Vascular grafts are used to restore or augment blood flow in cases of reduced or absent perfusion. Synthetic grafts have been used in large caliber vessels, including the aorta and pulmonary arteries, as the risk of thrombosis is lower with high flow rates and large lumens. In congenital heart disease, grafts are used in a number of indications, such as to connect the inferior vena cava to the pulmonary artery in the Fontan procedure. While these grafts have shown reasonable long-term outcomes, permanent synthetic conduits having no growth potential are implanted in children between 2 and 4 years of age, which can lead to complications due to somatic growth that require re-sizing operations (Chowdhury et al., 2005, Govindarajan et al., 2024).

Tissue engineered vascular grafts (TEVG) have been tested as an alternative to synthetic grafts and have demonstrated growth potential in clinical studies and animal models (Brennan et al., 2008, Sugiura et al., 2018). These grafts are made from synthetic scaffolds that degrade over time and are replaced by neotissue from the host. Several scaffold design parameters that modulate infiltration, proliferation, and matrix production of inflammatory and vascular cells. As clinical TEVGs for the Fontan procedure have demonstrated stenosis attributed to an exuberant foreign body response, modulating inflammation through altered scaffold design has been identified as a possible approach to mitigate adverse remodeling (Miller et al., 2015).

In previous work, we used numerical optimization and computations of growth and remodeling (G&R) to identify potential design improvements for TEVGs (Szafron et al., 2018, Szafron et al., 2019). For each design optimization, we chose an objective function as a quantitative metric representing unfavorable behavior, which was then minimized through an algorithmic search of design parameters that modulate this behavior. Specifically, we incorporated design parameters for the polymeric scaffold in a constrained mixture theory-based G&R framework that simulated the long-term evolution of TEVGs in vivo, including both inflammatory and mechanobiological stimuli for the neotissue formation (Szafron et al., 2018). We identified parameter sets that resulted in simulated TEVGs that better matched the targets, though we observed trade-offs between objective functions based on metrics that were interdependent. These proof-of-concept simulations were informed by data from an immuno-compromised mouse model, which did not exhibit the narrowing of concern (Miller et al., 2014, Hibino et al., 2015). Indeed, the optimized parameter set suggested that promoting additional immuno-mediated matrix deposition was needed to better match the properties of the adjoining vein, which was consistent with an impaired inflammatory response (Szafron et al., 2019). Yet, the ultimate goal is to optimize scaffolds for immuno-competent subjects, particularly to prevent the clinical complications in the current generation of TEVGs for congenital heart disease. Thus, our model in this study is informed by sheep TEVGs that exhibited stenosis with an immuno-competent foreign body response on the scale of the clinical cases (Drews et al., 2020, Latorre et al., 2022).

For parameter estimation and numerical optimization of the scaffold design in our G&R framework, we previously used an unconstrained derivative-free optimization technique, the Surrogate Management Framework (SMF) (Audet and Dennis Jr., 2004, Marsden et al., 2008, Ramachandra et al., 2015, Szafron et al., 2019). Derivative-free optimization is necessary in this context as the mathematical basis of G&R is complex, such that direct evaluation of derivatives with respect to design parameters is intractable. Combining multiple output metrics of interest into multi-objective functions allowed us to address clinical concerns related both to failure and functionality, such as minimizing deviations from the native radius and matching the native vessel compliance. Nevertheless, we are not able to easily rule out designs with unacceptable transient behavior, including early stenosis or dilatation. Fortunately, recent SMF formulations have included black-box non-linear constraints using the filter method (Verma et al., 2020), which guides the exploration of the parameter space to locate the minimum of the objective where the constraint is not violated.

In this work, we sought to optimize scaffold parameters using a G&R framework informed by ovine experiments, where stenosis severity was similar to that observed clinically (Drews et al., 2020, Blum et al., 2022). Unconstrained and constrained optimizations were performed using the SMF to determine the utility of constraints for identifying improved values of parameters that are readily changed by choice of material or modifying fabrication conditions. Sensitivity of the simulation to perturbations in parameter values was also compared between those parameters used experimentally and those determined by constrained optimization. Overall, we identified designs with promise to limit the observed stenosis and reduce the potential for adverse outcomes with small changes in the fabrication parameters. This approach shows promise to accelerate scaffold design for tissue engineering with functional long-term outcomes.