Mathematical models of developmental vascular remodelling: A review.

Over the past 40 years, there has been a strong focus on the development of mathematical models of angiogenesis, while developmental remodelling has received little such attention from the mathematical community. Sprouting angiogenesis can be seen as a very crude way of laying out a primitive vessel network (the raw material), while remodelling (understood as pruning of redundant vessels, diameter control, and the establishment of vessel identity and hierarchy) is the key to turning that primitive network into a functional network. This multiscale problem is of prime importance in the development of a functional vasculature. In addition, defective remodelling (either during developmental remodelling or due to a reactivation of the remodelling programme caused by an injury) is associated with a significant number of diseases. In this review, we discuss existing mathematical models of developmental remodelling and explore the important contributions that these models have made to the field of vascular development. These mathematical models are effectively used to investigate and predict vascular development and are able to reproduce experimentally observable results. Moreover, these models provide a useful means of hypothesis generation and can explain the underlying mechanisms driving the observed structural and functional network development. However, developmental vascular remodelling is still a relatively new area in mathematical biology, and many biological questions remain unanswered. In this review, we present the existing modelling paradigms and define the key challenges for the field.

Traffic Patterns of the Migrating Endothelium: How Force Transmission Regulates Vascular Malformation and Functional Shunting During Angiogenic Remodelling.

Angiogenesis occurs in distinct phases: initial spouting is followed by remodelling in which endothelial cells (ECs) composing blood vessels rearrange by migrating against the direction of flow. Abnormal remodelling can result in vascular malformation. Such is the case in mutation of the Alk1 receptor within the mouse retina which disrupts flow-migration coupling, creating mixed populations of ECs polarised with/against flow which aggregate into arteriovenous malformations (AVMs). The lack of live imaging options in vivo means that the collective EC dynamics that drive AVM and the consequences of mixed populations of polarity remain a mystery. Therefore, our goal is to present a novel agent-based model to provide theoretical insight into EC force transmission and collective dynamics during angiogenic remodelling. Force transmission between neighbouring agents consists of extrusive forces which maintain spacing and cohesive forces which maintain the collective. We performed migration simulations within uniformly polarised populations (against flow) and mixed polarity (with/against flow). Within uniformly polarised populations, extrusive forces stabilised the plexus by facilitating EC intercalation which ensures that cells remained evenly distributed. Excess cohesion disrupts intercalation, resulting in aggregations of cells and functional shunting. Excess cohesion between ECs prevents them from resolving diameter balances within the plexus, leading to prolonged flow reversals which exert a critical behaviour change within the system as they switch the direction of cell migration and traffic patterns at bifurcations. Introducing mixtures of cell polarity dramatically changed the role of extrusive forces within the system. At low extrusion, opposing ECs were able to move past each other; however, at high extrusion the pushing between cells resulted in migration speeds close to zero, forming traffic jams and disrupting migration. In our study, we produced vascular malformations and functional shunting with either excess cohesion between ECs or mixtures of cell polarity. At the centre of both these mechanisms are cell-cell adherens junctions, which are involved in flow sensing/polarity and must remodelling dynamically to allow rearrangements of cells during vascular patterning. Thus, our findings implicate junctional dysfunction as a new target in the treatment and prevention of vascular disease and AVMs.

A modular framework for multiscale, multicellular, spatiotemporal modeling of acute primary viral infection and immune response in epithelial tissues and its application to drug therapy timing and effectiveness.

Simulations of tissue-specific effects of primary acute viral infections like COVID-19 are essential for understanding disease outcomes and optimizing therapies. Such simulations need to support continuous updating in response to rapid advances in understanding of infection mechanisms, and parallel development of components by multiple groups. We present an open-source platform for multiscale spatiotemporal simulation of an epithelial tissue, viral infection, cellular immune response and tissue damage, specifically designed to be modular and extensible to support continuous updating and parallel development. The base simulation of a simplified patch of epithelial tissue and immune response exhibits distinct patterns of infection dynamics from widespread infection, to recurrence, to clearance. Slower viral internalization and faster immune-cell recruitment slow infection and promote containment. Because antiviral drugs can have side effects and show reduced clinical effectiveness when given later during infection, we studied the effects on progression of treatment potency and time-of-first treatment after infection. In simulations, even a low potency therapy with a drug which reduces the replication rate of viral RNA greatly decreases the total tissue damage and virus burden when given near the beginning of infection. Many combinations of dosage and treatment time lead to stochastic outcomes, with some simulation replicas showing clearance or control (treatment success), while others show rapid infection of all epithelial cells (treatment failure). Thus, while a high potency therapy usually is less effective when given later, treatments at late times are occasionally effective. We illustrate how to extend the platform to model specific virus types (e.g., hepatitis C) and add additional cellular mechanisms (tissue recovery and variable cell susceptibility to infection), using our software modules and publicly-available software repository.

A modular framework for multiscale, multicellular, spatiotemporal modeling of acute primary viral infection and immune response in epithelial tissues and its application to drug therapy timing and effectiveness: A multiscale model of viral infection in epithelial tissues.

Simulations of tissue-specific effects of primary acute viral infections like COVID-19 are essential for understanding disease outcomes and optimizing therapies. Such simulations need to support continuous updating in response to rapid advances in understanding of infection mechanisms, and parallel development of components by multiple groups. We present an open-source platform for multiscale spatiotemporal simulation of an epithelial tissue, viral infection, cellular immune response and tissue damage, specifically designed to be modular and extensible to support continuous updating and parallel development. The base simulation of a simplified patch of epithelial tissue and immune response exhibits distinct patterns of infection dynamics from widespread infection, to recurrence, to clearance. Slower viral internalization and faster immune-cell recruitment slow infection and promote containment. Because antiviral drugs can have side effects and show reduced clinical effectiveness when given later during infection, we studied the effects on progression of treatment potency and time-of-first treatment after infection. In simulations, even a low potency therapy with a drug which reduces the replication rate of viral RNA greatly decreases the total tissue damage and virus burden when given near the beginning of infection. Many combinations of dosage and treatment time lead to stochastic outcomes, with some simulation replicas showing clearance or control (treatment success), while others show rapid infection of all epithelial cells (treatment failure). Thus, while a high potency therapy usually is less effective when given later, treatments at late times are occasionally effective. We illustrate how to extend the platform to model specific virus types (e.g., hepatitis C) and add additional cellular mechanisms (tissue recovery and variable cell susceptibility to infection), using our software modules and publicly-available software repository.

Laryngeal closure impedes non-invasive ventilation at birth.

BACKGROUND: Non-invasive ventilation is sometimes unable to provide the respiratory needs of very premature infants in the delivery room. While airway obstruction is thought to be the main problem, the site of obstruction is unknown. We investigated whether closure of the larynx and epiglottis is a major site of airway obstruction. METHODS: We used phase contrast X-ray imaging to visualise laryngeal function in spontaneously breathing premature rabbits immediately after birth and at approximately 1 hour after birth. Non-invasive respiratory support was applied via a facemask and images were analysed to determine the percentage of the time the glottis and the epiglottis were open. HYPOTHESIS: Immediately after birth, the larynx is predominantly closed, only opening briefly during a breath, making non-invasive intermittent positive pressure ventilation (iPPV) ineffective, whereas after lung aeration, the larynx is predominantly open allowing non-invasive iPPV to ventilate the lung. RESULTS: The larynx and epiglottis were predominantly closed (open 25.5%±1.1% and 17.1%±1.6% of the time, respectively) in pups with unaerated lungs and unstable breathing patterns immediately after birth. In contrast, the larynx and the epiglottis were mostly open (90.5%±1.9% and 72.3%±2.3% of the time, respectively) in pups with aerated lungs and stable breathing patterns irrespective of time after birth. CONCLUSION: Laryngeal closure impedes non-invasive iPPV at birth and may reduce the effectiveness of non-invasive respiratory support in premature infants immediately after birth.

Effect of betamethasone, surfactant, and positive end-expiratory pressures on lung aeration at birth in preterm rabbits.

Antenatal glucocorticoids, exogenous surfactant, and positive end-expiratory pressure (PEEP) ventilation are commonly provided to preterm infants to enhance respiratory function after birth. It is unclear how these treatments interact to improve the transition to air-breathing at birth. We investigated the relative contribution of antenatal betamethasone, prophylactic surfactant, and PEEP (3 cmH2O) on functional residual capacity (FRC) and dynamic lung compliance (CDL) in preterm (28 day GA) rabbit kittens at birth. Kittens were delivered by cesarean section and mechanically ventilated. FRC was calculated from X-ray images, and CDL was measured using plethysmography. Without betamethasone, PEEP increased FRC recruitment and CDL Surfactant did not further increase FRC, but significantly increased CDL Betamethasone abolished the benefit of PEEP on FRC, but surfactant counteracted this effect of betamethasone. These findings indicate that low PEEP levels are insufficient to establish FRC at birth following betamethasone treatment. However, surfactant reversed the effect of betamethasone and when combined, these two treatments enhanced FRC recruitment irrespective of PEEP level.