**2. Mathematical background: summation of asymptotic series**

### **2.1 Analysis of power series**

We suppose that by the result of the asymptotic study, one obtains the following series:

$$f(\varepsilon) \sim \sum\_{n=0}^{\infty} \mathbb{C}\_n \varepsilon^n \text{ for } \qquad \varepsilon \to 0. \tag{1}$$

whose coefficients are determined from the condition

*DOI: http://dx.doi.org/10.5772/intechopen.93084*

*Padé Approximation to Solve the Problems of Aerodynamics and Heat Transfer…*

Padé coefficients of the numerator and denominator of the PAs.

2. PAs gives meromorphic continuation of a given power series.

PAs is invariant concerning Euler transformation (2).

functions. Let us analyze a function (3). Let

exists, then it is unique.

*q*ð Þ¼ *ε f*

If *c* þ *df*ð Þ 0 6¼ 0, then

provided that there is *f*½ � *n=n* ð Þ*ε* .

one has the following estimate:

Eq. (7) can be replaced by *f*ð Þ*ε* .

**79**

�1

1 þ *b*1*ε* þ … þ *bmεm* ð Þ *c*0 þ *c*1*ε* þ *c*2*ε*2 þ … ¼ *a*0 þ *a*1*ε* þ … þ *anεn* þ O *εn*þ*m*þ1

Equating coefficients near the same powers *ε*, one obtains a system of linear algebraic equations. In the case where this system is solvable, one can obtain the

We note some properties of the PAs [5, 13, 19]. If the PAs at the chosen m and n

1. If the PAs sequence converges to some function, the roots of its denominator tend to the poles of the function. This allows for a sufficiently large number of terms to determine the pole and then perform an analytical continuation.

3. PAs of the inverse function is treated as the PAs function inverse itself. This property is called duality and is more exactly formulated as follows. Let

ð Þ*ε* and *f*ð Þ 0 6¼ 0, then *q*½ � *n=m* ð Þ¼ *ε f*

4. Diagonal PAs are invariant under fractional linear transformations of the argument. Suppose that the function is given by their expansion (3). Consider the linear fractional transformation that preserves the origin *W* ¼ *aε=*ð Þ 1 þ *bε* and the function *q*(*W*) *= f*ð Þ*ε* . Then *q*½ � *n=n* ð Þ¼ *W f*½ � *n=n* ð Þ*ε* , provided that one of these approximations exist. In particular, the diagonal

5. Diagonal PAs are invariant under fractional linear transformations of

*q*ð Þ¼ *ε a* þ *bf*ð Þ*ε c* þ *df*ð Þ*ε :*

*q*½ � *n=n* ð Þ¼ *ε a* þ *bf*½ � *n=n* ð Þ*ε*

6. PAs can get the upper and lower bounds for *f*½ � *n=n* ð Þ*ε* . For the diagonal PAs,

Typically, this estimate is valid for the function itself, that is, *f*½ � *n=n* ð Þ*ε* in

7. Diagonal and close to them a sequence of PAs often possesses the property of autocorrection [17, 18]. It consists of the following. To determine the coefficients of the numerator and denominator of PAs, we have to solve

*c* þ *df*½ � *n=n* ð Þ*ε*

*f*½ � *n=n*�1 ð Þ*ε* ≤ *f*½ � *n=n* ð Þ*ε* ≤ *f*½ � *n=n*þ1 ð Þ*ε :* (7)

�1

½ � *n=m* ð Þ*ε* (6)

(5)

As is known, the radius of convergence *ε*0 series (1) is determined by the distance to the nearest singularity of the function *f*(*ε*) on the complex plane. To define *ε*0, the Domb-Sykes plot may be useful [8, 10]. In many cases, one can effectively use the conformal mapping of the series, a fairly complete catalog of which is given in [9]. In particular, it sometimes turns out to be a successful Euler transformation [8, 10], based on the introduction of a new variable:

$$
\tilde{\varepsilon} = \frac{\varepsilon}{1 - \varepsilon/\varepsilon\_0}. \tag{2}
$$

Recast the function *f* in terms of ~*ε*, *f* � P∞ *n*¼0*dn*~*εn*, transfer the singularity at the point ~*ε* ¼ ∞.

A natural generalization of Euler transformation looks as follows:

$$
\tilde{\varepsilon} = \frac{\varepsilon}{\left(\mathbf{1} - \varepsilon/\varepsilon\_0\right)^a},
$$

where *α* is the certain number.

#### **2.2 Padé approximants**

"The coefficients of the Taylor series in the aggregate have a lot more information about the values of features than its partial sums. It is only necessary to be able to retrieve it, and some of the ways to do this is to construct a Padé approximant" [11]. Padé approximants (PAs) allow us to transform of power series to a fractional-rational function. Let us define PAs, following Baker and Graves-Morris [25].

Suppose we are given the power series:

$$f(\varepsilon) = \sum\_{i=1}^{\infty} c\_i \varepsilon^i,\tag{3}$$

PAs can be written as the following expression:

$$f\_{\left[\mathfrak{n}/m\right]}(\varepsilon) = \frac{a\_0 + a\_1\varepsilon + \dots + a\_n\varepsilon^n}{1 + b\_1\varepsilon + \dots + b\_m\varepsilon^m},\tag{4}$$

*Padé Approximation to Solve the Problems of Aerodynamics and Heat Transfer… DOI: http://dx.doi.org/10.5772/intechopen.93084*

whose coefficients are determined from the condition

approximants for the summations of the asymptotic series. Section 3 discusses the method of combining of internal and external asymptotics (matching method) by means of Padé approximants. In the Section 4, the methods of solving specific problems of mathematical physics and mechanics of fluid and gas are demonstrated.

We suppose that by the result of the asymptotic study, one obtains the following

*Cnεn* for *ε* ! 0*:* (1)

*:* (2)

*n*¼0*dn*~*εn*, transfer the singularity at the

, (3)

1 þ *b*1*ε* þ … þ *bmεm* , (4)

**2. Mathematical background: summation of asymptotic series**

*f*ð Þ� *ε* X∞

*Mathematical Theorems - Boundary Value Problems and Approximations*

*n*¼0

transformation [8, 10], based on the introduction of a new variable:

A natural generalization of Euler transformation looks as follows:

~*ε* ¼ *ε*

"The coefficients of the Taylor series in the aggregate have a lot more information about the values of features than its partial sums. It is only necessary to

be able to retrieve it, and some of the ways to do this is to construct a Padé

to a fractional-rational function. Let us define PAs, following Baker and

approximant" [11]. Padé approximants (PAs) allow us to transform of power series

*f*ð Þ¼ *ε* X∞

*i*¼1

*f*½ � *n=m* ð Þ¼ *ε a*0 þ *a*1*ε* þ … þ *anεn*

*ciεi*

ð Þ 1 � *ε=ε*0 *α* ,

Recast the function *f* in terms of ~*ε*, *f* � P∞

where *α* is the certain number.

Suppose we are given the power series:

PAs can be written as the following expression:

**2.2 Padé approximants**

Graves-Morris [25].

**78**

As is known, the radius of convergence *ε*0 series (1) is determined by the distance to the nearest singularity of the function *f*(*ε*) on the complex plane. To define *ε*0, the Domb-Sykes plot may be useful [8, 10]. In many cases, one can effectively use the conformal mapping of the series, a fairly complete catalog of which is given in [9]. In particular, it sometimes turns out to be a successful Euler

> ~*ε* ¼ *ε* 1 � *ε=ε*0

Section 5 presents a discussion of the obtained.

**2.1 Analysis of power series**

series:

point ~*ε* ¼ ∞.

$$(\mathbf{1} + b\_1 \boldsymbol{\varepsilon} + \dots + b\_m \boldsymbol{\varepsilon}^m) \left( c\_0 + c\_1 \boldsymbol{\varepsilon} + c\_2 \boldsymbol{\varepsilon}^2 + \dots \right) = a\_0 + a\_1 \boldsymbol{\varepsilon} + \dots + a\_n \boldsymbol{\varepsilon}^n + \mathcal{O} \left( \boldsymbol{\varepsilon}^{n+m+1} \right) \tag{5}$$

Equating coefficients near the same powers *ε*, one obtains a system of linear algebraic equations. In the case where this system is solvable, one can obtain the Padé coefficients of the numerator and denominator of the PAs.

We note some properties of the PAs [5, 13, 19]. If the PAs at the chosen m and n exists, then it is unique.

$$q(\varepsilon) = f^{-1}(\varepsilon) \text{ and} \\ f(\mathbf{0}) \neq \mathbf{0}, \text{then} \\ q\_{[n/m]}(\varepsilon) = f^{-1}\_{[n/m]}(\varepsilon) \tag{6}$$

$$q(\varepsilon) = \frac{a + bf(\varepsilon)}{c + df(\varepsilon)} \cdot \varepsilon$$

If *c* þ *df*ð Þ 0 6¼ 0, then

$$q\_{\left[n/n\right]}(\varepsilon) = \frac{a + b f\_{\left[n/n\right]}(\varepsilon)}{c + d f\_{\left[n/n\right]}(\varepsilon)}.$$

provided that there is *f*½ � *n=n* ð Þ*ε* .

6. PAs can get the upper and lower bounds for *f*½ � *n=n* ð Þ*ε* . For the diagonal PAs, one has the following estimate:

$$f\_{\left[n/n-1\right]}(\varepsilon) \le f\_{\left[n/n\right]}(\varepsilon) \le f\_{\left[n/n+1\right]}(\varepsilon). \tag{7}$$

Typically, this estimate is valid for the function itself, that is, *f*½ � *n=n* ð Þ*ε* in Eq. (7) can be replaced by *f*ð Þ*ε* .

7. Diagonal and close to them a sequence of PAs often possesses the property of autocorrection [17, 18]. It consists of the following. To determine the coefficients of the numerator and denominator of PAs, we have to solve

systems of linear algebraic equations. This is an ill-posed procedure, so the coefficients of PAs can be determined with large errors. However, these errors in a certain sense are of self-consistent, so the accuracy of PAs is high. This is the radical difference the PAs from the Taylor series, the calculation error of which only increases with increasing number of terms.

*F*0ðÞ� *s F s*ð Þ at *s* ! 0 and *s* ! ∞*:*

*Padé Approximation to Solve the Problems of Aerodynamics and Heat Transfer…*

the regularity, coincide.

*DOI: http://dx.doi.org/10.5772/intechopen.93084*

max

� � � �

∞ð

0

respect to another function *φ(x),* enter the following definitions:

if ∀*δ*>0∃*A* : j j *x* � *x*0 <*δ* ) j j *f x*ð Þ ≤ *A*j j *φ*ð Þ *x* .

if ∀*δ*>0∃*ε* : j j *x* � *x*0 < *δ* ) j j *f x*ð Þ ≤ *ε φ*j j ð Þ *x* .

**3.2 Two-point Padé approximants**

Here *A* is a finite number, and *ε*, *δ* are infinitely small.

all real values *s* ≥ 0:

or *F*0

concepts.

that is,

**81**

implementation of equalities

0ðÞ� *s F*0

requirements (8).

2. Singular points of functions *F*0(*s*) and *F*(*s*), located on the exact boundary of

The free parameters of the function *F*0(*s*) are chosen so as to satisfy the conditions of the good approximation of *F*(*s*) in the sense of minimum relative error for

*F s*ð Þ � 1

∞ð

*F s*ð Þ*ds*

0

ð Þ*s* at *s* ! 0 leads to a rather precise fulfillment of the

Constructed in such a way function *F*0*(s)* is called asymptotically equivalent function for *F(s)* (AEF). Let's dwell on the terminology. In the following sections, we will use the symbols of ordinal relations. We will give strict definitions of these

Let's consider the function *f(x).* To describe the ordinal relationships with

**Definition 1.** Let us say that *f(x)* is a value of order *φ(x)* at *x* ! *x*0, that is,

*f x*ð Þ¼ *O*ð Þ *φ*ð Þ *x*

*f x*ð Þ¼ *o*ð Þ *φ*ð Þ *x*

**Definition 3.** Let us say that *f (x)* is asymptotically equal to *φ(x)* at *x* ! *x*0,

*φ*ð Þ *x* ! 1*:*

*f x*ð Þ� *φ*ð Þ *x* if *f x*ð Þ

Here we use the term "asymptotically equivalent function." Other terms ("reduced method of matched asymptotic expansions" [28], "quasi-fractional

The analysis of numerous examples confirms "complementarity principle": if for *ε* ! 0, one can construct a physically meaningful asymptotics, there is a nontrivial

approximants" (QAs) [29], and "mimic function" [30]) are also used.

**Definition 2.** Let us say that *f(x)* is a value of order less than *φ(x)* at *x* ! *x*0, that is,

� � �

� ! min (8)

*F*0ð Þ *s*, *α*1, *α*2, … , *αk*

Condition (8) is achieved by variation of free parameters *αk*. Often the

*F*0ð Þ*s ds* ¼

Autocorrection property is verified for a number of special functions. At the same time, even for elliptic functions, the so-called Froissart doublets phenomenon arises [26]. Thus, in general, having no information about the location of the poles of the PAs, but relying solely on the very PAs (computed exactly as you wish), we cannot say that you have found a good approximated function. Now consider the question: In what sense the available mathematical results on the convergence of the PAs can facilitate the solution of practical problems? Gonchar's theorem [16] states: If none of the diagonal PAs *f*½ � *n=n* ð Þ*ε* has poles in the circle of radius *R*, then the sequence *f*½ � *n=n* ð Þ*ε* is uniformly convergent in the circle to the original function *f*ð Þ*ε* . Moreover, the absence of poles of the sequence of the *f*½ � *n=n* ð Þ*ε* in a circle of radius *R* confirms convergence of the Taylor series in the circle. Since the diagonal PAs is invariant under fractional linear maps *ε* ! *ε=*ð Þ *aε* þ *b* , the theorem is true for any open circle containing the point of decomposition, and for any area, which is the union of these circles. A significant drawback in practice is the need to check all diagonal PAs. The fact is that if a circle of radius R has no poles only for a subsequence of the sequence of diagonal PAs, then the uniform convergence to its original holomorphic in the disk is guaranteed only with *r*<*r*0, where 0*:*583<*r*0 <0*:*584 [27]. How can we use these results? Suppose that there are a few terms of the perturbation series and one wants to estimate its radius of convergence *R*. Consider the interval [0,ε0], where the truncated perturbation series and the diagonal PAs of the maximal possible order differ by no more than 5% (adopted in the engineering accuracy of the calculations). If none of the previous diagonal PAs does not have in a circle of radius *ε*0 poles, then it is a high level of confidence to assert that *R*≥*ε*0.


*Case Report* **Butterflies, Dwarves, and Plastic Lollypops: A Case Report on Medical Clowning in a Children's Rehabilitation Hospital**

**Sigalit Ofer 1,2,3 and Shoshi Keisari 4,5,\***

**Abstract:** Medical clowning has been evolving in the past three decades and now plays a significant role in the rehabilitation processes of children who have suffered injuries and undergone complex medical procedures. The current paper focuses on this topic by presenting a case study of a young girl who lost most of her functional abilities due to brain damage. During the child's physiotherapy sessions at the rehabilitation hospital, a medical clown was brought in to work together with the physiotherapist in providing the treatment. The case study brings an in-depth perspective on the therapeutic process, as it is based on documentation of the sessions while addressing key stages in the child's rehabilitation, alongside core concepts in drama therapy. The qualitative analysis shows how the playful space in the rehabilitation process enhanced the child's inner motivation, provided a space for role expansion, and promoted the connection between the child and the environment. This paper demonstrates how the involvement of medical clowns can promote the rehabilitation processes of children who have suffered traumatic injuries and help them cope with functional losses.

**Keywords:** rehabilitation; medical clowning; drama therapy; physiotherapy; role theory

## **1. Introduction**

#### *1.1. The Role of the Medical Clown in the Hospital*

The character of the clown has accompanied humankind since the dawn of civilization, as a spiritual leader, shaman, and healer, and has played a counter role to key roles in society such as the ruler and the priest [1]. The clowns' humor stems from their ability to embody the gap between the spiritual and corporeal, as well as between the tragic and the comic, thus providing a broad and positive perspective on human existence [2].

The clowns' most prominent feature is their paradoxical nature. "Whatever predicate we use to describe them, the opposite can also be said, and with equal right" [3] (p. 307). The constant inner contradiction embodied in the character of the clowns constitutes their inner logic and allows them to be flexible in in-between situations, constantly shifting between dichotomies. The clown can serve as a mediator between contradictions, examine the relationship between them, and deliver an unconventional perspective on reality [4]. This quality is particularly meaningful and important in a hospital environment, where people often need to cope with stressful and even life-threatening situations.

The medical clown's role in a hospital is to contribute to the psychological wellbeing of patients, their families, and the attending staff [5–7]. Medical clowns operate within the hospital's reality and connect with patients by interacting with each in a unique way that is tailored to their specific needs and nature [6]. They rely on their ability to improvise and do so out of a sense of empathy, with an aim to build patients' resources and empower them [8,9].

**Citation:** Ofer, S.; Keisari, S. Butterflies, Dwarves, and Plastic Lollypops: A Case Report on Medical Clowning in a Children's Rehabilitation Hospital. *Children* **2022**, *9*, 1805. https://doi.org/ 10.3390/children9121805

Academic Editor: Dafna Regev

Received: 26 September 2022 Accepted: 21 November 2022 Published: 24 November 2022

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

Clowns invite patients into an imaginary realm, helping them to momentarily escape the harsh reality of hospitalization. This allows patients to delve into a world in which emotions and situations can be taken to extremes for the purpose of transformation, ultimately providing a fresh perspective on the situation. Studies show how the clown's working techniques can be conceptualized using drama therapeutic models and theory [2,10].

#### *1.2. Key Concepts in Drama Therapy*

Drama therapy is a health profession that uses dramatic and theater-based methods with the intention of promoting psychological growth within a therapeutic relationship [11,12]. This section describes how each of the drama therapy core concepts finds expression in the work of medical clowns.

*Dramatic reality* is a key concept in drama therapy. It is a safe space that integrates reality and fantasy and allows the individual to explore subjective experiences in the present [13]. "It is an *as if* made real, an island of imagination that becomes apparent in the midst of actual life" [13] (p. 272). Its therapeutic power stems from its ability to contain imaginary subjective content, some of which may be unacceptable under normal circumstances, thereby creating a legitimate space for such content within the "real" world [14,15]. Once personal content is projected and explored in the dramatic reality, it undergoes a transformation. This transformation seems to be supported by the fact that something real and concrete has been done with the subjective content. Thus, the dramatic reality is a type of lab in which people can explore emotions and situations and experience potential worlds [13,14].

Medical clowns' appearance, clothing, red nose, and accessories, create a dramatic reality that surrounds them like a type of aura [2,10]. As a medical clown walks down the hospital hallways, Winnicott's potential space is with them wherever they go. This is the space in between behavior and contemplation, as well as in between "me" and "not me"—the natural zone where play and creativity thrive [16]. The medical clown embodies this space, inviting patients to play and act in it together with her so they can experience change.

*Aesthetic distancing* is another key concept in drama therapy and is based in the world of theater [17,18]. The aesthetic experience of theater presents fictional characters and narratives that appear to be removed from the viewers' personal experience. However, paradoxically, this distancing, along with other aesthetic elements of the experience, allows viewers to draw emotionally closer to the events unfolding on stage, thereby drawing closer to themselves [19]. This is known as aesthetic distancing, and it serves a similar function in drama therapy [17,19]. It holds the balance between the emotional component, which fosters closeness and identification with the dramatic material, and the cognitive component, which allows the individual to reflectively observe what is taking place. Thus, aesthetic distancing makes it possible for individuals to distance themselves from personal content that is too close and painful, as well as reduce its emotional charge, creating a safe space for them to observe and explore their experiences [19,20]. Puppets and masks, for example, are well-known theatrical techniques used in drama therapy to facilitate projective expression and create a distance between the self and the characters presented in the process [21]. Similarly, the clown's red nose can be seen as a small mask of sorts, signaling the existence of a space of play and highlighting and creating an aesthetic distance for the patients [22].

Medical clowns reflect the emotions and situations that accompany patients' hospitalization experiences. These include fear, alienation, lack of understanding, helplessness, and pain [8,9]. They do so in an exaggerated and absurd way, so that patients can look at the clown from a safe distance, without the need to associate themselves with these emotions. When a patient identifies with an exaggerated experience that the clown portrays, they will often laugh or smile. For example, when encountering a frightened child, the clown will look for a way to be afraid, perhaps of a small dragon doll, a printed lion on a shirt, the honk of a toy, or anything else they find in the space. The child will laugh at the clown's reaction and will likely want to frighten the clown over and over again. This allows the child to play with the fear and befriend it from a position of power and a sense of security,

as the medical clown copes with the fear projected onto her, which they then perform and process. Therefore, maintaining an aesthetic distance is a significant element of the medical clown's work. It requires a great deal of sensitivity and the ability to adapt from one moment to the next.

*Dramatic role* is the third key concept we address in this paper. According to role theory in drama therapy and psychodrama, a role is the actual and tangible form of the self, comprising a set of qualities representing the various facets of the individual [23,24]. Each role has counter roles that often represent denied aspects of the self that the individual or society seeks to avoid. These counter roles contain unexpressed emotions, thoughts, beliefs, and experiences [20]. As the therapeutic process progresses, the role of "the guide" emerges to help integrate conflicting roles. At its core, drama therapy focuses on developing a balanced, flexible, and healthy system of roles, expanding the repertoire of roles available to us, and increasing our flexibility in shifting between them [24].

In the hospitalization process, a person steps into the role of "patient". They are removed from their daily life, stripped of their identity features, lose their privacy, and become defined by their illness [25]. In terms of role theory, the hospitalization process pushes the patient's role system out of balance, as the person shrinks into the role of "patient", which is destabilizing and stress-provoking. By playing in the dramatic reality, the medical clown helps patients shift out of this passive and painful role into more active and pleasurable roles that provide them with a sense of control and connect them to their strengths [2]. The role that clowns play in this regard is vital, especially when coping with traumatic events.

#### *1.3. Rehabilitation Following a Traumatic Event*

Some children who arrive at a rehabilitation hospital are coping with life-changing traumatic events that have significantly impaired their functioning and put their life in danger [26]. Such events change the life of the child's entire family and necessitate lengthy rehabilitation and adaptation processes, which at times involve reshaping their personal identity [27]. In some situations, the hospitalization itself, which includes the stages of diagnosis and medical intervention, is accompanied by fear, uncertainty, helplessness, pain, and life-threatening situations that could lead to post-traumatic stress disorder (PTSD) [28].

According to Ben Ari et al. (2018), PTSD in response to hospitalization is highly common among children; however, most of them recover from it naturally. Approximately 25–30% of all children develop chronic post-traumatic symptoms that affect their physical recovery and functioning. Others suffer from significant psychological stress and impaired functioning that continue long after hospitalization as a result of their illness or ongoing painful and invasive medical interventions. Symptoms include hyperarousal, avoidance, and re-experiencing the traumatic event [28]. During rehabilitation, children process the traumatic event and learn to adapt to the new reality; this also involves grieving the loss of abilities and aspects of identity [27].

Stroebe and Schut's (1999) dual process model of coping with bereavement describes an adaptive process for grief resulting from loss. This process involves coping with two types of stressors, leading to an investment of energy in two opposing coping strategies. The first is **loss-oriented** and involves processing emotions, thoughts, and actions related to loss, such as anger, crying, denial, longing for the past, sadness over lost abilities, and more. The second is **restoration-oriented** and includes coping with the new reality created by the loss. This involves the restructuring of daily life, forming new social relationships, and regrowth. When a grieving individual copes with loss in a healthy way they oscillate between these two strategies, and this creates a healthy adaptation process [29–31]. The current study presents a case study of a child who experienced a traumatic event and grieving processes following the loss of functions resulting from brain damage. This case study was designed to examine treatment processes with medical clowns who work with children within a rehabilitative framework, to determine the ways in which dramatic

therapeutic work can support the processing of traumatic events and grieving processes in situations of functional loss.

#### **2. Materials and Methods**

The case study presented here is based on treatments conducted as part of the rehabilitation of a 5 year old girl during physiotherapy sessions. The case study method involves an intensive and focused unit, and it provides access to information that might otherwise be inaccessible via other means of study [32].

Amira was hospitalized in the rehabilitation ward due to brain damage resulting from complications that occurred during a medical procedure (to preserve confidentiality, pseudonyms are used for the girl and physiotherapist). Her treatment at the rehabilitation hospital lasted over 2 years, and, in the current paper, we describe short vignettes from three different periods of the physiotherapy treatment. The physiotherapy sessions were co-conducted by Yael, the physiotherapist, and the medical clown, the first author of this paper, Sigalit Ofer, also known at the rehabilitation hospital by her clown name of Tsumi ("The Attention Seeker"). The analysis is based on treatment records written by the medical clown and an interview with the physiotherapist during which the records for each period were presented to elicit her perspective on the role of the medical clown in the process. The analysis of the records and the interview was designed to better understand the trajectory of the treatment process and the role of the medical clown in its different phases [32]. This study was approved by the Ethics Committee of the University of Haifa (UH approval 403/22).

#### *2.1. The Triadic Relationship in the Physiotherapy: The Clown, Physiotherapist, and Child*

Children hospitalized in the rehabilitation hospital enter into a treatment routine designed to meet their specific needs. To promote their rehabilitation process, the children are required to be active and cooperative; however, they are often in pain or emotionally overwhelmed by their medical condition. In such situations, moving a sore limb or shifting from one position to another can seem like an impossible task. The tension and uncertainty the children and their parents experience can leave them emotionally overwhelmed, hypervigilant, suspicious, or avoidant. In this context, physiotherapy treatments can cause many children to be resistant and experience great difficulty.

Medical clowns join physiotherapy treatments when the attending staff identifies situations of significant emotional difficulty that hinder rehabilitation processes. Their role is to support the children, reduce their anxiety, increase their sense of control, assist them in coping with the pain, and turn the physiotherapy session into a playful experience in which the children feel safe. At the same time, the clowns also support the physiotherapists and the therapy goals that they define. A medical clown's involvement in physiotherapy sessions is generally in collaboration and coordination with the physiotherapist.

The role of a medical clown is dual. They stand by the resisting child and support then while simultaneously supporting the goals defined by the physiotherapist. The clown attempts to identify the sources of the child's resistance and helps the child express this resistance, while simultaneously searching for creative ways to transform it. They seek to expose the child's motivation to do the work in order to promote the physiotherapist's goals. This duality is typical of the clown, which as aforementioned, is paradoxical in nature. The medical clown takes on the child's limitations, resistance, and fear, while simultaneously holding the faith and hope that the child can make progress, improve, and devote themself to the process.

#### *2.2. Amira*

Five year old Amira underwent a medical procedure during which multisystem failure occurred. As a result of a lack of oxygen to the brain, she suffered irreversible brain damage and went from being a healthy child to one who needed to cope with a severe disability. Amira lost her ability to speak and lost control of her organs. In the first 2 months of her hospitalization, she suffered from restlessness accompanied by a lot of crying, involuntary

limb movements, no control of her head, and hypertonia. Her condition at the time was characterized by drowsiness, and it was unclear whether she was responding to what was being said to her. The transition into this unfamiliar reality, which was accompanied by strange physical sensations, discomfort, and pain, while having no ability to express herself verbally as she once did, created great emotional distress. Amira was accompanied by her parents, who were also experiencing a deep rupture and loss following the traumatic event. The physiotherapy sessions were difficult for her and induced a lot of crying and uncontrollable emotional reactions. In light of this, the decision was made to have a medical clown join the treatments.

#### *2.3. Data Collection and Analysis*

The data include the treatment records written by the medical clown during Amira's rehabilitation process and an interview with the physiotherapist who co-conducted the sessions with the medical clown. The analysis was designed to better understand the trajectory of the treatment and the role of the medical clown in its different phases [32]. First, the researchers (the two authors) read through all the treatment records. They then looked for data segments that represented phases in the process and coded them to identify chronological developments corresponding to the research questions [33]. They next reviewed the codes to define main themes in each phase that related to the role of the medical clown during each phase. Then, the first author presented the treatment records to the physiotherapist to obtain another perspective on the role of the medical clown. During the interview, the physiotherapist was asked to reflect on the treatment records in relation to two questions: (a) What was your experience during these sessions? (b) What was the role of the medical clown in Amira's rehabilitation process? The next step was for the researchers to read through the interview transcript to identify data segments that represented themes in the process. The researchers reviewed and combined the themes from both data resources. These themes were defined and labeled, and selected quotes were chosen to illustrate each theme. Lastly, the findings section was structured chronologically to depict development in line with the research aim and questions [33].

#### **3. Findings**

The findings are presented as three phases in the process. Each phase captures one theme that relates to the role of the medical clown in the treatment process: (a) a playful space to enhance the inner motivation; (b) role expansion; (c) connection between the child and the environment.

#### *3.1. The "Butterfly" Game: A Playful Space to Enhance the Inner Motivation*

This theme relates to the ways the playful space provided by the medical clown enhanced the child's inner motivation during the physiotherapy sessions. At the beginning of her rehabilitation process, Amira was restless and cried a lot during her physiotherapy sessions. Yael, the physiotherapist who was treating her, understood that, in order to conduct the treatments, she would have to create a safe and quite space for Amira. The goal of the physiotherapy at the time was to relax and lower Amira's muscle tone, maintain her range of movement, and try to give her more control over her movements. Tsumi the medical clown began by making short visits to Amira's room in the hospital, to allow them to get to know each other before she joined a physiotherapy session for the first time. When Tsumi entered the physiotherapy hall, Amira showed great interest. The physiotherapist introduced her and invited to her come closer to Amira with a calming voice. Amira looked at the clown directly, with a gaze that was inquisitive, wide awake, and full of vitality, fascinated by the clown's red nose. This signaled to the clown that she could move even closer and advance the interaction.   She shared her discovery with Amira, which caused the child to laugh as well. At

this point, it was clear that, despite her impairment, Amira understood humor, that she was intelligent and highly communicative, and that she could use facial expressions to convey interest or dissatisfaction, even if she could not express herself with words.

The clown took one of the butterflies out of her hair and moved it in the air as if it was fluttering. She sang a well-known children's song about a fluttering butterfly in a soft, calming voice, as she let Amira follow it with her gaze. At this stage, Amira's body language became calmer, her muscle tone had decreased, and she appeared fascinated by the song and the butterfly's movement. The physiotherapist rocked her gently in her arms to the rhythm of the song and sang along. They sang the song together several times. The repetition of the pleasant sounds created a sense of safety and calm. After some time, the clown introduced another game. She put the butterfly on her shoulder as if it had landed there to rest, and then turned to it with an annoyed look. Amira was following this, waiting to see what would happen next. A moment later the clown sneezed, chasing the butterfly away, and Amira laughed with a big smile on her face. This game was repeated in several variations. Each time the butterfly landed on a different area (on the clown's head, arm, or nose), it would bother her, and she would get rid of it until the next time it landed, sharing with Amira how annoyed she was with the butterfly. The clown continued to sing the pleasant song; however, as soon as the butterfly disturbed her, she would sing it in a scolding tone. Amira laughed and enjoyed watching the clown getting angrier and angrier each time. In the next stage, the clown put the butterfly on Amira's hand as if it had landed there. The physiotherapist held Amira's hand and helped her chase the butterfly away. In that moment Amira became more active and attempted an intentional movement for the first time since the therapy session had begun.

While reading the records of these sessions, Yael noted:

*I remember this period with Amira. She was very, very restless and it was very, very difficult to try to do anything, any kind of deliberate movement.  *This was a very important step, both for her and for those around her, because we could start to see what was there and what was not and that it was not so scary and that it would be fine. We could move forward from there* . . .

Amira was suffering from restlessness and involuntary body movements; thus, the clown chose to sing a slow and calming lullaby. Singing and following the movement of the butterfly that had come to life allowed Amira to enter into a dramatic reality, into a world of the imagination. She managed to relax and focus her attention, and the involuntary movements subsided. This allowed her to transition to the next stage—a game that emerged from the shared imaginary world that had been created in the room. This new game, involving the butterfly that kept landing on the clown, embodied a relationship between two roles: an active and playful one versus a passive and irritated one. Metaphorically, this reflected Amira's physical and emotional state, as it dealt with the theme of wanting to rest versus the need to cope with restlessness and involuntary body movements that cause discomfort and exasperation. The irritating frantic butterfly was actually looking for a moment of peace; however, as soon as it stopped to rest, it made the clown restless. Thus, the butterfly represented the involuntary muscle movements acting on Amira. Amira could observe this dynamic as a bystander, from a safe distance, as the clown experienced the emotions of anger and discomfort while Amira watched and laughed, having a good time. Later on, when Amira chased the butterfly away, she became active. While she did not make the movement on her own, as Yael the physiotherapist made the movement for her, Amira was still able to play as if she were the one controlling the butterfly. This is a very simple game, but it allowed Amira to take on an active role and experience control, which was incredibly vital for her.

Yael commented on the role of the medical clown in enhancing the child's inner motivation:

*This is the place I am looking for in therapy. When the movement comes from within the child and from her own drive and motivation* . . . *Clowning plays an important role* . . . *the clown enters the room and during the interactions with the child, and this helps the child find motivation and place and what interests her and what causes her to be in movement. This is a very important point in treatment. There are children for whom we cannot get to this stage without the help of the clown.*

Later, Yael talked about her own experiences dealing with Amira's resistance to therapy at that time, and how the medical clown supported her in finding a way to stimulate Amira's motivation:

*I remember there was enormous distress* . . . *because it was very difficult for me to deal with Amira's current state. And there was a conflict, ok, I'm the physiotherapist and I have to do this and that. It is important to take care of her body, you have to take care of movement. But I quickly realized that there was no way we could work while she was crying and in distress. And you have to find another way. (At this point) I was also distressed and was looking for a way* . . . *And the clown* . . . *she was very important, she also helped me. The clown helps the therapist as well. It doesn't only help the child.*

#### *3.2. The Dwarves Game: Role Expansion*

This theme relates to the ways the playful activities allowed role expansion and the development of the self. The next encounter took place about 8 months after Amira's rehabilitation had begun. In this session, Amira was practicing a single intentional movement. The physiotherapist had been training her in different ways to move a hand or leg in an isolated, intentional, and controlled manner, and Amira's abilities were improving. She practiced putting hoops on a cone, popping soap bubbles, doing yoga poses, and more. One of the games she played with the clown during treatments was a song-game called "Dwarf Dwarf in the Forest". In this game, the child plays the dwarf, hiding curled up under a blanket or a piece of fabric and stretching out a hand or a leg according to the words of the song, until they come out entirely from under the cover and those present finally recognize who they are.

This structured game set the pace for Amira and gave her time to prepare herself before making each movement. She was met with great enthusiasm each time she managed to send out a hand or a leg from under the blanket. The clown, the physiotherapist, and Amira's mother sang together for her, "Who is this dwarf who's dressed up so beautifully?", with all three of them acting curious to meet the dwarf and admiring his beauty. The dwarf song is a metaphor that deals with the theme of drawing within and hiding as opposed to being discovered and going out into the world. The exposure is gradual, giving the child a sense of control, as she is asked to move a different limb each time and knows what to expect.

Yael explained how the playful space suggested by the clown, such as in the dwarf game, supported the goals of Amira's rehabilitation physiologically, as well as psychologically, by allowing her to re-explore the role of a child who engages in play like other children her age.

*During this period, we tried to work a little bit more on the control of movement, to achieve some kind of minimal control. So, for example the (dwarf) game really allowed her to* . . . *practice it over and over again* . . . *it's impossible with a 5 year old girl to practice something boring. The game allowed her to enjoy practicing and really, really try hard and be intent (on her movements). Because that's the meaning of this game* . . . *it was compatible with her age, compatible with her life and very suitable for the goals of the physio and she really liked it, and it was fun for her* . . . *it really brought back the feeling to her and maybe also to her mother that maybe it's still possible to be a girl who does things that children do.*

This quote illustrates how this process allowed for self-continuity, since Amira was able to re-experience the playful activities as she engaged in before the traumatic event. The dwarf game also enabled transitioning from the inside to the outside world, which

represents Amira's way of coping psychologically with the loss she experienced. The moments of hiding reflect the need to go within and make the necessary preparations required for such a difficult physical task, which previously would have been so easy for her to perform. Here, Amira was able to explore emotions such as loneliness, uncertainty, and fear of encountering the world. Coming out from under the blanket can be seen as a metaphor for Amira's growth, a rediscovery of her capabilities, and her ability to improve them, as if saying "I can move and play in my new condition". This is how Tsumi the clown described the game in her treatment diary: "When Amira came out from under the fabric completely, we were full of joy and admiration. I saw the light and excitement in her eyes, and thought to myself how important and meaningful it was that her mother was present there with us, that she had a chance to enjoy and celebrate her love for Amira". The game allowed Amira to experience the fact that she was loved, that she inspired enthusiasm, and that it was fun and enjoyable to be and play with her, all of which allowed her to develop her ability to adapt and accept her new condition.

In a sense, the game echoed Amira's physical and emotional state in the first stages of her hospitalization. It depicts the process of transitioning from the inner to the outer world, from unconsciousness to awakening and connecting with her surroundings. In light of the new disability to which Amira and those around her had to adapt, the game can also evoke the association of rebirth. The words of the song in the dwarf game, "Who is this dwarf?", contain a question pertaining to identity. This question is highly relevant to a child when one of their greatest tasks is becoming reacquainted with herself and allowing those around to become reacquainted with them. There is an expectation and perhaps even concern regarding what will happen when they encounter the outside world—how will they be received? Step by step, Amira is invited to come out into the outer reality in an organized and gradual manner.

Later on, it was Tsumi's turn to hide under the blanket, while Amira told her which body part to send out each time. Now, Amira was controlling the game. She could look at the clown, who, in a sense, was mirroring her own story, as she played the part of the audience and even directed and led the situation. The clown often got tangled up and did silly things, in an aim to heighten Amira's success and sense of competence.

At this stage of the game, Amira was experiencing a process of role reversal. No longer was she in the role of being passive and having no control; now, she was playing the role of a leader who could guide, control, choose, be mischievous and playful, and have fun as she used to before the trauma she had experienced. From this position, she was able to experience a sense of competence and control she so needed, while the shift between roles allowed her to explore various states of self.

Yael added her comments on the dwarf game, and how the interaction with the clown enriched the game and allowed for role expansion:

*I think that when the clown was there, the game was richer. I could play the dwarf game with her when the clown was not around. But once the clown was there, the focus was on the game* . . . *there was much more laughter and much more joy and much more movement. And then there is the positioning, which is very important, when they change roles, she tells the clown what to do* . . . *like the kids in kindergarten take turns, which doesn't usually happen in normal physiotherapy. So, she (Amira) could also be in the leader role not only the follower* . . . *The game became very complete.*

#### *3.3. The Shop Game: Connections between the Child and the Environment*

This theme relates to the role of the clown in creating connections between the child and the environment which was more visible during the last phase of the rehabilitation process. Toward the end of the therapeutic process, about a year and a half since Amira's rehabilitation had begun, she seemed to be experiencing greater acceptance and an ability to cope with her disability, alongside a sense of competence. She liked the familiar routine of treatment activities, she felt loved and protected by the staff and her family, and she was enjoying her ability to move. She could communicate, choose, laugh, and play. She

did not regain the ability to speak; however, she did learn to communicate "yes" and "no" by making a sound and moving her mouth and with facial expressions. She had been practicing walking with different aids and was now using a special walker that enabled assisted mobility for short distances. Each step she made was met with praise and admiration, and she was working hard and getting stronger. This was the final period of her rehabilitation, and she was preparing to go home and back to school. The physiotherapy sessions were devoted to working on strengthening and controlling her body and working on mobility. During the sessions, she would leave the physiotherapy room to practice walking in the hospital hallways.

One of the games Amira played with the physiotherapist and the clown during this period was the "shop" game. At the start of the session, while the physiotherapist was helping Amira stretch on the mattress, Amira and Tsumi played with sticking colorful balls onto sticks. Tsumi attached a ball to a stick and said to Amira, "Look! It's a lollypop! You want one too?" Amira said yes, and they made quite an impressive collection of lollypops, tasting them and sharing them with Amira's mother and the physiotherapist. They all ate the lollypops with delight. Yael the physiotherapist suggested they sell them outside the physiotherapy room, with the intention of training Amira to use the walker. Amira happily embraced the idea, and Tsumi enthusiastically added that they should go to the hospital cafeteria and sell them there. Yael sat Amira on the walker and fastened the straps and Amira began to walk out of the physiotherapy hall. At the entrance to the hallway, Tsumi blew an imaginary trumpet and announced Amira's arrival in a grand voice, as passersby smiled and took interest. "Dear audience, give it up for the one and only, Amira the sweetie-pie and her sweet lollypops! Now on sale! You taste—you pay! You wanna taste? These are very special lollypops that Amira made with her own two hands". They invited everyone who was there to buy a green pickle-flavored lollypop or a purple fried eggplant-flavored lollypop. Staff members, parents, and children showed interest and surprise, responding with a sense of humor when they heard about the bizarre flavors and outrageous prices. Step after step, happy and laughing, Amira progressed toward the cafeteria—the most central place in the hospital, where multiple interactions take place with a variety of people.

Choosing to leave the physiotherapy room and walk toward the cafeteria is indicative of a desire to explore possibilities and experience social belonging. It allowed Amira to play a central and active social role and experience herself as being able to give to others by "selling" the pretend lollypops she had made. Tsumi the medical clown encouraged uninhibited playfulness, connection, and interaction, thereby inviting Amira to playfully explore her environment.

Amira, who had experienced such a devastating loss, played a role that was full of confidence, the role of one who lacked nothing and, on the contrary, had something to give to those around her. She looked at people directly, feeling proud of herself, initiating contact with the world, and inviting others to take part in her goodness and sweetness. Amira, who was once completely helpless, was now regaining the control she had lost. She was learning to accept her disability, playing and enjoying what she did have, and feeling worthwhile as she experienced abundance and belonging.

Yael commented on the ways the medical clown supports the connection between the child and the environment:

*The clown makes all these connections, you know, connects it to life, to others, to the outside* . . . *Now that I think about it, she couldn't speak, she couldn't say that she was coming* . . . *She could play* . . . *with us, but she couldn't tell people: "come by, I made candy!" So, the clown was her voice. And this is an important role. She suddenly plays with everyone in the hallway, and everyone obeys her, because the clown is walking beside her and saying what she cannot say* . . . *thanks to the clown the environment was more appropriate and enabling.*

Finally, Yael also reflected upon what she learned from the medical clowns she worked with:

*I learned to be a bit of a clown myself and to use* . . . *a bit of these qualities* . . . *to take a step back, to give children their place, the stage, to let the children reveal themselves. I learned to work calmly and not out of need* . . . *the clowns allow all this, and I learned from them. Because the clowns are not always there. I wish there was always a clown in (physio)therapy.*

#### **4. Discussion**

Accidents and serious injuries are defined as life-changing traumatic events, especially when they involve a physical impairment that affects functioning [26]. Amira, once a healthy child, experienced severe trauma following complications that occurred during a medical procedure that almost cost her life and forced her to have to cope with an extreme disability. There is no doubt that Amira and her family experienced a major loss following the event, which required them to restore and restructure every aspect of Amira's life [34,35].

Physiotherapy treatments are a very significant part of the process of restoring functions and restructuring daily life after experiencing loss. These treatments build and enhance patients' physical capabilities and emotional resources [36]. When children are resistant to treatment, involving a medical clown in the process can help motivate them to cooperate. The qualitative analysis shows how the medical clown's ability to establish a playful space in the rehabilitation process enhanced the child's inner motivation, provided a space for role expansion, and promoted the connection between the child and the environment.

When Tsumi the medical clown joined Amira's physiotherapy sessions, she introduced a playful dimension that helped Amira progress toward the physical goals of the treatment. At the same time, this allowed her to deal with psychological content that was relevant to processing the loss she had experienced and helped her adapt to her new condition. The clown's participation made it possible to simultaneously focus on the two coping strategies referred to above [29,30]: the loss-oriented strategy of expressing and processing difficult feelings entailed in the loss, such as sorrow, pain, fear, and loss of control, and the restoration-oriented strategy of helping Amira organize and relearn her abilities, form new relationships, and rebuild her positive identity.

Theories that deal with processing loss and structuring meaning around situations of bereavement highlight the need to build an enveloping, containing environment that allows the individual to feel secure. As Neimeyer and Rynearson (2022) noted, in order to conduct a restorative work of the loss story in therapy, there is a need to establish a trusting and collaborative therapeutic relationship [37]. The various stages of Amira's therapeutic process describe play processes based on well-known rituals and songs as a means for calming her and strengthening her sense of security. The repetitive songs and games in which various situations were repeated allowed her to safely and gradually enter a playful dramatic space and explore various aspects of loss and growth.

The dramatic work in the butterfly and dwarf games enhanced her inner motivation and allowed Amira to shift between roles that had qualities of control and competence and roles that lacked control and were chaotic and passive. The games depict the dynamic between the roles created through aesthetic distancing [17,18]. The passive role played by the clown is in fact a reincarnation of the role of "patient" [25]. This role is characterized by the fact that the hospitalized person's privacy and control of their body is violated as a result of their injury and being hospitalized. It contains unexpressed emotions, thoughts, and experiences such as anger, helplessness in the face of feeling invaded, restlessness, and frustration. The situation played out in the games is a metaphoric reflection of the inner experience. However, in the dramatic reality, the medical clown reflected the situation for Amira in a way that was playful, spontaneous, and full of humor, by using aesthetic distancing: "It's the butterfly that's bothering me"; "It's the clown who got tangled up in the blanket and can't get out". This allowed Amira to encounter and explore the difficult emotions she was experiencing in her life.

Alongside roles that lack control, which represent the losses caused by the impairment, the games allow other roles to be expressed—roles that are active, in control, and competent.

For example, in the butterfly game, when the butterfly bothered Amira, it made her laugh and she was able to use those around her to get rid of it, as the butterfly was the one who was helpless. Thus, the dramatic game allowed Amira to expand her repertoire of roles [20] and express qualities of self that where active and able to experience pleasure, control, and strength. In this way, Amira could explore situations that had previously been inaccessible to her since her injury, while training her body to return to a state in which she was controlling it and not the other way round.

Playing with the opposing roles of passive and active through the various games created an experience of integration. Much like muscle training, the repetitive shifts between the opposing stances helped to practice narrowing the gap between anxiety and calmness, between helplessness and competence, and between the inner and the outer. The clown helps achieve this mission because she herself is a flexible character, full of contradictions, and able to constantly shift between opposites [2,22]. The goal of drama therapy is to develop a balanced, flexible, and healthy role system and expand the range of roles available to us, while helping integrate conflicting roles and accept the ones we deem less legitimate [20,24]. The clown can be viewed as a character that shifts between the conflicting roles, holding and exploring them and, thus, allowing them to become integrated.

In addition, the repetitive shifts between the opposing positions in the various games are similar to the oscillation described in Stroebe and Schut's (1999) adaptive model of coping with bereavement [29,31]. The oscillation between processing the sorrow and difficulty and focusing on restoration and taking action takes place within a game, as the clown sets the pendulum in motion and helps the child shift between the strategies while the physiotherapist holds the process of restoration and regrowth.

Successful rehabilitation processes are based on the individual's perception of selfefficacy, which stems from the way the environment perceives their disability and their own self-image, body-image, and mood [27]. Toward the end of her rehabilitation process, Amira had made peace with her new condition; she could accept it, could cope with it, and was able to communicate with the environment. In the "shop" game, Amira was happy and active as she confidently went out into the hospital space, knowing that she could contribute to the other children and parents at the hospital. She could initiate contact with them and draw them to her out of a sense of joy and self-worth. Amira experienced independence as she walked using her special walker, which supported her physically.

It is possible to see how personal content that was brought into and explored in the dramatic reality was transformed. Content that was difficult and oppressive was brought into a safe and playful space and was embodied in a way that was tangible, concrete, and alive, allowing for new perspectives of the loss story to be discovered [37]. The possibility of entering the reality of a game and acting within it provided the opportunity to be creative and active, as in an act of creation.

While this work discusses a particular case, it is undoubtedly representative of many others. The observation presented here contributes to our understanding of the role that medical clowns play in children's rehabilitation processes. Much like Amira, many children in rehabilitation experience a profound sense of loss and helplessness following traumatic events. These children need to rediscover their strengths, regain a sense of control and self-efficacy, and restore their self-worth. However, one limitation of this case study is that it is based on the medical clown's diary and the physiotherapist's point of view, but it does not include the child's or her parents' perspectives. Future studies should integrate information from diverse sources (such as the child, parents, and medical staff) to gain an in-depth understanding of the phenomenon. In addition, future studies that make use of additional research tools such as quantitative measurements or qualitative interviews would provide a broader perspective of the influence the processes described here have on psychological and physiological health indicators.

#### **5. Conclusions**

The primary contribution of the current work is the opportunity it provides to gain an in-depth understanding of the role of medical clowns in children's rehabilitation. It sheds light on the purpose of their red nose, their unique presence, and what they do as part of the rehabilitation process. An acquired disability such as Amira's requires coping with a substantial loss of functioning. Many children in rehabilitation face a similar task of having to adapt to a new reality and find the strength to cope with fear, pain, and emotional stress. Involving medical clowns in rehabilitation processes can help children surmount this essential and complex process.

Medical clowns invite these children into the playful space of a dramatic reality where they can process complex and difficult emotions, as the clowns use aesthetic distancing to approach this content. The current work demonstrates how the playful encounters with a medical clown provide a meaningful psychological exploration of feelings of helplessness and lack of control in the face of major losses, while helping the children access their ability to cope and grow from their new condition. The clown brings with her a flexible spirit, helping the children practice inner flexibility and move between various states of self, thereby allowing them to expand the repertoire of roles available to them. Children can transition from the role of the passive "patient" who has no control to roles that are strong, in order to enhance their sense of security and trust in the treatment and in themselves. This allows them to process the loss, create meaning in their new condition, and significantly promote their rehabilitation processes.

**Author Contributions:** Conceptualization, S.O. and S.K.; methodology, S.O. and S.K.; validation, S.O. and S.K.; data collection, S.O; writing—original draft preparation, S.O.; writing—review and editing, S.K.; validation—S.O. and S.K.; visualization—S.O. and S.K.; supervision—S.K. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the Dream Doctor Project, Medical Clowning in Action, Israel.

**Institutional Review Board Statement:** This study was approved by the Ethics Committee of the University of Haifa (UH approval 403/22), November 2022.

**Informed Consent Statement:** Informed consent was obtained from all subjects involved in the study.

**Data Availability Statement:** The data presented in this study are not available due to restrictions of privacy.

**Acknowledgments:** The authors wish to thank the management and staff members of Elin Hospital who enable the medical clowns, to develop, learn, and contribute to the rehabilitation processes in their unique way. The authors also specially thank Ruth Palmor, the Psychological Department, who accompanies and supervises the medical clowns, and who has promoted their work at the hospital for approximately two decades. The authors thank the dedicated team of physiotherapists headed by Orit Bartov and Vered Hedaya—a friend, partner, and teacher. We also wish to thank Dream Doctor Project, Medical Clowning in Action, Israel for their support in this study and their efforts in promoting medical clowning in Israel and around the world. Finally, we thank Amira and her family for their trust in our team and for the journey we went on together.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


Bentazon is a herbicide from the benzothiazinone class, which, after being absorbed, interferes in the photosynthesis process and is therefore a photosystem II photosynthesis inhibitor, affecting the carbohydrate synthesis in leaf areas that have received treatment, occasionally and may occasionally lead the plants to death, especially when they are in the early development stage. The photosynthesis inhibitors mechanism action is the removal or the inactivation of intermediary charge carriers from the electron transport process, and are considered to be inhibitors of electron transport [28]. The inhibitory mechanism of photosynthesis results in the blockade of the electron transport of the compound QB component of the photosynthetic system and, thus, makes impossible the occurrence of electron transport to plastoquinone B [29]. The aforementioned blockade occurs through the binding of the herbicides to the active site of QB in the D1 protein belonging to photosystem II, located on the membranes of the thylakoids of the chloroplasts. This process interrupts the fixation of CO2 and interferes in the production of essential elements to the plant growth, such as ATP and NADPH2 ; however, plant death usually occurs due to other factors. The interruption of the electron flow in photosystem II promotes a significant increase in the energy status of the chlorophyll, resulting in a state called "triplet," which causes an energy overload derived from the attenuation effect of the carotenoid pigments, and this characterizes the peroxidation process. In other study [30], lipid peroxidation due to excess triplet chlorophyll may occur through two mechanisms: direct formation of lipid radicals in unsaturated molecules of fatty acids constituting membranes and production of singlet oxygen through the reaction of chlorophyll triplet with oxygen. In both cases, the peroxidation process will corroborate with damage to cell membranes.

The *.mol2* files were converted to *.pdbqt* in AutoDock 1.5.6 (https://www.chpc.utah.edu/ documentation/software/autodock.php) and had the polar hydrogens removed, and their molecules were flagged with the Gasteiger parameters [31]. The structure of OsGSTU4 was obtained from a *.pdb* file modeled using homology which was converted to *.pdbqt* file in AutoDock and added hydrogens and Kollman load parameters [32, 33]. For this step, glutathione was treated as a cofactor. The docking calculations were run in AutoDock 1.5.6 program, and the simulations were performed using the Lamarckian genetic algorithm (LGA). In this work, the LGA was used in conjunction with the Goodford method, allowing simultaneous sampling of the ligand configurational space and calculating the receptor and ligand atomic interaction energy [34, 35]. The grid parameters are established in 126×126×126 Å by the program Autogrid (http://autodock.scripps.edu/wiki/AutoGrid) and receiver-centered (GST). The parameters used for simulations were as follows: 10,000 replicates, energy analyzes per 1,500,000 and 27,000 generations, population size of 150, and mutation rates and crossing over of 0.02 and 0.08, respectively. Ten conformations were generated that were ranked based on the lowest energy and analyzed in the VMD (http://www.ks.uiuc.edu/Research/vmd/).

**Herbicide name Molecular formula 2D structure Access code** Bentazon-sodium C10H12N2O3S ZINC05442053

Molecular Docking for Detoxifying Enzyme Studies http://dx.doi.org/10.5772/intechopen.73920 41

Metsulfuron-methyl C14H15N5O6S ZINC01532069

The docking result for the herbicide metsulfuron-methyl, performed in the AutoDock program, ranked ten possible complexes; **Table 4** shows the best possible complex. This procedure is based on intermolecular energy, binding energy, and hydrogen bond scores, showing the atoms (and residues) of the protein and the ligand that present favorable interactions for the model.

**4. Results**

Source: ZINC database (http://zinc.docking.org/).

**Table 3.** Compounds used as ligands for the calculation of docking.

#### **3.1. Molecular docking of rice GST and herbicides**

The atomic coordinates of the compounds were obtained from the ZINC database (http://zinc. docking.org/) on *.mol2* file extension (**Table 3**).

**Table 3.** Compounds used as ligands for the calculation of docking.

The *.mol2* files were converted to *.pdbqt* in AutoDock 1.5.6 (https://www.chpc.utah.edu/ documentation/software/autodock.php) and had the polar hydrogens removed, and their molecules were flagged with the Gasteiger parameters [31]. The structure of OsGSTU4 was obtained from a *.pdb* file modeled using homology which was converted to *.pdbqt* file in AutoDock and added hydrogens and Kollman load parameters [32, 33]. For this step, glutathione was treated as a cofactor. The docking calculations were run in AutoDock 1.5.6 program, and the simulations were performed using the Lamarckian genetic algorithm (LGA). In this work, the LGA was used in conjunction with the Goodford method, allowing simultaneous sampling of the ligand configurational space and calculating the receptor and ligand atomic interaction energy [34, 35]. The grid parameters are established in 126×126×126 Å by the program Autogrid (http://autodock.scripps.edu/wiki/AutoGrid) and receiver-centered (GST). The parameters used for simulations were as follows: 10,000 replicates, energy analyzes per 1,500,000 and 27,000 generations, population size of 150, and mutation rates and crossing over of 0.02 and 0.08, respectively. Ten conformations were generated that were ranked based on the lowest energy and analyzed in the VMD (http://www.ks.uiuc.edu/Research/vmd/).

## **4. Results**

promoting the resistance of grasses to its chemicals substances. In plants GST is also responsible through the metabolism of a huge name of commercial important herbicides [24] reducing damage that could occur through the toxically herbicides' action [25]. The reaction consists of the conjugation of the tripeptide glutathione to a hydrophobic compound, making it more soluble and less toxic [26], maintaining the cellular homeostasis. For this study two herbicides

The herbicide metsulfuron-methyl belongs to the group of sulfonylureas and acts on the enzyme acetolactate synthase (ALS), consequently inhibiting the synthesis of the amino acids leucine, valine, and isoleucine, interfering in the protein synthesis and inducing the death of the plant by interfering in the cellular division. Among its properties, it is reported that metsulfuron-methyl has a systemic action and is rapidly absorbed by the whole plant, besides presenting selectivity to the crops for which its use is recommended. In susceptible plants, the absorption of this herbicide results initially in growth stoppage; due to the rapid translocation of this group of molecules to the meristems, apices, and later, death is inevitable, considering the impossibility of the essential amino acid biosynthesis to the plant. This mechanism inhibi-

Bentazon is a herbicide from the benzothiazinone class, which, after being absorbed, interferes in the photosynthesis process and is therefore a photosystem II photosynthesis inhibitor, affecting the carbohydrate synthesis in leaf areas that have received treatment, occasionally and may occasionally lead the plants to death, especially when they are in the early development stage. The photosynthesis inhibitors mechanism action is the removal or the inactivation of intermediary charge carriers from the electron transport process, and are considered to be inhibitors of electron transport [28]. The inhibitory mechanism of photosynthesis results in the blockade of the electron transport of the compound QB component of the photosynthetic system and, thus, makes impossible the occurrence of electron transport to plastoquinone B [29]. The aforementioned blockade occurs through the binding of the herbicides to the active site of QB in the D1 protein belonging to photosystem II, located on the membranes of the

and interferes in the

; however,

were selected, metsulfuron and bentazon sodium.

40 Molecular Docking

tion of ALS was elucidated due to works done and published [27, 28].

thylakoids of the chloroplasts. This process interrupts the fixation of CO2

**3.1. Molecular docking of rice GST and herbicides**

docking.org/) on *.mol2* file extension (**Table 3**).

production of essential elements to the plant growth, such as ATP and NADPH2

plant death usually occurs due to other factors. The interruption of the electron flow in photosystem II promotes a significant increase in the energy status of the chlorophyll, resulting in a state called "triplet," which causes an energy overload derived from the attenuation effect of the carotenoid pigments, and this characterizes the peroxidation process. In other study [30], lipid peroxidation due to excess triplet chlorophyll may occur through two mechanisms: direct formation of lipid radicals in unsaturated molecules of fatty acids constituting membranes and production of singlet oxygen through the reaction of chlorophyll triplet with oxygen. In both cases, the peroxidation process will corroborate with damage to cell membranes.

The atomic coordinates of the compounds were obtained from the ZINC database (http://zinc.

The docking result for the herbicide metsulfuron-methyl, performed in the AutoDock program, ranked ten possible complexes; **Table 4** shows the best possible complex. This procedure is based on intermolecular energy, binding energy, and hydrogen bond scores, showing the atoms (and residues) of the protein and the ligand that present favorable interactions for the model.

**Table 4.** Results of AutoDock-ranked complexes in the metsulfuron-methyl docking.

In metsulfuron-methyl, binding energies were lower than those of bentazon. The results revealed by the metsulfuron-methyl docking show that some residuals (LYS 111, LYS 56, GTX1226) were extremely favorable, being these possibly anchor residues for the binding, in combination with results evidenced by previous studies. The identification of the GTX1226 molecule as an anchor residue (**Table 5**) is evidence of a possible conjugation process [36] between metsulfuron-methyl and glutathione, evidencing the possibility of detoxification of metsulfuron-methyl by OsGSTU4. The best complex result ranked by the AutoDock for metsulfuron-methyl can be visualized in **Figure 5**. The image shows a zoom in a pocket where probably conjugation occurs by a hydrogen bond between bentazon and glutathione. The complex generated suggests that the OsGSTU4 displays a relevant role on the resistance for this herbicide (**Figure 5**).

The result of the docking performed for the herbicide bentazon sodium, also executed in the AutoDock program, is presented in **Table 6**. This procedure is the same used for metsulfuron-methyl and is also based on intermolecular energy, binding energy, and hydrogen bond scores, showing the atoms (and residues) of the protein and the ligand that present favorable interactions for the mode (**Figure 6**).

The results of **Table 6** also show the identified repeated residue (GLN 75) that presents the lowest binding energy, possibly showing as an anchor residue for the herbicide bentazon sodium, corroborating with the results obtained on previous studies [37].

**Table 5.** Representation of the atoms of near residues belonging to metsulfuron-methyl, atoms used as corresponding in the ligand and their respective distances in angstroms in the output.

**Figure 6.** Deep view of catalytic site. In red, the chain A; in blue, the chain B. In green, the bentazon. Glutathione (purple)

**Figure 5.** Deep view of catalytic site. In red, the chain A; in blue, the chain B. In green, the metsulfuron. Glutathione

Molecular Docking for Detoxifying Enzyme Studies http://dx.doi.org/10.5772/intechopen.73920 43

(purple) and residues (white) from H-binding-site, an interchain region. Source: Research data.

**Table 6.** Results of AutoDock-ranked complexes in the bentazon sodium docking.

Source: Research data.

**Binding energy (kcal/mol) Intermolecular energy (kcal/mol) Hydrogen bond −0.86** −1.16 B: GLN 75 HE21-O3

and residues (white) from H-binding-site, an interchain region. Source: Research data.

**Figure 5.** Deep view of catalytic site. In red, the chain A; in blue, the chain B. In green, the metsulfuron. Glutathione (purple) and residues (white) from H-binding-site, an interchain region. Source: Research data.

**Table 6.** Results of AutoDock-ranked complexes in the bentazon sodium docking.

In metsulfuron-methyl, binding energies were lower than those of bentazon. The results revealed by the metsulfuron-methyl docking show that some residuals (LYS 111, LYS 56, GTX1226) were extremely favorable, being these possibly anchor residues for the binding, in combination with results evidenced by previous studies. The identification of the GTX1226 molecule as an anchor residue (**Table 5**) is evidence of a possible conjugation process [36] between metsulfuron-methyl and glutathione, evidencing the possibility of detoxification of metsulfuron-methyl by OsGSTU4. The best complex result ranked by the AutoDock for metsulfuron-methyl can be visualized in **Figure 5**. The image shows a zoom in a pocket where probably conjugation occurs by a hydrogen bond between bentazon and glutathione. The complex generated suggests that the OsGSTU4 displays a relevant role on the resistance for

C: GTX1226 H11-N3 B: LYS 111 HZ2-O6 C: LYS 56 HZ1-O2

**Binding energy (kcal/mol) Intermolecular energy (kcal/mol) Hydrogen bond −3.74** −5.53 B: LYS 111 HZ1-O2

**Table 4.** Results of AutoDock-ranked complexes in the metsulfuron-methyl docking.

The result of the docking performed for the herbicide bentazon sodium, also executed in the AutoDock program, is presented in **Table 6**. This procedure is the same used for metsulfuron-methyl and is also based on intermolecular energy, binding energy, and hydrogen bond scores, showing the atoms (and residues) of the protein and the ligand that present favorable

The results of **Table 6** also show the identified repeated residue (GLN 75) that presents the lowest binding energy, possibly showing as an anchor residue for the herbicide bentazon

**Table 5.** Representation of the atoms of near residues belonging to metsulfuron-methyl, atoms used as corresponding in

sodium, corroborating with the results obtained on previous studies [37].

ASP110: O <0>0:C14 3.43 GLU69:OE2 <0>0:C5 2.95 LYS56:HZ1 <0>0:O2 1.91 LYS111:HZ1 <0>0:O2 1.91 GLN134:OE <0>0:C10 2.87 HIS54:HE2 <0>0:C5 3.91

the ligand and their respective distances in angstroms in the output.

**Near residue atoms Reference atoms (ligand) Respective distance (Å)**

this herbicide (**Figure 5**).

**Source:** Research data.

Source: Research data.

42 Molecular Docking

interactions for the mode (**Figure 6**).

**Figure 6.** Deep view of catalytic site. In red, the chain A; in blue, the chain B. In green, the bentazon. Glutathione (purple) and residues (white) from H-binding-site, an interchain region. Source: Research data.

Since herbicide and insecticide resistance is one of the major constraints of agriculture and mosquito control, the information from this study may be extremely useful for the development of specific inhibitors for these GSTs, thereby reducing the amount of herbicides and insecticides

Molecular Docking for Detoxifying Enzyme Studies http://dx.doi.org/10.5772/intechopen.73920 45

New strategies of control can be applied too. The results point these enzymes as very promi-

The molecular docking is a powerful approach for understanding the interactions of molecules, and it is useful to elucidate biochemical processes. In the field of molecular modeling, this tool is an option of rapid, with low computational, requirements, to perform molecular simulations of many systems. Many software, including the commercial ones, have been developed, and new algorithms are quickly incorporated to the packages. In the fields of computational biology and bioinformatics, it has become one of the most popular tools, with a wide range of applications. The diffusion of this amazing technique is a great strategy on the

We thank the Biomaterial Modeling group for the computational resources granted for

to be used and consequently reducing the environmental impact and other side effects.

advance of molecular studies and must be applied in many fields of knowledge.

\* and Vinícius Costa Amador2

1 Federal University of Campina Grande (UFCG), Sumé, Paraíba State, Brazil

2 Federal Rural University of Pernambuco (UFRPE), Recife, Pernambuco State, Brazil

[1] Hayes JD, Flanagan JU, Jowsey IR. Glutathione transferases. Annual Review of Pharmacology and Toxicology. **45**:51-88. DOI: 10.1146/annurev.pharmtox.45.120403.095857

[2] Robinson A et al. Modelling and bioinformatics studies of the human Kappa class glutathione transferase predict a novel third transferase family with homology to prokaryotic 2-hydroxychromene-2-carboxylate isomerases. Biochemistry Journal. **379**(Pt 3):541-552.

[3] Sheehan D. Structure, function and evolution of glutathione transferases: Implications for classification of 54 non-mammalian members of an ancient enzyme superfamily.

Biochemistry Journal. **360**(Pt 1):1-16. DOI: 10.1590/S1984-29612008000200007

\*Address all correspondence to<EMAIL_ADDRESS>
sor targets for iRNA technique.

**Acknowledgements**

research.

**Author details**

**References**

DOI: 10.1042/BJ20031656

Rafael Trindade Maia1

**Table 7.** Representation of the atoms of near residues belonging to bentazon sodium, atoms used as corresponding in the ligand and their respective distances in angstroms in the output.

**Figure 6** depicts a catalytic cavity where a conjugation with metsulfuron may occur. In the image, the complex with lower binding energy was chosen. The interaction with glutathione is made by a hydrogen bond. This is evidence that OsGSTU4 is able to bind to metsulfuron in order to promote the conjugation reaction. Theoretically, this enzyme plays an important role in the resistance to this herbicide.

Complementing the information in the figure information, **Table 7** shows the atoms of surrounding amino acid residues at distances less than 4 Å and their respective distances to atoms of the ligand.

## **5. Conclusions**

Molecular docking has proved to be an extremely useful technique for studying GSTs, especially in the context of resistance to chemical insecticides and herbicides. The methodology applied in these studies may be excused for other GSTs and other compounds. The complexes obtained provide a better understanding of the detoxification process performed by these enzymes.

However, although we find strong evidence of metabolization of these compounds, experimental studies should be undertaken to validate the in silico experiments. Site-directed mutation studies can be extremely providential to complement the information obtained here.

Not surprisingly, we notified that the GSTs here studied showed an affinity for more than one compound. This corroborates with the fact that members of this enzyme family display a multi-specificity on their H-binding-site.

As promiscuous proteins, these GSTs may be involved in metabolization of a wide range of toxic compounds, including other insecticides and herbicides. Further studies must be performed to investigate this.

Once the herbicide and insecticide resistance are multigenic, multi-enzymatic, and multifactorial process, the molecular docking technique can help to elucidate other pathways. Other computational techniques, such as molecular dynamics, can also give more insights about these systems.

Since herbicide and insecticide resistance is one of the major constraints of agriculture and mosquito control, the information from this study may be extremely useful for the development of specific inhibitors for these GSTs, thereby reducing the amount of herbicides and insecticides to be used and consequently reducing the environmental impact and other side effects.

New strategies of control can be applied too. The results point these enzymes as very promisor targets for iRNA technique.

The molecular docking is a powerful approach for understanding the interactions of molecules, and it is useful to elucidate biochemical processes. In the field of molecular modeling, this tool is an option of rapid, with low computational, requirements, to perform molecular simulations of many systems. Many software, including the commercial ones, have been developed, and new algorithms are quickly incorporated to the packages. In the fields of computational biology and bioinformatics, it has become one of the most popular tools, with a wide range of applications. The diffusion of this amazing technique is a great strategy on the advance of molecular studies and must be applied in many fields of knowledge.

## **Acknowledgements**

**Figure 6** depicts a catalytic cavity where a conjugation with metsulfuron may occur. In the image, the complex with lower binding energy was chosen. The interaction with glutathione is made by a hydrogen bond. This is evidence that OsGSTU4 is able to bind to metsulfuron in order to promote the conjugation reaction. Theoretically, this enzyme plays an important role

**Table 7.** Representation of the atoms of near residues belonging to bentazon sodium, atoms used as corresponding in the

**Near residue atoms Reference atoms (ligand) Respective distance (Å)**

Val105:CG' <0>0:C8 3.38 ALA106:HN <0>0:C7 3.25 ARG102: O <0>0:C7 2.79 VAL105:CG' <0>0:C1 3.58 ALA106:HN <0>0:C1 3.45 ARG102:HE <0>0:O2 3.71 GLN75:2HE2 <0>0:N2 2.11 GLN75:1HE2 <0>0:O3 1.78

Complementing the information in the figure information, **Table 7** shows the atoms of surrounding amino acid residues at distances less than 4 Å and their respective distances to atoms of the ligand.

Molecular docking has proved to be an extremely useful technique for studying GSTs, especially in the context of resistance to chemical insecticides and herbicides. The methodology applied in these studies may be excused for other GSTs and other compounds. The complexes obtained provide a better understanding of the detoxification process performed by these enzymes.

However, although we find strong evidence of metabolization of these compounds, experimental studies should be undertaken to validate the in silico experiments. Site-directed mutation

Not surprisingly, we notified that the GSTs here studied showed an affinity for more than one compound. This corroborates with the fact that members of this enzyme family display a

As promiscuous proteins, these GSTs may be involved in metabolization of a wide range of toxic compounds, including other insecticides and herbicides. Further studies must be per-

Once the herbicide and insecticide resistance are multigenic, multi-enzymatic, and multifactorial process, the molecular docking technique can help to elucidate other pathways. Other computational techniques, such as molecular dynamics, can also give more insights about these systems.

studies can be extremely providential to complement the information obtained here.

in the resistance to this herbicide.

ligand and their respective distances in angstroms in the output.

multi-specificity on their H-binding-site.

formed to investigate this.

**5. Conclusions**

44 Molecular Docking

We thank the Biomaterial Modeling group for the computational resources granted for research.

## **Author details**

Rafael Trindade Maia1 \* and Vinícius Costa Amador2

\*Address all correspondence to<EMAIL_ADDRESS>

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**Molecular Docking for Medicinal Chemistry**

**Molecular Docking for Medicinal Chemistry**

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48 Molecular Docking

**Chapter 4**

**A Click Chemistry Approach to Tetrazoles: Recent**

Provisional chapterA Click Chemistry Approach to Tetrazoles: Recent

DOI: 10.5772/intechopen.75720

Introduction to tetrazole and click chemistry approaches was briefed in a concise way in order to help the readers have a basic understanding. Tetrazole and its derivatives play very important role in medicinal and pharmaceutical applications. The synthesis of tetrazole derivatives can be approached in ecofriendly approaches such as the use of water as solvent, moderate conditions, nontoxic, easy extractions, easy setup, low cost, etc. with

Keywords: click chemistry, tetrazoles, biological activity, synthesis and molecular docking

1H-Tetrazole (1) is a crystalline light yellow powder and odorless. Tetrazole shows melting point temperature at 155–157C. On heating, tetrazoles decomposed and emit toxic nitrogen

> © 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 eproduction in any medium, provided the original work is properly cited.

© 2018 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.

fumes. These are burst vigorously on exposed to shock, fire, and heat on friction.

**Advances**

Abstract

1. Introduction

1.1. Chemistry of tetrazoles

Advances

Ravi Varala and Bollikolla Hari Babu

Ravi Varala and Bollikolla Hari Babu

http://dx.doi.org/10.5772/intechopen.75720

good to excellent yields.

Additional information is available at the end of the chapter

Additional information is available at the end of the chapter