Rigorous mathematical optimization of synthetic hepatic vascular trees

In Silico Design of Heterogeneous Microvascular Trees Using Generative Adversarial Networks and Constrained Constructive Optimization

OBJECTIVE

Designing physiologically adequate microvascular trees is of crucial relevance for bioengineering functional tissues and organs. Yet, currently available methods are poorly suited to replicate the morphological and topological heterogeneity of real microvascular trees because the parameters used to control tree generation are too simplistic to mimic results of the complex angiogenetic and structural adaptation processes in vivo.

METHODS

We propose a method to overcome this limitation by integrating a conditional deep convolutional generative adversarial network (cDCGAN) with a local fractal dimension-oriented constrained constructive optimization (LFDO-CCO) strategy. The cDCGAN learns the patterns of real microvascular bifurcations allowing for their artificial replication. The LFDO-CCO strategy connects the generated bifurcations hierarchically to form microvascular trees with a vessel density corresponding to that observed in healthy tissues.

RESULTS

The generated artificial microvascular trees are consistent with real microvascular trees regarding characteristics such as fractal dimension, vascular density, and coefficient of variation of diameter, length, and tortuosity.

CONCLUSIONS

These results support the adoption of the proposed strategy for the generation of artificial microvascular trees in tissue engineering as well as for computational modeling and simulations of microcirculatory physiology.

Quantifying fat zonation in liver lobules: an integrated multiscale in silico model combining disturbed microperfusion and fat metabolism via a continuum biomechanical bi-scale, tri-phasic approach

Metabolic zonation refers to the spatial separation of metabolic functions along the sinusoidal axes of the liver. This phenomenon forms the foundation for adjusting hepatic metabolism to physiological requirements in health and disease (e.g., metabolic dysfunction-associated steatotic liver disease/MASLD). Zonated metabolic functions are influenced by zonal morphological abnormalities in the liver, such as periportal fibrosis and pericentral steatosis. We aim to analyze the interplay between microperfusion, oxygen gradient, fat metabolism and resulting zonated fat accumulation in a liver lobule. Therefore we developed a continuum biomechanical, tri-phasic, bi-scale, and multicomponent in silico model, which allows to numerically simulate coupled perfusion-function-growth interactions two-dimensionally in liver lobules. The developed homogenized model has the following specifications: (i) thermodynamically consistent, (ii) tri-phase model (tissue, fat, blood), (iii) penta-substances (glycogen, glucose, lactate, FFA, and oxygen), and (iv) bi-scale approach (lobule, cell). Our presented in silico model accounts for the mutual coupling between spatial and time-dependent liver perfusion, metabolic pathways and fat accumulation. The model thus allows the prediction of fat development in the liver lobule, depending on perfusion, oxygen and plasma concentration of free fatty acids (FFA), oxidative processes, the synthesis and the secretion of triglycerides (TGs). The use of a bi-scale approach allows in addition to focus on scale bridging processes. Thus, we will investigate how changes at the cellular scale affect perfusion at the lobular scale and vice versa. This allows to predict the zonation of fat distribution (periportal or pericentral) depending on initial conditions, as well as external and internal boundary value conditions.

Lumped parameter liver simulation to predict acute haemodynamic alterations following partial resections

Partial liver resections are routinely performed in living donor liver transplantation and to debulk tumours in liver malignancies, but surgical decisions on vessel reconstruction for adequate inflow and outflow are challenging. Pre-operative evaluation is often limited to radiological imaging, which fails to account for post-resection haemodynamic alterations. Substantial evidence suggests post-surgical increase in local volume flow rate enhances shear stress, signalling hepatic regeneration, but excessive shear stress has been postulated to result in small for size syndrome and liver failure. Predicting haemodynamic alterations throughout the liver is particularly challenging due to the dendritic architecture of the vasculature, spanning several orders of magnitude in diameter. Therefore, we developed a mathematical lumped parameter model with realistic heterogeneities capturing inflow/outflow of the human liver to simulate acute perfusion alterations following surgical resection. Our model is parametrized using clinical measurements, relies on a single free parameter and accurately captures established perfusion characteristics. We quantify acute changes in volume flow rate, flow speed and wall shear stress following variable, realistic liver resections and make comparisons with the intact liver. Our numerical model runs in minutes and can be adapted to patient-specific anatomy, providing a novel computational tool aimed at assisting pre- and intra-operative surgical decisions for liver resections.

The growth of capillary networks by branching for maximum fluid access

Here we document the deterministic evolution of capillary networks that morph by connecting more and more branches to water sources. The network grows with the objective of extracting in steady state higher and higher liquid flow rates. Growth happens through the generation of tree-shaped structures and the geometrical configuration of the dendritic network evolves as the number of connected sources increases. We present a novel methodology to generate capillary architectures and show how the evolution of the network leads to pump higher volumetric flow rates by capillary suction. The results suggest that networks generated within a plane lead to higher flow rates than networks generated within a three-dimensional domain, for the same volume of fluid.

Vascularization in Bioartificial Parenchymal Tissue: Bioink and Bioprinting Strategies

Among advanced therapy medicinal products, tissue-engineered products have the potential to address the current critical shortage of donor organs and provide future alternative options in organ replacement therapy. The clinically available tissue-engineered products comprise bradytrophic tissue such as skin, cornea, and cartilage. A sufficient macro- and microvascular network to support the viability and function of effector cells has been identified as one of the main challenges in developing bioartificial parenchymal tissue. Three-dimensional bioprinting is an emerging technology that might overcome this challenge by precise spatial bioink deposition for the generation of a predefined architecture. Bioinks are printing substrates that may contain cells, matrix compounds, and signaling molecules within support materials such as hydrogels. Bioinks can provide cues to promote vascularization, including proangiogenic signaling molecules and cocultured cells. Both of these strategies are reported to enhance vascularization. We review pre-, intra-, and postprinting strategies such as bioink composition, bioprinting platforms, and material deposition strategies for building vascularized tissue. In addition, bioconvergence approaches such as computer simulation and artificial intelligence can support current experimental designs. Imaging-derived vascular trees can serve as blueprints. While acknowledging that a lack of structured evidence inhibits further meta-analysis, this review discusses an end-to-end process for the fabrication of vascularized, parenchymal tissue.