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.

Measurement of Frontal Midline Theta Oscillations using OPM-MEG.

Optically pumped magnetometers (OPMs) are an emerging lightweight and compact sensor that can measure magnetic fields generated by the human brain. OPMs enable construction of wearable magnetoencephalography (MEG) systems, which offer advantages over conventional instrumentation. However, when trying to measure signals at low frequency, higher levels of inherent sensor noise, magnetic interference and movement artefact introduce a significant challenge. Accurate characterisation of low frequency brain signals is important for neuroscientific, clinical, and paediatric MEG applications and consequently, demonstrating the viability of OPMs in this area is critical. Here, we undertake measurement of theta band (4-8 Hz) neural oscillations and contrast a newly developed 174 channel triaxial wearable OPM-MEG system with conventional (cryogenic-MEG) instrumentation. Our results show that visual steady state responses at 4 Hz, 6 Hz and 8 Hz can be recorded using OPM-MEG with a signal-to-noise ratio (SNR) that is not significantly different to conventional MEG. Moreover, we measure frontal midline theta oscillations during a 2-back working memory task, again demonstrating comparable SNR for both systems. We show that individual differences in both the amplitude and spatial signature of induced frontal-midline theta responses are maintained across systems. Finally, we show that our OPM-MEG results could not have been achieved without a triaxial sensor array, or the use of postprocessing techniques. Our results demonstrate the viability of OPMs for characterising theta oscillations and add weight to the argument that OPMs can replace cryogenic sensors as the fundamental building block of MEG systems.

Enabling ambulatory movement in wearable magnetoencephalography with matrix coil active magnetic shielding.

The ability to collect high-quality neuroimaging data during ambulatory participant movement would enable a wealth of neuroscientific paradigms. Wearable magnetoencephalography (MEG) based on optically pumped magnetometers (OPMs) has the potential to allow participant movement during a scan. However, the strict zero magnetic field requirement of OPMs means that systems must be operated inside a magnetically shielded room (MSR) and also require active shielding using electromagnetic coils to cancel residual fields and field changes (due to external sources and sensor movements) that would otherwise prevent accurate neuronal source reconstructions. Existing active shielding systems only compensate fields over small, fixed regions and do not allow ambulatory movement. Here we describe the matrix coil, a new type of active shielding system for OPM-MEG which is formed from 48 square unit coils arranged on two planes which can compensate magnetic fields in regions that can be flexibly placed between the planes. Through the integration of optical tracking with OPM data acquisition, field changes induced by participant movement are cancelled with low latency (25 ms). High-quality MEG source data were collected despite the presence of large (65 cm translations and 270° rotations) ambulatory participant movements.

Choice of spatial discretisation influences the progression of viral infection within multicellular tissues.

There has been an increasing recognition of the utility of models of the spatial dynamics of viral spread within tissues. Multicellular models, where cells are represented as discrete regions of space coupled to a virus density surface, are a popular approach to capture these dynamics. Conventionally, such models are simulated by discretising the viral surface and depending on the rate of viral diffusion and other considerations, a finer or coarser discretisation may be used. The impact that this choice may have on the behaviour of the system has not been studied. Here we demonstrate that under realistic parameter regimes - where viral diffusion is small enough to support the formation of familiar ring-shaped infection plaques - the choice of spatial discretisation of the viral surface can qualitatively change key model outcomes including the time scale of infection. Importantly, we show that the choice between implementing viral spread as a cell-scale process, or as a high-resolution converged PDE can generate distinct model outcomes, which raises important conceptual questions about the strength of assumptions underpinning the spatial structure of the model. We investigate the mechanisms driving these discretisation artefacts, the impacts they may have on model predictions, and provide guidance on the design and implementation of spatial and especially multicellular models of viral dynamics. We obtain our results using the simplest TIV construct for the viral dynamics, and therefore anticipate that the important effects we describe will also influence model predictions in more complex models of virus-cell-immune system interactions. This analysis will aid in the construction of models for robust and biologically realistic modelling and inference.

Multiscale modelling of desquamation in the interfollicular epidermis.

Maintenance of epidermal thickness is critical to the barrier function of the skin. Decreased tissue thickness, specifically in the stratum corneum (the outermost layer of the tissue), causes discomfort and inflammation, and is related to several severe diseases of the tissue. In order to maintain both stratum corneum thickness and overall tissue thickness it is necessary for the system to balance cell proliferation and cell loss. Cell proliferation in the epidermis occurs in the basal layer and causes constant upwards movement in the tissue. Cell loss occurs when dead cells at the top of the tissue are lost to the environment through a process called desquamation. Desquamation is thought to occur through a gradual reduction in adhesion between cells, due to the cleaving of adhesion proteins by enzymes, in the stratum corneum. In this paper we will investigate combining a (mass action) subcellular model of desquamation with a three dimensional (cell centre based) multicellular model of the interfollicular epidermis to better understand maintenance of epidermal thickness. Specifically, our aim is to determine if a hypothesised biological model for the degradation of cell-cell adhesion, from the literature, is sufficient to maintain a steady state tissue thickness. These investigations show the model is able to provide a consistent rate of cell loss in the multicellular model. This loss balances proliferation, and hence maintains a homeostatic tissue thickness. Moreover, we find that multiple proliferative cell populations in the basal layer can be represented by a single proliferative cell population, simplifying investigations with this model. The model is used to investigate a disorder (Netherton Syndrome) which disrupts desquamation. The model shows how biochemical changes can cause disruptions to the tissue, resulting in a reduced tissue thickness and consequently diminishing the protective role of the tissue. A hypothetical treatment result is also investigated: we compare the cases of a partially effective homogeneous treatment (where all cells partially recover) and a totally effective heterogeneous treatment (in which a proportion of the cells totally recover) with the aim to determine the difference in the response of the tissue to these different scenarios. Results show an increased benefit to corneum thickness from the heterogeneous treatment over the homogeneous treatment.

1,3-Diamine-Derived Catalysts: Design, Synthesis, and the Use in Enantioselective Mannich Reactions of Ketones.

1,3-Diamine-derived catalysts were designed, synthesized, and used in asymmetric Mannich reactions of ketones. The reactions catalyzed by one of the 1,3-diamine derivatives in the presence of acids afforded the Mannich products with high enantioselectivities under mild conditions. In most cases, bond formation occurred at the less-substituted α-position of the ketone carbonyl group. Our results indicate that the primary and the tertiary amines of the 1,3-diamine derivative cooperatively act for the catalysis.

Free and Interfacial Boundaries in Individual-Based Models of Multicellular Biological systems.

Coordination of cell behaviour is key to a myriad of biological processes including tissue morphogenesis, wound healing, and tumour growth. As such, individual-based computational models, which explicitly describe inter-cellular interactions, are commonly used to model collective cell dynamics. However, when using individual-based models, it is unclear how descriptions of cell boundaries affect overall population dynamics. In order to investigate this we define three cell boundary descriptions of varying complexities for each of three widely used off-lattice individual-based models: overlapping spheres, Voronoi tessellation, and vertex models. We apply our models to multiple biological scenarios to investigate how cell boundary description can influence tissue-scale behaviour. We find that the Voronoi tessellation model is most sensitive to changes in the cell boundary description with basic models being inappropriate in many cases. The timescale of tissue evolution when using an overlapping spheres model is coupled to the boundary description. The vertex model is demonstrated to be the most stable to changes in boundary description, though still exhibits timescale sensitivity. When using individual-based computational models one should carefully consider how cell boundaries are defined. To inform future work, we provide an exploration of common individual-based models and cell boundary descriptions in frequently studied biological scenarios and discuss their benefits and disadvantages.

Naturalistic Hyperscanning with Wearable Magnetoencephalography.

The evolution of human cognitive function is reliant on complex social interactions which form the behavioural foundation of who we are. These social capacities are subject to dramatic change in disease and injury; yet their supporting neural substrates remain poorly understood. Hyperscanning employs functional neuroimaging to simultaneously assess brain activity in two individuals and offers the best means to understand the neural basis of social interaction. However, present technologies are limited, either by poor performance (low spatial/temporal precision) or an unnatural scanning environment (claustrophobic scanners, with interactions via video). Here, we describe hyperscanning using wearable magnetoencephalography (MEG) based on optically pumped magnetometers (OPMs). We demonstrate our approach by simultaneously measuring brain activity in two subjects undertaking two separate tasks-an interactive touching task and a ball game. Despite large and unpredictable subject motion, sensorimotor brain activity was delineated clearly, and the correlation of the envelope of neuronal oscillations between the two subjects was demonstrated. Our results show that unlike existing modalities, OPM-MEG combines high-fidelity data acquisition and a naturalistic setting and thus presents significant potential to investigate neural correlates of social interaction.

Triaxial detection of the neuromagnetic field using optically-pumped magnetometry: feasibility and application in children.

Optically-pumped magnetometers (OPMs) are an established alternative to superconducting sensors for magnetoencephalography (MEG), offering significant advantages including flexibility to accommodate any head size, uniform coverage, free movement during scanning, better data quality and lower cost. However, OPM sensor technology remains under development; there is flexibility regarding OPM design and it is not yet clear which variant will prove most effective for MEG. Most OPM-MEG implementations have either used single-axis (equivalent to conventional MEG) or dual-axis magnetic field measurements. Here we demonstrate use of a triaxial OPM formulation, able to characterise the full 3D neuromagnetic field vector. We show that this novel sensor is able to characterise magnetic fields with high accuracy and sensitivity that matches conventional (dual-axis) OPMs. We show practicality via measurement of biomagnetic fields from both the heart and the brain. Using simulations, we demonstrate how triaxial measurement offers improved cortical coverage, especially in infants. Finally, we introduce a new 3D-printed child-friendly OPM-helmet and demonstrate feasibility of triaxial measurement in a five-year-old. In sum, the data presented demonstrate that triaxial OPMs offer a significant improvement over dual-axis variants and are likely to become the sensor of choice for future MEG systems, particularly for deployment in paediatric populations.

Using OPM-MEG in contrasting magnetic environments.

Magnetoencephalography (MEG) has been revolutionised by optically pumped magnetometers (OPMs). "OPM-MEG" offers higher sensitivity, better spatial resolution, and lower cost than conventional instrumentation based on superconducting quantum interference devices (SQUIDs). Moreover, because OPMs are small, lightweight, and portable they offer the possibility of lifespan compliance and (with control of background field) motion robustness, dramatically expanding the range of MEG applications. However, OPM-MEG remains nascent technology; it places stringent requirements on magnetic shielding, and whilst a number of viable systems exist, most are custom made and there have been no cross-site investigations showing the reliability of data. In this paper, we undertake the first cross-site OPM-MEG comparison, using near identical commercial systems scanning the same participant. The two sites are deliberately contrasting, with different magnetic environments: a "green field" campus university site with an OPM-optimised shielded room (low interference) and a city centre hospital site with a "standard" (non-optimised) MSR (higher interference). We show that despite a 20-fold difference in background field, and a 30-fold difference in low frequency interference, using dynamic field control and software-based suppression of interference we can generate comparable noise floors at both sites. In human data recorded during a visuo-motor task and a face processing paradigm, we were able to generate similar data, with source localisation showing that brain regions could be pinpointed with just ∼10 mm spatial discrepancy and temporal correlations of > 80%. Overall, our study demonstrates that, with appropriate field control, OPM-MEG systems can be sited even in city centre hospital locations. The methods presented pave the way for wider deployment of OPM-MEG.

Peer supported Open Dialogue in the National Health Service: implementing and evaluating a new approach to Mental Health Care.

BACKGROUND: Open Dialogue is an internationally developing approach to mental health care based on collaboration between an individual and their family and social network. Our quest for better approaches to Mental Health Care with improved carer and service user experience led us to develop and test a model of Peer Supported Open Dialogue (POD). There is no research currently looking at the implementation and effectiveness of a standalone POD team in the NHS so we evaluate its implementation, clinical outcomes and value to service users and their families. METHOD: A before-after design was used. 50 service users treated by the POD Team were recruited and participants from their family and wider social network. Service user self report questionnaires covering wellbeing, functioning, satisfaction were collected and one carer self report measure; at baseline, three and six months. A clinician reported measure was collected at baseline and six months. Clinicians perceptions of practice were collected following network meetings. RESULTS: 50 service users treated were recruited with a mean age of 35 years with slightly more males than females. Service users reported signficant improvements in wellbeing and functioning. There was a marked increase in perceived support by carers. Over half the meetings were attended by carers. The Community Mental Health Survey showed high satisfaction rates for service users including carer involvement. CONCLUSIONS: The study indicated it was possible to transform to deliver a clinically effective POD service in the NHS. This innovative approach provided continuity of care within the social network, with improved carer support and significant improvements in clinical outcomes and their experiences. TRIAL REGISTRATION: ( isrctn.com/ISRCTN36004039 . Retrospectively registered 04/01/2019.

Composition of Pinot Noir Wine from Grapevine Red Blotch Disease-Infected Vines Managed with Exogenous Abscisic Acid Applications.

Grapevine red blotch disease (GRBD) has negative effects on grape development and impacts berry ripening. Abscisic acid (ABA) is a plant growth regulator involved in the initiation of berry ripening. Exogenous abscisic acid application was compared to an unsprayed control on GRBD-positive Pinot noir vines during two vintages, and the total monomeric anthocyanin, total phenolics, phenolic composition, and volatile profile were measured in wines. In addition, untargeted metabolites were profiled using high-resolution LC-MS/MS. Results showed that the wine composition varied by vintage year and was not consistent with ABA application. Wines from the ABA treatment had a lower total anthocyanin and total phenolic content in one year. The untargeted high-resolution LC-MS/MS analysis showed a higher abundance of phenolic compounds in ABA wines in 2019, but lower in 2018. The wine volatile compounds of ABA treatments varied by vintage. There were higher levels of free ß-damascenone, ß-ionone, nerol, and several fermentation-derived esters, acids, and alcohols in ABA wines, but these were not observed in 2019. Lower 3-isobutyl-2-methoxypyrazine (IBMP) was also observed in wines with ABA treatment in 2019. The results demonstrated that ABA application to the fruit zones did not consistently mitigate the adverse impacts of GRBD on Pinot noir wines.

Theoretical advantages of a triaxial optically pumped magnetometer magnetoencephalography system.

The optically pumped magnetometer (OPM) is a viable means to detect magnetic fields generated by human brain activity. Compared to conventional detectors (superconducting quantum interference devices) OPMs are small, lightweight, flexible, and operate without cryogenics. This has led to a step change in instrumentation for magnetoencephalography (MEG), enabling a "wearable" scanner platform, adaptable to fit any head size, able to acquire data whilst subjects move, and offering improved data quality. Although many studies have shown the efficacy of 'OPM-MEG', one relatively untapped advantage relates to improved array design. Specifically, OPMs enable the simultaneous measurement of magnetic field components along multiple axes (distinct from a single radial orientation, as used in most conventional MEG systems). This enables characterisation of the magnetic field vector at all sensors, affording extra information which has the potential to improve source reconstruction. Here, we conduct a theoretical analysis of the critical parameters that should be optimised for effective source reconstruction. We show that these parameters can be optimised by judicious array design incorporating triaxial MEG measurements. Using simulations, we demonstrate how a triaxial array offers a dramatic improvement on our ability to differentiate real brain activity from sources of magnetic interference (external to the brain). Further, a triaxial system is shown to offer a marked improvement in the elimination of artefact caused by head movement. Theoretical results are supplemented by an experimental recording demonstrating improved interference reduction. These findings offer new insights into how future OPM-MEG arrays can be designed with improved performance.

Measuring functional connectivity with wearable MEG.

Optically-pumped magnetometers (OPMs) offer the potential for a step change in magnetoencephalography (MEG) enabling wearable systems that provide improved data quality, accommodate any subject group, allow data capture during movement and potentially reduce cost. However, OPM-MEG is a nascent technology and, to realise its potential, it must be shown to facilitate key neuroscientific measurements, such as the characterisation of brain networks. Networks, and the connectivities that underlie them, have become a core area of neuroscientific investigation, and their importance is underscored by many demonstrations of their disruption in brain disorders. Consequently, a demonstration of network measurements using OPM-MEG would be a significant step forward. Here, we aimed to show that a wearable 50-channel OPM-MEG system enables characterisation of the electrophysiological connectome. To this end, we measured connectivity in the resting state and during a visuo-motor task, using both OPM-MEG and a state-of-the-art 275-channel cryogenic MEG device. Our results show that resting-state connectome matrices from OPM and cryogenic systems exhibit a high degree of similarity, with correlation values >70%. In addition, in task data, similar differences in connectivity between individuals (scanned multiple times) were observed in cryogenic and OPM-MEG data, again demonstrating the fidelity of the OPM-MEG device. This is the first demonstration of network connectivity measured using OPM-MEG, and results add weight to the argument that OPMs will ultimately supersede cryogenic sensors for MEG measurement.

Precision magnetic field modelling and control for wearable magnetoencephalography.

Optically-pumped magnetometers (OPMs) are highly sensitive, compact magnetic field sensors, which offer a viable alternative to cryogenic sensors (superconducting quantum interference devices - SQUIDs) for magnetoencephalography (MEG). With the promise of a wearable system that offers lifespan compliance, enables movement during scanning, and provides higher quality data, OPMs could drive a step change in MEG instrumentation. However, this potential can only be realised if background magnetic fields are appropriately controlled, via a combination of optimised passive magnetic screening (i.e. enclosing the system in layers of high-permeability materials), and electromagnetic coils to further null the remnant magnetic field. In this work, we show that even in an OPM-optimised passive shield with extremely low (<2 nT) remnant magnetic field, head movement generates significant artefacts in MEG data that manifest as low-frequency interference. To counter this effect we introduce a magnetic field mapping technique, in which the participant moves their head to sample the background magnetic field using a wearable sensor array; resulting data are compared to a model to derive coefficients representing three uniform magnetic field components and five magnetic field gradient components inside the passive shield. We show that this technique accurately reconstructs the magnitude of known magnetic fields. Moreover, by feeding the obtained coefficients into a bi-planar electromagnetic coil system, we were able to reduce the uniform magnetic field experienced by the array from a magnitude of 1.3±0.3 nT to 0.29±0.07 nT. Most importantly, we show that this field compensation generates a five-fold reduction in motion artefact at 0‒2 Hz, in a visual steady-state evoked response experiment using 6 Hz stimulation. We suggest that this technique could be used in future OPM-MEG experiments to improve the quality of data, especially in paradigms seeking to measure low-frequency oscillations, or in experiments where head movement is encouraged.

Maintaining the proliferative cell niche in multicellular models of epithelia.

The maintenance of the proliferative cell niche is critical to epithelial tissue morphology and function. In this paper we investigate how current modelling methods can result in the erroneous loss of proliferative cells from the proliferative cell niche. Using an established model of the inter-follicular epidermis we find there is a limit to the proliferative cell densities that can be maintained in the basal layer (the niche) if we do not include additional mechanisms to stop the loss of proliferative cells from the niche. We suggest a new methodology that enables maintenance of a desired homeostatic population of proliferative cells in the niche: a rotational force is applied to the two daughter cells during the mitotic phase of division to enforce a particular division direction. We demonstrate that this new methodology achieves this goal. This methodology reflects the regulation of the orientation of cell division.

A mathematical model of cell fate selection on a dynamic tissue.

Multicellular tissues are the building blocks of many biological systems and organs. These tissues are not static, but dynamically change over time. Even if the overall structure remains the same there is a turnover of cells within the tissue. This dynamic homeostasis is maintaned by numerous governing mechanisms which are finely tuned in such a way that the tissue remains in a homeostatic state, even across large timescales. Some of these governing mechanisms include cell motion, and cell fate selection through inter cellular signalling. However, it is not yet clear how to link these two processes, or how they may affect one another across the tissue. In this paper, we present a multicellular, multiscale model, which brings together the two phenomena of cell motility, and inter cellular signalling, to describe cell fate selection on a dynamic tissue. We find that the affinity for cellular signalling to occur greatly influences a cells ability to differentiate. We also find that our results support claims that cell differentiation is a finely tuned process within dynamic tissues at homeostasis, with excessive cell turnover rates leading to unhealthy (undifferentiated and unpatterned) tissues.

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.

Critical evaluation of stents in coronary angioplasty: a systematic review.

BACKGROUND: Coronary stents are routinely placed in the treatment and prophylaxis of coronary artery disease (CAD). Current coronary stent designs are prone to developing blockages: in-stent thrombosis (IST) and in-stent re-stenosis (ISR). This is a systematic review of the design of current coronary stent models, their structural properties and their modes of application, with a focus on their associated risks of IST and ISR. The primary aim of this review is to identify the best stent design features for reducing the risk of IST and ISR. To review the three major types of stents used in clinical settings today, determining best and relevant clinical practice by exploring which types and features of offer improved patient outcomes regarding coronary angioplasty. This information can potentially be used to increase the success rate of coronary angioplasty and stent technology in the future taking into account costs and benefits. METHODS: Scientific databases were searched to find studies concerning stents. After the exclusion criteria were applied, 19 of the 3192 searched literature were included in this review. Studies investigating three major types of stent design were found: bare-metal stents (BMS), drug-eluting stents (DES) and bioresorbable stents (BRS). The number of participants varied between 14 and 1264. On average 77.4% were male, with a mean age of 64 years. RESULTS: From the findings of these studies, it is clear that DES are superior in reducing the risk of ISR when compared to BMS. Conflicting results do not clarify whether BRS are superior to DES at reducing IST occurrence, although studies into newer BRS technologies show reducing events of IST to 0, creating a promising future for BRS showing them to be non-inferior. Thinner stents were shown to reduce IST rates, due to better re-endothelialisation. Scaffold material has also been shown to play a role with cobalt alloy stents reducing the risk of IST. This study found that thinner stents that release drugs were better at preventing re-blockages. Some dissolvable stents might be better at stopping blood clots blocking the arteries when compared to metal stents. The method and procedure of implanting the stent during coronary angioplasty influences success rate of these stents, meaning stent design is not the only significant factor to consider. CONCLUSIONS: Positive developments in coronary angioplasty could be made by designing new stents that encompass all the most desirable properties of existing stent technology. Further work is needed to investigate the benefits of BRS in reducing the risk of IST compared to DES, as well as to investigate the effects of different scaffold materials on IST and ISR outcomes.

Modelling Cellular Interactions and Dynamics During Kidney Morphogenesis.

Kidney disease and renal disorders account for a significant proportion of health complications in mid-late adulthood worldwide. Many renal deficiencies are due to improper formation of the kidneys before birth, which are caused by disorders in the developmental process that arise from genetic and/or environmental factors. Mathematical modelling can help build on experimental knowledge to increase our understanding of the complexities of kidney organogenesis. In this paper, we present a discrete cell-based model of kidney development. Specifically, we model the tip of the developing ureteric tree to investigate the behaviours of cap mesenchyme cells which are required to sustain ureteric tip growth. We find that spatial regulation of the differentiation of cap mesenchyme cells through cellular signalling is sufficient to ensure robust ureteric tip development. Additionally, we find that increased adhesion interactions between cap mesenchyme cells and the ureteric tip surface can lead to a more stable tip-cap unit. Our analysis of the various processes on this scale highlights essential components for healthy kidney growth and provides insight into mechanisms to be studied further in order to replicate the process in vitro.