have proven that the Brunnstrom stage of stroke patients can be automatically by using the ELM method. classified through the shoulder touch exercise by using the ELM method. Brunnstrom Stage III

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(e) Figure 10. (a)–(e) Reconstructed and raw accelerometer signals from Brunnstrom stages II to VI.

Figure 10. (a)–(e) Reconstructed and raw accelerometer signals from Brunnstrom stages II to VI.

Due to space limitations, here we present only the reconstructed and raw axis Y1 accelerometer

Due to space limitations, here we present only the reconstructed and raw axis Y1 accelerometer signals ranges from Brunnstrom stage II to VI in Figure 10. It is clear that as the Brunnstrom stage signals ranges from Brunnstrom stage II to VI in Figure 10. It is clear that as the Brunnstrom stage increases, the reconstruction error decreases. This is because the lower the Brunnstrom stage, the increases, thethe reconstruction This thefinish lower Brunnstrom stage, the weaker stroke patient’serror motordecreases. function, and heis orbecause she cannot thethe shoulder touch exercise weaker the stroke patient’s motor function, and he or she cannot finish the shoulder touch exercise

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freely. Additionally, with the Brunnstrom stage decreases, the smoothness of accelerometer signals freely. Additionally, with the Brunnstrom stage the smoothness of accelerometer signals becomes worse, which brings about difficulty in decreases, signal recovery. becomes worse, which difficulty in signal recovery. To investigate the brings effectsabout of reconstruction error on the predictive accuracy of the Brunnstrom investigate model, the effects of reconstruction error on the predictivemodel accuracy thereconstructed Brunnstrom stageTo classification we established the quantitative assessment withofthe stage classification model, we established the quantitative modelofwith reconstructed and raw accelerometer signals, respectively. To ensure assessment the consistency our the comparison, the and raw accelerometer signals, respectively. To ensure the consistency of our comparison, the feature feature extraction and ELM parameters were all set to be the same. More specifically, 12 features extraction wereamplitude all set to be(AMP) the same. More specifically, 12 features including root including and root ELM meanparameters square (RMS), from three axes of two accelerometer sensors mean square (RMS), amplitude (AMP) from three the axesoutput of twoofaccelerometer sensors were extracted were extracted and set as the input of ELM model, the ELM model was the Brunnstrom and as the input ELM model, the output of was the ELM was the Brunnstrom stage and stagesetlevel, and the of number of hidden neurons set tomodel 30. The training set contains 152level, samples the of hidden neurons was set to 30. The training set contains 152 samples and the testing set andnumber the testing set contains 38 samples. contains samples. The 38 results are shown in Figure 11 and Table 4, from which it can be seen that of the total 38 The in results are shown Figure 11 and Table 4, whose from which it can be seen were that ofaccurately the total samples the testing set, inthere were 34 samples Brunnstrom stages 38 samples the testing set, there were samples whose Brunnstrom stages were accurately predicted byinusing the reconstructed signal,34while 35 samples were accurately predicted using the predicted usingindicated the reconstructed signal, while 35 samples accurately using the raw signal,bywhich that the reconstruction error alonewere has no influencepredicted on the accuracy of raw signal, whichassessment indicated that the reconstruction aloneofhas no influence on theresult, accuracy of the the quantitative model. Actually, the error analysis variance (ANOVA) listed in quantitative assessment model. the analysis of difference variance (ANOVA) result, listed inaccuracy Table 5, Table 5, indicates that there is noActually, statistically significant between the predictive indicates is no statistically significant between the predictive accuracy the raw of the rawthat andthere reconstructed Brunnstrom stage difference classification model. Consequently, we canofconclude and Brunnstrom stage Consequently, can conclude that the that reconstructed the reconstruction error has no classification influence on model. the establishment of awe quantitative assessment reconstruction error has no influence on the establishment of a quantitative assessment model. model.

Quantitative Assessment Model Accuracy (%)

Comparison of compressed and raw signals on quantitative assessment model accuracy 100 Raw Signal Compressed Signal 95

90

85

80

75

70

II

III

IV V Brunnstrom Stage

VI

Total

Figure accuracy. Figure 11. 11. Comparison Comparison of of compressed compressed and and raw raw signals signals on on quantitative quantitative assessment assessment model model accuracy. Table raw signals signals on on quantitative quantitative assessment assessment model model accuracy. accuracy. Table 4. 4. Comparison Comparison of of compressed compressed and and raw

Brunnstrom Stage

Samples in Testing Set

II

2

Brunnstrom Stage

III IV V VI

II III IV V VI Total

Total

Predictive Accuracy

Samples in Testing Set

Accuracy Raw Model Predictive Compressed Sensing Model Raw Model Compressed Sensing Model

100 (2/2)

100 (2/2)

2 14 14 9 9 9 9 4 4 38

100 (2/2) 85.7 85.7 (12/14) (12/14) 88.8 (8/9) (8/9) 88.8 100 (9/9) 100 100 (9/9) (4/4) 92.1 100(35/38) (4/4)

100 (2/2) 78.6 (11/14) 78.6 (11/14) 100 (9/9) 100 (9/9) 88.8 (8/9) 88.8 (8/9) 100 (4/4) 89.5 (34/38) 100 (4/4)

38

92.1 (35/38)

89.5 (34/38)

Table 5. Analysis of variance results. Source

Table 5. Analysis of variance results. Sum of Squares df Mean Square

Source Sum of Squares Between Groups 0.0132 Between Within GroupsGroups 0.013296.9737 Total 96.9868 Within Groups 96.9737 Total 96.9868

df 1 1 74 74 75 75

F

Prob > F

Mean Square 0.01 F 0.9205 Prob > F 0.01316 1.31046 0.01316 0.01 0.9205 1.31046

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4. Conclusions To reduce the amount of data in a wearable sensor network during the sampling and transmission processes, this paper proposes a novel wearable sensor network based on compressed sensing technology, and applied it to the monitoring and quantitative assessment of stroke patients’ upper limb motor function. The experimental results showed that the proposed method can not only compress and precisely reconstruct the raw accelerometer signals, but can also apply the reconstructed signals to establish the Brunnstrom stage automatic classification model. It also indicated that the proposed system can provide a theoretical basis for individualized and remote rehabilitation. However, considering the fact that the clinical experiment only recruited 23 stroke patients, which is too small a number to verify the statistical reliability and validity of the proposed quantitative assessment model, in the future, we will gather more clinical data and improve the generalization performance of the model. Additionally, in this paper, the compressed signals need to be reconstructed on the computer side before the analysis process. In the future, we will try to investigate whether the analysis process can be directly implemented in the compressed domain. If yes, this could reduce the off-line computation burden and make the “on-node” analysis more possible. Supplementary Materials: Additional File 1: Bobath handshake exercise (Movies, MP4 format), Additional File 2: Shoulder touch exercise (Movies, MP4 format), Additional File 3: Introduction of Remote Rehabilitation Training and Assessment Software. Acknowledgments: This research is partly supported by the Jiangsu Province Science and Technology Support Program (Funds Number: BE2012654). The authors thank Drs. Xudong Gu and Jianming Fu who come from the Rehabilitation Medical Center of Jiaxing 2nd Hospital, for their valuable suggestions and guidance during the clinical experiment design and implementation processes. The authors also thank Zhilin Zhang for guidance and suggestions about the compressed sensing and BSBL algorithm. Author Contributions: LY carried out the study design, signal processing and manuscript drafting. DxX participated in the design of the study. LqG carried out the design of the wearable sensor network and accelerometer sensor node. JpW participated in the software and algorithm design. All authors read and approved the final manuscript. Conflicts of Interest: The authors declare that they have no competing interest.

Abbreviations The following abbreviations are used in this manuscript: CS WSN UE WMFT FAS RIP MP OMP BP SBL BSBL CR SNR ELM DCT RRTAS

Compressed Sensing Wearable Sensor Network Upper Extremity Wolf Motor Function Test Functional Ability Scale Restricted Isometry Property Matching Pursuit Orthogonal Matching Pursuit Basis Pursuit Sparse Bayesian Learning Block Sparse Bayesian Learning Compression Ratio Signal to Noise Ratio Extreme Learning Machine Discrete Cosine Transform Remote Rehabilitation Training and Assessment Software

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Appendix Without loss of generality, assume x can be divided into g blocks, i.e.: T x “ rx 1 , ¨ ¨ ¨ , xd1 , ¨ ¨ ¨ , xd g´1 `1 , ¨ ¨ ¨ , xd g s looooomooooon looooooooomooooooooon x1T

xTg

where di p@iq are not necessarily identical. Among the g blocks, only k pk ! gq blocks are nonzero but their locations are unknown. Each block xi PRdi ˆ 1 is assumed to satisfy a parameterized multivariate Gaussian distribution: p pxi ; γi , Bi q „ N p0, γi Bi q , i “ 1, ¨ ¨ ¨ , g where γi is a non-negative parameter controlling the block-sparsity of x. When γi =0, the ith block becomes zero. Bi PRdi ˆdi is a positive definite matrix, capturing the correlation structure of the ith block. Under the assumption that blocks are mutually uncorrelated, the prior of x is: p px; tγi , Bi ui q „ N p0, Σ0 q ( where Σ0 =diag γ1 B1 , ¨ ¨ ¨ , ¨ ¨ ¨ γg Bg . Assume the noise vector satisfies p pv; λq„N p0, λIq, where λ is a positive scalar. Therefore the posterior of x is given by: ´ ˇ ¯ g ˇ p xˇy; λ, tγi , Bi ui“1 “ N pµ x , Σ x q with:

´ ¯´1 µ x “ Σ0 Φ T λI ` ΦΣ0 Φ T y ˆ Σx “

1 Σ´ 0 `

˙ ´1 1 T Φ Φ λ

g

Once the parameters λ, tγi , Bi ui“1 are estimated, the Maximum-a-Posteriori (MAP) estimate of x, ^

denoted by x, can be directly obtained from the mean of the posterior, i.e.: ´ ¯´1 ^ x Ð Σ0 Φ T λI ` ΦΣ0 Φ T y The parameters can be estimated by a Type II maximum likelihood procedure. This is equivalent to minimizing the following cost function: ş ´2log p py|x; λqp px; tγi , Bi ui q dx ˇ ˇ ´ ¯´1 L pθq fi ˇ ˇ “ log ˇλI ` ΦΣ0 Φ T ˇ ` yT λI ` ΦΣ0 Φ T y ! ) g where θ denotes all the parameters, i.e., θfi λ, tγi , Bi ui“1 . References 1.

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