Original Article
Interaction model between capsule robot and intestine based on nonlinear viscoelasticity
Proc IMechE Part H: J Engineering in Medicine 2014, Vol. 228(3) 287–296 Ó IMechE 2014 Reprints and permissions: sagepub.co.uk/journalsPermissions.nav DOI: 10.1177/0954411914523404 pih.sagepub.com
Cheng Zhang1,2, Hao Liu1, Renjia Tan1,2 and Hongyi Li1
Abstract Active capsule endoscope could also be called capsule robot, has been developed from laboratory research to clinical application. However, the system still has defects, such as poor controllability and failing to realize automatic checks. The imperfection of the interaction model between capsule robot and intestine is one of the dominating reasons causing the above problems. A model is hoped to be established for the control method of the capsule robot in this article. It is established based on nonlinear viscoelasticity. The interaction force of the model consists of environmental resistance, viscous resistance and Coulomb friction. The parameters of the model are identified by experimental investigation. Different methods are used in the experiment to obtain different values of the same parameter at different velocities. The model is proved to be valid by experimental verification. The achievement in this article is the attempted perfection of an interaction model. It is hoped that the model can optimize the control method of the capsule robot in the future.
Keywords Interaction model, nonlinear viscoelasticity, intestine, capsule robot, dynamic mechanical analyzer
Date received: 26 May 2013; accepted: 10 January 2014
Introduction A robotic capsule endoscope that can move actively with the doctor’s operation has been not only the development direction of the capsule endoscopy but also a research hotspot in the field of robotics and medicine over recent decades. A magnetically guided capsule endoscope (MGCE) system had been developed by Siemens and Olympus, and more than 50 people conducted clinical practice at 2010.1 It is another landmark achievement after the first passive capsule endoscopy developed by Given Imaging at 2001.2 The MGCE system can only examine the stomach in clinic and need to be operated by the doctor in the entire checking process, although it solves some of the problems of the passive capsule endoscopy, such as time-consuming, misdiagnosis and ileus.3 The deficiency of the interaction model between capsule robot and intestine may be one of the dominating reasons that the MGCE system abandons the inspection in the gastrointestinal tract. As the main environment of the capsule endoscopy, the intestine is a complex flexible lumen, the inwall of which is covered by mucus. Any drive mode4–13 cannot neglect the influence of this complex environment on the capsule robot’s motion when the capsule robot
moves in the intestine. Currently, no mathematical model can describe the interaction force between the capsule robot and the intestine precisely. Many developers are engaged in the field of intestinal environment modeling. Hoeg et al. studied the tissue distention of the intestine under the condition of a robotic endoscope moving through. An analytical model and an experimental model were developed to predict the tissue behavior when the intestine was expanded.14 Huang and colleagues15 analyzed the interactive feature changes under the influence of various diameters, lengths and materials of the capsule robot by means of experimental investigation. Some similar researches were carried out by Wang and Meng,16 Wang and Yan17 and our group18 as well. Ciarletta et al.19 used the theory of hyperelasticity to make a stratified analysis of the 1
State Key Laboratory of Robotics, Shenyang Institute of Automation, Chinese Academy of Science, Shenyang, China 2 University of Chinese Academy of Sciences, Beijing, China Corresponding author: Hao Liu, State Key Laboratory of Robotics, Shenyang Institute of Automation, Chinese Academy of Science, Shenyang 110016, China. Email: [email protected]
Downloaded from pih.sagepub.com at UNIV CALIFORNIA BERKELEY LIB on March 9, 2015
288
Proc IMechE Part H: J Engineering in Medicine 228(3)
intestinal wall. The hyperelastic model is inapplicable to research the intestinal material property because it neglects the time effect. Woo et al.20 considered the interactive feature using a thin-walled model and Stokes’ drag equation. However, the model cannot fully describe the material characteristics of the intestine. Most of these research works establish a qualitative empirical interaction model by experimental investigation. In addition, the features of the capsule robot also affect the interaction force. These features contain not only dimension parameters but also motion parameters. At present, the viscoelastic constitutive relation is supposed to be the most effective method of describing the material properties of the intestine. Baek et al.21 investigated the frictional resistance of a capsule inside the porcine small intestine with respect to various capsule shapes using a specially designed tribological tester. Then, the group found that variations of resistance were correlated with the linear viscoelasticity of the intestine. A five-element model is used to describe the linear viscoelastic property of the intestine’s stress relaxation.22 Furthermore, the group first developed an analytical model for the frictional resistance prediction that was verified by finite element analyses.23 In our study, we show that the parameters in the viscoelastic constitutive relation are not constant.24 In other words, the linear viscoelastic constitutive relation is insufficient to describe the intestinal material property. Most researchers used in vitro experiment instead of in vivo experiment in the study process because the latter costs more and is difficult to carry out. It is considered a more convenient choice to simulate the in vivo environment in the in vitro experiment. In this article, an interaction model between the capsule robot and the intestine is developed to solve the problem that the capsule robot cannot complete the controlled movement in the intestine. The model has something to do with the motion parameters of the capsule and the nonlinear viscoelasticity of the intestine. The model parameters are identified by static mechanical test, such as shear stress relaxation test, and dynamic mechanical test with dynamic mechanical analyzer (DMA). At last, the validity of the model is verified by in vitro experiment. The achievement in this article is hoped to optimize the control method of the capsule robot.
Interaction model between capsule robot and intestine The interaction model is affected by the properties of the capsule robot and intestinal material parameters. The intestine is expanded when the capsule moves inside because of the intestinal contraction in a relaxed state (see Figure 1). The shape of the capsule is a cylinder in the middle section and two hemispheres on both ends. The middle section is acted upon by a radial pressure and axial friction, while the pressure perpendicular
Figure 1. Schematic diagram of the intestinal deformation with the insertion of a smooth capsule.25
to the contour line of the capsule is applied on the both ends of the capsule. When the capsule moves forward, the pressure on the rear end can be ignored. The interaction force along the x-direction is more important to the capsule robot’s movement, so it can be expressed as a resultant force of environmental resistance, viscous resistance and Coulomb friction25 F = Fe + Fv + Fc
ð1Þ
where Fe is the environmental resistance, Fv is the viscous resistance and Fc is the Coulomb friction. Environmental resistance is induced by the stress due to the viscoelastic deformation of the intestinal wall. Viscous resistance is caused by the rheological properties of the intestinal mucus. Coulomb friction is a product of the local contact pressure and the Coulomb friction coefficient. Then, environmental resistance, viscous resistance and Coulomb friction will be analyzed.
Intestinal deformation and environmental resistance analyses Principle of environmental resistance and assumptions. The deformation of the intestinal wall is the major influencing factor of the environmental resistance. As the front of the capsule is a hemisphere, the intestinal wall applies a contact force on its contact surface. The horizontal component of the contact force is defined as Fe . For further development of the model, the following assumptions should be made. 1. 2. 3.
The material of the intestine is incompressible. The intestine consists of an isotropic material and deforms symmetrically toward its radial direction. The deformation of the intestine is the same as the external shape of the contact surface of the capsule.
Based on the assumptions above, the deformation could be derived using the contact geometry between the intestine and the capsule.
Downloaded from pih.sagepub.com at UNIV CALIFORNIA BERKELEY LIB on March 9, 2015
Zhang et al.
289
Formula derivation of intestinal deformation and environmental resistance. The contact force is mainly caused by the hoop stress of the intestine. The relationship between the pressure P(x) and the hoop stress tu (x) can be expressed as ð2Þ
where Di (x) and lm are the inner diameter and the average wall thickness of the intestine at position x along the length of the intestine, respectively.26 A five-element model had been used to describe porcine intestinal constitutive relation.22 It consists of three springs and two dampers (see Figure 2). An equation that shows the relation between stress and strain with respect to time is obtained from the results of a stress relaxation test " # E t
h1
E t
h2
+ E2 e
1
+ E3
2
ð3Þ
where E1 , E2 and E3 indicate the moduli of elasticity of springs, while h1 and h2 are the viscosity coefficients of the dampers. e(t) and tu (t) are the strain and stress applied to the intestine, respectively, at the time t. When the capsule moves at a constant speed v, equation (3) can be written as a function of the position x " # E x
t u (x) = e(x) E1 e
Di (x) Di0 Di0
h1 v 1
E x
+ E2 e
h2 v 2
+ E3
ð4Þ
ð6Þ
Therefore, the contact pressure is " E x
e(x) E1 e
P(x)Di (x) t u (x) = 2lm
t u (t) = e(t) E1 e
e(x) =
h1 v 1
E x
+ E2 e
P(x) =
Di (x)
Di0 = 2R cos a
ð5Þ
where R is the radius of the hemisphere and a is the initial angle corresponding with the contact surface. The hoop strain with respect to position is defined as
2
# + E3 2lm ð7Þ
Then, the environmental resistance induced by the stress is R sin ða
Fe =
2pRP(x)dx 3 sin u
ð8Þ
0
where u is the angle of the equivalent contact force. The environmental resistance Fe varies not only with the intestinal constitutive parameters but also with the velocity of the capsule according to equation (8).
Viscous resistance analyses There is lot of mucus in the intestine because of its own physiological structure. The capsule robot is in complete lubrication condition in the whole moving process approximately. Viscous resistance is related to the relative velocity. It can be calculated from the empirical equation Fv = dv
The initial mean diameter of the intestinal inwall approximately equals
h2 v
ð9Þ
where d is the apparent viscosity coefficient. The intestinal mucus is a kind of non-Newtonian fluid. Its apparent viscosity decreases with increase in shear rate. When the shear rate is high enough, the apparent viscosity of the intestinal mucus becomes a constant. The apparent viscosity coefficient can be expressed as27 v0:7552 d = 11:24 + 0:1148 ð10Þ d where d is the mean value of the intestinal mucus thickness. The intestinal environment is complex. Different parts of the intestine have different morphology, such as mucus thickness and length of intestinal villi. The intestinal mucus thickness also varies depending on the force on the intestinal surface. An approximate value of d will be used in the model.
Coulomb friction analyses Coulomb friction is decided by the local contact pressure and the Coulomb friction coefficient Fc = mN
Figure 2. Five-element model.25
ð11Þ
where m is the Coulomb friction coefficient and N is the local contact pressure. The Coulomb friction coefficient is influenced by the surface texture of the intestine, especially the intestinal villi. The value of m can be
Downloaded from pih.sagepub.com at UNIV CALIFORNIA BERKELEY LIB on March 9, 2015
290
Proc IMechE Part H: J Engineering in Medicine 228(3)
calculated from the experimental results. The local contact pressure consists of the normal force and the radial pressure. The normal force is decided by the weight of the capsule, while the radial pressure is caused by the hoop stress of the intestine. The radial pressure is the vertical component of the skew resistance on the hemisphere of the capsule. The local contact pressure is expressed as R sin ða
N = mg +
2pRP(x)dx 3 cos u 0
R sinða + L
+
ð12Þ
2pRP(x)dx
Figure 3. Physical simulation measurement system.
R sin a
where m is the mass of the capsule and L is the length of the capsule’s middle section.
Model parameter identification Several parameters should be confirmed to complete the model. Some parameters are predetermined, others need to be determined by experience and some must be measured by experiment. The material, mass and dimension of the capsule are predetermined. The material is polydimethylsiloxane (PDMS). The mass m is 50.1 g. The length of middle section, that is, a cylinder, L is 20 mm, while the radius of the end, that is, a hemisphere, R is 6.5 mm. Based on practical experience, the initial angle corresponding with the contact surface a is 60°, the angle of the equivalent contact force u is 30°, the average intestinal wall thickness lm is 2.5 mm and the mean value of the intestinal mucus thickness d is 30 mm.28 The Coulomb friction coefficient and the parameters of the five-element model need to be measured by experiment.
Experiment of measuring Coulomb friction coefficient A custom-made physical simulation measurement system is used to measure the Coulomb friction coefficient. It consists of two parts: drive unit and data acquisition (DAQ) unit (see Figure 3). The main part of the drive unit is a NLA-7SL series coreless linear motor, which is produced by NIKKI DENSO. The encoder is RGH22X-lum resolution, which is produced by RENISHAW. The positioning accuracy of the system can reach 61 mm. The rotor of the linear motor is combined with a support, on which a single-degree-of-freedom micro-force sensor is fixed, whose accuracy is 1 mN. The right side of the drive unit is load platform. PCI 6229 DAQ card produced by NI is used to acquire the voltage signal of encoder and micro-force sensor. Then, the signal is transmitted to computer for saving and analysis. The negative pressure suction device is used to clamp the intestine and
Figure 4. 3D model of negative pressure suction device.25
make it expand to 13 mm (see Figure 4). After both ends of the intestine are fixed, the air in vacuum bin is extracted from bleeder hole with a syringe. Then, the intestinal wall is absorbed by the device and expanded compulsively. The device is fixed on the load platform, and a capsule dummy is inserted into the intestine that is fully expanded. Fresh intestine of a pig is used in the experiment. The intestine sample is stored and cleaned in Tyrode with oxygen ventilation. A length of intestine is placed in the negative pressure suction device. Then, the Coulomb friction is only caused by the weight of the capsule. The capsule whose dimension parameters are the same as that stated in the model is dragged by the drive unit at a speed of 0.5 mm/s. The mean value of Coulomb friction that is measured by the micro-force sensor is Fc = 40:07 mN. The Coulomb friction coefficient is m = 0:082 by calculation. This result agrees with the conclusion of Rentschler and colleagues.29
Experiment of measuring the parameters of the fiveelement model A shear stress relaxation test is used to measure the parameters of the five-element model also with the homemade physical simulation measurement system.
Downloaded from pih.sagepub.com at UNIV CALIFORNIA BERKELEY LIB on March 9, 2015
Zhang et al.
291
Table 1. Experimental results of the parameters of the five-element model.25 Shear strain (%)
E1 (kPa)
E2 (kPa)
E3 (kPa)
h1 (kPa)
h2 (kPa)
50 100 150 200
2.926 3.159 2.781 1.726
1.539 1.216 0.948 0.484
1.422 1.064 0.812 0.541
0.053 0.078 0.067 0.060
0.561 0.555 0.393 0.320
model-predicted results. Different contributions are made by three components of the force in the model. Environmental resistance is affected by the velocity greatly and occupies a major share in the frictional resistance. Viscous friction is also affected by the velocity, but in a small proportion. Coulomb friction has little relationship with the velocity. Therefore, the influence of the inaccuracy of the mucus thickness can be ignored easily. It is shown that the effect of the model prediction is great at the velocity lower than 20 mm/s, but that at a speed range from 20 to 60 mm/s is not satisfactory in Figure 5. We deduce that the parameters of the five-element model may be changed at a relatively higher velocity. Therefore, a new experimental method is proposed to accomplish the parameter identification.
Figure 5. Comparative data of the relation between the interaction force and the velocity.25
The capsule dummy is changed to a cylinder, whose diameter is 12.9 mm and length is 15.2 mm, and there are asperities on its surface. These asperities will ensure that there is no relative slippage between the dummy and the intestine. The experimental shear strains, which are the ratios of the intestinal elongation and the intestinal wall thickness, are 50%, 100%, 150% and 200%. The shear stress curves with different strains are obtained by means of curve fitting, and then, the parameters of the five-element model are confirmed (see Table 1).30 The moduli of elasticity and the viscosity coefficients of the five-element model are not constant, but vary with shear strains according to the data in Table 1. Therefore, the relations between the parameters of the five-element model and the shear strains are E1 = 0:1617e2 0:3175e + 3:348 E2 = 0:1729e2 1:078e + 2:078 E3 = 0:1653e2 0:9792e + 1:877
Parameter identification of the five-element model at a relatively higher velocity The classic shear stress relaxation test is not efficient to obtain the parameters of the model when the capsule robot moves at a relatively higher velocity. In other words, the viscoelasticity of intestinal material should be analyzed at a certain frequency. It is called dynamic viscoelasticity. Dynamic viscoelasticity of intestinal material. The constitutive equation of the five-element model needs to be derived according to the model structure and the properties of the springs and dampers31 8 s = s1 + s 2 + s 3 > > > > < e_1 = s_ 1 =E1 + s1 =h1 ð14Þ e_2 = s_ 2 =E2 + s2 =h2 > > s = E e > 3 3 3 > : e = e1 = e2 = e3
ð13Þ
2
h1 = 0:01386e + 0:03667e + 0:0442 h2 = 0:0185e2 0:2205e + 0:6971
Substituting the above parameters to the model, a curve that describes the relation between the interaction force and the velocity of the capsule is obtained. Figure 5 shows the comparison between the experimental results that had been obtained in our previous work18 and the
where s1 , s2 and s3 are the stresses of the three parallel branches of the model, while e1 , e2 and e3 are the strains, respectively. Solving equation (14), we get p0 s + p1 s_ + p2 s € = q0 e + q1 e_ + q2 €e
ð15Þ
where s and e are the stress and strain of the model, respectively
Downloaded from pih.sagepub.com at UNIV CALIFORNIA BERKELEY LIB on March 9, 2015
292
Proc IMechE Part H: J Engineering in Medicine 228(3)
Table 2. Experimental results of the shear test on DMA apparatus. v (Hz)
Sample 1
20 30 40 50 60
Sample 2
Y1 (MPa)
Y2 (MPa)
Y1 (MPa)
Y2 (MPa)
Y1 (MPa)
Y2 (MPa)
0.5494 0.6137 0.4825 0.7850 0.6749
0.4180 0.4507 0.5011 0.6466 0.4706
0.5477 0.6363 0.5042 0.8144 0.6942
0.4150 0.4456 0.5046 0.6600 0.4910
0.5911 0.6616 0.5373 0.8475 0.7358
0.4249 0.4597 0.5272 0.6814 0.5023
p0 = E1 E2 p 1 = E 2 h1 + E 1 h2
Let Y (iv) = Y1 (v) + iY2 (v)
p 2 = h 1 h2 q0 = E1 E2 E3
=
q1 = (E1 + E3 )E2 h1 + (E2 + E3 )E1 h2 q2 = (E1 + E2 + E3 )h1 h2
Equation (15) is the constitutive equation of the fiveelement model. The complex modulus of the intestinal material has something to do with not only the parameters of the five-element model but also the alternative frequency with the action of the alternating strain. Let the strain change with time harmonically e(t) = e0 eivt
2 X dk s pk k = qk (iv)k e0 eivt dt k=0 k=0
ð17Þ
where k = 0, 1 and 2. The stress response is obtained by solving equation (17). The stress response must contain factor eivt because the coefficients pk and qk are all real numbers. Let s(t) = s eivt , where s is the amplitude of the stress. Substituting this equation into equation (17) yields 2 X
k=0
qk (iv)k e0 eivt
ð18Þ
k=0
Let
Q (iv) =
2 X
qk (iv)k
k=0
P (iv) =
2 X
pk (iv)k
k=0
Then, we have
s(t) =
Q (iv)
P (iv)
e(t)
where Y1 (v) is the storage modulus and Y2 (v) is the loss modulus. Solving the equation yields Y1 (v) = E1 E2 E3 (E1 + E2 + E3 )h1 h2 v2 E1 E2 h1 h2 v2 ðE1 E2 h1 h2 v2 Þ2 + (E2 h1 + E1 h2 )2 v2 +
½(E1 + E3 )E2 h1 + (E2 + E3 )E1 h2 ðE2 h1 + E1 h2 Þv2 2
ðE1 E2 h1 h2 v2 Þ + (E2 h1 + E1 h2 )2 v2
Y2 (v) =
½(E1 + E3 )E2 h1 + (E2 + E3 )E1 h2 E1 E2 h1 h2 v2 v
2 X
pk (iv)k s eivt =
Q (iv)
P (iv) q0 + q1 (iv) q2 v2 = p0 + p1 (iv) p2 v2
ð16Þ
where i is the imaginary unit, v is the frequency and e0 is the amplitude of the strain. Substituting equation (16) into the constitutive equation (15) yields
2 X
Sample 3
ð19Þ
2
ðE1 E2 h1 h2 v2 Þ + (E2 h1 + E1 h2 )2 v2 ðE2 h1 + E1 h2 Þ E1 E2 E3 (E1 + E2 + E3 )h1 h2 v2 v
2
ðE1 E2 h1 h2 v2 Þ + (E2 h1 + E1 h2 )2 v2
Shear test with DMA and data processing. Dynamic mechanical analysis (DMA), is a technique where a small deformation is applied to a sample in a cyclic manner. This allows the materials’ response to stress, temperature, frequency and other values to be studied. This technique is appropriate to measure the relationship between the strain and the stress at a certain frequency. The equipment type used in this article is TA Instrument DMA Q800. Fresh intestine of a pig is used in the experiment. The intestine sample is stored in Tyrode with oxygen ventilation. A length of jejunum is chosen as the experimental subject. The jejunum is cut to small square samples whose average length of the side is 5.5 mm. The samples are placed in the shear test fixture and clamped in the direction of the arrows shown in Figure 6. After that the drive unit is controlled to move up and down. The experimental temperature is maintained at 37 °C. The experiment proceeds with a constant strain 4%
Downloaded from pih.sagepub.com at UNIV CALIFORNIA BERKELEY LIB on March 9, 2015
Zhang et al.
293
Figure 6. Shear test on DMA apparatus.
Table 3. Parameter values of the updated five-element model. E1 (kPa)
E2 (kPa)
E3 (kPa)
h1 (kPa)
h2 (kPa)
0.0226
6.6174
1.1917
8.8953 3 1025
0.3122
properties of materials, and the intestinal material has no exception. When the frequency is 20 Hz, the velocity of the shearing motion is 17.6 mm/s, which is calculated according to the size of the sample and the shearing strain. That is to say, the velocity of the shearing motion is higher than 17.6 mm/s when the frequency is greater than 20 Hz. Therefore, it is reasonable that the parameters of the five-element model at a speed range from 20 to 60 mm/s can be obtained from the shear test with DMA. The model-predicted result of the updated interaction model is shown in Figure 7. The data of interaction force ranging from 0 to 20 mm/s are obtained from the model with the parameters obtained by the shear stress relaxation test, while the data ranging from 20 to 60 mm/s are obtained from the updated mode. There is an obvious inflection point at the velocity of approximately 20 mm/s because of the change of the parameters of the five-element model.
Model validation and discussion
Figure 7. Updated interaction model related to the velocity.
and a varying frequency from 20 to 60 Hz. The experimental results of three samples are shown in Table 2. It is acceptable that the maximal deviation in Table 2 is 7.92%. Substituting the average value of the experimental results into the expression of the storage modulus and loss modulus yields the parameter values of the five-element model. These parameter values are shown in Table 3. Comparing with the parameter values of the fiveelement model obtained from the classic shear stress relaxation test, E1 and h1 in Table 3 decrease to a great extent. That is to say, when the frequency is higher than 20 Hz, the five-element model can be simplified to a parallel connection with both a Maxwell model and a spring. It is generally known that the frequency of applied stress or strain has great influence on the mechanical
The validity of the model-predicted results will be verified by an experiment. A homemade mechanical test platform is used in the experiment (see Figure 8). A stepper motor (86BYG350CH; SYNTRON) with its driver (SH32206; SYNTRON) is chosen to drive a guide screw (THK KR55). A micro-force sensor (FUTEK LSB200) is fixed on the slider of the guide screw. The probe of the force sensor is connected to a capsule that is placed inside the intestine with a polymer string. A length of jejunum is also chosen as the experimental subject, which is preconditioned with the same method as in the shear test with DMA. Flexible polyurethane foam (PUF) is used as the basement that is fixed on the load platform. The mesentery and one side of the intestine specimen are fixed on the basement. DAQ system (NI DAQ PCI6229) is used to acquire the voltage signal of the force sensor. Then, the signal is transmitted to the computer for saving and analysis. The capsule moves at a constant velocity in the intestine. The relationship between the velocity and the friction can be obtained with the test platform. Different parts of the intestine have different diameters, wall thicknesses, lengths of intestinal villi and so on. Different parts of the intestine also have different mechanical properties. Therefore, two samples of jejunum are used to overcome the biodiversity and improve the reliability of the experimental results. The experimental results are shown in Figure 9. The variation trends of the two experimental results are similar. It is shown that the results of the verification test are repeatable and reasonable. In addition, the experimental results are similar to those in Zhang et al.18 Figure 9 also shows the comparison between the experimental results and the theoretical results. Next, the goodness
Downloaded from pih.sagepub.com at UNIV CALIFORNIA BERKELEY LIB on March 9, 2015
294
Proc IMechE Part H: J Engineering in Medicine 228(3)
Figure 8. Mechanical test platform. DC: direct current; PUF: polyurethane foam.
Figure 9. Comparison between the theoretical results and the experimental results.
of fit will be estimated by R2 at the velocity larger than 20 mm/s. R2 is the square of the correlation between two sets of data. It is also used to measure how successful the fit is in explaining the variation of the data. The formula of R2 is n P ^ F 2 F(i)
R2 =
i=1 n P
ðF1 (i) FÞ
2
ð20Þ
i=1
where F1 is the theoretical results and F is the experimental results. The R2 between the theoretical results and the experimental results of sample 1 is 0.9928, while that of sample 2 is 0.9901. The analysis shows that the interaction model can describe the interaction force between the capsule and the intestine efficiently, and it is closely related to the intestinal constitutive relation and the capsule’s velocity. The parameters of the fiveelement model are not constant. The classic linear viscoelastic model is not sufficient to describe the material properties of the intestine. Moreover, these parameters
are proved to have something to do with the velocity of the intestinal deformation, which relates to the velocity of the capsule. The intestine is a complex physiological environment, which contains three parts: duodenum, jejunum and ileum. Every part of the intestine has different mechanical characteristics, and the intestine itself has biodiversity. The intestine has the ability to move autonomically, which manifests as periodic haustral segmentation, peristalsis and tonic contraction. This autonomic movement cannot be neglected in intestinal environment modeling. In this article, a length of jejunum is used in the experiment and the intestinal peristalsis is neglected. The interaction model that is applicable to other parts of the intestine will be developed too. More experiments will be done to obtain more accurate and systematic parameters. The wave of intestinal peristalsis is being researched intensively. It will make the interaction model more general. These ideas will also be our future work. Both our work and the research of Kim et al.22 have proved that the five-element model is suitable to describe the viscoelastic property of the intestine. Meanwhile, we find that the parameters of the fiveelement model change when the capsule moves in the intestine at different velocities. This change happens at a speed of approximately 20 mm/s. We speculate that the viscoelastic constitutive equation of the intestine alters when the velocity changes. Some research shows that intestinal mucous layer and muscularis have different material properties. The mucous layer has obviously viscoelastic characteristics, while the muscularis manifests as hyperelasticity.19 The intestine radially deforms with mucous layer’s significant viscoelastic effect when the capsule moves slowly, whereas the hyperelasticity of the muscularis plays a leading role. Therefore, intestinal constitutive model will change with the deformation rate, which is consistent with the experimental results in this article. Whether the velocity boundary between the lower velocity area and the higher velocity area is an accurate value needs to be studied continuously. Currently, most of the capsule robots move at a lower velocity in the intestine, such as bionic movement, spiral movement and legged movement. However, a vibro-impact capsubot with the ‘‘internal force–static friction’’ driving principle, which is first developed by our group, has an instantaneous speed that can reach up to 60 mm/s. A sliding mass reciprocates in the shell of the capsubot with different accelerations, and then, the capsubot can move forward or backward.32 The capsubot can move on a hard surface at an average velocity of 10 mm/s. But the efficiency decreases when the capsubot moves in the intestine. The main reason for the decrease in efficiency is that the control strategy used on the hard surface is used in the intestine directly. The imperfection of the interaction model between the capsule robot and the intestine makes the control strategy difficult to be optimized,
Downloaded from pih.sagepub.com at UNIV CALIFORNIA BERKELEY LIB on March 9, 2015
Zhang et al.
295
especially at a higher velocity. The achievement in this article is hoped to be useful to optimize the control strategy of the capsubot. More work needs to be done to make the capsubot to move in the intestine efficiently.
Conclusion An interaction model is established to describe the interaction force between the intestine and the capsule robot based on the nonlinear viscoelasticity of the intestinal material in this article. The nonlinear viscoelastic model is used to analyze the material properties of the intestine, and its parameters have something to do with the velocity of the intestinal deformation, which relates to the velocity of the capsule. Different experimental methods are used to measure the parameters of the model at different velocities of the capsule robot. The model is proved to be reasonable to describe the interaction force. The achievement in this article is hoped to perfect the interaction model and optimize the control method of the capsule robot, especially the vibro-impact capsubot. Declaration of conflicting interests The authors declare that there is no conflict of interest. Funding This work was supported by the National Natural Science Foundation of China (No. 61105099) and the National Technology R&D Program of China (No. 2012BAI14B03). References 1. Rey JF, Ogata H, Hosoe N, et al. Feasibility of stomach exploration with a guided capsule endoscope. Endoscopy 2010; 42: 541–545. 2. Iddan G, Meron G, Glukhovsky A, et al. Wireless capsule endoscopy. Nature 2000; 405: 417. 3. Carey EJ, Leighton JA, Heigh RI, et al. A single-center experience of 260 consecutive patients undergoing capsule endoscopy for obscure gastrointestinal bleeding. Am J Gastroenterol 2007; 102: 89–95. 4. Wang K, Wang Z, Zhou Y, et al. Squirm robot with full bellow skin for colonoscopy. In: Proceedings of the 2010 IEEE international conference on robotics and biomimetics, Tianjin, China, 14–18 December 2010, pp.53–57. New York: IEEE. 5. Quaglia C, Buselli E, Webster RJ, et al. An endoscopic capsule robot: a meso-scale engineering case study. J Micromech Microeng 2009; 19: 105007 (11 pp.). 6. Yang WA, Hu C, Meng MQH, et al. A new 6D magnetic localization technique for wireless capsule endoscope based on a rectangle magnet. Chinese J Electron 2010; 19: 360–364. 7. Gao M, Hu C, Chen Z, et al. Design and fabrication of a magnetic propulsion system for self-propelled capsule endoscope. IEEE Trans Biomed Eng 2010; 57: 2891–2902.
8. Wang XN, Meng QH and Chen XJ. A locomotion mechanism with external magnetic guidance for active capsule endoscope. In: Proceedings of the 2010 annual international conference of the IEEE, engineering in medicine and biology society (EMBC), Buenos Aires, Argentina, 31 August–4 September 2010, pp.4375–4378. New York: IEEE. 9. Kim B, Park S and Park JO. Microrobots for a capsule endoscope. In: Proceedings of the IEEE/ASME international conference on advanced intelligent mechatronics 2009, Singapore, 14–17 July 2009, pp.729–734. New York: IEEE. 10. Kim Y-T and Kim D-E. A novel propelling mechanism based on frictional interaction for endoscope robot. Adv Trib 2009; 288: 859–860. 11. Ito T, Ogushi T and Hayashi T. Impulse-driven capsule by coil-induced magnetic field implementation. Mech Mach Theory 2010; 45: 1642–1650. 12. Li H, Katsuhisa F and Chernousko FL. Motion generation of the capsubot using internal force and static friction. In: Proceedings of the 45th IEEE conference on decision and control, San Diego, CA, 13–15 December 2006, pp.6575–6580. New York: IEEE. 13. Kim B, Lee MG, Lee YP, et al. An earthworm-like micro robot using shape memory alloy actuator. Sensor Actuat A: Phys 2006; 125: 429–437. 14. Hoeg HD, Slatkin AB, Burdick JW, et al. Biomechanical modeling of the small intestine as required for the design and operation of a robotic endoscope. In: Proceedings of IEEE international conference on robotics and automation, San Francisco, CA, 24–28 April 2000, pp.1599–1606. New York: IEEE. 15. Li J, Huang P and Luo HD. Experimental study on friction of micro machines sliding in animal intestines. Lubr Eng 2006; 175: 119–122. 16. Wang X and Meng MQH. An experimental study of resistant properties of the small intestine for an active capsule endoscope. Proc IMechE, Part H: J Engineering in Medicine 2010; 224: 107–118. 17. Wang KD and Yan GZ. Research on measurement and modeling of the gastro intestine’s frictional characteristics. Meas Sci Technol 2009; 20015803. 18. Zhang C, Su G, Tan R, et al. Experimental investigation of the intestine’s friction characteristic based on ‘‘internal force-static friction’’ capsubot. In: Proceedings of the IASTED international conference on biomedical engineering, BioMed 2011, Innsbruck, 16–18 February 2011, pp.117–123. Calgary: IASTED. 19. Ciarletta P, Dario P, Tendick F, et al. Hyperelastic model of anisotropic fiber reinforcements within intestinal walls for applications in medical robotics. Int J Robot Res 2009; 28: 1279–1288. 20. Woo SH, Kim TW, Mohy-Ud-Din Z, et al. Small intestinal model for electrically propelled capsule endoscopy. Biomed Eng Online 2011; 10: 108. 21. Baek NK, Sung IH and Kim DE. Frictional resistance characteristics of a capsule inside the intestine for microendoscope design. Proc IMechE, Part H: J Engineering in Medicine 2004; 218: 193–201. 22. Kim JS, Sung IH, Kim YT, et al. Experimental investigation of frictional and viscoelastic properties of intestine for microendoscope application. Tribol Lett 2006; 22: 143–149.
Downloaded from pih.sagepub.com at UNIV CALIFORNIA BERKELEY LIB on March 9, 2015
296
Proc IMechE Part H: J Engineering in Medicine 228(3)
23. Kim JS, Sung IH, Kim YT, et al. Analytical model development for the prediction of the frictional resistance of a capsule endoscope inside an intestine. Proc IMechE, Part H: J Engineering in Medicine 2007; 221: 837–845. 24. Zhang C, Liu H, Su G, et al. Research of intestines’ dynamic viscoelasticity based on five-element model. Gaojishu Tongxin/Chin High Technol Lett 2012; 22: 964– 968. 25. Zhang C, Liu H, Tan RJ, et al. Modeling of velocitydependent frictional resistance of a capsule robot inside an intestine. Tribol Lett 2012; 47: 295–301. 26. Gregersen H. Biomechanics of the gastrointestinal tract: new perspectives in motility research and diagnostics. 1st ed. New York: Springer, 2003, p.283. 27. Wu JH, Cheng XY, Wei YL, et al. Rheological behavior of dog’s small intestinal mucus. J Chongqing Univ (Natural Science Edition) 2000; 23: 10–12. 28. Varum FJO, Veiga F, Sousa JS, et al. An investigation into the role of mucus thickness on mucoadhesion in the
29.
30.
31. 32.
gastrointestinal tract of pig. Eur J Pharm Sci 2010; 40: 335–341. Lyle AB, Luftig JT and Rentschler ME. A tribological investigation of the small bowel lumen surface. Tribol Int 2013; 62: 171–176. Tan R, Liu H, Su G, et al. Experimental investigation of the small intestine’s viscoelasticity for the motion of capsule robot. In: Proceedings of the IEEE international conference on mechatronics and automation, ICMA 2011, Beijing, China, 7–10 August 2011, pp.249–253. New York: IEEE Computer Society. Christensen RM. Theory of viscoelasticity. Mineola, NY: Dover Publications, 2003. Namkon Lee NK, Li Hongyi, Furuta Katsuhisa, et al. Control system design and experimental verification of capsubot. In: Proceedings of the IEEE/RSJ international conference on intelligent robots and systems, Nice, 22–26 September 2008, pp.1927–1932. New York: IEEE.
Downloaded from pih.sagepub.com at UNIV CALIFORNIA BERKELEY LIB on March 9, 2015
Interaction model between capsule robot and intestine based on nonlinear viscoelasticity
Proc IMechE Part H: J Engineering in Medicine 2014, Vol. 228(3) 287–296 Ó IMechE 2014 Reprints and permissions: sagepub.co.uk/journalsPermissions.nav DOI: 10.1177/0954411914523404 pih.sagepub.com
Cheng Zhang1,2, Hao Liu1, Renjia Tan1,2 and Hongyi Li1
Abstract Active capsule endoscope could also be called capsule robot, has been developed from laboratory research to clinical application. However, the system still has defects, such as poor controllability and failing to realize automatic checks. The imperfection of the interaction model between capsule robot and intestine is one of the dominating reasons causing the above problems. A model is hoped to be established for the control method of the capsule robot in this article. It is established based on nonlinear viscoelasticity. The interaction force of the model consists of environmental resistance, viscous resistance and Coulomb friction. The parameters of the model are identified by experimental investigation. Different methods are used in the experiment to obtain different values of the same parameter at different velocities. The model is proved to be valid by experimental verification. The achievement in this article is the attempted perfection of an interaction model. It is hoped that the model can optimize the control method of the capsule robot in the future.
Keywords Interaction model, nonlinear viscoelasticity, intestine, capsule robot, dynamic mechanical analyzer
Date received: 26 May 2013; accepted: 10 January 2014
Introduction A robotic capsule endoscope that can move actively with the doctor’s operation has been not only the development direction of the capsule endoscopy but also a research hotspot in the field of robotics and medicine over recent decades. A magnetically guided capsule endoscope (MGCE) system had been developed by Siemens and Olympus, and more than 50 people conducted clinical practice at 2010.1 It is another landmark achievement after the first passive capsule endoscopy developed by Given Imaging at 2001.2 The MGCE system can only examine the stomach in clinic and need to be operated by the doctor in the entire checking process, although it solves some of the problems of the passive capsule endoscopy, such as time-consuming, misdiagnosis and ileus.3 The deficiency of the interaction model between capsule robot and intestine may be one of the dominating reasons that the MGCE system abandons the inspection in the gastrointestinal tract. As the main environment of the capsule endoscopy, the intestine is a complex flexible lumen, the inwall of which is covered by mucus. Any drive mode4–13 cannot neglect the influence of this complex environment on the capsule robot’s motion when the capsule robot
moves in the intestine. Currently, no mathematical model can describe the interaction force between the capsule robot and the intestine precisely. Many developers are engaged in the field of intestinal environment modeling. Hoeg et al. studied the tissue distention of the intestine under the condition of a robotic endoscope moving through. An analytical model and an experimental model were developed to predict the tissue behavior when the intestine was expanded.14 Huang and colleagues15 analyzed the interactive feature changes under the influence of various diameters, lengths and materials of the capsule robot by means of experimental investigation. Some similar researches were carried out by Wang and Meng,16 Wang and Yan17 and our group18 as well. Ciarletta et al.19 used the theory of hyperelasticity to make a stratified analysis of the 1
State Key Laboratory of Robotics, Shenyang Institute of Automation, Chinese Academy of Science, Shenyang, China 2 University of Chinese Academy of Sciences, Beijing, China Corresponding author: Hao Liu, State Key Laboratory of Robotics, Shenyang Institute of Automation, Chinese Academy of Science, Shenyang 110016, China. Email: [email protected]
Downloaded from pih.sagepub.com at UNIV CALIFORNIA BERKELEY LIB on March 9, 2015
288
Proc IMechE Part H: J Engineering in Medicine 228(3)
intestinal wall. The hyperelastic model is inapplicable to research the intestinal material property because it neglects the time effect. Woo et al.20 considered the interactive feature using a thin-walled model and Stokes’ drag equation. However, the model cannot fully describe the material characteristics of the intestine. Most of these research works establish a qualitative empirical interaction model by experimental investigation. In addition, the features of the capsule robot also affect the interaction force. These features contain not only dimension parameters but also motion parameters. At present, the viscoelastic constitutive relation is supposed to be the most effective method of describing the material properties of the intestine. Baek et al.21 investigated the frictional resistance of a capsule inside the porcine small intestine with respect to various capsule shapes using a specially designed tribological tester. Then, the group found that variations of resistance were correlated with the linear viscoelasticity of the intestine. A five-element model is used to describe the linear viscoelastic property of the intestine’s stress relaxation.22 Furthermore, the group first developed an analytical model for the frictional resistance prediction that was verified by finite element analyses.23 In our study, we show that the parameters in the viscoelastic constitutive relation are not constant.24 In other words, the linear viscoelastic constitutive relation is insufficient to describe the intestinal material property. Most researchers used in vitro experiment instead of in vivo experiment in the study process because the latter costs more and is difficult to carry out. It is considered a more convenient choice to simulate the in vivo environment in the in vitro experiment. In this article, an interaction model between the capsule robot and the intestine is developed to solve the problem that the capsule robot cannot complete the controlled movement in the intestine. The model has something to do with the motion parameters of the capsule and the nonlinear viscoelasticity of the intestine. The model parameters are identified by static mechanical test, such as shear stress relaxation test, and dynamic mechanical test with dynamic mechanical analyzer (DMA). At last, the validity of the model is verified by in vitro experiment. The achievement in this article is hoped to optimize the control method of the capsule robot.
Interaction model between capsule robot and intestine The interaction model is affected by the properties of the capsule robot and intestinal material parameters. The intestine is expanded when the capsule moves inside because of the intestinal contraction in a relaxed state (see Figure 1). The shape of the capsule is a cylinder in the middle section and two hemispheres on both ends. The middle section is acted upon by a radial pressure and axial friction, while the pressure perpendicular
Figure 1. Schematic diagram of the intestinal deformation with the insertion of a smooth capsule.25
to the contour line of the capsule is applied on the both ends of the capsule. When the capsule moves forward, the pressure on the rear end can be ignored. The interaction force along the x-direction is more important to the capsule robot’s movement, so it can be expressed as a resultant force of environmental resistance, viscous resistance and Coulomb friction25 F = Fe + Fv + Fc
ð1Þ
where Fe is the environmental resistance, Fv is the viscous resistance and Fc is the Coulomb friction. Environmental resistance is induced by the stress due to the viscoelastic deformation of the intestinal wall. Viscous resistance is caused by the rheological properties of the intestinal mucus. Coulomb friction is a product of the local contact pressure and the Coulomb friction coefficient. Then, environmental resistance, viscous resistance and Coulomb friction will be analyzed.
Intestinal deformation and environmental resistance analyses Principle of environmental resistance and assumptions. The deformation of the intestinal wall is the major influencing factor of the environmental resistance. As the front of the capsule is a hemisphere, the intestinal wall applies a contact force on its contact surface. The horizontal component of the contact force is defined as Fe . For further development of the model, the following assumptions should be made. 1. 2. 3.
The material of the intestine is incompressible. The intestine consists of an isotropic material and deforms symmetrically toward its radial direction. The deformation of the intestine is the same as the external shape of the contact surface of the capsule.
Based on the assumptions above, the deformation could be derived using the contact geometry between the intestine and the capsule.
Downloaded from pih.sagepub.com at UNIV CALIFORNIA BERKELEY LIB on March 9, 2015
Zhang et al.
289
Formula derivation of intestinal deformation and environmental resistance. The contact force is mainly caused by the hoop stress of the intestine. The relationship between the pressure P(x) and the hoop stress tu (x) can be expressed as ð2Þ
where Di (x) and lm are the inner diameter and the average wall thickness of the intestine at position x along the length of the intestine, respectively.26 A five-element model had been used to describe porcine intestinal constitutive relation.22 It consists of three springs and two dampers (see Figure 2). An equation that shows the relation between stress and strain with respect to time is obtained from the results of a stress relaxation test " # E t
h1
E t
h2
+ E2 e
1
+ E3
2
ð3Þ
where E1 , E2 and E3 indicate the moduli of elasticity of springs, while h1 and h2 are the viscosity coefficients of the dampers. e(t) and tu (t) are the strain and stress applied to the intestine, respectively, at the time t. When the capsule moves at a constant speed v, equation (3) can be written as a function of the position x " # E x
t u (x) = e(x) E1 e
Di (x) Di0 Di0
h1 v 1
E x
+ E2 e
h2 v 2
+ E3
ð4Þ
ð6Þ
Therefore, the contact pressure is " E x
e(x) E1 e
P(x)Di (x) t u (x) = 2lm
t u (t) = e(t) E1 e
e(x) =
h1 v 1
E x
+ E2 e
P(x) =
Di (x)
Di0 = 2R cos a
ð5Þ
where R is the radius of the hemisphere and a is the initial angle corresponding with the contact surface. The hoop strain with respect to position is defined as
2
# + E3 2lm ð7Þ
Then, the environmental resistance induced by the stress is R sin ða
Fe =
2pRP(x)dx 3 sin u
ð8Þ
0
where u is the angle of the equivalent contact force. The environmental resistance Fe varies not only with the intestinal constitutive parameters but also with the velocity of the capsule according to equation (8).
Viscous resistance analyses There is lot of mucus in the intestine because of its own physiological structure. The capsule robot is in complete lubrication condition in the whole moving process approximately. Viscous resistance is related to the relative velocity. It can be calculated from the empirical equation Fv = dv
The initial mean diameter of the intestinal inwall approximately equals
h2 v
ð9Þ
where d is the apparent viscosity coefficient. The intestinal mucus is a kind of non-Newtonian fluid. Its apparent viscosity decreases with increase in shear rate. When the shear rate is high enough, the apparent viscosity of the intestinal mucus becomes a constant. The apparent viscosity coefficient can be expressed as27 v0:7552 d = 11:24 + 0:1148 ð10Þ d where d is the mean value of the intestinal mucus thickness. The intestinal environment is complex. Different parts of the intestine have different morphology, such as mucus thickness and length of intestinal villi. The intestinal mucus thickness also varies depending on the force on the intestinal surface. An approximate value of d will be used in the model.
Coulomb friction analyses Coulomb friction is decided by the local contact pressure and the Coulomb friction coefficient Fc = mN
Figure 2. Five-element model.25
ð11Þ
where m is the Coulomb friction coefficient and N is the local contact pressure. The Coulomb friction coefficient is influenced by the surface texture of the intestine, especially the intestinal villi. The value of m can be
Downloaded from pih.sagepub.com at UNIV CALIFORNIA BERKELEY LIB on March 9, 2015
290
Proc IMechE Part H: J Engineering in Medicine 228(3)
calculated from the experimental results. The local contact pressure consists of the normal force and the radial pressure. The normal force is decided by the weight of the capsule, while the radial pressure is caused by the hoop stress of the intestine. The radial pressure is the vertical component of the skew resistance on the hemisphere of the capsule. The local contact pressure is expressed as R sin ða
N = mg +
2pRP(x)dx 3 cos u 0
R sinða + L
+
ð12Þ
2pRP(x)dx
Figure 3. Physical simulation measurement system.
R sin a
where m is the mass of the capsule and L is the length of the capsule’s middle section.
Model parameter identification Several parameters should be confirmed to complete the model. Some parameters are predetermined, others need to be determined by experience and some must be measured by experiment. The material, mass and dimension of the capsule are predetermined. The material is polydimethylsiloxane (PDMS). The mass m is 50.1 g. The length of middle section, that is, a cylinder, L is 20 mm, while the radius of the end, that is, a hemisphere, R is 6.5 mm. Based on practical experience, the initial angle corresponding with the contact surface a is 60°, the angle of the equivalent contact force u is 30°, the average intestinal wall thickness lm is 2.5 mm and the mean value of the intestinal mucus thickness d is 30 mm.28 The Coulomb friction coefficient and the parameters of the five-element model need to be measured by experiment.
Experiment of measuring Coulomb friction coefficient A custom-made physical simulation measurement system is used to measure the Coulomb friction coefficient. It consists of two parts: drive unit and data acquisition (DAQ) unit (see Figure 3). The main part of the drive unit is a NLA-7SL series coreless linear motor, which is produced by NIKKI DENSO. The encoder is RGH22X-lum resolution, which is produced by RENISHAW. The positioning accuracy of the system can reach 61 mm. The rotor of the linear motor is combined with a support, on which a single-degree-of-freedom micro-force sensor is fixed, whose accuracy is 1 mN. The right side of the drive unit is load platform. PCI 6229 DAQ card produced by NI is used to acquire the voltage signal of encoder and micro-force sensor. Then, the signal is transmitted to computer for saving and analysis. The negative pressure suction device is used to clamp the intestine and
Figure 4. 3D model of negative pressure suction device.25
make it expand to 13 mm (see Figure 4). After both ends of the intestine are fixed, the air in vacuum bin is extracted from bleeder hole with a syringe. Then, the intestinal wall is absorbed by the device and expanded compulsively. The device is fixed on the load platform, and a capsule dummy is inserted into the intestine that is fully expanded. Fresh intestine of a pig is used in the experiment. The intestine sample is stored and cleaned in Tyrode with oxygen ventilation. A length of intestine is placed in the negative pressure suction device. Then, the Coulomb friction is only caused by the weight of the capsule. The capsule whose dimension parameters are the same as that stated in the model is dragged by the drive unit at a speed of 0.5 mm/s. The mean value of Coulomb friction that is measured by the micro-force sensor is Fc = 40:07 mN. The Coulomb friction coefficient is m = 0:082 by calculation. This result agrees with the conclusion of Rentschler and colleagues.29
Experiment of measuring the parameters of the fiveelement model A shear stress relaxation test is used to measure the parameters of the five-element model also with the homemade physical simulation measurement system.
Downloaded from pih.sagepub.com at UNIV CALIFORNIA BERKELEY LIB on March 9, 2015
Zhang et al.
291
Table 1. Experimental results of the parameters of the five-element model.25 Shear strain (%)
E1 (kPa)
E2 (kPa)
E3 (kPa)
h1 (kPa)
h2 (kPa)
50 100 150 200
2.926 3.159 2.781 1.726
1.539 1.216 0.948 0.484
1.422 1.064 0.812 0.541
0.053 0.078 0.067 0.060
0.561 0.555 0.393 0.320
model-predicted results. Different contributions are made by three components of the force in the model. Environmental resistance is affected by the velocity greatly and occupies a major share in the frictional resistance. Viscous friction is also affected by the velocity, but in a small proportion. Coulomb friction has little relationship with the velocity. Therefore, the influence of the inaccuracy of the mucus thickness can be ignored easily. It is shown that the effect of the model prediction is great at the velocity lower than 20 mm/s, but that at a speed range from 20 to 60 mm/s is not satisfactory in Figure 5. We deduce that the parameters of the five-element model may be changed at a relatively higher velocity. Therefore, a new experimental method is proposed to accomplish the parameter identification.
Figure 5. Comparative data of the relation between the interaction force and the velocity.25
The capsule dummy is changed to a cylinder, whose diameter is 12.9 mm and length is 15.2 mm, and there are asperities on its surface. These asperities will ensure that there is no relative slippage between the dummy and the intestine. The experimental shear strains, which are the ratios of the intestinal elongation and the intestinal wall thickness, are 50%, 100%, 150% and 200%. The shear stress curves with different strains are obtained by means of curve fitting, and then, the parameters of the five-element model are confirmed (see Table 1).30 The moduli of elasticity and the viscosity coefficients of the five-element model are not constant, but vary with shear strains according to the data in Table 1. Therefore, the relations between the parameters of the five-element model and the shear strains are E1 = 0:1617e2 0:3175e + 3:348 E2 = 0:1729e2 1:078e + 2:078 E3 = 0:1653e2 0:9792e + 1:877
Parameter identification of the five-element model at a relatively higher velocity The classic shear stress relaxation test is not efficient to obtain the parameters of the model when the capsule robot moves at a relatively higher velocity. In other words, the viscoelasticity of intestinal material should be analyzed at a certain frequency. It is called dynamic viscoelasticity. Dynamic viscoelasticity of intestinal material. The constitutive equation of the five-element model needs to be derived according to the model structure and the properties of the springs and dampers31 8 s = s1 + s 2 + s 3 > > > > < e_1 = s_ 1 =E1 + s1 =h1 ð14Þ e_2 = s_ 2 =E2 + s2 =h2 > > s = E e > 3 3 3 > : e = e1 = e2 = e3
ð13Þ
2
h1 = 0:01386e + 0:03667e + 0:0442 h2 = 0:0185e2 0:2205e + 0:6971
Substituting the above parameters to the model, a curve that describes the relation between the interaction force and the velocity of the capsule is obtained. Figure 5 shows the comparison between the experimental results that had been obtained in our previous work18 and the
where s1 , s2 and s3 are the stresses of the three parallel branches of the model, while e1 , e2 and e3 are the strains, respectively. Solving equation (14), we get p0 s + p1 s_ + p2 s € = q0 e + q1 e_ + q2 €e
ð15Þ
where s and e are the stress and strain of the model, respectively
Downloaded from pih.sagepub.com at UNIV CALIFORNIA BERKELEY LIB on March 9, 2015
292
Proc IMechE Part H: J Engineering in Medicine 228(3)
Table 2. Experimental results of the shear test on DMA apparatus. v (Hz)
Sample 1
20 30 40 50 60
Sample 2
Y1 (MPa)
Y2 (MPa)
Y1 (MPa)
Y2 (MPa)
Y1 (MPa)
Y2 (MPa)
0.5494 0.6137 0.4825 0.7850 0.6749
0.4180 0.4507 0.5011 0.6466 0.4706
0.5477 0.6363 0.5042 0.8144 0.6942
0.4150 0.4456 0.5046 0.6600 0.4910
0.5911 0.6616 0.5373 0.8475 0.7358
0.4249 0.4597 0.5272 0.6814 0.5023
p0 = E1 E2 p 1 = E 2 h1 + E 1 h2
Let Y (iv) = Y1 (v) + iY2 (v)
p 2 = h 1 h2 q0 = E1 E2 E3
=
q1 = (E1 + E3 )E2 h1 + (E2 + E3 )E1 h2 q2 = (E1 + E2 + E3 )h1 h2
Equation (15) is the constitutive equation of the fiveelement model. The complex modulus of the intestinal material has something to do with not only the parameters of the five-element model but also the alternative frequency with the action of the alternating strain. Let the strain change with time harmonically e(t) = e0 eivt
2 X dk s pk k = qk (iv)k e0 eivt dt k=0 k=0
ð17Þ
where k = 0, 1 and 2. The stress response is obtained by solving equation (17). The stress response must contain factor eivt because the coefficients pk and qk are all real numbers. Let s(t) = s eivt , where s is the amplitude of the stress. Substituting this equation into equation (17) yields 2 X
k=0
qk (iv)k e0 eivt
ð18Þ
k=0
Let
Q (iv) =
2 X
qk (iv)k
k=0
P (iv) =
2 X
pk (iv)k
k=0
Then, we have
s(t) =
Q (iv)
P (iv)
e(t)
where Y1 (v) is the storage modulus and Y2 (v) is the loss modulus. Solving the equation yields Y1 (v) = E1 E2 E3 (E1 + E2 + E3 )h1 h2 v2 E1 E2 h1 h2 v2 ðE1 E2 h1 h2 v2 Þ2 + (E2 h1 + E1 h2 )2 v2 +
½(E1 + E3 )E2 h1 + (E2 + E3 )E1 h2 ðE2 h1 + E1 h2 Þv2 2
ðE1 E2 h1 h2 v2 Þ + (E2 h1 + E1 h2 )2 v2
Y2 (v) =
½(E1 + E3 )E2 h1 + (E2 + E3 )E1 h2 E1 E2 h1 h2 v2 v
2 X
pk (iv)k s eivt =
Q (iv)
P (iv) q0 + q1 (iv) q2 v2 = p0 + p1 (iv) p2 v2
ð16Þ
where i is the imaginary unit, v is the frequency and e0 is the amplitude of the strain. Substituting equation (16) into the constitutive equation (15) yields
2 X
Sample 3
ð19Þ
2
ðE1 E2 h1 h2 v2 Þ + (E2 h1 + E1 h2 )2 v2 ðE2 h1 + E1 h2 Þ E1 E2 E3 (E1 + E2 + E3 )h1 h2 v2 v
2
ðE1 E2 h1 h2 v2 Þ + (E2 h1 + E1 h2 )2 v2
Shear test with DMA and data processing. Dynamic mechanical analysis (DMA), is a technique where a small deformation is applied to a sample in a cyclic manner. This allows the materials’ response to stress, temperature, frequency and other values to be studied. This technique is appropriate to measure the relationship between the strain and the stress at a certain frequency. The equipment type used in this article is TA Instrument DMA Q800. Fresh intestine of a pig is used in the experiment. The intestine sample is stored in Tyrode with oxygen ventilation. A length of jejunum is chosen as the experimental subject. The jejunum is cut to small square samples whose average length of the side is 5.5 mm. The samples are placed in the shear test fixture and clamped in the direction of the arrows shown in Figure 6. After that the drive unit is controlled to move up and down. The experimental temperature is maintained at 37 °C. The experiment proceeds with a constant strain 4%
Downloaded from pih.sagepub.com at UNIV CALIFORNIA BERKELEY LIB on March 9, 2015
Zhang et al.
293
Figure 6. Shear test on DMA apparatus.
Table 3. Parameter values of the updated five-element model. E1 (kPa)
E2 (kPa)
E3 (kPa)
h1 (kPa)
h2 (kPa)
0.0226
6.6174
1.1917
8.8953 3 1025
0.3122
properties of materials, and the intestinal material has no exception. When the frequency is 20 Hz, the velocity of the shearing motion is 17.6 mm/s, which is calculated according to the size of the sample and the shearing strain. That is to say, the velocity of the shearing motion is higher than 17.6 mm/s when the frequency is greater than 20 Hz. Therefore, it is reasonable that the parameters of the five-element model at a speed range from 20 to 60 mm/s can be obtained from the shear test with DMA. The model-predicted result of the updated interaction model is shown in Figure 7. The data of interaction force ranging from 0 to 20 mm/s are obtained from the model with the parameters obtained by the shear stress relaxation test, while the data ranging from 20 to 60 mm/s are obtained from the updated mode. There is an obvious inflection point at the velocity of approximately 20 mm/s because of the change of the parameters of the five-element model.
Model validation and discussion
Figure 7. Updated interaction model related to the velocity.
and a varying frequency from 20 to 60 Hz. The experimental results of three samples are shown in Table 2. It is acceptable that the maximal deviation in Table 2 is 7.92%. Substituting the average value of the experimental results into the expression of the storage modulus and loss modulus yields the parameter values of the five-element model. These parameter values are shown in Table 3. Comparing with the parameter values of the fiveelement model obtained from the classic shear stress relaxation test, E1 and h1 in Table 3 decrease to a great extent. That is to say, when the frequency is higher than 20 Hz, the five-element model can be simplified to a parallel connection with both a Maxwell model and a spring. It is generally known that the frequency of applied stress or strain has great influence on the mechanical
The validity of the model-predicted results will be verified by an experiment. A homemade mechanical test platform is used in the experiment (see Figure 8). A stepper motor (86BYG350CH; SYNTRON) with its driver (SH32206; SYNTRON) is chosen to drive a guide screw (THK KR55). A micro-force sensor (FUTEK LSB200) is fixed on the slider of the guide screw. The probe of the force sensor is connected to a capsule that is placed inside the intestine with a polymer string. A length of jejunum is also chosen as the experimental subject, which is preconditioned with the same method as in the shear test with DMA. Flexible polyurethane foam (PUF) is used as the basement that is fixed on the load platform. The mesentery and one side of the intestine specimen are fixed on the basement. DAQ system (NI DAQ PCI6229) is used to acquire the voltage signal of the force sensor. Then, the signal is transmitted to the computer for saving and analysis. The capsule moves at a constant velocity in the intestine. The relationship between the velocity and the friction can be obtained with the test platform. Different parts of the intestine have different diameters, wall thicknesses, lengths of intestinal villi and so on. Different parts of the intestine also have different mechanical properties. Therefore, two samples of jejunum are used to overcome the biodiversity and improve the reliability of the experimental results. The experimental results are shown in Figure 9. The variation trends of the two experimental results are similar. It is shown that the results of the verification test are repeatable and reasonable. In addition, the experimental results are similar to those in Zhang et al.18 Figure 9 also shows the comparison between the experimental results and the theoretical results. Next, the goodness
Downloaded from pih.sagepub.com at UNIV CALIFORNIA BERKELEY LIB on March 9, 2015
294
Proc IMechE Part H: J Engineering in Medicine 228(3)
Figure 8. Mechanical test platform. DC: direct current; PUF: polyurethane foam.
Figure 9. Comparison between the theoretical results and the experimental results.
of fit will be estimated by R2 at the velocity larger than 20 mm/s. R2 is the square of the correlation between two sets of data. It is also used to measure how successful the fit is in explaining the variation of the data. The formula of R2 is n P ^ F 2 F(i)
R2 =
i=1 n P
ðF1 (i) FÞ
2
ð20Þ
i=1
where F1 is the theoretical results and F is the experimental results. The R2 between the theoretical results and the experimental results of sample 1 is 0.9928, while that of sample 2 is 0.9901. The analysis shows that the interaction model can describe the interaction force between the capsule and the intestine efficiently, and it is closely related to the intestinal constitutive relation and the capsule’s velocity. The parameters of the fiveelement model are not constant. The classic linear viscoelastic model is not sufficient to describe the material properties of the intestine. Moreover, these parameters
are proved to have something to do with the velocity of the intestinal deformation, which relates to the velocity of the capsule. The intestine is a complex physiological environment, which contains three parts: duodenum, jejunum and ileum. Every part of the intestine has different mechanical characteristics, and the intestine itself has biodiversity. The intestine has the ability to move autonomically, which manifests as periodic haustral segmentation, peristalsis and tonic contraction. This autonomic movement cannot be neglected in intestinal environment modeling. In this article, a length of jejunum is used in the experiment and the intestinal peristalsis is neglected. The interaction model that is applicable to other parts of the intestine will be developed too. More experiments will be done to obtain more accurate and systematic parameters. The wave of intestinal peristalsis is being researched intensively. It will make the interaction model more general. These ideas will also be our future work. Both our work and the research of Kim et al.22 have proved that the five-element model is suitable to describe the viscoelastic property of the intestine. Meanwhile, we find that the parameters of the fiveelement model change when the capsule moves in the intestine at different velocities. This change happens at a speed of approximately 20 mm/s. We speculate that the viscoelastic constitutive equation of the intestine alters when the velocity changes. Some research shows that intestinal mucous layer and muscularis have different material properties. The mucous layer has obviously viscoelastic characteristics, while the muscularis manifests as hyperelasticity.19 The intestine radially deforms with mucous layer’s significant viscoelastic effect when the capsule moves slowly, whereas the hyperelasticity of the muscularis plays a leading role. Therefore, intestinal constitutive model will change with the deformation rate, which is consistent with the experimental results in this article. Whether the velocity boundary between the lower velocity area and the higher velocity area is an accurate value needs to be studied continuously. Currently, most of the capsule robots move at a lower velocity in the intestine, such as bionic movement, spiral movement and legged movement. However, a vibro-impact capsubot with the ‘‘internal force–static friction’’ driving principle, which is first developed by our group, has an instantaneous speed that can reach up to 60 mm/s. A sliding mass reciprocates in the shell of the capsubot with different accelerations, and then, the capsubot can move forward or backward.32 The capsubot can move on a hard surface at an average velocity of 10 mm/s. But the efficiency decreases when the capsubot moves in the intestine. The main reason for the decrease in efficiency is that the control strategy used on the hard surface is used in the intestine directly. The imperfection of the interaction model between the capsule robot and the intestine makes the control strategy difficult to be optimized,
Downloaded from pih.sagepub.com at UNIV CALIFORNIA BERKELEY LIB on March 9, 2015
Zhang et al.
295
especially at a higher velocity. The achievement in this article is hoped to be useful to optimize the control strategy of the capsubot. More work needs to be done to make the capsubot to move in the intestine efficiently.
Conclusion An interaction model is established to describe the interaction force between the intestine and the capsule robot based on the nonlinear viscoelasticity of the intestinal material in this article. The nonlinear viscoelastic model is used to analyze the material properties of the intestine, and its parameters have something to do with the velocity of the intestinal deformation, which relates to the velocity of the capsule. Different experimental methods are used to measure the parameters of the model at different velocities of the capsule robot. The model is proved to be reasonable to describe the interaction force. The achievement in this article is hoped to perfect the interaction model and optimize the control method of the capsule robot, especially the vibro-impact capsubot. Declaration of conflicting interests The authors declare that there is no conflict of interest. Funding This work was supported by the National Natural Science Foundation of China (No. 61105099) and the National Technology R&D Program of China (No. 2012BAI14B03). References 1. Rey JF, Ogata H, Hosoe N, et al. Feasibility of stomach exploration with a guided capsule endoscope. Endoscopy 2010; 42: 541–545. 2. Iddan G, Meron G, Glukhovsky A, et al. Wireless capsule endoscopy. Nature 2000; 405: 417. 3. Carey EJ, Leighton JA, Heigh RI, et al. A single-center experience of 260 consecutive patients undergoing capsule endoscopy for obscure gastrointestinal bleeding. Am J Gastroenterol 2007; 102: 89–95. 4. Wang K, Wang Z, Zhou Y, et al. Squirm robot with full bellow skin for colonoscopy. In: Proceedings of the 2010 IEEE international conference on robotics and biomimetics, Tianjin, China, 14–18 December 2010, pp.53–57. New York: IEEE. 5. Quaglia C, Buselli E, Webster RJ, et al. An endoscopic capsule robot: a meso-scale engineering case study. J Micromech Microeng 2009; 19: 105007 (11 pp.). 6. Yang WA, Hu C, Meng MQH, et al. A new 6D magnetic localization technique for wireless capsule endoscope based on a rectangle magnet. Chinese J Electron 2010; 19: 360–364. 7. Gao M, Hu C, Chen Z, et al. Design and fabrication of a magnetic propulsion system for self-propelled capsule endoscope. IEEE Trans Biomed Eng 2010; 57: 2891–2902.
8. Wang XN, Meng QH and Chen XJ. A locomotion mechanism with external magnetic guidance for active capsule endoscope. In: Proceedings of the 2010 annual international conference of the IEEE, engineering in medicine and biology society (EMBC), Buenos Aires, Argentina, 31 August–4 September 2010, pp.4375–4378. New York: IEEE. 9. Kim B, Park S and Park JO. Microrobots for a capsule endoscope. In: Proceedings of the IEEE/ASME international conference on advanced intelligent mechatronics 2009, Singapore, 14–17 July 2009, pp.729–734. New York: IEEE. 10. Kim Y-T and Kim D-E. A novel propelling mechanism based on frictional interaction for endoscope robot. Adv Trib 2009; 288: 859–860. 11. Ito T, Ogushi T and Hayashi T. Impulse-driven capsule by coil-induced magnetic field implementation. Mech Mach Theory 2010; 45: 1642–1650. 12. Li H, Katsuhisa F and Chernousko FL. Motion generation of the capsubot using internal force and static friction. In: Proceedings of the 45th IEEE conference on decision and control, San Diego, CA, 13–15 December 2006, pp.6575–6580. New York: IEEE. 13. Kim B, Lee MG, Lee YP, et al. An earthworm-like micro robot using shape memory alloy actuator. Sensor Actuat A: Phys 2006; 125: 429–437. 14. Hoeg HD, Slatkin AB, Burdick JW, et al. Biomechanical modeling of the small intestine as required for the design and operation of a robotic endoscope. In: Proceedings of IEEE international conference on robotics and automation, San Francisco, CA, 24–28 April 2000, pp.1599–1606. New York: IEEE. 15. Li J, Huang P and Luo HD. Experimental study on friction of micro machines sliding in animal intestines. Lubr Eng 2006; 175: 119–122. 16. Wang X and Meng MQH. An experimental study of resistant properties of the small intestine for an active capsule endoscope. Proc IMechE, Part H: J Engineering in Medicine 2010; 224: 107–118. 17. Wang KD and Yan GZ. Research on measurement and modeling of the gastro intestine’s frictional characteristics. Meas Sci Technol 2009; 20015803. 18. Zhang C, Su G, Tan R, et al. Experimental investigation of the intestine’s friction characteristic based on ‘‘internal force-static friction’’ capsubot. In: Proceedings of the IASTED international conference on biomedical engineering, BioMed 2011, Innsbruck, 16–18 February 2011, pp.117–123. Calgary: IASTED. 19. Ciarletta P, Dario P, Tendick F, et al. Hyperelastic model of anisotropic fiber reinforcements within intestinal walls for applications in medical robotics. Int J Robot Res 2009; 28: 1279–1288. 20. Woo SH, Kim TW, Mohy-Ud-Din Z, et al. Small intestinal model for electrically propelled capsule endoscopy. Biomed Eng Online 2011; 10: 108. 21. Baek NK, Sung IH and Kim DE. Frictional resistance characteristics of a capsule inside the intestine for microendoscope design. Proc IMechE, Part H: J Engineering in Medicine 2004; 218: 193–201. 22. Kim JS, Sung IH, Kim YT, et al. Experimental investigation of frictional and viscoelastic properties of intestine for microendoscope application. Tribol Lett 2006; 22: 143–149.
Downloaded from pih.sagepub.com at UNIV CALIFORNIA BERKELEY LIB on March 9, 2015
296
Proc IMechE Part H: J Engineering in Medicine 228(3)
23. Kim JS, Sung IH, Kim YT, et al. Analytical model development for the prediction of the frictional resistance of a capsule endoscope inside an intestine. Proc IMechE, Part H: J Engineering in Medicine 2007; 221: 837–845. 24. Zhang C, Liu H, Su G, et al. Research of intestines’ dynamic viscoelasticity based on five-element model. Gaojishu Tongxin/Chin High Technol Lett 2012; 22: 964– 968. 25. Zhang C, Liu H, Tan RJ, et al. Modeling of velocitydependent frictional resistance of a capsule robot inside an intestine. Tribol Lett 2012; 47: 295–301. 26. Gregersen H. Biomechanics of the gastrointestinal tract: new perspectives in motility research and diagnostics. 1st ed. New York: Springer, 2003, p.283. 27. Wu JH, Cheng XY, Wei YL, et al. Rheological behavior of dog’s small intestinal mucus. J Chongqing Univ (Natural Science Edition) 2000; 23: 10–12. 28. Varum FJO, Veiga F, Sousa JS, et al. An investigation into the role of mucus thickness on mucoadhesion in the
29.
30.
31. 32.
gastrointestinal tract of pig. Eur J Pharm Sci 2010; 40: 335–341. Lyle AB, Luftig JT and Rentschler ME. A tribological investigation of the small bowel lumen surface. Tribol Int 2013; 62: 171–176. Tan R, Liu H, Su G, et al. Experimental investigation of the small intestine’s viscoelasticity for the motion of capsule robot. In: Proceedings of the IEEE international conference on mechatronics and automation, ICMA 2011, Beijing, China, 7–10 August 2011, pp.249–253. New York: IEEE Computer Society. Christensen RM. Theory of viscoelasticity. Mineola, NY: Dover Publications, 2003. Namkon Lee NK, Li Hongyi, Furuta Katsuhisa, et al. Control system design and experimental verification of capsubot. In: Proceedings of the IEEE/RSJ international conference on intelligent robots and systems, Nice, 22–26 September 2008, pp.1927–1932. New York: IEEE.
Downloaded from pih.sagepub.com at UNIV CALIFORNIA BERKELEY LIB on March 9, 2015
