Procedural generation of vascular networks for tissue engineering
The greatest challenge in tissue engineering is that of vascularization: tissue constructs at length scales above the diffusive length without embedded perfusable channels will be unable to supply oxygen and nutrients to—or remove waste from—cells within the construct, leading to necrosis. This has historically limited tissue engineering to sub-millimetre lengths; in response, tissue engineers have developed a wealth of manufacturing methods to embed perfusable channels in hydrogel constructs, but there does not currently exist a software package to automatically generate these channel networks subject to manufacturability and cellular survival constraints. This thesis contributes a software package and associated design philosophy for generating vasculature specifically for use in tissue engineering. We first review the current manufacturing landscape and compare this to real vasculature, concluding that the aim of networks designed by our software should be ensuring short-term survival to enable embedded cells to self-assemble into the desired structure, particularly since functionality often requires the transfer of large molecules, with direct cell-capillary contact in vivo. This leads to two input parameters for our software: the critical cell-channel distance for oxygen-limited survival, and the minimum manufacturable feature size. Current methods of designing vasculature for tissue engineering do not scale well and are only suitable for small technology demonstrations: it is impossible to avoid at least one of dead zones, high perfusion pressures and non-uniform flow delivery, and manual intervention in the design is common. Attempting to copy real vasculature is also not suitable: reconstructed scan data is often noisy, incomplete and contains pathologies; further, small chunks of tissue do not have a well-defined single inlet and outlet for connecting to perfusion systems. The only suitable starting point is deemed to be the group of algorithms developed for simulating medical imaging data and organ perfusion by generating artificial vasculature, but even these are unable to guarantee uniform perfusion or correctly handle multiple interpenetrating networks to ensure fluid transfers between them only at their endpoints. In this work, a complete package for vascularizing arbitrary domains with an arbitrary number of distinct networks is developed, which can generate networks from a single starting point and radius (the typical engineering case) as well as being able to take existing networks and develop them further to ensure complete perfusion and water-tightness. A modified version of the most popular algorithm for generating vasculature for medical simulation (Constrained Constructive Optimization) is developed, which shows substantial performance benefits and better computational scaling compared to the traditional approach. However, CCO has a number of deficits which can only be overcome at great expense, such as high asymmetry and an inability to handle non-convex domains: to solve this, a novel algorithm has been developed using a biological analogy of vascular invasion and tissue growth, named Lattice Sequence Vascularization. This algorithm is shown to scale better, as well as enforcing hierarchy on the networks where possible (generating networks which show self-similarity across length scales, a key feature of real vasculature), resorting to generating tendrils only when necessary to meet the perfusion constraint. Constraints such as intersections with the domain boundary and other networks are enforced separately to growth, and this is handled in a way that ensures that the critical cell-channel distance is met throughout the domain. A suite of optimization methods is developed, with the most simple being global optimization of node positions for a number of physiologically justified costs. More complex approaches include heuristic-guided topological optimization of the networks, as well as a simulated annealing approach which is shown to be less expensive than previous implementations, whilst producing more optimal networks. The separation into distinct growth, optimization and constraint enforcement stages enables us to design highly-optimized (yet still manufacturable) networks with extremely low computational cost, generating networks at the complete organ scale in minutes on desktop hardware. Finally, we showcase some techniques developed to increase biomimicry within the artificial networks, such as vessel smoothing and flow rate dependent splitting laws, and demonstrate the ability to insert predefined functional structures at the microscale, including complex structures with multiple inlet/outlet points. In the course of developing increasingly complex networks, we find CAD packages become unstable and mesh sizes increase drastically, so a mesh decimation framework from the literature is adapted to export meshes piecewise. The software is validated in collaboration with experimentalists, showing that the generated designs are both manufacturable and able to keep cell populations alive. Data provided by a collaborator is used to show that the software is able to take reconstructed vessels as a starting point and completely fill real organ bounding geometries with vessels that are visually similar to real vasculature, although we do not perform any morphological comparisons to real vasculature. This work removes the major challenge to scaling up tissue engineering and sets the stage for multi-scale design, in which a template functional structure is designed using a combination of simulations and experiments, before using the software developed in this thesis to generate optimized distribution networks to supply these. When combined with imaging data, it also has potential applications to theoretical questions, such as whether metabolic optimality alone can recreate the features seen in real vasculature.
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