This lecture discusses the principles of aberrometry, and interpretation of aberrometry maps and its clinical uses. In addition the lecture discusses the strengths and limitations of different topographers in commercial use, and constructs a decision tree for the practicing ophthalmologist as to which topographer may best suit their practice.

Lecturer: Dr. Aravind Roy

Understanding Aberrometry from Cybersight on Vimeo.

#### Transcript

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DR ARAVIND ROY: Hello, everybody. And welcome to one more webinar on the continuation of the topography that we discussed last evening, and aberrometry in clinical practice. For those who are joining us newly, let me introduce myself. I am Aravind. I work as a cornea and anterior segment consultant at the LV Prasad Eye Institute in India. We have no financial disclosures or conflicts of interest. So while I start the lecture, let’s get the first of all question for the audience. Please state your position. Okay. So most of us who have joined us today are ophthalmologists. 77%. And residents or registrars. 18%. So let’s start the discussion. Like in the last discussion, we will have an interactive discussion. And please feel free to interrupt at any point in time. Send your questions. I will try my best to answer your queries. All your doubts. So I’ll start my discussion with the second poll question. That: What do you understand by optical wavefronts? Which of the following statements would best describe optical wavefronts? So there are four choices. Please feel free to select anything that best describes this phenomenon. So typically, light passes through here. So most of the participants have correctly answered all of the above. So when light passes through any optical media, it actually is diffracted or refracted, and if it is a perfect wavefront, it will have a particular orientation, which will differ from person to person. For example, whenever light passes through any optical media, then that is an ideal way in which it would get refracted, if there are no imperfections in the optical system. But if there are imperfections of the optical system, as for example in the eye, when there are imperfections in the cornea, in the lens, or any of the conducting media between the cornea to the retina, then the imperfections would be different at different points of time, across the pupils. So there will be a difference between what it should be and the way it actually is. Those differences are the wavefronts. And they are measured from the source. So those wavefronts which are in the same phase are in the same pathway. But they may be in front of or behind the reference plate. So all the aberrometries, which measure aberrations in the eye, are based on the Scheiner or the Scheimpflug’s principle. So the Scheiner disc is a disc with two holes in it. As shown here, the reference ray passes through the central axis of the eye. It passes undeflected. The aberrometer measures alpha and beta so that it comes into focus at B, so basically by measurements of the alpha and beta, one can calculate the degree of aberrations across the pupil. So this is the Hartmann-Shack lenslet. So there is a lenslet, which are a set of lenses. And whatever passes through them, through the pupil, actually goes into arrays of this lenslet, and then they are captured by the video camera and processed by the computer. From that, they calculate the aberrations of the eye. Now, one can calculate the aberrations of the eye either by passing rays of light into the eye, or they can use a laser source, which when reflected from the eye, passes through the lenslet array, and is analyzed after passing through the Hartmann-Shack lenslet into the sensor. So this is basically the output from the pupil. So the pupil is the circular thing that you’re seeing here. And each minor rod is actually the rays of light or the rays of energy from the retina, and as they pass through the pupillary aperture, there will be several aberrations that they suffer, when they pass through the optical medium of the eye, which produces a composite structure, which can be represented by a composite wavefront. That in turn can be the component of several such aberrations. For example, the normal aberration that is recorded from the human eye can have a component of defocus, astigmatism, coma, triangular astigmatism, and spherical astigmatism. I would like to take questions at this point in time, if you have any. And we will also be proceeding with the talk. Okay. So just to recap, there is a laser light, through which — which passes through the lenslet arrays of the Hartmann-Shack sensor. And this produces a composite wavefront, which can have several components. The defocus, astigmatism, coma, triangular astigmatism, and spherical astigmatism. So we have one question now. Let me take that. Yeah. All right. One of our viewers have asked: does defocus mean refractive error? Well, refractive error is actually a combination of sphere and cylinder. And all those components of the vision that cannot be corrected by the spherocylinder actually fall into the category of the higher order aberrations. So yes, defocus would be a refractive error. That’s correct. Okay. So we’ll go to the next poll question. That: Which of these are higher order aberrations? Tilt, defocus… I just partly answered this question. So I think this will be easy. Okay. So as most of the viewers have correctly answered, it is trefoil, pentafoil, coma, and spherical aberrations which are really higher order aberrations. So we’ll be learning more and more of this in the subsequent slides. So when the aberrations are analyzed, they are split into several components. These can be adjusted by several mathematical equations. They could be corneal analysis, or a polynomial. So Zernike polynomials are a common way of denoting the aberrations of the eye. So they keep on expanding exponentially, as the rays of light hit complexly, diffract the optical area of the eye. So as we can see, the tilt polynomials, and then would be the astigmatism. And they keep on progressing into co-mass, astigmatism, trefoil, tetrafoil, and so on. The common aberrometer in clinical practice is the Orbscan. So it typically gives the output, as you can see in your screens, which has a wavefront. So the colors that you see over here are actually which beams of light are in phase and which beams of light are not in phase. Meaning that those beams of light — rays which are in phase — are shown by one concentric circle that you are seeing over here, over a particular pupil size. So all reds are in phase and all blues are also in phase, but the reds are actually compared to the blues, which are behind. So that produces a conical or a complex kind of a wave shape, as you can see. And this is a three-dimensional structure. Now, if you just look at the polynomial here, the defocus would be something like this. The red is ahead and the blue is behind. And there are other components also to the output, which is what we are discussing now. So this is the tab selection, which gives you the number of ways that it can display. The summary, the 2D plot, the PPR, which is nothing but the autorefraction, which is done by the machine. And the higher order point source function. And there is the beta sector here. So the map on your right is the higher order map. The map on your left is the total wavefront map. The data below is the total data. And this is the interesting function, which we will discuss on in later slides. So this is the higher order point spread function, which is a key concept in understanding the interpretation of maps. So any questions at this point in time? So the data overview — typically from any patient would have the eye which is examined. Whether it’s the pre-op or post-op, the dilatation of the pupil, the diameter of the wavefront, which is important for refractive surgery. The maximum undilated pupil size. That will help you plan the treatment. The refraction. Or the predicted refraction at 3.5 millimeter and at full. Then it gives you the Zernike, which are typically 5 or 6 millimeter pupil, in terms of microns. And the higher order Zernike without the Z400. The Z400 is typically for spherical aberrations. So these two values are very important in interpreting the aberrometry map. Because they are the absolute degree of higher order aberrations that are denoted by this figure, which is the 6 millimeter size, and the higher order Zernike, without this aberration, which is denoted by the value below. So this tells us how much is the impact of the spherical aberrations on the total aberrations of the eye. This is an important thing to note when you are reading the aberrometry map. What is your total aberration, and what is the aberration without the Z400, or the impact of the spherical aberrations? Okay. Please ask any questions, in case you have any doubts at this point in time. Okay. So understanding the complexities of aberration — this would be a very useful article to refer to. And this article suggests several key points. In the interpretation of aberrations. So there are several important key concepts that one should understand. That the light rays from the center of the pupil play a greater role in defining visual acuity. Secondly, specific wavefronts, which are near the center of the Zernike pyramid tend to affect retinal image quality, as compared to those along the edge. Third, various combinations of aberrations can either improve or decrease the quality of the retinal image. It depends on the amount of aberration that are there and the way they are combined. Neural processing is important, and the amount of neuroplasticity is very important. So this is an important article to understand aberrations. We have one more question. Okay. So the Zernike pyramid is actually, as discussed in a couple of slides… When we try to fit the aberrations to mathematical models, we can use several analysis techniques. One would be the Fourier, the Taylor, or the Zernike. So as the wave, the rays, are diffracted, becomes more and more complex, the way it can be fit into mathematical models, are increasing. So when we see that, it’s the Zernike pyramid that we have discussed some slides ago. So for your reference, let me go back to that. Yeah. So as it increases in complexity, the pyramid — this is basically unrefracted. And as it increases in complexity, the base becomes more and more broad. This will be the Zernike. Okay? So we discussed these key concepts, which will be helpful in understanding the way the aberrations affect visual function. So with this, we’ll go to the fourth poll question. Which higher order aberrations are clinically significant? Okay. So… Yeah. So the majority have answered that coma and spherical aberrations are visually significant. Yes, that is correct. Most of the aberrations that are of clinical significance are coma and spherical aberrations. And this is followed by the other higher order aberrations. But probably in the visual processing, these may not play a significant role. So when we talk about aberrations, we have to understand that this is the complete optical map. It is not limited to the corneal aberrations. It is the total aberration of the eye. Because when the eye diffracts the ray of light, it’s the cornea, vitreous, and the lens before it hits the retina. So the aberrations that are measured are total. They involve the entire optics of the eye. And they are also analyzed in total. And they in turn are processed by the neural processing of the brain, which affect the visual function, finally. Coma and spherical aberration — they play a very important role in the vision. So we are going to discuss a little bit in detail about coma and spherical aberration. So spherical aberration, it will typically appear or be denoted as this. On the figure on your right is actually the total aberration map. And on your left is the foveola test. So that is all the points of light, at the place of the observer. So that will be typically a spiderweb pattern, or a typical halo. Again, observe the foveola test. So this will be a typical halo, and there will be spiderweb patterns. And look at the measurement of the higher order aberrations. For 6 millimeters, it’s something like 0.58 microns. And without the Z400, which is the spherical aberration, it’s 0.27. So this suggests a dominant effect of spherical aberration on the total aberrations of the eye. So whenever you see an aberration map, and you see a point source function, if it is circular or like a halo, having a spiderweb type of appearance, you can understand that this kind of aberration is dominated by spherical aberration. Compared to the other aberrations. And if there is a coma, then the coma will have a comet-like appearance. And there will be one apex and a base. As seen by this foveola test here. And typically there will be very little effect on the Z400. So if you see, the Z400 and the total aberrations of the eye — there is hardly any difference. The higher order aberration for 6 millimeters is 0.78, and without the Z400 is 0.76. Almost no difference. And you see a foveola test which is like a comet, and there is a small contribution of the spherical aberration. So this is a kind of aberration where spherical aberration plays a smaller role. So foveola test we have already discussed. It depends on the total aberrations of the eye, displays without the spherical aberrations. So it also shows how the point source of light will appear to the observer. Any further questions, at this point in time? Okay. So we have just had an overview of the several concepts of aberration. How aberration is measured. What is the principle. And how to interpret and understand how much aberrations play a role in our visual function. So continuing, a quick recap on what we discussed on topography last time. There are several topographers. There are topographers which are not only just measuring the topography, but give several functions which help in the clinical practice. So I will conclude the part of the discussion from the last webinar on topography, about choosing a topographer that will suit your practice well. So I’ll go to the quick poll question. What is the topographer that you commonly use in your clinical practice? Okay. So most of our users are using Pentacam, followed by the Orbscan. And then there are some of our viewers who are using the Nidek, Atlas, and Tomey. So we will see the topographers suited for which function and how it will potentially affect your practice. So topographers can have different principles on which they work. Typically they may be reflection-based. Including the keratometry, photokeratoscopy, videokeratoscopy, projection-based, slit scan-based, Scheimpflug based, spot reflection based, or hybrid topographers. So choosing a topographer depends upon the kind of practice that you have. So if you predominantly have a refractive practice, and you’re doing some amount of cataract, you can be aided in this by a Pentacam, Galilei, or any Placido-based system. If you also do topography or aberrometry, you may choose the Orbscan, OPD, or the iTrace. I have one question now, about what is iDesign Wavefront? I’m not really clear about that. But if you like, we could have a private chat. Detail your question, please. Okay. So… Going to the first type of topographers, which are based on the Placido system. So the keratoscope or the Placido — this is time-tested, and this is the standard of care. For a long, long time, in clinical ophthalmology. This article on chasing the suspect, Dr. Klyce speaks about keratoconus, which has a normal abortive kind of a syndrome, which typically does not evolve into keratoconus, and there are no signs of keratoconus in the other eye. As opposed to the keratoconic suspect which definitely has a disorder of the topography, but there is no clinical evidence of keratoconus in either of the eyes. So the keratoscope in a Placido-based topographer is a reflection-based topographer, and it picks up minute corneal irregularities. Pentacam has been widely in use, and in addition to topography, it has several other useful features. So it can be used for decision of premium IOL, can give you a cataract preoperative scan, gives a densitometry map, it’s useful for cataract grading, useful for planning IOL in the refractive surgery setting, and has a Belin-Ambrosio enhanced ectasia display. So the output from the Pentacam typically has these four components to it. So there is the actual spherical curvature… Sorry. The aberration maps, the corneal thickness, and the front and back elevations. So there is a reference surface, and anything which is above 6 diopters and up, 6 points above the reference, for the front elevation, as well as above the back elevation, is considered to be normal. In addition, it gives an array of numerical data, which is on the right, which gives the apex pachy, the anterior chamber depth, et cetera. It also provides summary statistics where deviations from normal parameters are flagged in red. This is the display of the Belin-Ambrosio enhanced ectasia display. It provides the front/back evaluation, the difference between that and the difference between the pachy. The corneal thickness is shown by a red line as two categories of CTSP, which is the corneal thickness spatial profile, and the percentage thickness index, and the average is following the central line, which is the median for the typical population, and two standard deviations above and below. So any line that crosses the two standard deviations is abnormal. The Sirius is another platform for topography. It uses also a Scheimpflug principle. And in addition to topography, it provides several universal clinical data, such as the lens densitometry analysis, glaucoma analysis, dry eye evaluation, keratoconus analysis, and contact lens analysis. It provides topographic data in terms of summary maps of corneal thickness. Tangential curvature, and posterior elevation maps. It provides a keratoconic summary, and corneal maps. And dry eye evaluation is done by detection of dry spots on the anterior tear film, and it can be done by a study of the lacrimal glands. Contact lens fitting — it has a database of different contact lens manufacturers, and it can estimate the fit and see what is the pooling pattern based on the maps. That is the contact lens fitting analysis feature of this topographer. The Galilei is another useful unit, which has a double Scheimpflug camera. The advantage of the double Scheimpflug camera is that it gives a 3D image of the cornea. The G6 software for IOL power calculation helps in giving an accurate calculation of the intraocular lens. Keratoconus analysis is much more sensitive, and it gives the best fit toric analysis. Now, most topographers give the best fit sphere. The best fit is actually in the evaluation which is much more sensitive than the analysis for keratoconus. This is the software for intraocular lenses. And as I was suggesting, the unit gives the anterior and posterior best fit. So these are very sensitive to detect any subclinical keratoconus, and the probability is given in the bottom right of the display. So technically, any indexes which is more than 52 or the corneal volume, more than 50.8, or a pachy of 508 or more… Are typically suitable for laser refractive procedure. So this can also be very accurately measured. And determined from point to point. Across a large area of the cornea. The Orbscan is one that is tested, tried, and very familiar unit in any clinical ophthalmology practice. It has been there for quite some time, and it has evolved from the first generation and so in addition, there is a white to white, which is very helpful for calculation of implantable lenses. So if you look at this Orbscan map, this is quite obviously a keratoconic eye. And there are a set of red flags, which are important in interpreting the Orbscan. So one is the ratio of the anterior to the posterior best fit sphere. This should not be above 1.27. So I’m talking basically about the elevation BFS. Which is 42.8 for the anterior and 49.40 for the posterior. So as for the red flags for the Orbscan, this ratio should not be more than 1.27. The best fit sphere should not be above 50 diopters. This should not be above 55, the max that is there. Then on the posterior float — I’m sorry. Let me be — the posterior best fit sphere should not be above 55. This is the red flag. I’m sorry for that. Yeah. Then the other parameter that one should look for is that on the posterior float, there will be a high point, which is demarcated by the red color, and there will be a low point, which will be the deep blue or violet. When you add up these two, this should not go above 100. So when you place on the Orbscan — actually, this will display it better. This will be 20, 30, 35. This will be another value, which will be 30, 20, 40. This is typically the elevation. So the difference adding these two should not go above 100. This is another red flag for keratoconus. Then there is the corneal thickness index. And this is basically the ratio between the central pachy and the peripheral pachy. This should not be 1.1. And there should not be an asymmetric or broken border, as is seen here. And the irregularity, the 3 and 5 millimeter zone, should not be more than 1.5 in the 3 millimeter zone or more than 2.5 for the 5 millimeter zone. So if there are… And then, when we interpret a suspicious map, there is a 1, 2, 3 rule. If there is one abnormal map, one should be cautious. If there are two abnormal maps, there is a cause for concern, and if there are three abnormal maps, it is definitely a contraindication for refractive procedures. The other newer topographers are the Cassini, which uses colored LED lights to map the corneal topography from the front and back surface of the cornea. So the distance between the lights is measured, to know the elevation of one point of the cornea. This can also be integrated with the LensAR laser system, for cataract surgery. The iTrace helps in evaluating aberrations. It uses a dynamic spiroscopy for evaluating the optical aberrations. It is using for planning the intraocular lenses, and also has several parameters, by which we can know the quality of vision. So any questions up to this point in time? Okay. So it’s very common to have patients in your clinic who would be having discomfort in night driving or difficulty with night vision. And at the same time, they are in their mid-50s or 60s and so when we see these patients and check for their aberrations, it’s not uncommon to see there is a lot of higher order aberrations. So this could be a preclinical or subclinical lenticular opacification, which is changing the eye and causing distortion of visual phenomena, especially in dim light, when the pupil is slightly larger in size. So this is called dysfunctional lens syndrome, and this may also warrant an early intervention, in terms of cataract extraction. So these subtle findings of the density of the lens, the change in the aberrations, the increased internal higher order aberrations can actually warrant and help the clinician to go for early cataract surgery. The OPD III from Nidek is another platform, which can help in many ways. In addition to topography. It can act as a keratometer, it can be a topographer, and it can help in giving a cataract summary analysis, which can help with toric IOL planning. In addition, one can also take topography of the meibomian glands, and thus it can act as a meibographer, and help in evaluation of dry eye spots. Okay. Any questions up to this point in time? Okay. So when we see across the board, these are some of the common topographers that are in clinical use. One is the Pentacam. Which is very widely used. As also seen by our poll, most of our users are using Pentacam in their clinical practice. It has elevation display. It has a Belin-Ambrosio enhanced ectasia display, it helps in premium IOL planning. And ERK maps. So this is widely used and accepted. However, it may be a little expensive, compared to the other topographers that are in use. The Orbscan is time tested. It has very clear criteria for detecting keratoconus. It has been in the clinics for quite some time. So there is a lot of familiarity with these maps. And it gives the white to white, which helps us plan the ICL parameters. The Galilei is not widely used, but it is emerging slowly. It has the G6 software for accurate IOL calculations, and it also gives several important keratoconic parameters, such as the best fit reference surface. The Sirius is helpful for both keratoconic indices and dry eye. In addition, it can have a role in your contact lens practice, and helps in detection of dry eye by meibography. However, again, it is not widely used. The OPD III has an aberrometer in addition to its other roles. It may have repeatability issues. The Cassini is good to accurately measure the posterior astigmatism. It may be helpful to plan your premium IOLs. Factor for the posterior astigmatism. But then again, it may have some difference in its measurements, compared to the other commercially available topographers. So the need of a good topographer for a cataract and refractive surgeon can be manifold, and it also depends on what kind of data that you use commonly. So if there are refractive indices, and there is a keratoconic screening, and a wide variety of refractive surgeries that you do in your practice, then the Pentacam or Placido-based system can be more useful. The Q value is measured by the amount of corneal asphericity. And this can be useful to optimize the IOL for refractive treatment. The white to white value is calculated best for ICL calculations by the Orbscan. So I would like to thank my colleagues who have helped with the material. And I would also like to take questions from all on any other doubts or any other key concepts that you might like to discuss with me on this. Thank you very much. Okay. We have one question. Excuse me. I just lost my slides. Okay. So we have one question about how Q value affects the vision. So Q value is the degree of corneal asphericity that is there. So whenever there is a high degree of corneal asphericity, the quality of vision will suffer. And in these cases, you would preferably implant an aspheric IOL. So this is probably a good indication to use any of the aspheric IOLs in common clinical use, such as the IQ or the Bausch and Lomb Adaptive Optics intraocular lens. One of the questions are… About aberrometry. Okay. One of the articles that I have shown in my slide — this is a good read to people who want to understand aberrometry. This is making sense of the wavefront sensing, from 2005. And from there you can definitely branch out and read different aspects of it. Okay. We have some more questions. The calculation of IOL post-LASIK — there are several calculations by which you can do. The clinical method is very accurate. One can also do post contact lens overrefraction, and you can also use the several software that are incorporated in either your G6 software in Galilei, or you can use the iTrace. So there are several such software, which are now coming incorporated into your IOL-calculating units, that are there in addition to topography. And you can also use the online calculator to calculate the intraocular lens that you need to implant. Post-refractive surgery. Okay. So one more question that is coming up is: what is the use of aberrometry in refractive surgery? This is a very interesting question. There are two ways of looking at this. So one is that there is something — the wavefront optimized refractive surgery. And the other is called the wavefront-guided refractive surgery. Or the wavefront-guided ablation. So wavefront-optimized ablation is basically that the blend zone is created at the periphery of the aberration. So that there is no abrupt areas of ablated and non-ablated cornea. Those areas which are on the periphery of the ablation may not have the same density of the ablating laser that is being done there, as compared to the central cornea. This would be the category of wavefront-optimized ablation, because there are blend zones. The wavefront-guided ablation would probably be — not only correct for the power of the eye, but would also attempt to correct the preoperative higher order aberrations. So that you at least would not end up with more higher order aberrations than you would normally expect, if you had corrected without factoring in the aberrations. I hope my answer is clear to you. And if we do a wavefront-customized ablation, the hypothesis is that typically these treatments are more accurate and use less higher order aberrations, and the quality of vision is better. Our studies, which have been done using both the techniques, have found that the results are pretty much similar. Whether they are myopic or hyperopic corrections. Okay. We have some more time here. Any further questions? Okay. Aberration having any relation with age and gender? Yes, with the aging eye, the density of the lens changes, and that may affect the quality of vision. Gender, probably not. And a patient presenting with sudden increase in cylindrical power, and Orbscan is normal? Unlikely. It can, but unlikely. Usually if there is a corneal component to the cylinder, then there will be a change in Orbscan. However, if it could be due to trauma or a tilt in the lens, or we are looking into a genetic condition, like Marfan’s, or homocystinuria, then it could also produce a change in the cylindrical power. Change of — during pregnancy? Do you mean the aberrometry or the topography by this? Change during pregnancy? Topography will definitely change during pregnancy, due to the effect of the hormones. And also, they revert back to normal, about 6 to 8 months after nursing. Is it necessary to check aberrations in all LASIK patients? Preoperatively, probably it’s a good idea to have a record of the aberrations that are there. And you may choose to correct a higher amount of spherical aberrations by doing aspheric treatment, or offering aspheric treatment. Can the posterior corneal astigmatism affect calculation of IOL power in refractive surgery? Yes, it can do that. The orientation of the posterior cornea changes with age. And it needs to be factored in for your toric IOLs. So technically, yes, it can affect your outcomes. And also needs to be factored in, and some of the newer algorithms and topographers factor in the posterior astigmatism. They also measure a component of the total astigmatism called corneal astigmatism, which is also useful in planning your toric IOLs. The other question that a number of viewers have asked is is the Zernike pyramid useful? Yes, Zernike pyramid is commonly used. It is helpful for researchers to discuss the degree of spherical aberration that is there. It is useful to discuss with the patient what kind of aberrations are there in the components of total aberrations of the eye. And mostly the coma and the higher order aberrations are important. Visually. There are changes in the way the lenses are, in some lenticular changes — that may lead to similar kind of visual phenomena. I hope that answers your question. So I think we have a little bit of time left. So we would be very happy to take any further questions that you will have. Okay. We have one more question. Just let me see. Okay. So the Allegretto versus the VISX — I think the VISX integrates the aberrations. Allegretto — I’m not sure about that. Does post-cataract persistent visual problems… Like arcuate flash means lens tilting? If you mean that flashes that are seen by a patient who has been operated for cataract surgery… Well, then, that would mean that one needs to check the retina, to see if there are any breaks, or any diffraction of the retina. Lens tilting would probably cause distortion of the images or decrease in the quality and quantity of vision. If the retina is okay, then one should look at the total aberrations of the eye. One of our viewers have asked if the lecture is available online. I think Lawrence can answer that for you. And maybe you can get back to Lawrence and get in touch with him. Okay. Yeah, I answered this question. This is a question about the difference between wavefront-guided versus wavefront-optimized. So wavefront-guided actually creates a blend zone so there are zones between the posterior and anterior cornea. And the wavefront-optimized surface — the wavefront-guided laser is basically where you take into account the aberrations of the eye and try to decrease the higher order aberrations. So you try to basically either bring down the total amount of aberrations that are induced by the refractive surgeon, or decrease the amount of aberration that will be there, post-refractive surgery. Does that answer your question? So if… There are no further questions, then maybe we can end the session here. Thank you very much. And it was a pleasure discussing the concepts with you. And I hope you also had a very informative session. Have a great day. Thank you.

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