Electrospinning process parameters optimization for biofunctional curcumin/gelatin nanofibers

The impact of nanotechnology on health sciences is widespread. The potential roles of nanofibers in biomedical applications, such as drug release and tissue engineering have been investigated recently. Preparation of polymeric fibers is not a simple task. There are many preparation processes possible which can vary the characteristics of polymeric fibers of the available techniques, electrospinning is considered as an efficient technique to prepare polymeric nanofibers that are polymeric, synthetic or natural, biodegradable or non-biodegradable, etc, having uniform diameters (5 nm to several hundred nanometers) from a wide variety of polymers and composite solutions [1–3]. Electrospinning is preferred over other conventional methods in recent research papers to prepare polymer nanofibers. The apparatus is relatively easy to operate which makes this process cost effective [4–6]. The nanofibers produced so far have applications in many disciplines of engineering and medical sciences. The basics of nanofiber spinning of biopolymers have been described by Jamil et al [7]; Pham et al [8]; Vasita and katti et al [9]; Kriegel et al [10]; Shekh et al [11]; Tuerdimaimaiti et al [12]; Amariei et al [13]; Yoon et al [14]; Alharbi et al [15]; Chen et al [16].

The proteins and their derivatives as well as biodegradable and nontoxic biopolymers such as chitosan, cellulose, collagen, gelatin, etc, are extracted from living organisms and they are used for electrospinning of polymeric nanofibers. The limitations of biopolymers such as their limited solubility in organic solvents due to their high crystallinity, their expensive purification processes and further their viscous solutions due to their tendency to form hydrogen bonds, are overcome after blending with synthetic polymers otherwise these limitations may restrict their electrospinning into nanofibrous mats [10]. The nanofibrous mats prepared from electrospun collagen nanofibers have been used as scaffolds for tissue engineering applications [7]. Aloe vera, a natural polymer also holds potential for tissue engineering applications due to its antioxidant and nontoxic nature [11]. The biomedical applications of few electrospun nanofibers are listed in table 1.

Table 1. Use of ultrathin electrospun curcumin based nanofibers for biomedical applications.

About curcumin based nanofibers	Biomedical applications	References
Curcumin with polycaprolactone-polyethylene glycol nanofibers, Curcumin with poly(3-hydroxybutyric acid-co-3-hydroxyvaleric acid) (PHBV), Curcumin with poly(lactic acid)-hyperbranched polyglycerol, and Curcumin with $\varepsilon$ -polycaprolactone / polyvinylalcohol multilayer nanofibers	Better wound healing potential	[17–20]
Curcumin with gum tragacanth/poly(ε-caprolactone) nanofibers	Improved antibacterial implementation and diabetic wound healing (in vivo)	[21]
Curcumin with almond gum/ polyvinyl alcohol (PVA) composite nanofibers	Improved bioavailability and therapeutic potential	[22]
Zinc-curcumin with coaxial nanofibers	As bone substitute	[23]
Curcumin with zein fibers	Improved antibacterial potential	[24]
Curcumin with cellulose acetate/polyvinylpyrrolidone nanofibers, Curcumin with polyurethanes nanofibers, and Curcumin with gelatin nanofibers	Antibacterial performance	[25–27]
Curcumin nanofibers	Anti-adhesion potential	[28]
Curcumin with chitosan/ poly (vinyl alcohol) (PVA) nanofibers	Drug delivery potential	[29]

Gelatin (a mixture of proteins and peptides) is a natural polymer which is biocompatible, nontoxic and biodegradable, and hence is considered as a fair and safe choice when selecting fiber material for dressing problematic wounds such as diabetic chronic ulcers. The light weight ultrathin nanofibers can serve as mechanical support during wound dressings due to their significant tensile strength as compared to conventional fibers (having diameters in the range of over 100 nm) and also act as barriers to cover the wound [30–33]. Gelatin is also known for its excellent water absorption and fluid affinity, which makes it a good choice to support moist wound healing. Gelatin (a natural biopolymer which is a denatured form of collagen) is quite soluble in formic acid. Collagen is a protein available in the extra cellular matrix (ECM) of animals and humans, and is expensive due to its manufacturing processes. However, gelatin is easily available at a much lower price than collagen and thus is a preferred source for biomaterials. Gelatin nanofibers (like collagen) have been used in biomedical applications such as cosmetics, wound dressing, tissue engineering, surgical treatments, etc [34]. Gelatin nanofibers (having sufficient mechanical properties to be used in these applications as nanofibrous mats) have been electrospun for ultrathin nanofibers [34–44]. These authors also reported that the properties of these nanofibers can be tailored as per requirements by optimizing input parameters such as voltage, viscosity, distance between the spinneret and rotating drum collector, and flow rate. These authors have spun nanofibers of diameters in the range of 76–100 nm for drug delivery and wound dressing applications. It is evident that formic acid is used as an organic volatile solvent to dissolve gelatin at room temperature for the electrospinning.

The use of gelatin nanofibers having enough tensile strength for fabricating nonwoven mats has received attention recently for use for antimicrobial applications [45–49]. Successful spinning of minimum diameter nanofibers results in the surface areas of these nanofibers being increased in addition to their light weight. This is basically required for wound dressings and other biomedical applications as listed in table 1. For instance Mindru et al [50] were successful in preparing nonwoven mats of required thickness and improved strengths for biomedical applications using a solvent system consisting of formic acid. Numerous questions have arisen however, due to use of cytotoxic solvents while preparing solutions for electrospinning of gelatin nanofibers to be used in real biomedical applications. Instead of cytotoxic solvents, Maleknia et al [51] used formic acid/water to prepare solutions for electrospinning of gelatin nanofibers for biomedical applications such as wound dressing, drug release, and tissue engineering. These authors were successful in spinning gelatin nanofibers with diameters as small as 197 nm. Chen et al [52] used formic acid and ethanol (to improve volatility of the solvent) instead of cytotoxic solvents while preparing the solvent for synthesizing electrospun gelatin nanofibers. These authors were successful in spinning gelatin nanofibers of 85 nm diameters, the lowest reported to date. During their investigations, they found that crosslinked gelatin nanofibers (after soaking the nanofibers in 2.5% of glutaraldehyde aqueous solution for 72 h and then being washed using de-ionized water before drying) were compatible with mouse mesangial cells. The drug delivery nanofibrous mats are required to be dissolved quickly in aqueous solutions. Aytac et al [42] found that the electrospun gelatin nanofibers encapsulated with ciprofloxacin/hydroxypropyl-beta-cyclodextrin-inclusion complex could dissolve faster in water than electrospun gelatin nanofibers loaded with ciprofloxacin. Yabing et al [40] synthesized drugs (inhibitors such as SP600125, c-Jun N-terminal kinase and SB203580, p38 MAP kinase)-loaded micelles (poly(ethylene glycol)-block-caprolactone copolymer) using dialysis method and incorporated these drugs into electrospun gelatin nanofibers. The dual drugs delivery electrospun gelatin nanofibrous mats were used as scaffolds for the treatment of infections around the teeth. Nanofibrous mats prepared from electrospun nanofibers have large surface areas and they are expected to play a significant role in tissue engineering. The use of formic acid as a solvent for electrospinning biofunctional nanofibers has resulted in their use in various biomedical applications, such as immobilization of enzymes, bone regeneration materials, antibacterial and antifungal activities in release of drugs, encapsulation of bioactive materials during food packaging and wound dressing [53].

Turmeric is derived from Curcuma longa (common turmeric, an herbaceous plant) and has been widely used in India and China as a bioactive compound with powerful anti-inflammatory and antioxidant medicinal properties. Curcumin is one of the components of turmeric. It has been shown that synthetic dimethoxycurcumin is more potent to destroy cancer (a leading cause of every sixth death worldwide) cells than natural curcumin (derived from the plant) [54–64]. Ramírezagudelo et al [55] incorporated antibiotic doxycycline drugs (inhibitors of mitochondrial biogenesis, could restrict cancer stem cells in initial breast cancer stages) into electrospun hybrid poly-caprolactone/gelatin/hydroxyapatite soft nanofibrous mats and evaluated these drug delivery meshes as effective anti-tumor and antibacterial scaffolds. The use of formic acid as solvent for solutes such as curcumin and gelatin has been the preferred choice in many biomedical researches. Authors have prepared solutions of curcumin and dimethoxycurcumin using formic acid [54, 65–67]. Curcumin is a natural monomer (as shown in figure 1(a)), and nanofibers containing poly(curcumin) (as shown in figure 1(b)) can be used in medical treatments such as curing the skin injuries, as shown in figure 2(a). More curcumin would be expected to release with a specific rate from higher concentrations, such as 17% curcumin loaded poly (ε-caprolactone) (PCL) nanofibers than the lower concentrations, such as 3% curcumin loaded PCL nanofibers, after 12 h (as shown in figure 2(b)) [30]. Using PCL-curcumin solutions, biofunctional electrospun nanofibers were prepared [30–33, 68]. Hoang et al [68] fabricated curcumin loaded PCL/chitosan nonwoven mats (for wound dressings) using formic acid and acetone together as solvents while electrospinning nanofibers. They also investigated the release of curcumin (via an in vitro approach) from nonwoven mats of these fibers (having fiber diameters in the range between 267 nm to 402 nm); it was found to be nearly 80% during the initial 100 h. The gelatin nanofibers were found to serve as vehicles to release the drugs in controlled manner. These electrospun nanofibers were prepared in such a way that they had highly functionalized surface areas and their mats had excellent porosity to both, incorporate curcumin and allow curcumin diffusion out of the matrix, thereby improving their drug releasing capabilities. Xinyi et al [33] prepared curcumin/gelatin nanofibrous mats and investigated the release of curcumin on rat models (acute wounds) via in vitro approach, as shown in figure 2(c) [33]. While investigating crosslinked curcumin/gelatin nanofibers (after placing in a 25% glutaraldehyde solution with ethanol (1% v/v) before vacuum drying for 72 h at 4 °C), the authors found improved mechanical strength of this electrospun nanofibers, as shown in figure 3 [33].The wound healing was tested by treating rats using the curcumin/gelatin nanofibrous mats (healing analyses are shown in figure 4 for the 3rd, 7th, and 15th days after wounding). This encouraged us to prepare curcumin loaded gelatin nanofibers suitable for fabrication of nanofibrous mats for the application of sustained release of curcumin and oxygen to the wound (during healing).

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In the present study, an electrospining method was adapted to prepare the curcumin loaded gelatin nanofibers; characterizations of the nanofibers were done using scanning electron microscopy (SEM). Investigations were done to find the effects of critical process parameters such as distance between the spinneret and collector, polymer solution flow rate, voltage and viscosity on the preparation of uniform and ultrathin porous nanofibers having applications in wound dressings. In the present investigation the curcumin loaded gelatin nanofibers were selected in the hope of having improved mechanical and wound healing properties assuming these nanofibers should release the curcumin at appropriate rates which is of extreme importance to permit application of its biological effects during wound healing applications. It has been shown that the electrospun curcumin/gelatin nanofibers with lower diameters have larger surface area to volume ratios and porosity than larger diameter fibers and thus these nanofibers can be developed for sustained release of curcumin and oxygen (due to enough porosity) to the wound [31]. Curcumin/gelatin nanofibers can be further crosslinked for improved mechanical (tensile) strength (if required) for further development of nanofibrous mats for wound healing. These nanofibrous mats would have then anti-oxidant and anti-inflammatory features that could address wound healing in a very efficient way [31, 68–86].

Electrospinning uses an electric field which is applied across a spinneret and a ground electrode to withdraw a jet of polymer solution from the orifice of the spinneret. In electrospinning the Maxwell or electrical stress is given as $\tfrac{\varepsilon {V}^{2}}{{d}^{2}},$ where $\varepsilon$ is the permittivity, $V$ is the voltage, and $d$ is the electrode separation. The critical voltage $({V}_{c})$ which is $\sqrt{\tfrac{\gamma {d}^{2}}{\varepsilon R}},$ must be exceeded before any jet can spread out from the electrospinning tip. In particular, for $\gamma ={10}^{-2}kg/{s}^{2},\,d={10}^{-2}m,\,\varepsilon ={10}^{-10}{C}^{2}/(Jm)\,\,{\rm{and}}\,R={10}^{-4}m,$ a voltage of order 10 KV is required to form any jet [87].

Yeo et al [87] assumed a priori equilibrium conical shape for the Taylor cone (for the fluid drop) formation at the tip of the spinneret. The solution of the Laplace equation (used in the formulation) in the weak polarization limit describes the electrostatics in the fluid phases in an axisymmetric spherical coordinate system $(r,\theta ,\phi )$ with the vertex of the Taylor cone at the origin which can be shown using equation (1).

$$\begin{eqnarray}&&\begin{array}{c}{\varphi }_{l}(r,\theta )={A}_{n}{r}^{n}{P}_{n}(\cos \,\theta );\,for\,{\theta }_{0}\geqslant \theta \geqslant 0,\\ {\rm{and}}\\ {\varphi }_{g}(r,\theta )={B}_{n}{r}^{n}{P}_{n}\,\cos \,(\pi -\theta );\,for\,\pi \geqslant \theta \geqslant {\theta }_{0}\end{array}\end{eqnarray} \tag{ 1 }$$

In the above equation (1), the volume of the fluid drop is given by $V=\tfrac{4}{3}\pi {r}^{3},$ where $r$ is the distance from the cone vertex of angle $2{\theta }_{0}$ to the tip of the spinneret and the shape of drop is represented using a Taylor cone, thus $r$ is characterized as $r=R(z).$ Further, the $z-axis$ is parallel to the applied electric field with $z\in [\begin{array}{cc}-l & l\end{array}],$ where $l$ is the length of the semi long axis of the drop and the boundary condition ${\theta }_{0}\geqslant \theta \geqslant 0$ represents the region occupied by the fluid. ${P}_{n}[x]$ is the Legendre function, and ${A}_{n}$ and ${B}_{n}$ are constants. They suggested a model for electrospinning composite nanofibers which is based on a sink-like flow towards the vertex of the Taylor cone. The solution of the flow in axisymmetric polar coordinates $(r,\varepsilon ,0)$ was given using equations (2) and (3).

$$\begin{eqnarray}&&{v}_{r}=\displaystyle \frac{vF(\varepsilon )}{r}\end{eqnarray} \tag{ 2 }$$

$$\begin{eqnarray}&&F(\varepsilon )=b\left\{3{\tanh }^{2}\,\,\left[\left(\sqrt{\displaystyle \frac{-b}{2}}\right)\,\left(\alpha -\varepsilon \right)+1.146\right]\,-2\right\}\end{eqnarray} \tag{ 3 }$$

In the above equations (2) and (3), ${v}_{r}$ is the radial velocity of flow, $v$ is the kinematic viscosity of flow, $\alpha$ is the wedge/Taylor cone half angle, $b$ is a parameter which determines the inertial concentration of flow into the Taylor cone vertex/Taylor cone. Mass and charge conservations led to expressions for $v$ and $\sigma$ in terms of $R$ and $E,$ and the momentum and E-field equations were recast using second-order differential equations. Slope of the jet surface $\left(R^{\prime} \right)$ is supposed to be highest at the origin of the nozzle and thus initial value of $z$ is equal to zero. Further, boundary conditions were set using the set of equation (4) [88, 89].

$$\begin{eqnarray}&&\begin{array}{l}R(0)=1\\ E(0)={E}_{0}\\ {\tau }_{prr}=2{r}_{\eta }\displaystyle \frac{{R}_{0}^{{\prime} }}{{R}_{0}^{3}}\\ {\tau }_{pzz}=-2{\tau }_{prr}\end{array}\end{eqnarray} \tag{ 4 }$$

In the above equation (4), ${R}_{0}$ is the initial radius of jet and the jet velocity $({\upsilon }_{0})$ is calculated using the formula ${\upsilon }_{0}=\tfrac{Q}{\pi {R}_{0}^{2}K},$ where $Q$ is the flow rate of the solution, and $K$ is the conductivity of liquid solution. The electric field $({E}_{0})$ is calculated using the formula ${E}_{0}=\tfrac{I}{\pi {R}_{0}^{2}K}$ and the surface charge density $({\sigma }_{0})$ is calculated using the formula $\bar{\varepsilon }{E}_{0},$ where $\bar{\varepsilon }$ is the dielectric constant of ambient air and ${E}_{0}$ is the constant to be used during simulation of the electrospinning. The viscous stress $({\tau }_{0})$ is calculated using the formula ${\tau }_{0}=\tfrac{{\eta }_{0}{\upsilon }_{0}}{{R}_{0}}.$ A power-law fluid is a generalized Newtonian fluid and for that the shear stress $(\tau ),$ is given as $\tau =K^{\prime} {\left(\tfrac{\partial v}{\partial y}\right)}^{m}.$ It is observed that the electric field is induced by the surface charge gradient and thus it is insensitive to the thinning of the electrospun jet, as shown in equation (5) [88].

$$\begin{eqnarray}&&\displaystyle \frac{d\left(\sigma R\right)}{dz}\simeq -\left(2R\displaystyle \frac{dR}{dz}\right)/Pe\end{eqnarray} \tag{ 5 }$$

Thus, the variation of $E$ with respect to axial position $(z)$ can be shown using equation (6) [88].

$$\begin{eqnarray}&&\displaystyle \frac{d\left(E\right)}{dz}=\,\mathrm{ln}\,\chi \left(\displaystyle \frac{{d}^{2}{R}^{2}}{d{z}^{2}}\right)/Pe\end{eqnarray} \tag{ 6 }$$

In figure 5 plots are shown for the changes of various parameters, radius of jet $(R),$ electric field $(E),$ radial normal stress $({\tau }_{prr})$ and axial viscous normal stress $({\tau }_{pzz})$ with the respect to axial position $(Z).$ It is observed that the electric field $(E)$ increased to a peak and then relaxed to some extent. The model discussed so far was shown to be capable of predicting the behavior of the process parameters of electrospinning [88]. Through these plots the flow procedure in relation to the jetting process involved in the electric field is outlined.

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Ultrathin porous nanofibrous mats can be prepared using electrospinning for various biomedical applications. Various researchers have emphasized the curcumin based nanofibers in their investigations to find their potential uses in wound healing, drug-delivery and antibacterial applications (as shown in table 1). The structures of these electrospun nanofibers can be tailored for large surface area and length up to kilometers using the electrostatically driven jet of polymer solution. Further, it was found that bioactive molecules of graphene oxide and a Zn-curcumin complex, when combined with the electrospun nanofibers, had potential application in bone regeneration, as shown in table 1.

The 2^k factorial design was implemented to conduct the experiments after considering the four independent variables (each varied at two different levels i.e. low (−) and high (+)); these were the distance between the spinneret and collector, flow rate, voltage and viscosity [90–92]. Thus, the total number of observations were 2⁴ i.e. 16.

All 16 samples were examined under scanning electron microscopy (SEM) for diameters in nanometers (as shown in table 2). A few sample images of the curcumin/gelatin nanofibers examined under SEM are shown in figures 6(c)–(h). The ultrathin porous nanofibers membranes were prepared under all process conditions.

It was done to find the significance of the contributions of the individual parameters in achieving the minimum diameter of the nanofibers. Calculations for the correction factor, CF (to compute the sum of squares of input variables) were conducted using equation (7).

3.2.1. Correction factor (CF)

The CF for diameter (nm) was calculated as

$$\begin{eqnarray}&&CF=\displaystyle \frac{{\left(\sum X\right)}^{2}}{n}=\displaystyle \frac{{(4085.5)}^{2}}{16}\cong 1043207\end{eqnarray} \tag{ 7 }$$

Where, the $\sum X$ is the gross total of observed diameters and n is the number of iterations, i.e. 16 (both as shown in table 2)

The effect of the factors can be given using equation (8).

$$\begin{eqnarray}&&\displaystyle \frac{{\left[\sum {Y}_{low}\right]}^{2}}{n}+\displaystyle \frac{{\left[\sum {Y}_{high}\right]}^{2}}{n}-CF\end{eqnarray} \tag{ 8 }$$

Where, Y is an input variable, such as the distance (A), and ${Y}_{high}$ and ${Y}_{low}$ stand for the sum of all average diameters prepared at high (+) and low (−) levels, respectively, for the particular input variable with each sum taken over the high and low values of the other variables. The corresponding values of average diameters for the high (+) and low (−) levels of the particular input variable were taken from table 2.

• 1.  
  Sum of squares, distance factor (cm), SS_A

  $$\begin{eqnarray*}&&\begin{array}{l}\displaystyle \frac{{\left[\sum {A}_{low}\right]}^{2}}{n}+\displaystyle \frac{{\left[\sum {A}_{high}\right]}^{2}}{n}-CF\\ =\displaystyle \frac{{\left[205+270+260+147+287+375+308+235\right]}^{2}}{8}\\ +\displaystyle \frac{{\left[181+280+254+286+288+206+229.5+274\right]}^{2}}{8}\\ -1043207=489.5\end{array}\end{eqnarray*}$$

  Similarly,
• 2.  
  Sum of squares, flow rate factor (ml h⁻¹), SS_B

  $$\begin{eqnarray*}&&\displaystyle \frac{{\left[\sum {B}_{low}\right]}^{2}}{n}+\displaystyle \frac{{\left[\sum {B}_{high}\right]}^{2}}{n}-CF=228.5\end{eqnarray*}$$
• 3.  
  Sum of squares, voltage factor (KV), SS_C

  $$\begin{eqnarray*}&&\displaystyle \frac{{\left[\sum {C}_{low}\right]}^{2}}{n}+\displaystyle \frac{{\left[\sum {C}_{high}\right]}^{2}}{n}-CF=606\end{eqnarray*}$$
• 4.  
  Sum of squares, viscosity factor (cP), SS_D

$$\begin{eqnarray*}&&\displaystyle \frac{{\left[\sum {D}_{low}\right]}^{2}}{n}+\displaystyle \frac{{\left[\sum {D}_{high}\right]}^{2}}{n}-CF=6380\end{eqnarray*}$$

To examine the interaction, table 3 was formulated. The Sum of squares for each pair of interactions is given using equation (9).

$$\begin{eqnarray}&&\displaystyle \frac{{\left[\sum A{B}_{low}\right]}^{2}}{n}+\displaystyle \frac{{\left[\sum A{B}_{high}\right]}^{2}}{n}-CF\end{eqnarray} \tag{ 9 }$$

Where, $AB$ represents interaction between distance (cm), A, and flow rate (ml h⁻¹), B. The corresponding values of average diameters for the high (+) and low (−) levels of the particular interaction between variables were taken from table 3.

Table 3. Interaction table (curcumin nanofibers).

S. no.	AB	AC	AD	BC	BD	CD	ABC	BCD	ACD	ABCD	Diameters $\left({\rm{nm}}\right)$ as in table 2
1	+	+	+	+	+	+	—	—	—	+	205 ± 22.5
2	—	—	—	+	+	+	+	—	+	—	181 ± 66
3	—	+	+	—	—	+	+	+	—	—	270 ± 16
4	+	—	—	—	—	+	—	+	+	+	280 ± 20
5	+	—	+	—	+	—	+	+	+	—	260 ± 26.5
6	—	+	—	—	+	—	—	+	—	+	254 ± 28
7	—	—	+	+	—	—	—	—	+	+	147 ± 34
8	+	+	—	+	—	—	+	—	—	—	286 ± 31
9	+	+	—	+	—	—	—	+	+	—	287 ± 77
10	—	—	+	+	—	—	+	+	—	+	288 ± 57
11	—	+	—	—	+	—	+	—	+	+	375 ± 96
12	+	—	+	—	+	—	—	—	—	—	206 ± 56
13	+	—	—	—	—	+	+	—	—	+	308 ± 74
14	—	+	+	—	—	+	—	—	+	—	229.5 ± 60
15	—	—	—	+	+	+	—	+	—	—	235 ± 47
16	+	+	+	+	+	+	+	+	+	+	274 ± 53

The values of the sum of squares for the various interactions are as follows

• 1.  
  Sum of squares for interaction AB, SS_AB

  $$\begin{eqnarray*}&&\begin{array}{l}\displaystyle \frac{{\left[\sum A{B}_{low}\right]}^{2}}{n}+\displaystyle \frac{{\left[\sum A{B}_{high}\right]}^{2}}{n}-CF\\ =\displaystyle \frac{{\left[181+270+254+147+288+375+229.5+235\right]}^{2}}{8}\\ +\displaystyle \frac{{\left[205+280+260+286+287+206+308+274\right]}^{2}}{8}\\ -1043207=1000\end{array}\end{eqnarray*}$$

  Similarly,
• 2.  
  Sum of squares for interaction AC, SS_AC

$$\begin{eqnarray*}&&\displaystyle \frac{{\left[\sum A{C}_{low}\right]}^{2}}{n}+\displaystyle \frac{{\left[\sum A{C}_{high}\right]}^{2}}{n}-CF=4743.5\end{eqnarray*}$$

• 1.  
  Sum of squares for interaction AD, SS_AD

  $$\begin{eqnarray*}&&\displaystyle \frac{{\left[\sum A{D}_{low}\right]}^{2}}{n}+\displaystyle \frac{{\left[\sum A{D}_{high}\right]}^{2}}{n}-CF=6662.5\end{eqnarray*}$$
• 2.  
  Sum of squares for interaction BC, SS_BC

  $$\begin{eqnarray*}&&\displaystyle \frac{{\left[\sum B{C}_{low}\right]}^{2}}{n}+\displaystyle \frac{{\left[\sum B{C}_{high}\right]}^{2}}{n}-CF=4882.5\end{eqnarray*}$$
• 3.  
  Sum of squares for interaction BD, SS_BD

  $$\begin{eqnarray*}&&\displaystyle \frac{{\left[\sum B{D}_{low}\right]}^{2}}{n}+\displaystyle \frac{{\left[\sum B{D}_{high}\right]}^{2}}{n}-CF=695.5\end{eqnarray*}$$
• 4.  
  Sum of squares for interaction CD, SS_CD

  $$\begin{eqnarray*}&&\displaystyle \frac{{\left[\sum C{D}_{low}\right]}^{2}}{n}+\displaystyle \frac{{\left[\sum C{D}_{high}\right]}^{2}}{n}-CF=907.5\end{eqnarray*}$$
• 5.  
  Sum of squares for interaction ABC, SS_ABC

  $$\begin{eqnarray*}&&\displaystyle \frac{{\left[\sum AB{C}_{low}\right]}^{2}}{n}+\displaystyle \frac{{\left[\sum AB{C}_{high}\right]}^{2}}{n}-CF=9925\end{eqnarray*}$$
• 6.  
  Sum of squares for interaction BCD, SS_BCD

  $$\begin{eqnarray*}&&\displaystyle \frac{{\left[\sum BC{D}_{low}\right]}^{2}}{n}+\displaystyle \frac{{\left[\sum BC{D}_{high}\right]}^{2}}{n}-CF=2769\end{eqnarray*}$$
• 7.  
  Sum of squares for interaction ACD, SS_ACD

  $$\begin{eqnarray*}&&\displaystyle \frac{{\left[\sum AC{D}_{low}\right]}^{2}}{n}+\displaystyle \frac{{\left[\sum AC{D}_{high}\right]}^{2}}{n}-CF=21\end{eqnarray*}$$
• 8.  
  Sum of squares for interaction ABCD, SS_ABCD

$$\begin{eqnarray*}&&\displaystyle \frac{{\left[\sum ABC{D}_{low}\right]}^{2}}{n}+\displaystyle \frac{{\left[\sum ABC{D}_{high}\right]}^{2}}{n}-CF=1947\end{eqnarray*}$$

Highest value = 9925 for ABC interaction

Errors, which are listed in table 4 can be pooled together and the $Ratio,\,M{S}_{error}$ can be calculated using the equation (10).

$$\begin{eqnarray}&&M{S}_{error}=S{S}_{error}/{V}_{error}=21\end{eqnarray} \tag{ 10 }$$

Where, ${V}_{error}$ represents the number of errors, and in our case it is one.

Table 4. Effect estimation-final ANOVA table.

Remark	MODEL/ERROR	Factor/Interaction	Effect estimation	Sum of square (SOS)	% Contribution
Factors/interactions having significant contributions	MODEL	ABC	50	9925	24
	MODEL	AD	−41	6662.5	16
	MODEL	D	40	6380	15.5
	MODEL	BC	−35	4882.5	12
	MODEL	AC	34.5	4743.5	11.5
	MODEL	BCD	26	2769	6.7
	MODEL	ABCD	22	1947	4.7
	MODEL	AB	16	1000	2.4
	MODEL	CD	−15	907.5	2.2
	MODEL	BD	−13	695.5	1.7
	MODEL	C	−12	606	1.5
	MODEL	A	−11	489.5	1.2
	MODEL	B	7.5	228.5	0.5
Factor/interaction NOT having significant contribution	ERROR	ACD	−2	21	0.05
				$\sum SOS=41257.5$

Now, in the calculation of the F ratio, using the F-distribution table, we have found the F value for 95% level of confidence as 7.71 and further concluded that the diameter primarily depends upon factors: (a) ABC-Interaction between distance (cm), flow rate (ml h⁻¹) and voltage (KV), (b) AD-Interaction between distance (cm) and viscosity (cP), (c) D-Viscosity (cP), (d) BC-Interaction between flow rate (ml h⁻¹) and voltage (KV), (e) AC-Interaction between distance (cm) and voltage (KV), (f) BCD-Interaction between flow rate (ml h⁻¹), voltage (KV) and viscosity (cP), (g) ABCD-Interaction between distance (cm), flow rate (ml h⁻¹), voltage (KV) and viscosity (cP), (h) AB-Interaction between distance (cm) and flow rate (ml h⁻¹), (i) CD-Interaction between voltage (KV) and viscosity (cP), (j) BD-Interaction between flow rate (ml h⁻¹) and viscosity (cP), (k) C-Voltage (KV), (l) A-Distance (cm), and (m) B-Flow rate (ml h⁻¹). These are treated as models and further tested for their contribution to the diameters of nanofibers (nm) (at 5% level of significance) in table 4. During the effect estimation, it is found about the factor ACD-Interaction between distance (cm), voltage (KV) and viscosity (cP) that it affects the diameter (nm) by 0.05% which is not significant and thus it is indicated as an error in table 4.

As each input variable has two levels i.e. high (+) and low (−) levels and has one degree of freedom, thus an ordinary regression model was employed to calculate the minimum diameter of nanofibers after substitution of suitable values of the interaction effects such as ${\beta }_{1},\,{\beta }_{2},\,{\beta }_{4},{\beta }_{5},{\beta }_{6},{\beta }_{7},{\beta }_{8},{\beta }_{9},$ and ${\beta }_{10}$ (in terms of contributions of interactions between ABC-Interaction between distance (cm), flow rate (ml h⁻¹) and voltage (KV), AD-Interaction between distance (cm) and viscosity (cP), BC-Interaction between flow rate (ml h⁻¹) and voltage (KV), AC-Interaction between distance (cm) and voltage (KV), BCD-Interaction between flow rate (ml h⁻¹), voltage (KV) and viscosity (cP), ABCD-Interaction between distance (cm), flow rate (ml h⁻¹), voltage (KV) and viscosity (cP), AB-Interaction between distance (cm) and flow rate (ml h⁻¹), CD-Interaction between voltage (KV) and viscosity (cP), BD-Interaction between flow rate (ml h⁻¹) and viscosity (cP), respectively) as well as the main effects, such as ${\beta }_{3},\,{\beta }_{11},\,{\beta }_{12},$ and ${\beta }_{13}$ (in terms of contributions of D-Viscosity (cP), C-Voltage (KV), A-Distance (cm), and B-Flow rate (ml h⁻¹), respectively), in equation (11).

$$\begin{eqnarray}&&Y={\beta }_{0}+{\beta }_{1}{X}_{1}+{\beta }_{2}{X}_{2}+{\beta }_{3}{X}_{3}+\ldots +\,{\beta }_{n}{X}_{n}+\xi \end{eqnarray} \tag{ 11 }$$

Where,

$$\begin{eqnarray*}&&{\beta }_{0}=\displaystyle \sum _{i=1}^{N}\displaystyle \frac{{Y}_{i}}{N}=\displaystyle \frac{4085.5}{16}=255.344\end{eqnarray*}$$

Further, the effect of each factor, P, was calculated using the formula ${Y}_{P}={\bar{Y}}_{P+}-{\bar{Y}}_{P-},$ where, ${\bar{Y}}_{P+}$ and ${\bar{Y}}_{P-}$ stand for the sums of all average diameters prepared at high (+) and low (−) levels, respectively, for the particular input variable. The corresponding values of the average diameters for the high (+) and low (−) levels of the particular input variable were taken from tables 2 and 3.

As an example, the effect of factor B can be calculated as follows:

$$\begin{eqnarray*}&&\begin{array}{l}D={\bar{Y}}_{D+}-{\bar{Y}}_{D-}\\ =\displaystyle \frac{\left[287+288+375+206+308+229.5+235+274\right]}{8}\\ -\displaystyle \frac{\left[205+181+270+280+260+254+147+286\right]}{8}=40\end{array}\end{eqnarray*}$$

Similarly, the effects of the other factors, such as $ABC,\,AD,\,BC,\,AC,\,{\rm{B}}CD,\,ABCD,\,AB,\,{\rm{C}}D,\,BD,\,C,\,A,\,B,$ and $ACD$ were calculated as 50, −41, −35, 34.5, 26, 22, 16, −15, −13, −12, −11, 7.5, and −2, respectively (as shown in table 4).

Therefore, the $\% \,contribution\,for\,ABC=\left(9925/41257.5\right)\times 100=24$

$$\begin{eqnarray*}&&{\beta }_{1}=\displaystyle \frac{1}{2}\left(effect\,estimate\,for\,factor\,ABC\right)=25\end{eqnarray*}$$

$$\begin{eqnarray*}&&{\beta }_{2}=\displaystyle \frac{1}{2}\left(effect\,estimate\,for\,factor\,AD\right)=-20.5\end{eqnarray*}$$

$$\begin{eqnarray*}&&{\beta }_{3}=\displaystyle \frac{1}{2}\left(effect\,estimate\,for\,factor\,D\right)=20\end{eqnarray*}$$

$$\begin{eqnarray*}&&{\beta }_{4}=\displaystyle \frac{1}{2}\left(effect\,estimate\,for\,factor\,BC\right)=-17.75\end{eqnarray*}$$

$$\begin{eqnarray*}&&{\beta }_{5}=\displaystyle \frac{1}{2}\left(effect\,estimate\,for\,factor\,AC\right)=17.25\end{eqnarray*}$$

$$\begin{eqnarray*}&&{\beta }_{6}=\displaystyle \frac{1}{2}\left(effect\,estimate\,for\,factor\,BCD\right)=13\end{eqnarray*}$$

$$\begin{eqnarray*}&&{\beta }_{7}=\displaystyle \frac{1}{2}\left(effect\,estimate\,for\,factor\,ABCD\right)=11\end{eqnarray*}$$

$$\begin{eqnarray*}&&{\beta }_{8}=\displaystyle \frac{1}{2}\left(effect\,estimate\,for\,factor\,AB\right)=8\end{eqnarray*}$$

$$\begin{eqnarray*}&&{\beta }_{9}=\displaystyle \frac{1}{2}\left(effect\,estimate\,for\,factor\,CD\right)=-7.5\end{eqnarray*}$$

$$\begin{eqnarray*}&&{\beta }_{10}=\displaystyle \frac{1}{2}\left(effect\,estimate\,for\,factor\,BD\right)=-6.5\end{eqnarray*}$$

$$\begin{eqnarray*}&&{\beta }_{11}=\displaystyle \frac{1}{2}\left(effect\,estimate\,for\,factor\,C\right)=-6\end{eqnarray*}$$

$$\begin{eqnarray*}&&{\beta }_{12}=\displaystyle \frac{1}{2}\left(effect\,estimate\,for\,factor\,A\right)=-5.5\end{eqnarray*}$$

$$\begin{eqnarray*}&&{\beta }_{13}=\displaystyle \frac{1}{2}\left(effect\,estimate\,for\,factor\,B\right)=3.75\end{eqnarray*}$$

The general form of the regression analysis equation is shown in equation (12). The minimum diameter of curcumin/gelatin nanofibers (nm) attainable using our system, can be calculated after substituting the suitable values of the coefficients (such as ${\beta }_{1},\,{\beta }_{2},\,{\beta }_{4},{\beta }_{5},{\beta }_{6},{\beta }_{7},{\beta }_{8},{\beta }_{9},$ and ${\beta }_{10}$) of the interaction effects (such as ${X}_{ABC},\,{X}_{AD},\,{X}_{BC},\,{X}_{AC},\,{X}_{BCD},\,{X}_{ABCD},\,{X}_{AB},\,{X}_{CD},$ and ${X}_{BD}$) as well as the coefficients (such as ${\beta }_{3},\,{\beta }_{11},\,{\beta }_{12},$ and ${\beta }_{13}$) of the main effects (such as ${X}_{D},\,{X}_{C},\,{X}_{A},$ and ${X}_{B}$) in equation (12).

$$\begin{eqnarray}&&\begin{array}{l}Diameter\,(nm)=255.344+25{X}_{ABC}-20.5{X}_{AD}+20{X}_{D}-17.75{X}_{BC}\\ \,\,+\,17.25{X}_{AC}+13{X}_{BCD}+11{X}_{ABCD}+8{X}_{AB}\\ \,\,-\,7.5{X}_{CD}-6.5{X}_{BD}-6{X}_{C}-5.5{X}_{A}+3.75{X}_{B}\end{array}\end{eqnarray} \tag{ 12 }$$

The above model equation (12) is valid in the regions such as (a) $10\leqslant {X}_{A}\leqslant 15$(cm), (b) $0.10\leqslant {X}_{B}\,\leqslant 0.15$(ml h⁻¹), (c) $10\leqslant {X}_{C}\leqslant 15$(KV), and (d) $65\leqslant {X}_{D}\leqslant 70$(cP).

The plot of the variation in average diameters of nanofibers versus the runs (also known as the time series plot of average diameters) for a random correlation is shown in figure 7(a) as per the values listed in table 2 for all sixteen iterations. The main effects and interactions plots for the means of the average diameters (nm) with respect to the critical process parameters were plotted using MINITAB 17 software, as shown in figure 7(b) and (c). They show that ABC-Interaction between distance (cm), flow rate (ml h⁻¹) and voltage (KV), AD-Interaction between distance (cm) and viscosity (cP), D-Viscosity (cP), BC-Interaction between flow rate (ml h⁻¹) and voltage (KV), AC-Interaction between distance (cm) and voltage (KV), BCD-Interaction between flow rate (ml h⁻¹), voltage (KV) and viscosity (cP), ABCD-Interaction between distance (cm), flow rate (ml h⁻¹), voltage (KV) and viscosity (cP), AB-Interaction between distance (cm) and flow rate (ml h⁻¹), CD-Interaction between voltage (KV) and viscosity (cP), BD-Interaction between flow rate (ml h⁻¹) and viscosity (cP), C-Voltage (KV), A-Distance (cm), and B-Flow rate (ml h⁻¹) have the significant impact over preparation of minimum diameter of curcumin/gelatin nanofibers, as shown in table 4, figures 7(b) and (c).

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The variations in diameters of nanofibers with respect to all four critical process parameters are shown in figure 7(b). It was found that with an increase in distance and voltage, the diameter of nanofibers was reduced. However, with an increase in flow rate and viscosity, the diameter of nanofibers was increased. A good interaction among all the four critical process parameters occurred is shown in figure 7(c). The effects of the contribution of ABC-Interaction between distance (cm), flow rate (ml h⁻¹) and voltage (KV), AD-Interaction between distance (cm) and viscosity (cP), D-Viscosity (cP), BC-Interaction between flow rate (ml h⁻¹) and voltage (KV), and AC-Interaction between distance (cm) and voltage (KV) were found to be considerable (table 4 and figure 7(c)).

The response contour lines maps of the average diameters (nm) of curcumin/gelatin nanofibers as a function of the critical process parameters are shown in figures 7(d), (f), (h), (j), (l), and (n) to define the relationships between two variables and a response. The predicted 3D response surface plots of the average diameters (nm) of curcumin/gelatin nanofibers produced by the fitted model, are shown in figures 7(e), (g), (i), (k), (m), and (o). The darkest shade in contour plots represents locations where the diameters of the nanofibers, was maximum ($\gt$ 280 nm) and the lightest shade represents locations where the diameters of the nanofiber was minimum ($\lt$ 240 nm).

It was clear after the ANOVA calculations (final ANOVA, table 4), that the factor ACD-Interaction between distance (cm), voltage (KV) and viscosity (cP) had the least contribution (in producing minimum diameters of curcumin/gelatin nanofibers because of the fact that it was coming as an error in DOE analysis. The effects of the contribution of ABC-Interaction between distance (cm), flow rate (ml h⁻¹) and voltage (KV), AD-Interaction between distance (cm) and viscosity (cP), D-Viscosity (cP), BC-Interaction between flow rate (ml h⁻¹) and voltage (KV), and AC-Interaction between distance (cm) and voltage (KV) had the considerable impacts of 24%, 16%, 15.5%, 12%, and 11.5% respectively, over the preparation of the minimum diameters of the curcumin/gelatin nanofiber.

The optimized parameter settings are shown in figure 7(p). The impacts of the critical process parameters on the average diameters (nm) of curcumin/gelatin nanofibers could be estimated by shifting the red lines to find optimal values of process parameters within the range. In our case the composite desirability, D, is 0.8129, which is close to 1. The horizontal blue line represents the current response values (figure 7(p)). The average diameter of ultrathin curcumin/gelatin nanofibers was predicted around 189.6563 nm using the optimized setting of a solution having 1.5% gelatin, 1% curcumin in 10 ml of 98% concentrated formic acid, with the electrospining unit having a voltage of 10 KV, distance from the spinneret to collector drum of 15 cm, flow rate of 0.1 ml h⁻¹, viscosity of 65 cP and drum collector speed of 1000 rpm. The figure 6(c) shows the SEM image of the curcumin/gelatin nanofibers having a 181 nm (181 ± 66 nm) average diameter, prepared under similar condition using the same solution. Thus, the estimated diameter (nm) of curcumin/gelatin nanofibers in the optimization process only has an 8% difference with the prepared diameter which shows the efficacy of present investigation.

We suggest these light weights, and ultrathin nanofibers having enough film porosity could be used in wound dressing applications due to their high surface area to volume ratio with respect to length and diameter. Researchers have been optimizing the input parameters to prepare minimum diameters of curcumin based nanofibers for various biomedical applications for the last 12 years as shown in figure 8 and table 5. In the present investigation, the optimum conditions were achieved to synthesize the minimum average diameter (181 ± 66 nm) of ultrathin curcumin/gelatin nanofibers so far which could be suitable for dressing diabetic chronic ulcers due to its unique properties such as light weight, nontoxic, biocompatible as well as water absorbent and fluid affinity.

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Sharjeel et al [100] were successful in electrospinning a novel and hybrid polymeric nanofibrous meshes for dressing the burn wounds after incorporating gabapentin (a neuropathic pain killer) into polyethylene nanofibers and acetaminophen (a class of analgesics) into sodium alginate nanofibers, using the optimized setting of a polymeric solution of the polyethylene oxide and sodium alginate mixed in 80:20 blend proportion. The hybrid mechanism could be a safe choice in wound dressing applications. Sharjeel et al [101] used acetic acid and water (50:50, v/v) while preparing the solvent for synthesizing electrospun polyethylene oxide and chitosan (each dissolved separately in acetic acid and water solution in 5% weight-to-volume ratio) nanofibers (the ratio of polyethylene oxide and chitosan in the polymeric solution was 80:20). The authors incorporated nanoparticles of zinc oxide and ciprofloxacin drugs into electrospun polyethylene oxide-chitosan nanofibers and evaluated these drug delivery meshes as effective antibacterial systems. The authors were successful in optimizing electrospun polyethylene oxide-chitosan nanofibers of 116 nm diameters (with standard deviation of only 21 nm) using response surface methodology. They also observed that (a) a higher distance yielded lower diameters, (b) a higher voltage resulted in lower diameters, (c) with an increase in flow rate, the diameters of the nanofibers were increased, and (d) with an increase in concentration of zinc oxide nanoparticles and ciprofloxacin, the diameters of the nanofibers were increased from 116 to 210 nm and enhanced the antibacterial efficiency.