Contents

Preface

Postoperative pain (POP) is a health problem that has not yet been resolved. Without a doubt, multimodal analgesia is the greatest advance in the prevention and comprehensive management of patients with POP. Despite this advance, healthcare professionals require more knowledge to effectively manage POP since its deleterious effects manifest not only in the immediate post-surgical phase but can also be prolonged as postoperative chronic pain that is difficult to manage and interferes substantially with patient quality of life. In addition, poorly treated POP facilitates prolonged stays

Opioids have long been the basis for the management of post-surgical pain. However, the overprescription of these drugs and their illegal use have led to the current opioid crisis worldwide, which has caused more than 96,700 deaths in the United States. The current trend is to reduce the use of opioids in pain management as well as search for

*Topics in Postoperative Pain* presents some selected subjects with the goal of improving the care of surgical patients and reducing both the sequelae of POP and the side effects

The editors of this book completed residencies at the same hospital, at very different times, with teachers and changing programs that have gradually adapted to the academic and care needs of our alma mater, the Instituto Nacional de Ciencias Médicas y Nutrición Salvador Zubirán. As graduates from the Division of Anesthesiology and Critical Care Medicine, we know about the goals, challenges, successes, and failures of the founders of our group and we wish to dedicate this book to them: Javier Ramírez Acosta, Ramon De Lille Fuentes, J. Antonio Jimenez Borreiro, and Gabriel Camacho Romero began training specialists in anesthesiology and critical medicine

Thank you very much for your wisdom, your dedication, and above all your valuable

**Victor M. Whizar-Lugo** Anesthesiologist, Lotus Med Group,

Tijuana, México

Institutos Nacionales de Salud,

and/or hospital readmissions that increase care costs.

new opioids with fewer side effects.

of its management.

in 1972.

friendship!


*3.1. ADMA in Pregnancy*

In normotensive pregnancy, the maternal plasma ADMA levels are generally reduced when comparing to non-pregnant group. The lowest concentration of ADMA is described during the first trimester, when the early fall in blood pressure is accompanied by a significant fall in ADMA concentration. The ADMA levels increase with gestational age in the second and third trimester [24,26]. These findings lead to a conclusion that, in early pregnancy, the reduction in ADMA and concomitant increase in NO are responsible for previously described hemodynamic adaptation, a higher need of organ perfusion in pregnancy, and uterine relaxation. In advanced pregnancy, physiologically increased ADMA levels thus help to prepare the uterine muscle fibers for the higher contractile activity before the labour. This is reflected by the higher ADMA concentrations after caesarean birth when compared with vaginal delivery and it may contribute to decreased nitric oxide production and bioavailability in neonatal vascular beds [88].


#### Massimo Aria a, Corrado Cuccurullo b, Agostino Gnasso a a Department of Economics and Statistics, University of Naples Federico II, Italy b Department of Economics, University of Campania Lugi Vanvitelli, Italy **Supporting decision-makers in healthcare domain. A comparative study of two interpretative proposals for Random Forests**

**Supporting decision-makers in healthcare domain. A comparative study of two interpretative proposals for Random Forests**

Massimo Aria, Corrado Cuccurullo, Agostino Gnasso

## **1. Introduction**

Today, the availability of data is growing exponentially in all sectors, especially in the healthcare sector. Machine Learning (ML) techniques allow to analyze big data to exctrat knowledge and support healthcare activities (Miotto et al., 2018), such as models for the diagnosis of complex diseases (Dhillon and Singh, 2019), (Aria et al., 2020). Despite the use of ML is spreading in many applications, it is characterized by some limitations and disadvantages.

ML main drawback corresponds to its lack of interpretability which does not allow users to represent causal relationships and interactions between predictors and response. This leads to the inability to learn how particular decisions are made. From this problem derives the definition of the Black Box model, a highly accurate model with a large complexity that cannot be represented by a relational structure. In other words, it is not possible to visualize how it internally works.

Furthermore, the opaque nature of these models hinders application in various sectors, especially in critical ones such as healthcare. To undertake a decision-making process, having faith in a machine learning model is essential, to feel reassured when analyzing and using it.

Ribeiro et al. (2016) identify a different but at the same time-related definitions of trust: trust in a prediction and trust in a model. Trusting a prediction implies that the user will take a certain action based on it; it is important to determine this confidence given that the model will be used to make decisions think for example of the use of a decisionmaking process in the clinical field, the consequence of acting with absolute confidence on the predictions obtained without being able to understand how they are obtained. Having faith in a model is equivalent to evaluating the model as a whole and testing its ability to generalize with appropriate evaluation metrics. A problem that recurs in using data from real contexts is that they are often significantly different and the chosen metric may not be adequate, therefore an inspection procedure of individual predictions and their interpretations may be the optimal choice.

In this work, we pay attention to one of the most used, accurate, and performing models in Machine Learning, the Random Forest model (RF) (Breiman, 2001).

Random Forest is an evolution of Bagging which aims to reduce the variance of a statistical model, simulates the variability of data through the random extraction of bootstrap samples from a single training set, and aggregates predictions on a new record (see Breiman, 1996). Being an evolution of Bagging, Random Forest aims to obtain even more different and unrelated trees. It is known as an efficient ensemble learning model, as it ensures high predictive accuracy, flexibility, and immediacy; it is recognized as an intuitive and understandable approach to the construction process, but is also considered a Black Box model due to the large number of deep decision trees produced within it (Haddouchi and Berrado, 2019).

Massimo Aria, University of Naples Federico II, Italy<EMAIL_ADDRESS>0000-0002-8517-9411

165 Corrado Cuccurullo, University of Campania Luigi Vanvitelli, Italy<EMAIL_ADDRESS>0000-0002-7401-8575 Agostino Gnasso, University of Naples Federico II, Italy<EMAIL_ADDRESS>0000-0002-9220-9754

FUP Best Practice in Scholarly Publishing (DOI 10.36253/fup\_best\_practice)

Massimo Aria, Corrado Cuccurullo, Agostino Gnasso, *Supporting decision-makers in healthcare domain. A comparative study of two interpretative proposals for Random Forests*, pp. 179-184, © 2021 Author(s), CC BY 4.0 International, DOI 10.36253/978-88- 5518-461-8.34, in Bruno Bertaccini, Luigi Fabbris, Alessandra Petrucci (edited by), *ASA 2021 Statistics and Information Systems for Policy Evaluation. Book of short papers of the on-site conference*, © 2021 Author(s), content CC BY 4.0 International, metadata CC0 1.0 Universal, published by Firenze University Press (www.fupress.com), ISSN 2704-5846 (online), ISBN 978-88-5518-461-8 (PDF), DOI 10.36253/978-88-5518-461-8

The results deriving from the use of the Random Forest are valuable. Various studies have confirmed RF effectiveness in many sectors, such as biomedical for genetic selection (D´ıaz-Uriarte and De Andres, 2006). Breiman et al. (2001) states that Random Forest has A + performance but, having a prediction process that is difficult to understand, evaluates an F on interpretability. This leads to Occam's dilemma (Domingos, 1998) (Domingos, 1999).

The poor interpretability has prevented the adoption of the model in some sectors where there is little or no tolerance for errors, such as healthcare and clinical context (Ahmad et al., 2018). Having set the common goal of interpretability, in recent years the scientific community has fueled considerable interest in Interpretable Machine Learning, which today is an extremely open and active research field with numerous approaches that continually emerge every year (Adadi and Berrada, 2018) (Du et al., 2019) (Guidotti et al., 2018).

This research focuses on the comparison between two approaches proposed in the literature that attempt to overcome the interpretative problem. These approaches, Node Harvest by Meinshausen (2010) and inTrees by Deng (2019), are based on a post-processing interpretation method. They are also defined as Rule Extraction (Haddouchi and Berrado, 2019) approaches as they are focused on the extraction of rule sets. Both proposals use an understandable model based on the rules extracted from a Random Forest. The general idea is to identify a representative weak model to provide the interpretation. This one is selected from the sequence of weak models generated by the ensemble procedure. In particular, Node Harvest selects the set of rules through weights that are assigned based on quadratic programming with linear inequality constraints. Performing this task manages to coincide with two objectives, such as interpretability and accuracy in prediction.

Similarly, inTrees obtain interpretable information through the extraction and processing of rules deriving from a tree ensemble sequence. The extracted rules are used for the realization of a learner, which serves to make predictions on new data.

inTrees works through a series of algorithms that, at first, extract the rules and classify them; subsequently, they carry out a pruning phase on each rule, eliminating the rules that produce background noise or that are irrelevant. Subsequently, these algorithms select a compact set of rules considered relevant and not redundant. Frequent interactions are extracted and finally, everything is summarized in a learner that will be used to make predictions on new data.

## **2. Comparison Study**

We compare Node Harvest and inTrees on four health datasets.

Comparison analysis is performed in an empirical context, where their performance is evaluated using performance metrics. These are obtained from the output and are compared to a reference standard (Aria et al., 2021).

The metrics that evaluate the performance of predictive models, when used for classification, are based on the confusion matrix, which contains the expected and observed class labels, as well as the predicted target category and the source category, as can be seen from Table 1 which represents the structure of a 2x2 confusion matrix.

Regarding comparison, the goal is to compare these approaches through the use of different health datasets. The analysis is conducted on four binary classification health datasets. These datasets are available in the UCI Machine Learning repository. They have different characteristics (see Table 2).

Table 1: Confusion Matrix

Table 2: Main characteristics of the selected health datasets.

The analysis follows the following structure: we proceed with carrying out the random forest for each of the four datasets to obtain the performance of the standard model, in terms of the confusion matrix and prediction of the target variable; the extraction of the set of rules is carried out to investigate the paths taken by each observation, of which the most important and frequent rules of the set itself will also be shown.

Finally, the comparison of the various sets of rules obtained from the two investigated methodologies is performed. The final performance evaluation is conducted through nine parameters obtained from the confusion matrices: Accuracy, Precision, Sensitivity, Specificity, G-Mean, F1 Score, Youden's Index, Balanced Accuracy, Kappa (see Sokolova et al., Garc´ıa et al., Akosa).

Examples are provided of the outputs obtained from the Node Harvest and inTrees approaches. These examples derive from the analysis conducted on Pima Indians Diabetes data: Node Harvest allows you to view the set of rules through an explanatory plot, provided in figure 1, while inTrees allows easy reading through summary tables that show the most frequent rule sets, such as in the table 3.

Table 3: inTrees (STEL) on Pima Indians Diabetes: set of decision rules that are easily applicable to new data. The impRRF value measures the relative percentage decrease in the Gini index for each rule derived from the random forest. The impRRF consider the length of each rule as a proxy of its complexity.

Table 4 shows the nine performance metrics calculated on the four health datasets. The highest score, for each metric, is marked in bold. First of all, the interpretative solutions

Figure 1: Rule set plot obtained from Node Harvest on Pima Indians Diabetes.

proposed by Node Harvest (NH) and inTrees (STEL) represent an understandable approximation that provides an accurate summary of Random forest structure. All datasets show accurate measures very close to the reference value, provided by RF.

Focusing on the comparison, inTrees obtained higher scores in all the analyzed datasets. In particular, for EEG Eye State and Diabetic Retinopathy Debreceen, it shows much higher classification performances. It worth to noting, Node Harvest reports higher scores of sensitivity for all datasets. Maybe, it depends on the fact that this classifier can better recognize positive observations.

## **3. Conclusion**

InTrees represents an excellent strategy for obtaining interpretative learners from Random Forest models.

The results deriving from this methodology are just as good, considering that the simplified rules based on the STEL classifier can be implemented in any programming language.

This work is a starting point for understanding the potential of Interpretable Machine Learning, which requires the development of innovative approaches that can meet the interpretative needs of each application context, such as the healthcare framework. A more complete comparative analysis should focus on analyzing data characterized by unbalanced responses and the presence of missing data (D'Ambrosio et al., 2012), and multiclass responses.

Precision 0.78 0.74 **0.78** G-mean 0.66 0.62 **0.68** F1 0.79 **0.82** 0.79

Youden's Index 0.35 0.35 **0.38**

Table 4: Summary tables on the performance metrics performed on the four health datasets.

# **References**

Precision 0.71 0.64 **0.70** G-mean 0.73 0.68 **0.71** F1 0.74 0.72 **0.73**

Youden's Index 0.47 0.38 **0.43**

pp. 37–43.

*pattern recognition and image analysis*, pp. 441–448. Springer.

Meinshausen, N. (2010). Node harvest. *The Annals of Applied Statistics*, pp. 2049–2072.

Miotto, R., Wang, F., Wang, S., Jiang, X., and Dudley, J. T. (2018). Deep learning for healthcare: review, opportunities and challenges. *Briefings in bioinformatics*, **19**(6).

Ribeiro, M. T., Singh, S., and Guestrin, C. (2016). " why should i trust you?" explaining the predictions of any classifier. In *Proceedings of the 22nd ACM SIGKDD international conference on knowledge discovery and data mining*, pp. 1135–1144.

Sokolova, M., Japkowicz, N., and Szpakowicz, S. (2006). Beyond accuracy, f-score and roc: a family of discriminant measures for performance evaluation. In *Australasian joint conference on artificial intelligence*, pp. 1015–1021. Springer.


Contents

*by Zhao Xueying, Zhang Shunfu and Zhao Xiaoqiu*

Preface

When we interact with nature, we generally do so to gain something like space, resources, or some other advantage; and we may get just what we expect. But we may also generate risks or dangers with which we must eventually contend. Undesirable outcomes present challenges for our lives, health, or properties. Hazard management requires our awareness and understanding of the sources of risk. How is it manifested? What triggers dangerous conditions? What can be done to avoid

This volume includes 12 studies that address aspects of hazards from several perspectives. This research was undertaken by scholars working in diverse settings on an array of hazardous processes. The chapters are organized into four sections that reflect themes of this collection: risk assessment, hazard assessment, human responses to perceived or realized hazards, and social vulnerability and resilience. This preface introduces these themes and briefly describes the studies to highlight

In the first section, "Assessing Risk: Elucidating Extreme Events," three studies reflect the use of mathematical modeling and risk assessment to predict the dimensions and distributions of earthquakes, torrential rainstorms, and the intersections of extreme natural events and nuclear power plants. In "Assessing Seismic Hazard in Chile Using Deep Neural Networks," Plaza, Salas, and Nicolis employ machine-learning techniques, principally neural networks, to tackle the vexing problem of anticipating earthquakes. In "Strong Rainfall in Mato Grosso do Sul, Brazil: Synoptic Analysis and Numerical Simulation," Franchito, Gan, and Reyes Fernandez mathematically model meteorological conditions synoptically to determine the development of a torrential rainstorm that struck southwestern Brazil. And in "Natural Hazards and Nuclear Power Plant Safety," Katona asks whether the challenge of preparing nuclear facilities for the contingencies associated with an array of extreme natural events exceeds the industry's ability to plan for them.

The second section of this book, "Revealing Hazard: Imagining Exposure and Impact," contains five studies that examine the nature of the hazards generated by natural events impacting people and their built environments. Each study involves mathematical and graphical modeling of both the physical processes that yield the "natural" risks and the human processes that drive either activities that might be impacted or the use of hazardous environments. In "Estimation of Shear-wave Velocity Profiles Employing Genetic Algorithms and the Diffuse Field Approach on Microtremors Array: Implications on Liquefaction Hazard at Port of Spain, Trinidad," Salazar, Mannette, Reddock, and Ash employ genetic algorithms to estimate shear-wave velocity and examine the implications of microtremors in a coastal setting in Trinidad. In "Long-wave Generation Due to Atmosphericpressure Variation and Harbor Oscillation in Harbors of Various Shapes and Countermeasures against Meteotsunamis," Kakinuma models the meteorology of pressure patterns over the East China Sea that generate atmospheric disturbances that can be transferred to ocean surfaces. These oscillations are amplified to produce long-period sea waves, so-called "meteotsunamis" that can impact coastlines,

hazards? Can we live with extreme events?

their connections.


**4. Conclusion**

We have discovered that there are many methods used in quantifying operational risk. Therefore, it is proven handy for a risk analyst or anyone that is working in the risk analysis department of any institution to possess vast knowledge of multiple statistical concepts, and methods to apply in any given situation as each risk requires a different quantification approach. The Taxi claims data we have analyzed provides a good foundation for analyzing operational risk, but it does not represent all possible situations one might find in real life. Because Taxi claims are limited to the highest replacement value of a Taxi; in our case, we have realized that our data does not contain very extreme values; therefore, high losses are limited. The possibility of ruin would likely be due to the risk class of "high frequency and low magnitude." Using the Taxi claim data, we have provided a good example of how operational risk may be quantified and observed that the log-normal distribution is a better fit in this case. Nevertheless, it failed to model the extreme values of the Taxi claims data. Hence, the GEV distribution can be used to model those extreme values. However, in our research work, we did not dwell much on the GEV distribution. We used four approaches to calculate VaR in our analysis.

According to existing empirical evidence, the overall pattern of operational loss severity data is characterized by significant kurtosis, severe right-skewness, and a very heavy right tail caused by multiple outlying incidents. Fitting some of the common parametric loss distributions such as Weibull, log-normal, Pareto, gamma distributions, and so on is one way to calibrate operational losses. One disadvantage of utilizing these distributions is that they may not suit both the centre and the tails perfectly. Mixture distributions may be explored in this scenario. EVT can be used to fit a GPD to extreme losses surpassing a high predetermined threshold. The characteristics of the GPD distributions which are derived using the EVT approach are very sensitive to extreme data and the choice of threshold, which is a drawback of this approach.

The disadvantages of using loss distributions are that they do not model well many datasets in the presence of outliers and extreme values. Consequently, [2]'s Chapters 7 and 8 discuss other possible replacements for the loss distributions, e.g. alpha-stable distributions, GEV distribution, and GPD. The latter two distributions are part of EVT family of distributions.

Overall, it appears from the literature study done for this chapter that operational risk managers are focused on developing a model that would accurately represent the likelihood of the tail occurrences and producing a model that would realistically account for the probability of losses reaching a large amount is essential. Because, the latter is important for estimating the VaR.

Since we mainly focused on parametric distributions, and it might be interesting to use the nonparametric approach to quantify risk and some other mixture of distributions method. Therefore, this means that some of the possible additions to research work can be looking at more complex statistical distributions with better tail capturing ability. We also looked at multiple ways of finding VaR and from our findings, and we noticed that the empirical approach was the better way of quantifying the Taxi claims data's risk—note though the conclusion reached is data-dependent, which means it that a different conclusion will be made for a different dataset.


**2. Classification of water**

Based on its source, water can be divided into ground water and surface water [5]. Both types of water can be exposed to contamination risks from agricultural, industrial, and domestic activities, which may include many types of pollutants such as heavy metals, pesticides, fertilizers, hazardous chemicals, and oils [6].

Water quality can be classified into four types—potable water, palatable water, contaminated (polluted) water, and infected water [7]. The most common scientific definitions of these types of water quality are as follows:

1.*Potable water:* It is safe to drink, pleasant to taste, and usable for domestic purposes [1, 7].


**3. Learning through art**

For some years, the humanities, specially the arts, have also been used for the development of skills in learning environments. One of these sectors is that of basic and continuing medical education in the area of care (medicine, health professions) and more generally of the health sector in which for several years the Human Sciences have been introduced. These disciplines have been applied in innovative learning models for the development of skills useful to the care profession for building a Medical Humanities approach. Recent studies have shown how activities related to the arts can help; for example, medical students have benefitted from such activities to develop a certain type of skills and, moreover, to limit the risk of stress and burnout during the years of clinical practice [8].

It should be noted that already in 1948, the Constitution of the World Health Organization gave an alternative definition of health to that considered by the biomedical model: "A state of complete physical, social and mental well-being, and not only the 'absence of disease or infirmity..." [9], and subsequently describing health promotion in the Ottawa charter: "Health is considered not so much an abstract condition as a means aimed at an objective which, in operational terms, can be considered a resource that allows people to lead a productive life on an individual, social and economic level. Health is a resource for daily life and not the purpose of existence. It is a positive concept that enhances social and personal resources, as well as physical abilities" [10].

This holistic vision of health led to the research and definition of a new biopsycho-social approach applied to the medical and health area with the assumption that every health condition or disease is the consequence of the interaction between biological, psychological, and social. In addition, the basic methodological triad for the clinical trial is defined consisting of observation (external vision), introspection (internal vision), and dialog (interview) and these ultimately render the patient's data as scientific [11].

We can therefore talk to extend the concept of health about "global well-being."

This approach places the patient at the center of the treatment process and solicits the doctor or health professional to review his preparation in order to face the knowledge of the disease in a holistic context trying to improve "The medical gaze", the so-called clinical eye considered the "semiological ability to use the senses to produce the diagnosis of a disease." The skills and abilities useful in this context are therefore linked to soft skills, teamwork, understanding the other through

empathy and self-care of the health worker to limit the stress that this type of activity can feed. Among the activities useful for the development of skills we also find pedagogical methods that use the arts and in particular the visual arts. Regarding the adoption of these methods in medical and health education, a lot of scientific literature can be found indicating growing evidence that traits associated with empathy, for example, can be cultivated and taught through guided observation of works of visual art [12]. In addition, visual arts help in the development of clinical skills, including the observation, analysis, and communication of visual information. Representational art allows students to focus on identifying recognizable shapes and contextual information, while abstract art encourages the development of pattern recognition skills and greater tolerance of ambiguity with the freedom to follow one's imagination and emotion. Also in Italy, the introduction of pedagogical methods that use visual art as a tool for improving certain skills and abilities in the field of Medical Education is being experimented with positive results [13].

An important element in this context is training for all those who work to improve the relations between professional care and patients. Important skills are those related to collaborative work, communication, and empathy. Being empathetic, patient-centered, compassionate, humble, and respectful is essential for healthcare professionals to deliver holistic care. Another important activity to practice is to facilitate useful strategies for limiting stress and burnout in operators with a decrease in empathy and observation and analysis skills starting from basic training to continuing education. Furthermore, an important skill is that related to critical thinking to keep an open mind, self-awareness and respect and appreciation of different points of view that make each situation and patient experience unique [14].

### **4. Art practice and medical education**

The art works represent the moods, the relational dynamics, and the emotions that can be learned and recognized through exercise. Some collaborative activities related to the observation of a work of art can also help to change the approach with the other and therefore with the patient and his family.

One of the methods that use artistic images and which has been applied for years in the United States and experimented in Italy for basic and continuing training in the medical and health area is Visual Thinking Strategies (VTS). VTS originated in 1988 from the integration of the research of the cognitive psychologist Abigail Housen and Philip Yenawine educator at the Museum of Modern Art in New York [15, 16].

This structured method for involving museum visitors becomes an important tool for learning in school and an important activity in the medical and health education sector [17]. The practice of VTS takes place in small groups, in front of a work of art, considered equal for basic knowledge and culture. An experienced facilitator will use only three questions to lead the discussion. It is important to listen to the opinions of others, as everyone will be able to enrich their point of view, creating a collective consciousness.

The questions are as follows: What is going on in this picture? What do you see that makes you say that? What else can you find?

It is therefore important that the observations and opinions of the participants are always substantiated by visual elements. This apparently simple step activates cognitive mechanisms for recognizing reality on the basis of one's previous experiences.

The experience of observing the image with the VTS method stimulates the awareness of how perception works: at the beginning, we have an overview, we

#### *Learning through Art in Medical Education DOI: http://dx.doi.org/10.5772/intechopen.101213*

identify details that, based on our knowledge and experience, lead us to an elaboration of the information perceived by assigning a certain meaning, the subsequent observation and listening to other possible interpretations, based on new details or the same decoded in a different way, lead us to a further elaboration and assignment of meaning, thus activating a problem-solving process. This experience also suggests that we need to take time in front of an image to understand its meaning. This exercise makes us reflect on the multiple interpretations that the same image can suggest; in fact, if we are based on previous knowledge and experiences, the same image can be understood and therefore described differently by each participant, thus learning to accept the ambiguity of the perception related to our knowledge and that of others. This exercise helps us to develop divergent thinking at the basis of creativity. Group discussion also allows to improve communication and listening skills.

In summary, we can list a series of objectives and purposes that have emerged in the various studies conducted on VTS related to the medical and health profession:

An interesting analogy that we can focus on is that between the modality of discussion in small groups that the VTS stimulates in front of a work of art and the visits or meetings organized with the care team during which doctors present, discuss, and plan for patient health with students' request for hypothesis with experts acting as mentors and facilitators to guide discussion and formulate a care plan [18].

These activities with art can be very useful for improving the skills such as observation, problem solving, and critical thinking. In this context, the clinical observation, which includes the identification of data, the recognition of patterns in the collected data, and the interpretation and re-reading of the same, is the basis of the complex decision-making process of the doctor, through which he collects data, achieves the conclusions and chooses the most suitable therapy.

The skills of problem solving and critical thinking are also considered key and fundamental skills in the care sector, and art can help in their development. This arrangement is linked to the essence of the artistic artifact: the work of art can be defined as a "text" open to multiple levels of reading and the information it offers can be correlated with each other even if with a different meaning, as they can be

represented as conceptual nodes of a hypertext that is configured while the perception continues to be applied with the identification of new details and therefore with the elaboration of new contents starting from the attributed meanings. In relation to the development of Critical Thinking, we find an interesting example that represents a useful collaboration between the cultural sector and medicine. Ohio State University College of Medicine (OSUCOM), in partnership with the Columbus Museum of Art (CMA), during the 2010–2011 academic year conducted an innovative experience for medical students who applied the analysis of works of art using observation supported by a column on critical thinking combined with a group discussion called "Art of Analysis." The critical thinking column is called "ODIP", an acronym for "observe, describe, interpret, and demonstrate." The goals of the Art of Analysis (AoA) are to encourage critical thinking skills, generate empathy, create a foundation for cooperative outcomes, increase students' tolerance for ambiguity, and improve the observation skills of junior doctors. This activity includes a form that suggests activating an observation, a description, an interpretation and a test, stimulating the students to learn to collect information objectively, to identify different possible interpretations to choose the best one based on evidence and therefore to implement a problem solving and critical thinking process [19]. Another fundamental skill for doctors and care staff is empathy. The term empathy derives from the Greek word "εμπαθεία" (> en and patheo, that is "inside" and "feel" = "feel inside", "put yourself in the other's shoes"); it indicated the emotional relationship of participation that bound the author-cantor to his audience. The term "empathy" has been equated with the German "Einfühlung", coined by the philosopher Robert Vischer at the end of the nineteenth century and only later it was translated into the English term "empathy." Vischer also defined for the first time the specific meaning of esthetic sympathy, or the feeling, not otherwise definable, that one feels in front of a work of art.

Vischer conceived this term as the ability to feel inside and to allow, that is, to perceive the external nature, as internal, belonging to our own body. It therefore represents the ability to project feelings from us to others and to the things we perceive [20].

In the human sciences, empathy designates an attitude toward others characterized by a commitment to understanding the other, excluding any personal affective attitude (sympathy, antipathy) and any moral judgment. Fundamental in this context was the discovery of mirror neurons by the research group of Prof. G. Rizzolatti. It is a particular class of cells that are activated both when a person performs an action and when he sees him doing, thus allowing us to understand what others are doing or feeling. It is therefore a fundamental mechanism not only for learning through imitation, but also to make the observer participates in the emotions of others or rather recognize the state of the other [21]. It is now clear that we cannot ignore taking care of the whole person to treat his illness and therefore empathy is considered essential for a good doctor-patient relationship. Also, for this type of ability, the work of art can be a valid tool for understanding the complexity of human nature. In particular, courses based on the observation of art have been shown to help students be more aware of emotions, their role in medicine, and to express empathy.

An interesting example concerns the program of the course for medical students of the Weill Cornell Medical College in collaboration with the Frick Collection art museum of New York published in 2001. The program included the examination of the portraits of the museum by students with the help of experts of art and by doctors according to indications that they had to replicate with photographs of the faces of patients. This activity is useful not only to improve observation skills but also to learn to understand the different states mood and the different emotions of the faces developing a greater emotional awareness [22].

A capacity whose concept was defined not so long ago is the Tolerance of Ambiguity.

Intolerance to ambiguity, or aversion to ambiguity, was first identified more than 50 years ago. It has been described as a personality trait in which "new, complex or insoluble" situations are perceived as "sources of threat." Given that the field of medicine and healthcare can be characterized by novelty, complexity, and sometimes insolubility, it is extremely important to understand how clinicians, and others, react to such circumstances. In general, individuals with high tolerance for ambiguity are attracted or fascinated by the unknown. Conversely, those with low tolerance tend to deny, avoid, or minimize ambiguity and experience significant stress on account of it. In medical practice, low tolerance of ambiguity is associated with the biomedical model rather than a bio-psycho-social vision of care [23].

The increase in the intolerance of ambiguity can be associated with stress [24]. Yet studies indicate that medical students or healthcare staff may feel uncomfortable with ambiguity. The use of Medical Humanities and in particular art can help improve this ability.

Another important practice that uses art is icono-diagnosis, which can help in learning a correct diagnosis process. The concept of icono-diagnosis was introduced in 1983 by A. Pontius, a psychiatrist at Harvard University, committed to demonstrate the ancient presence of Crouzon syndrome in the Cook archipelago, examining the features of the statues found in these islands [25]. In recent years, several doctors such as V. Franco, pathologist of the University of Palermo [26] or F.J. Barbado bring their students to the Prado Museum for a "medical examination" to the artworks exposed [27]. The enormous talent of the great masters of painting allows only by looking at a portrait to imagine the thoughts of this person and his state of mind. With our didactic activity, however, we can go further, and by observing carefully, know more intimate details such as; a disease that may have plagued the person, their past history and their wishes. For example, always with careful observation, a spot on the skin, a knot in the neck or a strange formation in the fingers can show signs of specific pathologies. These can be traced back to the models that have been immortalized and confirm our theoires with other historical sources. Thus, through this practice, it is possible to "train" the clinical eye. It allows also to rewrite the history of the people portrayed or of the artists. An Italian study published in the Journal of the Royal Society of Medicine analyzed three portraits of Michelangelo, arguing that the joints of the artist's left hand were almost certainly affected by arthrosis, a disease that would have affected Michelangelo at the end of the seventh decade of his life. In the details of the portraits, we can see the nodules precisely, the typical deformities of arthrosis, the diagnosis of which offers a plausible explanation for Michelangelo's loss of dexterity in old age and also underlines his victory over the disease. The continuous and intense work would have helped the artist to maintain the use of his hands as long as possible [28]. There are several studies that are represented in the scientific literature and that give us an idea of how to use a multidisciplinary team for research on particular pathologies and offer students suggestions for the development of clinical skills [29–31].

This brief description can give an idea of how art and medicine have a lot in common and how one can support the other. As you will see, art can promote the development of skills useful to doctors and medicine can help in understanding the history of the characters and communities represented but also be able to rewrite the history of art by suggesting other visions.

The experimentation of art as a tool in medical education is being carried out in many different countries. In Italy, at the Sapienza University of Rome, a special course that applies art practice was introduced in the curriculum of medicine and nursing. From the 2014–2015 academic year, a Sapienza research group began

experimenting this type of activities and currently the Laboratory of Art and Medical Humanities has been developed to coordinate art courses for the training of physicians and nursing and healthcare operators and continues in the context of study and research in this sector. The results were very interesting; even the activities organized in distance learning in the pandemic period were effective [32]. These courses are acquiring a curricular character with positive qualitative and quantitative results in line with those presented by the international literature of the sector.

These experiences also led to the validation of a useful grid to measure the improvement of some of the skills previously mentioned after participating in the proposed discussion and art production activities [33]. Other experiences in other countries reported the positive results obtained by adopting this useful evaluation system [34].

Other experiences in the field of continuing education, always in the health sector, have found a positive welcome by the attendants. In the United States, the use of works of art has become an approach used in the care sector by many universities to involve medical students, residents, doctors, and nurses in an innovative learning process. Medical schools are expanding their educational programs by collaborating with local art museums [35]. In Italy too, an experimentation linked to the activities applied in the United States is underway.

The last notation that is considered important to report is the one that is linked to these experiences carried out at a distance in period of COVID pandemic with extremely positive results in the various areas in which they have been applied university environment, groups connected to palliative care, patients in psychotherapy, in distance teaching.

These experiences have helped to raise awareness of how much arts, and in this case visual art, can be a valuable tool for developing to upgrade useful skills and abilities in the care sector and improve the state of well-being of professionals in the medicine and healthcare field.


**5. The example of calculation of temperature field and phase transformations in welded flats**

In the considered example, it is assumed that the welded material is steel S235 with the following material constants: specific heat *Cp* = 670 J/(kg·K), density *ρ* = 7800 kg/m3 , thermal diffusivity *a* = 1.2 × 10−5 m2 /s, the temperatures at the beginning and end of austenite transfor‐ mation, respectively, *A1* = 996 K (723°C) and *A3* = 1108K (835°C), solidus temperature *TS* = 1763K (1490°C) and the liquidus temperature *TL* = 1793K (1520°C). The model of joining two buttwelded flats with a thickness of 0.012 m and a width of 0.1 m is shown in **Figure 5**.

**Figure 5.** Scheme of the welded joint with technology chamfering.

The speed and power of the movement source are assumed to be *v* = 0.005 m/s and *P* = 18000 W, respectively. Time-varying temperature field was determined according to the formulas (Eqs. (11)–(15)). The temperature field on the upper surface of the welded flats and in the longitudinal section determined by the trace of the source transition is shown in **Figures 6** and **7**.

while *εTrc* is the strain caused by phase transformation during cooling:

e

e

**transformations in welded flats**

**Figure 5.** Scheme of the welded joint with technology chamfering.

diffusivity *a* = 1.2 × 10−5 m2

solid state material:

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*Trc*

,,,

( ,,, 0 ) *SOL*

In the considered example, it is assumed that the welded material is steel S235 with the

mation, respectively, *A1* = 996 K (723°C) and *A3* = 1108K (835°C), solidus temperature *TS* = 1763K (1490°C) and the liquidus temperature *TL* = 1793K (1520°C). The model of joining two butt-

The speed and power of the movement source are assumed to be *v* = 0.005 m/s and *P* = 18000 W, respectively. Time-varying temperature field was determined according to the formulas (Eqs. (11)–(15)). The temperature field on the upper surface of the welded flats and in the

following material constants: specific heat *Cp* = 670 J/(kg·K), density *ρ* = 7800 kg/m3

welded flats with a thickness of 0.012 m and a width of 0.1 m is shown in **Figure 5**.

**5. The example of calculation of temperature field and phase**

*i PFBM*

=

*i Ai*

<sup>=</sup> å (31)

*x y z t for T T* = > (32)

/s, the temperatures at the beginning and end of austenite transfor‐

, thermal

 jg

where *TSOL* denotes solidus temperature, *Ts* the initial temperature of phase transformation, *Tsi* the initial temperature of austenite transformation in the *i*-th structure and *γAi* the structural strain of austenite in the *i*-th structure. In addition, due to the limitation of the existence of

**Figure 6.** Temperature distribution (°C) on the surface of flats at time *t* = 102 s from beginning of welding.

**Figure 7.** Temperature distribution (°C) in longitudinal section at time *t* = 102 s from beginning of welding.

The quantities *B1* = *B2* = *B* are considered in calculations, which are equal to the width of one flat, thereby obtaining a temperature field symmetrical to the plane defined by vertical axis of the source and the direction of its movement. Thus, both this and the further calculation illustrations are shown on the right symmetrical cross-section which is perpendicular to a moving heat source. The image of maximum temperature isotherms in a cross-section of the joint (on the front contact of flats) is shown in **Figure 8**.

The analysis of the cooling speed *v8/5* showed that after complete cooling in both weld and heat-affected zone, wherein there has been complete and partial transformation of ferrite and pearlite into austenite, supercooled austenite resulted in a ferrite-pearlite structure. Changes in the temperature and structure in the considered cross-section for the selected time of the welding cycle are shown in **Figures 11**–**19**. The analysis of these changes was investigated on a symmetrical half of the cross-section of the flats' connection, which is perpendicular to the direction of source movement and *x0* = 0.5 m from the beginning of the flats (in half their length), that is, from the beginning of the coordinate system associated with flats. For *t* = *0*, the beginning of the coordinate systems associated with the source and the welded object overlaps. **Figures 11**–**13** illustrate the condition where the joint area was completely filled with the welded material, there were no cooling phase transitions and the largest participation of austenite is observed. By contrast, **Figures 14**–**19** illustrate the gradual decrease in the share of

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**Figure 10.** TTT-welding diagram for S235 steel.

austenite which forms a ferritic-pearlitic structure following the temperature drop.

**Figure 11.** Volume fraction of austenite in cross-section at time *t* = 109 s from process beginning.

**Figure 8.** Maximum temperatures (°C) in half of cross-section of welded flats.

On the basis of the maximum temperature field achieved in particular areas of the weld joint, specific heat-affected zones were determined (**Figure 9**) specified by limit temperatures *TL*, *TS*, *A3* and *A1*. The weld area is limited by a liquidus isotherm, which implies covering the part of the section wherein complete melting of the material occurred. Incomplete melting is limited by both liquidus and solidus temperatures. The heat-affected zone is determined by solidus isotherms and *A1*. In addition, in the region between the solidus and *A3* temperatures, ferrite and pearlite, the starting components of steel, have been completely transformed into austen‐ ite, whereas in the temperature range *A1*-*A3*, there is an incomplete conversion. In the area where the temperature did not exceed *A1*, certainly, phase transitions did not occur and the structure of the parent material (ferritic-pearlitic) was thus preserved. The participation of the heating structures was determined on the basis of the Fe-C diagram. The participation of the cooling structure was determined on the basis of knowledge of the TTT-welding diagram for welding steel S235 and the variations in temperature during cooling (**Figure 10**) [45].

**Figure 9.** Heat-affected zones (HAZ) with selected points.

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**Figure 10.** TTT-welding diagram for S235 steel.

the source and the direction of its movement. Thus, both this and the further calculation illustrations are shown on the right symmetrical cross-section which is perpendicular to a moving heat source. The image of maximum temperature isotherms in a cross-section of the

On the basis of the maximum temperature field achieved in particular areas of the weld joint, specific heat-affected zones were determined (**Figure 9**) specified by limit temperatures *TL*, *TS*, *A3* and *A1*. The weld area is limited by a liquidus isotherm, which implies covering the part of the section wherein complete melting of the material occurred. Incomplete melting is limited by both liquidus and solidus temperatures. The heat-affected zone is determined by solidus isotherms and *A1*. In addition, in the region between the solidus and *A3* temperatures, ferrite and pearlite, the starting components of steel, have been completely transformed into austen‐ ite, whereas in the temperature range *A1*-*A3*, there is an incomplete conversion. In the area where the temperature did not exceed *A1*, certainly, phase transitions did not occur and the structure of the parent material (ferritic-pearlitic) was thus preserved. The participation of the heating structures was determined on the basis of the Fe-C diagram. The participation of the cooling structure was determined on the basis of knowledge of the TTT-welding diagram for

welding steel S235 and the variations in temperature during cooling (**Figure 10**) [45].

joint (on the front contact of flats) is shown in **Figure 8**.

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**Figure 8.** Maximum temperatures (°C) in half of cross-section of welded flats.

**Figure 9.** Heat-affected zones (HAZ) with selected points.

The analysis of the cooling speed *v8/5* showed that after complete cooling in both weld and heat-affected zone, wherein there has been complete and partial transformation of ferrite and pearlite into austenite, supercooled austenite resulted in a ferrite-pearlite structure. Changes in the temperature and structure in the considered cross-section for the selected time of the welding cycle are shown in **Figures 11**–**19**. The analysis of these changes was investigated on a symmetrical half of the cross-section of the flats' connection, which is perpendicular to the direction of source movement and *x0* = 0.5 m from the beginning of the flats (in half their length), that is, from the beginning of the coordinate system associated with flats. For *t* = *0*, the beginning of the coordinate systems associated with the source and the welded object overlaps. **Figures 11**–**13** illustrate the condition where the joint area was completely filled with the welded material, there were no cooling phase transitions and the largest participation of austenite is observed. By contrast, **Figures 14**–**19** illustrate the gradual decrease in the share of austenite which forms a ferritic-pearlitic structure following the temperature drop.

**Figure 11.** Volume fraction of austenite in cross-section at time *t* = 109 s from process beginning.

**Figure 15.** Volume fraction of ferrite in cross-section at time *t* = 134 s from process beginning.

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**Figure 16.** Volume fraction of pearlite in cross-section at time *t* = 134 s from process beginning.

**Figure 17.** Volume fraction of austenite in cross-section at time *t* = 146 s from process beginning.

**Figure 12.** Volume fraction of ferrite in cross-section at time *t* = 109 s from process beginning.

**Figure 13.** Volume fraction of pearlite in cross-section at time *t* = 109 s from process beginning.

**Figure 14.** Volume fraction of austenite in cross-section at time *t* = 134 s from process beginning.

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**Figure 15.** Volume fraction of ferrite in cross-section at time *t* = 134 s from process beginning.

**Figure 12.** Volume fraction of ferrite in cross-section at time *t* = 109 s from process beginning.

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**Figure 13.** Volume fraction of pearlite in cross-section at time *t* = 109 s from process beginning.

**Figure 14.** Volume fraction of austenite in cross-section at time *t* = 134 s from process beginning.

**Figure 16.** Volume fraction of pearlite in cross-section at time *t* = 134 s from process beginning.

**Figure 17.** Volume fraction of austenite in cross-section at time *t* = 146 s from process beginning.

**Figure 18.** Volume fraction of ferrite in cross-section at time *t* = 146 s from process beginning.

**Figure 19.** Volume fraction of pearlite in cross-section at time *t* = 146 s from process beginning.

Changes in temperature and volume fraction of the individual structural components at the selected points in the cross-section (comp. **Figure 9**) are shown in **Figure 20**.

*α* **[1/°C]** *γ*

**Figure 20.** Welding thermal cycles and volume fractions of phases at selected points: T—temperature, A—austenite, P

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Dilatometric graphs (thermal and structural strains as a function of temperature) for selected points of the section (comp. **Figure 9**) are shown in **Figure 21**. In **Figure 21a**, a dilatometric graph for point *1* of the weld area is presented, where the material is deposited in the liquid phase as the molten material of the electrode, flux and partially melted edges of the flats; therefore, we observe only shrinkage "negative" strains of the cooling metal with a clear fault

Austenite 2.178 × 10−5 *γ*F,P,S→A 1.986 × 10−3 Ferrite 1.534 × 10−5 γB→A 1.440 × 10−3 Pearlite 1.534 × 10−5 *γ*A→F,P 3.055 × 10−3 Bainite 1.171 × 10−5 *γ*A→B 4.0 × 10−3

**Table 1.** Structural (*γ*) and thermal (*α*) expansion coefficients of phases.

Martensite 1.36 × 10−5

—pearlite, F—ferrite.

Point *1* is located in the area of chamfering of flats; hence, the graph of temperature and austenite volume fraction starts at the moment of the joint execution. At points *2* (fusion zone) and *3* (full-transformation zone), a complete austenite transformation occurs. But at point *2*, apart from phase transformations in the solid state, melting and solidification phase transfor‐ mations occur, resulting in a diverse dendritic structure shown during metallographic testing. At point 4, a partial transformation of the primary structure into austenite occurs, which is visible on the graph.

In strain calculations, linear expansion coefficients of the particular structural elements were assumed and structural stresses (**Table 1**) were determined on the basis of the author's own dilatometric research [46].

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**Figure 20.** Welding thermal cycles and volume fractions of phases at selected points: T—temperature, A—austenite, P —pearlite, F—ferrite.

**Table 1.** Structural (*γ*) and thermal (*α*) expansion coefficients of phases.

**Figure 18.** Volume fraction of ferrite in cross-section at time *t* = 146 s from process beginning.

**Figure 19.** Volume fraction of pearlite in cross-section at time *t* = 146 s from process beginning.

selected points in the cross-section (comp. **Figure 9**) are shown in **Figure 20**.

visible on the graph.

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dilatometric research [46].

Changes in temperature and volume fraction of the individual structural components at the

Point *1* is located in the area of chamfering of flats; hence, the graph of temperature and austenite volume fraction starts at the moment of the joint execution. At points *2* (fusion zone) and *3* (full-transformation zone), a complete austenite transformation occurs. But at point *2*, apart from phase transformations in the solid state, melting and solidification phase transfor‐ mations occur, resulting in a diverse dendritic structure shown during metallographic testing. At point 4, a partial transformation of the primary structure into austenite occurs, which is

In strain calculations, linear expansion coefficients of the particular structural elements were assumed and structural stresses (**Table 1**) were determined on the basis of the author's own Dilatometric graphs (thermal and structural strains as a function of temperature) for selected points of the section (comp. **Figure 9**) are shown in **Figure 21**. In **Figure 21a**, a dilatometric graph for point *1* of the weld area is presented, where the material is deposited in the liquid phase as the molten material of the electrode, flux and partially melted edges of the flats; therefore, we observe only shrinkage "negative" strains of the cooling metal with a clear fault reflecting the strain of austenite transformation into ferrite and pearlite. Point *2* (**Figure 21b**) is located in the area of melting of the starting material, and the dashed line in the figure reflects the change of state from solid to liquid. The solid line (bottom) is initiated by weld solidifica‐ tion.

of ferrite and pearlite in austenite was observed, that is, at that point, the temperature during heating has exceeded the temperature of the beginning of austenitizing *A1*, but has not reached the final temperature of austenitizing *A3*. The stage of the austenite transformation is deter‐ mined linearly in a numerical model by making the austenite transformation progress conditionally on the ratio (*Tmax* – *A1*)/(*A3* – *A1*), where *Tmax* is the maximum temperature reached

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**6. Verification of the results of numerical simulation of phase transitions**

In order to verify the results of the numerical calculations, metallographic tests of the buttwelded joint were carried out. For this purpose, two flats with identical geometry as calculated, that is, two flats with a thickness of 0.012 m and width of 0.1 m, were welded. The material of the flats was steel S235. Before making the joint, sheet chamfering was conducted. Then, welding was carried out with the submerged arc welding method, under welding flux Taste-3 and with SPG*Φ*15 wire. Welding parameters were voltage U = 30 V, current I = 600 A and welding speed 20 m/h. The diagram of the elements prepared for joining is presented in **Figure 5** (identical to the welded joint adopted for numerical analysis). Cross-section of the weld joint (the image of the sample taken for metallographic examinations) is presented in **Figure 22**. Metallographic analysis was performed for specific zones of a welded joint, that is, for the area of weld, heat-affected zone and parent material. **Figure 23** shows an image of the middle part of the welded joint (at the junction of welded flats) with a clearly visible dendritic structure which is characteristic of solidification. **Figure 24** shows an image of the structure in the right symmetrical part of the welded joint in the area from the weld to the ferrite-pearlite structure of the parent material. On the border of the weld, dendrites are visible, which change in the heat-affected zone into a structure with the Widmannstatten structure elements.

**Figure 22.** Cross-section of a welded joint: sample taken for metallographic analysis, magnification 2×.

at a particular point of the weld joint.

**with the results of metallographic research**

**Figure 21.** Dilatometric curves for selected points of cross-section.

Dilatometric graph in point *3* (**Figure 21c**) illustrates the history of strain changes for a full thermal cycle. In the considered point, the material with a ferritic-pearlitic structure is completely transformed into austenite during heating (lower line), which is shown with a fault in the diagram in the temperature range 723–835°C. At point 4 (**Figure 21d**) partial conversion of ferrite and pearlite in austenite was observed, that is, at that point, the temperature during heating has exceeded the temperature of the beginning of austenitizing *A1*, but has not reached the final temperature of austenitizing *A3*. The stage of the austenite transformation is deter‐ mined linearly in a numerical model by making the austenite transformation progress conditionally on the ratio (*Tmax* – *A1*)/(*A3* – *A1*), where *Tmax* is the maximum temperature reached at a particular point of the weld joint.

reflecting the strain of austenite transformation into ferrite and pearlite. Point *2* (**Figure 21b**) is located in the area of melting of the starting material, and the dashed line in the figure reflects the change of state from solid to liquid. The solid line (bottom) is initiated by weld solidifica‐

**Figure 21.** Dilatometric curves for selected points of cross-section.

Dilatometric graph in point *3* (**Figure 21c**) illustrates the history of strain changes for a full thermal cycle. In the considered point, the material with a ferritic-pearlitic structure is completely transformed into austenite during heating (lower line), which is shown with a fault in the diagram in the temperature range 723–835°C. At point 4 (**Figure 21d**) partial conversion

tion.

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