**1. Introduction**

Nanomaterials (NMs) are engineered chemical substances or materials with a particle size of 1–100 nm in diameter. Today NMs are extensively explored and engaged for commercial purposes in different fields, and many sophisticated NMs have shown great promise in biotechnology and biomedicine [1]. NMs display inimitable physicochemical attributes due to their size range in nanometers, high surface area, tunable surface charge, unique composition, various morphologies, and surface composition. Due to their remarkable physicochemical attributes, NMs are significantly different from their bulk materials of a similar symphony, allowing them to perform remarkably well with improved functionality, sensitivity, competence, and selectivity towards developing biomedicines. Various NMs are evaluated to get desired biomedical efficacy for nanomedicine-related applications, including different metal nanoparticles, liposomes, quantum dots, polymeric micelles, dendrimers, and carbon-based nanoparticles. Two critical mechanisms for delivering drug-loaded NMs to the diseased sites are passive targeting and active targeting. A passive targeting mechanism happens via enhanced permeability and retention (EPR) [2]. Inactive targeting mechanism relies on surface functionalized NMs with various biomarkers that bind with receptors over-expressed at the pathological tissue [3].

The importance of cell culture advances in the medical sector has long been recognized. Mammalian cell culture (MCC) entails first isolating cells from a specific organ tissue and then creating a culture in a suitable artificial setting. Disaggregation using different methods may be used to obtain preliminary separation of cells from the identified organ tissues. The isolated primary cells are typically obtained from an *in vivo* setting, although some cells come as established cell lines. MCCs are widely used in the biomedical field to investigate numerous applications [4]. Since cell culture-based studies provide highly stable and repeatable results, researchers consider this technique as an essential model system in cellular and molecular biology. MCC needs an ideal environment for development, which can be divided into nutritional and physicochemical requirements.

Nutritional necessities comprise an adherent substrate or growing medium that offers conditions like essential amino acids, sugars, vitamins, minerals, growth factors, hormones, and gases (O2, CO2). All these features regulate physicochemical factors such as pH, osmotic pressure, and temperature. Many cell lines need solid or semi-solid support in the form of a substrate, while others can be grown in a suspension culture medium. These technologies have evolved as a means of assessing the efficacy and side effects of novel active pharmaceutical ingredients (APIs), immunotherapeutic, and biopharmaceuticals [5]. Animal, plant, and bacterial cells are regularly cultured in fixed culture medium under precise laboratory circumstances; among this, animal-based cell cultures are more complex than others due to their genetic complexity. Directed differentiation of adult stem cells and pluripotent stem cell culture is another challenging aspect. Recent advances in stem cell culture technology have provided significant input for the successful culture of tissue-mimicking 3D organoids [4, 6].

In recent years, nanotechnology (NT) and associated disciplines have gained rapid escalation in biomedical implementations such as diagnosis, testing, tracking, drug

### *Nanotechnology Application and Intellectual Property Right Prospects of Mammalian Cell... DOI: http://dx.doi.org/10.5772/intechopen.99146*

delivery, nanomedicine, medical implants, and electronics due to their camaraderie with biological entities. Biomedicine embraces the design and synthesis of NMs, along with other nanoparticles (NPs) and nano-devices [7]. Once properly formulated, NMs show their natural aptitude to traverse with the blood flow via various routes based on their attributes and eventually get access to all the organs. Due to their intrinsic biocompatible interactions, the NPs exhibit unique physicochemical attributes associated with lesser immunogenicity and non-toxicity. There are numerous advantages of using NMs for various biological applications: i) it increases the concentration of drug in the pathological tissues and control the slow release of the drug; ii) it solves issues connected to the low solubility and bioavailability of the drug; and iii) enhanced biodegradability and biocompatibility iv) drugs/genes/imaging agents can be easily loaded due to their tunable surface functionalities [1, 7, 8]. Imaging agents could endow *in vivo* drug tracking ability to determine drug delivery efficacy during treatment. In recent years, various nanoparticles such as liposomes, polymers, metal nanoparticles, inorganic nanoparticles have been developed for selectively targeting tumor cells and other pathological tissues without causing any destruction to healthy cells or organs. In this chapter, the application of nanotechnology and Intellectual property rights (IPR) prospects of mammalian cell culture will be discussed in the subsequent sections.


**1. Introduction**

66 Recent Advances in Crystallography

subunit. *Nature*, Vol.407, pp.327-339

Wimberly, B. T., Brodersen, D. E., Clemons, W. M., Morgan-Warren, R. J., Carter, A. P., Vonrhein, C., Hartsch, T. & Ramakrishnan, V. (2000). Structure of the 30S ribosomal

Xu, J., Mao, H. K., Hemley, R. J. & Hines, E. (2002). The moissanite anvil cell: a new tool for

Zhurov, V. V., Zhurova, E. A. & Pinkerton, A. A. (2008). Optimization and evaluation of the

high-pressure research. *J. Phys.: Condens. Matter*, Vol.14, pp.11543-11548

data quality for charge density studies. *J. Appl. Cryst.*, Vol.41, pp.340-349

In the field of X-ray crystal structure analysis, while the absolute values of structure factors are directly observed, phase information is lost in general. However, this problem (phase problem) has been overcome mainly by the direct method developed by Hauptmann and Karle except for protein crystals. In the case of protein crystal structure analysis, the isomorphous replacement method and/or anomalous dispersion method are mainly used to solve the phase problem. Phasing the structure factors is sometimes the most difficult process in protein crystallography.

On the other hand, It has been recognized for many years since the suggestion by Lipscomb in 1949 [12] that the phase information can be physically extracted, at least in principle, from X-ray diffraction profiles of three-beam cases in which transmitted and two reflected beams are simultaneously strong in the crystal. This suggestion was verified by Colella [3] that stimulated many authors [2, 4, 5, 21, 22] and let them investigate the multiple-beam (*n*-beam) method to solve the phase problem in protein crystallography.

The most primitive *n*-beam diffraction is the cases *n* = 3. The shape of three-beam rocking curve simply depends on the triplet phase invariant. In the case of protein crystallography, however, it is extremely difficult to realize such three-beam cases that transmitted and only two reflected beams are strong in the crystal, which is due to the extremely high density of reciprocal lattice nodes owing to the large size of unit cell of the crystal. Therefore, X-ray *n*-beam dynamical diffraction theory is necessary to solve the phase problem in protein crystallography. The Ewald-Laue (E-L) dynamical diffraction theory [7, 11] was extended to the three-beam cases in the late 1960's [8–10]. The numerical method to solve the *n*-beam (*n* ≥ 3) E-L theory was given by Colella [3]. Colella's method [3] to solve the *n*-beam E-L theory is applicable only to the case of crystals with planar surfaces.

©2012 Okitsu et al., licensee InTech. This is an open access chapter 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. ©2012 Okitsu et al., licensee InTech. This is a paper 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.

On the other hand, Okitsu and his coauthors [13, 14, 16, 17] extended the Takagi-Taupin (T-T) dynamical diffraction theory [18–20] to *n*-beam cases (*n* ∈ {3, 4, 5, 6, 8, 12}) and presented a numerical method to solve the theory. They showed six-beam pinhole topographs experimentally obtained and computer-simulated based on the *n*-beam T-T equation, between which excellent agreements were found. In reference [16], it was shown that the *n*-beam T-T equation can deal with X-ray wave field in an arbitrary-shaped crystal.

In the *n*-beam method to solve the phase problem in the protein crystal structure analysis, one of the difficulty is the shape of the crystal which is complex in general. Then, the above advantage of *n*-beam T-T equation over the E-L dynamical theory is important. The present authors have derived an *n*-beam T-T equation applicable for arbitrary number of *n*, which will be published elsewhere.

The *n*-beam T-T equation was derived in references [13, 17] from Takagi's fundamental equation of the dynamical theory [19]. In section 2 of the present chapter, however, the *n*-beam E-L theory is described at first. The *n*-beam T-T equation is derived by Fourier-transforming the *n*-beam E-L dynamical theory. Then, it is also described that the E-L theory can be derived from the T-T equation. This reveals a simple relation between the E-L and T-T formulations of X-ray dynamical diffraction theory. This equivalence between the E-L and T-T formulations has been implicitly recognized for many years but is explicitly described for the first time. In section 5, experimentally obtained and computer-simulated pinhole topographs are shown for *n* ∈ {3, 4, 5, 6, 8, 12}, which verifies the theory and the computer algorithm to solve it.

#### **2. Derivation of the** *n***-beam Takagi-Taupin equation**

#### **2.1. Description of the** *n***-beam Ewald-Laue dynamical diffraction theory**

The fundamental equation with the E-L formulation is given by [1, 2]

$$\frac{k\_i^2 - K^2}{k\_i^2} \mathcal{D}\_i = \sum \chi\_{h\_l - h\_l} \left[ \mathcal{D}\_j \right]\_{\perp, \mathbf{k}\_l}. \tag{1}$$

Here, *ki* is wavenumber of the *i*th numbered Bloch wave whose wave vector is **k**0 + **h***i* where **k**0 is the wave vector of the forward-diffracted wave in the crystal, *K*(= 1/*λ*) is the wavenumber of X-rays in vacuum, *Di* and *Dj* are complex amplitude vectors of the *i*th and *j*th numbered Bloch waves, ∑ is an infinite summation for all combinations of *i* and *j*, *χhi*−*hj* is Fourier coefficient of electric susceptibility and [*Dj*]⊥**k***i* is component vector of *Dj* perpendicular to **k***i*, respectively.

By applying an approximation that *ki* + *K* ≈ 2*ki* to (1), the following equation is obtained,

$$\mathfrak{F}\_{i}\mathfrak{D}\_{i} = \frac{K}{2} \sum \chi\_{h\_{i}-h\_{j}} \left[ \mathfrak{D}\_{j} \right]\_{\perp \mathbf{k}\_{i}} \, \, \, \, \tag{2}$$

$$\text{where } \mathfrak{F}\_{i} = k\_{i} - \mathbf{K}.$$

Let the electric displacement vector *Di* be represented by a linear combination of scalar amplitudes as follows:

$$\mathcal{D}\_i = \mathcal{D}\_i^{(0)} \mathbf{e}\_i^{(0)} + \mathcal{D}\_i^{(1)} \mathbf{e}\_i^{(1)}.$$

Here, **e** (0) *i* and **e** (1) *i* are unit vectors perpendicular to **s***i*, where **s***i* is a unit vector parallel to **k***i*. **s***i*, **e** (0) *i* and **e** (1) *i* construct a right-handed orthogonal system in this order. (2) can be described as follows:

$$\begin{aligned} \xi \cos \Theta\_{\mathcal{B}} \mathcal{D}\_i^{(l)} &= -K \left( \mathcal{S}\_{i,0}^{(0)} \mathcal{\beta}^{(0)} + \mathcal{S}\_{i,0}^{(1)} \mathcal{\beta}^{(1)} \right) \mathcal{D}\_i^{(l)} \\ &+ \frac{K}{2} \sum\_{j=0}^{n-1} \sum\_{m=0}^1 \mathcal{C}\_{i,j}^{(l,m)} \chi\_{h\_i \cdots h\_j} \mathcal{D}\_j^{(m)}. \end{aligned} \tag{3}$$

where, *i*, *j* ∈ {0, 1, ··· , *n* − 1}, *n* ∈ {3, 4, 5, 6, 8, 12},

*l*, *m* ∈ {0, 1}.

Here, *S* and *C* are polarization factors defined by

2 Will-be-set-by-IN-TECH

On the other hand, Okitsu and his coauthors [13, 14, 16, 17] extended the Takagi-Taupin (T-T) dynamical diffraction theory [18–20] to *n*-beam cases (*n* ∈ {3, 4, 5, 6, 8, 12}) and presented a numerical method to solve the theory. They showed six-beam pinhole topographs experimentally obtained and computer-simulated based on the *n*-beam T-T equation, between which excellent agreements were found. In reference [16], it was shown that the *n*-beam T-T

In the *n*-beam method to solve the phase problem in the protein crystal structure analysis, one of the difficulty is the shape of the crystal which is complex in general. Then, the above advantage of *n*-beam T-T equation over the E-L dynamical theory is important. The present authors have derived an *n*-beam T-T equation applicable for arbitrary number of *n*, which will

The *n*-beam T-T equation was derived in references [13, 17] from Takagi's fundamental equation of the dynamical theory [19]. In section 2 of the present chapter, however, the *n*-beam E-L theory is described at first. The *n*-beam T-T equation is derived by Fourier-transforming the *n*-beam E-L dynamical theory. Then, it is also described that the E-L theory can be derived from the T-T equation. This reveals a simple relation between the E-L and T-T formulations of X-ray dynamical diffraction theory. This equivalence between the E-L and T-T formulations has been implicitly recognized for many years but is explicitly described for the first time. In section 5, experimentally obtained and computer-simulated pinhole topographs are shown for *n* ∈ {3, 4, 5, 6, 8, 12}, which verifies the theory and the computer algorithm to solve it.

equation can deal with X-ray wave field in an arbitrary-shaped crystal.

**2. Derivation of the** *n***-beam Takagi-Taupin equation**

*k*2 *i* − *K*2 *k*2 *i*

The fundamental equation with the E-L formulation is given by [1, 2]

*ξiDi* = *K*

*Di* = D(0) *i* **e** (0) *i* + D(1) *i* **e** (1) *i* .

**2.1. Description of the** *n***-beam Ewald-Laue dynamical diffraction theory**

*Di* = ∑*χhi*−*hj*

Here, *ki* is wavenumber of the *i*th numbered Bloch wave whose wave vector is **k**0 + **h***i* where **k**0 is the wave vector of the forward-diffracted wave in the crystal, *K*(= 1/*λ*) is the wavenumber of X-rays in vacuum, *Di* and *Dj* are complex amplitude vectors of the *i*th and *j*th numbered Bloch waves, ∑ is an infinite summation for all combinations of *i* and *j*, *χhi*−*hj* is Fourier coefficient of electric susceptibility and [*Dj*]⊥**k***i* is component vector of *Dj*

By applying an approximation that *ki* + *K* ≈ 2*ki* to (1), the following equation is obtained,

2 ∑*χhi*−*hj*

Let the electric displacement vector *Di* be represented by a linear combination of scalar

 *Dj* ⊥**k***i*

where *ξi* = *ki* − *K*.

 *Dj* ⊥**k***i*

. (1)

, (2)

be published elsewhere.

perpendicular to **k***i*, respectively.

amplitudes as follows:

$$\mathbf{e}\_{j}^{(m)} = \mathbf{S}\_{i,j}^{(m)} \mathbf{s}\_{i} + \mathbf{C}\_{i,j}^{(0,m)} \mathbf{e}\_{i}^{(0)} + \mathbf{C}\_{i,j}^{(1,m)} \mathbf{e}\_{i}^{(1)} \,\prime \tag{4}$$

where *i* and *j* are ordinal numbers of waves (*i*, *j* ∈ {0, 1, 2, ··· , *n* − 1}) and *l* and *m* are ordinal numbers of polarization state (*l*, *m* ∈ {0, 1}). When deriving (3) from (2), all reciprocal lattice nodes lying on the surface of Ewald sphere are assumed to be on a circle in reciprocal space. Then number of waves *n* are limited to be *n* ∈ {3, 4, 5, 6, 8, 12} even in the case of cubic crystals with the highest symmetry. Θ*B* is the angle spanned by −→*PQ* and **k***i* which is an identical value for every *i* (*i* ∈ {0, 1, 2, ··· , *n* − 1}), where *P* and *Q* are centers of the Ewald sphere and the circle on which the reciprocal lattice nodes lie, respectively. *ξ* is such a value that

$$
\overrightarrow{P\_1 P\_1^\flat} = -\mathfrak{F} \overrightarrow{P} \overrightarrow{Q} / \left| \overrightarrow{P} \overrightarrow{Q} \right|. \tag{5}
$$

where *P*� 1 is the common initial point of **k***i* [whose terminal points are *Hi* (*i* ∈ {0, 1, ··· , *n* − 1})] and *P*1 is a point on the sphere whose distance from the origin *O* of reciprocal space is *K*. Hereafter, this surface of sphere is approximated as a plane whose distance from *O* is *K* in the vicinity of the Laue point *La* whose distance from *Hi* (*i* ∈ {0, 1, ··· , *n* − 1}) is the identical value *K*. For description in the next section, it is described here that −−→ *P*1*P*� 1 is represented by a linear combination of **s***i*, **e** (0) *i* and **e** (1) *i* as follows:

$$\overrightarrow{P\_1 P\_1^\dagger} = -\xi \left( \cos \Theta\_B \mathbf{s}\_i + \eta\_i^{(0)} \sin \Theta\_B \mathbf{e}\_i^{(0)} + \eta\_i^{(1)} \sin \Theta\_B \mathbf{e}\_i^{(1)} \right) \dots$$

*P*1 is such a point that

$$
\overrightarrow{P\_1 L a} = K \left( \boldsymbol{\beta}^{(0)} \mathbf{e}\_0^{(0)} + \boldsymbol{\beta}^{(1)} \mathbf{e}\_0^{(1)} \right). \tag{6}
$$

(2) and (3) can also be represented using matrices and vector as follows:

$$
\xi \cos \Theta\_{\mathsf{B}} \mathsf{E} \mathcal{D} = \mathsf{A} \mathcal{D}.\tag{7}
$$

Here, **E** is a unit matrix of size 2*n*, *D* is a amplitude column vector of size 2*n* whose *q*th element is *D*(*m*) *j* (*q* = 2*j* + *m* + 1) and **A** is a square matrix of size 2*n* whose element *ap*,*q* is given by

$$a\_{p,q} = \frac{K}{2} \chi\_{h\_i - h\_j} \mathbf{C}\_{i,j}^{(l,m)} - \delta\_{p,q} K \left( \mathbf{S}\_{i,0}^{(0)} \boldsymbol{\mathcal{B}}^{(0)} + \mathbf{S}\_{i,0}^{(1)} \boldsymbol{\mathcal{B}}^{(1)} \right).$$

Here, *p* = 2*i* + *l* + 1 and *δp*,*q* is Kronecker delta. 2*n* couples of *ξ* and *D* can be obtained by solving eigenvalue-eigenvector problem of (7). This problem was solved by Colella [3] for the first time. Dispersion surfaces on which the initial point *P*� 1 of wave vectors of Bloch waves should be, is given as 2*n* sets of eigenvalues for (7).

#### **2.2. Derivation of the** *n***-beam Takagi-Taupin equation from the Ewald-Laue theory**

In this section, the *n*-beam theory of T-T formulation is derived by Fourier-transforming the *n*-beam E-L theory described by (3).

A general solution of dynamical diffraction theory is considered to be coherent superposition of Bloch plane-wave system when X-ray wave field **D**˜ (**r**) is given as follows:

$$\tilde{\mathbf{D}}(\mathbf{r}) = \sum\_{i=0}^{n-1} \sum\_{l=0}^{1} \mathbf{e}\_i^{(l)} D\_i^{(l)}(\mathbf{r}) \exp\left(-\mathrm{i}2\pi \overrightarrow{\mathrm{La}H\_i} \cdot \mathbf{r}\right),\tag{8}$$

where **r** is the location vector. For the following description, **r** is described by a linear combination of **s***i*, **e** (0) *i* and **e** (1) *i* as follows,

$$\mathbf{r} = s\_l \mathbf{s}\_l + e\_i^{(0)} \mathbf{e}\_i^{(0)} + e\_i^{(1)} \mathbf{e}\_i^{(1)}.\tag{9}$$

The amplitude of the *i*th component wave whose polarization state is *l* is described as,

$$\begin{split} \mathcal{D}\_{i}^{(l)}(\Delta \mathbf{k}) \exp\left(-\mathrm{i}2\pi \overrightarrow{P\_{1}^{\prime}H\_{i}} \cdot \mathbf{r}\right) &= \mathcal{D}\_{i}^{(l)}(\Delta \mathbf{k}) \exp\left(-\mathrm{i}2\pi \Delta \mathbf{k} \cdot \mathbf{r}\right) \exp\left(-\mathrm{i}2\pi \overrightarrow{LaH\_{i}} \cdot \mathbf{r}\right), \\ & \text{where } \Delta \mathbf{k} = \overrightarrow{P\_{1}^{\prime}La}. \end{split}$$

In this section, the amplitude of plane wave whose wave vector is **k***i* and polarization state is *l* is denoted by D(*l*) *i* (Δ**k**) in place of D(*l*) *i* in order to clarify this value depends on Δ**k**. *D*(*l*) *i* (**r**) in (8) is represented by superposing coherently D(*l*) *i* (Δ**k**) as follows:

$$D\_i^{(l)}(\mathbf{r}) = \int\_{\Delta \mathbf{k}}^{D.S.} \mathcal{D}\_i^{(l)}(\Delta \mathbf{k}) \exp\left(-\mathbf{i}2\pi\Delta \mathbf{k} \cdot \mathbf{r}\right) \mathrm{d}S\_k. \tag{10}$$

Substituting (4) with *j* = 0, (5), (6) and (9) into (10),

$$\begin{split} D\_{i}^{(l)}(\mathbf{r}) &= \int\_{\Delta \mathbf{k}}^{D.S.} \mathcal{D}\_{i}^{(l)}(\Delta \mathbf{k}) \\ &\times \exp\left\{-\mathrm{i}2\pi \left[ \left( \xi \cos \Theta\_{\mathsf{B}} + K\beta^{(0)} S\_{i,0}^{(0)} + K\beta^{(1)} S\_{i,0}^{(1)} \right) s\_{i} + T\_{i} (\xi\_{\prime} e\_{i}^{(0)}, e\_{i}^{(1)}) \right] \right\} \mathrm{d} \mathbf{S}\_{k}. \tag{11} \end{split}$$

Here, *D*.*S*. Δ*k* d*Sk* means an integration over the dispersion surfaces in reciprocal space and *Ti*(*ξ*,*e* (0) *i* ,*e* (1) *i* ) is a term that does not depend on *si*. *∂D*(*l*) *i* (**r**)/*∂si* can be calculated as follows:

$$\begin{split} \frac{\partial}{\partial \mathbf{s}\_{l}} D\_{i}^{(l)}(\mathbf{r}) &= \frac{\partial}{\partial \mathbf{s}\_{l}} \int\_{\Delta \mathbf{k}}^{D.S.} \mathcal{D}\_{i}^{(l)}(\Delta \mathbf{k}) \exp\left(-\mathrm{i}2\pi \Delta \mathbf{k} \cdot \mathbf{r}\right) \mathrm{d}\mathbf{S}\_{k} \\ &= \int\_{\Delta \mathbf{k}}^{D.S.} \frac{\partial}{\partial \mathbf{s}\_{l}} \left[\mathcal{D}\_{i}^{(l)}(\Delta \mathbf{k}) \exp\left(-\mathrm{i}2\pi \Delta \mathbf{k} \cdot \mathbf{r}\right)\right] \mathrm{d}\mathbf{S}\_{k} \\ &= -\mathrm{i}2\pi \int\_{\Delta \mathbf{k}}^{D.S.} \left[\mathcal{J} \cos \Theta\_{\mathcal{B}} + K \left(\mathcal{S}\_{i,0}^{(0)} \mathcal{J}^{(0)} + \mathcal{S}\_{i,0}^{(1)} \mathcal{J}^{(1)}\right)\right] \mathcal{D}\_{i}^{(l)}(\Delta \mathbf{k}) \exp\left(-\mathrm{i}2\pi \Delta \mathbf{k} \cdot \mathbf{r}\right) \mathrm{d}\mathbf{S}\_{k}. \end{split} \tag{12}$$

Substituting (3) into (12),

4 Will-be-set-by-IN-TECH

Here, **E** is a unit matrix of size 2*n*, *D* is a amplitude column vector of size 2*n* whose *q*th

Here, *p* = 2*i* + *l* + 1 and *δp*,*q* is Kronecker delta. 2*n* couples of *ξ* and *D* can be obtained by solving eigenvalue-eigenvector problem of (7). This problem was solved by Colella [3] for the

In this section, the *n*-beam theory of T-T formulation is derived by Fourier-transforming the

A general solution of dynamical diffraction theory is considered to be coherent superposition

*i* (**r**) exp

where **r** is the location vector. For the following description, **r** is described by a linear

where Δ**k** = −−→

In this section, the amplitude of plane wave whose wave vector is **k***i* and polarization state is

*S*(0)

*i*,0 + *Kβ*(1)

(0) *i* **e** (0) *i* + *e* (1) *i* **e** (1)

The amplitude of the *i*th component wave whose polarization state is *l* is described as,

 −i2*π*

*i* (Δ**k**) exp (−i2*π*Δ**k** · **r**) exp

*P*� 1*La*. −−→*LaHi* · **r**

**2.2. Derivation of the** *n***-beam Takagi-Taupin equation from the Ewald-Laue**

*j* (*q* = 2*j* + *m* + 1) and **A** is a square matrix of size 2*n* whose element *ap*,*q* is

*i*,0 *β*(0) + *S*(1)

*i*,0 *β*(1) .

1 of wave vectors of Bloch waves

, (8)

−−→*LaHi* · **r** ,

*i* (**r**)

d*Sk*. (11)

*i* . (9)

 −i2*π*

*i* in order to clarify this value depends on Δ**k**. *D*(*l*)

*i* (Δ**k**) exp (−i2*π*Δ**k** · **r**) d*Sk*. (10)

*si* + *Ti*(*ξ*,*e*

(0) *i* ,*e* (1) *i* )

*i* (Δ**k**) as follows:

*S*(1) *i*,0

 *S*(0)

element is *D*(*m*)

*ap*,*q* = *K*

should be, is given as 2*n* sets of eigenvalues for (7).

**D**˜ (**r**) =

(0) *i* and **e**

 −i2*π* *n*−1 ∑ *i*=0

(1)

−−→ *P*� 1*Hi* · **r**

*i* (Δ**k**) in place of D(*l*)

 *D*.*S*. Δ**k**

*ξ* cos Θ*B* + *Kβ*(0)

D(*l*)

in (8) is represented by superposing coherently D(*l*)

*D*(*l*) *i* (**r**) =

Substituting (4) with *j* = 0, (5), (6) and (9) into (10),

D(*l*) *i* (Δ**k**)

 *D*.*S*. Δ**k**

× exp −i2*π*

*n*-beam E-L theory described by (3).

2 *χhi*−*hj*

first time. Dispersion surfaces on which the initial point *P*�

*C*(*l*,*m*) *i*,*j* − *δp*,*qK*

of Bloch plane-wave system when X-ray wave field **D**˜ (**r**) is given as follows:

1 ∑ *l*=0 **e** (*l*) *i D*(*l*)

*i* as follows,

**r** = *si***s***i* + *e*

= D(*l*)

given by

**theory**

combination of **s***i*, **e**

D(*l*)

*l* is denoted by D(*l*)

*D*(*l*) *i* (**r**) =

*i* (Δ**k**) exp

$$\frac{\partial}{\partial S\_i} D\_i^{(l)}(\mathbf{r}) = -i\pi K \int\_{\Delta \mathbf{k}}^{D.S.} \sum\_{j=0}^{n-1} \sum\_{m=0}^{1} \mathbb{C}\_{i,j}^{(l,m)} \chi\_{h\_i - h\_j} \mathcal{D}\_j^{(m)}(\Delta \mathbf{k}) \exp\left(-i2\pi \Delta \mathbf{k} \cdot \mathbf{r}\right) \mathrm{d}S\_k$$

$$= -i\pi K \sum\_{j=0}^{n-1} \sum\_{m=0}^{1} \mathbb{C}\_{i,j}^{(l,m)} \chi\_{h\_i - h\_j} \int\_{\Delta \mathbf{k}}^{D.S.} \mathcal{D}\_j^{(m)}(\Delta \mathbf{k}) \exp\left(-i2\pi \Delta \mathbf{k} \cdot \mathbf{r}\right) \mathrm{d}S\_k. \tag{13}$$

Incidentally, when the crystal is perfect, the electric susceptibility *χ*(**r**) is represented by Fourier series as *χ*(**r**) = ∑**h***i χhi* exp[−i2*π***h***i* · **r**]. However, when the crystal has a lattice displacement field of **u**(**r**), the electric susceptibility is approximately given by *χ*[**r** − **u**(**r**)] and represented by Fourier series as follows,

$$\chi[\mathbf{r} - \mathbf{u}(\mathbf{r})] = \sum\_{\mathbf{h}\_l} \chi\_{\mathbf{h}\_l} \exp[\mathbf{i}2\pi \mathbf{h}\_l \cdot \mathbf{u}(\mathbf{r})] \exp(-\mathbf{i}2\pi \mathbf{h}\_l \cdot \mathbf{r}).$$

Then, in the case of crystal with a lattice displacement field of **u**(**r**), *χhi*−*hj* can be replaced by *χhi*−*hj* exp[i2*π*(**h***i* − **h***j*) · **u**(**r**)]. Therefore, the following equation is obtained from (13),

$$\frac{\partial}{\partial \mathbf{s}\_i} D\_i^{(l)}(\mathbf{r}) = -i\pi K \sum\_{j=0}^{n-1} \sum\_{m=0}^{1} \mathbb{C}\_{i,j}^{(l,m)} \chi\_{h\_i - h\_j} \exp\left[i2\pi (\mathbf{h}\_i - \mathbf{h}\_j) \cdot \mathbf{u}(\mathbf{r})\right] D\_j^{(m)}(\mathbf{r}), \tag{14}$$

$$\text{where, } \quad i, j \in \{0, 1, \dots, n-1\}, n \in \{3, 4, 5, 6, 8, 12\},$$

$$l, m \in \{0, 1\}.$$

The above equation is nothing but the *n*-beam T-T equation that appeared as eq. (4) in reference [17].

#### **2.3. Derivation of the** *n***-beam E-L dynamical theory from the T-T equation**

In this section, it is described that the *n*-beam E-L theory given by (3) can be derived from the *n*-beam T-T equation (14).

#### 6 Will-be-set-by-IN-TECH 72 Recent Advances in Crystallography

When plane-wave X-rays are incident on the crystal to excite 2*n* tie points on the dispersion surfaces, each Bloch plane-wave system is described by

$$\tilde{\mathcal{D}} = \sum\_{i=0}^{n-1} \sum\_{l=0}^{1} \mathbf{e}\_i^{(l)} \mathcal{D}\_i^{(l)} \exp\left(-\mathbf{i}2\pi\Delta\mathbf{k}\cdot\mathbf{r}\right) \exp\left(-\mathbf{i}2\pi\overline{\mathbf{L}aH\_l}\cdot\mathbf{r}\right).$$

Even when *D*(*l*) *i* (**r**) = D(*l*) *i* exp(−i2*π***k**(*l*) *i* · **r**), *D*(*l*) *i* (**r**) should satisfy (14) with **u**(**r**) = 0,

$$\frac{\partial}{\partial \mathbf{s}\_i} \left[ \mathcal{D}\_i^{(l)} \exp \left( -\mathbf{i} 2\pi \Delta \mathbf{k} \cdot \mathbf{r} \right) \right] = -\mathbf{i} \pi \mathbf{K} \sum\_{j=0}^{n-1} \sum\_{m=0}^{1} \mathbb{C}\_{i,j}^{(l,m)} \chi\_{h\_i - h\_j} \left[ \mathcal{D}\_j^{(m)} \exp \left( -\mathbf{i} 2\pi \Delta \mathbf{k} \cdot \mathbf{r} \right) \right]. \tag{15}$$

Applying the same procedure as used when deriving (11),

$$\begin{split} &\frac{\partial}{\partial s\_{i}}\left[\mathcal{D}\_{i}^{(l)}\exp\left(-\mathrm{i}2\pi\Delta\mathbf{k}\cdot\mathbf{r}\right)\right] \\ &=\mathcal{D}\_{i}^{(l)}\frac{\partial}{\partial s\_{i}}\exp\left\{-\mathrm{i}2\pi\left[\left(\xi\cos\Theta\_{B}+\mathsf{K}\beta^{(0)}S\_{i,0}^{(0)}+\mathsf{K}\beta^{(1)}S\_{i,0}^{(1)}\right)s\_{i}+T\_{i}(\xi,\mathcal{E}\_{i}^{(0)},\mathcal{E}\_{i}^{(1)})\right]\right\} \\ &=-\mathrm{i}2\pi\left(\xi\cos\Theta\_{B}+\mathsf{K}\beta^{(0)}S\_{i,0}^{(0)}+\mathsf{K}\beta^{(1)}S\_{i,0}^{(1)}\right)\left[\mathcal{D}\_{i}^{(l)}\exp\left(-\mathrm{i}2\pi\Delta\mathbf{k}\cdot\mathbf{r}\right)\right]. \end{split} \tag{16}$$

Comparing (15) and (16), the same equation as (3) is obtained. The equivalence between the *n*-beam E-L and T-T X-ray dynamical diffraction theories (*n* ∈ {3, 4, 5, 6, 8, 12}) described by a Fourier transform as defined by (10) is verified. As far as the present authors know, description on this equivalence between the E-L and T-T dynamical diffraction theories for two-beam case is found just in section 11.3 of Authier's book [1].

#### **3. Algorithm to solve the theory**

Figure 1(*a*) and 1(*b*) are schematic drawings for explanation of the algorithm to solve the *n*-beam T-T equation (14) for a six-beam case whose computer-simulated and experimentally obtained results are shown in Figure 9 of the present chapter. Vectors −−−−−→ *R*(0) *i R*(1) in Figure 1(*a*) are parallel to **s***i*. When the length of −−−−−→ *R*(0) *i R*(1) is sufficiently small compared with the extinction length −1/(*χ*0*K*) of the forward diffraction, The T-T equation (14) can be approximated by

$$\frac{D\_i^{(l)}(\mathcal{R}^{(1)}) - D\_i^{(l)}(\mathcal{R}\_i^{(0)})}{\left| \overline{R\_i^{(0)} \mathcal{R}^{(1)}} \right|}$$

$$= -\text{i}\pi K \sum\_{j=0}^{n-1} \sum\_{m=0}^1 \left\{ \chi\_{h\_i - h\_j} \exp\left[ \text{i}2\pi \left( \mathbf{h}\_i - \mathbf{h}\_j \right) \cdot \mathbf{u}(Rm\_i) \right] \right. $$

$$\times C\_{i,j}^{(l,m)} \left[ D\_j^{(m)}(\mathcal{R}\_i^{(0)}) + D\_j^{(m)}(\mathcal{R}^{(1)}) \right] / 2 \right\}. \tag{17}$$

72 Recent Advances in Crystallography X-ray N-beam Takagi-Taupin Dynamical Theory and N-beam Pinhole Topographs Experimentally Obtained and Computer-Simulated 7 73 X-Ray N-Beam Takagi-Taupin Dynamical Theory and N-Beam Pinhole Topographs Experimentally Obtained and Computer-Simulated

6 Will-be-set-by-IN-TECH

When plane-wave X-rays are incident on the crystal to excite 2*n* tie points on the dispersion

*i* exp (−i2*π*Δ**k** · **r**) exp

1 ∑ *m*=0

*C*(*l*,*m*) *i*,*j χhi*−*hj*

*S*(0)

*S*(1) *i*,0 D(*l*)

Comparing (15) and (16), the same equation as (3) is obtained. The equivalence between the *n*-beam E-L and T-T X-ray dynamical diffraction theories (*n* ∈ {3, 4, 5, 6, 8, 12}) described by a Fourier transform as defined by (10) is verified. As far as the present authors know, description on this equivalence between the E-L and T-T dynamical diffraction theories for

Figure 1(*a*) and 1(*b*) are schematic drawings for explanation of the algorithm to solve the *n*-beam T-T equation (14) for a six-beam case whose computer-simulated and experimentally

the extinction length −1/(*χ*0*K*) of the forward diffraction, The T-T equation (14) can be

−−−−−→ *R*(0)

*i*,0 + *Kβ*(1)

*i* · **r**), *D*(*l*)

*n*−1 ∑ *j*=0 −i2*π*−−→*LaHi* · **r**

*i* (**r**) should satisfy (14) with **u**(**r**) = 0,

 D(*m*)

*S*(1) *i*,0

*i* exp (−i2*π*Δ**k** · **r**)

 .

*j* exp (−i2*π*Δ**k** · **r**)

*si* + *Ti*(*ξ*,*e*

(0) *i* ,*e* (1) *i* )

−−−−−→ *R*(0)

*i R*(1) is sufficiently small compared with

· **u**(*Rmi*)

. (17)

*i R*(1) in Figure

 . (15)

. (16)

surfaces, each Bloch plane-wave system is described by

1 ∑ *l*=0 **e** (*l*) *i* D(*l*)

*i* exp(−i2*π***k**(*l*)

Applying the same procedure as used when deriving (11),

= −i*πK*

*ξ* cos Θ*B* + *Kβ*(0)

*i*,0 + *Kβ*(1)

*S*(0)

two-beam case is found just in section 11.3 of Authier's book [1].

obtained results are shown in Figure 9 of the present chapter. Vectors

*i* (*R*(0) *i* )

*n*−1 ∑ *i*=0

*D*˜ =

*i* (**r**) = D(*l*)

*i* exp (−i2*π*Δ**k** · **r**)

*i* exp (−i2*π*Δ**k** · **r**)

*ξ* cos Θ*B* + *Kβ*(0)

Even when *D*(*l*)

*∂ ∂si* D(*l*)

= D(*l*) *i ∂ ∂si* exp −i2*π*

= −i2*π*

approximated by

**3. Algorithm to solve the theory**

1(*a*) are parallel to **s***i*. When the length of

*D*(*l*)

*i* (*R*(1)) − *D*(*l*)

−−−−−→ *R*(0) *i R*(1)

> *n*−1 ∑ *j*=0

> > *D*(*m*) *j* (*R*(0)

1 ∑ *m*=0

*χhi*−*hj* exp

*i* ) + *D*(*m*)

 i2*π* **h***i* − **h***j*

*j* (*R*(1) ) /2

×*C*(*l*,*m*) *i*,*j*

= −i*πK*

*∂ ∂si* D(*l*)

**Figure 1.** This Figure shows small hexagonal pyramids used when solving the T-T equation (14) in a six-beam case whose results are shown in Figure 9.

The above equation (17) can be described using matrix and vectors as follows:

$$\begin{split} \mathbf{A} &= \mathbf{B} \mathbf{D} \\ \text{where, } a\_p &= -\mathbf{i}\frac{1}{2}\pi K \sum\_{j=0}^{n-1} \sum\_{m=0}^{1} \chi\_{h\_i - h\_j} \exp\left[i2\pi (\mathbf{h}\_i - \mathbf{h}\_j) \cdot \mathbf{u}(\mathcal{R}m\_i)\right] \mathbf{C}\_{i,j}^{(l,m)} \mathbf{D}\_j^{(m)}(\mathbf{R}\_i^{(0)}) \\ &+ \frac{\mathbf{D}\_i^{(l)}(\mathbf{R}\_i^{(0)})}{\left|\mathbf{R}\_i^{(0)}\mathbf{R}^{(1)}\right|}, \\ b\_{p,q} &= \mathbf{i}\frac{1}{2}\pi K \chi\_{h\_l - h\_j} \exp\left[i2\pi (\mathbf{h}\_i - \mathbf{h}\_j) \cdot \mathbf{u}(\mathcal{R}m\_i)\right] \mathbf{C}\_{i,j}^{(l,m)} + \frac{\delta\_{p,q}}{\left|\mathbf{R}\_i^{(0)}\mathbf{R}^{(1)}\right|}, \\ d\_q &= D\_j^{(m)}(\mathbf{R}^{(1)}), \\ p &= 2i + l + 1, \\ q &= 2j + m + 1. \end{split} \tag{18}$$

#### 8 Will-be-set-by-IN-TECH 74 Recent Advances in Crystallography

Here, **A** and **D** are column vectors of size 2*n* whose *p*th and *q*th elements are *ap* and *dq*, respectively, and **B** is a square matrix of size 2*n* whose element of the *p*th column and the *q*th raw is *bp*,*q*.

**Figure 2.** This Figure shows a top view of Figure 1(*b*).

Figure 2 is a top view of Figure 1(*b*). The X-ray amplitudes *D*(*m*) *j* (*R*(1) *i* ) were calculated from the X-ray amplitudes at the incidence point *D*(*l*) 0 (*Rinc*) of the crystal surface. In this case, 0 0 0-forward-diffracted and 4 0 4-, 4 2 6-, 0 6 6-, 2 6 4- and 2 2 0-reflected X-rays are simultaneously strong. The angle spanned by *nx*- and *ny*-axes is 120◦. −−−−−→ *RincR*(1) *i* in Figure 1(*b*) are parallel to the wave vectors of 0 0 0-forward-diffracted and 4 0 4-, 4 2 6-, 0 6 6-, 2 6 4 and 2 2 0-reflected X-rays. As a boundary condition on the crystal surface, amplitude array *Deven*(*i*,*l*,*nx*,*ny*) has nonzero value (unity) when (*i*,*l*,*nx*,*ny*)=(0,0,0,0) or (*i*,*l*,*nx*,*ny*)=(0,1,0,0). On the first layer, nonzero X-ray amplitudes *Dodd*(*j*, *m*, *nx*, *ny*) are calculated when (*nx*, *ny*) = [*n*� *x*(*i*), *n*� *y*(*i*)] (*i* ∈ {0, 1, ··· , *n* − 1}). Here, [*n*� *x*(*i*), *n*� *y*(*i*)] = (0, 0),(0, 2),(1, 3),(3, 3),(3, 2) and (1, 0) for *i* = 0, 1, 2, 3, 4, 5, respectively. In general, *Deven*(*i*,*l*,*nx*,*ny*) [or *Dodd*(*i*,*l*,*nx*,*ny*)] is calculated as *D*(*l*) *i* (*R*(1)) by substituting *Dodd*(*j*,*m*,*nx* − *n*� *x*(*i*),*ny* − *n*� *y*(*i*)) [or *Deven*(*j*,*m*,*nx* − *n*� *x*(*i*),*ny* − *n*� *y*(*i*))] into *D*(*m*) *j* (*R*(0) *i* ) in (17). The calculation was performed layer by layer scanning *nx* and *ny* in a range of *NMin*[*n*� *x*(*i*)] ≤ *nx* ≤ *N Max*[*n*� *x*(*i*)] and *NMin*[*n*� *y*(*i*)] ≤ *ny* ≤ *N Max*[*n*� *y*(*i*)], where *N* is the ordinal number of layer. The values of *χhi*−*hj* were calculated by using *XOP* version 2.3 [6].

#### **4. Experimental**

#### **4.1. Phase-retarder system**

When taking four-, five-, six- and eight-beam pinhole topographs shown in section 5, the horizontally polarized synchrotron X-rays monochromated to be 18.245 keV with a water-cooled diamond monochromator system at BL09XU of SPring-8 were incident on the 'rotating four-quadrant phase retarder system' [15, 17].

Figure 3 shows (*a*) a schematic drawing of the phase retarder system and (*b*) a photograph of it. [100]-oriented four diamond crystals *PRn* (*n* ∈ {1, 2, 3, 4}) with thicknesses of 1.545, 74 Recent Advances in Crystallography X-ray N-beam Takagi-Taupin Dynamical Theory and N-beam Pinhole Topographs Experimentally Obtained and Computer-Simulated 9 75 X-Ray N-Beam Takagi-Taupin Dynamical Theory and N-Beam Pinhole Topographs Experimentally Obtained and Computer-Simulated

8 Will-be-set-by-IN-TECH

Here, **A** and **D** are column vectors of size 2*n* whose *p*th and *q*th elements are *ap* and *dq*, respectively, and **B** is a square matrix of size 2*n* whose element of the *p*th column and the *q*th

case, 0 0 0-forward-diffracted and 4 0 4-, 4 2 6-, 0 6 6-, 2 6 4- and 2 2 0-reflected X-rays are

are parallel to the wave vectors of 0 0 0-forward-diffracted and 4 0 4-, 4 2 6-, 0 6 6-, 2 6 4 and 2 2 0-reflected X-rays. As a boundary condition on the crystal surface, amplitude array *Deven*(*i*,*l*,*nx*,*ny*) has nonzero value (unity) when (*i*,*l*,*nx*,*ny*)=(0,0,0,0) or (*i*,*l*,*nx*,*ny*)=(0,1,0,0). On the first layer, nonzero X-ray amplitudes *Dodd*(*j*, *m*, *nx*, *ny*) are calculated when (*nx*, *ny*) =

(1, 0) for *i* = 0, 1, 2, 3, 4, 5, respectively. In general, *Deven*(*i*,*l*,*nx*,*ny*) [or *Dodd*(*i*,*l*,*nx*,*ny*)] is

When taking four-, five-, six- and eight-beam pinhole topographs shown in section 5, the horizontally polarized synchrotron X-rays monochromated to be 18.245 keV with a water-cooled diamond monochromator system at BL09XU of SPring-8 were incident on the

Figure 3 shows (*a*) a schematic drawing of the phase retarder system and (*b*) a photograph of it. [100]-oriented four diamond crystals *PRn* (*n* ∈ {1, 2, 3, 4}) with thicknesses of 1.545,

*x*(*i*), *n*�

*x*(*i*)] ≤ *nx* ≤ *N Max*[*n*�

*y*(*i*)], where *N* is the ordinal number of layer. The values of *χhi*−*hj* were calculated

*j* (*R*(1)

0 (*Rinc*) of the crystal surface. In this

*y*(*i*)] = (0, 0),(0, 2),(1, 3),(3, 3),(3, 2) and

*x*(*i*)] and *NMin*[*n*�

*x*(*i*),*ny* − *n*�

*i* ) in (17). The calculation was performed layer by layer

−−−−−→ *RincR*(1)

*i* ) were calculated

*i* in Figure 1(*b*)

*y*(*i*)) [or *Deven*(*j*,*m*,*nx* −

*y*(*i*)] ≤ *ny* ≤

raw is *bp*,*q*.

[*n*� *x*(*i*), *n*�

*n*�

calculated as *D*(*l*)

**4. Experimental**

*x*(*i*),*ny* − *n*�

*N Max*[*n*�

**Figure 2.** This Figure shows a top view of Figure 1(*b*).

from the X-ray amplitudes at the incidence point *D*(*l*)

*y*(*i*)] (*i* ∈ {0, 1, ··· , *n* − 1}). Here, [*n*�

'rotating four-quadrant phase retarder system' [15, 17].

*j* (*R*(0)

*y*(*i*))] into *D*(*m*)

scanning *nx* and *ny* in a range of *NMin*[*n*�

by using *XOP* version 2.3 [6].

**4.1. Phase-retarder system**

Figure 2 is a top view of Figure 1(*b*). The X-ray amplitudes *D*(*m*)

simultaneously strong. The angle spanned by *nx*- and *ny*-axes is 120◦.

*i* (*R*(1)) by substituting *Dodd*(*j*,*m*,*nx* − *n*�

**Figure 3.** (*a*) is a schematic drawing of the 'rotating four-quadrant phase retarder system' (reproduction of Figure 3 in reference [17]). (*b*) is a photograph of it.

2.198, 1.565 and 2.633 mm were mounted on tangential-bar type goniometers such that the deviation angles Δ*θPRn* from the exact Bragg condition of 1 1 1 reflection in an asymmetric Laue geometry can be controlled. See Figure 4 in reference [17] for more detail. The four tangential-bar type goniometers were mounted in a *χ*-circle goniometer [see Figure 3 (*b*)] such that the whole system of the phase retarders can be rotated around the beam axis of transmitted X-rays. The rotation angle of the *χ*-circle *χPR* and Δ*θPRn* were controlled as summarized in Table 3 in reference [17] such that horizontal-linearly (LH), vertical-linearly (LV), right-screwed circularly (CR), left-screwed circularly (CL), −45◦-inclined-linearly (L−45) and +45◦-inclined-linearly (L+45) polarized X-rays were generated to be incident on the sample crystal.

In the cases of three- and twelve-beam pinhole topographs, horizontally polarized synchrotron X-rays monochromated to be 18.245 keV and to be 22.0 keV, respectively, but not transmitted through the phase retarder system were incident on the sample crystals.

### **4.2. Sample crystal**

Figure 4 is a reproduction of Fig 7 in reference [17] showing the experimental setup when the six-beam pinhole topographs shown in reference [17] were taken. Also in the case of *n*-beam pinhole topographs (*n* ∈ {3, 4, 5, 6, 8, 12}) the [1 1 1]-oriented floating-zone silicon crystal with thickness 9.6 mm (for three-, four-, five-, six- and eight-beam topographs) and 10.0 mm (for twelve-beam topographs) were also mounted on the four-axis goniometer whose *χ*-, *φ*-, *ω*and *θ*-axes can be rotated. Transmitted X-rays through the sample and two reflected X-rays were searched by three *PIN* photo diodes as shown in Figure 4. The positions of the two *PIN* photo diodes for detecting the reflected X-rays were determined using a laser beam guide reflected by a mirror. The mirror was mounted at the sample position on the goniometer whose angular positions were calculated such that the mirror reflects the laser beam to the direction of X-rays to be reflected by the sample crystal.

**Figure 4.** A schematic drawing of the goniometer on which the sample crystal was mount (reproduction of Figure 7 in reference [17]).

After adjusting the angular position of the goniometer such that the *n*-beam simultaneous reflection condition was satisfied, the size of slit *S* in Figure 3 (*a*) was limited to be 25×25 *μ*m.

*N* images of *n*-beam pinhole topographs were simultaneously recorded on an imaging plate placed behind the sample crystal.


5. Genomic markers, prognosis, and personalized treatment

In the past, breast cancers were simply treated based on some clinicopathological features, such as tumor size, lymph node status, patients age and menopausal status, and tumor biomarkers such as ER, PR, and HER2/neu. Then, systemic chemotherapy was applied nearly universally to locally advanced breast cancers regardless of their biomolecular profile, and to about 60% of early breast cancers, but often without any significant effect on women prognosis [105]. As a consequence, a great debate has emerged about quality-of-life issues, acute and long-term side effects of systemic therapies, and the cost of unnecessary treatments [54, 106]. Therefore, in the last decades, quantitative approaches for prognosis prediction and treatment individualization have been developed, and genomic and molecular technologies are routinely applied to prevent overtreatments.

Recently, thanks to the increased level of knowledge regarding the molecular pathways and underlying genetic changes in breast cancer, the molecular signatures of gene expression have been correlated with breast cancer recurrence risk [7, 107, 108]. Anyway, their current clinical application is still limited due to reproducibility questions and the need for fresh or frozen tissue.

In this section, we discuss about susceptibility genes, the carriers of which results to have an increased breast cancer risk and consequently deserve a more frequent and specific screening, and about some signatures, which are usually used to predict breast cancer responsiveness to adjuvant and neoadjuvant therapies.

Mutations in BRCA1 and BRCA2 genes are the most frequent hereditary genetic aberrations in breast cancer and account for approximately half of all hereditary breast cancers. Initial estimates found BRCA1 mutations to be responsible for 45–90% of breast cancer cases in families with apparent autosomal dominant transmission of breast cancer, and this percentage rises if the median age at onset of breast cancer is younger than 45 years [120, 121]. Estimates of BRCA1 and BRCA2 mutation prevalence in unselected patients with breast cancer are in the

Biomarkers in Breast Cancer

13

http://dx.doi.org/10.5772/intechopen.77320

Among BRCA1 mutation carriers, the estimated breast cancer risk is about 65%, the estimated risk of contralateral breast cancer occurrence results 60%, the cumulative risk of ovarian cancer varies between 27 and 45%, and there is also a significantly increased risk of fallopian tube, uterine and cervical cancer, as well as of male breast cancer, stomach, pancreatic, colon and

Among BRCA2 mutation carriers, the estimated lifetime breast cancer risk ranges between 45 and 84%, and that of ovarian cancer between 10 and 20% [123, 127]. There is an increased male breast cancer risk of about 6%, as well as an increased risk of prostate, pancreatic, stomach,

More than 500 coding region sequence variations have been detected in BRCA1 and 250 in BRCA2. Most unequivocally confirmed mutations reported to date are truncating mutations, adding little in the way of clues for defining functional regions. Although few mutations have been identified in either gene in sporadic breast cancers, a phenotype termed "BRCAness" exist, in which the BRCA1 and BRCA2 proteins act may be somehow disrupted also in sporadic cancer [129]. Finally, there are also some syndromes characterized by an increased

Although germline mutations in BRCA1 and BRCA2 confer a high risk of breast cancer, a great deal of variability has been observed in cancer risk among individuals, both between and within families, as many environmental or genetic factors can modify the penetrance of BRCA1 and BRCA2 mutations. The Consortium of Investigators of Modifiers of BRCA1 and BRCA2 (CIMBA), analyzing DNA and clinical data from approximately 10,000 BRCA1 and 5000 BRCA2 mutation carriers, demonstrated the role of a number of gene variants in affecting

The most important prognostic modifiers of BRCA1 and BRCA2 mutation carriers are prophylactic oophorectomy and the use of tamoxifen for chemoprevention, which approximately halve the breast cancer risk and decrease the risk of ovarian cancer by about 95% [131, 132].

In comparison with sporadic breast cancers, those related with high-penetrance susceptibility genes correlate with younger age at diagnosis, more aggressive tumor biological behavior, bilaterality, and the eventual coexistence of other cancers in the same individual or in other individuals of the same family, including ovarian, colon, prostate, pancreatic, and endometrial

Breast cancers arising in BRCA1 mutation carriers are frequently, although not exclusively, basal-like and ER-negative, probably because BRCA1 plays a crucial role in the transcriptional

gallbladder and bile duct cancers, and malignant melanoma [122, 128].

breast cancer susceptibility, which are discussed in the following section.

range of 2–3% [122].

testicular cancer [123–126].

the penetrance in mutation carriers [130].

cancers, as well as sarcomas and male breast cancer [133].

#### 5.1. BRCA1 and BRCA2

Inherited susceptibility to breast cancer has been hypothesized due to the discovery and characterization of a number of high-risk, relatively uncommon genes responsible for the clustering of breast cancer in certain families, which thereafter had a significantly increased risk in comparison with the general population [109, 110]. Many studies suggest that breast cancer susceptibility is transmitted in an autosomal dominant mendelian way [111], but the actual risk of developing breast cancer in a mutation carrier is based on the penetrance of the gene, which consists in the likelihood that the effect (phenotype) of a mutation (genotype) will become clinically apparent.

The BRCA1 gene was firstly identified in 1994 [112] and is localized on the 17th chromosome, whereas the BRCA2 gene was found some years after and is localized on the 13th chromosome [113]. The big size of these genes is important in the context of genetic testing because of the increased probability of mutations and the consequent technically demanding and costly mutations testing, but fortunately the use of modern next generation DNA sequencing is already overcoming these technical and cost issues. Moreover, the BRCA1 gene contains a large number of repetitive elements that facilitate the generation of large deletions and duplications.

BRCA1 is a nuclear protein with two important regions of sequence similarity with known functional motifs: a 42–amino-acid RING (Really Interesting New Gene) domain at the beginning of BRCA1 which binds zinc and is essential in cell growth and differentiation, and the BRCT (breast cancer-1 terminus) motif at the carboxyl terminus, which acts as a phosphoprotein docking motif and a transcriptional activation domain [114, 115]. BRCA2 is also a nuclear protein composed of the following major structural motifs: the eight tandem BRC repeats in the central portion of the protein, which mediates the critical interaction of BRCA2 and RAD51, the TR2 at the carboxyl terminus, which binds RAD51 exists, a single-strand and double-strand DNA binding domain in the C-terminus [113, 116].

Both BRCA1 and BRCA2 genes encode large proteins with multiple functions, which act mainly as tumor suppressor gene products, affecting transcription, cell cycle regulation, genome stability maintenance, and repair of doublestranded DNA breaks for protection of the genome during replication [117, 118]. In particular, BRCA1 prevents replication of damaged DNA by altering chromatin structure and nucleosome organization at the local site of damage, facilitates access by repair complexes, and promotes the use of the error-free repair pathway of homologous recombination-mediated repair rather than the error-prone process of nonhomologous end joining [118]. BRCA2 affects the choice between the two homologous recombination pathways in favor of the error-free one, by interacting with RAD51 [118]. When the wild-type BRCA1 or BRCA2 allele is lost, mutated, or silenced, a high degree of chromosome instability is observed and defective DNA repair may occur, with the consequent accumulation of additional mutations during replication and promotion of carcinogenesis [119].

Mutations in BRCA1 and BRCA2 genes are the most frequent hereditary genetic aberrations in breast cancer and account for approximately half of all hereditary breast cancers. Initial estimates found BRCA1 mutations to be responsible for 45–90% of breast cancer cases in families with apparent autosomal dominant transmission of breast cancer, and this percentage rises if the median age at onset of breast cancer is younger than 45 years [120, 121]. Estimates of BRCA1 and BRCA2 mutation prevalence in unselected patients with breast cancer are in the range of 2–3% [122].

and about some signatures, which are usually used to predict breast cancer responsiveness to

Inherited susceptibility to breast cancer has been hypothesized due to the discovery and characterization of a number of high-risk, relatively uncommon genes responsible for the clustering of breast cancer in certain families, which thereafter had a significantly increased risk in comparison with the general population [109, 110]. Many studies suggest that breast cancer susceptibility is transmitted in an autosomal dominant mendelian way [111], but the actual risk of developing breast cancer in a mutation carrier is based on the penetrance of the gene, which consists in the likelihood that the effect (phenotype) of a mutation (genotype) will

The BRCA1 gene was firstly identified in 1994 [112] and is localized on the 17th chromosome, whereas the BRCA2 gene was found some years after and is localized on the 13th chromosome [113]. The big size of these genes is important in the context of genetic testing because of the increased probability of mutations and the consequent technically demanding and costly mutations testing, but fortunately the use of modern next generation DNA sequencing is already overcoming these technical and cost issues. Moreover, the BRCA1 gene contains a large number of repetitive elements that facilitate the generation of large deletions and dupli-

BRCA1 is a nuclear protein with two important regions of sequence similarity with known functional motifs: a 42–amino-acid RING (Really Interesting New Gene) domain at the beginning of BRCA1 which binds zinc and is essential in cell growth and differentiation, and the BRCT (breast cancer-1 terminus) motif at the carboxyl terminus, which acts as a phosphoprotein docking motif and a transcriptional activation domain [114, 115]. BRCA2 is also a nuclear protein composed of the following major structural motifs: the eight tandem BRC repeats in the central portion of the protein, which mediates the critical interaction of BRCA2 and RAD51, the TR2 at the carboxyl terminus, which binds RAD51 exists, a single-strand and

Both BRCA1 and BRCA2 genes encode large proteins with multiple functions, which act mainly as tumor suppressor gene products, affecting transcription, cell cycle regulation, genome stability maintenance, and repair of doublestranded DNA breaks for protection of the genome during replication [117, 118]. In particular, BRCA1 prevents replication of damaged DNA by altering chromatin structure and nucleosome organization at the local site of damage, facilitates access by repair complexes, and promotes the use of the error-free repair pathway of homologous recombination-mediated repair rather than the error-prone process of nonhomologous end joining [118]. BRCA2 affects the choice between the two homologous recombination pathways in favor of the error-free one, by interacting with RAD51 [118]. When the wild-type BRCA1 or BRCA2 allele is lost, mutated, or silenced, a high degree of chromosome instability is observed and defective DNA repair may occur, with the consequent accumulation of additional mutations during replication and promotion of carcinogenesis [119].

double-strand DNA binding domain in the C-terminus [113, 116].

adjuvant and neoadjuvant therapies.

12 Biomarker - Indicator of Abnormal Physiological Process

5.1. BRCA1 and BRCA2

become clinically apparent.

cations.

Among BRCA1 mutation carriers, the estimated breast cancer risk is about 65%, the estimated risk of contralateral breast cancer occurrence results 60%, the cumulative risk of ovarian cancer varies between 27 and 45%, and there is also a significantly increased risk of fallopian tube, uterine and cervical cancer, as well as of male breast cancer, stomach, pancreatic, colon and testicular cancer [123–126].

Among BRCA2 mutation carriers, the estimated lifetime breast cancer risk ranges between 45 and 84%, and that of ovarian cancer between 10 and 20% [123, 127]. There is an increased male breast cancer risk of about 6%, as well as an increased risk of prostate, pancreatic, stomach, gallbladder and bile duct cancers, and malignant melanoma [122, 128].

More than 500 coding region sequence variations have been detected in BRCA1 and 250 in BRCA2. Most unequivocally confirmed mutations reported to date are truncating mutations, adding little in the way of clues for defining functional regions. Although few mutations have been identified in either gene in sporadic breast cancers, a phenotype termed "BRCAness" exist, in which the BRCA1 and BRCA2 proteins act may be somehow disrupted also in sporadic cancer [129]. Finally, there are also some syndromes characterized by an increased breast cancer susceptibility, which are discussed in the following section.

Although germline mutations in BRCA1 and BRCA2 confer a high risk of breast cancer, a great deal of variability has been observed in cancer risk among individuals, both between and within families, as many environmental or genetic factors can modify the penetrance of BRCA1 and BRCA2 mutations. The Consortium of Investigators of Modifiers of BRCA1 and BRCA2 (CIMBA), analyzing DNA and clinical data from approximately 10,000 BRCA1 and 5000 BRCA2 mutation carriers, demonstrated the role of a number of gene variants in affecting the penetrance in mutation carriers [130].

The most important prognostic modifiers of BRCA1 and BRCA2 mutation carriers are prophylactic oophorectomy and the use of tamoxifen for chemoprevention, which approximately halve the breast cancer risk and decrease the risk of ovarian cancer by about 95% [131, 132].

In comparison with sporadic breast cancers, those related with high-penetrance susceptibility genes correlate with younger age at diagnosis, more aggressive tumor biological behavior, bilaterality, and the eventual coexistence of other cancers in the same individual or in other individuals of the same family, including ovarian, colon, prostate, pancreatic, and endometrial cancers, as well as sarcomas and male breast cancer [133].

Breast cancers arising in BRCA1 mutation carriers are frequently, although not exclusively, basal-like and ER-negative, probably because BRCA1 plays a crucial role in the transcriptional regulation of ER [129, 134]. On the other hand, breast cancer originated in BRCA2 mutation carriers are typically much more similar to sporadic cases, despite with higher grading, higher frequency of ER-positivity and lower frequency of HER2/neu overexpression [135].

The three multigene tests for breast cancer which are commercially available and currently used in the clinical practice are the Oncotype DX test (Genomic Health, Redwood, CA, USA), the MammaPrint test (Netherlands Cancer Institute™ and Agendia™, Netherland), and the Prosigma one (NanoString Technologies, Seattle, WA, USA). The Oncotype DX test is the most widely used molecular test in the therapeutic decision-making, is strongly predictive for endocrine responsiveness in hormone receptor-positive breast cancers with 0–3 positive nodes, and is recommended by both the National Comprehensive Cancer Network (NCCN) and the

Biomarkers in Breast Cancer

15

http://dx.doi.org/10.5772/intechopen.77320

The Oncotype DX is a real-time reverse transcriptase chain reaction (RT-PCR) assay, which measures the expression of a panel of 21 genes in formalin-fixed paraffin-embedded samples, including 16 cancer-related genes (ER, PR, Bcl2, SCUBE2, HER2, GRB7, Ki-67, STK15, survivin, cyclin B1, MYBL2, stromelysin 3, cathepsin L2, GSTM1, CD68, and BAG1) and 5 housekeeping control genes (beta-actin, GAPDH, RPLPO, GUS, and TFRC), to generate a recurrence score to stratify breast cancer patients into three risk groups. The low risk group (score < 18), the intermediate (score 18–30), and the high risk one (score ≥ 31) have a 10-year distant recurrence

The MammaPrint assay is the second most commonly ordered molecular test approved by the US-FDA and measure the expression of 70 genes involved in the cell cycle, invasion, proliferation, angiogenesis, metastasis, and signal transduction, none of which is tested by the Oncotype DX assay. The MammaPrint customized microarray contains a reduced set of 1900 probes suitable for high-throughput processing, and allows the use of less RNA and a short processing time of 5 days. This assay can be applied in both node-positive and node-negative and both hormone-positive and hormone-negative cancers, it is predictive for responsiveness to chemotherapy and prognostic for early distant recurrence within the first 10 years after diagnosis, which results 13 and 56% respectively in the low- and high-risk group [147–149].

The Prosigna test is an assay approved by the US-FDA which measures the expression of 50 target genes and 5 constitutively expressed normalization genes, using a proprietary technology called the "nCounter Dx Analysis System." The assay is highly sensitive and precise and uses 250 ng of RNA from formalin-fixed paraffine-embadded tumor tissue, and generates a risk of recurrence score, which assesses the 10-year risk of distant recurrence for hormone receptor-positive stage I–III breast cancers to be treated with adjuvant endocrine therapy, and correlates to one of the five molecular subtypes previously described [143, 150]. The Prosigna assay results superior to the Oncotype DX test in predicting late distant recurrence after

The authors would like to thank the whole collaborating staff of the Universitât dal Friûl, and

St. Gallen Consensus [7, 145, 146].

5–10 years [9, 151].

Acknowledgements

the support from Ennergi research non-profit association.

rate of respectively 6.8, 14.3, and 30.5% [144].

Breast cancer prognosis in BRCA1 and BRCA2 mutation carriers is still controversial, and if some authors describe a worse prognosis even in classically low-risk node-negative disease [136], other exclude any significant difference if compared to the general breast cancer population [137]. Furthermore, BRCA1 and BRCA2 mutation carriers result to have an increased risk of contralateral breast cancer occurrence [138].

New drugs have been purposed as a promising therapeutic strategy in BRCA defective tumor cells, such as the inhibitors of the poly(adenosine diphosphate-ribose) polymerase-1 (PARP1), which is an enzyme involved in the single-stranded DNA repair that use base excision repair.

Other breast cancer susceptibility genes have been described, which can be divided into three categories in terms of mutation risk and the frequency of mutation. Along with BRCA1 and BRCA2 gene mutation, the first category includes PTEN and TP53 gene mutations, which are classified as high-penetrance, low-frequency predisposition genes, and the occurrence of even one of these mutations can increase the risk of breast cancer to 25% [139, 140]. The second category includes the CHEK2, ATM, PALB and BRIP1 2 genes, which are moderate-penetrance, low-frequency predisposition genes, and lead to an increased risk of cancer of twofold to fourfold [110]. Finally, the third category consists of the FGFR2, MAP3K1,and TGFB1 gene mutations, which are low-penetrance, high-frequency predisposition genes [141].

#### 5.2. Multigene signatures

In the last decades, many genomic and molecular classification have been described with a prognostic intent. The most famous divides breast cancers into the following subtypes: luminal A, luminal B, HER2-enriched, basal-like, and normal-like [142]. Luminal subtypes express high levels of ER, they usually have an indolent clinical course, with a low distant recurrence rate, which anyway persists even up to 15 years after the diagnosis. Luminal B subtypes express fewer ER-related genes, have a higher proliferation rate and may overexpress HER2/neu, so that they usually require to be treated with both hormonal therapy and chemotherapy. HER2 enriched subtype exhibits HER2/neu gene amplification but does not express ER-related genes, they have an aggressive natural clinical course but fortunately respond very well to HER2 targeted therapy. The basal-like or triple-negative subtype does not express ER, PR, and HER2/ neu but expresses basal cytokeratins 5/6 and 17, they have a poor prognosis and a high recurrence rate.

The first molecular signature of breast cancer was determined in 2000 by the expression of a set of genes within the tumor, which were able to predict the clinical outcome [143]. The main limitations of gene signature profiling include difficulties in reproducing the specific gene sets, testing expense, and reporting standardization. However, gene signature cannot be substituted by IHC surrogates which have significant discordances with genetic profiling [144].

The three multigene tests for breast cancer which are commercially available and currently used in the clinical practice are the Oncotype DX test (Genomic Health, Redwood, CA, USA), the MammaPrint test (Netherlands Cancer Institute™ and Agendia™, Netherland), and the Prosigma one (NanoString Technologies, Seattle, WA, USA). The Oncotype DX test is the most widely used molecular test in the therapeutic decision-making, is strongly predictive for endocrine responsiveness in hormone receptor-positive breast cancers with 0–3 positive nodes, and is recommended by both the National Comprehensive Cancer Network (NCCN) and the St. Gallen Consensus [7, 145, 146].

The Oncotype DX is a real-time reverse transcriptase chain reaction (RT-PCR) assay, which measures the expression of a panel of 21 genes in formalin-fixed paraffin-embedded samples, including 16 cancer-related genes (ER, PR, Bcl2, SCUBE2, HER2, GRB7, Ki-67, STK15, survivin, cyclin B1, MYBL2, stromelysin 3, cathepsin L2, GSTM1, CD68, and BAG1) and 5 housekeeping control genes (beta-actin, GAPDH, RPLPO, GUS, and TFRC), to generate a recurrence score to stratify breast cancer patients into three risk groups. The low risk group (score < 18), the intermediate (score 18–30), and the high risk one (score ≥ 31) have a 10-year distant recurrence rate of respectively 6.8, 14.3, and 30.5% [144].

The MammaPrint assay is the second most commonly ordered molecular test approved by the US-FDA and measure the expression of 70 genes involved in the cell cycle, invasion, proliferation, angiogenesis, metastasis, and signal transduction, none of which is tested by the Oncotype DX assay. The MammaPrint customized microarray contains a reduced set of 1900 probes suitable for high-throughput processing, and allows the use of less RNA and a short processing time of 5 days. This assay can be applied in both node-positive and node-negative and both hormone-positive and hormone-negative cancers, it is predictive for responsiveness to chemotherapy and prognostic for early distant recurrence within the first 10 years after diagnosis, which results 13 and 56% respectively in the low- and high-risk group [147–149].

The Prosigna test is an assay approved by the US-FDA which measures the expression of 50 target genes and 5 constitutively expressed normalization genes, using a proprietary technology called the "nCounter Dx Analysis System." The assay is highly sensitive and precise and uses 250 ng of RNA from formalin-fixed paraffine-embadded tumor tissue, and generates a risk of recurrence score, which assesses the 10-year risk of distant recurrence for hormone receptor-positive stage I–III breast cancers to be treated with adjuvant endocrine therapy, and correlates to one of the five molecular subtypes previously described [143, 150]. The Prosigna assay results superior to the Oncotype DX test in predicting late distant recurrence after 5–10 years [9, 151].


Telenursing Future in Solving the Nursing Global Workforce Gap

*Zainab Attia Abdallah, Engy Abdel Rahman Khamis, Fatma M. Ibrahim and Ayiat Allah Wagdy Farag*

### **Abstract**

Although there are 28 million nurses worldwide, it is not enough to meet patient needs. So we face a future with too much work, with too few workers. Telenursing can help in solving this issue by utilizing the technology in providing distance healthcare and health education to patients/clients with lower costs, effective services and proper clients' satisfaction especially in rural areas through insufficient accessibility to local clinics or hospitals. Telenursing can use phone calls, video visits and remote monitoring devices in different nursing fields as family, pediatric, geriatric nursing and/or others. Telenursing can improve the quality of nursing care for patients by building relationships with them and improve the preferable outcomes. Telenursing also can decrease the work burden on nurses and direct contacts with patients with negative related health consequences specially after COVID 19 pandemic.

**Keywords:** telenursing, telehealth, telemedicine, distance healthcare, nursing practice, nursing education, nursing shortage, technology, COVID 19 pandemic

### **1. Introduction**

Telenursing means use of digital devices as phone calls, video visits and remote monitoring devices in different nursing fields as family, pediatric, geriatric nursing and/ or others. Telenursing means as the nursing services can be provided through electronic platforms, which includes phone calls, video conferences and remote patients' monitoring through different electronic devices. Applying of telenursing in healthcare systems with related health and safety benefits, can provide high quality of life and significant financial benefits to all of patients, family and health and welfare services. It creates the necessary for the development of electronic learning (e-learning) in nursing, telenursing simulation, evidence based nursing practice and nursing research. Telenursing also includes health education services, vital signs' regular remote monitoring, ECG or blood pressure and remote doctor or nurse-patient consultations as needed [1].

According to the American Telemedicine Association, 50% of health services could be provided by telehealth. To cover the needs of healthcare systems and to achieve the balance between the health team workforce and the quality of care, we need to 1.1 million new registered nurses at least. The Global Healthcare Expert, Dr. Mark Britnell, reported that by 2030, the global will face a future with too much work, with too few workers. He said: "We will reach 18 million health workers short by 2030 and this represents a gap to care." So, the need for solving the nursing and health team workforce become very necessary from now. Appearance of many global technological methods in health care delivery systems through COVID 19 pandemic, may make the problem solution slightly easy [2].

Telehealth offers flexibility and accessibility of patients to their documents and nurses and health care providers safely from home, with more control of their health care. Additionally, nurses can be accessed with telehealth equipment to host virtual meetings with their patients. Using telenursing in providing health care has several advantages as cost savings, convenience, and overcoming patients' care with mobility limitations especially rural areas' citizens who meet difficulties in accessibility to healthcare resources [3].

The integration of telenursing principles in academic programs becomes very necessary to expand the documentation bases for telenursing services and to develop such a new nursing theory involving the impact of telenursing on patient, family, community, health care delivery systems and research protocols. The future challenges in telenursing could be the technological advancement in health care systems and the training of future nurses and health care providers based on clinical simulation and online courses to apply distance-based nursing care [4].

## **2. Overview of telehealth and telenursing**

Telehealth or telemedicine is defined as where a health provider can provide care or health services without a direct face-to-face office visit, but from a distance and is done electronically, online with internet access with different devices as a computer, tablet or smartphone. Telemedicine also has many other definitions as Mobile Health or Health Mobile, Telehealth and E-Health. Telehealth Nursing is applying of different telehealth technologies as tools to provide health care in a variety of ways as addressing of social determinants of health such as [5]:

Telenursing refers to using of information technology in providing nursing care and services through mobile devices and computers whenever distance exists between patient-nurse, or between a number of nurses or health care providers. Based on accessibility of mobile devices, telehealth becomes more prevalent as one of healthcare options. Telenursing as a field, is a part of telemedicine, and has a direct and indirect contacts with other medical applications and others of non-medical, as tele-diagnosis, teleconsultation and tele-monitoring. Telenursing enables patients from connecting nurses through mobile devices/applications, video technology, computers and also remote patient monitoring. So healthcare does not be limited to in-patient clinical setting, patient can access nurse and/or primary care providers at any location [6].

### *Telenursing Future in Solving the Nursing Global Workforce Gap DOI: http://dx.doi.org/10.5772/intechopen.110745*

There is a variety of tools using in providing health care through telenursing. As well as, nurses can use telenursing for sending information to patients through websites or mobile applications. They can monitor patient condition regularly through remote monitoring. However, telehealth and telenursing are not comprehensive enough and still being developed, they become more utilized than ever as clients are preferring face to face interaction with nurses or other healthcare providers. Recently, telenursing is growing up in many countries. This growing in some countries may be because of the preoccupation in driving down the affordability of health care services, increasing of aging and chronically ill persons and the increase in desiring of coverage of health care to distant, rural areas, small/sparsely populated regions. There are many examples of applying telenursing technology as a tool of providing care as the following [7]:

### **3. Historical background of telehealth and telenursing**

In 1870s, Graham Bell the inventor of telephone carried out the first telephonic call aiming for management of battery acid burns. In 1912, Australian Inland Mission applied nursing care for nurses in remote areas. In 1929, The first telenursing service was through the Trager pedal radio processing services communication between outpost nurses and flying doctors. In 1960 National Aeronautics and Space Administration (NASA) invented and applied a telemedicine to monitor astronauts' health. During 1970s, some health organizations used nurses to give advices through telephone. In 1974, Mary Quinn documented the Logan airport care providing to patients from Boston through telemedicine [5]. In 1997, the Indian Apollo group of hospitals carried out telemedicine via the first outreach use of communication technology. Following that in 2003, a telehealth certificated course was started by Apollo group of hospitals with cooperation with Annamalai University by training of 30 students in each batch. In 2005, International Council for Nurses (ICN) conducted the international telenursing survey which revealed that nearly 719 tele-nurses responded positively. After 2005 and all over the world, telenursing became to be applied more, and nurses and patients' tele-interaction become more noticed and advanced gradually [8]. By spreading of COVID 19 pandemic in the end of 2019, different countries have directed to use innovative methods for fighting against COVID 19 virus. The main challenges for all healthcare systems all over the world were large number of patients, in addition to who could be cared at home, shortage of health team members especially doctors and nurses, lack of intensive care units' facilities and lack of

hospital capacities. Therefore, recent methods had been proposed, tele-nursing was one of the good ways to control COVID 19 pandemic [9].

### **4. Telenursing' legal, ethical and regulatory issues**

Telenursing is surrounded by legal, ethical and many regulatory issues, as what happens with telehealth. Those legal issues such as malpractice, negligence and accountability, etc. are also still repeated and difficult to address. Ethical issues also include maintaining autonomy, patient's integrity as well as harmless of clients. In many countries, practical telenursing is forbidden because, the tele-nurse must have a doubled license; one in state/country of residence and another in the location where patient receiving telecare and services. So, the *telenursing licensure* helps in resolving some of these issues [10].

Telenursing professionals store and chart patient data using an electronic medical record (EMR). Transmission of digital clinical data can increase the risk that outside sources may break the confidentiality of sensitive patient information by intercepting and exploiting them. Therefore, tele-nurses should strongly audit all of their current and available security measures and assess how to protect their patient privacy and protection through applying of policies. Most of tele-nurses are working for a hospital or organization which providing them by laptops with a recent and very high level of security and encryption, so that hackers and/or other outside sources cannot intercept patients' confidential sensitive and personal information [11].

Currently, the Health Insurance Portability and Accounting Act (HIPAA) summarize rules and regulations discussing how nurses and healthcare providers protect patients' personal data through storing and sharing. HIPAA declares that patients' identifiable information should to be encrypted so that only the nurses and other healthcare professionals involved in patients' care can access it. In addition to, many other considerations related to the patients' confidentiality and safety of their clinical data [10, 11].

### **5. Types of telenursing delivery models in nursing practice**

Mainly, there are three types of Telenursing delivery models. The *first model* is storing and forwarding technologies to enable transferring of diagnostic imaging and physiologic data starting with digitally generated, stored then transferred as needed, without necessary of patient's presence. For example, vital signs, lab results, diagnostic tests such as MRI, CT, ultrasound and x-rays. *Second model* is live videoconferencing which is carried out by using of advanced telecommunication technologies such as virtual two-way, real-time using computers, microphones, audio and video transfer. It can be used for live visits specially for mental health, urgent care, patient education and other care management. Remote monitoring is the *third model*, using remotely for monitoring patients through digital technology to collect medial information then transmitting it to other specified healthcare providers at another location which named as Center for Connected Health Practice (CCHP). *Fourth model* is mobile health (MHealth) which means using of smart phones or mobile devices in healthcare provision. It means that any nursing care or health services can be provided through a combination of all or some of the other telehealth types. For example, using of mobile

devices in patients' home which can transmit daily vitals, lab results for more frequent access to care, as diabetes and cardiac diseases [12].


**1. Introduction**

16 Will-be-set-by-IN-TECH

238 Principal Component Analysis

Wright, J., Peng, Y., Ma, Y., Ganesh, A. & Rao, S. (2009). Robust principal component

Yamazaki, M., Xu, G. & Chen, Y. (2006). Detection of moving objects by independent component analysis, *Asian Conference on Computer Vision (ACCV) 2006* pp. 467–478.

*Neural Information Processing Systems, NIPS 2009* .

analysis: Exact recovery of corrupted low-rank matrices by convex optimization,

Batch processes play an important role in the production and processing of low-volume, high-value products such as specialty polymers, pharmaceuticals and biochemicals. Generally, a batch process is a finite-duration process that involves charging of the batch vessel with specified recipe of materials; processing them under controlled conditions according to specified trajectories of process variables, and discharging the final product from the vessel.

Batch processes generally exhibit variations in the specified trajectories, errors in the charging of the recipe of materials, and disturbances arising from variations in impurities. If the problem not being detected and remedied on time, at least the quality of one batch or subsequent batches productions is poor under abnormal conditions during these batch operations. Prior to completion of the batch or before the production of subsequent batches, batch processes need effective strategy of real-time, on-line monitoring to be detected and diagnosed the faults and hidden troubles earlier and identified the causes of the problems for safety and quality.

Based on multivariable statistical analysis, several chemometric techniques have been proposed for online monitoring and fault detection in batch processes. Nomikos and MacGregor (1994, 1995) firstly developed a powerful approach known as multiway principal component analysis (MPCA) by extending the application of principal component analysis (PCA) to three-dimensional batch processes. By again projecting the information contained in the process-variable trajectories onto low-dimensional latent-variable space that summarizes both the variables and their time trajectories, the main idea of their approach is to compress the normal batch data and extract information from massive batch data. A batch process can be monitored by comparing with its time progression of the projections in the reduced space with those of normal batch data after having set up normal batch behaviour. Several studies have investigated the applications of MPCA (Chen & Wang, 2010; Jung-hui & Hsin-hung, Chen, 2006; Kosanovich et al., 1996; Kourti, 2003; Westerhuis et al., 1999).

Many of the variables monitored in one process are not independent in some cases, may be combination of independent variables not being measured directly. Independent component analysis (ICA) can extract the underlying factors or components from non-Gaussian

On-Line Monitoring of Batch Process with Multiway PCA/ICA 241

the new batch trajectory and historical trajectories, to fill the subsequent unknown portion of the new batch trajectory with the corresponding part of the history one with

Recently, for online monitoring of batch process, some papers were involved in GCC prediction after DTW synchronization with MPCA/MICA (Bai et al., 2009a, 2009b; Gao et al., 2008b), other works were concerned with GCC prediction after OFA synchronization with MPCA/MICA (Bian 2008; Bian et al., 2009; Gao et al., 2008a). These examples proved that both DTW and OFA are integrated with GCC prediction perfectly with MPCA/MICA. In this chapter, a set of online batch process monitoring approaches are discussed. On real industrial batch process, the process data is not always followed Gaussian distribution, Compared with MPCA, MICA may reveal more hidden variation than MPCA though its complexity of computation; the methods of synchronization DTW and OFA, are applied in compound monitoring approaches respectively; four solutions for missing data of future

The chapter is organized as follows. Section 2 gives introduction of the principle of DTW and relevant method of synchronization. In section 3, the principle of OFA is also introduced in advance and narration of how the extracted coefficients from the trajectories are used for model and monitoring. Then the traditional three solutions of Nomikos and MacGregor (1995) and GCC estimation are discussed in Section 4. An industrial polyvinyl chloride (PVC) polymerization process is employed to illustrate the integrative approaches

Dynamic Time warping (DTW) is a flexible, deterministic pattern matching method for comparing two dynamic patterns that may not perfectly aligned and are characterized by similar, but locally transformed, compressed and expanded, so that similar features within (Kassidas et al.,1998) the two patterns are matched. The problem can be discussed from two

Let *R* and *T* express the multivariate trajectories of two batches, whose matrices of dimension *t*×*N* and *r*×*N*, separately, where *t* and *r* are the number of observations and *N* is the number of measured variables. In most case, *t* and *r* are not always equal, so that the two batches are not synchronized because they have not common length. Even if *t*=*r*, their trajectories may not be synchronized because of their different local characteristics. If one applies the monitoring scheme of MPCA (Nomikos and MacGregor, 1994), or the scheme of MICA (Yoo et al., 2004), by simply add or delete some measured points artificially, unnecessary variation will be included in statistical model and the subsequent statistical

On the principle of dynamic programming to minimize a distance between two trajectories, DTW warps the two trajectories so that similar events are matched and a minimum distance between them is obtained, because DTW will shift, compress or expand some feature vectors

maximum GCC.

value, are applied in an example comparatively.

**2. Dynamic time warping**

general trajectories, *R* and *T*.

in Section 5. Finally, a conclusion is presented in Section 6.

**2.1 Symmetric and asymmetric DTW algorithm**

tests will not detect the faulty batches sensitively.

to achieve minimum distance (Nadler and Smith, 1993).

multivariate statistical data in the process, and define a generative model for massive observed data, where the variables are assumed to be linear or nonlinear mixtures of unknown latent variables called as independent components (ICs) (Lee et al., 2004; Ikeda and Toyama, 2000). Unlike capturing the variance of the data and extracting uncorrelated latent variable from correlated data on PCA algorithm, ICA seeks to extract separated ICs that constitute the variables. Furthermore, without orthogonality constraint, ICA is different from PCA whose direction vectors should be orthogonal. Yoo et al. (2004) extended ICA to batch process on proposing on-line batch monitoring using multiway independent component analysis (MICA), and regarded that ICA may reveal more information in non-Gaussian data than PCA.

Although the approach proposed by Nomikos and MacGregor (1994, 1995) is based on the strong assumption that all the batches in process should be equal duration and synchronized, every operational period of the batches is almost different from others actually because of batch-to-batch variations in impurities, initial charges of the recipe component, and heat removal capability from seasonal change, therefore operators have to adjust the operational time to get the desired product quality. There are several methods to deal with the different durations for the algorithm MPCA. However, neither stretching all the data length to the maximum by simply attaching the last measurements nor cutting down all 'redundant trajectories' to the minimum directly could construct the process model perfectly. Kourti et al. (1996) used a sort of indicator variable which is followed by other variables to stretch or compress them applied on industrial batch polymerization process. Kassidas et al. (1998) presented an effective dynamic time warping (DTW) technique to synchronize trajectories, which is flexible to transform the trajectories optimally modelling and monitoring with the concept of MPCA. DTW appropriately translates, expands and contracts the process measurements to generate equal duration, based on the principle of optimally of dynamic programming to compute the distance between two trajectories while time aligning the two trajectories (Labiner et al., 1978). Chen and Liu (2000) put forward an approach to transform all the variables in a batch into a series of orthonormal coefficients with a technique of orthonormal function approximation (OFA), and then use those coefficients for MPCA and multiway partial least square (MPLS) modelling and monitoring (Chen and Liu, 2000, 2001). One group of the extracted coefficients can be thought as abbreviation of its source trajectory, and subsequent relevant information of the projection from PCA can reveal the variation information of process well.

About the measures of online monitoring MPCA, Nomikos and MacGregor (1995) presented three solutions: filling the future observation with mean trajectories from the reference database; attaching the current deviation as the prediction values of incomplete process; and partial model projection that the known data of appeared trajectories are projected onto the corresponding partial loading matrix. The former two schemes are introduced to estimate the future group of data by just filling hypothesis information simply, without consideration of possible subsequent variations; and on the latter scheme only part information of MPCA model is used with the appeared trajectories projection onto the corresponding part of loading matrix of MPCA to analyze the variation of local segments. Therefore the indices of monitoring may be inaccurate on the above three solutions. To eliminate the errors of monitoring, Gao and Bai (2007) developed an innovative measure to estimate the future data of one new batch by calculation of the Generalized Correlation Coefficients (GCC) between 240 Principal Component Analysis

multivariate statistical data in the process, and define a generative model for massive observed data, where the variables are assumed to be linear or nonlinear mixtures of unknown latent variables called as independent components (ICs) (Lee et al., 2004; Ikeda and Toyama, 2000). Unlike capturing the variance of the data and extracting uncorrelated latent variable from correlated data on PCA algorithm, ICA seeks to extract separated ICs that constitute the variables. Furthermore, without orthogonality constraint, ICA is different from PCA whose direction vectors should be orthogonal. Yoo et al. (2004) extended ICA to batch process on proposing on-line batch monitoring using multiway independent component analysis (MICA), and regarded that ICA may reveal more information in non-

Although the approach proposed by Nomikos and MacGregor (1994, 1995) is based on the strong assumption that all the batches in process should be equal duration and synchronized, every operational period of the batches is almost different from others actually because of batch-to-batch variations in impurities, initial charges of the recipe component, and heat removal capability from seasonal change, therefore operators have to adjust the operational time to get the desired product quality. There are several methods to deal with the different durations for the algorithm MPCA. However, neither stretching all the data length to the maximum by simply attaching the last measurements nor cutting down all 'redundant trajectories' to the minimum directly could construct the process model perfectly. Kourti et al. (1996) used a sort of indicator variable which is followed by other variables to stretch or compress them applied on industrial batch polymerization process. Kassidas et al. (1998) presented an effective dynamic time warping (DTW) technique to synchronize trajectories, which is flexible to transform the trajectories optimally modelling and monitoring with the concept of MPCA. DTW appropriately translates, expands and contracts the process measurements to generate equal duration, based on the principle of optimally of dynamic programming to compute the distance between two trajectories while time aligning the two trajectories (Labiner et al., 1978). Chen and Liu (2000) put forward an approach to transform all the variables in a batch into a series of orthonormal coefficients with a technique of orthonormal function approximation (OFA), and then use those coefficients for MPCA and multiway partial least square (MPLS) modelling and monitoring (Chen and Liu, 2000, 2001). One group of the extracted coefficients can be thought as abbreviation of its source trajectory, and subsequent relevant information of the projection

About the measures of online monitoring MPCA, Nomikos and MacGregor (1995) presented three solutions: filling the future observation with mean trajectories from the reference database; attaching the current deviation as the prediction values of incomplete process; and partial model projection that the known data of appeared trajectories are projected onto the corresponding partial loading matrix. The former two schemes are introduced to estimate the future group of data by just filling hypothesis information simply, without consideration of possible subsequent variations; and on the latter scheme only part information of MPCA model is used with the appeared trajectories projection onto the corresponding part of loading matrix of MPCA to analyze the variation of local segments. Therefore the indices of monitoring may be inaccurate on the above three solutions. To eliminate the errors of monitoring, Gao and Bai (2007) developed an innovative measure to estimate the future data of one new batch by calculation of the Generalized Correlation Coefficients (GCC) between

from PCA can reveal the variation information of process well.

Gaussian data than PCA.

the new batch trajectory and historical trajectories, to fill the subsequent unknown portion of the new batch trajectory with the corresponding part of the history one with maximum GCC.

Recently, for online monitoring of batch process, some papers were involved in GCC prediction after DTW synchronization with MPCA/MICA (Bai et al., 2009a, 2009b; Gao et al., 2008b), other works were concerned with GCC prediction after OFA synchronization with MPCA/MICA (Bian 2008; Bian et al., 2009; Gao et al., 2008a). These examples proved that both DTW and OFA are integrated with GCC prediction perfectly with MPCA/MICA.

In this chapter, a set of online batch process monitoring approaches are discussed. On real industrial batch process, the process data is not always followed Gaussian distribution, Compared with MPCA, MICA may reveal more hidden variation than MPCA though its complexity of computation; the methods of synchronization DTW and OFA, are applied in compound monitoring approaches respectively; four solutions for missing data of future value, are applied in an example comparatively.

The chapter is organized as follows. Section 2 gives introduction of the principle of DTW and relevant method of synchronization. In section 3, the principle of OFA is also introduced in advance and narration of how the extracted coefficients from the trajectories are used for model and monitoring. Then the traditional three solutions of Nomikos and MacGregor (1995) and GCC estimation are discussed in Section 4. An industrial polyvinyl chloride (PVC) polymerization process is employed to illustrate the integrative approaches in Section 5. Finally, a conclusion is presented in Section 6.


**10. Conclusion**

126 Advanced Aspects of Spectroscopy

salinity 8.78mS/cm.

**9. Comparison of results**

us to characterize the results:

 It should be mentioned that the embodiment of the vast majority of measurements for suspension was made with the HP4192A impedance analyzer, considering the structure and existing coil system, the utilization ratio of the impedance analyzer is because the probes used to interconnect arrangement coils are constructed on purpose, greatly decreasing the

**Figure 25.** Impedance Representation of Biological Suspension, comparatively to the coil system.

After 35 minutes, the yeast was deposited at the bottom of the container; we proceeded to extract 350ml of water and recovered the same amount of water (350ml), but now with a

The interesting thing in this experiment as shown in Figure 25, having increased conductivity, as a result of water replaced without electrolytes, with water with electrolytes (8.78mS/cm) decreased by 6% the impedance of the suspension by the lower proportion of

Measurements of saline cell and a biological suspension with HP impedance analyzer, allow

yeast and major salinity, Zlev = 384.37Ω, Zlev + NaCl = 361.87Ω, ΔΩ = 22.5

amount of error attributable to the length of the coaxial cables.

The presentation of results, by their very short nature, could be interpreted as an activity which is not time consuming, but the opposite is true, because from the moment of preparation of the experiments, there are always a number of imponderables, such as materials or materials that are needed to carry out the measurements do not have them, at least, operating conditions, climate, lighting, etc..

For the characterization of substances, suspensions and / or solutions must take into account, and in a very particular, maintain the same amounts, and make measurements in a repetitive manner, so as to place on record its findings to conditions geometric, physical and mechanical properties, different and contrast with conditions similar to those obtained. The measurements carried out with the Network Analyzer, which was mostly used equipment, are quite contrasting with measurements made with the HP impedance analyzer. As we can see with the first, which strongly influences the distance at which measurements were made, not with the impedance analyzer as it had a "fixture" on purpose.

Speaking of the actual material used and specific the experiment with saline cell, it was found that one of the factors that influence in the admittance at low frequencies is the electrical permittivity of water. The values depend on the frequency of measurements, and the frequency sweep, this due to the response of the dielectric constant of the solution, which varies considerably with frequency.

Using a saline solution with a high degree of salinity, more than 9 g / l of salt, we see that in the graphs of the results if ε'' / ε '<2, the ε" accuracy degrades. This may be because the impedance of solutions with high salt is essentially resistive. In an opposite manner with a "window" at 999 KHz frequency on average, before the resonance frequency of the coil circuit, the impedance of the solution is essentially reactive, and since this type of impedance measurements of reflection / transmission were performed mainly with the network analyzer is a significant higher level of uncertainty in measuring the smaller capacitive component where ε" is derived.

The HP impedance analyzer measurements, both saline solutions and suspensions, allowed us to compare results, specifically ε" values. In the suspensions could be evaluated especially an increase in the impedance, over time, possibly due to increased cell growth, hence an increase in the capacitive reactance of the suspension.

Considering the results obtained, we can consider the approach to the characterization as reasonably good since the relative permittivity is much greater than unity for the dielectric (both saline solutions and biological suspensions).

One of the properties of biological tissue, such as conductivity, is well reflected by the frequency dependence, particularly in the range of 10 KHz-10MHz (β dispersion range). The conductivity at low frequencies denotes the volume of extracellular fluid essence, the additional contribution of intracellular fluid volume with a significant increase in the applied frequency causes a significant increase in conductivity.

And finally and considering the substantial increase in interest in the development of magnetic induction spectroscopy (MIS) as a valid option for obtaining the conductivity of the human body without the need for direct contact with tissue (Korzhenevskii and Cherepenin 1997 Griffiths et al. 1999, Korjenevsky et al. 2000); In addition to other passive electrical properties of biological tissues (Hermann Scharfetter, Casañas Roberto and Javier Rosell, 2003).

Since MIS is based on measurements of small changes in magnetic fields, typically of the order of 1% or less at frequencies up to 10 MHz, and also because of their physical limitations is not recommended at frequencies below 10 kHz, this also represents a great challenge in electronic design, possibly one of its greatest disadvantages.