\r\n\tThe LED can be lingering further into three major categories are (i) Traditional inorganic LEDs, (ii) Organic LEDs (Small Molecule OLED, Polymer LED, Passive Matrix OLED Active Matrix OLED), (iii) High brightness LEDs, (iv) Deep-UV LEDs, (v) Active Matrix Organic Light-Emitting Diodes (AMOLED).
",isbn:"978-1-83968-886-7",printIsbn:"978-1-83968-885-0",pdfIsbn:"978-1-83968-887-4",doi:null,price:0,priceEur:0,priceUsd:0,slug:null,numberOfPages:0,isOpenForSubmission:!1,hash:"97e861d1556a639f0e5cc6ee8bdb0a0f",bookSignature:"Prof. Jagannathan Thirumalai",publishedDate:null,coverURL:"https://cdn.intechopen.com/books/images_new/10559.jpg",keywords:"Aluminum Gallium Arsenide, Gallium Arsenide Phosphide, Indium Phosphide, Thin-Film-Display, Organic Rare-Earth Complexes, Colour Rendering Index, High Brightness Leds, Luminous Control, Air Purification, Skin Therapy, Organic Compounds Form the Electroluminescent Material, Specific Type of Thin-Film-Display",numberOfDownloads:14,numberOfWosCitations:0,numberOfCrossrefCitations:0,numberOfDimensionsCitations:0,numberOfTotalCitations:0,isAvailableForWebshopOrdering:!0,dateEndFirstStepPublish:"September 21st 2020",dateEndSecondStepPublish:"October 19th 2020",dateEndThirdStepPublish:"December 18th 2020",dateEndFourthStepPublish:"March 8th 2021",dateEndFifthStepPublish:"May 7th 2021",remainingDaysToSecondStep:"3 months",secondStepPassed:!0,currentStepOfPublishingProcess:4,editedByType:null,kuFlag:!1,biosketch:"As an expert in the optoelectronics and nanotechnology area, Dr.Thirumalai has been invited to examine several MSc and Ph.D. theses, invited to give a talk in various forums, and to review papers for international and national journals.",coeditorOneBiosketch:null,coeditorTwoBiosketch:null,coeditorThreeBiosketch:null,coeditorFourBiosketch:null,coeditorFiveBiosketch:null,editors:[{id:"99242",title:"Prof.",name:"Jagannathan",middleName:null,surname:"Thirumalai",slug:"jagannathan-thirumalai",fullName:"Jagannathan Thirumalai",profilePictureURL:"https://mts.intechopen.com/storage/users/99242/images/system/99242.png",biography:"Dr. J. Thirumalai received his Ph.D. from Alagappa University, Karaikudi in 2010. \n\nHe was awarded the Post-doctoral Fellowship from Pohang University of Science and Technology (POSTECH), Republic of Korea, in 2013.\nHe worked as an Assistant Professor of Physics, B.S. Abdur Rahman University, Chennai, India (2011 to 2016). \nCurrently, he is working as an Assistant Professor & Head of the Department of Physics, SASTRA Deemed to be University, Kumbakonam (T.N.), India. \n\nHis research interests focus on luminescence, self-assembled nanomaterials, thin-film optoelectronic devices & Supercapacitors. \n\nHe has published more than 60 SCOPUS/ISI indexed papers, 11 book chapters, and he edited 5 books. He is serving as a member in various national and international societies. Currently, he is acting as a principal investigator for a funded project towards the application of luminescence-based thin-film optoelectronic devices, funded by the Science and Engineering Research Board (SERB), India. \nAs an expert in optoelectronics and nanotechnology area, he has been invited to examine several MSc and Ph.D. theses, invited to give a talk in various forums and to review papers for international and national journals.",institutionString:"SASTRA University",position:null,outsideEditionCount:0,totalCites:0,totalAuthoredChapters:"10",totalChapterViews:"0",totalEditedBooks:"6",institution:{name:"SASTRA University",institutionURL:null,country:{name:"India"}}}],coeditorOne:null,coeditorTwo:null,coeditorThree:null,coeditorFour:null,coeditorFive:null,topics:[{id:"11",title:"Engineering",slug:"engineering"}],chapters:[{id:"74673",title:"Economic Applications for LED Lights in Industrial Sectors",slug:"economic-applications-for-led-lights-in-industrial-sectors",totalDownloads:14,totalCrossrefCites:0,authors:[{id:"150046",title:"Prof.",name:"Muhammad M.A.S.",surname:"Mahmoud",slug:"muhammad-m.a.s.-mahmoud",fullName:"Muhammad M.A.S. Mahmoud"}]}],productType:{id:"1",title:"Edited Volume",chapterContentType:"chapter",authoredCaption:"Edited by"},personalPublishingAssistant:{id:"297737",firstName:"Mateo",lastName:"Pulko",middleName:null,title:"Mr.",imageUrl:"https://mts.intechopen.com/storage/users/297737/images/8492_n.png",email:"mateo.p@intechopen.com",biography:"As an Author Service Manager my responsibilities include monitoring and facilitating all publishing activities for authors and editors. From chapter submission and review, to approval and revision, copyediting and design, until final publication, I work closely with authors and editors to ensure a simple and easy publishing process. I maintain constant and effective communication with authors, editors and reviewers, which allows for a level of personal support that enables contributors to fully commit and concentrate on the chapters they are writing, editing, or reviewing. 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Examples of the above can be observed in different disciplines such as transport [1, 2], mining [3] and agriculture [4] among others. However, in the area of optimization, many problems still work at the level of reference instances [5, 6, 7, 8]. To solve real optimization problems, we must consider that these are generally multi-variable problems with restrictions and trade-off between them. In many instances, when a problem is modeled, a point that is not taken into consideration is the uncertainty to which the system is subject. In this sense, our solution can be submitted to questions of the type: How feasible is this solution according to the different scenarios? What is the optimality of this solution? How strict should the treatment of uncertainty be? One way to approach uncertainty is to consider the robustness of the solution. However, the definition of robustness is not trivial and there are several definitions. Ideally, you want to get the best solution and also the most robust one but usually there is a trade-off between these two concepts [9]. Due to the importance and particularity for each problem of this trade-off between the quality and robustness of the solution, a series of definitions have been generated and a series of methods developed to adequately address or estimate the trade-off [10, 11].
Because each problem has its own level of demand regarding the quality of the solution and its treatment with respect to its robustness, it is difficult to provide a single definition of robustness. In some cases, our solution could be considered robust if under certain conditions of the search space or under certain operational conditions, the solution behaves reasonably with respect to its quality, feasibility or optimality. Under other conditions where the management of uncertainty is very strict, the most appropriate result is associated with scenarios that consider the worst case [12].
On the other hand, it has been methodologically argued [13] that instead of transforming and solving the optimization problem with uncertainty in a robust problem, this can be solved in two stages considering the robustness as a separate objective [13]. The argument is based on the fact that a separate analysis allows obtaining more information and understanding about the solution and its robustness, facilitating the decision-making process. On the other hand, considering robustness as part of the problem has advantages over implementation, computational cost and alternatives to solve the problem. In the latter case, modeling the choice of scenarios and the measure of robustness is essential [14].
The aforementioned discussion indicates that the concepts of robustness are still in the process of maturation and there is no clear methodology on how to address robust problems. There are conceptual, computational and application challenges in the area of robust optimization. Usually, the few state of the art reviews found about robust optimization, focus on identifying what areas and types of problems have been addressed. In this article, as a starting point, we present a collection of the different definitions and models with which robust optimization problems have been addressed. Knowledge of the different models used in robust optimization is essential for a proper understanding of the field. Once the main concepts are defined, we proceed to provide an update on the main robust optimization works that have been carried out over the last few years. In Section 2, we will describe the basic concepts associated with uncertainty. We will describe the main robustness models in Section 3. Finally, in Section 4, we will describe the main areas of application.
Suppose an engineer who must make constant decisions and face the difficulty of multidimensional problems with some degree of ambiguity or errors in the parameters to analyze and some kind of stochastic uncertainty of the process and its environment. Then this engineer must also determine if the proposed solution is robust. This means that the solution is feasible to apply for any parameter scenario and stochastic uncertainty and that this feasibility remains close to the optimality condition. Then two fundamental concepts appear: the uncertainty of the feasibility of the solution and the uncertainty of the objective value of the function.
Ideally, the engineer would like his or her solution to be feasible for any value of the parameters analyzed; however, this feasibility has consequences. The first consequence corresponds to having a significant computational cost when considering all the possible parameter values. The second consequence is related to the deterioration in the quality of the solution. The more demanding it is with regard to the feasibility of the parameters, the greater the probability of moving away from optimality. Therefore, there is a trade-off, which is related to the problem that is being solved. Then solutions in the area of control theory related to equipment failures should be much stricter regarding the feasibility of the solution than solutions obtained in marketing areas where the effect on a set of clients is not so critical. Therefore, the choice of the uncertainty set plays a fundamental role in the feasibility of solving the problem and in the quality of the solution obtained.
It may happen that depending on the set of uncertainty chosen, the optimality of the solution is altered. In this case, robust optimization tries to obtain a solution that performs adequately in the different scenarios; however, all scenarios do not require the same treatment with respect to optimality. Due to the above, in the literature, we can find different concepts of robustness; among the most mentioned are: strict robustness [15], cardinality constrained robustness [16], adjustable robustness [17], lightweight robustness [18], soft robustness [19], lexicographic robustness and regret robustness.
Each real optimization problem suffers from some type of uncertainty that are mainly caused by uncertainty at the level of the measurements or by uncertainties due to changes in the environment of the system. The first case we will refer to microscopic uncertainties and the second will be macroscopic. The optimization problem can be approached in a standard way through a nominal scenario which would describe, for example, the most typical case or an average case. However, in general, the most probable scenario is not trivial to obtain and for some problems, having a more frequent scenario is not the natural way to approach the problem [20]. An optimization problem with constraints can be formally written as shown in Eq. (1).
where
In most problems, it is not known exactly what the value of
Finite uncertainty
Interval-based uncertainty
Norm-based uncertainty
Polytopic uncertainty
Constraint-wise uncertainly
This section aims to formally define the main concepts of robustness used to solve optimization problems with uncertainty. In each of the ways to approach robustness, the intuition that exists behind the definition is described; later, the sets that model the uncertainty are characterized and then the problem is written in its robust version. Finally, articles where the definition has been used are referenced.
Let
Then the strict robust problem corresponds to the problem formulated in Eq. (4),
To the best of our knowledge, the first to use strict robustness was Soster in [21], where he applied uncertainty to convex sets, solving the problem using linear programming. Later, this work was extended and placed in a theoretical framework in the articles [22, 23]. The essence of strict robustness is that all scenarios can occur and all of them have an important criticality. In real problems, this type of robustness is necessary in critical systems where a failure is not tolerable. For example, the case of air planes and nuclear plants. However, in other types of problems, such as revenue management, public or scheduling, this type of robustness can be relaxed.
One way to relax the strict robustness is to restrict the space of uncertainty. There are several ways to achieve this restriction. In cardinality constrained robustness, the property is used that it is unlikely that all the uncertainty parameters change at the same time when analyzing the worst case. Then, we can restrict the cardinality of the uncertainty space by varying only some parameters; the others are modeled with their representative values.
Let
This approach was conceptualized by Bertsimas and Sim [16] for continuous problems. Later, this approach was extended to combinatorial problems in the articles [24, 25].
Another way to relax the space of uncertainty of strict robustness, corresponds to divide the space into groups of variables. A first group will be called here and now variables. These variables correspond to variables that must be evaluated before the scenario
Let
Then once we have fixed the variables here and now, we must make sure that for any of the selected
where
Given a u, the worst case
And therefore, the split robustness is given by Eq. (10).
The first one to introduce the concept of adjustable robustness was Ben Tal et al. [17] applied to uncertainly problems in linear programming. However, the concept has continued to develop and adapt and nowadays, applications are being seen in portfolio selection [26], in power systems [27], capacity extension planning [28], aperiodic timetabling [29], among others.
A completely different way of relaxing the concept of strict robustness corresponds to instead of reducing the space of uncertainty, we can relax the constraints in favor of the quality of the solution. This new concept that is called light robustness, this concept considers as a fundamental hypothesis that if we are able to adequately solve the optimization problem considering the nominal (or average) case, the solution should not be bad and basically, we can concentrate on finding relatively close solutions of the fitness that also fulfill in the best possible way the restrictions of the problem considering all
The concept of light robustness was introduced by Fischetti and Monaci [30], the main objective of its new definition was to allow a trade-off between robustness and quality of the solution. A constraint is added by entering the parameter
Originally, the concept of light robustness was conceived to be applied to problems of linear programming [30] and specifically, in time optimizations in Italian single-line instances. Later, in [31] light robustness was applied to determine the best route to traveling in a public transport network in Germany. Later in [18] the concept was generalized taking into account any optimization problem and any set of uncertainty.
The regret robustness described by [32] uses a way to relax the problem through the objective function. Let
Today, we see used in the concept of regret robustness in different areas. In [33], it was used in portfolio optimization problems. In safety investment problems, it was used in [34]. In [35] it was used to solve evacuation planning models.
Recoverable robustness uses the concept of recovery algorithm and, like adjustable robustness, it obtains the solution in two stages. Give a family of algorithms
The concept of recoverable robustness was developed in the article [36] applied to shunting problems and later refined in [37] applying recoverable robustness to railway problems with linear programming. Today, we find the concept of recoverable robustness applied to location planning [38], scheduling and delivering routing [39], allocation and network design problems [40], robust traveling salesman problem [41] and transit network design [42], among others.
In this section, we will describe some examples where robust optimization has been applied. Mainly identified areas have been logistics, finance, water management, energy management and machine learning.
Energy management has received significant attention with respect to robust optimization. In [43] a strategic planning model applied to the integrated oil chain was designed. For the design, it was considered as sources of uncertainty: crude oil production, demand for refined products and market prices. The robust version of the demands for a power plant problem was studied in [44]. In this article the phases of unit commitment and economic dispatch were considered to minimize the local cost. A robust model of energy distribution under uncertainties with respect to wind energy was studied in [45]. In this article, it was shown that the proposed method can be solved in suitable times in addition to being able to effectively capture the ambiguous distribution of wind power generation. In [46], the configuration of the energy consumption of household appliances under the uncertainty of manually operated devices (MOAs) was modeled as a problem of robust optimization. When evaluating all the possible cases of the energy of MOAs, the traditional approach was chosen, that is, using the worst case with the intention of reducing the payment of electricity for all the household appliances. To determine the reduction in the payment, the price of electricity in real time was considered as information in addition to the inclining block rate.
In [47] robust optimization was used to handle the uncertainties of water planning resources. In [48] the authors developed a new methodology for the optimizing daily operations of pumping stations. This methodology takes into consideration the fact that a water distribution system is actually unavoidably affected by uncertainties. A multi-objective robust decision-making approach was developed in [49]. This approach supports seasonal water management. In [51], a comparison of Robust Optimization and Info-Gap Methods for Water Resource Management under Deep Uncertainty was made. A multi-objective design of water distribution systems under uncertainty was developed in [50]. The main objectives are (1) minimize the total water distribution system (WDS) design cost and (2) maximize WDS robustness. In the article, the WDS robustness is defined as the probability of simultaneously satisfying minimum pressure head constraints at all nodes in the network.
In [52] regularized support vector machines (SVMs) were considered, and they were shown to be equivalent to a robust formulation of the problem. The authors show that this equivalence between robust optimization and regularization has implications for both algorithms and analysis. The equivalence of robustness and regularization provides a robust optimization interpretation for the success of regularized SVMs. On the other hand, Fertis in his doctoral thesis [53], studied the connection between regularizations like Lazo and robustness. Specifically, he showed that in classical regression, regularized estimators like lasso can be obtained by applying robust optimization to the classical least squares problem. He discovers an explicit connection between the size and the structure of the uncertainty used in the robust estimator, with the coefficient and the kind of norm used in regularization. Xu et al. [54], investigated a probabilistic interpretation of robust optimization. They established a connection between robust optimization and distributionally robust stochastic programming (DRSP). In the article, they showed that the solution to any robust optimization problem is also a solution to a DRSP problem. In [55] the problem of constructing robust classifiers when the training is subject to uncertainty was studied. The problem is posed by a chance-constrained programming, which ensures that the uncertainty of the data is correctly defined with high probability.
In the area of logistics problems such as the traveling salesman and routing problem have been explored in their robust versions. A Swarm intelligence system was designed in [56] to solve the vehicle routing problem with time windows and uncertain travel times. The uncertainty here models the perturbation in the data. This perturbation, is caused by the effects of unpredictable events, such as traffic jams, road building, etc. In the article, the authors proposed a heuristic approach using ant colony optimization as a metaheuristic. In [57], the open vehicle routing problem with uncertain demands was studied. In this problem, the vehicles have as an additional function that they do not necessarily return to their original locations after delivering the products to the customers. First, the authors modeled the demand of the clients as specific sets of limited uncertainty with expected values of demand and nominal values. Having the sets modeled, they later proposed a robust optimization model that aims to minimize transport costs and unsatisfied demands on the specific uncertainty sets defined. The robust vehicle routing problem with time windows was solved in [58]. They proposed two new formulations for the robust problem, each based on a different robust approach. They proposed two new formulations for the robust problem, each based on a different robust approach. The first formulation uses adjustable robustness with the aim of extending the well-known formulation of resource inequalities. The second formulation generalizes a path inequalities formulation to the uncertain context. In this case, uncertainty is modeled in the formulation of the problem. In [41], an uncertain traveling salesman problem was developed. In this problem, the distances between the nodes are not exactly known, but they can be obtained from a set of uncertainties of possible scenarios. This set of uncertainties is modeled as intervals, including an additional limit associated with the number of distances that can deviate from their expected nominal values. In the study, a recoverable robust model was proposed. This model allows a tour to change only a limited number of borders once a scenario is known; all these with the goal of minimizing the complexity in calculations. The robust traveling salesman problem with interval data was studied in [59]. In the article, travel times are specified as a range of possible values. They applied the robust deviation criterion to drive the optimization over the interval data problem thus obtained.
Another interesting group of problems in the logistics area corresponds to facility location problems. The robust formulation of these problems aims to obtain an optimal design of a system considering uncertainty. The authors introduce a robust optimization-based approach to obtain some capacity expansion solutions that are not sensitive to this uncertainty. In this area, we highlight the work carried out by [60], where they considered the question of how to make a decision about capacity expansions for a network flow problem that is subject to demand and travel time uncertainty. The authors introduce a robust optimization-based approach to obtain some capacity expansion solutions that are not sensitive to this uncertainty. They show that the robust modeled solution is a computationally tractable problem when considering general uncertainty sets together with reasonable conditions for network flow applications. Another interesting problem in this area is the robust transmission expansion planning. In [61] the authors address the problem of transmission expansion planning, considering uncertainties in the electric power system. They consider varied sources of uncertainty such as: the growth of future demand, the availability of generation facilities, geographical characterization within the electric power system. A robust adaptive optimization model is used to obtain investment decisions with the objective of minimizing the total costs of the system and anticipating the worst-case materialization of the uncertain parameters within a uncertainty set.
Public goods can be understood as a merchandise or service that is provided non-profit to all members of a society. This merchandise or service, can be provided by the government, an individual or an organization. When we consider public goods and robust optimization, interesting applications appear. An interesting first application corresponds to radiation therapy. When a radiation therapy examination is performed, there are uncertainties that are fundamental to consider in defining the correct treatment in patients with cancer. In this context, addressing problems through robust optimization makes a lot of sense. In [62] the authors constructed an uncertainty model of the movement of respiration based on probability density functions. These functions allowed them to robustly model the optimization of intensity-modulated radiation therapy.
Another interesting implementation associated with the application of robust optimization to public goods corresponds to intrahospital transport. Intrahospital transport is often required for reasons associated with a diagnosis or some therapy that the patient must perform. Depending on the design of the hospital, transportation between the nursing rooms and the service units is provided by ambulances or by trained personnel accompanying patients on foot. When the hospital is large, the patient transport service is often poorly managed and there is no associated flow coordination; on the other hand, there is no clarity of all the necessary transports since they are dependent on the diagnoses. In [63] the authors address the problem of defining robustness to patient flow management in the context of optimized patient transport in hospitals. In [64] a methodology was proposed to obtain a robust logistics plan to mitigate the uncertainty of the demand for humanitarian relief supply chains. More specifically, the authors formulated the problem as a robust optimization problem with the objective of dynamically assigning emergency response and generate evacuation traffic flow, all this in the context of time-dependent demand uncertainty.
In this article, we have carefully reviewed the different definitions that have appeared in the literature to address the concept of robust optimization. We have taken special care to formalize each of the definitions and cite specific examples where they have been used. Subsequently, a review was made in areas where robust optimization has been applied. In particular, the areas of water management, energy management, machine learning, logistics and public goods stood out. With the advent of the concepts and technologies associated with the Internet of Things and Big Data, it is expected that the problems described above have a greater amount of data to build more robust models; however, this brings challenges regarding the complexity of the algorithms, in addition to the learning and operation of these in real time.
When we analyze the research works developed in the area of robust optimization, we found that there is a lack of a formal argument that clearly defines the uncertainty set to be used to solve the problem in a robust way. Usually, the choice is guided by business intuition together with the need to adapt the uncertainty set to solve the problem in a reasonable time.
Therefore, there is an important space to develop quantitative studies to determine what kind of robustness and uncertainty set should be used to solve a problem. Identifying how different uncertainty sets behave for a defined problem is fundamental. To be able to answer questions such as: How is the quality of the solutions perturbed with the choice of the uncertainty set?, Is this perturbation important for the problem that is being solved?, How is the convergence of the algorithm altered against different sets of uncertainty?, Can we classify problems according to some degree of robustness? Can this classification be related to the type of uncertainty to be used? The answer to these questions allows developing a methodology that allows identifying which is the robustness required by the problem, what type of uncertainty set should be chosen and how is the behavior of the algorithm in terms of quality of its results and convergence.
As future lines of research in the area of robust optimization, we see that considering these group of definitions together with the different applications mentioned earlier, we can work on developing a methodology that gives a specific problem, allows in a simple way to identify which definition is the most appropriate and which methods they are the most appropriate to solve the problem at reasonable times.
Regarding the tractability of robust problems, we have not found solutions where the hybridization of metaheuristics with other techniques is exploited such as integration with mathematical programming, with simulations or integration with machine learning, all these with the goal of improving convergence times of algorithms.
Particularly, according to our experience in the integration of machine learning and metaheuristics, a line that must be explored corresponds to the use of a general scheme of integration of these two areas through the use of metalearning techniques. Considering that we have a set of algorithms or settings of some algorithm, we use a mechanism that selects the best algorithm or settings for given an instance to obtain the best convergence and results. Furthermore, the use of reinforced learning can be explored to enrich the meta-model with the new results generated.
Coronary heart diseases remain a prominent cause of morbidity and mortality [1]. Percutaneous coronary intervention (PCI) is the current standard treatment and aims to widen the lumen, restore the blood flow into the vessel and consequently re-perfuse the ischaemic myocardium. A catheter is fed through the femoral artery until the blocked coronary and the balloon inflated. A stent is then placed and maintains the artery opened to limit adverse vessel remodelling and elastic recoil.
Since 2003, the standard of care is the balloon-expandable, drug-eluting metallic stent. Steady improvement of stent technology promoted a rapid evolution from the first generation of the bare-metal stents (BMS, permanent metallic structure without drug release) to the last generation of drug-eluting stents (DES, permanent metallic structure with anti-proliferative drug release). The BMS and DES are mostly made of a cobalt-chromium alloy and remain lifelong in the artery of the patient. Several studies showed, however, that life-threatening complication, emerging several months or years after implantation, may occur, including restenosis due to neointimal hyperplasia and late in-stent thrombosis [2]. Novel therapeutic approaches to reduce persistent inflammation, stenosis and thrombosis are focused on anti-proliferative and anti-inflammatory processes such as drug-eluting stents [3], pharmaceutical [4, 5] or laser-based approaches [6, 7] as well as bioresorbable stents [8].
In this context, an appropriate animal model is paramount to foster the development of new therapies, to provide in vivo preclinical proof of concept, to evaluate the treatment performance and to promote translation to the clinic. The rabbit-injured iliac artery model has been well established to investigate the vascular response to hyperplasia and stenosis or thrombosis [3, 8, 9].
In the present study, we evaluated the vascular responses to bilateral iliac artery injuries performed by balloon denudation and stent overexpansion, using a high-resolution ultrasound imaging system. We explored the longitudinal evolution of the vessel morphometries and the blow flow.
Three male New Zealand white rabbits (3.5–4 kg) were obtained from the Charles River Laboratories, France. The animals were housed in the animal centre facility at the University of Fribourg (Switzerland). All animals received humane care in compliance with the European Convention on Animal Care and in accordance with the Swiss Animal Protection Law after obtaining permission from the State Veterinary Office, Fribourg approved by the Swiss Federal Veterinary Office, Switzerland (FR-2016/16).
Angioplasty: Under general anaesthesia induced with s.c. injection of Narketan (65 mg/ml) and Xylapan (4 mg/ml) and maintained by perfusion (Narketan 65 mg/50 ml, Xylapan 4 mg/50 ml, infusion 15–20 ml/h), heparin (100 UI/ml) was administered in the marginal vein using a 24 GA (BD Insyte) catheter. Body parameters, including temperature, heart rate and pO2 were controlled by a veterinary monitor (Midmark Cardell touch). In clean condition, an arteriotomy of the left coronary artery was performed, and a 6-French introducer sheath (Glidesheath Slender, Terumo) positioned. Two ml of a contrast agent (Bracco, Iomeprol 35 g) was injected, and a 0.36-mm guidewire is advanced through an introducer sheath up to the right iliac artery. Under angiographic monitoring of the pelvic area (Figure 1), the stent from Baxter (Coroflex Blue Neo) was deployed and overexpanded. The balloon was then retracted and then directed within the contralateral iliac artery (left), positioned at the same distance from the aortic bifurcation and inflated at 10 atm for 30 seconds to induce endothelial injury. At the end of the procedure, s.c. injection of Temgésic (1 ml/kg), Trimethazol (Werner Stricer, composed of sulfadoxine 40 mg/kg and trimethoprim 8 mg/kg) and carprofen 2.2 mg/kg (Rimadyl, Zoetis) were performed. The rabbit awoke within 1 h. Animals were kept on a normal diet for up to 8 weeks.
Bilateral iliac artery injuries performed by an inflated balloon (left artery) and stent overexpansion (right artery). (A) Diagram showing the positioning of the stent and contralateral balloon placement. Each animal received a single stent that was placed either close to the aortic bifurcation or distally. (B) Angiography of both iliac arteries: The stent was placed first in the right artery and overexpanded, and the balloon was then retracted back to the aorta and introduced into the left artery. Balloon inflation was performed at a similar distance from the aortic bifurcation. S, stent; B, balloon. (C) Illustration of the positioning of the stent: 8 weeks post-intervention, the right iliac was exposed, and the transmural visualisation of the stent confirmed the site of the stent placement.
High-resolution ultrasound image acquisitions were performed every week under general gaze anaesthesia induced by isoflurane 4–5% and O2 2–3 L/h. The animals were placed on an in-house-made platform, on a heating pad. The animal temperature was monitored through the rectal probe provided with the Vevo3100. ECG stainless steel needle electrodes provided with the Vevo3100 were placed subcutaneously on the four limbs (right and left upper, right and left lower). The respiration rate was derived from the ECG signal. Longitudinal analyses were performed with a Vevo3100, VisualSonic high-resolution ultrasound system equipped with a transducer MX400 (20–46 Mhz) hold with the imaging station arm. The images were acquired at day 0, 14, 28, 42 and 56 or 63 in all animals. The image analyses were performed with the VevoVasc analysis module. The following parameters were quantified: wall thickness, lumen diameter and cross-sectional area (CSA). Using a Doppler pulse-wave mode, the velocity-time integral (VTI) was extracted. The following calculation was performed with the measured parameters: the blood flow was calculated as the product of the VTI and the CSA of the respective segments. The percentage changes in parameters relative to the values before the intervention were calculated as a ratio of the parameter at day 14, 28 or 42 to the same parameter at day 0 and multiplied by 100.
Artery harvesting was performed after euthanasia. Distal aortic segment and both iliac arteries were harvested according to the well-established procedure [10] and cut in short segments for histological analysis.
Histology characterisation: OCT embedding the vessel segments was frozen in the vapour of 2-methylbutane placed in liquid nitrogen. Sections of 5 μm are obtained using a cryocut and were processed for Movat Pentachrome staining. Briefly, sections were fixed 1 h in Bouin for 56°C, stained with Alcian Blue followed by Verhoeff’s Elastic Stain, differentiated in ferric chloride solution, stained in brilliant crocein 1% and acid fuchsin 1%, placed in 5% phosphotungstic acid and stained with crocin. Sections were mounted with EUKITT®.
Stented segments were embedded in epoxy. 0.8-μm sections were cut with an ultramicrotome and stained with methyl blue.
The Bersoft Image Analysis software (Bersoft Technology and Software; Lunenburg, Canada) was used to quantify the vessel diameter and the wall thickness (including intimal, media and adventitia layers).
Values are presented as mean ± SEM. The percentage changes in wall thickness, cross-sectional area and blood flow were analysed using two-way ANOVA; Fisher’s LSD multi-comparisons were performed for the different segments and for the time effect. Linear regression and the parametric Pearson test were computed in a two-tailed manner. Analyses were performed using Prism software. Values were considered significantly different when p < 0.05.
We report the results from three rabbits that received a Coroflex Blue Neo BMS. In concordance with the standard clinical procedure, each animal received a stent with an appropriate diameter defined under angiographic monitoring. The respective diameter (mm) and length (mm) of the stents were 2.5/9, 3/13 and 3.5/8. The stent positioning and contralateral balloon injury were proximal from the abdominal aortic bifurcation for the two animals and distal for one animal, as shown in Figure 1. The interventions were performed successfully without complication. All animals appeared healthy without significant weight loss. No infection, oedema or arterial thrombosis was encountered. The wound area was normal.
The ultrasonographic vascular parameters were recorded before and after stenting or balloon injury every second week up to 8 weeks to evaluate the vessel structure. The imaging and measurements were performed at the injured and stented segments of the arteries as well as at the intact segments free from intervention situated distally and proximally of the lesion or stent, as controls (Figure 2A). The distal part of the abdominal aorta was also imaged and analysed (Figure 2B).
Longitudinal evaluation of the vessel structure. (A) The longitudinal measurements of the wall thickness and the lumen diameter of the right and left iliac arteries performed in different segments: at the site of the intervention (i.e. stent placement for the right artery and balloon inflation for the left artery) and at the proximal and distal uninjured segments as controls. Each animal and the corresponding stent are indicated and represented by a colour line. (B) Structure and VTI measured at the distal abdominal aorta. (C) Percentages of change in the crosssectional area of the vessel and the wall thickness relative to day 0 (preintervention, grey line) represented according to the vessel segment. Each line represents a different time post-intervention (day 14, 28 and 42). The results are shown as the mean of three animals and SEM. * p < 0.05 vs. day 0 and p < 0.05 vs. distal and proximal control segments.
We report in Figure 2A the values of the diameters and wall thicknesses of the stented and balloon-injured iliac arteries obtained for each animal. We chose to present each animal data to visualise the individual variations. For instance, after balloon injury, the vessel diameter increased transiently up to 14 days at the site of the injury. However, for two animals the diameter returned to initial size while staying enlarged for the third animal. A transient vessel enlargement was also observed for the distal and proximal controls. Likewise, the aorta wall thickness followed three different evolutions from day 14 to day 60 when considering each animal separately, the aorta wall thickness increased consistently for one animal (that received 3.5/8 the stent), alternate phases of augmentation and diminution for the second one (stent 3/13), while it decreased for the last rabbit (stent 2.5/9) after a transient increase (Figure 2B).
For the iliac arteries, as presented in Figure 2C, we calculated the mean percentage changes both, the wall thickness and the CSA relative to the pre-intervention. We showed a change of the wall thickness at the site of the stent. At day 14, the wall thickness showed a 133 ± 13% increase as compared with pre-intervention. For the proximal control segments, the wall thickness was not significantly altered over time.
In contrast, following balloon injury, the wall thickness remained constant, over time with a slight, but statistically significant, reduction (94 ± 1%, p = 0.01) observed after 42 days in the proximal segment.
In parallel, we report a significant increase (150 ± 9%, p = 0.03) in the CSA in the stented segment. The CSA remained elevated over time.
In contrast, the lumen CSA transiently increased in the left artery. The maximal significant change was 192 ± 35% in the injured segment as compared to the proximal (131 ± 31%, p = 0.02) and distal (145 ± 31%, p = 0.006) controls at day 14. The lumen area returned then to initial values.
Employing a pulsed wave (PW) Doppler mode, we recorded the velocity, extracted the velocity-time integral (VTI) and calculated the blood flow. As presented in Figure 3, for each animal, VTI gradually decreased over time in both, the balloon and stent-injured areas, and consequently in the distal control except for one animal.
Height and weeks for longitudinal evaluation of the VTI and blood flow. (A) Illustration of the PW Doppler recording of left stented iliac artery velocity. The measurements were performed in the distal segment. (B) The measurements of the VTI in the right and left iliac arteries before (day 0) and post-intervention were performed in different segments: at the site of the intervention—Stent placement for the right artery and balloon inflation for the left artery and at the proximal and distal uninjured segments as controls. Each animal and the corresponding stents implanted are indicated and represented by a colour line. (C) Percentages of change in the blood flow relative to day 0 (pre-intervention, grey line) represented in the function of the vessel segment. Each line represents a different time post-intervention (day 14, 28 and 42). The results are shown as the mean of three animals and SEM * p < 0.05 vs. day 0.
Overall, in the right artery, there was no significant difference in the mean percentage changes of the blood flow in the stented segments (Figure 3C) although a maximal mean reduction of 72 ± 12% was observed at day 14. Looking at the individual data of the VTI, we observed a large variability. In contrast, in the left artery, the longitudinal analysis showed a significant change of the blood flow, respectively, 62 ± 4% (p = 0.01) at day 28 in the distal segment, and 68 ± 3% (p = 0.01) recorded at day 42 in the left iliac artery. The transient increase of the blood flow observed at day 14 (173 ± 66%) was not statistically significant.
The lumen diameters at seven sites of the iliac arteries and aorta in the three rabbits subjected to balloon injury and stenting were quantified using both high-resolution ultrasound and histology. The correlations between the measurements performed by ultrasound and the histological analysis of the vessel diameter and the wall thickness, 8 weeks after the intervention, are presented in Figure 4A. We demonstrated a significant correlation between the two analytical procedures for both parameters, respectively, for the vessel diameter, r2 = 0.5, p = 0.006 and for the wall thickness, r2 = 0.21, p = 0.04. The thickening of the intima was observed prominently in the stented segment (Figure 4B) and for one animal in the distal area of the balloon-injured segment (Figure 4C). Alignments were performed on the different parts of the figures.
Histology evaluation of rabbit iliac arteries. (A) Correlation between the high-resolution ultrasound and histological measurements of the vessel diameters and wall thicknesses. The individual dots represent each value obtained in all the segments assessed 8 weeks post-intervention. (B) Representative methyl blue stained histologic cross section of an 8-week rabbit-stented right iliac artery showing the intimal hyperplasia. The staining pattern shows prominent intimal thickening in the stented segment of the iliac artery. S indicates the stent struts. (C) Movat Pentachrome stained histologic cross section of a rabbit left iliac artery 8 weeks after the balloon injury. N indicates luminal neointimal formation. Arrow indicates internal elastic lamina (IEL).
Mechanical endothelium injury is a standard strategy to induce hyperplasia in various animal models such as mice, rabbits or minipigs [9, 10, 17]. In the present study, the endothelial injury was induced by two different approaches in rabbits: first by overexpansion of a BMS in the right iliac artery and second with an inflated balloon in the contralateral left iliac artery. Stenting and balloon injury resulted in a respective permanent and transient overexpansion of the vessel inducing a well-recognised vascular response [11]. An acute inflammation rapidly follows the induced endothelium injury or denudation and peaks after a few days; then, the inflammation temporally declines during the resolution phase. Acute inflammation is accompanied by the proliferation of smooth muscle cells that results in hyperplasia. Consequent thickening of the wall (hyperplasia) may induce a narrowing of the vessel lumen (stenosis) and reduction of the blood flow.
In the present study, we showed that the rabbit iliac arteries and the distal abdominal aorta could be successfully monitored using high-resolution ultrasound for longitudinal and non-invasive investigation. The quality of the images acquired allowed rigorous measurements of the wall and vessel sizes. It is important to note that for some measurements, the possible presence of oedema could impair the quality of the image acquisition and may explain variations of the parameters in consecutive weekly measurements.
Besides, the metallic structures of the BMS were visualised as shadows. Although the presence of the metallic stent did not impair the wall thickness and vessel diameters’ quantification, the blood flow velocity measurements were often challenging to perform.
Comparing the acute balloon injury with the chronic injury associated with stent implantation, we reported that the response of the vessel differed with the type of intervention. The primary function of the BMS stent is to provide mechanical support. As expected, the stent allowed the maintenance of increased vessel diameter in all animals. In contrast, balloon inflation induced a short-term increase in the lumen size followed by a reduction suggesting a weakening of the artery.
Notably, the overexpansion of the stent affected the wall thickness that increased rapidly and remained elevated. Histology analysis revealed the formation of neointimal hyperplasia. In contrast, balloon injury results in a transient wall thickening recorded 2 weeks post-intervention with a successive return to the initial dimensions. Transient inflammatory response to the balloon injury may explain the wall. Accordingly, Welt et al. [12] reported a transient inflammation following a balloon injury model as compared with a sustained accumulation of inflammatory cells such as monocytes in stented iliac arteries of rabbits up to 14 days.
Furthermore, Virmani et al. [13] reviewed the temporal vascular response to BMS implanted in the rabbit iliac artery. Between 7 and 14 days, the intimal thickness increased due to inflammation and cell proliferation and then peaked at 1 month with a return of the cell proliferation to the basal level. Further shrinkage has been reported from 3 to 6 months due to the extracellular matrix remodelling. In agreement, we also report the shrinkage of the wall thickness observed at day 28 in the left artery.
As far as the evaluation of the blood flow is concerned, the VTI and the calculated changes in flow revealed notable individual variations. Nevertheless, the longitudinal evaluation showed that in all animals, the VTI decreased overtime in the left and right segments but remained stable in the proximal segments. Meanwhile, the calculated blood flow was significantly reduced at the site of the balloon injury and the distal segment but maintained unchanged in the stented segment.
Despite the neointimal hyperplasia developed within the stent, the blood flow was maintained due to the diameter enlargement resulting from the stent overexpansion. Nevertheless, it is essential to note a maximal 72% reduction of the blow flow, although the statistical significance was not reached due to the small number of animal and large variability.
The aorta underwent twice the passage of the catheter, once with the crimped stent followed by its retraction and second with the successive introduction into the contralateral artery. The vessel structure remained similar in all the animals, suggesting the absence of injury due to the procedure. An exception was observed for one animal that showed a continuous increase in the wall thickness. These effects may be explained by the large stent diameter and the placement site, close to the aortic bifurcation. Notably, the variations observed in the right artery and the aorta might be dependent on the size and location of the stents that varied between animals.
Moreover, we provide evidence that the wall thickness and the vessel diameter significantly correlated with the histological evaluation. Besides, histology provides evidence that the wall thickening in the stented area resulted in intimal hyperplasia. Neointimal hyperplasia was also observed in the left and right proximal control segments of two animals. Our results corroborate the well-established proliferation of smooth muscle cells resulting in the wall artery thickening induced by the stent and balloon injury [14, 15, 16].
In agreement with the literature, under conventional diet and following injury, rabbits developed wall hyperplasia that is known to be associated with inflammation and smooth muscle proliferation rather than atherosclerotic plaques that can be observed in hyperlipidemic rabbits [9, 17].
Although histological analysis is essential to evaluate wall composition, inflammation and smooth muscle proliferation, longitudinal study provides a useful tool to record transient variation in the vessel dimensions.
The non-invasive, real-time imaging of the rabbit iliac arteries and the distal abdominal aorta for the quantification of lumen diameter and wall thickness using high-resolution ultrasound permit the monitoring of the progression of the wall and vessel following balloon angioplasty and endovascular stent implantation. Conveniently combined with the blood flow analysis, this methodological approach would be essential to evaluate novel therapeutic approaches to prevent hyperplasia.
The study was supported by the Swiss National Science Foundation (SNF 316030_157658), the University of Fribourg and the Fonds Scientifique Cardiovasculaire FSC, Fribourg Hospital.
This is a brief overview of the main steps involved in publishing with IntechOpen Compacts, Monographs and Edited Books. Once you submit your proposal you will be appointed a Author Service Manager who will be your single point of contact and lead you through all the described steps below.
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\n\nPlease complete the publishing proposal form. The completed form should serve as an overview of your future Compacts, Monograph or Edited Book. Once submitted, your publishing proposal will be sent for evaluation, and a notice of acceptance or rejection will be sent within 10 to 30 working days from the date of submission.
\n\n2. SUBMIT YOUR MANUSCRIPT
\n\nAfter approval, you will proceed in submitting your full-length manuscript. 50-130 pages for compacts, 130-500 for Monographs & Edited Books.Your full-length manuscript must follow IntechOpen's Author Guidelines and comply with our publishing rules. Once the manuscript is submitted, but before it is forwarded for peer review, it will be screened for plagiarism.
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\n\nExternal reviewers will evaluate your manuscript and provide you with their feedback. You may be asked to revise your draft, or parts of your draft, provide additional information and make any other necessary changes according to their comments and suggestions.
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\n\nIf the manuscript is formally accepted after peer review you will receive a formal Notice of Acceptance, and a price quote.
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