\r\n\t• Role of technological innovation and corporate risk management \r\n\t• Challenges for corporate governance while launching corporate environmental management among emerging economies \r\n\t• Demonstrating the relationship between environmental risk management and sustainable management \r\n\t• Contemplating strategic corporate environmental responsibility under the influence of cultural barriers \r\n\t• Risk management in different countries – the international management dimension \r\n\t• Global Standardization vs local adaptation of corporate environmental risk management in multinational corporations. \r\n\t• Is there a transnational approach to environmental risk management? \r\n\t• Approaches towards Risk management strategies in the short-term and long-term.
",isbn:"978-1-83968-906-2",printIsbn:"978-1-83968-905-5",pdfIsbn:"978-1-83968-907-9",doi:null,price:0,priceEur:0,priceUsd:0,slug:null,numberOfPages:0,isOpenForSubmission:!1,hash:"9b65afaff43ec930bc6ee52c4aa1f78f",bookSignature:"Dr. Muddassar Sarfraz and Prof. Larisa Ivascu",publishedDate:null,coverURL:"https://cdn.intechopen.com/books/images_new/10226.jpg",keywords:"Global Risk Management, Risk Assessment, Climate Risk, Environmental Management, International Business, Business Sustainability, Corporate Governance, Financial Market, Financial Risks, Sustainable Economic Environment, Business Valuation, Organizational Behavior",numberOfDownloads:131,numberOfWosCitations:0,numberOfCrossrefCitations:0,numberOfDimensionsCitations:0,numberOfTotalCitations:0,isAvailableForWebshopOrdering:!0,dateEndFirstStepPublish:"September 24th 2020",dateEndSecondStepPublish:"October 22nd 2020",dateEndThirdStepPublish:"December 21st 2020",dateEndFourthStepPublish:"March 11th 2021",dateEndFifthStepPublish:"May 10th 2021",remainingDaysToSecondStep:"4 months",secondStepPassed:!0,currentStepOfPublishingProcess:4,editedByType:null,kuFlag:!1,biosketch:"Dr. Muddassar Sarfraz focuses on corporate social responsibility, human resource management, strategic management, and business management. He is a member of the British Academy of Management (UK), Chinese Economists Society (USA), World Economic Association (UK), American Economic Association (USA), and an Ambassador of the International MBA program of Chongqing University, PR China, for Pakistan.",coeditorOneBiosketch:"Dr. Larisa Ivascu's area of research includes sustainability, management, and strategic management. She has published over 190 papers in international journals. She is vice-president of the Society for Ergonomics and Work Environment Management, Timisoara, and a member of the World Economics Association (WEA), International Economics Development and Research Center (IEDRC), Engineering, and Management Research Center (CCIM).",coeditorTwoBiosketch:null,coeditorThreeBiosketch:null,coeditorFourBiosketch:null,coeditorFiveBiosketch:null,editors:[{id:"260655",title:"Dr.",name:"Muddassar",middleName:null,surname:"Sarfraz",slug:"muddassar-sarfraz",fullName:"Muddassar Sarfraz",profilePictureURL:"https://mts.intechopen.com/storage/users/260655/images/system/260655.jpeg",biography:"Dr Muddassar Sarfraz is working at the Binjiang College, Nanjing University of Information Science and Technology, Wuxi, Jiangsu, China. He has obtained his PhD in Management Sciences and Engineering from the Business School of Hohai University. He holds an International Master of Business Administration (IMBA) from Chongqing University (China) and Master of Business Administration (HR) from The University of Lahore. He has published tens of papers in foreign authoritative journals and academic conferences both at home and abroad.\nHe is the Book Editor of Sustainable Management Practices, Analyzing the Relationship between Corporate Governance, CSR, Sustainability, and Cogitating the Interconnection between Corporate Social Responsibility and Sustainability. He is the Associate and Guest Editor of Frontiers in Psychology, International Journal of Humanities and Social Development Research and the Journal of Science and Innovative Technologies. He is an Editorial Board Member of the International Journal of Human Resource as well as a member of the British Academy of Management (UK), Chinese Economists Society (USA), World Economic Association (UK), American Economic Association (USA), and an Ambassador of the International MBA program of Chongqing University, PR China, for Pakistan. \nHis research focuses on corporate social responsibility, human resource management, strategic management, and business management.",institutionString:"Binjiang College, Nanjing University of Information Science &Technology, Wuxi, Jiangsu",position:null,outsideEditionCount:0,totalCites:0,totalAuthoredChapters:"0",totalChapterViews:"0",totalEditedBooks:"1",institution:null}],coeditorOne:{id:"288698",title:"Prof.",name:"Larisa",middleName:null,surname:"Ivascu",slug:"larisa-ivascu",fullName:"Larisa Ivascu",profilePictureURL:"https://s3.us-east-1.amazonaws.com/intech-files/0030O00002bRfMOQA0/Profile_Picture_1594716735521",biography:"Dr Larisa IVAȘCU is currently an associate professor at the Politehnica University of Timisoara. 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1. Introduction
Fractional-order calculus is an area of mathematics that deals with derivatives and integrals from non-integer orders. In other words, it is a generalization of the traditional calculus that leads to similar concepts and tools, but with a much wider applicability. In the last two decades, fractional calculus has been rediscovered by scientists and engineers and applied in an increasing number of fields, namely in the area of control theory. The success of fractional-order controllers is unquestionable with a lot of success due to emerging of effective methods in differentiation and integration of non-integer order equations.
Fractional-order proportional-integral-derivative (FOPID) controllers have received a considerable attention in the last years both from academic and industrial point of view. In fact, in principle, they provide more flexibility in the controller design, with respect to the standard PID controllers,because they have five parameters to select (instead of three). However, this also implies that the tuning of the controller can be much more complex. In order to address this problem, different methods for the design of a FOPID controller have been proposed in the literature.
The concept of FOPID controllers was proposed by Podlubny in 1997 (Podlubny et al., 1997; Podlubny, 1999a). He also demonstrated the better response of this type of controller, in comparison with the classical PID controller, when used for the control of fractional order systems. A frequency domain approach by using FOPID controllers is also studied in (Vinagre et al., 2000). In (Monje et al., 2004), an optimization method is presented where the parameters of the FOPID are tuned such that predefined design specifications are satisfied. Ziegler-Nichols tuning rules for FOPID are reported in (Valerio & Costa, 2006). Further research activities are runnig in order to develop new tuning methods and investigate the applications of FOPIDs. In (Jesus & Machado, 2008) control of heat diffusion system via FOPID controllers are studied and different tuning methods are applied. Control of an irrigation canal using rule-based FOPID is given in (Domingues, 2010). In (Karimi et al., 2009) the authors applied an optimal FOPID tuned by Particle Swarm Optimzation (PSO) algorithm to control the Automatic Voltage Regulator (AVR) system. There are other papers published in the recent years where the tuning of FOPID controller via PSO such as (Maiti et al., 2008) was investigated.
The aim of this chapter is to study some of the well-known tuning methods of FOPIDs proposed in the recent literature. In this chapter, design of FOPID controllers is presented via different approaches include optimization methods, Ziegler-Nichols tuning rules, and the Padula & Visioli method. In addition, several interesting illustrative examples are presented. Simulations have been carried out using MATLAB via Ninteger toolbox (Valerio & Costa, 2004). Thus, a brief introduction about the toolbox is given.
The rest of this chapter is organized as follows: In section 2, basic definitions of fractional calculus and its frequency domain approximation is presented. Section 3 introduces the Ninteger toolbox. Section 4 includes the basic concepts of FOPID controllers. Several design methods are presented in sections 5 to 8 and finally, concluding remarks are given in section 9.
2. Fractional calculus
In this section, basic definitions of fractional calculus as well as its approximation method is given.
2.1. Definitions
The differintegral operator, denoted byDatq, is a combined differentiation-integration operator commonly used in fractional calculus. This operator is a notation for taking both the fractional derivative and the fractional integral in a single expression and is defined by
Datq={dqdtqq>01q=0∫at(dτ)-qq<0E1
Where q is the fractional order which can be a complex number and a and t are the limits of the operation. There are some definitions for fractional derivatives. The commonly used definitions are Grunwald–Letnikov, Riemann–Liouville, and Caputo definitions (Podlubny, 1999b). The Grunwald–Letnikov definition is given by
where n is the first integer which is not less than q i.e. n-1≤q<nand Γ is the Gamma function.
Γ(z)=∫0∞tz-1e-tdtE4
For functions f(t) having n continuous derivatives for t≥0wheren-1≤q<n, the Grunwald–Letnikov and the Riemann–Liouville definitions are equivalent. The Laplace transforms of the Riemann–Liouville fractional integral and derivative are given as follows:
Unfortunately, the Riemann–Liouville fractional derivative appears unsuitable to be treated by the Laplace transform technique because it requires the knowledge of the non-integer order derivatives of the function att=0. This problem does not exist in the Caputo definition that is sometimes referred as smooth fractional derivative in literature. This definition of derivative is defined by
where m is the first integer larger than q. It is found that the equations with Riemann–Liouville operators are equivalent to those with Caputo operators by homogeneous initial conditions assumption. The Laplace transform of the Caputo fractional derivative is
Contrary to the Laplace transform of the Riemann–Liouville fractional derivative, only integer order derivatives of function f are appeared in the Laplace transform of the Caputo fractional derivative. For zero initial conditions, Eq. (7) reduces to
L{D0tqf(t)}=sqF(s)E8
In the rest of this paper, the notationDq, indicates the Caputo fractional derivative.
2.2. Approximation methods
The numerical simulation of a fractional differential equation is not simple as that of an ordinary differential equation. Since most of the fractional-order differential equations do not have exact analytic solutions, so approximation and numerical techniques must be used. Several analytical and numerical methods have been proposed to solve the fractional-order differential equations. The method which is considered in this chapter is based on the approximation of the fractional-order system behavior in the frequency domain. To simulate a fractional-order system by using the frequency domain approximations, the fractional order equations of the system is first considered in the frequency domain and then Laplace form of the fractional integral operator is replaced by its integer order approximation. Then the approximated equations in frequency domain are transformed back into the time domain. The resulted ordinary differential equations can be numerically solved by applying the well-known numerical methods.
One of the best-known approximations is due to Oustaloup and is given by (Oustaloup, 1991)
sq=k∏n=1N1+sωzn1+sωpnq>0E9
The approximation is valid in the frequency range[ωl,ωh]; gain kis adjusted so that the approximation shall have unit gain at 1 rad/sec; the number of poles and zeros N is chosen beforehand (low values resulting in simpler approximations but also causing the appearance of a ripple in both gain and phase behaviours); frequencies of poles and zeros are given by
In Table 1, approximations of 1/sqhave been given for q∈{0.1,0.2,...,0.9}with maximum discrepancy of 2 dB within (0.01, 100) rad/sec frequency range (Ahmad & Sprott, 2003).
Ninteger is a toolbox for MATLAB intended to help developing fractional-order controllers and assess their performance. It is freely downloadable from the internet and implements fractional-order controllers both in the frequency and the discrete time domains. This toolbox includes about thirty methods for implementing approximations of fractional-order and three identification methods. The Ninteger toolbox allow us to implement, simulate and analyze FOPID controllers easily via its functions. In the rest of this chapter, all the simulation studies have been carried out using the Ninteger toolbox.
In order to use this toolbox in our simulation studies, the function nipid is suitable for implementing FOPID controllers. The toolbox allow us to implement this function either from command window or SIMULINK. In order to use SIMULINK, a library is provided called Nintblocks. In this library, one can find the Fractional PID block which implements FOPID controllers. We can specify the following parameters of a FOPID via nipid function or Fractional PID block:
proportional gain
derivative gain
fractional derivative order
integral gain
fractional integral order
bandwidth of frequency domian approximation
number of zeros and poles of the approximation
the approximating formula
It was pointed out in (Oustaloup et al., 2000) that a band-limit implementation of fractional order controller is important in practice, and the finite dimensional approximation of the fractional order controller should be done in a proper range of frequencies of practical interest. This is true since the fractional order controller in theory has an infinite memory and some sort of approximation using finite memory must be done.
In the simulation studies of this chapter, we will use the Crone method within the frequency range (0.01, 100) rad/s and the number of zeros and poles are set to 10.
The most common form of a fractional order PID controller is the PIλDμcontroller (Podlubny, 1999a), involving an integrator of order λ and a differentiator of order μ where λ and μ can be any real numbers. The transfer function of such a controller has the form
Gc(s)=U(s)E(s)=kP+kI1sλ+kDsμ,(λ,μ>0)E15
where Gc(s) is the transfer function of the controller, E(s) is an error, and U(s) is controller’s output. The integrator term is1/sλ, that is to say, on a semi-logarithmic plane, there is a line having slope -20λ dB/decade. The control signal u(t) can then be expressed in the time domain as
u(t)=kPe(t)+kID-λe(t)+kDDμe(t)E16
Fig. 1 is a block-diagram configuration of FOPID. Clearly, selecting λ = 1 and μ = 1, a classical PID controller can be recovered. The selections of λ = 1, μ = 0, and λ = 0, μ = 1 respectively corresponds conventional PI & PD controllers. All these classical types of PID controllers are the special cases of the fractional PIλDμ controller given by (Eq. 15).
Figure 1.
Block-diagram of FOPID
It can be expected that the PIλDμ controller may enhance the systems control performance. One of the most important advantages of the PIλDμ controller is the better control of dynamical systems, which are described by fractional order mathematical models. Another advantage lies in the fact that the PIλDμ controllers are less sensitive to changes of parameters of a controlled system (Xue et al., 2006). This is due to the two extra degrees of freedom to better adjust the dynamical properties of a fractional order control system. However, all these claimed benefits were not systematically demonstrated in the literature. In the next sections, different design methods of FOPID controllers are discussed. In all cases, we considered the unity feedback control scheme depicted in Fig.2.
Figure 2.
The considered control scheme; G(s) is the process, Gc(s) is the FOPID controller, R(s) is the reference input, E(s) is the error, D(s) is the disturbance and Y(s) is the output
5. Tuning by minimization
In (Monje et al., 2004) an optimization method is proposed for tuning of FOPID controllers. The analytic method, that lies behind the proposed tuning rules, is based on a specified desirable behavior of the controlled system. We start the section with basic concepts of this design method, and then control pH neutralization process is presented as an illustrative example.
5.1. Basic concepts
In this method, the desirable dynamics is described by the following criteria:
No steady-state error:
Properly implemented a fractional integrator of order k +λ, k ∈ N, 0 < λ < 1, is, for steady-state error cancellation, as efficient as an integer order integrator of order k + 1.
The gain-crossover frequency ωcg is to have some specified value
|Gc(jωcg)G(jωcg)|=0dBE17
The phase margin φm is to have some specified value
-π+φm=arg(Gc(jωcg)G(jωcg))E18
So as to reject high-frequency noise, the closed loop transfer function must have a small magnitude at high frequencies; thus it is required that at some specified frequency ωt its magnitude be less than some specified gain
So as to reject output disturbances and closely follow references, the sensitivity function must have a small magnitude at low frequencies; thus it is required that at some specified frequency ωs its magnitude be less than some specified gain
|S(jω)=11+Gc(jω)G(jω)|<BdB∀ω≤ωs→|S(jω)|=BdBE20
So as to be robust in face of gain variations of the plant, the phase of the open-loop transfer function must be (at least roughly) constant around the gain-crossover frequency
ddωarg(Gc(jω)G(jω))|ω=ωcg=0E21
A set of five of these six specifications can be met by the closed-loop system, since the FOPID has five parameters to tune. The specifications 2-6 yield a robust performance of the controlled system against gain changes and noise and the condition of no steady-state error is fulfilled just with the introduction of the fractional integrator properly implemented, as commented before.
In (Monje et al., 2004), the use of numerical optimization techniques is proposed to satisfy the specifications 2-6. Motivated from the fact that the complexity of a set of five nonlinear equations (Eq. 17 – Eq. 21) with five unknown parameters (kP, kI,\n\t\t\t\t\tkD, λ and μ) is very significant, the optimization toolbox of MATLAB has been used to reach out the better solution with the minimum error. The function used for this purpose is called fmincon, which finds the constrained minimum of a function of several variables. In this case, the specification in Eq. (17) is taken as the main function to minimize, and the rest of specifications (Eq. 18 – Eq. 21) are taken as constrains for the minimization, all of them subjected to the optimization parameters defined within the function fmincon.
5.2. Example: pH neutralization process
The pH dynamic model of a real sugar cane raw juice neutralization process can be modelled by the following FOPDT dynamic:
G(s)=0.55e-s62s+1E22
Assume that the design specifications are as follows:
Gain crossover frequencyωcg=0.08
Phase marginφm=0.44π
Robustness to variations in the gain of the plant must be fulfilled.
|T(jω)|≤-20dB,∀ω≥ωt=10E23
|S(jω)|≤-20dB,∀ω≤ωs=0.01E24
Using the function fmincon, the FOPID controller to control the plant is
Gc(s)=7.9619+0.2299s0.9646+0.1594s0.0150E25
Simulation block-diagram of the system is depicted in Fig. 3 and the step response of the closed-loop system is illustrated in Fig. 4.
Figure 3.
Simulation block-diagram for control of pH neutralization process
Figure 4.
Step responses of closed loop and open loop pH neutralization process
Figure 5.
Bode plot of pH neutralization process
As shown in the Fig.4 the closed loop step response has no steady state error and a fulfilling rise time in the comparison of the open loop response. In order to evaluate the effect of FOPID in frequency response of the process, let us consider Fig.5 as bode plot of the open loop pH neutralization process. The diagram is provided via “Control System Toolbox” of MATLAB. The bode diagram of the FOPID defined in (Eq. 23) is also depicted in Fig. 6 and finally, the bode plot of G(s)Gc(s)is depicted in Fig. 7.
Figure 6.
Bode plot of FOPID controller designed for pH neutralization process
Figure 7.
Bode plot of pH neutralization process when the controller is applied
6. Ziegler-Nichols type tuning rules
In the previous section, a tuning method based on optimization techniques is proposed. The method is effective but allows local minima to be obtained. In practice, most solutions found with this optimization method are good enough, but they strongly depend on initial estimates of the parameters provided. Some may be discarded, because they are unfeasible or lead to unstable loops, but in many cases it is possible to find more than one acceptable FOPID. In others, only well-chosen initial estimates of the parameters allow finding a solution. Motivated from the fact that the optimization techniques depend on initial estimates, Valerio and Costa have introduced some Ziegler-Nichols-type tuning rules for FOPIDs. In this section, we will explain these tuning rules, and two illustrative examples will be presented. These tuning rules are applicable only for systems that have S-shaped step response. The simplest plant to have S-shaped step response can be described by
G(s)=KTs+1e−sLE26
Valerio and Costa have employed the minimisation tuning method to plants given by (Eq. 24) for several values of L and T, with K = 1. The parameters of FOPIDs thus obtained vary in a regular manner. Having translated the regularity into formulas, some tuning rules are obtained for particular desired responses.
6.1. First set of tuning rules
A first set of rules is given in Tables 2 and 3. These are to be read as
and so on. They may be used if 0.1≤T≤50,L≤2and were designed for the following specifications:
ωcg=0.5E28
φm=2/3E29
ωt=10E30
ωs=0.01E31
A=-10E32
d
B=-20E33
d
kP
kI
λ
kD
μ
1
-0.0048
0.3254
1.5766
0.0662
0.8736
L
0.2664
0.2478
-0.2098
-0.2528
0.2746
T
0.4982
0.1429
-0.1313
0.1081
0.1489
L2
0.0232
-0.1330
0.0713
0.0702
-0.1557
T2
-0.0720
0.0258
0.0016
0.0328
-0.0250
LT
-0.0348
-0.0171
0.0114
0.2202
-0.0323
Table 2.
Parameters for the first set of tuning rules when 0.1≤T≤5
kP
kI
λ
kD
μ
1
2.1187
-0.5201
1.0645
1.1421
1.2902
L
-3.5207
2.6643
-0.3268
-1.3707
-0.5371
T
-0.1563
0.3453
-0.0229
0.0357
-0.0381
L2
1.5827
-1.0944
0.2018
0.5552
0.2208
T2
0.0025
0.0002
0.0003
-0.0002
0.0007
LT
0.1824
-0.1054
0.0028
0.2630
-0.0014
Table 3.
Parameters for the first set of tuning rules when 5≤T≤50
6.2. Second set of tuning rules
A second set of rules is given in Table 4. These may be applied for 0.1≤T≤50 andL≤0.5. Only one set of parameters is needed in this case because the range of values of L these rules cope with is more reduced. They were designed for the following specifications:
ωcg=0.5E34
φm=1E35
ωt=10E36
ωs=0.01E37
A=-20E38
d
B=-20E39
d
kP
kI
λ
kD
μ
1
-1.0574
0.6014
1.1851
0.8793
0.2778
L
24.5420
0.4025
-0.3464
-15.0846
-2.1522
T
0.3544
0.7921
-0.0492
-0.0771
0.0675
L2
-46.7325
-0.4508
1.7317
28.0388
2.4387
T2
-0.0021
0.0018
0.0006
-0.0000
-0.0013
LT
-0.3106
-1.2050
0.0380
1.6711
0.0021
Table 4.
Parameters for the second set of tuning rules
6.3. Example: High-order process control
Consider the following high-order process
G(s)=1(s+1)4E40
The transfer function of the process is not on the form of FOPDT. In order to control the process via FOPID, let us approximate the process by a FOPDT model. The process can be approximated by the following model (see (Astrom & Hagglund, 1995))
G(s)=12s+1e−2sE41
where K=1, L=2 and T=2. Fig.8 shows the step response of the process (Eq. 26) and its approximated model. As we see, the model can approximate the process with satisfying accuracy. The step response of the process is of S-shaped type and we can use the Ziegler-Nichols type tuning rules for our FOPID controller.
Using the first set of tuning rules, one can obtain the following FOPID controller.
Gc(s)=1.1900+0.60961s1.2316+1.0696s0.8686E42
The closed step response of the system is depicted in Fig. 9.
Figure 8.
Step response of the process and its approximated model
Figure 9.
Step response of high order process controlled by FOPID
6.4. Example: Non-minimum phase process control
When the transfer function of a process is not a FOPDT model, an approximated FOPDT model can be developed; this fact was shown in the previous example. Here, we consider a Non-Minimum phase process. We need to approximate a FOPDT model in order to use Ziegler-Nichols tuning rules. The following non-minimum phase process is considered
G(s)=1−s(s+0.5)(s+2)E43
The process can be approximated by the following model
G(s)=11.8s+1e−1.7sE44
The step response of the transfer function (Eq. 30) is compared with the process (Eq. 29) and depicted in Fig. 10. As we see, the FOPDT model of the process presents a good accuracy.
Figure 10.
Step response of the process and its approximated model
After having approximated the process with a FOPDT transfer function, application of the first set of tuning rules gives the following FOPID controller
Gc(s)=1.0721+0.65081s1.2297+0.8140s0.9786E45
while the step response of the closed loop control system for set point and is depicted in Fig. 11.
Figure 11.
Step response of non-minimum phase process controlled by FOPID
7. The Padula & Visioli method
In (Padula & Visioli, 2010a), a new set of tuning rules are presented for FOPID controllers. Based on FOPDT models, the tuning rules have been devised in order to minimise the integrated absolute error with a constraint on the maximum sensitivity. In this section, the tuning rules are presented and then the problem of heat exchanger temperature is given.
7.1. Tuning rules
Let us consider a process defined by FOPDT model as one given by Eq. (24). The process dynamics can be conveniently characterised by the normalised dead time and defined as
τ=LL+TE46
which represents a measure of difficulty in controlling the process. The proposed tuning rules are devised for values of the normalised dead time in the range0.05≤τ≤0.8. In fact, for values ofτ<0.05the dead time can be virtually neglected and the design of a controller is rather trivial, while for values of τ>0.8the process is significantly dominated by the dead time and therefore a dead time compensator should be employed. By the methodology developed in (Padula & Visioli, 2010a), the FOPID controller is modeled by the following transfer function
Gc(s)=KpKisλ+1KisλKdsμ+1KdNsμ+1E47
The major difference of FOPID defined by (Eq. 33) with the standard form of FOPID defined by (Eq. 15) is that an additional first-order filter has been employed in (Eq. 33) in order to make the controller proper. The parameterNis chosen asN=10T(μ-1). The performance index is integrated absolute error which is defined as follows
which represents the inverse of the maximum distance of the Nyquist plot from the critical point (-1,0). Obviously, the higher value of Ms yields the less robustness against uncertainties. Tuning rules are devised such that the typical values of Ms = 1.4 and Ms = 2.0 are achieved. If only the load disturbance rejection task is addressed, we have
Kp=1K(aτb+c)E50
Ki=T(a(LT)b+c)E51
Kd=T(a(LT)b+c)E52
where the values of the parameters are shown in Tables 5-8.
a
b
c
kP
0.2776
-1.097
-0.1426
kD
0.6241
0.5573
0.0442
kI
0.4793
0.7469
-0.0239
Table 5.
Tuning rules for kP, kD and kI when Ms = 1.4
λ
μ
1
1.0 if τ<0.1 1.1 if 0.1≤τ<0.4 1.2 if 0.4≤τ
Table 6.
Tuning rules for λ and μ when Ms = 1.4
a
b
c
kP
0.164
-1.449
-0.2108
kD
0.6426
0.8069
0.0563
kI
0.5970
0.5568
-0.0954
Table 7.
Tuning rules for kP, kD and kI when Ms = 2.0
λ
μ
1
1.0 if τ<0.2 1.1 if 0.2≤τ<0.6 1.2 if 0.6≤τ
Table 8.
Tuning rules for λ and μ when Ms = 2.0
7.2. Example: Heat exchanger temperature control
A chemical reactor called "stirring tank" is depicted in Fig. 12. The top inlet delivers liquid to be mixed in the tank. The tank liquid must be maintained at a constant temperature by varying the amount of steam supplied to the heat exchanger (bottom pipe) via its control valve. Variations in the temperature of the inlet flow are the main source of disturbances in this process.
Figure 12.
Stirring Reactor with Heat Exchanger
The process can be modelled adequately by FOPDT models as shown in the Fig. 13.
Figure 13.
Open loop process model
The transfer function
G(s)=e-14.7s21.3s+1E53
models how a change in the voltage V driving the steam valve opening effects the tank temperature T, while the transfer function
Gd(s)=e-35s25s+1E54
models how a change d in inflow temperature affects T.
The control problem is to regulate tank temperature T around a given setpoint. From Eq. (32), the normalized dead-time of the process (Eq. 38) is obtained as 0.4083 which implies that we can utilize the proposed tuning rules. From tuning table 5 and 6, the following FPOID can be obtained for the case of Ms = 1.4
Simulation results are presented in Fig. 14. It is assumed that a load disturbance is applied at t=500 seconds, and the disturbance rejection of both controllers are verified. Simulations also show that the transient states of both controllers are approached.
9. Conclusion
In this chapter, some of the well-known tuning methods of FOPID controllers are presented and several illustrative examples, verifying the effectiveness of the methods are given.
Figure 14.
Closed response of heat exchanger system and disturbance rejection of controllers (a) Gc1(s)(b) Gc2(s)
Simulations have been carried out using MATLAB/SIMULINK software via Ninteger toolbox. After discussion on fractional calculus and its approximation methods, the Ninteger toolbox is introduced briefly. Then optimization methods, Ziegler-Nichols tuning rules and a new tuning method were introduced. We have considered control of pH neutralization process, high-order process, Non-Minimum phase process and temperature control of heat exchanger as case studies. In spite of extensive research, tuning the parameters of a FOPID controller remains an open problem. Other analytical methods and new tuning rules may be further studied.
\n',keywords:null,chapterPDFUrl:"https://cdn.intechopen.com/pdfs/18567.pdf",chapterXML:"https://mts.intechopen.com/source/xml/18567.xml",downloadPdfUrl:"/chapter/pdf-download/18567",previewPdfUrl:"/chapter/pdf-preview/18567",totalDownloads:10175,totalViews:996,totalCrossrefCites:8,totalDimensionsCites:14,hasAltmetrics:0,dateSubmitted:"November 21st 2010",dateReviewed:"April 24th 2011",datePrePublished:null,datePublished:"September 9th 2011",dateFinished:null,readingETA:"0",abstract:null,reviewType:"peer-reviewed",bibtexUrl:"/chapter/bibtex/18567",risUrl:"/chapter/ris/18567",book:{slug:"applications-of-matlab-in-science-and-engineering"},signatures:"Mohammad Reza Faieghi and Abbas Nemati",authors:[{id:"48599",title:"Mr.",name:"Mohammad Reza",middleName:null,surname:"Faieghi",fullName:"Mohammad Reza Faieghi",slug:"mohammad-reza-faieghi",email:"m.faieghi@gmail.com",position:null,institution:{name:"Islamic Azad University",institutionURL:null,country:{name:"Iran"}}}],sections:[{id:"sec_1",title:"1. Introduction",level:"1"},{id:"sec_2",title:"2. Fractional calculus",level:"1"},{id:"sec_2_2",title:"2.1. Definitions",level:"2"},{id:"sec_3_2",title:"2.2. Approximation methods",level:"2"},{id:"sec_5",title:"3. The Ninteger toolbox",level:"1"},{id:"sec_6",title:"4. Fractional-order Proportional-Integral-Derivative controller ",level:"1"},{id:"sec_7",title:"5. Tuning by minimization",level:"1"},{id:"sec_7_2",title:"5.1. Basic concepts",level:"2"},{id:"sec_8_2",title:"5.2. Example: pH neutralization process",level:"2"},{id:"sec_10",title:"6. Ziegler-Nichols type tuning rules ",level:"1"},{id:"sec_10_2",title:"6.1. First set of tuning rules ",level:"2"},{id:"sec_11_2",title:"6.2. Second set of tuning rules ",level:"2"},{id:"sec_12_2",title:"6.3. Example: High-order process control",level:"2"},{id:"sec_13_2",title:"6.4. Example: Non-minimum phase process control",level:"2"},{id:"sec_15",title:"7. The Padula & Visioli method",level:"1"},{id:"sec_15_2",title:"7.1. Tuning rules",level:"2"},{id:"sec_16_2",title:"7.2. Example: Heat exchanger temperature control",level:"2"},{id:"sec_18",title:"9. Conclusion",level:"1"}],chapterReferences:[{id:"B1",body:'AhmadW. M.SprottJ. C.2003Chaos in fractional-order autonomous nonlinear systems, Chaos, Solitons & Fractals\n\t\t\t\t\t16339351'},{id:"B2",body:'ÅströmK. J.HägglundT.1995PID Controllers: Theory, Design and Tuning, ISA Press, Research Triangle Park, 1995'},{id:"",body:'Charef, A., Fergani, N.\n\t\t\t\t\t2010. PIλDμController Tuning For Desired Closed-Loop Response Using Impulse Response, Proceedings of Fractional Differentiation and its Applications, Badajoz, Spain, October 2010'},{id:"B4",body:'DelavariH.GhaderiR.RanjbarA.HosseinniaS. H.MomaniS.2010Adaptive Fractional PID Controller for Robot Manipulator, Proceedings of Fractional Differentiation and its Applications, Badajoz, Spain, October 2010'},{id:"B5",body:'DominguesJ.Vale´rioD.CostaJ. 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Proposals for fractional PIλDμ tuning, Proceedings of Fractional Differentiation and its Applications, Bordeaux, 2004'},{id:"B10",body:'OustaloupA.1991La commande CRONE: commande robuste d’ordre non entier. Hermès, Paris, 1991'},{id:"B11",body:'OustaloupA.LevronF.MathieuB.NanotF. M.2000Frequency-band complex noninteger differentiator: characterization and synthesis, IEEE Transactions on Circuits and Systems I, 472539'},{id:"B12",body:'PadulaF.VisioliA.2010aTuning rules for optimal PID and fractional-order PID controllers, Journal of Process Control, doi:10.1016/j.jprocont.2010.10.006'},{id:"B13",body:'PadulaF.VisioliA.2010bSet-point Weighting for Fractional PID Controllers, Proceedings of Fractional Differentiation and its Applications, Badajoz, Spain, October 2010'},{id:"B14",body:'PadulaF.VisioliA.2010cTuning of Fractional PID Controllers for Integral Processes, Proceedings of Fractional Differentiation and its Applications, Badajoz, Spain, October 2010'},{id:"",body:'PodlubnyI., 1999a. Fractional-Order Systems and PIλDμControllers, IEEE Transactions on Automatic Control, Vol. 44, No. 1, January 1999, pp. 208-214'},{id:"B16",body:'PodlubnyI.1999bFractional Differential Equations, Academic Press, USA'},{id:"",body:'Podlubny, I., Dorcak, L., Kostial, I.\n\t\t\t\t\t1997. On Fractional Derivatives, Fractional-Order Dynamic Systems and PIλDμ controllers, Proceedings of the 36th Conference on Decision & Control, San Diego, California, USA, December 1997'},{id:"B18",body:'ShinskeyF. G.1994Feedback Controllers for the Process Industries, McGraw-Hill, New York, USA'},{id:"B19",body:'TabatabaeiM.HaeriM.2010Loop Shaping Design of Fractional PD and PID Controllers, Proceedings of Fractional Differentiation and its Applications, Badajoz, Spain, October 2010'},{id:"B20",body:'Vale´rioD.CostaJ. S.2004NINTEGER: A Non-Integer Control Toolbox for MATLAB, Proceedings of Fractional Differentiation and its Applications, Bordeaux, 2004'},{id:"B21",body:'Vale´rioD.CostaJ. S.2006Tuning of fractional PID controllers with Ziegler-Nichols-type rules, Signal Processing, 8627712784\n\t\t\t'},{id:"B22",body:'VinagreB. M.PodlubnyI.DorcakL.FeliuV.2000On Fractional PID Controllers: A Frequency Domain Approach, Proceedings of IFAC Workshop on Digital Control: Past, Present and Future of PID Control. Terrasa, Spain, 5358'},{id:"B23",body:'XueD.ZhaoC.ChenY. Q.2006Fractional Order PID Control of A DC-Motor with Elastic Shaft: A Case Study, Proceedings of the 2006 American Control Conference, Minneapolis, Minnesota, USA, June, 2006'},{id:"",body:'Yeroglu, C., Özyetkin, M. M., Tan, N.\n\t\t\t\t\t2010. Design of Robust PIλDμController for FOPDT Systems, Proceedings of Fractional Differentiation and its Applications, Badajoz, Spain, October 2010'}],footnotes:[],contributors:[{corresp:"yes",contributorFullName:"Mohammad Reza Faieghi",address:"",affiliation:'
Department of Electrical Engineering, Miyaneh Branch, Islamic Azad University, Miyaneh,, Iran
Department of Electrical Engineering, Miyaneh Branch, Islamic Azad University, Miyaneh,, Iran
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Arif",authors:[{id:"21687",title:"Dr.",name:"Sayyad Zahid",middleName:null,surname:"Qamar",fullName:"Sayyad Zahid Qamar",slug:"sayyad-zahid-qamar"},{id:"21688",title:"Prof.",name:"Anwar Khalil",middleName:null,surname:"Sheikh",fullName:"Anwar Khalil Sheikh",slug:"anwar-khalil-sheikh"},{id:"21689",title:"Prof.",name:"Abul Fazal M.",middleName:null,surname:"Arif",fullName:"Abul Fazal M. Arif",slug:"abul-fazal-m.-arif"},{id:"21690",title:"Prof.",name:"Tasneem",middleName:null,surname:"Pervez",fullName:"Tasneem Pervez",slug:"tasneem-pervez"}]},{id:"14041",title:"Loss of Load Expectation Assessment in Electricity Markets using Monte Carlo Simulation and Neuro-Fuzzy Systems",slug:"loss-of-load-expectation-assessment-in-electricity-markets-using-monte-carlo-simulation-and-neuro-fu",signatures:"H. Haroonabadi",authors:[{id:"20037",title:"Dr.",name:"Hossein",middleName:null,surname:"Haroonabadi",fullName:"Hossein Haroonabadi",slug:"hossein-haroonabadi"}]},{id:"14042",title:"Automating First- and Second-order Monte Carlo Simulations for Markov Models in TreeAge Pro",slug:"automating-first-and-second-order-monte-carlo-simulations-for-markov-models-in-treeage-pro",signatures:"Benjamin P. Geisler",authors:[{id:"19631",title:"Dr.",name:"Benjamin",middleName:"Peter",surname:"Geisler",fullName:"Benjamin Geisler",slug:"benjamin-geisler"}]},{id:"14043",title:"Monte Carlo Simulations of Adsorbed Molecules on Ionic Surfaces",slug:"monte-carlo-simulations-of-adsorbed-molecules-on-ionic-surfaces",signatures:"Abdulwahab Khalil Sallabi",authors:[{id:"22986",title:"Prof.",name:"A",middleName:null,surname:"Slabi",fullName:"A Slabi",slug:"a-slabi"}]}]}]},onlineFirst:{chapter:{type:"chapter",id:"74325",title:"Role of Magnetic Resonance Imaging in Patients with Rectal Cancer",doi:"10.5772/intechopen.94868",slug:"role-of-magnetic-resonance-imaging-in-patients-with-rectal-cancer",body:'
1. Introduction
The purpose of this chapter is to provide the reader with detailed information about imaging of rectal cancer in the context of standardized and novel therapy options of rectal cancer. It is essential to put the rectal cancer in the correct stage group based on different imaging markers- local invasion (T-stage), local infiltration of mesorectum, intra- and extravascular invasion, lymph node spreading. Another important imaging biomarker is the tumor regression grade visualized on magnet-resonance imaging after neoadjuvant therapy. All markers correspond to substantial oncologic parameters such as survival rates. The connecting bridge is magnet-resonance imaging.
2. Rectal cancer imaging
Imaging of rectal cancer is more specific than imaging of the other colonic cancers. Rectal cancer staging is based on two principles. The first is an anatomic definition of the tumor and the second is prognostic stage grouping. Both are achieved by magnet-resonance imaging. Additional imaging modalities such as ultrasound US, computed tomography CT and positron emission tomography PET are discussed later on.
2.1 Anatomic definition of rectum
Knowing the anatomy, especially the anatomy on MR studies is the key to the right treatment of rectal cancer. Important anatomical landmarks are sigmoid take-off (transition rectum-sigma), mesorectal fascia MRF and mesorectum, presacral fascia, anterior peritoneal reflection, retrorectal space, anorectal sling (m. levator ani) and anal verge, shown on the pictures below.
The rectum is the most distal part of the gastrointestinal tract, located before the anal canal. There are different definitions of the distal and proximal borders of the rectum – distal border is linea dentata ani, and proximal part is the sigmoid colon and the transitional part called sigmoid take-off. It is a radiological reference point used to identify the connection of the sigmoid mesocolon with the mesorectum and therefore the connection of the sigmoid colon with the rectum (Figure 1).
Figure 1.
Anatomical presence of sigmoid take-off (sagittal T2 weighted MR image).
2.1.1 Mesorectum and mesorectal fascia MRF
It is a hypointense line that surrounds the mesorectum. Above this layer it connects with the mesorectal fascia, which lies above the levator muscles and, respectively, connects with the peritoneal reflection forward and with the parietal fascia backward (Figure 2).
Figure 2.
Mesorectum and mesorectal fascia MRF (axial T2 weighted MR image).
2.1.2 Anorectal sling (m. levator ani) and anal verge
Anatomically, the anal canal is at the level at which the anorectal sling envelops the rectum and creates the anorectal transition (Figure 3).
Figure 3.
Anorectal complex (coronal T2 weighted MR image).
2.1.3 Anterior peritoneal reflection
It is a thickened parietal fascia that covers the terminal veins and adipose tissue in the proximal part of rectum.
2.2 Mucosal layers of rectal wall
Another anatomical landmark is differentiating the mucosal layers (Figure 4) in relation to the TNM classification of the rectal cancer.
Figure 4.
Mucosal layers of rectal wall (axial T2 weigted MR image).
T1- submucosal invasion.
T2- invasion of muscularis propria.
T3- through the muscularis propria to the submucosa.
T4- perforation of the visceral peritoneum or direct invasion of the peritoneum.
Important fact is that T3 and T4 tumors are associated with extramural invasion. The more pronounced penetration of the mesorectum is associated with a worse prognosis and a higher probability of local recurrence. Many tumors are staged as pT3, but there is actually a heterogeneous T3 group, which is why a subclassification of T3 has been created:
T3a - minimal invasion <1 mm by muscularis propria.
T3b- light-walled invasion 1-5 mm from muscularis propria.
T3c- moderate invasion 5-15 mm from muscularis propria.
T3d- extensive invasion>15 mm by muscularis propria.
T3a and T3b are associated with better outcome for the patient compared with T3c and T3d stages, suggested they are T4 tumors because of worse outcome and poor prognosis [1].
When talking about staging it is important to notice that low rectal cancer is a separate subgroup again due to different anatomical features- the anorectal sling:
Staging of low rectal cancer with MRI (recently validated in the prospective study Mercury II: Low Rectal Cancer study [2].
stage 1 - the tumor is visualized in the rectal wall, but not throughout its thickness (preserved outer muscle layer).
stage 2- the tumor displaces the muscle layer without crossing the intersphincteric line.
stage 3- the tumor invades the intersphincteric line or is 1 mm from the levator ani.
stage 4- the tumor invades the external anal sphincter and infiltrates the levator ani and/or invades neighboring organs.
2.3 Pathways of spreading
For understanding of the neoplastic behavior of rectal cancer it is of great importance to analyze the pathways of spreading of tumorous tissue. They are:
direct invasion in the rectal wall,
involvement of local lymph vessels and lymph node metastases,
venous invasion (intra- and extramural venous invasion- EMVI) and
tumor deposits.
Demonstration of any invasion both histologically and by MRI [3] is always associated with a poor prognosis. The detection of EMVI is associated with the presence of synchronous distant metastases. Involvement of extramural venous vessels is more closely associated with poor prognosis, as well as invasion of larger veins. This leads to the conclusion, that detection of EMVI on MRI is of great prognostic importance and it is explained in details below.
2.4 Surgery of rectal cancer
Explaining the anatomy by the radiologists helps the surgeons plan the surgical procedure. Surgeons have 3 options:
TEM- Transanal Endoscopic Microsurgery in T1 stage
TME- Total Mesorectal Excision is the universally established standard for optimal oncological surgery in rectal cancer [4]. TME is an independent predictor of local recurrence. TME includes excision of the rectum and surrounding adipose tissue, the lymphovascular cuff, the mesorectum, in which the locoregional lymph nodes are located. The outermost border of the mesorectum, the mesorectal fascia, plays the role of an oncological barrier. Thus, if the surgical principles for TME are followed, the prognostic effect of regional lymph nodes may be neglected [5], as they themselves are removed en block in TME.
Deferral of surgery or Watch and Wait strategy- novel strategy based on organ preservation if complete clinical response is achieved by neoadjuvant therapy (references on EURECCA (European Registration of Cancer Care [6] and TRIGGER) [7]
No surgery and stoma placement in locally advanced and unresectable T4b tumors
2.5 Treatment options
Before discussing the imaging of rectal cancer one should understand the treatment options for the disease. The ideal prognostic stage allows selection of the patient according to the risk of local and/or systemic recurrence. This leads to three main treatment options:
Surgery alone,
neoadjuvant therapy before surgery and
palliative pharmacotherapy/radiotherapy alone.
Planning and decision making are listed in the European [8] and Nord- American guidelines [9].
Main goal is to achieve downstaging and downsizing of the tumor and therefore optimal mesorectal excision. This is possible with neoadjuvant therapy and it has a leading role in treatment of rectal cancer. Synchronous to better therapeutical options many imaging markers for response measurement are found out.
In order to objectively measure the rate of tumor response to this therapy, several systems called histopathological tumor regression grades (pTRG) have been developed, the most commonly used being those of Dworak [10] and Mandard [11] Both systems determine the response to treatment based on the residual/residual cells in the fibrous stroma, and the gradation is between “no response” to “complete response”. A pathological complete response (pCR) is defined as “no residual tumor cells in the material”. A novel radiological method for tumor response has been developed based on pCR - magnetic resonance imaging of the tumor response tumor regression grade (mrTRG) [7] MRI can be used to predict a favorable response and to assess the extent of subsequent treatment.
Therefore we can use some imaging predictors on pretreatment (primary) MRI-scan and on posttreatment (secondary) MRI-scan. This is how we could reach out to the second principle of rectal cancer staging - prognostic stage grouping.
2.6 MRI of rectal cancer
The main imaging modality for local staging of rectal cancer is magnetic resonance imaging (MRI), as it provides the most accurate information about important prognostic markers that could affect the choice of treatment. In addition, there are many new studies on the role of MRI in assessing the response after neoadjuvant radiation therapy.
Тechnical parameters for MRI: 1,5 T or 3 T, FOV (160 x 160 mm, 256 x 256 matrix), 0.6 x 0.6 x 3 mm, high-resolution image (1 mm 3 voxel size), sequences: first series - T2-weighted sagittal, turbo spin-echo sequences for tumor identification, second series – axial T2 to the whole pelvis, third series - T2-weighted thin-section axial through the neoplasia, and they should be perpendicular to the long axis of the rectum and to the level of the neoplasm (3-mm slices). Addition: for low rectal cancer there is a fourth series - high resolution, coronary images for the levators, the sphincter complex, the intersphincter axis and the relationship to the rectal wall. Follow-up MRI after treatment follows the same protocol.
Diffusion-weighted imaging (DWI) images of magnetic resonance show the random movement of water molecules in the body. The degree of water restriction in biological tissues is directly proportional to the tissue cellularity and integrity of the cell membrane. Therefore, the contrast of tissues at D The apparent diffusion coefficient (ADC) is recalculated by the DWI, using these two techniques to compare different tissue compartments depending on the cell composition. Evaluates the response to treatment. DWI could be useful in the primary detection of rectal cancer and lymph nodes, but not for follow-up assessment or measurement of tumor regression, incl. mrTRG.
Gadolinium-enhanced MRI is not recommended.
MRI has the ability to distinguish each individual layer of mucosa and muscle due to their different signaling characteristics. For this purpose, the T2 sequence is used:
Mucosa - fine hypointense line
Submucosa - thicker hyperintense layer
Muscularis propria - a double layer of inner circular and outer longitudinal layer, the latter having an irregular appearance due to the passing vessels
Perirectal adipose tissue/mesorectum - high signal tissue
Mesorectal fascia - a thin hypointense band surrounding all of the above (Figure 5)
Figure 5.
Mucosal layers of rectal wall (axial T2 weigted MR image).
Patients with rectal cancer will receive a series of MRIs during the course of their treatment:
the initial (primary) MRI will guide whether neoadjuvant therapy is needed, will guide the operative plan, and factors such as mrEMVI will determine the type of neoadjuvant therapy
the secondary MRI follows the neoadjuvant therapy, and the response is assessed by mrTRG. In patients with a good mrTRG response [1, 2], it is possible to wait with surgery or reduce the volume of the operation or continue with radical surgery. The first two options potentially lead to the preservation of the integrity of the rectum, but additional MR examinations are needed. In case of a weak response (mrTRG4–5) it is possible to choose surgery or continuation with chemotherapy with intensification and/or experimental pharmacotherapy and change of mrTRG to a prognostically better group.
the third MRI is for the group waiting for surgery and MRI is used to monitor recurrence.
As already mentioned, we have to separate some imaging markers on the pre- and posttreatment studies that are essential for predicting response and outcome from the disease.
In the first group is the pretreatment MRI and the imaging features for predicting the tumor response:
Tumor height - low rectal cancer is more likely to have a bad response;
T stage- T1, T2, T3a, T3b are more likely to have a good response;
EMVI - the presence of mrEMVI is associated with a worse prognosis.
In the second groups is the posttreatment MRI and evaluation of the post-therapeutic response (used prefix “y”- after neoadjuvant therapy):
Tumor height from the intersphincteric line to the distal TME line
Rectal tumor high. Source: MRI of Rectal Cancer: Tumor Staging, Imaging Techniques, and Management”, Horvat et al. [12].
Low rectal cancer:
Distal border is 0–5 cm from the anorectal angle.
Mid rectal cancer:
Distal border is 5–10 cm from the anorectal angle.
High rectal cancer:
Distal border is 10–15 cm from the anorectal angle.
Involvement of the intersphincteric plane, external sphincter and levator musculature should be assessed. Low cancer localization increases the risk of CRM engagement.
2.6.2 Assessing T-stage
Determination of the T-stage (Figure 7) depends on the correct visualization of each individual layer in compliance with the MR-protocol. T category is characterized by the depth of tumor penetration into the rectal wall and extramural spread into the mesorectum and adjacent structures.
Figure 7.
Different T stages of rectal cancer: T2 rectal cancer (left) and T3d rectal cancer (right) (axial T2 weighted MR images).
in T1 and T2 rectal tumors is an intact external muscularis layer, which is identified as a hypointense thin line surrounding the rectum. T3-tumors grow through the external muscularis into the surrounding mesorectum, important is to classify T3 to T3a, b, c, d.
Consistency between MRI and histopathology in determining the T-stage was initially studied by Brown et al. [3], who found a 94% match between MRI and pT-stage. The MERCURY multicentre study directly compared the extramural depth of invasion as measured by MRI and histopathology.
Numerous histopathological studies have shown the importance of the T-stage. The T3 subclassification was developed because the majority of patients have a T3 tumor, but the heterogeneity in survival values is high:
pT3 with>5 mm tumor invasion have a worse 5-year survival (disease-free survival (DFS)) than tumors with an invasion below 5 mm (pT3b); and this regardless of the nodal status.
T3a tumors, with an invasion below 1 mm, have a very good prognosis
The values for local recurrence and overall survival of T2 and T3a are identical
The palpable difference in DFS between T3b and T3c shows that their differentiation is of greater clinical significance than the distinction between T2 and T3.
CRM is the surface of the nonperitonealized part of the rectum that is resected during surgery. In the description of T3-tumors, the report should include the shortest distance between the tumor margin and the mesorectal fascia MRF because of increased risk for local recurrence. MRF often refers to CRM. CRM > 5 mm measured by MRI is sufficient to predict microscopically clear resection lines (Figure 8).
Positive mrEMVI is associated with low survival rates. The 3-year survival in mrEMVI-positive patients was 35% compared to 74% in mrEMVI-negative patients. mrEMVI-positive patients have a fourfold increased risk of developing distant metastases.
The radiological characteristics of EMVI observed on MRI are described in detail -The veins around the rectum are recognized on the T2 sequence as serpiginous or curved linear structures; in the tubular structures considered to be blood vessels, in addition to changes in the contour, there is a weakening of the signal. A complete evaluation of mrEMVI should include the following: (entry into small veins may produce a nodular border); location of the tumor relative to the large vessels; vascular caliber (the tumor causes the vessels to dilate and amplify the tumor signal in the lumen) and the vessel boundary.
2.6.5 Assessing N- stage
The N-stage is an important risk factor for local recurrence. The size of the lymph node itself is not indicative, as 15–42% of patients with rectal cancer have small (<5 mm) mesorectal lymph nodes containing tumor cells (Figure 10, arrowheads).
Figure 10.
Lymph nodes (arrowheads).
2.6.6 Assessing mrTRG (special focus)
Tumor regression refers to the effect of neoadjuvant radiotherapy or chemotherapy on the tumor. The degree of tumor regression (TRG) is determined by the amount of residual tumor cells and the degree of fibrosis induced by non-adjuvant therapy. High tumor regression correlates with higher survival and lower rate of local recurrence. Several scales have been developed for TRG, such as Mandard and Dworak, but no consensus has been reached on which to use routinely.
After chemoradiotherapy, a number of tissue changes induced by radiation occur. These include swelling, inflammation, necrosis and fibrosis. mrTRG evaluates the changes on MRI after 12 weeks of neoadjuvant chemo-, radiotherapy.
This mrTRG system uses a 5-point scale. The low points [1, 2, 3] correspond to a more significant regression, and the high points [4, 6] mean no regression. The system also divides the categories according to the type of answer (complete, good, moderate, poor, none).
mrTRG1- radiologically complete response- linear, eccentric scar of 1–2 mm, limited in the mucosa or submucosa.
mrTRG2- good response- dense fibrosis without visualizing a residual tumor and without suspecting (Figure 11).
Figure 11.
Tumor regression grade on MRI: First picture T3d rectal cancer before neoadjuvant therapy. Second picture mrTRG 2/3 same patient after neoadjuvant therapy. Third and fourth picture another patient with T3 tumor before (third) and after (fourth) neoadjuvant therapy- mrTRG 4/5.
mrTRG3- incomplete response - over 50% fibrosis or mucin and visible intermediate signal intensity.
mrTRG4- weak response- small areas of fibrosis or mucin among tumor tissue (Figure 11).
mrTRG5- no response- intermediate signal intensity, tumor visualization without tumor dynamics or growth.
Many studies show that mrTRG is a prognostic and predictive biomarker- MERCURY trial, EXPERT-C trial [14], GEMCAD study, CORE study [5]. EXPERT – C study shows significant difference in rates of disease-free survival DFS and overall survival OS: mrTRG 1 & 2 (good response), mrTRG3 (medium response) and mrTRG4–5 (poor response) have a 3-year DFS survival of 82, 72 and 61%, respectively. These independent studies show that mrTRG predicts different groups- mrTRG could distinguish between “good” and “poor” responses to chemotherapy (‘good’ and ‘poor’ responders). It could be suggested that mrTRG can be used as a biomarker to stratify the choice of treatment for rectal cancer. Good responses (mrTRG1–2) are similar to good pCR, so surgery rejection and intensive follow-up of these patients can be chosen (watch and wait strategy). Poor responses (mrTRG3–5) could be subject to additional chemotherapy in order to improve mrTRG status to a lower grade. This requires the use of MRI to repeat the assessment of mrTRG.
mrTRG and pTRG were compared in patients with rectal cancer in two clinical trials (EXPERT and EXPERT-C). [14] The concurrence of the opinions of radiologists and pathologists was assessed with the weighted k test. The Kaplan–Meier method was used to evaluate the results of overall survival. Results: 191 patients were included in the study. The mean time from completion of neoadjuvant treatment to preoperative MRI and surgery was 4.1 weeks (IQR: 3.7–4.7) and 6.6 weeks, respectively (IQR: 5.9–7.6). good agreement was found between mrTRG and pTRG, with regression classified according to standard five-stage systems (kj0.24) or modified three-stage systems (kj0.25). Sensitivity and specificity of mrTRG 1–2 (complete / good radiological regression) for predicting the pathological complete response was 74.4% (95% CI: 58.8–86.5) and 62.8%, respectively (95% CI: 54.5–70.6) Survival outcomes in patients with intermediate pTRG 2 were numerically better if complete/good regression was also observed with mrTRG 1–2, compared with poor regression of mrTRG4–5 (5-year recurrence-free survival 76.9% vs. 65.9%, P00.18; 5-year overall survival 80.6% vs. 68.8%, P0.22).
Conclusions: The coherence between mrTRG and pTRG is low and mrTRG cannot be used as a substitute for pTRG. Further studies are needed to assess the ability of mrTRG to detect patients with a complete response to pTRG and to provide additional prognostic information to pTRG for better risk stratification after surgery.
Evaluation of the preoperative response to treatment of rectal cancer by MRI is an area of growing importance both in terms of predicting results and in determining the complete response. Clinical use is currently limited. The MERCURY study [13] shows that tumor regression can be assessed by MRT (mrTRG) after preoperative chemotherapy and radiation, using the differences in signal intensity between tumor and fibrous tissue. In this study, the 5-year overall survival (OS) was 27% for poor response (mrTRG4–5) versus 72% (p = 0.007) for good response (mrTRG 1–2), and the 5-year free survival was relapse survival (DFS) resp. 31% vs. 64% (p = 0.007). Nougart et al. [15] reported that volume assessment with MRI in patients receiving preoperative therapy was of prognostic significance. In this study, a reduction in tumor volume of at least 70% was associated with a better DFS value (HR 13.7; 95% CI 3.98–31.93).
Another PAN-EX study [16] by the same study group again demonstrated that mrTRG had greater value for prognostic factors such as relapse-free survival (RFS), long-term relapse-free survival (DFS), and overall survival (OS).
The main advantage of mrTRG is that it is not based on evaluation of resection material. The degree of tumor regression with MRI can be assessed before any surgery. This information provides a potential opportunity to consider other preoperative therapies. Previous analyzes of the PAN-EX study showed that patients who achieved mrTRG 1–2 after completion of CLT had a significantly better prognosis than patients who were assessed as mrTRG 3–5. mrTRG can potentially be used as an imaging parameter for the selection of patients with a good prognosis, in whom a non-operative approach after neoadjuvant treatment may be preferred. mrTRG appears as a dynamic, non-invasive, surrogate method for assessing tumor regression after neoadjuvant treatment and before surgical resection.
Be aware that the classification of patients as good and poor responders on the basis of mrTRG makes it possible not only to predict the outcome of the disease, but also to modulate therapeutic behavior. This means that patients may be advised to delay surgery, modulate chemo-, radiotherapy or choose another approach. The TRIGGER study [17] evaluated mrTRG as a new biomarker for stratification of patients with good and poor response to neoadjuvant therapy for rectal cancer and the inclusion of good responders in a new strategy, namely Watch & Wait.
2.7 Additional imaging modalities
Computed tomography, ultrasound and positron-emission tomography are imaging studies that could be complementary to MRI and be incorporated in the management of rectal cancer in some cases. Be aware that MRI is not available imaging tool in some institutions and CT and/or US are the only diagnostic choice for rectal cancer.
2.7.1 Computed tomography CT
Computed tomography CT (Figure 12) is not a modality of choice in the staging of rectal cancer due to the low resolution of the method and the inability to distinguish the different layers of the intestinal wall required for T-staging compared to MRI. CT is not applicable for detection of accurate T-stage, CRM- or EMVI involvement, but a method of choice for N- and M-staging and CT is still used in many centers. CT is not recommended for follow-up or for monitoring after therapy.
Figure 12.
CECT of rectal cancer, axial view, soft tissue window.
2.7.2 Ultrasound US
Endorectal ultrasound is effective diagnostic modality in the assessment of rectal cancer. Its accuracy in numerous trials is around 80% for T-staging and 70% for N-staging.
ERUS images of the rectal wall comprise three hyperechoic and two hypoechoic layers, which alternate with each other and correspond to anatomic layers. (Figure 13).
Figure 13.
Endorectal ultrasound illustrating rectal cancer invading beyond the rectal wall into perirectal fat.
On endorectal ultrasound, rectal tumors appear as hypoechoic lesions and are staged according to level of invasion through the rectal wall. Ultrasound stages are labeled with the prefix “u”.
ERUS can also be used to monitor for rectal cancer recurrence postoperatively. After surgery, the excision site appears as a pattern of mixed echogenicity, replacing the normal five-layer image.
ERUS is a method of staging rectal cancer which is human dependent. ERUS is less accurate for T staging of stenotic tumors, but the accuracy may still be within acceptable limits. Surgeons use ERUS to adopt a treatment protocol, knowing the risk of under-staging and over-staging of this method. The accuracy of ERUS is higher in diagnosing rectal cancer in stages T1, T2 and with less sensitivity for T3 and T4 tumors.
2.7.3 Positron emission tomography PET
Positron emission tomography PET with computed tomography is an additional method for functional staging by imaging in the following cases: [1] in unconvincing computed tomography and magnetic resonance data for primary tumor or distant visceral metastases with elevated values of tumor markers; [2] for N-staging; 3) for M-staging. Disadvantages are the high cost and low availability of the method. Inaccuracies in the differentiation of changes in the mesorectum and pelvic lymph nodes and inaccuracies in the assessment of mucinous tumors are known. It also cannot stratify patients with complete and incomplete response (Figure 14).
Figure 14.
PET/CT of rectal cancer.
3. Conclusion
In this chapter about rectal cancer there is content about rectal anatomy in relation to magnet-resonance imaging and TME- surgery (total mesorectal excision). There is a detailed description of imaging strategies concerning neoadjuvant and adjuvant radiotherapy and chemotherapy for rectal cancer patients. The staging and choice of treatment for rectal cancer are the main goal of any national and international organization in choosing guidelines and resp. guideline. The main guidelines are those of the European Society of Medical Oncology (ESMO), the European Rectal Cancer Consensus Conference (EURECCA-CC2) and the National Comprehensive Cancer Network (NCCN), but they also differ in their recommendations in some aspects of rectal cancer management.
Conflict of interest
The authors declare no conflict of interest.
Notes/Thanks/Other declarations
All figures (except Figure 6) are provided by Teneva MD from Department of Imaging Diagnostics, University Hospital St. Marina, Varna, Bulgaria.
Abbreviations
MRI
magnet-resonance imaging
DWI
diffusion-weighted imaging
US
ultrasound
CT
computed tomography
PET
positron emission tomography
MRF
mesorectal fascia
EMVI
extramural venous invasion
CRM
circumferential resection margin
pCR
pathological complete response
mrTRG
magnetic resonance imaging of the tumor response tumor regression grade
pTRG
histopathological tumor regression grades
TEM
transanal endoscopic microsurgery
TME
total mesorectal excision
DFS
disease-free survival
OS
overall survival
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Conclusion",level:"1"},{id:"sec_26",title:"Conflict of interest",level:"1"},{id:"sec_23",title:"Notes/Thanks/Other declarations",level:"1"},{id:"sec_26",title:"Abbreviations",level:"1"}],chapterReferences:[{id:"B1",body:'Siddiqui MRS, Simillis C, Bhoday J, Battersby NJ, Mok J, Rasheed S, et al. A meta-analysis assessing the survival implications of subclassifying T3 rectal tumours. Eur J Cancer Oxf Engl 1990. 2018;104: 47-61.'},{id:"B2",body:'Patel UB, Taylor F, Blomqvist L, George C, Evans H, Tekkis P, et al. Magnetic resonance imaging-detected tumor response for locally advanced rectal cancer predicts survival outcomes: MERCURY experience. J Clin Oncol Off J Am Soc Clin Oncol. 2011 Oct 1;29(28):3753-60.'},{id:"B3",body:'Sclafani F, Brown G, Cunningham D, Wotherspoon A, Mendes LST, Balyasnikova S, et al. Comparison between MRI and pathology in the assessment of tumour regression grade in rectal cancer. Br J Cancer. 2017 Nov 7;117(10):1478-85.'},{id:"B4",body:'Campa-Thompson M, Weir R, Calcetera N, Quirke P, Carmack S. Pathologic Processing of the Total Mesorectal Excision. Clin Colon Rectal Surg. 2015 Mar;28(1):43-52.'},{id:"B5",body:'Martin-Richard M, Gallego R, Pericay C, Garcia Foncillas J, Queralt B, Casado E, et al. Multicenter phase II study of oxaliplatin and sorafenib in advanced gastric adenocarcinoma after failure of cisplatin and fluoropyrimidine treatment. A GEMCAD study. Invest New Drugs. 2013 Dec;31(6):1573-9.'},{id:"B6",body:'van Gijn W, van den Broek CBM, Mroczkowski P, Dziki A, Romano G, Pavalkis D, et al. The EURECCA project: Data items scored by European colorectal cancer audit registries. Eur J Surg Oncol EJSO. 2012 Jun 1;38(6):467-71.'},{id:"B7",body:'Battersby NJ, Dattani M, Rao S, Cunningham D, Tait D, Adams R, et al. A rectal cancer feasibility study with an embedded phase III trial design assessing magnetic resonance tumour regression grade (mrTRG) as a novel biomarker to stratify management by good and poor response to chemoradiotherapy (TRIGGER): study protocol for a randomised controlled trial. Trials. 2017 29;18(1):394.'},{id:"B8",body:'Glynne-Jones R, Wyrwicz L, Tiret E, Brown G, Rödel C, Cervantes A, et al. Rectal cancer: ESMO Clinical Practice Guidelines for diagnosis, treatment and follow-up†. Ann Oncol. 2017 Jul 1;28:iv22-40.'},{id:"B9",body:'Benson AB, Venook AP, Al-Hawary MM, Cederquist L, Chen Y-J, Ciombor KK, et al. Rectal Cancer, Version 2.2018, NCCN Clinical Practice Guidelines in Oncology. J Natl Compr Cancer Netw JNCCN. 2018;16(7):874-901.'},{id:"B10",body:'Dworak O, Keilholz L, Hoffmann A. Pathological features of rectal cancer after preoperative radiochemotherapy. Int J Colorectal Dis. 1997;12(1):19-23.'},{id:"B11",body:'Mandard AM, Dalibard F, Mandard JC, Marnay J, Henry-Amar M, Petiot JF, et al. Pathologic assessment of tumor regression after preoperative chemoradiotherapy of esophageal carcinoma. Clinicopathologic correlations. Cancer. 1994 Jun 1;73(11):2680-6.'},{id:"B12",body:'Horvat N, Carlos Tavares Rocha C, Clemente Oliveira B, Petkovska I, Gollub MJ. MRI of Rectal Cancer: Tumor Staging, Imaging Techniques, and Management. RadioGraphics. 2019 Feb 15;39(2):367-87.'},{id:"B13",body:'Bhoday J, Balyasnikova S, Wale A, Brown G. How Should Imaging Direct/Orient Management of Rectal Cancer? Clin Colon Rectal Surg. 2017 Nov;30(5):297-312.'},{id:"B14",body:'Dewdney A, Cunningham D, Tabernero J, Capdevila J, Glimelius B, Cervantes A, et al. Multicenter randomized phase II clinical trial comparing neoadjuvant oxaliplatin, capecitabine, and preoperative radiotherapy with or without cetuximab followed by total mesorectal excision in patients with high-risk rectal cancer (EXPERT-C). J Clin Oncol Off J Am Soc Clin Oncol. 2012 May 10;30(14):1620-7.'},{id:"B15",body:'Nougaret S, Castan F, de Forges H, Vargas HA, Gallix B, Gourgou S, Rouanet P; GRECCAR Study Group. Early MRI predictors of disease-free survival in locally advanced rectal cancer from the GRECCAR 4 trial. Br J Surg. 2019 Oct;106(11):1530-1541. doi: 10.1002/bjs.11233. Epub 2019 Aug 22. PMID: 31436325.'},{id:"B16",body:'Sclafani F, Brown G, Cunningham D, Wotherspoon A, Tait D, Peckitt C, Evans J, Yu S, Sena Teixeira Mendes L, Tabernero J, Glimelius B, Cervantes A, Thomas J, Begum R, Oates J, Chau I. PAN-EX: a pooled analysis of two trials of neoadjuvant chemotherapy followed by chemoradiotherapy in MRI-defined, locally advanced rectal cancer. Ann Oncol. 2016 Aug;27(8):1557-65. doi: 10.1093/annonc/mdw215. Epub 2016 May 23. PMID: 27217542.'},{id:"B17",body:'Battersby NJ, Dattani M, Rao S, Cunningham D, Tait D, Adams R, Moran BJ, Khakoo S, Tekkis P, Rasheed S, Mirnezami A, Quirke P, West NP, Nagtegaal I, Chong I, Sadanandam A, Valeri N, Thomas K, Frost M, Brown G. A rectal cancer feasibility study with an embedded phase III trial design assessing magnetic resonance tumour regression grade (mrTRG) as a novel biomarker to stratify management by good and poor response to chemoradiotherapy (TRIGGER): study protocol for a randomised controlled trial. Trials. 2017 Aug 29;18(1):394. doi: 10.1186/s13063-017-2085-2. PMID: 28851403; PMCID: PMC5576102.'}],footnotes:[],contributors:[{corresp:"yes",contributorFullName:"Tsvetelina Teneva",address:"tenevaz@gmail.com",affiliation:'
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