Volume 17 Number 5
September 2020
Article Contents
Zhen Hu, Xiao Li, Ting Guan. A Study on Performance and Reliability of Urethral Valve Driven by Ultrasonic-vaporized Steam. International Journal of Automation and Computing, 2020, 17(5): 752-762. doi: 10.1007/s11633-016-1026-y
Cite as: Zhen Hu, Xiao Li, Ting Guan. A Study on Performance and Reliability of Urethral Valve Driven by Ultrasonic-vaporized Steam. International Journal of Automation and Computing, 2020, 17(5): 752-762. doi: 10.1007/s11633-016-1026-y

A Study on Performance and Reliability of Urethral Valve Driven by Ultrasonic-vaporized Steam

Author Biography:
  • Xiao Li   received the Ph.D. degree in mechanical manufacturing and automation from Northeastern University, China in 1999. He is currently a professor at the School of Electromechanical Engineering, Guangdong University of Technology, China. He is a fellow of the Chinese Mechanical Engineering Society
    His research interests include automation and robotics, simulation and control of electrohydraulic system, and biomedical equipment
    E-mail:lixiao@gdut.edu.cn

    Ting Guan   received the Ph.D. degree in obstetrics and gynecology from Jilin University, China in 2000. She is currently a professor and chief physician at the Department of Obstetrics and Gynecology, Guangzhou General Hospital of Guangzhou Military Command, China. She is a member of the standing committee of the Guangdong Provincial Institute of Obstetrics and Gynecology, China
    Her research interests include laparoscopic operation technology, diagnosis and treatment of tumor, and biomedical equipment
    E-mail:lxgdut@163.com

  • Received: 2015-09-27
  • Accepted: 2016-03-18
  • Published Online: 2016-10-27
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

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A Study on Performance and Reliability of Urethral Valve Driven by Ultrasonic-vaporized Steam

Abstract: The aim of this study is to investigate the performance and reliability of urethral valve driven by ultrasonic-vaporized steam. The performance model of urethral valve is established to analyze the driving and opening/closing performances of urethral valve. The reliability model of urethral valve is obtained, and the reliability simulation algorithm is proposed to calculate the reliability index of urethral valve. The numerical simulation and experimental results show that urethral valve has a good opening/closing performance, the driving performance can be improved by increasing ultrasonic intensity, radiation area and ultrasonic frequency, and the corrosion and aging of driving bags are the weak links of urethral valve.

Recommended by Associate Editor Giuliano Premier
Zhen Hu, Xiao Li, Ting Guan. A Study on Performance and Reliability of Urethral Valve Driven by Ultrasonic-vaporized Steam. International Journal of Automation and Computing, 2020, 17(5): 752-762. doi: 10.1007/s11633-016-1026-y
Citation: Zhen Hu, Xiao Li, Ting Guan. A Study on Performance and Reliability of Urethral Valve Driven by Ultrasonic-vaporized Steam. International Journal of Automation and Computing, 2020, 17(5): 752-762. doi: 10.1007/s11633-016-1026-y
  • Urinary incontinence is caused by urethral sphincter dysfunction or trauma, which not only brings serious trouble to patients in social life but also leads to urinary tract infections and other complications. At present, the disease is hardly cured by drugs or surgery because of a wide variation in the age and gender of patients and various causes of this disorder[1, 2]. So it is fairly important to take some measures to control the urethra's opening and closing.

    At present, the implanted devices, which control the urethra's opening and closing autonomously, mainly include the artificial urinary sphincter (AUS) and urethral valve. The concept of AUS was firstly suggested by Foley in 1947[3], he put forward a kind of AUS device which uses a manual hydraulic pump to control the urethra's opening and closing. For the moment, American medical systems (AMS) 800 AUS has developed into a sophisticated system to help the patients with severe urinary incontinence, and over 100000 devices have now been implanted worldwide, but the occurrence of complications caused by the uncontrollable urethra closing pressure is still possible in these patients[4]. Moreover, because of the expensive price of AMS 800, it is rarely used in the developing countries[5].

    Urethral valve was proposed by Kohler in the late-1960s[6]. From 1997 to 2003, Chonan et al.[7-11] developed an artificial urethral valve using shape memory alloy (SMA) actuators, they discussed the opening/closing performance, durability and mechanical properties of urethral valve, and studied the transcutaneous energy transmission system to achieve the wireless energy transmission of urethral valve. In 2012, Liu et al.[12, 13] designed a urethral valve driven by the electromagnetic force, they established the mathematical models of urine flow rate performance and reliability, and they analyzed the urine flow rate performance and reliability. So far, the urethral valve has not been used for clinical purposes. But it is possible to reduce the occurrence of complications due to its controllable urethra closing pressure.

    In this paper, a new urethral valve driven by ultrasonic-vaporized steam is presented. The performance and reliability of urethral valve are studied by numerical simulation and experiment. The findings can provide the basis for structure design, performance research and reliability analysis of the suitable clinical urethral valve.

  • Fig. 1 shows the working principle of urethral valve. The urethral valve is composed of ultrasonic generator and ultrasonic transducer outside the human body, and driving bags, working medium, valve body, valve spool, permanent magnets and rubber pads are inside the human body. Ultrasonic generator generates high frequency oscillation signals to the ultrasonic transducer for transforming ultrasound. Ultrasonic transducer is pressed in the anterior abdominal wall at the stage of urination. Valve spool and valve body are made of non-metallic material. Driving bags as the pneumatic actuator are made of flexible, resilient material. Working medium stored in the driving bags is dichloromethane, a low boiling point (39.8$ {^\circ}) $ liquid substance. Permanent magnets are made of neodymium iron boron material, one is fixed on the valve body, and the other one is fixed on the valve spool. Rubber pads are fixed on the permanent magnets to protect the urethra.

    Figure 1.  Working principle diagram of urethral valve. (a) Urethral valve closed; (b) Urethral valve open. 1 ultrasonic generator, 2 ultrasonic transducer, 3 and 10 driving bag, 4 and 11 working medium, 5 valve body, 6 valve spool, 7 and 12 permanent magnet, 8 and 13 rubber pad, 9 urethra.

    The working principle of urethral valve can be described as follows: at the stage of urine storage, ultrasonic generator does not generate high frequency oscillation signals, ultrasonic transducer does not generate ultrasound, working medium is not vaporized, driving bags are in the initial relaxed state, and valve spool keeps the urethra closed by the magnetic force, as shown in Fig. 1(a). At the stage of urination, ultrasonic generator generates high frequency oscillation signals, ultrasonic transducer transforms the signals to generate ultrasound, and working medium radiated by ultrasound is vaporized. With the increasing of steam, driving bags expand and contact with valve spool. When the driving force acting on the valve spool is more than the magnetic force, the valve spool shifts to open the urethra, and bladder urinates, as shown in Fig. 1(b). After urination, ultrasonic generator and ultrasonic transducer stop working, steam in driving bags is liquefied with the decreasing of temperature of working medium, driving bags shrink and valve spool reset to close the urethra by the magnetic force. As the process is repeated, patients can control urination timely.

    Thus it can be seen, the urethral valve driven by ultrasonic-vaporized steam has following features: ultrasound passing on the tissue of human has penetrability, which avoids damaging physiological structure and function; the space of ultrasonic transducer is flexible; the urethra need not be cut for mounting the device, which prevents muscle tissue from wound infections; the parts of urethral valve do not contact with urine, which avoids urinary tract infections or complications; rubber pads contact with urethral wall, which protects the urethra from mechanical damage; urethral inner wall conforming to the physiological structure is used for sealing, which does not cause the urine leakage; the magnetic force is used for closing the urethra, which can control the urethra closing pressure remaining constant by the reasonable design of permanent magnet.

  • The performance model of urethral valve consists of driving force model, magnetic force model and opening/closing condition. In order to facilitate modeling, the following assumptions are given according to the principle and structural features of urethral valve: the losses of ultrasonic intensity and energy are ignored when the ultrasound goes through the urethral valve body and driving bag; driving bags do not break; contact area between driving bags and valve spool remains constant; energy damage and driving pressure change caused by the deformation of driving bags are ignored; friction and mass forces between valve body and valve spool are ignored; permanent magnets are uniformly magnetized; the value and direction of surface magnetic charge are the same; and permanent magnets always remain parallel.

  • The process of ultrasound radiating in the working medium through the anterior abdominal wall and the urethral valve body is divided into two stages. One is that ultrasound passes through the anterior abdominal wall tissue. The other is simply passed through the working medium because the thickness of the urethral valve body and driving bag is very small relative to the working medium. The sketch map of ultrasound radiating in the working medium is shown in Fig. 2.

    Figure 2.  Sketch map of ultrasound radiating in the working medium. 1 ultrasonic transducer, 2 anterior abdominal wall, 3 urethral valve body, 4 driving bag, 5 working medium.

    In the first stage, ultrasonic transducer clings to the anterior abdominal wall, when ultrasound propagates in the medium, the ultrasonic intensity decreases exponentially with the increase of ultrasonic propagation distance[14]. Therefore, ultrasound penetrates the anterior abdominal wall tissue, and the ultrasonic intensity is weakened:

    where $ I_{1} $ is the ultrasonic intensity through the anterior abdominal wall tissue; $ I_{0} $ is the original ultrasonic intensity; $ \alpha_{1} $ is the attenuation coefficient of ultrasound in the anterior abdominal wall tissue, $ \alpha_1 = k_1f^2 $, $ k_1 $ is the characteristic coefficient of anterior abdominal wall tissue, $ f $ is the ultrasonic frequency; $ d_{1} $ is the ultrasonic propagation distance in the anterior abdominal wall tissue.

    Thus, ultrasound penetrating the anterior abdominal wall tissue induces some energy loss, and the anterior abdominal wall tissue absorbs the loss of ultrasonic energy and converts it into the thermal energy. According to the law of energy conservation, the thermal energy from the anterior abdominal wall tissue can be obtained:

    where $ Q_{0} $ is the energy of ultrasound radiating in the anterior abdominal wall tissue, $ Q_{0} = I_{0}S_{r}t $, $ S_{r} $ is the ultrasonic radiation area, $ t $ is the ultrasonic radiation time; $ Q_{1} $ is the energy of ultrasound penetrating the anterior abdominal wall tissue, $ Q_{1} = I_{1}S_{r}t $.

    Thereby, the thermal energy from the anterior abdominal wall tissue can be described as

    In the second stage, ultrasound continues to go through the urethral valve body after permeating the anterior abdominal wall tissue. Then, ultrasound radiates the working medium. According to the propagation law of ultrasound in the medium, the ultrasonic intensity of ultrasound radiating in the working medium can be obtained

    where $ \alpha_2 $ is the attenuation coefficient of ultrasound in the working medium, $ \alpha_2 = k_2f^2 $, $ k_2 $ is the characteristic coefficient of working medium; $ d_{2} $ is the ultrasonic propagation distance in the working medium; $ T_{c} $ is the ultrasonic intensity transmission coefficient of ultrasound from the anterior abdominal wall tissue into the working medium.

    In the same way, the loss of ultrasonic energy caused by ultrasound penetrating the working medium can be gained:

    The working medium absorbs the loss of ultrasonic energy, and its temperature changes gradually. With the increasing energy of working medium being absorbed from ultrasonic radiation, the temperature of working medium rises to reach the boiling point. Then, the working medium is vaporized into steam. The driving pressure equation has been got from the definition of latent heat of vaporization and thermodynamic equation of gas state[15]

    where $ Z $ is the compression factor of steam; $ R_{m} $ is the molar gas constant; $ T_{b} $ is the boiling point of working medium; $ V_{d} $ is the volume of driving bags; $ \Delta H $ is the latent heat of vaporization of working medium.

    The driving force acting on the valve spool is expressed according to the assumptions:

    where $ S_{c} $ is the contact area between driving bags and valve spool.

    By (5)–(7), the driving force can be expressed as

    Equation (8) is the driving force model of urethral valve, which reflects the driving performance of urethral valve under ultrasonic radiation. It indicates that the driving performance of urethral valve mainly relates to the structural parameters of urethral valve ($ V_{d} $, $ S_{c} $, $ d_{1} $, $ d_{2}) $ and ultrasonic control parameters ($ I_{0} $, $ S_{r} $, $ f) $. Taking into account the structural parameters of urethral valve can not be adjusted in this study, they are set to constant, and the effect of ultrasonic control parameters on the driving performance will be discussed in the following sections.

  • The urethra is closed by the magnetic force exerted between two same rectangular permanent magnets. Length, width and height of rectangular permanent magnet are expressed by $ a $, $ b $, $ c $ respectively, the spatial coordinate system $ o $-xyz and $ O $-XYZ are set up. The relative position of permanent magnets is shown in Fig. 3.

    Figure 3.  Relative position of permanent magnets

    Absolute value of surface magnetic charge is equal to residual magnetism[16]. Based on the energy equation between cuboidal magnets[17] and relative position of permanent magnets, the energy between permanent magnets is got

    where $ \sigma _{m} $ is the surface magnetic charge of permanent magnet, $ \vert $$ \sigma $$ _{m}\vert = B_{r} $, $ B_{r} $ is the residual magnetism; $ \mu _{0} $ is the magnetic permeability; $ r $ is the distance between permanent magnets.

    The energy $ W $ between permanent magnets is a function of distance $ r $, the magnetic force can be derived from the derivative of $ W $[17]

    Taking into account certain factors, for instance, the magnetic force is affected by ambient temperature, and then the correction coefficient $ k_{m} $ is added, the magnetic force is updated

    Equation (11) is the magnetic force model of urethral valve, which reflects the magnetic force determined by the residual magnetism, size of permanent magnet and distance. It follows that the magnetic force is minimal at the maximal distance when the urethra is open, and the magnetic force is maximal at the minimal distance when the urethra is closed.

  • The opening/closing condition of urethral valve can be described as follows: at the stage of urine storage, urethral valve keeps the urethra closed because driving force is less than magnetic force. Urethral valve opens the urethra when driving force is more than the maximal magnetic force $ F_{\max}. $ Bladder begins to urinate. During urination, if driving force is more than the minimal magnetic force $ F_{\min} $, bladder urinates continuously. Urethral valve keeps the urethra open until driving force is less than the minimal magnetic force. Therefore, the opening/closing performance of urethral valve is analyzed by the performance model.

  • In order to study the performance of urethral valve, a simulated experimental system is designed in this paper, as shown in Fig. 4(a). As the pressure of liquid decreases approximately linearly with the liquid level dropping in the cylindrical cup, which is similar to the change of intravesical pressure during urination, a cylindrical cup is used as the simulated bladder to simulate the change of intravesical pressure. Pressure sensors detect the intravesical pressure and driving pressure, and temperature sensor detects the temperature of working medium. Steam generator is used to generate steam and facilitate the detection of driving pressure and temperature. Ultrasonic generator can adjust ultrasonic intensity and radiation area. Flowmeter measures the urine flow rate and urine output. All data detected by the sensors are sent to the computer for processing through the DAQ card.

    Figure 4.  Simulated experimental system. (a) The schematic diagram; (b) The setup diagram. 1 simulated bladder, 2 and 3 pressure sensor, 4 temperature sensor, 5 steam generator, 6 ultrasonic transducer, 7 measuring cup, 8 simulated urethra, 9 urethral valve.

    The simulated experimental system is set up according to Fig. 4(a), as shown in Fig. 4(b). The details of experimental instruments are listed in Table 1.

    Table 1.  Details of experimental instruments

  • The validity of performance model is tested by Matlab numerical simulation and experiment. The parameters are set as follows: $ I $ = 1W/cm$ ^{2} $, $ S_{r} $ = 14cm$ ^{2} $ and others are listed in Table 2. The driving force is obtained by the pressure sensor 3 and (8). The magnetic force is measured by MBO 2000 magnetic measuring instrument.

    Table 2.  Simulation parameters

    Figs. 5 and 6 show the numerical simulation and experimental curves of driving force and magnetic force respectively. As it can be seen, the driving force changes linearly with radiation time, the magnetic force rapidly decreases with the increase of distance, and the numerical simulation and experimental results are consistent by comparing the curves. Therefore, the driving force model and magnetic force model are effective.

    Figure 5.  Numerical simulation and experimental curves of driving force

    Figure 6.  Numerical simulation and experimental curves of magnetic force

  • The essential function of urethral valve is to control the urethra opening and closing, thus, the opening/closing performance of urethral valve needs to be investigated. In this study, the opening/closing performance is evaluated according to the changes of driving force, bladder volume and urine flow rate with radiation time. In experiment, $ F_{\max} $ = 3.2N, $ F_{\min} $ = 0.45N, the initial temperature of working medium is 36.5$ {^\circ} $, and simulated bladder is filled with 500ml water, its hydrostatic pressure is adjusted to about 75cm H$ _{2} $O. The ultrasonic control parameters are set as follows: $ I $ = 2W/cm$ ^{2} $, $ S_{r} $ = 14cm$ ^{2} $.

    Fig. 7 shows the experimental curve of opening/closing performance. As it can be seen, the driving force increases when ultrasonic radiation begins. As the driving force is less than $ F_{\rm max} $, the urethral valve still closes the urethra and urine flow rate is zero. With the increasing of radiation time, the driving force reach $ F_{\rm max} $, the urethral valve opens the urethra, urine flow rate reaches the maximum value rapidly, and urine discharges continuously until urine flow rate drops to zero. When ultrasonic radiation stops, working medium is liquefied as temperature decreases, and the driving force reduces. When the driving force drops to $ F_{\rm min} $, the simulated bladder is injected 500ml water again. It is found from the experiment that urine flow rate keeps zero. The experimental result indicates that the opening/closing performance is good, and urethral valve can control the urethra opening and closing according to the opening/closing condition.

    Figure 7.  Experimental curve of opening/closing performance. (a) The working status of ultrasonic generator; (b) Change of driving force; (c) Change of bladder volume; (d) Change of urine flow rate.

  • From Fig. 7, it can be seen that the opening time of urethral valve is determined by the change of driving force. In order to optimize the opening/closing performance, it's necessary to study the driving performance of urethral valve. In this study, the driving performance is evaluated by radiation time needed when the driving force reaches $ F_{\rm max} $. The effect of ultrasonic control parameters on the driving performance are studied by the method of numerical simulation and experiment, but the effect of ultrasonic frequency on the driving performance is only analyzed by numerical simulation, because the ultrasonic generator can only generate the 840kHz ultrasound.

    Fig. 8 presents the numerical simulation and experiment curves of the change of driving force with radiation time under different ultrasonic intensity. The ultrasonic control parameters are set as follows: $ S_{r} $ = 14cm$ ^{2} $, $ I $ = 2W/cm$ ^{2} $, 1.5W/cm$ ^{2} $ and 1W/cm$ ^{2} $. As it can be seen, the numerical simulation value of radiation time is respectively 91s, 123s, 141s, and the measured value of radiation time is respectively 90s, 120s, 140s when the driving force reaches $ F_{\rm max} $. The radiation time is shortened and the driving performance is improved by increasing ultrasonic intensity when radiation area is constant.

    Figure 8.  Numerical simulation and experimental curves of the effect of ultrasonic intensity on driving force

    Fig. 9 illustrates the numerical simulation and experiment curves of the change of driving force with radiation time under different radiation area. The ultrasonic control parameters are set as follows: $ I $ = 2W/cm$ ^{2} $, $ S_{r} $ = 14cm$ ^{2} $, 7cm$ ^{2} $. As it can be seen, the numerical simulation value of radiation time is respectively 91s, 149s, and the measured value of radiation time is respectively 95s, 145s when the driving force reaches $ F_{\rm max} $. The radiation time is shortened and the driving performance is improved by increasing radiation area when ultrasonic intensity is constant.

    Figure 9.  Numerical simulation and experimental curves of the effect of radiation area on driving force

    Fig. 10 illustrates the numerical simulation curves of the change of driving force with radiation time under different ultrasonic frequency. The ultrasonic control parameters are set as follows: $ I $ = 2W/cm$ ^{2} $, $ S_{r} $ = 14cm$ ^{2} $, $ f $ = 600kHz, 840kHz, 1000kHz. As it can be seen, the numerical simulation value of radiation time is respectively 177s, 90s, 64s when the driving force reaches $ F_{\max} $. The radiation time is shortened and the driving performance is improved by increasing ultrasonic frequency when ultrasonic intensity is constant.

    Figure 10.  Numerical simulation curves of the efiect of ultrasonic frequency on driving force

    Thus, the analysis results of ultrasonic intensity, radiation area and ultrasonic frequency not only show the effect of ultrasonic control parameters on the driving performance, but also provide the important theoretical basis for the reasonable choice of ultrasonic generator and ultrasonic transducer.

  • In the system reliability analysis, some analysis methods are used, such as fault tree analysis, causality analysis, operational risk analysis, dynamic Petri nets analysis, Markov analysis, Monte Carlo method and other methods[18-23]. However, they are commonly applicable to a simple or linear system. For the reliability analysis of urethral valve, it is not suitable to adopt one of the above methods. But it is effective to use fault tree analysis combined with Monte Carlo method according to the structural features of urethral valve.

  • Fault tree analysis is a top down, deductive failure analysis, which includes the establishment of fault tree, qualitative analysis and quantitative analysis of fault tree[23]. Firstly, the fault tree of urethral valve needs to be built. Fig. 11 shows the fault tree of urethral valve built according to the working principle of urethral valve. As it can be seen, the fault tree consists of eight basic events $ Z_{n} $ ($ n $ = 1, 2, $ \cdots $, 8) which influence the reliability of top event $ T $ through a series of intermediate events $ G_{m} $ ($ m $ = 1, 2, $ \cdots $, 4). So the model of top event is then $ T $ = {$ Z_{1} $, $ Z_{2} $, $ \cdots $, $ Z_{n} $}, and the failure distribution function of basic event is written as $ F_{i}(x) $ ($ i = 1, 2, \cdots, n $).

    Figure 11.  Fault tree of urethral valve. $ T $, urethral valve failure, $ G_1 $, failure of opening, $ G_2 $, failure of closing, $ G_3 $, driving source fault, $ G_4 $, driving bags fault, $ Z_1 $, permanent magnets demagnetization, $ Z_2 $, rubber pads fall off, $ Z_3 $, valve spool stuck, $ Z_4 $, ultrasonic generator damage, $ Z_5 $, ultrasonic transducer damage, $ Z_6 $, driving bag corrosion, $ Z_7 $, driving bag aging, $ Z_8 $, driving bag wear

    Secondly, the importance of basic events of fault tree of urethral valve needs to be analyzed using the qualitative analysis. From Fig. 11, it is well known that the fault tree of urethral valve has eight minimum cut sets {$ Z_{n} $} ($ n $ = 1, 2, $ \cdots $, 8), and each cut set has a basic event which is crucial for the state of urethral valve.

    Thirdly, the fault tree of urethral valve needs to be analyzed to get the probability of top event, importance degree of parts and so on through the quantitative analysis. All the basic events are respectively independent according to the qualitative analysis. So the variable $ x_{i} $ can be used to express the state of basic event, the basic event is assumed to occur and the corresponding part of urethral valve is in failure when $ x_{i} $ = 1; on the contrary, it does not occur when $ x_{i} $ = 0. Because the state of top event is a function of the state of basic event, the structural function of fault tree of urethral valve can be written as

    where $ \phi(X) $ reflects the state of urethral valve, if the top event occurs and the urethral valve is in failure, $ \phi (X) = 1 $; otherwise, it does not occur, and $ \phi(X) = 0 $.

    Logic gates usually include AND gate and OR gate in fault tree analysis. The fault tree of urethral valve is composed of OR gate, so the structural function is deduced

    Thus, the probability of top event is got

    where $ P(x_{i}) $ is the probability of basic event.

    Equation (14) is the reliability model of urethral valve. If the reliability index is calculated by this equation directly, the calculation is complex and difficult because the basic events meet several failure distributions according to the features of structure and parts of urethral valve. Therefore, in this study, in order to calculate simply and quickly, Monte Carlo method is adpoted based on simple calculation and widespread use of this method in the field of reliability engineering[24-26].

  • In this study, a reliability simulation algorithm of urethral valve is presented based on fault tree analysis of urethral valve and Monte Carlo method. The reliability simulation algorithm is set up as follows according to the steps of Monte Carlo simulation.

    First of all, the random sampling on the failure distribution function $ F_{i}(x) $ of basic event is carried out, and the simple random sampling corresponding to each basic event is obtained. The sampling value of each basic event is then $ x_{ji} $($ j = 1, 2, \cdots, M $), and they form a matrix $ A $:

    Then, the corresponding sampling values of the life of urethral valve are obtained when the basic event occurs in each row of matrix $ A $, and sorted from small to large

    In accordance with the order, the basic event $ z_{1} $ is set to occur and the rest does not occur, the top event should be judged whether it occurs according to the fault tree of urethral valve. If the top event occurs, then it is recorded. If the top event does not occur, the basic event $ z_{2} $ is set to occur, and then the top event should be checked whether it occurs. And so on, it does not stop until the top event occurs. In the simulation, the $ k $-th sampling value of the life of urethral valve $ x_{kf} $ is equal to the minimum value $ x_{kn} $ ($ k = 1, 2, \cdots, M $) in the $ k_{th} $ row of matrix $ A $.

    Thus, the simulation finishes.

    $ N $ samples of the life of urethral valve can be got from $ N $ times simulation. The maximum value of the life of urethral valve is then $ x_{\rm max} $, and the section [0, $ x_{\rm max} $] is divided into $ m $ intervals. Then, the failure times of top event can be counted from [0, $ x_{r} $] ($ r = 1, 2, \cdots, m $). According to (14), the failure times of urethral valve is gained

    The failure probability point estimates of urethral valve can be got

    Thus, the reliability probability point estimates of urethral valve can be expressed as

    Then, the average life point estimates of urethral valve can be gained

    The importance of basic events of urethral valve can be expressed as

    The mode importance of urethral valve can be written as

    where $ A $ is the failure times of urethral valve when basic event $ Z_{i} $ occurs, $ B $ is the times of basic event $ Z_{i} $ occurs, $ C $ is the failure times of urethral valve.

    The importance of basic events of urethral valve reflects the importance degree of basic events $ Z_{i} $ for the failure of urethral valve. When $ W(Z_{i}) $ = 1, if the basic event $ Z_{i} $ occurs, urethral valve must be in failure. The mode importance of urethral valve is used to judge the weak link of urethral valve. The bigger the mode importance degree $ W_{N}(Z_{i}) $ is, the weaker link the basic event $ Z_{i} $ has.

    Fig. 12 shows the simulation program flowchart of reliability of urethral valve designed by the reliability simulation algorithm.

    Figure 12.  Simulation program flowchart of reliability of urethral valve

  • A Matlab simulation program is written to compute the reliability index based on the reliability model and reliability simulation algorithm. The parameters of failure distribution of basic event are got according to the materials and life attributes of the parts of urethral valve, as listed in Table 3.

    Table 3.  Parameters of failure distribution of basic event

    The simulation results obtained by Monte Carlo method are more precise with the increasing simulation times. Thus, the average life of urethral valve in different simulation times is listed in Table 4.

    Table 4.  Average life of urethral valve

    In Table 4, the simulation results tend to stabilize ultimately with the increasing simulation times. Therefore, the simulation result performed for 10000 times is used as the final result of reliability index on the premise of meeting accuracy, and the average life of urethral valve is 114850 times.

    Figs. 13 and 14 are the curves of reliability and failure probability of urethral valve. As it can be seen, the simulation curve and calculation curve are identical, which indicate that the reliability simulation algorithm is effective and can be used instead of the numerical calculation. Besides, the reliability of urethral valve reaches 0.85 when its average life is 50000 times.

    Figure 13.  Curve of reliability

    Figure 14.  Curve of failure probability

    Table 5 lists the importance and mode importance of basic events, the simulation result suggests that every basic event has a decisive role in the failure of urethral valve, and the corrosion and aging of driving bags are the weak links of urethral valve.

    Table 5.  Importance W(Zi) and mode importance WN(Zi) of basic event

  • 1) The principle of urethral valve driven by ultrasonic-vaporized steam is feasible, the performance model and reliability simulation algorithm of urethral valve are simple and effective.

    2) The driving performance can be enhanced by increasing ultrasonic intensity, radiation area and ultrasonic frequency. The opening/closing performance is good. The corrosion and aging of driving bags are the weak links of urethral valve.

    3) For clinical application, further research will focus on improving the material of urethral valve to fit the human body, and developing the animal-based experiments to guide the structural optimization and performance improvement of urethral valve.

  • This work was supported by National Natural Science Foundation of China (No. 51175089) and National Natural Science Foundation of Guangdong Province (No. S2013010014018).

    The authors would like to thank colleagues, Professor Rui Xiong, Dr.Yuan-Song Xiao, Mr.Huai-Zhou Zhou, Mr.Zhi-Chao Shi, Mr. Zu-Hui Xiao, Mr.Peng-Peng Gong and Mr.Fan-Yu Nie, for many valuable discussions and supports to the research program.

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