*2.1. Materials*

Gelatin (Type A, 300 bloom from porcine skin) and Pluronic F127 was purchased from Sigma Co. Ltd. (St. Louis, MO, USA). Microbial transglutaminase (mTG) was purchased from Ajinomoto Inc. (Kanagawa, Japan); its activity was approximately 100 U/g.

Gelatin was dissolved in deionized water and was continuously stirred in a 60 ◦C water bath for 30 min. When the temperature of the gelatin solution dropped to 37 ◦C, mTG was added and thoroughly blended with the gelatin solution. The gelatin/mTG solution contains 14% (wt) gelatin and 1.4% (wt) mTG. The fugitive ink was composed of 40% (wt) Pluronic F127 in deionized water. The ink was homogenized using a mixer until the powder was fully dissolved, and then centrifuged to remove any air bubbles. The fugitive ink was subsequently loaded in a syringe and stored at 4 ◦C.

### *2.2. Geometry of the Tissue Engineered Vascular Grafts (TEVG)*

The left coronary artery (LCA) consists of the left main artery (LM) that bifurcates into the left anterior descending (LAD) and the left circumflex (LCX) [29]. The constructed geometry model is presented in Figure 1. The wall thicknesses of the middle layer and the outermost layer are set to be 0.5 mm and 0.5 mm, respectively. The innermost layer was formed by seeding human umbilical vein endothelial cells (HUVECs) on the inner wall of the channel. The dimensions of the proposed TEVG geometry are based on the clinically accurate dimensions of the LCA. The dimensions of the inner channel of the TEVG are presented in Table 1 [30]. The tapering e ffects were considered when constructing the LAD and LCX. The angle of 60◦ was used between the two branches [6]. The curvature was set to be 60 mm.

**Figure 1.** The geometry model of the proposed tissue engineered vascular grafts (TEVGs) based on left coronary artery. LCX–left circumflex; LAD–left anterior descending; LM–left main artery.

**Table 1.** Dimensions of the inner channel of the tissue engineered vascular grafts (TEVGs).


### *2.3. Fluid-Structure Interaction Simulation*

The strength of a fabricated TEVG under native blood pressure is crucial for its application in the clinic. To investigate the property of the wall compliance of the constructed TEVG under the influence of the blood flow, a fluid-structure interaction (FSI) simulation was performed via COMSOL Multiphysics. The geometrical model is presented in Figure 2a along with the mesh model used in the simulation (Figure 2b). The engineered vascular construct is embedded in biological tissue, specifically the cardiac muscle. The fluid domain was also constructed. The flowing blood applies pressure to the internal surfaces, thereby deforming the vascular construct and the cardiac muscle.

**Figure 2.** (**a**) The geometry of the bioengineered vascular construct embedded in the cardiac muscle used for the simulations, and (**b**) the mesh model created for the simulation.

The simulation consists of two distinct but coupled studies: first, a fluid-dynamics study of the blood; second, a mechanical study of the deformation of the bioengineered vascular construct and cardiac muscle. To correctly estimate the deformation response of the TEVG, the mechanical study must consider the cardiac muscle because it exerts a stiffness that resists the vascular construct deformation due to the applied pressure.

Blood was modeled as a Newtonian fluid with the use of the incompressible Navier-Stokes equations; as for LAC dimensions, the shear rate is well over the limit where blood exhibits shear-thinning behavior for the cardiac cycle. A laminar flow model was chosen as the calculated Reynolds number was below 100. The density and viscosity of the blood were set to be 1050 kg/m<sup>3</sup> and 4.0 × 10−<sup>3</sup> Pa·<sup>s</sup> [31]. No slip boundary condition was imposed for the inner walls of the construct. An incompressible Neo-Hookean solid model was chosen for the TEVG and cardiac muscle so as to better predict its nonlinear stress-strain behavior. The Poisson's ratio (υ) of the TEVG and cardiac muscle was set to be 0.45 [32,33]. As for the Lamé's coefficients of the neo-Hookean hyperelastic materials, the Lamé's second coefficients (μ) of the TEVG and muscle were set to be 6.20 × 10<sup>6</sup> <sup>N</sup>/m<sup>2</sup> and 7.20 × 10<sup>6</sup> <sup>N</sup>/m2, respectively. Therefore, the Lamé's first coefficients (λ) could be calculated by the following equations [34]:

$$
\lambda = K - \frac{2}{3}G \tag{1}
$$

$$\upsilon = \frac{3K - 2G}{6K + 2G} \tag{2}$$

$$
\mu = G \tag{3}
$$

where K and G represent the bulk modulus and shear modulus of the hyperelastic materials, respectively.

During a heart beating cycle, the pressure varies between a minimal and a maximal value [35]. Therefore, for the time-dependent analysis, a simplified waveform of the pressure for the inlet boundary condition of the fluid domain was used and is shown in Figure 3. The maximal pressure value occurs at the time t = 0.5 s. The pressure between 0 and 1 s makes the pressure vary between the minimal and

maximal value during a heart beating cycle. The pressure variation during a cardiac cycle is within the range of the normotensive pulse pressure.

**Figure 3.** The time variation of the pressure used as the inlet boundary condition for the TEVG.

Additionally, the compliance of the vascular construct can be calculated as follows:

$$\% \text{compliance} = \frac{(R\_{p\_2} - R\_{p\_1}) / R\_{p\_1}}{(p\_2 - p\_1)} \times 10^4 \tag{4}$$

where

*p*1 is the lower pressure value (mmHg); *p*2 is the higher pressure value (mmHg); *Rp*1 is the internal radius at the lower pressure value (mm);*Rp*2 is the internal radius at the higher pressure value (mm).
