To cut a long story short, Sanctorius brought together theoretical and practical knowledge from different contexts—dietetics, pharmacology, mechanics—and fused it in novel combinations. In the process, he reorganized and reinterpreted the medical system of his time, Galenic medicine, exploring to what extent quantifcation and measurements, as new epistemic tools, could serve to develop and to legitimize the physician's pursuit of medical knowledge. By integrating practical and theoretical knowledge, he decidedly brought medical practice into the realm of medical theory, which is best illustrated by his inclusion of instruments in his teaching of physiology, a highly theoretical discipline, in his day. Still, according to him, the physician was both a philosopher and an artist and thus Sanctorius, the learned Galenist, and Sanctorius, the diligent practitioner, existed side by side. Similarly, his work highlights both the elasticity of Renaissance Galenism and the incremental shifts in views of how the human body functions. His novel approach to physiology was a response not only to changing medical ideas and practices, but also culturally driven—by the contemporary enthusiasm for instruments and measurements and by concerns and habits regarding health advice. After this refection on the epistemic constellations that led Sanctorius to produce new knowledge, I will now turn more specifcally to his use of measuring instruments in medicine and briefy consider what has been learnt from their analysis.

#### **8.3 Quantifying Health**

Wind, water currents, pulse, body heat, humidity of the air, insensible perspiration—as this book has shown, the spectrum of parameters that Sanctorius proposed to measure and for which he developed instruments is quite impressive. Over the course of Chap. 7, it was demonstrated that it is often diffcult to assess whether Sanctorius's various measuring devices actually worked and could be used in the way he described them; and in the same vein, to what extent Sanctorius used them in his daily medical practice, and on how many different people, frequently remains unclear. With the exception of the weighing procedures with the Sanctorian chair, the Venetian physician hardly ever referred to the numerical outcomes of his measurements. And even in the *De statica medicina*, compared to the overall length of the treatise, only a fraction of aphorisms specify quantitative values.

This lack of numerical data might be explained by the impossibility of producing them. Another aspect to consider in this regard is that Sanctorius often directed his readers to his proposed but never published book *De instrumentis medicis* for more information on his instruments and quantitative observations. However, the scarce remarks on quantitative data might also point to the way in which Sanctorius conceived and used his instruments: as comparators. In this connection, the dissemination of precise quantitative measuring results and the elaboration of uniform scales most probably took a backseat. What was important was that the physician always used the same instrument with the same scale for an individual patient in order to make the measurements comparable and to monitor health trends. Although Sanctorius did not state this explicitly, with regard to his thermoscopes, he pointed to the fact that different instruments would produce different measuring results. He repeatedly indicated that, due to the considerable differences between individual patients, it was very diffcult to generalize measurements and make them applicable to many individuals. In view of this, concrete measuring results could indicate general tendencies, but a physician would nonetheless always have to take measurements of his own, of his specifc patient and using his specifc instruments. Even though Sanctorius explained in the *Commentary on Galen* that he used his *pulsilogium*, the thermoscope, and the weighing chair to assess the condition of a patient whom he had never seen before, he immediately qualifed this statement in the next sentence by explaining that he believed, along with Galen, that the exact and specifc quantity will not be comprehended by the physician. This implies that Sanctorius used his measuring instruments to generalize, if necessary, but was fully aware of the shortcomings of such a procedure. Against this backdrop, his silence on the quantitative results of his measurements appears in a different light—they were simply of secondary interest (Sanctorius 1612b: 376).

The preceding paragraphs have demonstrated that it is crucial to not isolate Sanctorius's measuring instruments from their original medical context. In fact, it is exactly this context that makes Sanctorius's undertakings special. Notwithstanding that he mostly based his devices on well-known phenomena and techniques such as the oscillation of the pendulum, or weighing, it was he who frst *applied* these to medical diagnosis, prognosis, and therapy—be it in thought or in deed. Therefore, the measuring instruments and their use can be understood only when considered in the framework of contemporary Galenic medicine. As was seen, Galen's concept of latitudes provided the starting point for Sanctorius's innovative idea of measuring deviations from the natural, healthy state of a body by means of his four most famous instruments. Although Sanctorius, in doing so, signifcantly departed from traditional medical theory and practice, his measurements must still always be related to these. Thus, his use of *pulsilogia* was deeply embedded in contemporary pulse theory, according to which the pulse frequency was but one of several parameters that indicated to a physician his patient's state of health. Similarly, the thermoscopes allowed Sanctorius to replace the subjective appreciation of body heat by means of touch, but in the face of traditional fever theory, it was not enough to determine the degree of heat in a patient to diagnose the disease. The impact of measured degrees of air's humidity on the body could only be understood when knowing the individual complexions of people living in a certain region, and even here many differences occurred. In order to defne a healthy excretion of insensible perspiration, Sanctorius considered it necessary to examine the effects of the six non-natural things on this bodily evacuation. Hence, on the one hand Sanctorius

ascribed a very important role to the quantitative observations which he made with his measuring instruments, but on the other, he considered them as new techniques of Galenic medicine, as complementary methods that mostly added to traditional, qualitative procedures and only occasionally replaced them. Sanctorius did at times aspire to a medical practice more systematically informed by quantifcation, but as the foregoing analysis has revealed, he did not consistently formulate a quantitative medical program. To be sure, quantitative methods played an important part in his medicine, but they were far from being wholly constitutive of it. Experience, measurements, and instruments served Sanctorius as a means to refne prior theory (Ragland 2017: 505, 527).

In this regard, it should be remembered that Sanctorius designed his instruments to enhance the certainty of medical knowledge with the aim of improving the practical work of physicians. This implies that he addressed his quantitative studies exclusively to colleagues. The inclusion of the illustrations and descriptions of his measuring instruments in the *Commentary on Avicenna*, an extensive medical textbook, further corroborates this assumption. It seems that Sanctorius held that every physician needed his devices in his daily practice. Accordingly, not the devices themselves, but their use was the main focus of attention. Operating these measuring devices called not for details of how they worked, but rather manual skill—this was far more important at the time than technological or mechanical knowledge. This might then explain why Sanctorius did not reveal more technical details of his devices and limited his descriptions of them to purely medical applications. However, in the 1626 edition of the *Commentary on Avicenna*, he stated that he had not published illustrations of his *pulsilogium* in previous works, since to properly convey to the reader how to build the device would require many plates; and this is why he decided to postpone a detailed description and illustration of the instrument until the work *De instrumentis medicis* (Sanctorius 1626: 21). From this it would appear that Sanctorius thought his readers, most of them physicians, capable of understanding the technical and mechanical details of his *pulsilogium*, if they just had enough detailed illustrations. Yet, evidently, Sanctorius and his fellow physicians, too, relied on the support of craftspeople to build the medical measuring instruments. Unfortunately, there are no sources regarding whether Sanctorius had assistants, not to mention their identities, and it is only by analyzing the material, practical dimensions of Sanctorius's work that we can seek to uncover their contribution to his quantitative approach to physiology.

With the weighing chair Sanctorius seems to have gone even a step further. The instrument not only enabled physicians to observe their patients' insensible perspiration of, but also offered laymen the opportunity to fnd and maintain an ideal weight. To this end, the weight watcher needed neither understand the mechanical properties of the device, nor have expert medical knowledge, as my own experimentation with the reconstruction illustrated. Even though it sometimes seems as if Sanctorius invited his readers in the *De statica medicina* to perform the weighing procedures themselves (Sect. 5.4.1), the treatise reads not so much as a guide to experimentation, but rather as a dietetic handbook for physicians, students, or other well-educated persons fuent in Latin (Sect. 4.1). In all likelihood, it served Sanctorius to demonstrate his authority and expertise (Steinle et al. 2019: 8). However, eleven years later, with the illustration and description of the weighing chair in the *Commentary on Avicenna*, Sanctorius seems to have been ready to ascribe some authority to his readers: to physicians, the observation of the *perspiratio insensibilis* in their patients, and to patients, the monitoring of their own body weight. In doing so, he ascribed authority also to another actor—the Sanctorian chair.

Turning to the impact of Sanctorius's works, it is interesting to note that a preliminary assessment regarding the reception of his measuring instruments suggests that they did not widely enter medical practice, let alone the household. Testimonies of Sanctorius's pupils and contemporary physicians show that there was a great interest in his devices, and scholars all over Europe made their own copies of them. Yet, these undertakings were often not related to medicine, but to other felds of study. Isaac Beeckman, for example, drew inspiration from Sanctorius's *pulsilogia* for his observations on vibrating chords. Agostino da Mula informed Giovan Francesco Sagredo about Sanctorius's thermoscopes not because the latter was interested in their medical application, but in the instruments *per se*. Even a century later, at the beginning of the eighteenth century, Giovanni Battista Morgagni approved of Sanctorius's quantitative approach to physiology, but I could fnd no evidence that he himself used a *pulsilogium* or a thermometer in his medical practice. Hygrometers, anemometers and other instruments to measure climatic conditions never gained a strictly medical identity. Only much later did the fever thermometer and bathroom scales fnd their way into medical practice and the household. All this implies that integrating Sanctorius's measuring instruments into medical practice was a lengthy process; indeed, the revised and novel versions of only some of his instruments eventually succeeded on this path.

Hence, contrary to what the new mechanistic vision of the body that evolved in the seventeenth century might lead one to expect, quantitative measurements with thermometers, balances, or *pulsilogia* did not gain in importance, either in diagnostics or everyday general medical practice. Quite the reverse, in fact: as Volker Hess has shown with regard to the thermometer, the concepts of fever the seventeenth and eighteenth centuries made the measurement of body heat a mere secondary interest (Hess 2000: 19–33). Only in the nineteenth century did the measurements of pulse, body temperature, and weight start to become established as standard diagnostic methods.15 The conceptual framework in which these practices and their attendant instruments gained importance was, of course, far removed from the one in which Sanctorius frst proposed their use. That this may have given rise to an anachronistic reading of the original instruments owing to their roots in the Galenic medicine become obsolete for the later devices, has been often overlooked or neglected by historians. But my study has clarifed how important it is to apprehend knowledge related to technical instruments and to the practices surrounding them *in its*

15Comprehensive studies of why pulse measurement and weighing became widespread or indeed, standard diagnostic methods in medical practice only in the course of the nineteenth century have yet be written. Kümmel (1974) touches upon the issue with regard to pulse measurement, and Frommeld (2019), with regard to bathroom scales.

*historical specifcity*, for only so can one understand and make sense of how knowledge was transformed in earlier times. Thus, to separate Sanctorius's measuring instruments from their Galenic context is to lose their historical meaning. Indeed, the late application of thermometers, scales, and pulse meters to medical practice fts with the more general historiographical observation that practices associated with the body in sickness and in health tend to be particularly resistant to the innovation and change forged by new scientifc theories or discoveries (Stolberg 2012: 519).

Contrary to this, with respect to medical research, Sanctorius's quantitative approach to physiology, especially his method of investigating the *perspiratio insensibilis*, immediately fell on fertile ground. Sanctorius's novel ideas paved the way for subsequent scholars to a mathematical and experimental analysis of physiological and pathological phenomena. Dissatisfed with the concepts of traditional Galenic medicine, these scholars were inspired by Sanctorius's novel approach in their creation of new medical theories. In the process, Sanctorius's name became inextricably linked to the quantitative investigation of the *perspiratio insensibilis* and his research method, weighing, was used until as late as the twentieth century.16 It seems ironic, in hindsight, that Sanctorius set the stage for a new medical science in which medical practice remained largely unchanged—the very opposite of what he intended.

#### **References**

16See: Benedict and Root 1926, Jores 1930, Newburgh et al. 1931, Wiley and Newburgh 1931, Müller 1991: 264, 275.

———. 1634. *Ars Sanctorii Sanctorii de statica medicina et de responsione ad Staticomasticem*. Venice: Apud Marcum Antonium Brogiollum.

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# **Appendices**

**Appendix I: Annotator Used to Study Sanctorius's Books**

#### *Brief Description*

Here, a screenshot of the digital annotator that I used to study Sanctorius's published works shows a sample page, namely from the frst edition of his *Commentary on Hippocrates*: the digitized image of the original page can be seen on the left, while the transcribed and searchable version of this same original page can be seen on the right. The words highlighted in yellow are my annotations, which become visible at the touch of a mouse and can be opened for editing with a click. This is illustrated by two examples: the word "quantitate," which I marked and categorized as a keyword; and the term "ratione idiosyncrisiae," for which I entered (in German) a brief summary of the (German) content of the next passages and accordingly categorized the annotation by subject matter, as in: "Inhalt" (content). In the far-right column, all the annotations that I made on the sample page from the *Commentary on Hippocrates* are listed in chronological order and their content is noted in full. The button in the top left-hand corner can be used to search through all the annotations that I made in a book and the tool directly above it, to scroll through the book page by page.

#### **Appendix II: Editions and Translations of the**  *De statica medicina*

It is diffcult to gain an overview of the numerous editions of the *De statica medicina*. Among the previous scholars who endeavored to compile a complete list of them, Arturo Castiglioni, and L. S. Ettari and M. Procopio succeeded at least in providing considerable detail (Castiglioni 1931: 783 f.; Ettari & Procopio 1968: 70–4). The following compilation of editions and translations of the *De statica medicina* is based on information gathered in online library catalogues using the *Karlsruher Virtueller Katalog* (KVK) and with the support of the Library of the Max Planck Institute for the History of Science, with slight modifcations based on my archival research in Padua and Venice. The editions and translations marked with an asterisk (\*) are those mentioned by Castiglioni and/or Ettari and Procopio, but which I was unable to fnd. I cannot claim the list is exhaustive, but I hope it illustrates the book's broad diffusion, particularly in its frst 150 years.

#### **Editions**

Appendices

Many of the eighteenth-century editions of the *De statica medicina* included a commentary by Giorgio Baglivi (*Canones de medicina solidorum*) and/or by Martin Lister. Here, only the frst editions published with one or both of the two commentaries are indicated.

#### **Translations**


2.1.2. Materials for Polyurethane Synthesis

The two types of polyester-polyols (named RP1 and RP2 in this paper, according to the compositions described below in 'Methods' section) that resulted from PET degradation were vacuum dried for 24 h at 50 ◦C and were subsequently used for polyurethane synthesis. Setathane D1160, hydroxyl content 5.4%, (SET, Allnex, Brussels, Belgium) was vacuum dried for 24 h at 50 ◦C before being employed in polyurethane synthesis. Diphenylmethane– 4,4 –diisocyanate, -NCO content 31.5% (MDI, technical product Desmodur® 44V20L, Covestro, Leverkusen, Germany), was used as received. The energetic plasticizer, triethylene glycol dinitrate (TEGDN), was synthesized and purified in the Military Technical Academy (MTA) according to a procedure found in the literature [36].

#### 2.1.3. Materials for Composite Rocket Propellants Based on Polyurethane Binders

The above-mentioned synthesized polyurethanes were employed as binder for the new rocket propellant composite formulations. The "green" oxidizer, phase-stabilized ammonium nitrate (PSAN), was prepared in MTA: ammonium nitrate (AN, min. 98%, Honeywell Fluka™, Seelze, Germany) and potassium nitrate (KN, 99%, ACROS Organics™, Fair Lawn, NJ, USA) were co-crystallized from aqueous solution, according to the procedure described in the literature [37]. As metallic fuel, two types of aluminum powder, with an average particle size <5 μm (99.5%, Sigma Aldrich, St. Louis, MO, USA) and 100 μm (99.5%, Sigma Aldrich, St. Louis, MO, USA), were used as received. As catalyst, iron oxide (99.9%, powder, Fe2O3, Sigma Aldrich, St. Louis, MO, USA) was employed as received.

#### *2.2. Methods*

2.2.1. Polyester-Polyols Synthesis through the Catalytic Degradation of Polyethylene Terephthalate (PET)

The polyester-polyols (RP1 and RP2) necessary for the synthesis of the binder were obtained following two main steps. In the first step, 1 mol of PET, 1.8 mol of PEG600, and tin(II) 2-ethylhexanoate (0.5% from PET wt.) were introduced in a four-neck round-bottom flask (with inlets fitted for a mechanical stirrer, a thermometer, a reflux condenser, and a nitrogen gas purging line), and they were maintained under an inert atmosphere, at total reflux, with continuous stirring, for 3 h at 190 ◦C. The reaction mixture was then cooled below 100 ◦C. In the second step were added 0.3 mol of PEG600, 0.5 mol of AS, 0.5 mol of AA, and TIPT (0.5% from PET wt.), and the reaction mixture was maintained under inert atmosphere, at total reflux, with continuous stirring, for another 4–6 h at 190–200 ◦C. The main possible reaction products obtained through this two-step catalytic degradation are illustrated in Scheme 1. RP1 and RP2 were obtained according to the procedure described, with the following observations: RP1 was obtained by employing both AA and SA (0.5 mol of AS, 0.5 mol of AA), while RP2 was obtained by employing only AA (0.75 mol of AA).

**Scheme 1.** Schematic presentation of the synthesis and curing of the polyurethane binders (PM: polyols mixture; PPM: plasticizer-polyols mixture; PU-L: polyurethane liquid state; PU-C: polyurethane cured state).

#### 2.2.2. Synthesis of Polyurethane Binder

Starting from the reaction products described, a series of miscible blends was prepared by mixing (Scheme 1, Step 1 and Step 2) the newly synthesized polyester-polyols (RP1 or RP2) with the commercial polyol (SET) and with the synthesized energetic plasticizer (TEGDN). Therefore, RP1, RP2, SET, and TEGDN were mixed in different molar ratios, as detailed in Table 1 (Scheme 1, Step 1 and Step 2), before polyurethanes synthesis.

**Table 1.** The composition of the investigated polyols.

1 -OH molar ratios for SET and RP blends. 2 TEGDN added to SET:RP blends, as weight percentage calculated from the total weight of the binder.

To investigate the possibility of utilizing these newly obtained polyurethanes as binders in rocket propellant composites, polyurethane formulations were obtained by following two working strategies: the first one employing only a commercial polyesterpolyol (SET) and the second one consisted in the addition of the polyester-polyols that resulted from the catalytic degradation of PET (RP1 and RP2) to the commercial polyol (SET), as described in Table 1. Thus, the polyurethanes were obtained by reacting the commercial polyol (SET) and the recycled polyols (RP1 and RP2) with the curing agent Desmodur® 44V20L (MDI, diphenylmethane-4,4 -diisocyanate) by adjusting the -NCO/- OH molar ratios, according to the compositions detailed in Table 2. The energetic plasticizer, TEGDN, was added in two different proportions: 15 wt.% and 30 wt.% of the total binder content, according to Tables 1 and 2. The polyurethane synthesis process occurred in one simple step: MDI was added to the polyol blends (Tables 1 and 2) and the mixture was stirred vigorously (except for binders that also included energetic plasticizer (TEGDN), which was introduced into the polyol blends before the addition of the curing agent). The mixing process was carried out at 50 ◦C to improve processability. The resulting compounds were poured into glass molds, and they were allowed to cure at 60 ◦C in a vacuum oven. The polyurethane films were exfoliated from the glass molds after the completion of the curing process and were subjected to specific investigations, as described in Results section.

**Table 2.** Composition of the polyurethane binders.

2.2.3. Rocket Propellant Composite Formulations

The new composite formulations consisted in a solid–liquid mixture, in which the liquid component, represented by the novel polyurethane binders, incorporated the solid components, comprising an oxidizer (PSAN, two granulometric sizes), a metallic fuel (two granulometric sizes of aluminum powder), and catalyst (iron oxide). To provide adequate mechanical strength for these rocket propellant composites and to facilitate the mixing process, the oxidizer chosen for this application used bi-granular (200 μm and 50 μm) mixture. To ensure a good homogeneity of the composite rocket propellant, the liquid and the solid phases were mixed separately, as follows: the liquid mixture was prepared by simply mixing the polyols with the curing agent (MDI); separately, the solid mixture containing the oxidant (PSAN), the metallic fuel (Al), and the catalyst (Fe2O3) was sieved and sorted by granule size, then dried. Then, the liquid and the solid phases were thoroughly mixed and introduced in cylindrical molds with 45 mm diameter and allowed to cure at 60 ◦C in a vacuum oven. The described procedure can be better understood in conjunction with the illustrations presented in Scheme 2.

**Scheme 2.** Schematic representation of the rocket propellant composite fabrication process.

The novel composite rocket propellant formulations were produced in small batches (25 g) and pressed at 10 bar (as required by the characteristic tests necessary for the evaluation of the performances of solid rocket propellants: evaluation of combustion behavior, evaluation of the mechanical properties, and morphological analysis) [38]. Subsequently, the samples were cured under vacuum for 96 h at 60 ◦C. The binders employed in this processing step were selected according to their homogeneity and their thermal and mechanical properties. Therefore, only the polyurethanes with molar ratio -NCO/-OH of 2:1 plasticized with 30 wt.% TEGDN were eligible to be used as binders for the rocket propellant formulations. Table 3 provides information regarding the composition of the new eco-friendly composite propellants (ECP) obtained in this study. All the formulations contained 57 wt.% PSAN with 200 μm granulation and 16 wt.% of PSAN with 50 μm granulation, as well as 1 wt.% of burn rate regulator Fe2O3.

**Table 3.** Formulations for the rocket propellant composite.


**3.1 Data preprocessing**

The satellite altimeter transmits and receives the reflected pulse signals to the subsatellite point, and the distance from the satellite altimeter to the sub-satellite point is obtained by calculating the time difference between the transmitted and received pulse signals [26–28]. Where the echo signal waveform reflected from the sub-satellite point is recorded in the CryoSat-2 satellite L1b data, the shape of which is shown in **Figure 6**. The echo signal information needs to be pre-processed to reduce the background radiation, the instrument noise, or the waveform anomalies. The satellite data in the region north of 60°N latitude is also screened to remove waveforms with missing or mutilated information.


**4. Other representative applications**

Despite the abovementioned applications of phage-based biosensors, **Table 1** highlights some other representative applications of phage-based biosensors in detection of pathogenic bacteria, food safety, and environmental monitoring.


**2. Methodology**

Within the theoretical study, we present the phenomenon of dialogue. At the theoretical level, we provide a brief insight into the issue, specifically focusing on the characteristics of dialogue while paying attention to causal factors. The reason for choosing the topic is that the dialogue is the socialisation component of the personality and, at the same time, reflects the state and functionality of society. The research aims to provide insight into the dialogue at its theoretical level. Based on the set goal of the study, we set out a research question of an exploratory nature of *RQ: What are the status and characteristics of the dialogue within the framework of inclusion at its theoretical level?*

We chose the type of research for the selected topic – theoretical research. It was qualitative research, and the exploratory design of the work was chosen. The orientation of the study had an analytical-synthetic nature. The primary method of work was content analysis.

The following methods were used to collect meanings: literary method, analogy, and, at the same time, the processing method – analysis. We used the academic method when studying the sources. The research file consisted of available communications – text in verbal form, namely monographs, scientific studies, professional articles, and development agenda. We obtained the research file from available printed sources. We received resources from platforms for science and research: UNESCO, *Frontiers*, *Elsevier, Internet Archive, Taylor & Francis*, *Social Pedagogy Professional Association, Thempra, UCL Press.* We also drew resources from *the official website of the European Union.* We obtained information mainly from journal publications focused on humanities, such as *the International Journal of Social Pedagogy*, the *European Educational Research Journal, the British Educational Research Journal*, *The Journal of Experimental Education, Humanities & Social Sciences Reviews*, etc. Selecting the initial text documents, we determined the criterion – keywords, and therefore, the set selection was deliberate. From the basic set, there were included just 69 communications to the research. We present the communications in the bibliography.

The processing method – content analysis – was primarily used to process the documents. Logical qualitative methods (analysis, synthesis, induction, deduction) processed meaning units from theoretical sources. We also used the analogy method to evaluate the suitability of theoretical sources for research based on keywords. The direction of analysis of text documents was inductive based on the established criteria. Also, based on the determined criteria, selective coding was used to process text documents. We primarily focused on the dialogue expressed explicitly, and in the first analysis – informative reading, we obtained information about the headlines. As part of the second analysis – with the help of cursive reading, we familiarised ourselves with the contents of the text documents. Through relational analysis, we investigated connections and relationships between meaning units. We grouped meaningful units through the synthesis method, resulting in the identification and content. We were

secondarily interested in the latent content – the expressive value of the text. We searched for other sources based on the informative value and focus of the range of the available sources. Using the deductive method, we obtained the meaning, which were implicitly expressed within the context. We have ensured the credibility of the research by including quotations and paraphrases.


Meet the editor

Dr. Hind Manaa Alkatan, MD, is Associate Professor, Consultant (Ophthalmology and Pathology), Chief of Ophthalmic Pathology, Director of the Post-Graduate Training Programs in Ophthalmology, and Associate Director for External Accreditation at Postgraduate Medical Education, King Saud University (KSU), Riyadh, Saudi Arabia. She obtained her Saudi Ophthalmology Board from KSU, and completed her postdoctoral studies in Oculoplastic, Pediatric Ophthalmology, and Ophthalmic Pathology from the University of Manitoba and the University of British Columbia, Canada. She is a member of international organizations: Eastern Ophthalmic Pathology, Canadian, and Saudi Ophthalmology Societies. She has been invited as a distinguished speaker to international symposia. She has published around 140 papers in reputed local and international journals and has been serving as an editorial board member for a number of other journals.

Contents

**Section 1**

**Section 2**

Childhood

*and Saad Aldahmash*

History and Genetics of Retinoblastoma

*by Spencer T. Langevin and Brian P. Marr*

*by Fahad Albader and Dalal Fatani*

*by Amani Al Kofide and Eman Al-Sharif*

*by Alena Furdova and Juraj Sekac*

Uses of Radiological Imaging in Retinoblastoma

Retinoblastoma: Update on Current Management

*by Heba Alsharif, Hala Helmi and Azza Maktabi*

Retinoblastoma Management: Advances in Chemotherapy

**Preface III**

Basic Knowledge **1**

**Chapter 1 3**

**Chapter 2 17**

Clinical Aspects, Management and Prognosis **25**

**Chapter 3 27**

**Chapter 4 41**

**Chapter 5 55**

**Chapter 6 71**

**Chapter 7 89** Histopathological Characteristics and Classification for Prognostic Indicators

**Chapter 8 107** Secondary Malignancies in Adulthood and after Retinoblastoma Treatment in

*by Abdullah Almater, Abdulrahman Alfaleh, Khalid Alshomar and Saleh AlMesfer*

*by Tariq Alzahem, Waleed Alsarhani, Abdullah Albahlal, Leen Abu Safieh*

Epidemiological and Genetic Considerations in Retinoblastoma *by Ido Didi Fabian, Faisal Al Qahtani and Covadonga Bascaran*

Retinoblastoma: Presentation, Evaluation, and Diagnosis


**1. Introduction**

Soybean (*Glycine max* (L.) Merr.) has become one of the most important, versatile globally traded commodities, being a widely used source of protein, oil, and biofuel. Its uses include as a source of protein and fibre for livestock and an alternative to meat and dairy products in

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2020 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

humans. Soya products are also increasingly used widely in the food industry, in particular as texturisers, emulsifiers, and protein fillers; soya flour is often added to bakery products, such as bread, biscuits, pastry, etc. Soybean oil is the second largest source of vegetable oil globally and is also used in products such as biodiesel and detergents.

The major forms of soya usually encountered in end-user countries in the EU are:

fat/lipid.

40–49% and 3% fibre.

and characterised [8].

compaction in the hold of the ship.

those in pure soya meal (**Figure 2**).

**1.** Soybean, after removal of hull covering the bean, containing about 40% protein and 20%

Respiratory Health Risks from Exposure to Dust from Soybean and Its Products

http://dx.doi.org/10.5772/intechopen.92839

65

**2.** Soya meal (see **Figure 1**). This may be of two forms: pure meal produced after de-hulling and possibly extraction of oil or with subsequent added hull to extend the product. Soybean meal made from de-hulled beans has a total protein content of approximately

**3.** Soybean hull, these are often pelletised as a commercial product to make a more handleable, less dusty product (see **Figure 1**). The protein content of hull is around 9–19%, with a fibre content of 53–74%. The proteins in hull tend to be of lower molecular weight than

**4.** Soya oil is produced by crushing and/or chemical extraction. Soya oil, particularly the more highly purified, is considered less allergenic due to the low concentration of soya

**5.** Soya flour—milled in a similar way to cereal flour (e.g. wheat, rye). Flours from various cereals have the propensity to be "dusty", and the control of their handling is necessary to prevent airborne exposure to flour dust and consequent health effects [6, 7]. Soya flour has become increasingly used in food processing. Allergens in soya flour have been identified

**Figure 2** shows electrophoresis gels of extracts of a soya hull and soya meal, respectively, after extraction at 10% w/v using 0.1% Tween 20 in phosphate buffered saline. These gels separate proteins on the basis of their molecular weights. The patterns of proteins in soya hull show considerable differences to soya meal. There is a predominance of high molecular weight proteins in meal in comparison with hull where the majority of proteins appear to be less

**Figure 1.** The left hand image shows an image of a soya meal imported in the UK. The right-hand image shows a sample of soya hull imported into the UK. The pelletised hull material shows some evidence of breakdown, probably due to

proteins within it [4, 5]. It is used widely in food processing.

Soybeans are crushed to form meal, typically used in animal feed, and oil. The hull or husk of the soybean is a by-product of soybean oil and meal production where the beans are de-hulled prior to crushing. Soya hull is also internationally traded as an animal feedstuff, providing a good source of digestible fibre, albeit of lower protein content of soya meal.

The EU imported about 18 million metric tons of soya in 2018 [1]. Approximately 90% of these imports are used to feed livestock and reflect about 28% of global soya imports. China imports approximately 88 million metric tons. Although the USA remains the largest exporter of soya, projected export growth is concentrated in South America, particularly Brazil, Argentina, Paraguay, and Bolivia. The UK imports some 3 million tons annually with more than 70% directly from Argentina and Brazil. There is also an inter-trade within Europe, with the Netherlands being an important hub. The UK imports approximately two thirds as soya meal/hulls and one third as soybeans [2]. The UK only imports a relatively small quantity of soya oil, approximately 200,000 tons. The UK does not produce biofuels to any extent from imported soya.

Therefore, there is considerable bulk transportation by sea, involving handling at ports equipped to handle bulk grains and foodstuffs. Thereafter there is onward transportation for use in the animal feed industry, further processing, and the human food sector.

However, soya is not without associated risks to health. Soya products are recognised as one of the EU's 14 major food allergens and listed in Annex II of the EU Regulation 1169/2011 on labelling of foods and UK equivalent domestic legislation [3]. It is also listed as a major food allergen by the FDA (USA) labelling regulations. As soybean and its products are used in many processed foods, it is difficult for the allergic consumer to avoid and is often classified as a "hidden allergen". Additionally, evidence from a number of sources identify proteins found in soybean and its products as respiratory allergens capable of producing a range of ocular and upper and lower respiratory symptoms, including asthma.

This chapter focuses on both published evidence and our own studies related to the respiratory risk from airborne dusts related to soya.


**3. Fundamental solution and modal analysis**

One way to analyze PDE (7) is to discretize the PDE in its spatial coordinates (*r*, *θ*). Thereby, the spatial differential operator ∇4 and the boundary conditions (9)-(11) can be approximated by finite difference or finite element methods and the PDE is reduced to a finite set of coupled ordinary differential equations (ODE). The Eigenfrequencies and the eigenvectors of the resulting generalized eigenvalue problem correspond to the spatially discretized eigenfunctions of the PDE. Thereby, the spatial discretization has strong influence on the remaining temporal system dynamics and can even mislead to wrong results if performed insufficiently. The typically large set of ordinary differential equations requires high computing power for dynamic simulation and is ill-suited for model-based controller design, in general.

Another way to analyze PDE (7) is a modal transformation based on the eigenfunctions of PDE (7) fulfilling the homogeneous boundary conditions (9)-(11). The modal transformation leads to an infinite set of ordinary differential equations in modal coordinates describing only the temporal evolution of the eigenfunctions of PDE (7). Thereby, all spatial and temporal properties are preserved and a reduced set of the ODEs can be used for dynamic simulation and controller design.

The eigenfuntions *Wk*(*r*, *θ*) of PDE (7) can be derived by separation of variables with

$$\Gamma: \quad w(r, \theta, t) = \sum\_{k=1}^{\infty} W\_k(r, \theta) f\_k(t), \tag{13}$$

10.5772/52726

107

= 0 , (16)

http://dx.doi.org/10.5772/52726

Modeling and Control of Deformable Membrane Mirrors

Λ*c*(*βk*)

since the matrix elements are rather extensive.

since the matrix elements are rather extensive.

  *A*1*k A*2*k A*3*k A*4*k*

to infinitely many eigenvalues *βk* related to the eigenfunction *Wk*(*r*, *θ*).

= 0, Λ*s*(*βk*)

where Λ*c*(*β*) and Λ*s*(*β*) are [4 × 4] matrices containing linear combinations of Bessel functions depending on the eigenvalue *βk* for the cosine and sine parts of *Wk*(*r*, *θ*). A computation of matrices Λ*c* and Λ*s* should be performed using computer algebra software

where Λ*c*(*β*) and Λ*s*(*β*) are [4 × 4] matrices containing linear combinations of Bessel functions depending on the eigenvalue *βk* for the cosine and sine parts of *Wk*(*r*, *θ*). A computation of matrices Λ*c* and Λ*s* should be performed using computer algebra software

In order to compute a non-trivial solution of the homogeneous equations (16), the parameter *βk* needs to determined such that Λ*c* and Λ*s* contain a non-trivial kernel. This can be achieved by numerically searching for zeros in the determinant of the matrices Λ*c* and Λ*s* and leads

In Figure 4, the consine parts of the first 21 analytical eigenfunctions *Wk*(*r*, *θ*), *k* = 1, . . . , 21 of a deformable mirror with clamped inner radius and free outer radius are shown based on the calculations given before. The eigenfunctions *Wk*(*r*, *θ*) and eigenvalues *βk* were compared with a detailed finite element model of the same mirror and show excellent compliance.

**Figure 4.** First 21 eigenfunctions of a deformable mirror model (7) with clamped edge boundary conditions (9) at the inner

radius *r*1 and free edge boundary conditions (11) at the outer radius *r*2 ordered by increasing eigenfrequency.

  *B*1*k B*2*k B*3*k B*4*k*

where the eigenfunctions *Wk*(*r*, *θ*) describe the spatial characteristics and the modal coefficients *fk*(*t*) describe the time-varying amplitude. At the same time, equation (13) can be used to perform a transformation from modal coordiantes *fk*(*t*) to physcial coordinates *w*(*r*, *θ*, *t*) and back, which will be needed for feedback controller design in Section 4.3.

After inserting (13) in the homogeneous PDE (7) with *q*(*r*, *θ*) = 0, an analytical description of the eigefunctions *Wk*(*r*, *θ*, *t*) can be found as described in [23] reading

$$\begin{split} \mathcal{W}\_{k}(r,\theta) &= \left( A\_{1k}I\_{k}(\beta r) + A\_{2k}Y\_{k}(\beta r) + A\_{3k}I\_{k}(\beta r) + A\_{4k}K\_{k}(\beta r) \right) \cos(k\theta) \\ &+ \left( B\_{1k}I\_{k}(\beta r) + B\_{2k}Y\_{k}(\beta r) + B\_{3k}I\_{k}(\beta r) + B\_{4k}K\_{k}(\beta r) \right) \sin(k\theta). \end{split} \tag{14}$$

Here, *Jk*,*Yk*, *Ik*, *Kk* are Bessel functions and modified Bessel functions of first and second kind. The eigenfunctions fulfill the relation

$$
\nabla^4 \mathcal{W}\_k(r, \theta) = \mathcal{J}^4 \mathcal{W}\_k(r, \theta) \tag{15}
$$

and are self-adjoint due to the biharmonic operator ∇4.

After inserting the fundamental solution (14) in the boundary conditions (9)-(11), the free parameters *A*1*k*,..., *A*4*k* and *B*1*k*,..., *B*4*k* can be found by computing a non-trivial solution of the resulting homogeneous equations

$$
\Lambda\_{\mathfrak{C}}(\beta\_k) \begin{bmatrix} A\_{1k} \\ A\_{2k} \\ A\_{3k} \\ A\_{4k} \end{bmatrix} = 0, \quad \Lambda\_{\mathfrak{s}}(\beta\_k) \begin{bmatrix} B\_{1k} \\ B\_{2k} \\ B\_{3k} \\ B\_{4k} \end{bmatrix} = 0 \,, \tag{16}
$$

where Λ*c*(*β*) and Λ*s*(*β*) are [4 × 4] matrices containing linear combinations of Bessel functions depending on the eigenvalue *βk* for the cosine and sine parts of *Wk*(*r*, *θ*). A computation of matrices Λ*c* and Λ*s* should be performed using computer algebra software since the matrix elements are rather extensive.

8 Adaptive Optics

design, in general.

and controller design.

The eigenfunctions fulfill the relation

the resulting homogeneous equations

and are self-adjoint due to the biharmonic operator ∇4.

**3. Fundamental solution and modal analysis**

One way to analyze PDE (7) is to discretize the PDE in its spatial coordinates (*r*, *θ*). Thereby, the spatial differential operator ∇4 and the boundary conditions (9)-(11) can be approximated by finite difference or finite element methods and the PDE is reduced to a finite set of coupled ordinary differential equations (ODE). The Eigenfrequencies and the eigenvectors of the resulting generalized eigenvalue problem correspond to the spatially discretized eigenfunctions of the PDE. Thereby, the spatial discretization has strong influence on the remaining temporal system dynamics and can even mislead to wrong results if performed insufficiently. The typically large set of ordinary differential equations requires high computing power for dynamic simulation and is ill-suited for model-based controller

Another way to analyze PDE (7) is a modal transformation based on the eigenfunctions of PDE (7) fulfilling the homogeneous boundary conditions (9)-(11). The modal transformation leads to an infinite set of ordinary differential equations in modal coordinates describing only the temporal evolution of the eigenfunctions of PDE (7). Thereby, all spatial and temporal properties are preserved and a reduced set of the ODEs can be used for dynamic simulation

> ∞ ∑ *k*=1

where the eigenfunctions *Wk*(*r*, *θ*) describe the spatial characteristics and the modal coefficients *fk*(*t*) describe the time-varying amplitude. At the same time, equation (13) can be used to perform a transformation from modal coordiantes *fk*(*t*) to physcial coordinates *w*(*r*, *θ*, *t*) and back, which will be needed for feedback controller design in Section 4.3.

After inserting (13) in the homogeneous PDE (7) with *q*(*r*, *θ*) = 0, an analytical description

*Wk*(*r*, *θ*) = (*A*1*k Jk*(*βr*) + *A*2*kYk*(*βr*) + *A*3*k Ik*(*βr*) + *A*4*kKk*(*βr*)) cos(*kθ*)

Here, *Jk*,*Yk*, *Ik*, *Kk* are Bessel functions and modified Bessel functions of first and second kind.

After inserting the fundamental solution (14) in the boundary conditions (9)-(11), the free parameters *A*1*k*,..., *A*4*k* and *B*1*k*,..., *B*4*k* can be found by computing a non-trivial solution of

+ (*B*1*k Jk*(*βr*) + *B*2*kYk*(*βr*) + *B*3*k Ik*(*βr*) + *B*4*kKk*(*βr*)) sin(*kθ*). (14)

∇4*Wk*(*r*, *θ*) = *β*4*Wk*(*r*, *θ*) (15)

*Wk*(*r*, *θ*)*fk*(*t*), (13)

The eigenfuntions *Wk*(*r*, *θ*) of PDE (7) can be derived by separation of variables with

Γ : *w*(*r*, *θ*, *t*) =

of the eigefunctions *Wk*(*r*, *θ*, *t*) can be found as described in [23] reading

where Λ*c*(*β*) and Λ*s*(*β*) are [4 × 4] matrices containing linear combinations of Bessel functions depending on the eigenvalue *βk* for the cosine and sine parts of *Wk*(*r*, *θ*). A computation of matrices Λ*c* and Λ*s* should be performed using computer algebra software since the matrix elements are rather extensive.

In order to compute a non-trivial solution of the homogeneous equations (16), the parameter *βk* needs to determined such that Λ*c* and Λ*s* contain a non-trivial kernel. This can be achieved by numerically searching for zeros in the determinant of the matrices Λ*c* and Λ*s* and leads to infinitely many eigenvalues *βk* related to the eigenfunction *Wk*(*r*, *θ*).

In Figure 4, the consine parts of the first 21 analytical eigenfunctions *Wk*(*r*, *θ*), *k* = 1, . . . , 21 of a deformable mirror with clamped inner radius and free outer radius are shown based on the calculations given before. The eigenfunctions *Wk*(*r*, *θ*) and eigenvalues *βk* were compared with a detailed finite element model of the same mirror and show excellent compliance.

**Figure 4.** First 21 eigenfunctions of a deformable mirror model (7) with clamped edge boundary conditions (9) at the inner radius *r*1 and free edge boundary conditions (11) at the outer radius *r*2 ordered by increasing eigenfrequency.

In the following, a modal decomposition of PDE (7) is used to analyze the mirror dynamics and to derive model-based feedforward control commands in modal coordinates. The modal decomposition of (7) is performed by inserting relation (13) in (7) and using property (15) yielding

10.5772/52726

109

*um*(*τ*)d*τ*, (20)

http://dx.doi.org/10.5772/52726

*k*)2 − 4*Dρhβ*4

2 is derived from the

*u*1 *u*2 ... *uM*

*k* .

*w*(*r*, *θ*, *t*) =

− *t*

2*ρh* (*λd*+*κdβ*4

be used for every actuator/sensor pair of the DM.

control loop when designing the AO loop controller.

**4. Model-based controller design**

time *T* from an initial deformation △*w*∗

respect to the *L*2 scalar product �*Wk* , *Wk* � = 1.

with

*gk*(*t* − *τ*) = *e*

*t*

∞ ∑ *k*=1

*k*+*ζk* ) − *e*

*M* ∑ *m*=1

1 *ζk*

− *t*

2*ρh* (*λd*+*κdβ*4

Equation (20) can be used to compute the actuator influence functions for any input signal *um*(*τ*), *m* = 1... *M*. Thereby, not only the resulting static deformation of the mirror can be computed, but also the transient motion of the plate for time-varying input forces.3 Additionally, relation (20) can be used to compute the frequency responses of a deformable mirror at different actuator locations as shown in Figure 5 for a deformable mirror with clamped inner edge, free outer edge, and co-located force actuators and position sensors. The infinite sum of eigenfunctions *Wk*(*r*, *θ*) in Equation (20) can be approximated with a finite *k* using only a limited number of eigenfunctions. The right number of eigenfunctions can either be driven by a sufficient static coverage of mirror deformations with linear combinations of *k* eigenfunctions *Wk*(*r*, *θ*), or by considering a certain number of eigenvalues *βk* in order to sufficiently describe the mirror dynamics up to a certain eigenfrequency.

Obviously, the frequency responses shown in Figure 5 reveal essential variations of local mirror dynamics depending on the co-located actuator/sensor position. From a control point of view, this behavior illustrates the difficulty of designing a decentralized controller that can

In a typical AO system, the requirement of changing the mirror shape within a predefined

higher-ranking AO control loop (see Figure 6). This control loop runs at a fixed cycle time and sends mirror deformations △*w*∗(*t*) to the shape controller in order to correct for measured optical disturbances in the AO system (not shown in Figure 6). The step inputs △*w*∗(*t*) for the model-based shape controller in Figure 6 are in general ill-suited for model-based feedforward control and need to be filtered beforehand. The transition time *T* for changing the mirror shape from its initial shape △*w*1 to its new desired shape △*w*2 is assumed to be smaller than the cycle time of the higher-ranking AO control loop. This requirement assures that the closed loop mirror dynamics can be neglected with respect to the higher-ranking AO

For model-based shape control of deformable mirrors, the control scheme shown in Figure

3 In Equation (20) and for the following analysis, it is assumed that the eigenfunctions *Wk* (*r*, *θ*) are normalized with

6 can be used. It consists of a deformable mirror with multiple inputs *u* =

1 to a final deformation △*w*∗

*Wk*(*r*, *θ*) *Wk*(*rm*, *θm*)*gk*(*t* − *τ*)

*k*−*ζk* ), *ζk* =

(*λd* + *κdβ*4

Modeling and Control of Deformable Membrane Mirrors

 *G*(*r*,*θ*,*rm*,*θm*,*t*−*τ*)

*τ*=0

$$\sum\_{k=1}^{\infty} \left( D\beta\_k^4 f\_k(t) + (\lambda\_d + \kappa\_d \beta^4) f\_k(t) + \rho h f\_k(t) \right) W\_k(r, \theta) = \sum\_{m=1}^{M} \frac{u\_m(t)}{r\_m} \delta(r - r\_m) \delta(\theta - \theta\_m). \tag{17}$$

A multiplication with any eigenfunction *Wj* and integration over domain *S* on both sides gives

$$\begin{aligned} \left\| \iint \mathcal{W}\_{\vec{j}}(\mathbf{r}, \theta) \sum\_{k=1}^{\infty} \left( D\beta\_{k}^{4} f\_{k}(t) + (\lambda\_{d} + \kappa\_{d}\beta\_{k}^{4}) \dot{f}\_{k}(t) + \rho h \ddot{f}\_{k}(t) \right) \mathcal{W}\_{k}(\mathbf{r}, \theta) \mathrm{d}S = \\ \iint \mathcal{W}\_{\vec{j}}(\mathbf{r}, \theta) \sum\_{m=1}^{M} \frac{u\_{m}(t)}{r\_{m}} \delta(r - r\_{m}) \delta(\theta - \theta\_{m}) \mathrm{d}S. \end{aligned} \tag{18}$$

Changing order of summation and integration, using the orthonormality property of the eigenfunctions *Wk*(*r*, *θ*), and considering the sifting property of the Dirac delta function *δ* on the right hand side of Equation (18) leads to an infinite set of second order ordinary differential equations

$$\dot{f}\_{\dot{f}}(t) + \frac{\lambda\_d + \kappa\_d \beta\_{\dot{f}}^4}{\rho h} \dot{f}\_{\dot{f}}(t) + \frac{D\beta\_{\dot{f}}^4}{\rho h} f\_{\dot{f}}(t) = \frac{1}{\rho h} \sum\_{m=1}^{M} \mathcal{W}\_{\dot{f}}(r\_{m\nu}\theta\_{\mathcal{W}}) u\_m(t), \tag{19}$$

$$f\_{\dot{f}}(0) = 0, \quad \dot{f}\_{\dot{f}}(0) = 0, \quad \qquad \qquad \dot{j} \in \mathbb{N}.$$

For each *j*, the resulting ODE (19) describes the temporal evolution of the corresponding eigenfunction *Wj*(*r*, *θ*) by the modal coefficient *fj*(*t*). For simplicity, homogeneous initial conditions are assumed describing a flat and steady mirror surface.

Since there is no coupling between different modal coefficients *fk*(*t*) and *fj*(*t*), *j* �= *k*, the ODEs (19) can be used for dynamic simulation of a mirror surface described by a specific eigenfunction *Wj*(*r*, *θ*) or a linear combination of eigenfunctions. Any physically relevant mirror deformation can be decomposed into a linear combination of the orthonormal eigenfunctions *Wk*(*r*, *θ*) and all relevant dynamic properties of the deformable mirror can be covered with this approach. The decoupled description of the mirror dynamics in modal coordinates (19) allows for simplified system analysis and is the foundation for the following controller design.

Based on the derived normalized eigenfunctions *Wk*(*r*, *θ*), an analytical solution of the biharmonic equation (7) with initial conditions *w*(*r*, *θ*, 0) = 0 and *w*˙(*r*, *θ*, 0) = 0 can be derived in spectral form reading

$$w(r,\theta,t) = \underbrace{\int\_{\tau=0}^{t} \sum\_{k=1}^{\infty} \sum\_{m=1}^{M} \frac{1}{\mathcal{I}\_{k}} \mathcal{W}\_{k}(r,\theta) \, \mathcal{W}\_{k}(r\_{m},\theta\_{m}) \mathcal{g}\_{k}(t-\tau) \, u\_{m}(\tau) \, \text{d}\tau}\_{\mathcal{G}(r\theta,r\_{m}\theta\_{m}t-\tau)} \tag{20}$$

with

10 Adaptive Optics

yielding

∞ ∑ *k*=1 *Dβ*4

gives

*Wj*(*r*, *θ*)

differential equations

controller design.

in spectral form reading

¨ *fj*(*t*) +

∞ ∑ *k*=1 *Dβ*4

*S*

*k fk*(*t*)+(*λd* + *κdβ*4) ˙

In the following, a modal decomposition of PDE (7) is used to analyze the mirror dynamics and to derive model-based feedforward control commands in modal coordinates. The modal decomposition of (7) is performed by inserting relation (13) in (7) and using property (15)

A multiplication with any eigenfunction *Wj* and integration over domain *S* on both sides

*fk*(*t*)+*ρh* ¨

*S*

Changing order of summation and integration, using the orthonormality property of the eigenfunctions *Wk*(*r*, *θ*), and considering the sifting property of the Dirac delta function *δ* on the right hand side of Equation (18) leads to an infinite set of second order ordinary

For each *j*, the resulting ODE (19) describes the temporal evolution of the corresponding eigenfunction *Wj*(*r*, *θ*) by the modal coefficient *fj*(*t*). For simplicity, homogeneous initial

Since there is no coupling between different modal coefficients *fk*(*t*) and *fj*(*t*), *j* �= *k*, the ODEs (19) can be used for dynamic simulation of a mirror surface described by a specific eigenfunction *Wj*(*r*, *θ*) or a linear combination of eigenfunctions. Any physically relevant mirror deformation can be decomposed into a linear combination of the orthonormal eigenfunctions *Wk*(*r*, *θ*) and all relevant dynamic properties of the deformable mirror can be covered with this approach. The decoupled description of the mirror dynamics in modal coordinates (19) allows for simplified system analysis and is the foundation for the following

Based on the derived normalized eigenfunctions *Wk*(*r*, *θ*), an analytical solution of the biharmonic equation (7) with initial conditions *w*(*r*, *θ*, 0) = 0 and *w*˙(*r*, *θ*, 0) = 0 can be derived

*Wk*(*r*, *θ*) =

*fk*(*t*)

*Wj*(*r*, *θ*)

*ρh*

*M* ∑ *m*=1

*fj*(0) = 0, *j* ∈ **N** .

*M* ∑ *m*=1

*Wk*(*r*, *θ*)d*S* =

*M* ∑ *m*=1

*um*(*t*) *rm*

*um*(*t*) *rm*

*δ*(*r* − *rm*)*δ*(*θ* − *θm*). (17)

*δ*(*r* − *rm*)*δ*(*θ* − *θm*)d*S*.

*Wj*(*rm*, *θm*)*um*(*t*), (19)

(18)

*fk*(*t*) + *ρh* ¨

*k fk*(*t*)+(*λd* + *κdβ*4

*λd* + *κdβ*4 *j ρh* ˙

*fj*(*t*) +

conditions are assumed describing a flat and steady mirror surface.

*fj*(0) = 0, ˙

*Dβ*4 *j ρh fj*(*t*) = 1

*fk*(*t*)

*k*) ˙

$$g\_k(t - \tau) = e^{-\frac{l}{2\mu l} \left(\lambda\_d + \kappa\_d \beta\_k^4 + \zeta\_k\right)} - e^{-\frac{l}{2\mu l} \left(\lambda\_d + \kappa\_d \beta\_k^4 - \zeta\_k\right)}, \quad \zeta\_k = \sqrt{(\lambda\_d + \kappa\_d \beta\_k^4)^2 - 4D\rho h \beta\_k^4}.$$

Equation (20) can be used to compute the actuator influence functions for any input signal *um*(*τ*), *m* = 1... *M*. Thereby, not only the resulting static deformation of the mirror can be computed, but also the transient motion of the plate for time-varying input forces.3 Additionally, relation (20) can be used to compute the frequency responses of a deformable mirror at different actuator locations as shown in Figure 5 for a deformable mirror with clamped inner edge, free outer edge, and co-located force actuators and position sensors.

The infinite sum of eigenfunctions *Wk*(*r*, *θ*) in Equation (20) can be approximated with a finite *k* using only a limited number of eigenfunctions. The right number of eigenfunctions can either be driven by a sufficient static coverage of mirror deformations with linear combinations of *k* eigenfunctions *Wk*(*r*, *θ*), or by considering a certain number of eigenvalues *βk* in order to sufficiently describe the mirror dynamics up to a certain eigenfrequency.

Obviously, the frequency responses shown in Figure 5 reveal essential variations of local mirror dynamics depending on the co-located actuator/sensor position. From a control point of view, this behavior illustrates the difficulty of designing a decentralized controller that can be used for every actuator/sensor pair of the DM.


*3.5. Relationship between Dimer Strength and the C*··· *H Distance*

As has been shown in the previous subsections, many of the dimers considered here have some secondary interactions accompanying the leading C··· H-D hydrogen bond. The strength of at least some of them may be considerable. Therefore, one should not expect a good overall (i.e., for all the IR2 ··· HD dimers) correlation between the dissociation energy, *D*0, and the distance C··· H. Moreover, good correlations are also not to be expected even in cases where individual proton-donor molecules are considered. Of course, the exception here is HF, and perhaps HCN, which more often forms linear or nearly linear C··· H hydrogen bonds (Table 1). This is confirmed in Figure 11 (left), where it is shown that the *R*2 (coefficient of determination) values for the linear correlation between *D*0 and *d*C···H are very poor for NH3 (even with the rejection of the clearly outlier point for I··· NH3), H2O and MeOH (0.217, 0.319, 0.550, respectively) and much better for HCN (0.886) and especially for HF (0.930).

**Figure 11.** The dependence of either the dissociation energy (**left**) or the binding energy according to Equation (1) (**right**) on the distance C··· H in the IR2 ··· HD dimers.

This result clearly shows that in the case of more complex dimers, i.e., having more significant intermolecular contacts, one should not expect a good relationship between the dimer dissociation energy and the length of any single intermolecular contact. Rather, a good correlation can be expected in the case of a clearly local parameter, which is the

binding (interaction) energy determined from Equation (1), and therefore based on the electron density value at the critical point of the C··· H-D hydrogen bond. Indeed, as shown in Figure 11 (right), for HF, MeOH and NH3, the linear correlations between *Eb* and *d*C···H are very good (*R*2 > 0.98) and only slightly worse for HCN and H2O (0.968 and 0.962, respectively). Importantly, for all the IR2 ··· HD dimers, an excellent exponential relationship, *Eb* = −755.8 *e*−2.38 *d*C···H , has been found (black curve in Figure 11). This result is not unexpected as a good common exponential relationship between *ρ*bcp and the hydrogen bond length has been found for both different X and Y atoms in the X-H··· Y hydrogen bond [128–131].


**2. Gas turbine engines**

The typical aero-engine is designed in sectional-modular architecture type that can be assembled and disassembled, or even interchanged with modules from another compatible engine, without the need for specific retesting or balancing. This unique advantage supports production maintenance and reduces process downtime for the operator. The target to reduce emissions caused by conventional gas turbine engines in realization of the growing air transport demand drives research for new product architectures.

Previous work lacks the understanding on how interactions between components behave in varying modular platforms. Hence, it is important to know the dependency of each individual component (dependent, parallel, or coupled) in relation to the coordinated activities in the development lifecycle. **Figures 1**-**5** shows various gas turbine engine configurations and interconnected components.


**Ali Sulaiman Alsagri 1, Saleem Nasir 2, Taza Gul 3, Saeed Islam 2, K.S. Nisar 4, Zahir Shah 2 and Ilyas Khan 5,\***

Received: 9 February 2019; Accepted: 25 February 2019; Published: 6 March 2019

**Abstract:** Our main objective in the present work is to elaborate the characteristics of heat transport and magneto-hydrodynamics (MHD) finite film flow of human blood with Carbon Nanotubes (CNTs) nanofluids over a stretchable upright cylinder. Two kinds of CNTs nanoparticles, namely (i) SWCNTs (single walled carbon nanotubes) and (ii) MWCNTs (multi walled carbon nanotubes), are used with human blood as a base liquid. In addition, a uniform magnetic field (*B*) has been conducted perpendicularly to the motion of nanoliquid. The transformation of the partial differential structure into a non-linear ordinary differential structure is made by using appropriate dimensionless quantities. The controlling approach of the Homotopy analysis method (HAM) has been executed for the result of the velocity and temperature. The thickness of the coating film has been kept variable. The pressure distribution under the variable thickness of the liquid film has been calculated. The impacts of different variables and rate of spray during coating have been graphically plotted. The coefficient of skin friction and Nusselt number have been presented numerically. In addition, it is noticed that the thermal field of a nanoliquid elevates with rising values of *φ* and this increase is more in SWCNTs nanofluid than MWCNTs nanofluid.

**Keywords:** thin film casson nanofluid; SWCNTs and MWCNTs; stretching cylinder; MHD; HAM


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### Chapter 38 Post-liquefaction Cyclic Shear Strain: Phenomenon and Mechanism

Rui Wang, Pengcheng Fu, Jian-Min Zhang, and Yannis F. Dafalias

Abstract Under undrained cyclic loading, sand experiences decrease in effective stress, which can result in liquefaction. Test results show that large cyclic shear strain is generated at zero effective stress during undrained cyclic loading. This postliquefaction shear strain has been observed to progressively increase in amplitude with increasing number of loading cycles until it eventually stabilizes at a bounded value. However, there has been no clear explanation on why and how this cyclic shear strain is generated. The fabric mechanism behind this post-liquefaction shear strain phenomenon is briefly discussed in this study.

#### 38.1 The Basic Phenomenon

Under undrained cyclic loading, a sand sample experiences decrease in effective stress p, which can be large enough so that p approaches zero where the phenomenon of liquefaction takes place. The undrained stress path follows what is commonly known as the butterfly path shown in Fig. 38.1. Along with the reduction of p, some test results show that large cyclic shear strain is generated at a low but nontrivial shear stress values (Fig. 38.1a), but more recent evidence suggests that it is in fact generated at low enough shear stress values to be seen as zero (Fig. 38.1b, c). Zhang

P. Fu

Y. F. Dafalias (\*) Department of Civil and Environmental Engineering, University of California, Davis, CA, USA

Department of Mechanics, School of Applied Mathematical and Physical Sciences, National Technical University of Athens, Athens, Greece e-mail<EMAIL_ADDRESS>
R. Wang · J.-M. Zhang

Department of Hydraulic Engineering, Tsinghua University, Beijing, China

National Engineering Laboratory for Green and Safe Construction Technology in Urban Rail Transit, Tsinghua University, Beijing, China

Atmospheric, Earth, and Energy Division, Lawrence Livermore National Laboratory, Livermore, CA, USA

Fig. 38.1 Typical results from undrained cyclic laboratory and numerical tests on sand: (a) simple shear test on Nevada sand (Arulmoli et al. 1992); (b) cyclic torsional test on Toyoura sand (Chiaro et al. 2013); (c) 2D DEM biaxial test on circular particles (Wang et al. 2016)

and Wang (2012) referred to this shear strain as post-liquefaction shear strain γ0, considered to be generated at zero effective stress (i.e., liquefaction) state and has been observed to progressively increase in amplitude with increasing number of loading cycles until it eventually stabilizes at a bounded value. However, there has been no clear explanation on why, when and how this cyclic shear strain is generated. Without a clear understanding of this phenomenon, constitutive modelling would inevitably deviate from the actual behavior of the material, impeding the progress of validation of constitutive models by analyzing relevant BVP related to liquefaction as in the LEAP project.

#### 38.2 Fabric Mechanism

Using DEM simulation, we were able to connect post-liquefaction shear deformation development to a new, theoretically measurable intrinsic fabric metric with a clear physical interpretation (Wang et al. 2016). This new fabric measurement, "Mean Neighboring Particle Distance" (MNPD), is the mean value over all particles of the "Neighboring Particle Distance" (NPD) as depicted in Fig. 38.2a, which is the mean surface-to-surface distance between a particle and its n closest neighbor particles,

Fig. 38.2 The concept of MNPD (Mean Neighboring Particle Distance) and its correlation with post-liquefaction shear strain: (a) illustration of the surface-to-surface distance between a particle and its three closest neighboring particles; (b) development of γ0 and MNPDmax in a typical DEM test; (c) correlation between γ0 and MNPDmax in each half loading cycle after initial liquefaction in 17 tests

with n being the number of contacts needed to support a stable load-bearing structure (n ¼ 3 in 2D and 4 in 3D). MNPD is formulated to capture a microstructural feature of granular materials that is closely related to deformation behavior in the postliquefaction state by actually being a measure of "distance to establishing loadbearing contact" as opposed to a conventional measure of contact intensity, the coordination number. MNPD's strong, unique correlation with γ0 is evident from Fig. 38.2b, c. It has also been shown to influence the liquefaction resistance of sand (Wang et al. 2019). Therefore, it is expected that consideration of MNPD can provide a promising path to incorporating the mechanism of the post-liquefaction cyclic shear strain phenomenon into a continuum constitutive framework for practical purposes.

Acknowledgement Support from the European Research Council under FP7-ERC-IDEAS Advanced Grant Agreement n 290963 (SOMEF) is acknowledged.

#### References

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