Wearable Monitoring and Predicting System for Knee Joint Fatigue Based on Curvature and Pressure Sensing

14 Background: Knee injury is always a trouble for people in daily life. It not only threatens 15 the career of an athlete but also affects a normal engineer through morning running. The 16 injury of the knee joint is found to be directly related to the fatigue caused by excessive 17 exercise. 18 Methods : An economical embedded system with a designed acceleration-weighted curve 19 fitting method was developed to estimate and predict the knee fatigue state. Then the 20 warning message and recommended lasting time were sent to users to avoid excessive 21 exercise. 24 healthy volunteers were involved in the experiments to verify the effectiveness 22 of the system compared to human perception. 23 Results: Only using human perception to prevent knee joint fatigue had a risk of failure 24 while the designed wearable system could protect knee successfully. It was also found that 25 the knee of female was more likely to be injured than the one of male in intense exercises and a high BMI value could influence the risk of knee injuries during sports. However, a 27 short break in sports could significantly extend the healthy time for knee. 28 Conclusions: Early warning from the specially designed embedded system can successfully 29 help people avoid knee joint fatigue and injuries during exercises, such as running, 30 badminton, table tennis and basketball. 31

the knee of female was more likely to be injured than the one of male in intense exercises 26 and a high BMI value could influence the risk of knee injuries during sports. However, a 27 short break in sports could significantly extend the healthy time for knee. 28 Conclusions: Early warning from the specially designed embedded system can successfully 29 help people avoid knee joint fatigue and injuries during exercises, such as running, 30 badminton, table tennis and basketball. 31 Keywords: knee joint; fatigue; wearable device; exercise; health 32

Background 33
Knee joint injuries often occur during exercise and cause more than four weeks absence from jobs 34 or team-sports competitions. The anterior cruciate ligament (ACL) lesions and meniscal and medial 35 collateral ligament (MCL) sprains are most common knee joint injuries in daily life. The rate of ACL 36 lesions even reaches 2.8 and 3.2 injury per 10,000 h of exposure in basketball and soccer players from 37 university, respectively [1]. Moreover, ACL rupture usually needs surgical reconstruction and a 38 recovery period over six months which may bring a shadow to the career of an athlete or normal work 39 of an engineer [2]. People's daily strenuous physical exercise without restriction may also cause acute 40 or chronic injury to the knee joint, resulting in body and economic losses. Therefore, prevention of that 41 fatigue. It can be found that the degree of knee fatigue increased with time during the exercises and the 78 designed system is successful to estimate the fatigue of knee joint in real time. Figure 2(a) shows the 79 healthy time of different genders for knee joint during the four exercises without break which can keep 80 the fatigue degree of knee less than 80 present. It is obvious that the knee of female is more likely to be 81 injured during these exercises and the tendency is more significant in sports like basketball and 82 running in which the movements are more intense in the lower limb. Figure 2(b) shows the healthy 83 time of different BMI situation during the exercises without break. When playing badminton and table 84 tennis, the participants with BMI value less than 24 are able to have more time to stay healthy for knee 85 joint. The difference is not significant in playing basketball and running although their mean values 86 have the same tendency. This may be due to the large time variance caused by the deviation of people's 87 personal tolerance to playing basketball and running. Thus, the people with larger BMI value may have 88 higher risk of knee injuries during playing badminton and table tennis. This may be due to the fact that 89 excessive body weight puts more loads on the leg muscles during exercise. As shown in Figure 2(c), 90 the short break during sports can significantly extend the healthy time for these exercises and avoid 91 knee injuries efficiently; conversely, long-term high-intensity continuous exercise will increase the risk 92 of knee injury. After 14 days of first stage testing, none of the participants reported discomfort or pain 93 in their knee joint. 94 In the second stage of experiment, the testing group equipped the sensoring device for warning 95 fatigue of knee joint while the control group depended on the feeling of themselves. As shown in 96 Figure 3(a) and (b), the Lysholm scores and IKDC scores of control group were significantly 97 decreased after running and playing basketball while the ones of testing group did not changed 98 obviously. This proved that only using human perception to prevent fatigue of knee joint and avoid 99 injury had a risk of failure; and the use of a suitable electronic predicting system could achieve this 100 goal. Because playing basketball is more intense than running for knee joint, the reduction in scale 101 scores is more significant, and the changes in Figure 3 and (d) shows the Lysholm sores and IKDC scores of control group for different genders before and 103 after playing basketball and running. It can be found that female suffered more decrement in scale 104 sores than male during these two sports, which implied that women is more dangerous to be injured in 105 knee than man in these sports. This trend is consistent with the conclusion in the first stage of 106 experiment. Figure 3 (e) and (f) also shows that the BMI value could influence the risk of knee injuries 107 during sports. 108  BMI situation before and after playing basketball and running. (* p < 0.05, ** p < 0.01, *** p 128 < 0.001) 129

Discussion 130
According to the experimental results, the designed estimation and predicting algorithm has ability 131 to warn the risk of knee joint injuries for users during exercises. The economical electronic prototype 132 of sensoring system is able to acquire the data successfully in real time which can help to make a 133 correct decision. It can also be found in Figure 2 and 3 that playing basket had the greatest risk of knee 134 fatigue in these four sports due to its fast running and strong physical confrontation while playing table 135 tennis had the lowest risk, which is consistent with previous report [3]. Furthermore, female gender 136 and high BMI value are two factors to increase the risk of knee injuries. From the scale scores of 137 participants, the designed sensoring system is proved to be able to prevent exercisers from knee joint 138 injuries caused by fatigue. However, only using human perception to prevent fatigue of knee joint and 139 avoid injury during exercise has a risk of failure. 140

Conclusions 141
In order to reduce the risk of knee injuries during exercise, a wearable system with STM32 142 microcontroller and multiple sensors was developed to acquire the parameters of knee joint. Then an 143 acceleration-weighed curve fitting estimation was proposed to estimate the fatigue state. According to 144 the experimental results, the system is helpful to prevent knee joint from injuries induced by excessive 145 exercise and lead the users to take a suitable exercise rhythm, intensity and time. 146

Materials and Methods 147
Because the fatigue state of knee joint is affected by the exercise load and the degree of flexion and 148 extension, it can be estimated and predicted according to the moving parameters. In this paper, 149 exercise load and flexion angle of knee joint are taken into consideration, and an acceleration-weighted 150 curve fitting method is introduced to estimate and predict the percentage of knee fatigue. Then the 151 excessive load during exercise is able to be avoided and the knee joint can be protected. 152

Mechanism and Characterization of Knee Injury 153
The knee joint is composed of the lower end of the femur, the upper end of the tibia and the patella 154 with many ligaments and muscles around it. The main ligaments are medial collateral ligament (MCL), 155 lateral collateral ligament (LCL), and anterior cruciate ligament (ACL), posterior cruciate ligament 156 (PCL), etc. Although the fibula does not participate in the formation of the knee joint, it has a role in 157 the stability of the knee joint that cannot be ignored because of the origin of the lateral collateral 158 ligament [12]. Stability maintaining mechanism of knee joint includes active stabilizing structure, 159 passive stabilizing structure and innervation [13]. The active stabilization structure includes the 160 muscles and skin around the knee joint; the passive stabilization structure includes the knee ligament, 161 joint capsule, meniscus, articular cartilage, etc. Both of them are under the control of the nervous 162 system to jointly maintain the stability of the knee joint. Passive stabilization structure is the basis for 163 maintaining knee joint stability, so that the structure of each part of the knee joint moves according to a 164 certain direction with participation of the active stabilization structure and innervation. 165 The knee joint is an approximate ginglymus, whose range of flexion and extension in the sagittal 166 plane is larger, while the range of motion in the other two planes is smaller [14]. The range of motion 167 of a normal knee joint is defined as the steady range of knee, that is, the range of motion of normal 168 adduction, abduction, internal rotation, external rotation, and hyperextension. When the range of 169 motion exceeds the normal one, the knee joint at this time is considered to be in an unstable state 170 called instability. Injuries to the knee include bone, cartilage, and ligament injuries. There are many 171 ligament injuries, and bone or cartilage injuries are generally combined with one or several ligament 172 injuries [1,15]. 173 Common knee injuries include ligament injury, meniscus injury, and patella strain [13]. Ligament 174 injuries mostly occur in basketball, football and other ball sports, as well as gymnastics and running 175 [16]. In these exercises, the knee joint is often in a state of flexion. The calf suddenly abducts and 176 externally rotates, or the foot and calf are fixed, and the thigh suddenly rotates and adducts. This is 177 very likely to cause damage to the medial collateral ligament of the knee joint. Most of the collateral 178 ligaments are damaged at the same time as the joint capsule, cruciate ligament, or meniscus. After the 179 injury, the knee joint was partially swollen, and the flexion and extension function was limited. The 180 meniscus injury is due to the inconsistent movement of the medial and lateral meniscus when the knee 181 is suddenly extended from the flexed position. The misalignment of the thigh and calf positions will 182 squeeze the meniscus, causing tearing or abrasive chronic injury of the meniscus. Furthermore, the 183 patella strain is mainly due to the repeated flexion and extension of the knee joint, which causes the 184 corresponding joint surface of the patella and femur to be abnormally misaligned, and the impact of the 185 twisting and friction causes local tissue and cell metabolism abnormalities. 186 Excessive exercise and fatigue of the knee joint have been shown to significantly increase the risk 187 of knee injury [4,17]. While the knee joint is gradually fatigued, the flexion angle and frequency of its 188 movement will slightly decrease [1]. By observing the changes of these external parameters, combined 189 with the corresponding exercise data, the progressive degree of knee fatigue can be analysed and 190 predicted, then the exercise plan is able to be adjusted in time to reduce the risk of knee injuries. 191

Comprehensive load for knee joint 192
The knee joint fatigue is closely related to the contact force, flexion angle and moving frequency of 193 the joint. During the exercise, the greater the contact force, the larger the flexion angle, and the higher 194 the moving frequency is, the faster the knee joint will be fatigue. Thus, a comprehensive load formula 195 is proposed to estimate the total burden of knee joint during sports involving the three factors as show 196 in Equation (1). 197 where l t is comprehensive load at time slice t; P represents the maximum plantar pressure acquired 198 by sensors on the insoles in a small sampling time window around the time slice t, which reflects the 199 contact force of knee joint; P bm denotes the benchmark value of plantar pressure which is sampled 200 during standing still of user; C is the maximum radian of flexion angle obtained by flex sensors in a 201 small sampling time window around the time slice t; C bm is the benchmark value of flexion angle 202 sampled during standing still of user; BMI represents body mass index, which is currently the most 203 commonly used tool in the world to measure whether a person is too thin or too fat. The highest BMI 204 value for normal weight is usually 25 in the world and 24 in China; δ is an adjustment parameter 205 specified by the user; k denotes the base of an exponential function used to adjust the shape of the 206 curve; Δt nr represents the interval time of knee joint flexion sampled under usual walking state of the 207 user; Δt g is the interval time between the last knee flexion and the current one, used to describe the 208 frequency of knee motion; ρ is an adjustment factor, specified by the user; b denotes the base of 209 another exponential function used to adjust the shape of the curve; ε is also an adjustment factors, 210 specified by the user. Before each experimental test, there needs to be a calibration procedure to 211 acquire the parameter Δt nr , P bm and C bm automatically from the user for the system through standing 212 still and normal walking.
As shown in Equation (2), the comprehensive load l t accumulates over time to make total load s t 214 and the increase of flexion angle, plantar pressure and motion frequency will accelerate accumulation 215 of the value. 216

Acceleration-weighted curve fitting estimation 217
Because the knee fatigue is closely related to the active intensity of the muscles around the joint, the 218 acceleration of the end of the tibial, which is measured by the acceleration sensor MPU-6050, can be 219 viewed as an indicator of the muscle activity in the exercises. A higher acceleration value may increase 220 the fatigue of the knee joint. Thus, this value can be taken as a weight in the fitting estimation. A 221 proportional-integral (PI) controller [18] is introduced to involve the influence of strenuous muscle. In 222 addition to affecting curve fitting through proportional term, continuous intense muscle movements 223 also produce cumulative effects through integral term. The longer the duration, the greater the 224 cumulative impact on the knee fatigue. As shown in Equation (3), Δa(t) represents the acceleration 225 redundancy at time t which exceeds the threshold a thr , and it can be got in calibration procedure under 226 normal walking of user . Equation (4) shows the computational formula of PI controller. 227 where K P represents the proportional gain, T I denotes the integral time and w(t) is the acceleration 228 redundancy at time t which can be used as weight in the curve fitting. Because the Equation (4) can 229 only be used in analogue systems, the integral component should be discretized for the digital 230 equipment. Equation (5) shows the formula for conversion from the integral term to the sum of discrete 231 errors: 232 where Δt = T represents the sampling period. In our experiments, the value of T is set to 1. Equation (5)  233 can then be rewritten in discrete form as Equation (6): 234 According to Equation (7), Equation (6) can be further converted to the incremental form as 235 Equation (8). That formula can simplify the calculation and save storage space. 236

where K I =K P (T/T I ) is the integral coefficient. Then each w(k) should be standardized within the array 237
W which is consist of all the w(k) values following Equation (9), where Max(W) represents the 238 maximum element inside the array and Min(W) is the minimum one. Furthermore, the array W norm is 239 made of all the w norm (k) values and can be used for the next weighted curve fitting step. 240 After obtaining the normalized acceleration redundancy w norm (i), the weighted curve fitting is able 241 to be run on the database to figure out the prediction of knee fatigue using Equation (10). 242 1 ( ) where ŵ represents the fitting coefficient; S denotes the vector of total load s i at each point; F is the 243 vectors of knee fatigue percentage f i ; W norm is a weight diagonal matrix as shown in Equation (11)  244 containing acceleration redundancy w norm (i) as its elements. 245

Fatigue judgement and predication 246
Due to the fact that knee fatigue will be reflected in the peak knee flexion angle [1], the angle can 247 be used to help estimate the degree of knee fatigue. However, a key function of the system is to 248 calculate the exercise load on the knee joint and evaluate the suitable duration for different exercises. 249 Thus, the system needs to find the mapping from the total load s t to the percentage of knee fatigue f t at 250 time slice t using the peak flexion angle as a tool. From the initial moment to the latest moment in 251 which the knee joint is fatigue, the peak knee flexion reduces nearly 10 degree [1]. According to this 252 basis, the mapping from the total load to the percentage of knee fatigue can be built in a calibration 253 procedure. In that procedure, let the participant do sport until he feels tired of his knee joint. During 254 that process, at the exact time of each 1 degree reduction of the peak knee flexion, the corresponding 255 total load s i is calculated, where i is a serial number. Then the percentage of knee fatigue f i is estimated 256 by the peak knee flexion degree and the pair (s i , f i ) can be viewed as a point in the mapping 257 relationship. After acquiring these (s i , f i ) key points, the cubic polynomial fitting can be performed to 258 finish the whole curve of the mapping from s t to f t . 259 Run calibration procedure to acquire the parameter t nr , P bm , C bm and a thr automatically Build the mapping from total load s t to knee fatigue percentage f t Sense C, P and w(t) to calculate the comprehensive load l t at each time slice The whole sensing and predicting procedure is shown in Figure 4 for getting the fitting coefficient 262 ŵ. After the calibration procedure and mapping building, C, P and w(t) are sensed by the device to 263 evaluate the current percentage of knee fatigue. For that purpose, a dealing time window, which can be 264 set to 1, 2, 3 or 5 minutes in usual, is needed for finding key points in the estimation. At the end of 265 each window, the data acquired before will be calculated to find the fitting coefficient ŵ and the 266 predicting curve will be refreshed. Then the healthy remaining time t rem which indicates the suitable 267 time left for the current exercise state without knee injury can be estimated by Equation (12), where 268 f end represents the final fatigue state of knee decided by user; the ŵ is the fitting coefficient; the s now is 269 the total load at this moment and l now denotes the comprehensive load value at current time.

Wearable Sensoring Device for Knee Joint 278
In order to acquire the exercise data in real time, a wearable sensoring device is implemented on the 279 STM32F103 microcontroller platform from ST Microelectronics Corporation (Geneva, Switzerland). 280 As shown in Figure 5(a) three kinds of sensors are adopted in the device. The Flexiforce A301 is a 281 pressure sensor from Tekscan Corporation (Boston, US) with only 0.203 mm thickness and less than 5 282 ms response time, which can be deployed on the insole of the shoe to measure the plantar pressure as 283 shown in Figure 5(c) and (d). A Flex Sensor 4.5" from Spectra-Symbol Corporation (Salt Lake City, 284 US) is used to reflect the flexion angle of knee joint. An MPU-6050 module from InvenSense 285 Corporation (Sunnyvale, US) containing a 3-axis gyroscope and a 3-axis accelerometer is adopted to 286 acquire the acceleration of the end of the tibial for weighted curve fitting. The hardware of the 287 sensoring device is shown in Figure 5(b), in which the integrated operational amplifier OPA333 from 288 Texas Instrument (Dallas, US) is designed to regulate the input signal. A BC417143 Bluetooth module 289 from Cambridge Silicon Radio (Cambridge, UK) is used to send messages out through wireless. The 290 Figure 5(e) shows the wearing situation of the device and with the help of it the parameters of knee 291 joint can be measured during sports and the knee fatigue state is able to be estimated. 292

Experiment and participants 293
The experiments were performed involving 24 healthy volunteers (12 males, 12 females; for male, 294 age = 22.9±0.8 years, height 174.5±3.3 cm, body mass 67.1±6.8 kg; for female, age = 23.2±0.9 295 years, height 162.9±2.9 cm, body mass 55.4±6.9 kg) without heart disease, nervous system disease, 296 unsound limbs, etc. Four popular exercises in daily life are adopted for the tests, including running, 297 badminton, table tennis and basketball. Participants were excluded if they had any pain (acute or 298 chronic) during sports. Flexion angle of knee, plantar pressure and the acceleration of the end of the 299 tibial were sensed by the device and involved in the estimation and predication of knee fatigue after 300 mean filtering. For the experiments, the parameters of the system were set as follow: ε=ρ=1, k=b=e 301 (the natural logarithm), δ=24, K P = 3, T I = 6, T = 1 for the w(k) calculation, the sampling time window 302 was set to 1 second and the dealing time window was set to 2 minutes. A calibration procedure was 303 performed before testing to get parameter Δt nr , P bm , C bm , a thr and build the mapping from total load to 304 knee fatigue percentage. The designed system showed warning messages to participants when the 305 fatigue degree reached 60 percent, provided the estimated left time for healthy exercise, and the 306 participants stopped the exercise at 80 percent of the knee fatigue. There are two kinds of test mode, 307 the test without break and with break. In the mode without break, the participants do continuous 308 exercise without break until stopping time. While, in the mode with break, the participants make a 5-309 minute break after 20 minutes of exercise and continue to do the exercise. The exercising time for 310 these separate parts is added to be counted as the total duration. 311 The whole procedure of experiment was divided into two stages. In the first stage, all the 312 participants were organized into a same group and equipped fatigue predicting devices for warning. All 313 the participants were asked to attend those four kinds of exercises every day in the two test mode with 314 full recovery and the whole testing procedure lasted two weeks. During running exercise the 315 participants were asked to keep a 2.3 m/s pace. The predicting capability of the device, the gender-316 comparable situation, and the influence of BMI and break during exercises were studied in this stage. 317 In the second stage, the participants were divided into two groups, testing group (6 males, 6 females; 318 age = 23.2 ± 0.7 years, height 168.9 ± 6.7 cm, body mass 61.0 ± 9.1 kg) and control group (6 males, 6 319 females; age = 22.9 ± 0.9 years, height 168.5 ± 6.3 cm, body mass 61.5 ± 8.8 kg). The participants in 320 testing group equipped the sensoring devices and stopped the exercise at 80 percent of the knee fatigue. 321 However, the participants in control group had not stopped their exercise until they felt tired in leg or 322 knee by themselves. All the participants were asked to play basketball at least once every day and that 323 procedure lasted two weeks with the same parameters of the first stage but without break. Data were 324 acquired through the designed hardware and the average values were taken for analysis. Moreover, the 325 Lysholm score [19,20] and the International Knee Documentation Committee (IKDC) score [21, 22] 326 of the participants were judged by two independent experienced orthopedists from the Department of 327 Orthopedics, Fujian Medical University Union Hospital. After that, the participants were given a three-328 month rest to restore their knee joints for the next running test. Before the running test, these two scale 329 scores of the participants were evaluated to ensure complete recovery of their knee joints. All the 330 setting of the running test was just the same as the playing basketball. In addition, Lysholm score is a 331 condition-specific score for evaluating knee ligament injury and widely used in various knee diseases. 332 It is simple, non-traumatic and easy to be accepted. IKDC has relatively high reliability, effectiveness 333 and sensitivity for the assessment of ligament injuries, especially anterior cruciate ligament injuries 334 and defects. Thus, it is suitable for evaluating post-exercise injuries of knee joint.   (a) The healthy time of different genders for knee joint during the four exercises without break; (b) The healthy time of different BMI situation for knee joint during the four exercises without break; (c) The healthy time for knee joint during the four exercises with and without break. (* p < 0.05, ** p < 0.01, *** p < 0.001) Figure 3 (a) Lysholm sores of testing and control groups before and after playing basketball and running; (b) IKDC sores of testing and control groups before and after playing basketball and running; (c) Lysholm sores of control group for different genders before and after playing basketball and running; (d) IKDC sores of control group for different genders before and after playing basketball and running; (e) Lysholm sores of control group for different BMI situation before and after playing basketball and running; (f) IKDC sores of control group for different BMI situation before and after playing basketball and running. (* p < 0.05, ** p < 0.01, *** p < 0.001)

Figure 4
The sensing and predicting procedure for knee fatigue judgment.