Experimental Uncertainties

Figs. 4.8A-F illustrates variation of the compression elastic modulus of the alginate scaffolds with respect to alginate precursor and crosslinker concentration and incubation time for the three ionic crosslinkers considered. The compression elastic modulus of the scaffolds dramatically decreased with incubation time for all three crosslinkers but the effect of alginate precursor and crosslinker concentration varied. For scaffolds crosslinked with CaCl2 (Fig. 4.8A) and BaCl2

(Fig. 4.8C), decreasing the alginate precursor concentration significantly reduced the elastic modulus in the first 10-15 days of incubation in PBS; however, this effect became insignificant thereafter. In contrast, no concentration effect of hydrogel precursor on the elastic modulus of

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Zn²⁺ ion crosslinked alginate scaffolds was evident (Fig. 4.8E). For the 3% alginate precursor crosslinked with lower concentrations of CaCl2 (Fig. 4.8B) and ZnCl2 (Fig. 4.8F), a moderate fall in the elastic modulus occurred with time; this decline was significant for BaCl2, especially within the first 10-15 days (Fig. 4.8D).

Fig. 4.8 Variation of scaffold compression elastic modulus with respect to alginate concentration, crosslinker concentration, and incubation time for crosslinking solutions containing (A, B) CaCl2, (C, D) BaCl2, and (E, F) ZnCl2 for fixed crosslinker concentrations of

100 mM (A, C, E) and a fixed alginate concentration of 3% (w/v) (B, D, F).

104 4.4.5 Multiple regression analysis

Multiple regression equations were derived for the swelling, degradation, and elastic modulus of the alginate scaffolds (Table 4.1A). The swelling equation for CaCl2 crosslinked alginate scaffolds features both quadratic and linear relationships to the alginate concentration, whereas the equations for BaCl2 and ZnCl2 crosslinked alginate scaffolds indicate a linear relationship with alginate concentration and incubation time. The swelling equation for ZnCl2 crosslinked alginate scaffold also features a quadratic relationship with alginate and crosslinker concentrations. Because the multiple regression equations show good agreement with experimental values (R²~0.75), the equations can be used to predict swelling in characterizing mechanical properties of alginate scaffold in a physiological environment.

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Table 4.1 (A) Multiple regression equations for estimating the elastic modulus, swelling, and degradation of alginate scaffolds with respect to crosslinking variables for three ionic crosslinkers having significant effects (pb<0.05); (B) summary of the crosslinking variables with

significant effects on the compression elastic modulus and swelling of 3D alginate scaffold for three ionic crosslinkers.

*Statistically significant effect; ^a representing linear and quadratic relationship with swelling; ^b representing the effect of interaction between incubation time and alginate concentration; ^c representing quadratic relationship with swelling

(A)

(B)

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The degradation of CaCl2 crosslinked alginate scaffolds has a quadratic relationship with crosslinker concentration and a linear relationship with alginate and crosslinker concentrations.

In contrast, the degradation equation for BaCl2 crosslinked alginate scaffold features a linear relationship with alginate and crosslinker concentrations. The degradation of ZnCl2 crosslinked alginate scaffolds features a linear relationship with incubation time, crosslinker concentration, and alginate concentration. The multiple regression equations presented in Table 4.1A for predicting degradation of the alginate scaffolds show good agreement with experimental values (R²~0.80).

The multiple regression equations in Table 4.1A demonstrate that the elastic modulus has a linear and quadratic relationship with incubation time, and a linear relationship with the crosslinking solution concentration and/or alginate concentration or their interactions with incubation time for all crosslinker ions considered. The coefficient of determination of ~0.75 represents a reasonably good agreement between predicted values from equations and the measured values for the elastic modulus of the scaffolds.

Based on Fig. 4.8, multiple regression equations were developed to predict the Young’s modulus of alginate scaffolds as a function of incubation time, hydrogel concentration, and crosslinker concentration. Fig. 4.9A-F illustrates the relationship between predicted and measured values of elastic modulus for the scaffolds and the distribution of residual error of prediction for the multiple regression equations given in Table 4.1A. Figs. 4.9A, C, and E indicate relatively good agreement between the experimental and predicted elastic moduli of the scaffolds, particularly below 40 kPa. For stiffer scaffolds with an elastic modulus above 55 kPa, the multiple regression equations underestimate the elastic modulus with respect to measured value. The random distribution of the prediction error, as shown in Figs. 4.9B, D, and F, represents unbiased predictability of the multiple regression equations in Table 4.1A.

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Fig. 4.9 Predictability assessment of the multiple regression equations for the 3D-printed crosslinked alginate scaffolds with respect to hydrogel and crosslinking solution variables for (A,

B) CaCl2, (C, D) BaCl2, and (E, F) ZnCl2 solutions.

Table 4.1B presents the variables involved in the hydrogel crosslinking process and their statistical significance (pb-value) with respect to the swelling and elastic modulus (compression) of alginate hydrogels for the three ionic crosslinking solutions considered. The concentrations of alginate precursor significantly (pb-value<0.05) affect the swelling of the alginate scaffolds crosslinked with CaCl2, BaCl2, or ZnCl2 solutions. Notably, the incubation time of the BaCl2 and ZnCl2 crosslinked scaffolds significantly affects (pb-value<0.05) the swelling of the scaffolds in PBS. In contrast, only the concentration of ZnCl2 significantly (pb-value<0.05) influences the swelling of the alginate hydrogel regardless of alginate concentration (Table 4.1B). The interaction between alginate and crosslinking agent concentrations significantly (pb-value<0.05) affects the elastic modulus of the alginate scaffolds for CaCl2,BaCl2, and ZnCl2. In addition, the square of the incubation time of the crosslinked hydrogel following 3D-printing has a very significant effect (pb-value<0.001) on the compression elastic modulus. In particular, the interaction between incubation time and alginate concentration is a significant factor (pb -value<0.05) affecting the compression elastic modulus for the CaCl2 and BaCl2 crosslinking solutions. Unlike the ZnCl2 crosslinking solution for which alginate concentration has no significant effect on the elastic modulus, the elastic modulus is significantly influenced by the squared alginate concentration for the CaCl2 and BaCl2 crosslinking solutions (Table 4.1B).