*3.5. Reactive Index*

The reactive index quantifies how fast the actuation system is able to change the orientation of the resulting force **F***B* (ideally, **F***d B*). Suppose that the robot is traveling in a direction with a set of thruster forces **F***m*1 induced from desired force vector **F***d B*1. The robot wants to change to another direction (or the same direction with a different magnitude) with the desired force vector **F***d B*2, so the thrusters have to produce another set of thruster forces **F***m*2. The two-norm of the deviation of the thruster forces, %**F***m* = **F***m*1 − **F***m*2 = [%*Fm*1%*Fm*2 ···%*Fmm*] *T*, is considered as the reactive capability of the robot. Referring to the approximation of the characteristics of the thrusters, as Figure 9, the change from *Fm*1 to *Fm*2 is closer than that from *Fm*1 to *Fm*3 (in the linear section, the dead-zone of the thruster characteristics is neglected in this paper). Hence, we have:

$$
\triangle \mathbf{F}\_{\mathcal{W}} = \mathbf{A}^+ (\mathbf{F}\_{B1}^d - \mathbf{F}\_{B2}^d) = \mathbf{A}^+ \triangle \mathbf{F}\_B^d \tag{9}
$$

$$\|\triangle \mathbf{F}\_m\| = \|\mathbf{A}^+ \triangle \mathbf{F}\_B^d\| \le \|\mathbf{A}^+\| \|\triangle \mathbf{F}\_B^d\| \tag{10}$$

$$\frac{\|\triangle \mathbf{F}\_{\mathsf{m}}\|}{\|\triangle \mathbf{F}\_{\mathsf{B}}^{d}\|} \leq \|\mathbf{A}^{+}\|\tag{11}$$

From Equation (11), the sensitivity of the thruster forces with respect to the desired forces, in other words the variation of the thruster forces w.r.t. the desired forces, is upperbounded by the norm of the pseudo-inverse of the configuration matrix, **A**+. We define the reactive index as:

$$I\_{\rm ref} = \|\mathbf{A}^+\|\tag{12}$$

It is obvious to see that if this index is lower, the robot is more reactive. Then, the objective of the design process is to minimize the reactive index.

**Figure 9.** Thruster characteristics' approximation.

#### *3.6. Robustness Index*

This criterion measures the robustness level of the AS of an underwater robot. This means that if any thruster of the robot fails, the remaining ones can still perform the robot's mission. In particular, for any **F***d B* vector, there always exists a **F***m* vector to satisfy the equation **F***B* = **AF***m*, and **F***B* is as close as possible to **F***d B*.

We have:

$$\mathbf{F}\_B = \mathbf{A} \mathbf{F}\_m = \sum\_{i=1}^m \mathbf{a}\_i F\_{m,i} \tag{13}$$

where **a***i* is the *i*th column of the matrix **A** and *Fm*,*i* is the force magnitude of the *i*th thruster.

When one or more thrusters completely fail, the value of *Fm*,*i* = 0. Note that in the case that the *i*th thruster has partly failed, the value of *Fm*,*i* remains small (not addressed in this paper). This is equivalent, as we considered that a corresponding column **a***i* of the configuration matrix **A** equals the zero vector. Therefore, Equation (13) is equivalent to:

$$\mathbf{F}\_B = \mathbf{A}^\prime \mathbf{F}\_m \tag{14}$$

where the **A** matrix is the **A** matrix with one or more corresponding columns equal to the zero vectors.

We discuss hereafter two questions: What are the conditions of the matrix **A** to guarantee the robustness? What is the maximum number of failed thrusters?

To address these two questions, we supposed that *k* thrusters fail, and Equation (14) is a linear equation system with six equations (the dimensions of **F***B* are 6 × 1) and (*m* − *k*) variables, because the matrix **A** is 6 × *m*, where *k* columns are zero vectors. It is obvious to see that if *rank*(**A** ) = 6, for a given **F***d B*, there always exits **F***m* such that **F***B* = **A F***m* and **F***B* is as close as possible to **F***d B*. This can be interpreted as *m* − *k* ≥ 6 or *k* ≤ *m* − 6. The condition on the configuration matrix and that on the maximum number of failed thruster that guarantee the robustness of an underwater robot are stated as:

*Iro* = *rank*(**A**|≤*m*−6) = 6 (15)

where **A**|≤*m*−6 is the **A** matrix where the maximum number of columns being zero is (*m* − 6). This index is verified in the solving process of the problem.

#### *3.7. Configuration Matrix Design Problem*

With all the performance indices discussed above, we propose the following design problem:

$$\min\_{\mathbf{A}} \mathbf{V}(\mathbf{A}) = \min\_{\mathbf{A}} \left[ I\_m \, I\_c \, \frac{1}{I\_{\text{uv}}} \, I\_{rc} \right]^T \tag{16}$$
  $s.t. \quad \mathbf{A} \in \mathbb{A}$

where **V**(**A**) is the objective function vector. A is the feasible set of the configuration matrix (**A**) including the constraints of the configuration matrix (**A**) and the robustness index. The reciprocal of the workspace index, 1 *Iw* , is in Equation (16), because we wanted to maximize the workspace index.

This is a multi-objective optimization problem, and the unique solution belongs to the convexity of each objective function in the objective vector and the feasible set, A. Note that this optimization problem is with respect to a matrix variable (*matrix optimization*), not a vector variable. However, the optimization techniques for vector variables (*vector optimization*) can be applied here because we do not lose the physical meaning when converting a matrix variable to a vector variable in this optimization problem (because of the independency of each column in the matrix derived from the independent positions and orientations of the thrusters).

Specifically, Equation (16) can be rewritten as:

$$\min\_{\mathbf{A}} \mathbf{V}(\mathbf{A}) = \min\_{\mathbf{A}} [I\_{\text{m}} \, \, \_{l} \, \frac{1}{I\_{\text{w}}} \, \_{l} \mathbf{r}\_{\text{c}}]^{T} \tag{17}$$

$$\begin{aligned} s.t. \quad & ||\mathbf{u}\_{i}|| = 1, i = 1, 2, \dots, m \\ & ||\mathbf{r}\_{i}|| \le 1, i = 1, 2, \dots, m \\ & \mathbf{r}\_{i}^{T} \mathbf{u}\_{i} = 0, i = 1, 2, \dots, m \\ & \mathbf{I}\_{\text{r}0} = \text{rank}(\mathbf{A})\_{\le m-6}) = 6 \end{aligned} $$

The problem (17) is to minimize an objective vector **V**(**A**), including the manipulability index, the energetic index, the reciprocal of the workspace index, and the reactive index, with respect to configuration matrix, **A**, and to satisfy the constraints of the matrix structure itself and the robustness index. It is clear that this is a nonconvex and multiobjective optimization problem, which normally has many solutions. In the following sections, we propose a mathematical analysis and a method for solving the multi-objective optimization problem.

#### **4. Problem Solution**

Our final objective was to find a distribution (position and orientation) of the thrusters of an underwater robot. This means obtaining the **u***i* and **r***i* vectors for *i* = 1, 2, ... , *m*. These vectors can be extracted from configuration matrix **A**, which is the solution of the problem (17). Recall that our problem (17) is the multi-objective optimization problem with nonconvexity, and theoretically, this problem has infinitely many Pareto-optimal solutions. Our objective was to find one Pareto-optimal solution to build the robot. Analyzing the underlying mathematical properties of the problem helped us simplify the solving process. Thus, the mathematical analysis of the problem is shown in the next section.

#### *4.1. Mathematical Analysis*

The configuration matrix **A** has the form:

$$\mathbf{A} = \begin{pmatrix} \mathbf{u}\_1 & \mathbf{u}\_2 & \cdots & \mathbf{u}\_m \\ \mathbf{\tau}\_1 & \mathbf{\tau}\_2 & \cdots & \mathbf{\tau}\_m \end{pmatrix} \tag{18}$$

We have:

$$\mathbf{B} = \mathbf{A}^T \mathbf{A} = \begin{pmatrix} \mathbf{u}\_1 & \mathbf{u}\_2 & \cdots & \mathbf{u}\_m \\ \mathbf{\tau}\_1 & \mathbf{\tau}\_2 & \cdots & \mathbf{\tau}\_m \end{pmatrix}^T \begin{pmatrix} \mathbf{u}\_1 & \mathbf{u}\_2 & \cdots & \mathbf{u}\_m \\ \mathbf{\tau}\_1 & \mathbf{\tau}\_2 & \cdots & \mathbf{\tau}\_m \end{pmatrix} \tag{19}$$

**B** is an *m* × *m* symmetric matrix where each element is denoted as *bij*. We have:

$$\begin{aligned} \text{Tr}(\mathbf{B}) &= \sum\_{i=1}^{m} b\_{ii} \\ &= \sum\_{i=1}^{m} \lambda\_i \end{aligned} \tag{20}$$

where *λi* is the *i*th eigenvalue of matrix **B**.

From Equations (19) and (20), we have:

$$\begin{aligned} \sum\_{i=1}^{m} \lambda\_i &= \sum\_{i=1}^{m} \mathbf{u}\_i^T \mathbf{u}\_i + \mathbf{r}\_i^T \mathbf{r}\_i \\ &= \sum\_{i=1}^{m} ||\mathbf{u}\_i||^2 + ||\mathbf{r}\_i||^2 \\ \sum\_{i=1}^{m} \lambda\_i &= \sum\_{i=1}^{m} (1 + ||\mathbf{r}\_i||^2) \end{aligned} \tag{21}$$

In the case of manipulability index optimization, the condition of configuration matrix **A** is one, *cond*(**A**) = 1. This means that the maximum singular value equals the minimum singular value, *σmax* = *σmin*. Note that the matrix **A** is the *n* × *m* matrix with *n* < *m*. The matrix **A** has *n* nonzero singular values (we have to guarantee that *rank*(**A**) = *n*), then the matrix **B** has *n* nonzero eigenvalues and *m* − *n* zero eigenvalues.

In the optimization case of the manipulability index, *cond*(**A**) = 1 ⇒ *σmax* = *σmin*, we have *λi* = *λmax* = *λmin* = *λ* (*σ* = √*λ*). Equation (21) is rewritten as:

$$m\lambda = m + \sum\_{i=1}^{m} ||\pi\_i||^2$$

$$\lambda = \frac{m}{n} + \frac{1}{n} \sum\_{i=1}^{m} ||\pi\_i||^2 \tag{22}$$

Considering the fact that *τi* 2 ≤ 1, we have:

$$
\lambda \le 2.\frac{m}{n} \tag{2.3}
$$

Therefore, we have *λmax* = 2 *m n* when *τi* 2 = 1.

In the singular-value decomposition of a matrix, when *cond*(**A**) = 1, the matrix **A** can be written as:

$$\mathbf{A} = \mathbf{U}\mathbf{S}\mathbf{V}^T = \mathbf{U}[\sigma]\_{n \times m}\mathbf{V}^T \tag{24}$$

where **U** ∈ R*n*×*n*, **V** ∈ R*m*×*m* are orthogonal matrices, **S** = [*σ*]*n*×*m* = ⎛ ⎜⎝ *σ* 0 ··· 0 . . . *σ* ··· 0 0 ··· *σ* 0 ⎞ ⎟⎠ ∈

R*n*×*m*

The pseudo-inverse of matrix **A** is **A**+ and can be written as:

$$\mathbf{A}^{+} = \mathbf{V}\mathbf{S}^{+}\mathbf{U}^{T} = \mathbf{V}[\frac{1}{\sigma}]\_{m \times n}\mathbf{U}^{T} \tag{25}$$

$$\text{where } \mathbf{S}^+ = [\frac{1}{\sigma}]\_{m \times n} = \begin{pmatrix} \frac{1}{\sigma} & \cdots & 0 \\ \vdots & \frac{1}{\sigma} & 0 \\ 0 & 0 & \frac{1}{\sigma} \\ 0 & \cdots & 0 \end{pmatrix} \in \mathbb{R}^{m \times n}$$

Our objective for the reactive index was to minimize **A**+. From Equation (25), the reactive index *Ire* = **A**+ = 1 *σ* , and the minimum value of the reactive index is equivalent to the maximum value of *σ*. This leads to the equality of Equation (23).

In order to minimize the reactive index and the manipulability index, the configuration matrix **A** has the following structure:

$$\begin{aligned} \mathbf{A} &= \mathbf{U} \mathbf{S} \mathbf{V}^T \\ &= \mathbf{U} \begin{pmatrix} \sigma & 0 & \cdots & 0 & 0 & 0 \\ 0 & \sigma & 0 & \cdots & 0 & 0 \\ 0 & 0 & \sigma & 0 & \cdots & 0 \\ \vdots & \vdots & \vdots & \vdots & \vdots & \vdots \\ 0 & 0 & 0 & \sigma & 0 & 0 \end{pmatrix} \mathbf{V}^T \end{aligned} \tag{26}$$

where **S**(*n* × *m*) is like-diagonal and *σ* = √*λ* = - 2 *m n* ; **U**(*n* × *n*) and **V**(*m* × *m*) are orthogonal matrices (**UU***T* = **I**, **VV***T* = **I**). This result can be used as the initial value of the numerical optimization process and is useful for solving the problem.

We continue to discuss the energetic index. First, we introduce a proposition as follows:

$$\begin{aligned} \textbf{Proposition 1.} \text{ Let } \mathbf{M} \text{ be a } p \times q \text{ matrix } (p \ge q), \mathbf{M} \in \mathbb{R}^{p \times q}. \text{ For all } \mathbf{x} \in \mathbb{R}^q, \text{ if } \mathbf{M} = \mathbf{P} \mathbf{Z} \mathbf{Q}^T, \\\\mathbf{P} \in \mathbb{R}^{p \times p}, \mathbf{Q} \in \mathbb{R}^{q \times q} \text{ are orthogonal matrices, } \mathbf{E} = \begin{pmatrix} \mu & 0 & \cdots & 0 \\ 0 & \mu & \cdots & 0 \\ 0 & \cdots & \mu & 0 \\ 0 & \cdots & 0 & \mu \\ \vdots & \vdots & \vdots & \vdots \\ 0 & 0 & 0 & 0 \end{pmatrix} \in \mathbb{R}^{p \times q}, \text{ then} \end{aligned}$$

 **Mx** = **M x** *.*

**Proof.** We have:

$$\|\mathbf{M}\mathbf{x}\|^2 = (\mathbf{M}\mathbf{x})^T(\mathbf{M}\mathbf{x}) = \mathbf{x}^T\mathbf{M}^T\mathbf{M}\mathbf{x} \tag{27}$$

With **M** = **PΣQ***T*:

$$\begin{aligned} \|\mathbf{M}\mathbf{x}\|^2 &= \mathbf{x}^T (\mathbf{P}\mathbf{\Sigma}\mathbf{Q}^T)^T (\mathbf{P}\mathbf{\Sigma}\mathbf{Q}^T) \mathbf{x} \\ &= \mathbf{x}^T \mathbf{Q} \mathbf{\Sigma}^T \mathbf{P}^T \mathbf{P} \mathbf{\Sigma} \mathbf{Q}^T \mathbf{x} \\ &= \mathbf{x}^T \mathbf{Q} \mathbf{\Sigma}^T \mathbf{\Sigma} \mathbf{Q}^T \mathbf{x} \end{aligned} \tag{28}$$

We have:

$$\mathbf{E}^T \mathbf{E} = \begin{pmatrix} \mu & 0 & \cdots & 0 \\ 0 & \mu & \cdots & 0 \\ 0 & \cdots & \mu & 0 \\ 0 & \cdots & 0 & \mu \\ \vdots & \vdots & \vdots & \vdots \\ 0 & 0 & 0 & 0 \end{pmatrix}^T \begin{pmatrix} \mu & 0 & \cdots & 0 \\ 0 & \mu & \cdots & 0 \\ 0 & \cdots & \mu & 0 \\ 0 & \cdots & 0 & \mu \\ \vdots & \vdots & \vdots & \vdots \\ 0 & 0 & 0 & 0 \end{pmatrix}$$

$$= \begin{pmatrix} \mu^2 & 0 & \cdots & 0 \\ 0 & \mu^2 & \cdots & 0 \\ \vdots & \vdots & \vdots & \vdots \\ 0 & \cdots & 0 & \mu^2 \end{pmatrix} = \mu^2 \mathbf{I} \tag{29}$$

where **I** is a *q* × *q* identity matrix.

Replacing Equation (29) to (28), we have:

$$\begin{aligned} \left\| \mathbf{M} \mathbf{x} \right\|^2 &= \mathbf{x}^T \mathbf{V} \mu^2 \mathbf{I} \mathbf{V}^T \mathbf{x} \\ &= \mu^2 \mathbf{x}^T \mathbf{x} = \left\| \mathbf{M} \right\|^2 \left\| \mathbf{x} \right\|^2 \end{aligned} \tag{30}$$

Therefore, **Mx** = **M x**.

The energetic index is stated as:

$$I\_{\varepsilon} = \frac{1}{S} \int\_{S} (w\_{\varepsilon f} \| \mathbf{A}^{+} (\mathbf{F}\_{B}^{d}(f)) \| + w\_{\varepsilon \Gamma} \| \mathbf{A}^{+} \mathbf{F}\_{B}^{d}(\Gamma) \| \right) dS \tag{31}$$

Choosing *we f* = *we*Γ = 1 (because the desired force vectors, **F***d B*(*f*), **F***d B*(*τ*), are units), we have:

$$I\_{\mathbf{f}} = \frac{1}{S} \int\_{S} (||\mathbf{A}^{+}\mathbf{F}\_{B}^{d}(f)|| + ||\mathbf{A}^{+}\mathbf{F}\_{B}^{d}(\Gamma)||)dS\tag{32}$$

In the case in which the reactive index and the manipulability index are minimum, the configuration matrix **A**(*n* × *m*) has the form of Equation (26); therefore, the pseudoinverse matrix **A**+(*m* × *n*, *m* > *n*) has the following structure:

$$\mathbf{A}^{+} = \mathbf{V} \mathbf{S}^{+} \mathbf{U}^{T} = \mathbf{V} \begin{pmatrix} \frac{1}{\sigma} & 0 & \cdots & 0 \\ 0 & \frac{1}{\sigma} & \cdots & 0 \\ 0 & \cdots & \frac{1}{\sigma} & 0 \\ 0 & \cdots & 0 & \frac{1}{\sigma} \\ \vdots & \vdots & \vdots & \vdots \\ 0 & 0 & 0 & 0 \end{pmatrix} \mathbf{U}^{T} \tag{33}$$

where **V**, **U** are orthogonal matrices.

It is clear that matrix **A**+ satisfies the condition of Proposition 1. Applying this proposition, we have: **A**+**F***d B*(*f*) = **A**+ **F***d B*(*f*) and **A**+**F***d B*(Γ) = **A**+ **F***d B*(Γ). Therefore, Equation (32) becomes:

$$\begin{split} I\_{\mathfrak{c}} &= \frac{1}{S} \int\_{S} (||\mathbf{A}^{+}|| \, ||\mathbf{F}\_{B}^{d}(f)|| + ||\mathbf{A}^{+}|| \, ||\mathbf{F}\_{B}^{d}(\Gamma)||) dS \\ &= \frac{1}{S} ||\mathbf{A}^{+}|| \int\_{S} (||\mathbf{F}\_{B}^{d}(f)|| + ||\mathbf{F}\_{B}^{d}(\Gamma)||) dS \\ &= 2 \|\mathbf{A}^{+}\| \end{split} \tag{34}$$

From the aforementioned mathematical analysis of the energetic index, we can see that the energetic index belongs to the norm of the pseudo-inverse of the configuration matrix, *Ire* = 2 **A**+, when the configuration matrix **A** has the form of (26).

We then discuss the upper-bound of the workspace index. For the units' consistency, the workspace index for the force space and that for the torque space were investigated separately, denoted as *Iw f* and *Iwτ*, respectively. Recall that the objective of the workspace index is to maximize the volume of the resulting force space (**F***B* space), including the resulting space for the force and the resulting space for the torque with given thrusters' force (the **F***m* space).

The fact that for all vectors **F***m* ∈ R*m*, **AF***m*≤**A F***m*. The volume of the resulting force space is maximum when the equality holds.

Following Figure 10, the volumes of the resulting force spaces (**F***B*) (the force and torque spaces) are always less than the volumes of the exterior hypersphere of **F***B* spaces of the force and torque (this may be the circumscribed spheres or not). This means that:

**Figure 10.** Upper-bound of the resulting force space.

$$I\_{wF} \le Vol(\mathbf{B}(R1))$$

$$I\_{wT} \le Vol(\mathbf{B}(R2)) \tag{35}$$

where **B**(*R*1) and **B**(*R*2) are Euclidean balls of radius *R*1 = **A**(**1** : **3**, :)**F***m* = **A**1 **F***m* and of radius *R*2 = **A**(**4** : **6**, :)**F***m* = **A**2 **F***m*, respectively; **A**(**1** : **3**, :) is composed of the first three rows of **A**, and **A**(**4** : **6**, :) is composed of the last three rows of **A**.

The volume of a Euclidean ball of radius *R* in *n*-dimensional Euclidean space is [21]:

$$V\_{\mathbb{M}}(R) = \begin{cases} \frac{\pi^k}{k!} R^{2k}, & \text{if } \mathbb{M} = 2k\\ \frac{2^{k+1}\pi^k}{(2k+1)!!} R^{2k+1}, & \text{if } \mathbb{M} = 2k+1. \end{cases} \tag{36}$$

where (2*k* + 1)!! = 1.3.5, . . . ,(2*k* − 1).(2*k* + 1).

**Proposition 2.** *If the configuration matrix* **A** *has the form of* (26)*, then cond*(**A**1) = *cond*(**A**2) = 1 *and* **A**1 = **A**2 = *σ.*

**Proof.** We have:

$$\begin{split} \mathbf{A} \mathbf{A}^T &= (\mathbf{U} \mathbf{S} \mathbf{V}^T)(\mathbf{U} \mathbf{S} \mathbf{V}^T)^T = \mathbf{U} \mathbf{S} \mathbf{V}^T \mathbf{V} \mathbf{S}^T \mathbf{U}^T \\ &= \mathbf{U} \mathbf{S} \mathbf{S}^T \mathbf{U}^T = \sigma^2 \mathbf{I} \end{split} \tag{37}$$

On the other hand:

$$\begin{aligned} \mathbf{A}\mathbf{A}^T &= \begin{pmatrix} \mathbf{A}\_1 \\ \mathbf{A}\_2 \end{pmatrix} \begin{pmatrix} \mathbf{A}\_1 \\ \mathbf{A}\_2 \end{pmatrix}^T = \begin{pmatrix} \mathbf{A}\_1 \\ \mathbf{A}\_2 \end{pmatrix} (\mathbf{A}\_1^T \mathbf{A}\_2^T) \\ &= \begin{pmatrix} \mathbf{A}\_1 \mathbf{A}\_1^T & \mathbf{0} \\ \mathbf{0} & \mathbf{A}\_2 \mathbf{A}\_2^T \end{pmatrix} \end{aligned} \tag{38}$$

From (37) and (38), we have:

$$\mathbf{A}\_1 \mathbf{A}\_1^T = \sigma^2 \mathbf{I}\_1$$

$$\mathbf{A}\_2 \mathbf{A}\_2^T = \sigma^2 \mathbf{I}\_2\tag{39}$$

where **I**1 and **I**2 are partitioned matrices of matrix **I**.

From (39) and the uniqueness of singular-value decomposition [22], it is obvious to see that the structures of **A**1 and **A**2 are the same as (26) with different dimensions. Therefore, *cond*(**A**1) = *cond*(**A**1) = 1 and **A**1 = **A**2 = *σ*.

From (35) and (36) and Proposition 2, it is obvious to obtain the upper-bound of the resulting spaces of the force and torque of the system and then the upper-bound of the workspace index. Normally, the weighting coefficients in the workspace index are chosen as one because of our assumption of *di*.

#### *4.2. Problem Solution*

Based on the above mathematical analysis, the goal-attainment method was chosen to solve the problem with the given desired values. The idea of this method is to minimize the deviation of the desired values and the obtained values. One advantage of the goalattainment method is that the problem does not need to be normalized to a dimensionless problem. The solution of this method has been proven to be Pareto-optimal. This method is also suitable when the feasible objective set is nonconvex [23]. All Pareto-optimal solutions may be found by changing the attainment vector; however, this depends on the properties of the problem.

Our problem using the goal-attainment method becomes:

$$\begin{aligned} \min\_{\mathbf{A}, \gamma} & \gamma\\ \text{s.t.} & \mathbf{A} \in \mathbb{A} \\ & \mathbf{V}(\mathbf{A}) - \mathbf{w}\gamma \le \mathbf{V}\_{\text{goal}} \end{aligned} \tag{40}$$

where A¯ = A \ *Iro*, i.e., the feasible set of configuration matrices, **A**, without robustness index *Iro*, *γ* is a slack vector variable, and **V***goal* = [*Id m Id e* 1 *Id w Id re*] is the desired objective vector, **w** is an attainment vector, which can be chosen. The goal-attainment method with two objective functions is illustrated in Figure 11. By altering **w** vector, we searched for the Pareto-optimal solutions.

Therefore, our solving process included two phases:

The optimization toolbox in the MATLAB environment was used to solve our problem. Note that our problem was formulated as a multi-objective optimization problem. One objective has one desired value excluding the robustness index, which is as a constraint, and therefore, the desired vector is set up. The goal-attainment method was used to solve the problem. An attainment vector was chosen as a trade-off between the underachievement and overachievement of the objective functions. In multi-objective optimization, an optimal solution depends on a decision maker. Theoretically, there is no method for this choice. In our work, this vector was selected by trial and error. In particular, for the

manipulability, reactivity, and energetic indices, we know exactly the desired values, so the corresponding values in the attainment vector were chosen as zero, which means that these are hard constraints. For the workspace index, we only know the upper-bound of the desired value; therefore, a positive value was chosen for underachievement.

**Figure 11.** Goal-attainment method with two objective functions.


*Article* **The Prognosis Performance of a Neutrophil- and Lymphocyte-Associated Gene Mutation Score in a Head and Neck Cancer Cohort**

**Tsung-Jang Yeh 1,2,3, Hui-Ching Wang 1,2,4, Shih-Feng Cho 1,3,4, Chun-Chieh Wu 5, Tzu-Yu Hsieh 1, Chien-Tzu Huang 1,2, Min-Hong Wang 1,2, Tzer-Ming Chuang 1, Yuh-Ching Gau 1,2, Jeng-Shiun Du 1,2, Yi-Chang Liu 1,3,4, Hui-Hua Hsiao 1,3,4, Mei-Ren Pan 2,6,7, Li-Tzong Chen 3,8,9 and Sin-Hua Moi 2,10,\***

**Abstract:** The treatment of head and neck squamous cell carcinomas (HNSCCs) is multimodal, and chemoradiotherapy (CRT) is a critical component. However, the availability of predictive or prognostic markers in patients with HNSCC is limited. Inflammation is a well-documented factor in cancer, and several parameters have been studied, with the neutrophil-to-lymphocyte ratio (NLR) being the most promising. The NLR is the most extensively researched clinical biomarker in various solid tumors, including HNSCC. In our study, we collected clinical and next-generation sequencing (NGS) data with targeted sequencing information from 107 patients with HNSCC who underwent CRT. The difference in the NLR between the good response group and the poor response group was significant, with more patients having a high NLR in the poor response group. We also examined the genetic alterations linked to the NLR and found a total of 41 associated genes across eight common pathways searched from the KEGG database. The overall mutation rate was low, and there was no significant mutation difference between the low- and high-NLR groups. Using a multivariate binomial generalized linear model, we identified three candidate genes (*MAP2K2*, *MAP2K4*, and *ABL1*) that showed significant results and were used to create a gene mutation score (GMS). Using the NLR-GMS category, we noticed that the high-NLR-GMS group had significantly shorter relapse-free survival compared to the intermediate- or low-NLR-GMS groups.

**Keywords:** genomic mutation signature; neutrophil to lymphocyte ratio; head and neck cancer; prognostic biomarker

**Citation:** Yeh, T.-J.; Wang, H.-C.; Cho, S.-F.; Wu, C.-C.; Hsieh, T.-Y.; Huang, C.-T.; Wang, M.-H.; Chuang, T.-M.; Gau, Y.-C.; Du, J.-S.; et al. The Prognosis Performance of a Neutrophil- and Lymphocyte-Associated Gene Mutation Score in a Head and Neck Cancer Cohort. *Biomedicines* **2023**, *11*, 3113. https:// doi.org/10.3390/biomedicines11123113

Academic Editor: Vui King Vincent-Chong

Received: 8 May 2023 Revised: 16 November 2023 Accepted: 21 November 2023 Published: 22 November 2023

**Copyright:** © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

7

#### **1. Introduction**

Head and neck squamous cell carcinoma (HNSCC) is mostly derived from the mucosal epithelium of the oral cavity, pharynx, and larynx [1]. It is the most common malignancy of the upper aerodigestive tract and was ranked fourth in a Taiwanese male cohort study [2,3]. HNSCC treatment is generally multimodal and differs according to the disease stage, anatomical location, and surgical accessibility to achieve the most curative approach while optimizing the preservation of function [1,4]. Some early-stage diseases are curable with surgery or definitive radiotherapy; however, more than 60% of patients present with locally advanced disease upon diagnosis [5].

Concurrent platinum-based chemotherapy and radiotherapy, also referred to as chemoradiotherapy (CRT) or concurrent chemoradiotherapy (CCRT), plays an important role in HNSCC treatment. When considering organ preservation, definite CRT is recommended as a nonsurgical treatment for most patients with advanced pharyngeal and laryngeal cancers [6]. In postoperative management, the efficacy of adjuvant CRT has been proven in two multicenter randomized trials (EORTC 22931 and RTOG 9501) for highrisk patients with HNSCC, especially those with extranodal extension or positive surgical margins [7,8]. Despite the development of risk-adapted curative treatment strategies and other progress in therapeutic modalities, the overall 5-year survival is only 50%, and 65% of patients with an advanced stage of the disease have significantly compromised survival [9]. Therefore, in addition to the development of novel treatment approaches, the search for predictive or prognostic markers in patients with HNSCC is necessary.

To date, approximately 70 markers have been evaluated and reported from either blood or tumor tissues [10–12]. In the conventional treatment era, epidermal growth factor receptor (EGFR), p16, human papillomavirus (HPV), cyclin D1 (CCND1), B cell lymphomaextra large (Bcl-xL)/Bcl-2 and excision repair cross complementation group 1 (ERCC1) have been identified as possible prognostic markers in clinical trials [11,12]. In the current immunotherapy era, programmed death ligand-1 (PD-L1) expression, tumor mutational burden (TMB), microsatellite instability (MSI), HPV status, smoking status, circulating tumor cells (CTCs), circulating tumor DNA (ctDNA), gut or oral cavity microbiota, and tumor-microenvironment-related gene expression profiles have been suggested as potential immune biomarkers to predict the efficacy of immune checkpoint inhibitors [12].

In 1863, Virchow established a connection between inflammation and cancer based on his observations [13]. Since then, research on the association between inflammation and carcinogenesis has increased, supporting Virchow's theory [14]. Inflammation is now characterized as a critical component of tumor progression based on its contribution to the multiple hallmarks of tumorigenesis [15–18]. Several inflammatory parameters have been reported, such as C-reactive protein, the neutrophil-to-lymphocyte ratio (NLR), the platelet-to-lymphocyte ratio (PLR), and the lymphocyte-to-monocyte ratio (LMR) [19–24]. Among these, the NLR is the most studied and promising clinical biomarker and has been shown to be prognostic in many solid tumors, including HNSCC [10,25–33]. However, there are still many unknown areas to explore, and research on inflammatory biomarkers and cancer genomic mutations is lacking. This study aimed to decipher the predictive value of the NLR in patients with locally advanced HNSCC treated with CRT and to explore the associations between the NLR and the cancer genomic landscape.

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

#### *2.1. Data Source*

In this retrospective cohort study, all data were collected via the health information system of Kaohsiung Medical University Hospital under an approved protocol (KMUHIRB-E(I)-20210401). Eligible patients with histologically proven HNSCC (grades 1 to 3) originating in the oral cavity (OC), oropharynx (OPC), hypopharynx (HPC), or larynx (LC) were recruited between 2016 and 2022 at Kaohsiung Medical University Hospital, Taiwan. The Head and Neck Cancer Committee confirmed the tumor stage according to the 8th edition of the American Joint Committee on Cancer (AJCC)'s staging system.

All patients underwent CRT, including 75 who received postoperative adjuvant therapy and 32 who received initial definitive treatment. CRT treatment included a total radiotherapy dose of 60–70 Gy and cisplatin-based chemotherapy. Other clinical data included detailed information on patient age, sex, tumor location, histological grade, clinical staging, body weight before and after CRT, changes in body mass index (BMI), and laboratory findings.

#### *2.2. Treatment Response*

All patients were followed up with regularly at the Medical Oncology and Otorhinolaryngology outpatient departments. Disease status evaluation included tumor site inspection, laboratory examinations, and imaging studies. Treatment response was assessed and determined using computed tomography or magnetic resonance imaging at baseline and at three- to six-month intervals after treatment initiation. The treatment response of the patients was evaluated using Response Evaluation Criteria in Solid Tumors (RECIST) 1.1-measurable lesions and classified into four categories: complete response (CR), partial response (PR), stable disease (SD), and progressive disease (PD). CR and PR were classified as good responses, whereas SD and PD were classified as poor responses. The median follow-up duration in this cohort was 16.6 (range 2.2–80.9) months.

#### *2.3. Neutrophil-to-Lymphocyte Ratio (NLR)*

The NLR was calculated as the simple ratio between the neutrophil and lymphocyte counts measured in the peripheral blood. Absolute lymphocyte count (ALC) and absolute neutrophil count (ANC) data were retrieved from four weeks prior to commencing radiotherapy. If multiple values were available before treatment, those closest to the start date of radiotherapy were selected. The neutrophil-to-lymphocyte ratio (NLR) was computed using neutrophil and lymphocyte measurements and dichotomized into low- and high-NLR categories using a receiver operating characteristic (ROC) analysis.

#### *2.4. Somatic Gene Mutation Profiles and Candidate Genes*

The somatic gene mutation profiles of the study cohort were determined using nextgeneration sequencing (NGS) and FoundationOne CDx (F1CDx), according to the Illumina® HiSeq 4000 platform, using formalin-fixed paraffin-embedded (FFPE) HNSCC tissue specimens. The F1CDx-targeted NGS platform method was validated previously [34]. Neutrophil- and lymphocyte-associated pathways were identified, and the genes involved in these pathways were retrieved from the Kyoto Encyclopedia of Genes and Genomes (KEGG) database. The results of the somatic gene mutation profiles in our study cohort were subsequently mapped. A total of 41 genes associated with lymphocyte and neutrophil signaling pathways were mapped from the somatic gene mutation profiles of the study cohort and considered as candidate gene panels for later analyses. The somatic mutation rates of the candidate genes in the study cohort and the NLR categories were summarized, and the difference between the NLR categories was estimated using Fisher's exact or Pearson's chi-squared test.

#### *2.5. Gene Mutation Score (GMS)*

A multivariate binomial generalized linear model was used to evaluate the association between the NLR and somatic mutations in the candidate genes. Candidate genes with significant results derived from the multivariate model were further selected to generate the GMS, which was calculated by multiplying the estimated coefficient in the multivariate model by the gene mutation status (wild as 0, mutated as 1). Subsequently, the study cohort was dichotomized into low- and high-GMS categories using an ROC analysis. NLR-GMS categories were generated using both the NLR and GMS, and the study cohort was reassigned into low-, intermediate-, and high-NLR-GMS categories based on their NLR and GMS categories. Patients with both a low NLR and GMS were categorized as having a

low NLR-GMS, those with both a high NLR and GMS were categorized as having a high NLR-GMS, and the remaining patients were considered to have an intermediate NLR-GMS.

#### *2.6. Statistical Analysis*

The baseline characteristics of the study cohort were summarized using frequencies and percentages, and laboratory measurements were summarized using medians and interquartile ranges. Differences in baseline characteristics and laboratory measurements between the good- and poor-response subgroups were estimated using Fisher's exact test, Pearson's chi-squared test, or the Wilcoxon rank-sum test. The predictive performances of both the NLR and NLR-GMS for treatment response and short-term relapse-free survival within 36 months were evaluated using an ROC analysis. The area under the ROC curve (AUC) was used to determine the predictive performance of both the NLR and NLR-GMS for progression-free survival (PFS). A higher AUC indicated a better predictive performance. The survival rate of each NLR and NLR-GMS category was estimated using the Kaplan– Meier estimator, and the survival difference between subcategories was estimated using the log-rank test. All *p*-values were two-sided, and *p* < 0.05 was considered statistically significant. All analyses were performed using R 4.1.2 software (R Core Team, 2021, Vienna, Austria).

#### *2.7. Immunohistochemistry*

The HNSCC specimens were fixed on paraffin-embedded biopsies and sectioned. The slices were deparaffinized using xylene and then dehydrated with ethanol. Endogenous peroxidase activity was quenched with 3% hydrogen peroxide containing methanol for 15 min. The sections were heated in 100 mmol/L citrate buffer for 10 min to revive the antigens. The tissues were incubated with 3 primary antibodies at room temperature for 30 min and then rinsed three times with phosphate-buffered saline (PBS) according to the manufacturer's protocol. Following color development, we applied cover slips to the sections and observed them under a microscope. Staining intensity in the cancer tissue was independently examined by pathologists who were blinded to the patients' clinical features and outcomes. The following primary antibodies were used: anti-ABL1 (1:100, Elabscience, Houston, TX, USA), anti-MAP2K2 (1:100, Elabscience, Houston, TX, USA), and anti-MAP2K4 (1:100, Elabscience, State of Texas, USA). In the assessment of IHC staining, staining intensity ranged from 0 (negative) to 3+ (high strength) with the percentage of positively labeled cells.

#### **3. Results**

#### *3.1. Baseline Characteristics of Patients*

Between 2016 and 2022, 107 patients were enrolled in this study. All patients were diagnosed with HNSCC and underwent CRT. Patient characteristics, including age, sex, tumor location, pathological grade, stage, pre-CRT BMI, post-CRT BMI, body weight loss, white blood cell count, ANC, ALC, and the NLR, are summarized in Table 1. The majority of the patients were middle-aged (65.4% between 45 and 64 years), male (93.5%), had oral cavity cancer (67.3%), had grade 2 disease (55.8%), and were stage IV (85.0%). Overall, 84 patients had a good response to CRT, and 23 patients had a poor response to CRT.

There were no statistically significant differences between the good- and poor-response groups with regards to age, sex, pathological grade, clinical cancer stage, pre-CRT BMI, post-CRT BMI, body weight loss, white blood cell count, ANC, and ALC. However, there were significantly more oral cavity cancers in the poor-response group (*p* = 0.038). The difference in the NLR between the good-response group and poor-response group was also prominent (*p* = 0.037), with more patients having a high NLR (≥2.7) in the poor-response group (87.0% vs. 64.3%).

**Table 1.** Baseline characteristics of HNSCC cohort.

Abbreviation: BMI, body mass index; CRT, chemoradiotherapy; NLR, neutrophil-to-lymphocyte ratio.

#### *3.2. Signaling Pathways Associated with Lymphocytes and Neutrophils*

After confirming that a high NLR was related to a poor treatment response, we further analyzed the genetic alterations associated with lymphocytes and neutrophils. Table 2 summarizes eight common pathways associated with lymphocytes and neutrophils which were identified using the KEGG database, including phosphoinositide 3-kinase (PI3K) and Fc gamma receptor IIb (FcγRIIb) signaling in B lymphocytes, protein kinase C (PKC) and 4-1BB signaling in T lymphocytes, the regulation of IL-2 expression in activated and anergic T lymphocytes, cytotoxic T-lymphocyte antigen 4 (CTLA4) signaling in cytotoxic T lymphocytes, CD27 signaling in lymphocytes, and N-formyl methionyl-leucyl-phenylalanine (fMLP) signaling in neutrophils.

Table 2 reports the pathways associated with the lymphocytes and neutrophils derived using the mutated genes detected in this cohort. The "involved genes" column indicates the mutated genes found in our study cohort, which are simultaneously involved in the corresponding pathways. The "genes in pathways" column reported the overall number of genes involved in the correspond pathways, and the "pathway percentage" was computed by dividing the "involved genes" column by the "genes in pathways" column, denoting the percentage of mutated genes found in this study cohort involving a correspondence pathway. The raw NGS data for the somatic mutation profiles of this study cohort are in Supplementary Table S1.

**Table 2.** Pathways associated with lymphocytes and neutrophils derived using mutated genes in the HNSCC cohort.

Abbreviation: PI3K, phosphoinositide 3-kinase; FcγRIIb, Fc gamma receptor IIb; PKC, protein kinase C; fMLP, N-formyl methionyl-leucyl-phenylalanine; CTLA4, cytotoxic T-lymphocyte antigen 4.

#### *3.3. Somatic Mutation Profiles of Candidate Genes*

We matched the genes in these eight pathways with the somatic gene mutation profiles of the patients. A total of 41 genes were identified and were considered candidate gene panels for subsequent analyses, as shown in Table 3. Overall, gene mutation rates were low. Only nine genes had mutation rates of over 10%: *PIK3CA* (23.4%), *PRKCI* (18.7%), *CASP8* (18.7%), *PIK3C2G* (15.0%), *MAP3K13* (13.1%), *ATM* (11.2%), *JAK2* (11.2%), *PTEN* (10.3%), and *CARD11* (10.3%). Among these 41 genes, there were no mutation differences between the low-NLR group and the high-NLR group.

#### *3.4. Predictive Performance of GMS and NLR-GMS*

Due to the relatively low mutation rate, we used a multivariate binomial generalized linear model to evaluate the association between the NLR and somatic mutations of the candidate genes (Table 4). Three candidate genes (*MAP2K2*, *MAP2K4,* and *ABL1*) exhibiting significant results derived from the multivariate model were selected to generate the GMS. *MAP2K2* mutations were associated with a low NLR, whereas *ABL1* and *MAP2K4* mutations were associated with a high NLR.

**Table 3.** Gene mutation rate of 41 genes associated with lymphocyte and neutrophil signaling pathways.

*p*-value is estimated using Fisher's exact test or Pearson chi-squared test.

**Table 4.** Binomial generalized linear model result for the association between the NLR category and the mutation status of 41 associated genes.

SE, standard error. The significant genes were abstracted to generate a GMS (gene mutation score) = coefficient × gene mutation status (0: wild, 1: mut).

NLR-GMS categories were generated using both the NLR and GMS, and the study cohort was reassigned into low-, intermediate-, and high-NLR-GMS categories based on their NLR and GMS categories. Figure 1A,B display ROC plots for the NLR category and the NLR-GMS for treatment response and relapse events within 36 months, respectively.

Both exhibited improved predictive performance using the NLR-GMS categories compared to the NLR categories.

**Figure 1.** Predictive performance of NLR and NLR-GMS in treatment response and short-term relapsefree survival (within 36 months). ROC plots for NLR category and NLR-GMS for (**A**) treatment response and (**B**) relapse event within 36 months. Kaplan–Meier plot for short-term relapse-free survival comparison according to (**C**) NLR and (**D**) NLR-GMS category. ROC, receiver operating characteristics. AUC, area under ROC curve.

Although the high-NLR group exhibited poorer survival than the low-NLR group, no significant survival difference was found between the groups (Figure 1C). However, when we used the NLR-GMS categories, the difference in relapse-free survival between the NLR-GMS groups was significant (overall *p* = 0.003; Figure 1D). The high NLR-GMS group had a significantly shorter relapse-free survival period than the intermediate (*p* = 0.004) and low (*p* = 0.002) NLR-GMS groups.

#### *3.5. Somatic Mutation Validation via Immunohistochemistry Staining*

Based on the result of the multivariate binomial generalized linear model, three candidate genes (*MAP2K2*, *MAP2K4* and *ABL1*) exhibited significant results and were used to generate the GMS. We further validated the expression of three candidate genes by immunohistochemistry (IHC) staining cancer tissues from HNSCC patients. Figure 2 shows representative images of IHC staining for the mutated and wild type of each candidate gene. The yellow words in the upper-left corner of each picture indicate the staining intensity and the percentage of positively labeled cells. Cancer tissues with somatic mutations of the three candidate genes showed a higher staining intensity and percentage of positive

cells compared to wild-type specimens. Overall, it showed an increasing IHC intensity in somatic mutated samples.

**Figure 2.** Representative immunohistochemistry (IHC) images of *MAP2K2*, *MAP2K4*, and *ABL1* expression from cancer tissues from HNSCC patients.

#### **4. Discussion**

The relationship between inflammation and cancer is highly associated. Inflammation predisposes patients to cancer development and promotes all stages of tumorigenesis [15–18]. Several acquired factors are already proven to be carcinogenic and are often associated with chronic inflammation, including chronic bacterial and viral infections, autoimmune diseases, environmental factors (asbestos exposure), lifestyle factors (obesity, tobacco smoking, and excessive alcohol consumption), and aging, which are thought to promote tumor-extrinsic inflammation [14,35]. In contrast, tumor-intrinsic inflammation, also referred to as cancer-elicited inflammation, is induced after tumor initiation and contributes to malignant progression by recruiting and activating inflammatory cells [14,17,36]. Moreover, anticancer therapies can also induce inflammation via the necrosis and necroptosis of cancer cells [14,17]. Overall, cancer cells and surrounding stromal and inflammatory cells engage in well-orchestrated reciprocal interactions to form an inflammatory tumor microenvironment [17].

Several parameters have been reported to represent the degree of systemic inflammation, such as C-reactive protein and the NLR, PLR, and LMR [19–24]. The NLR is the most promising clinical biomarker and has been shown to be prognostic in many solid tumors, including HNSCC [25–33]. The NLR reflects the dynamic relationship between neutrophils (innate immune response) and lymphocytes (adaptive immune response). During stress, trauma, surgery, systemic infection, inflammation, sepsis, or critical illness, the dysregulation of innate and adaptive immune responses results in neutrophilia and lymphocytopenia [37]. Initially, the NLR was used as an index of systemic inflammatory response syndrome (SIRS) and stress in critically ill patients [38]. However, more recently, the NLR has been applied in almost all medical scenarios as a reliable and easily available marker of immune response to various stimuli [37].

The NLR was first applied as a prognostic factor for colorectal cancer in 2005 by Walsh et al. [39]. Two meta-analyses [25,26] and various studies have demonstrated that the NLR is a prognostic factor in different solid tumors, including esophageal cancer [40], gastric cancer [41,42], pancreatic cancer [43], and biliary tract cancer [44], etc. The role of the NLR in HNSCC was also evaluated in many studies, and all of them concluded that the NLR is a reliable prognostic marker [28–30,33,45–54]. Similarly, our cohort demonstrated patients with a high NLR in the poor-response group (87.0% vs. 64.3%), although there was no difference in the 36-month relapse-free survival between the high- and low-NLR groups.

To further evaluate the genetic alterations of the immune response associated with the NLR, we analyzed the NGS data of HNSCC patients and matched them with the KEGG database. Eight pathways and forty-one associated genes were identified. Different statistical methods were applied to determine the association between the NLR and somatic mutations in these candidate genes. Three candidate genes (*MAP2K2*, *MAP2K4*, and *ABL1*) were selected using a multivariate binomial generalized linear model and were further advanced to GMS generation.

*MAP2K2* and *MAP2K4* both belong to the mitogen-activated protein kinase (MAPK) family. *MAP2K2* regulates the phosphorylation and activation of extracellular signalregulated kinases (ERKs) [55]. *MAP2K4* can activate p38 via the phosphorylation of c-Jun-N-terminal kinases (JNK) [56]. MAPK cascades regulate a wide variety of cellular processes including proliferation, differentiation, transcriptional regulation, and stress responses [55,57]. MAPK activation also plays critical roles in the production of proinflammatory cytokines and the induction of the expression of multiple inflammatoryassociated genes [58–62]. A variety of pharmacological inhibitors have been developed to specifically block MAPK kinase 1 and 2 (MEK1/2) [63,64]. Four MEK inhibitors, Trametinib, Cobimetinib, Binimetinib, and Selumetinib, have already been approved by the FDA to date [65]. An emerging technology, named proteolysis targeting chimera (PROTAC), could break the limitation of acquired resistance during long-term treatment by inducing MEK1/2 degradation [65]. Unlike *MAP2K2*, inhibitors specifically targeting *MAP2K4* are few. PLX8725, a novel *MAP2K4* inhibitor, demonstrates promising in vivo activity against patient-derived xenografts of uterine leiomyosarcomas harboring gain-of-function alterations in the *MAP2K4* gene [66]. In fact, *MAP2K4* mutations are sensitive to MEK inhibitors in multiple cancer models [67]. There are also a variety of potent inhibitors of the p38 MAP kinases have been developed, such as SB203580, SB202190, and BIRB-796 [64].

*ABL1* is a proto-oncogene that encodes a protein tyrosine kinase involved in a variety of cellular processes, including cell division, adhesion, differentiation, and response to stress. *ABL1* is involved in the occurrence and development of several types of cancers including colon, kidney, and breast cancer [68,69]. Some inflammatory conditions are also associated with *ABL1* [70]. *ABL1* mediates inflammation by regulating the NF-κB and STAT3 signaling pathways. The blockade of *ABL1* suppresses inflammatory signaling and cytokines [71]. To date, there are several approved *ABL1* inhibitors, such as imatinib, nilotinib, dasatinib, bosutinib, ponatinib, and so on. Most of them are treatments for chronic myeloid leukemia, which is *BCR-ABL1*-positive.

In short, three candidate genes (*MAP2K2*, *MAP2K4*, and *ABL1*) are all associated with inflammation and carcinogenesis. In our study, by using the NLR-GMS categories to divide patients into three groups, we noticed that the high-NLR-GMS group had a significantly shorter relapse-free survival than the intermediate- and low-NLR-GMS groups. In conclusion, the GMS could further target extremely high-risk patients with worse shortterm survival based on the NLR-GMS categories.

This article possesses some strengths and limitations. Initially, the previous publications only affirmed the association between the NLR and treatment response. However, in this study, we conducted a comprehensive genetic investigation along with an investigation of clinical biomarkers in patients with HNSCC who underwent CRT and devised NLR-GMS categories to predict survival. Nonetheless, this cohort has a relatively small sample size, and there were differences in the tumor locations between the two groups. Specifically, the poor-response group had more oral cavity cancers, while the good-response group had more oropharynx cancers. Since different anatomical sites represent distinct etiological factors and background genetic alterations, this may have affected the study results. The longitudinal pattern (or variation) in the NLR of the study population was not investigated due to the nature of the study's design. Additionally, further experiments are necessary to elucidate the role, influence, and mechanism of the candidate genes (*MAP2K2*, *MAP2K4*, and *ABL1*), which could serve as a valuable theme for future research.

#### **5. Conclusions**

In our cohort of HNSCC patients that underwent CRT, a high pre-treatment NLR is linked to a poor response. We conducted a further analysis on the genetic alterations associated with the NLR using somatic gene mutation profiles and identified 41 associated genes. However, there was no significant difference observed between the high- and low-NLR groups. Through the use of a multivariate binomial generalized linear model, we selected *MAP2K2*, *MAP2K4*, and *ABL1* to develop a GMS. By utilizing the NLR-GMS categories, we could effectively target high-risk patients with an extremely poor short-term survival outcome.

**Supplementary Materials:** The following supporting information can be downloaded at: https:// www.mdpi.com/article/10.3390/biomedicines11123113/s1, Table S1: Raw NGS data of the somatic mutation profiles.

**Author Contributions:** Conceptualization, T.-J.Y., H.-C.W., L.-T.C., M.-R.P. and S.-H.M.; formal analysis, H.-C.W. and S.-H.M.; data curation, T.-J.Y., H.-C.W. and S.-H.M.; writing—original draft preparation, T.-J.Y., T.-Y.H., T.-M.C., J.-S.D. and Y.-C.G.; writing—review and editing, T.-J.Y., H.- C.W., S.-F.C., C.-T.H., M.-H.W., Y.-C.L. and S.-H.M.; validation, C.-C.W. and M.-R.P.; supervision, H.-H.H., L.-T.C., M.-R.P. and S.-H.M. All authors have read and agreed to the published version of the manuscript.

**Funding:** We acknowledge the support from the following grants: (1) 112-2321-B-037-004-, 111-2321-B-037-002, 111-2628-B-037-008, 111-2320-B-037-030, and 110-2327-B-037-001 from the Ministry of Science and Technology, Taiwan; and (2) KMUH111-1M14, KMUH111-1M15, and KMUH110-0T04 from the Kaohsiung Medical University Hospital; (3) KMU-KI110001, KMU-TC109A03, KMU-TC108A03- 6, KMU-TC111A04, KMU-TC112A04, and KMU-TC109B05 from Kaohsiung Medical University Research Center Grant.

**Institutional Review Board Statement:** This study was approved by the Institutional Review Board and Ethics Committee of Kaohsiung Medical University Hospital (KMUHIRB-E(I)-20210401). The data were analyzed anonymously and therefore, no additional informed consent was required. All methods were performed in accordance with the approved guidelines and regulations.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The data that support the findings of this study are available upon reasonable request (e.g., for research purposes) from the authors.

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

#### **References**

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**5. Biopolymers and biodegradable textiles industry**

The textile industry has played a important role in the exchanging of goods and impacted by novel techniques through the development of more environmentally friendly processes [64–67]. Many biodegradable fibers may be natural, regenerated or synthetic such as Ingeo (Natureworks), LLC produced from corn, a biodegradable thermoplastic polyatide (PLA); Lenpur produced from wood pulp of harvested white pine tree clippings; and Modal and Tencel/Lyocell produced by Lenzing from wood pulp of beech and eucalyptus trees, and biodegradable aliphatic/aromatic multi-block co-polyesters. The largest application of alginates in textiles can be found in textile printing, the spinning and weaving of temporary fibers from calcium alginate [15]. Bio-based fibers like X-Static, Meryl Skinlife, Diolen Care, Trevira Bioactive are enriched with innovative antimicrobial products such as technical products, working uniforms, sportswear [68].

#### **5.1 Fibers industry and biodegradable polymers**

The melt spinning processing technologies with availability of biodegradable materials along have aided in qualitative and quantitative improvements [69]. The fibers reinforcing improve the relationship between the process parameters and the material properties [70]. Many natural fibers added to biopolymers as reinforcements (flax, cellulose acetate, bamboo, pineapple, ramie, kenaf, henequen, jute, sisal, and hemp); improving the strength without affecting the biodegradability [71]. Fibers of the poly(β-hydroxybutyrate) were produced via multistage melt-extrusion as well as gel-spinning [72]. The dry-jet wet spinning method was used to extrude the cellulose/ NH3/NH4SCN solution [15]. By "dry-jet wet spinning" and using a cellulose/hydrolyzed starch-grafted-polyacrylonitrile solution, the mechanical properties of Lyocell fibers were improved [73]. An extruded Lyocell fibers were reported have potential uses in filters, geo-textiles, surgical gauze [74]. Cellulose fibers are used for the design of intelligent, bioactive, and biocompatible composites [75]. Preparing sol–gel derived biodegradable SiO2 gel fibers [76] for drug release consists of three steps: an initial burst, followed by a diffusion-controlled release behavior, and finally a step with a slower release rate. By incorporating responsive hydrogels in textiles, the surface energy switches between hydrophilic/hydrophobic, with the results listed in **Table 3** [77].

There is good compatibility between the chitosan obtained from shrimp shells and starch-based polymers when forming a chitosan/starch fiber. Some researchers have made fiber from starch and biodegradable glycerine-based polymers with/ without PLA and glucitol, while others extrude high strength PLLA fibers. The type LA 0200 K of PLA is processed at a high speed spinning (draw ratio = 6)in a spin drawing [78]. A fiber from soya bean protein is crafted by forcing a globular protein to become a fiber forming protein; the fiber has to be cross-linked if fibrous products are to be obtained [79]. Fibrous materials are segregated into two basic groups, the first can be placed on the surface of materials (i.e., surgical covers, gauzes, diapers and tampons), and the second can be placed inside an organic tissue (i.e., surgical threads, tendons and ligament implants, meshes, stents, and vascular grafts).

**Table 3.**

*Monomers, origin and fiber formation of smart biopolymers [77].*

#### **5.2 Fabric industry and biodegradable polymers**

Weaving, knitting, nonwoven web forming (carding, spun-bond and wet-laid) and nonwoven-bonding (stitch-bonding, needling, calendaring and hot air bonding) are fabric forming technologies. Biodegradable non-woven webs and disposable articles contain fibers such as cotton, hemp, milkweed floss, flax fiber, wool, silk, chitin and chicken feathers [80]. There are many examples in biodegradable nonwoven such as biodegradable cotton-based nonwovens (cotton/cellulose, or cotton/ biodegradable co-polyester) and (PTAT co-polyester and PLA). Cotton/(co-polyester/PP) nonwovens along with absorbency and flexural rigidity have suitable mechanical properties and they are better than that of cotton/co-polyester nonwovens [81–83].

Sanitary and medical textiles, geotextiles, filtration media, within the automotive industry, PLA based hair caps, Bionolle 3001 nonwovens, Landlok biodegradable erosion control coconut fibers mats, Kenaf fiber nonwovens, refuse bags, drain filters made from fine denier PLA nonwovens, and biodegradable filter materials are used for both air and liquids. A biodegradable thermoplastic polymer and a plasticizer could be used to produce a starch matrix of the finely attenuated fibers which could have applications as environmentally degradable nonwoven webs and articles [84].

Researchers have produced biodegradable cotton-based, nonwovens by using blends of cotton, flax and biodegradable thermoplastic fibers that act as binders [85]; Biodegradability was monitored, with 40% of the initial weight lost after 8 weeks composting [86]. To reduce the cost, researchers have made a pure nonwoven material from co-polyester by a direct melt-blowing process [87]. Woven tubes (3 to 6.5) mm are developed using Polyglactin 910 biodegradable yarn on a narrow width loom [88].

Biodegradable poly (L-lactide-co-caprolactone) fabrics of nano/micro- structured can be made Using CH2Cl2 as a solvent in electro-spinning. The electro-spun elastomeric nano-fiber fabric is used as a functional scaffold in tissue engineering (i.e., cardiovascular, muscular) [89]. The Belgian Textile Research Centre's projects include: Noterefiga for

*Characterization, Modeling and the Production Processes of Biopolymers in the Textiles Industry DOI: http://dx.doi.org/10.5772/intechopen.96864*

bio-based comfort textiles, Bioagrotex for agro-textiles (agriculture, horticulture, gardening and construction), Green-Nano-Mesh for medical areas, Dura cover for woven PLA taped ground covers, Hortaflex and Weed Control for PLA based nonwovens, and the BiobasedFilbio project for knitted PLA insect screens for climate control.

There are various commercialized fabrics made from naturally derived biopolymers such as those found in the Ethical Fashion Forum in London: POLY Acid Ingeo bio fibers; QMilchfibers, Lenzing's Modal fiber, Micro Modal fiber, Lyocell fiber, POLARTEC polyester, unique corn-based PLA fleece; and Cork shell made from cork to form high quality textiles for lightweight spring and summer jackets. Biopolymers based in intelligent and/or stimuli responsive polymeric systems have been developed and reported by researchers for the functional finishing of textiles [90]. Scientists proposed changes of the polymer backbone in a reversible formation of PLA-dye complexes [91]. Sorona is used in the coat fabric for jackets, trench coats and outerwear with its 37% renewably sourced plant-based components; they lose their wrinkles with one quick snapping motion. Bio-based fabrics made of wool and "BIOPHYL" or "TENCEL". Some commercial products are made from spider silk [92] and could be used in the bullet-proof vests industry [15].

#### **5.3 Fiber and fabric coatings and biodegradable polymers**

Modification techniques of the biopolymer's surface includes coating, oxidation by low-temperature plasma, and surfactant addition blending with various derivatives [93]. Cyclodextrins or linear carbohydrate biopolymers were attached to the textile to allow frequent use and washing [94]. Regenerated cellulose fibers were treated by plasma activation using a chitosan solution [95]. Cellulose was coated by chitosan nano-particles to reduce the cost and non-toxic methodology [75]. While studying their development as well as characterization, both the organic cotton based bandages and cotton were coated separately on the gauze structure using chitosansodium alginate polymer, calcium-sodium alginate polymer and subsequent mixtures of the two, thereby improving its antibacterial and wound healing properties [96]. For dyeing and printing, the dextrin derivative surfactant improves the whiteness and wetting properties of cotton fabrics [97]. The chemical surface treatments of jute fabrics involve bleaching, dewaxing, cyanoethylation, alkali treatment and vinyl grafting are used as reinforcing components in biodegradable matrix composites, which are environmentally friendly materials [98]. A Knitted Dacron graft made of polyethylene oxidepolylactic acid were coated with a polymeric biodegradable sealant [99]. Layer-by-layer electrostatic deposition is used to coat the material by adding dextran sulphate and chitosan to a soybean based polymer [100]. The functional finishing of the micro- and nano-sized hydrogels improve response times [101].

Nano-composites and nano-structured coatings improve mechanical strength and flexibility, temperature and moisture stability, as well as durability. "Metal Rubber"(Nano Sonic Inc.) combines the rubber and metal properties, and it is used in artificial muscles, electrically charged aircraft wings, and protective biopolymer clothing [102]. Hydrogel-based biopolymers are used for the functional finishing of textiles by surface modifying systems [103].

#### **6. Case study: modeling of biopolymers' melt spinning process**

All the production process parameters must be controlled to ensure the quality and then the significant main factors must be analyzed [104]. Commercially, it is a challenge to develop a new competitive product [105]. Some research is based on statistical analysis, mathematical simulation and modeling of the processes of fiber formation, and examples of their post-processes have been reported in literature [106–116]. The practical software-based approach has improved the confidence benefits of experimental design and simulation [117]. **Figure 3** shows a flow chart for the methodologies used for obtaining the program, starting from the data and statistical modeling methods and SED. Online quality control tools were utilized for prediction, measurement, correction as well as adjustment and feedback [118].

The aliphatic aromatic co-polyester fibers extrusion process was investigated in this work, and statistically modeled [119]. A linear biodegradable oil-based polymer (LAAC-flexibility component of Solanyl) and branched aliphatic-aromatic copolyester (BAAC-Ecoflex F BX 7011) were used to study the effects of the extrusion process and the properties of fibers. The study describes the melt spinning of aromatic-aliphatic co-polyester depending on the extrusion thermal profile effect on asspun fiber properties. The molten material flowed easily when the viscosity decreased and smoother extrudates were obtained at shear rates greater than 4.5 s-1 [120].

## **6.1 Factorial experimental design for melt spinning of biodegradable fibers**

Factorial experimental design provides data about the optimization of the average response values in regards to the factor levels [121]. The STATGRAPHICS program is used to design the experiment random order matrix and to simulate the main data in one block experiments.

The studied factors for the fiber extrusion process include: speed of spin finish, quenching air speed, metering pump speed, and winding speed, as well as, meltspinning or extrusion temperature. The analyzed levels of each parameter were listed in **Table 4**; the thirty-two trials matrix for the five control factors was applied for as-spun fibers analysis. **Figure 4** shows an SEM photomicrograph of the crosssection and surface of the fibers; fibers had an acceptable uniform surface and possessed a uniform circular cross section.

In this case study [122–124], several statistical tools were utilized for statistical analysis including the surface plot, normal probability plot, the main effect plot, pareto chart, interaction plot, as well as analysis of variance (ANOVA). Implementation of forecasting statistical methods plays a major role in creating a planning program and

**Figure 3.**

*The flow chart of the statistical method.*

**Table 4.**

*Factors and the selected levels for the spinning experiments of as-spun fibers.*

### *Characterization, Modeling and the Production Processes of Biopolymers in the Textiles Industry DOI: http://dx.doi.org/10.5772/intechopen.96864*

a plan for the production process regression.  According to the drawability characterization, biodegradable fibers (i.e., as-spun) should consist of a drawn construction and be conducive to orient along the fiber axis of the chain [125]. There is a clear relationship between the draw down ratio and the orientation of the fibers and having a significant effect on the drawability. In other words, the overall orientation of fibers was increased and the draw ratio decreased as the spin draw ratio increased. Temperature significantly influenced the spin (down) draw ratio and fiber drawability that affects the flow rate and tension value. To study the effects of the factors as well as their statistical significance an ANOVA study was conducted. A factor was considered to have a significant effect if the F ratio (an ANOVA statistic) was shown to be more than the statistical value (F /4.49/at the appropriate level α =0.05) or had P-value smaller than 0.05. The ANOVA results from the experiments are presented in **Table 5**.

**Figure 4.** *The surface and cross section of the biodegradable fibers [119].*

**Table 5.** *ANOVA results of factor effects on the drawability.*

The significance of factors were PWS > PMPS> PT in the drawability analysis, while no significant effect was observed due to other factors. The P-value (0.016) of T&WS is lower than 0.05 and therefore is significant. The most significant factors were T, MPS and WS. Metering pump speed was observed to have interaction with winding speed; the speeds' relationship oriented the fiber chains as well as added different spin draw ratio, having an effect on drawability later. Multiple and individual regressions optimized for the quality required for various applications and identified the factors' effects and interactions to determine the direction of those that are significant by using the estimated response surfaces. A twist was observed in the 3D surface response diagrams for T and WS (**Table 5**), thus the interaction is significant and agrees with the previous statistical results. This interaction will affect the structure of the as-spun fibers and help to extend the chains to achieve high orientation along the axis of fiber. The regression Eq. (1) was obtained from the analysis and forms the simplified models of the experimental data (coded values in **Table 4**). The regression equations forecast the fiber properties and accurately predict the properties in the final fibers produced. The mathematical regression model forms one of the basic source codes in the designed forecasting application, which will present the extrusion of aromatic-aliphatic co-polyester fiber.

> Drawability a b T c MPS d QA e SF f WS b T MPS b T QA b T SF b T WS b MPS QA b MPS SF b MPS WS b QA SF b QA WS b SF WS = + ∗ +∗ − ∗ −∗ +∗ + ∗∗ + ∗∗ + ∗∗ − ∗∗ −∗ ∗ − ∗ ∗−∗ ∗ −∗ ∗+∗ ∗ − ∗∗ 1 2 34 5 67 8 9 10 (1)

Where: a, b, c, d, e, f b1–10, are statistical constants for the drawability calculated by the **STATGRAPHICS** program.

They were also affected by high extrusion speed at which the shear rate affects the morphological structure [126].  The statistical analysis models simulated the significant factors, their interactions, and gave useful results with some expected outliers which could be due to experimental and/or testing errors.

### **6.2 Forecasting program for the fiber extrusion**

In the programming process, the relationship between the key inputs (factors) and the performance measures (responses) using factorial statistical experimental design technology are reported. The statistical data and regression formulas are represented as a computer application. Microsoft Visual Basic was used to write a forecasting program that could be utilized for the as-spun AAC fibers' extrusion process. The program offers the management of regression models for responses based on statistical factorial design, design analysis and process simulation. Conversion and summarization of the C++ source code into a simple flow chart was completed (**Figure 5**).

After selecting the polymer grade, the program requests the parameters' values, calculates the values' responses by using regression equations and then gives the results. The data from the input conditions was used to obtain the structural, mechanical and physical data. The program was designed as two windows. The first window is the input window for process conditions (**Figure 6**); the second interface is the output result window (**Figure 7**).

*Characterization, Modeling and the Production Processes of Biopolymers in the Textiles Industry DOI: http://dx.doi.org/10.5772/intechopen.96864*

**Figure 5.** *Schematic program process.*

#### **Figure 6.**

*The main input interface/window for process conditions input.*

#### **Figure 7.**

*The output interface/window for filament temperature in the machine's cooling window and the fiber's structural, mechanical and physical properties.*

Each factor is represented as a record and it may be owned by more than one record, leading to a network-like structure. The multiple regression analysis and previous forecasting models provide a basis for identifying the relationship between process-input and process-output data; and formation of a source code to be used in the forecasting program. The 30 hole spinneret (diameter is 0.4 mm, l/d ratio is 1.2) was used. The programmed application powerfully supports product development, design process control, quality assurance and product performance evaluation; it displays data on the screen or sends data to a file or other devices. **Figure 7** shows the output interface/window for filament temperature in the machine's cooling window and the fiber's structural, mechanical and physical properties. Each factor is represented as a record and relationships between other factors through a matrix design.


**INTERNET OF THINGS - TECHNOLOGY, APPLICATIONS AND STANDARDIZATION**

#### **Internet of Things - Technology, Applications and Standardization**

http://dx.doi.org/10.5772/intechopen.70907 Edited by Jaydip Sen

#### **Contributors**

Moonkun Lee, Sunghyeon Lee, Yeongbok Choe, Menachem Domb, Arpan Pal, Hemant Kumar Rath, Samar Shailendra, Abhijan Bhattacharyya, Albena Mihovska, Mahasweta Sarkar, Hyun Jung Lee, Myungho Kim, Alexandru Averian

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