Modelling the Impact of Cell Seeding Strategies on Cell Survival and Vascularisation in Engineered Tissue

Currently, the design of tissue engineered constructs for peripheral nerve repair is informed predominantly by experiments. However, translation to the clinical setting is slow, and engineered tissues have not surpassed the outcomes achieved by nerve grafts. Therapeutic cell survival and vascularisation are important for the assimilation of engineered tissue, and vascularisation provides vital directional cues for regenerating nerves. In this thesis, mathematical modelling informed by experimental data is used to investigate the impact of different therapeutic cell seeding strategies on cell survival and vascularisation in engineered tissue nerve repair constructs. A mathematical model of interactions between cells, oxygen and vascular endothelial growth factor (VEGF), consisting of three partial differential equations, is developed and parameterised against in vitro data. Key cell type-specific parameter values are derived, and the model is then used to simulate cell-solute interactions in a nerve repair construct over the first five days post-implantation in vivo. Simulations using uniform seeding cell densities of 88 and 13 × 10⁶ cells/ml result in the highest mean viable cell densities across the construct after 1 and 5 days respectively. However, simulations using seeding densities in the range of 200 – 300 ×10⁶ cells/ml result in steeper VEGF gradients and higher total VEGF concentrations across the construct, which could be beneficial for vascularisation. Simulations incorporating a porous construct sheath result in higher viable cell density predictions, but also lower total VEGF concentrations, than those run using an impermeable sheath. Subsequently, the cell-solute model is combined with a discrete model of angiogenesis that simulates vascular growth in response to gradients of VEGF. Simulation results suggest that different cell seeding strategies could influence the density, rate and morphology of vascularisation. The predictions generated in this work demonstrate how mathematical modelling as part of a wider multidisciplinary approach can provide direction for future experimental work

Cell migration and capillary plexus formation in wounds and retinae

Cell migration is a fundamental biological phenomenon that is critical to the development and maintenance of tissues in multi-cellular organisms. This thesis presents a series of discrete mathematical models designed to study the migratory response of such cells when exposed to a variety of environmental stimuli. By applying these models to pertinent biological scenarios and benchmarking results against experimental data, novel insights are gained into the underlying cell behaviour. The process of angiogenesis is investigated first and models are developed for simulating capillary plexus expansion during both wound healing and retinal vascular development. The simulated cell migration is coupled to a detailed model of blood perfusion that allows prediction of dynamic flow-induced evolution of the nascent vascular architectures – the network topologies generated in each case are found to successfully reproduce a number of longitudinal experimental metrics. Moreover, in the case of retinal development, the resultant distributions of haematocrit and oxygen are found to be essential in generating vasculatures that resemble those observed in vivo. An alternative cell migration model is then derived that is capable of more accurately describing both individual and collective cell movement. The general model framework, which allows for biophysical cell-cell interactions and adaptive cell morphologies, is seen to have the potential for a range of applications. The value of the modelling approach is well demonstrated by benchmarking in silico cell movement against experimental data from an in vitro fibroblast scrape wound assay. The results subsequently reveal an unexplained discrepancy that provides an intriguing challenge for future studies

Multiscale modelling of blood flow in cerebral microcirculation: Details at capillary scale control accuracy at the level of the cortex

Aging or cerebral diseases may induce architectural modifications in human brain microvascular networks, such as capillary rarefaction. Such modifications limit blood and oxygen supply to the cortex, possibly resulting in energy failure and neuronal death. Modelling is key in understanding how these architectural modifications affect blood flow and mass transfers in such complex networks. However, the huge number of vessels in the human brain—tens of billions—prevents any modelling approach with an explicit architectural representation down to the scale of the capillaries. Here, we introduce a hybrid approach to model blood flow at larger scale in the brain microcirculation, based on its multiscale architecture. The capillary bed, which is a space-filling network, is treated as a porous medium and modelled using a homogenized continuum approach. The larger arteriolar and venular trees, which cannot be homogenized because of their fractal-like nature, are treated as a network of interconnected tubes with a detailed representation of their spatial organization. The main contribution of this work is to devise a proper coupling model at the interface between these two components. This model is based on analytical approximations of the pressure field that capture the strong pressure gradients building up in the capillaries connected to arterioles or venules. We evaluate the accuracy of this model for both very simple architectures with one arteriole and/or one venule and for more complex ones, with anatomically realistic tree-like vessels displaying a large number of coupling sites. We show that the hybrid model is very accurate in describing blood flow at large scales and further yields a significant computational gain by comparison with a classical network approach. It is therefore an important step towards large scale simulations of cerebral blood flow and lays the groundwork for introducing additional levels of complexity in the future

The Ageing Brain: Investigating the Role of Age in Changes to the Human Cerebral Microvasculature With an in silico Model

Ageing causes extensive structural changes to the human cerebral microvasculature, which have a significant effect on capillary bed perfusion and oxygen transport. Current models of brain capillary networks in the literature focus on healthy adult brains and do not capture the effects of ageing, which is critical when studying neurodegenerative diseases. This study builds upon a statistically accurate model of the human cerebral microvasculature based on ex-vivo morphological data. This model is adapted for “healthy” ageing using in-vivo measurements from mice at three distinct age groups—young, middle-aged, and old. From this new model, blood and molecular exchange parameters are calculated such as permeability and surface-area-to-volume ratio, and compared across the three age groups. The ability to alter the model vessel-by-vessel is used to create a continuous gradient of ageing. It was found that surface-area-to-volume ratio reduced in old age by 6% and permeability by 24% from middle-age to old age, and variability within the networks also increased with age. The ageing gradient indicated a threshold in the ageing process around 75 years old, after which small changes have an amplified effect on blood flow properties. This gradient enables comparison of studies measuring cerebral properties at discrete points in time. The response of middle aged and old aged capillary beds to micro-emboli showed a lower robustness of the old age capillary bed to vessel occlusion. As the brain ages, there is thus increased vulnerability of the microvasculature—with a “tipping point” beyond which further remodeling of the microvasculature has exaggerated effects on the brain. When developing in-silico models of the brain, age is a very important consideration to accurately assess risk factors for cognitive decline and isolate early biomarkers of microvascular health.</jats:p

In silico trials for treatment of acute ischemic stroke: Design and implementation

An in silico trial simulates a disease and its corresponding therapies on a cohort of virtual patients to support the development and evaluation of medical devices, drugs, and treatment. In silico trials have the potential to refine, reduce cost, and partially replace current in vivo studies, n

On the sensitivity analysis of porous finite element models for cerebral perfusion estimation

AbstractComputational physiological models are promising tools to enhance the design of clinical trials and to assist in decision making. Organ-scale haemodynamic models are gaining popularity to evaluate perfusion in a virtual environment both in healthy and diseased patients. Recently, the principles of verification, validation, and uncertainty quantification of such physiological models have been laid down to ensure safe applications of engineering software in the medical device industry. The present study sets out to establish guidelines for the usage of a three-dimensional steady state porous cerebral perfusion model of the human brain following principles detailed in the verification and validation (V&amp;V 40) standard of the American Society of Mechanical Engineers. The model relies on the finite element method and has been developed specifically to estimate how brain perfusion is altered in ischaemic stroke patients before, during, and after treatments. Simulations are compared with exact analytical solutions and a thorough sensitivity analysis is presented covering every numerical and physiological model parameter.The results suggest that such porous models can approximate blood pressure and perfusion distributions reliably even on a coarse grid with first order elements. On the other hand, higher order elements are essential to mitigate errors in volumetric blood flow rate estimation through cortical surface regions. Matching the volumetric flow rate corresponding to major cerebral arteries is identified as a validation milestone. It is found that inlet velocity boundary conditions are hard to obtain and that constant pressure inlet boundary conditions are feasible alternatives. A one-dimensional model is presented which can serve as a computationally inexpensive replacement of the three-dimensional brain model to ease parameter optimisation, sensitivity analyses and uncertainty quantification.The findings of the present study can be generalised to organ-scale porous perfusion models. The results increase the applicability of computational tools regarding treatment development for stroke and other cerebrovascular conditions.</jats:p

Towards brain-scale modelling of the human cerebral blood flow : hybrid approach and high performance computing

The brain microcirculation plays a key role in cerebral physiology and neuronal activation. In the case of degenerative diseases such as Alzheimer’s, severe deterioration of the microvascular networks (e.g. vascular occlusions) limit blood flow, thus oxygen and nutrients supply, to the cortex, eventually resulting in neurons death. In addition to functional neuroimaging, modelling is a valuable tool to investigate the impact of structural variations of the microvasculature on blood flow and mass transfers. In the brain microcirculation, the capillary bed contains the smallest vessels (1-10 μm in diameter) and presents a mesh-like structure embedded in the cerebral tissue. This is the main place of molecular exchange between blood and neurons. The capillary bed is fed and drained by larger arteriolar and venular tree-like vessels (10-100 μm in diameter). For the last decades, standard network approaches have significantly advanced our understanding of blood flow, mass transport and regulation mechanisms in the human brain microcirculation. By averaging flow equations over the vascular cross-sections, such approaches yield a one-dimensional model that involves much fewer variables compared to a full three-dimensional resolution of the flow. However, because of the high density of capillaries, such approaches are still computationally limited to relatively small volumes (<100 mm3). This constraint prevents applications at clinically relevant scales, since standard imaging techniques only yield much larger volumes (∼100 cm3), with a resolution of 1-10 mm3. To get around this computational cost, we present a hybrid approach for blood flow modelling where the capillaries are replaced by a continuous medium. This substitution makes sense since the capillary bed is dense and space-filling over a cut-off length of ∼50 μm. In this continuum, blood flow is characterized by effective properties (e.g. permeability) at the scale of a much larger representative volume. Furthermore, the domain is discretized on a coarse grid using the finite volume method, inducing an important computational gain. The arteriolar and venular trees cannot be homogenized because of their quasi-fractal structure, thus the network approach is used to model blood flow in the larger vessels. The main difficulty of the hybrid approach is to develop a proper coupling model at the points where arteriolar or venular vessels are connected to the continuum. Indeed, high pressure gradients build up at capillary-scale in the vicinity of the coupling points, and must be properly described at the continuum-scale. Such multiscale coupling has never been discussed in the context of brain microcirculation. Taking inspiration from the Peaceman “well model” developed for petroleum engineering, our coupling model relies on to use analytical solutions of the pressure field in the neighbourhood of the coupling points. The resulting equations yield a single linear system to solve for both the network part and the continuum (strong coupling). The accuracy of the hybrid model is evaluated by comparison with a classical network approach, for both very simple synthetic architectures involving no more than two couplings, and more complex ones, with anatomical arteriolar and venular trees displaying a large number of couplings. We show that the present approach is very accurate, since relative pressure errors are lower than 6 %. This lays the goundwork for introducing additional levels of complexity in the future (e.g. non uniform hematocrit). In the perspective of large-scale simulations and extension to mass transport, the hybrid approach has been implemented in a C++ code designed for High Performance Computing. It has been fully parallelized using Message Passing Interface standards and specialized libraries (e.g. PETSc). Since the present work is part of a larger project involving several collaborators, special care has been taken in developing efficient coding strategies