Flow and transport in tissue engineering scaffolds: A network modelling approach

This paper was presented at the 2nd Micro and Nano Flows Conference (MNF2009), which was held at Brunel University, West London, UK. The conference was organised by Brunel University and supported by the Institution of Mechanical Engineers, IPEM, the Italian Union of Thermofluid dynamics, the Process Intensification Network, HEXAG - the Heat Exchange Action Group and the Institute of Mathematics and its Applications.Tissue engineers aim to grow functional tissues in the laboratory. One approach is to seed cells on a porous biomaterial scaffold, which is then cultured in a flow perfusion bioreactor. Such bioreactors enhance the transport of nutrients and growth factors to the cells by convection, and provide mechanical loads to mechanosensitive tissues. In this paper, we adopt a network modelling approach to provide insight into the nature of the flow, nutrient transport and cell distribution through the porous scaffold. The approach resolves flow and nutrient transport at the pore scale, and thus enables the local cellular environment to be determined. We demonstrate how this method can be used to study the impact of scaffold geometry (e.g. porosity, connectivity) on the cellular environment, and hence provide insight into the optimum culture conditions required to obtain functional tissues.This study is funded by the EPSRC

Spatial development of transport structures in apple (Malus x domestica Borkh.) fruit

The void network and vascular system are important pathways for the transport of gases, water and solutes in apple fruit (Malus x domestica Borkh). Here we used X-ray micro-tomography at various spatial resolutions to investigate the growth of these transport structures in 3D during fruit development of ‘Jonagold’ apple. The size of the void space and porosity in the cortex tissue increased considerably. In the core tissue, the porosity was consistently lower, and seemed to decrease towards the end of the maturation period. The voids in the core were more narrow and fragmented than the voids in the cortex. Both the void network in the core and in the cortex changed significantly in terms of void morphology. An automated segmentation protocol underestimated the total vasculature length by 9 to 12% in comparison to manually processed images. Vascular networks increased in length from a total of 5 meter at 9 weeks after full bloom, to more than 20 meter corresponding to 5 cm of vascular tissue per cubic centimeter of apple tissue. A high degree of branching in both the void network and vascular system and a complex three-dimensional pattern was observed across the whole fruit. The 3D visualisations of the transport structures may be useful for numerical modeling of organ growth and transport processes in fruit

Multiscale modelling of vascular tumour growth in 3D: the roles of domain size & boundary condition

We investigate a three-dimensional multiscale model of vascular tumour growth, which couples blood flow, angiogenesis, vascular remodelling, nutrient/growth factor transport, movement of, and interactions between, normal and tumour cells, and nutrient-dependent cell cycle dynamics within each cell. In particular, we determine how the domain size, aspect ratio and initial vascular network influence the tumour's growth dynamics and its long-time composition. We establish whether it is possible to extrapolate simulation results obtained for small domains to larger ones, by constructing a large simulation domain from a number of identical subdomains, each subsystem initially comprising two parallel parent vessels, with associated cells and diffusible substances. We find that the subsystem is not representative of the full domain and conclude that, for this initial vessel geometry, interactions between adjacent subsystems contribute to the overall growth dynamics. We then show that extrapolation of results from a small subdomain to a larger domain can only be made if the subdomain is sufficiently large and is initialised with a sufficiently complex vascular network. Motivated by these results, we perform simulations to investigate the tumour's response to therapy and show that the probability of tumour elimination in a larger domain can be extrapolated from simulation results on a smaller domain. Finally, we demonstrate how our model may be combined with experimental data, to predict the spatio-temporal evolution of a vascular tumour

Efficient vasculature investment in tissues can be determined without global information

Cells are the fundamental building blocks of organs and tissues. Information and mass flow through cellular contacts in these structures is vital for the orchestration of organ function. Constraints imposed by packing and cell immobility limit intercellular communication, particularly as organs and organisms scale up to greater sizes. In order to transcend transport limitations, delivery systems including vascular and respiratory systems evolved to facilitate the movement of matter and information. The construction of these delivery systems has an associated cost, as vascular elements do not perform the metabolic functions of the organs they are part of. This study investigates a fundamental trade-off in vascularization in multicellular tissues: the reduction of path lengths for communication versus the cost associated with producing vasculature. Biologically realistic generative models, using multicellular templates of different dimensionalities, revealed a limited advantage to the vascularization of two-dimensional tissues. Strikingly, scale-free improvements in transport efficiency can be achieved even in the absence of global knowledge of tissue organization. A point of diminishing returns in the investment of additional vascular tissue to the increased reduction of path length in 2.5- and three-dimensional tissues was identified. Applying this theory to experimentally determined biological tissue structures, we show the possibility of a co-dependency between the method used to limit path length and the organization of cells it acts upon. These results provide insight as to why tissues are or are not vascularized in nature, the robustness of developmental generative mechanisms and the extent to which vasculature is advantageous in the support of organ function

Quantification of Nematic Cell Polarity in Three-dimensional Tissues

How epithelial cells coordinate their polarity to form functional tissues is an open question in cell biology. Here, we characterize a unique type of polarity found in liver tissue, nematic cell polarity, which is different from vectorial cell polarity in simple, sheet-like epithelia. We propose a conceptual and algorithmic framework to characterize complex patterns of polarity proteins on the surface of a cell in terms of a multipole expansion. To rigorously quantify previously observed tissue-level patterns of nematic cell polarity (Morales-Navarette et al., eLife 8:e44860, 2019), we introduce the concept of co-orientational order parameters, which generalize the known biaxial order parameters of the theory of liquid crystals. Applying these concepts to three-dimensional reconstructions of single cells from high-resolution imaging data of mouse liver tissue, we show that the axes of nematic cell polarity of hepatocytes exhibit local coordination and are aligned with the biaxially anisotropic sinusoidal network for blood transport. Our study characterizes liver tissue as a biological example of a biaxial liquid crystal. The general methodology developed here could be applied to other tissues or in-vitro organoids.Comment: 27 pages, 9 color figure

3D hybrid wound devices for spatiotemporally controlled release kinetics

This paper presents localized and temporal control of releasekinetics over 3-dimensional (3D) hybridwounddevices to improve wound-healing process. Imaging study is performed to extract wound bed geometry in 3D. Non-Uniform Rational B-Splines (NURBS) based surface lofting is applied to generate functionally graded regions. Diffusion-based releasekinetics model is developed to predict time-based release of loaded modifiers for functionally graded regions. Multi-chamber single nozzle solid freeform dispensing system is used to fabricate wounddevices with controlled dispensing concentration. Spatiotemporal control of biological modifiers thus enables a way to achieve target delivery to improve wound healing

The Small World of Osteocytes: Connectomics of the Lacuno-Canalicular Network in Bone

Osteocytes and their cell processes reside in a large, interconnected network of voids pervading the mineralized bone matrix of most vertebrates. This osteocyte lacuno-canalicular network (OLCN) is believed to play important roles in mechanosensing, mineral homeostasis, and for the mechanical properties of bone. While the extracellular matrix structure of bone is extensively studied on ultrastructural and macroscopic scales, there is a lack of quantitative knowledge on how the cellular network is organized. Using a recently introduced imaging and quantification approach, we analyze the OLCN in different bone types from mouse and sheep that exhibit different degrees of structural organization not only of the cell network but also of the fibrous matrix deposited by the cells. We define a number of robust, quantitative measures that are derived from the theory of complex networks. These measures enable us to gain insights into how efficient the network is organized with regard to intercellular transport and communication. Our analysis shows that the cell network in regularly organized, slow-growing bone tissue from sheep is less connected, but more efficiently organized compared to irregular and fast-growing bone tissue from mice. On the level of statistical topological properties (edges per node, edge length and degree distribution), both network types are indistinguishable, highlighting that despite pronounced differences at the tissue level, the topological architecture of the osteocyte canalicular network at the subcellular level may be independent of species and bone type. Our results suggest a universal mechanism underlying the self-organization of individual cells into a large, interconnected network during bone formation and mineralization