Photo-responsive biomaterials are attractive because of the ability to non-invasively alter and control the material properties, thus allowing control over the cell response at the interface with the bioamaterial surface. While in silico mathematical models have been implemented for simulating single-cell force spectroscopy (SCFS) experiments on static and some dynamic biomaterials, these models have yet to be extended to light-responsive biointerfaces. So here, we develop a mathematical model that describes and predicts the strength of integrin-mediated cell adhesions to a photoswitchable biomaterial surface. The fluctuating biomaterial comprises photoswitchable azobenzene attached to a glass surface and terminated with peptide c(RGDfK). Upon irradiation with light at 530 nm, the azobenzenes rapidly fluctuate between an extended and contracted conformation, leading to a change in the length of the azobenzene that stimulates integrins bound to c(RGDfK). The mathematical model mimics the nascent adhesion and spatial fluctuations in the extra-cellular matrix (ECM) and is calibrated using single-cell force microscopy retraction curves. It relies on spring-based mechanics to describe the stretch and deformation of a cell and ensembles of integrins when applied to a fluctuating biomaterial. We use the model to simulate retraction curves and the proportion of bound integrins on the surface as the material fluctuates. Additionally, we use the model to predict SCFS retraction curves for varying experimental conditions. This includes the length of time the cell (attached to the tip of the atomic force microscopy cantilever) is kept in contact with the biomaterial before retraction, and for varying frequency of light-induced movement of the azobenzene conformations. These model outcomes provide an attractive route to integrate and rigorously control certain experimental variables, thus accelerating experimental design of the study of cell adhesion to light-responsive biomaterials. Furthermore the model complements experiments by providing estimates of variables that are experimentally inaccessible. Thus, the outcomes of the model provide a valuable resource to aid in the interpretation and design of light-responsive biointerface functionalities. ### Competing Interest Statement The authors have declared no competing interest. Engineering and Physical Sciences Research Council (EPSRC), EP/S023054/1

OBJECTIVE:To use digital twins constructed based on data from patients with acute respiratory distress syndrome (ARDS) to calculate all key indices of ventilator-induced lung injury (VILI) during airway pressure release ventilation (APRV), and to compare them with corresponding values obtained during pressure-controlled ventilation (PCV). DESIGN:Digital twins were created by matching a high-fidelity cardiopulmonary simulation model to each patient's data. SETTING:Interdisciplinary Collaboration in Systems Medicine Research Network. SUBJECTS:A dataset consisting of pairs of ventilator settings and arterial blood gases for 98 patients with ARDS receiving PCV. INTERVENTIONS:VILI indices were calculated for each recorded PCV datapoint, and for typical APRV settings in fixed and time-controlled adaptive modes, in the same digital twins. Global optimization algorithms evaluated greater than 4.8 million changes to these settings to identify the lowest values of VILI indices that could be achieved in both modes while preserving adequate gas-exchange. MEASUREMENTS AND MAINS RESULTS:In digital twins, APRV settings of inspiratory pressure equals to 25 cm H 2 O, low-pressure setting equals to 0 cm H 2 O, inspiration time equals to 5 s, and expiration time set to achieve 75% of peak expiratory flow rate (mean 0.5 s), reduced mean mechanical power (MP) by 32% and mean tidal alveolar recruitment/de-recruitment by 34% compared with documented PCV settings, at the cost of moderate hypercapnia (mean PaC O2 58.5 mm Hg, pHa 7.32 vs. Pa CO2 45.6 mm Hg, pHa 7.37). Mean driving pressure, tidal volume, and lung stress/strain were similar in both modes. Computational optimization showed that these settings were close to optimal in terms of minimizing both mean MP and mean levels of tidal recruitment/de-recruitment during APRV. CONCLUSIONS:Using digital twins we found possible lung-protective conditions and beneficial effects of APRV which need further evaluation in randomized clinical trials.

This report relates to a study group hosted by the EPSRC funded network, Integrating data-driven BIOphysical models into REspiratory MEdicine (BIOREME), and supported by SofTMech and Innovate UK, Business Connect. This report summarises the work undertaken on a challenge presented by two of the authors, Mathew Bulpett and Dr Emily Fraser. The aim was to identify approaches to analyse data collected using structured light plethysmography (SLP) from (n=31) healthy volunteers and (n=67) patients with Breathing Pattern Disorder (BPD) attributed to "long COVID", i.e. post-acute COVID-19 sequelae. This report explores several approaches including dimensionality reduction techniques on the available data and alternative indices extracted from variation in the time-series data for each measurement. Further proposals are also outlined such as different spatial indices that could be extracted from the SLP data, and the potential to couple to mechanical models of the lungs, chest and abdomen. However, running these latter analyses was beyond the scope of the limited study group timeframe. This exploratory analysis did not identify any clear SLP biomarkers of BPD in these cohorts, however recommendations are made for using SLP technologies in future BPD studies based on its findings.

This report relates to a study group hosted by the EPSRC funded network, Integrating data-driven BIOphysical models into REspiratory MEdicine (BIOREME), and supported by The Insigneo Institute and The Knowledge Transfer Network. The BIOREME network hosts events, including this study group, to bring together multi-disciplinary researchers, clinicians, companies and charities to catalyse research in the applications of mathematical modelling for respiratory medicine. The goal of this study group was to provide an interface between companies, clinicians, and mathematicians to develop mathematical tools to the problems presented. The study group was held at The University of Sheffield on the 17 - 20 April 2023 and was attended by 24 researchers from 13 different institutions. This report relates to a challenge presented by Arete Medical Technologies relating to impulse oscillometry (IOS), whereby a short pressure oscillation is imposed at a person's mouth during normal breathing, usually by a loudspeaker. The resulting pressure and flow rate changes can be used to the impedance of the airways, which in turn can provide proxy measurements for (patho)physiological changes in the small airways. Disentangling the signal so that airway mechanics can be measured accurately (and device properties/environmental effects can be accounted for) remains an open challenge that has the potential to significantly improve the device and its translation to clinic. In this report, several approaches to this problem, and the wider problem of interpreting oscillometry resuts are explored.

Excessive activation of the regulatory cytokine transforming growth factor β (TGF-β) via contraction of airway smooth muscle (ASM) is associated with the development of asthma. In this study, we develop an ordinary differential equation model that describes the change in density of the key airway wall constituents, ASM and extracellular matrix (ECM), and their interplay with subcellular signalling pathways leading to the activation of TGF-β. We identify bistable parameter regimes where there are two positive steady states, corresponding to either reduced or elevated TGF-β concentration, with the latter leading additionally to increased ASM and ECM density. We associate the former with a healthy homeostatic state and the latter with a diseased (asthmatic) state. We demonstrate that external stimuli, inducing TGF-β activation via ASM contraction (mimicking an asthmatic exacerbation), can perturb the system irreversibly from the healthy state to the diseased one. We show that the properties of the stimuli, such as their frequency or strength, and the clearance of surplus active TGF-β, are important in determining the long-term dynamics and the development of disease. Finally we demonstrate the utility of this model in investigating temporal responses to bronchial thermoplasty, a therapeutic intervention in which ASM is ablated by applying thermal energy to the airway wall. The model predicts the parameter-dependent threshold damage required to obtain irreversible reduction in ASM content suggesting that certain asthma phenotypes are more likely to benefit from this intervention.

Airway remodelling occurs in chronic asthma leading to increased airway smooth muscle (ASM) mass and extra-cellular matrix (ECM) deposition. Whilst extensively studied in murine airways; studies report only selected larger airways at one time point meaning the spatial distribution and resolution of remodelling are poorly understood. Here we use a new method allowing comprehensive assessment of the spatial and temporal changes in ASM, ECM and epithelium in large numbers of murine airways after allergen challenge. Using image processing to analyse 20-50 airways from a whole lung section revealed increases in ASM and ECM after allergen challenge were greater in small and large rather than intermediate airways. ASM predominantly accumulated adjacent to the basement membrane whereas ECM was distributed across the airway wall. Epithelial hyperplasia was most marked in small and intermediate airways. Post challenge, ASM changes resolved over seven days whereas ECM and epithelial changes persisted. The new method suggests large and small airways remodel differently and the long-term consequences of airway inflammation may depend more on ECM and epithelial changes than ASM. The method reduces the number of animals needed, reveals important spatial differences in remodelling and could set new analysis standards for murine asthma models.

Healthy lung function depends on a complex system of interactions which regulate the mechanical and biochemical environment of individual cells to the whole organ. Perturbations from these regulated processes give rise to significant lung dysfunction such as chronic inflammation, airway hyperresponsiveness and airway remodelling characteristic of asthma. Importantly, there is ongoing mechanobiological feedback where mechanical factors including airway stiffness and oscillatory loading have considerable influence over cell behavior. The recently proposed area of mechanopharmacology recognises these interactions and aims to highlight the need to consider mechanobiology when identifying and assessing pharmacological targets. However, these multiscale interactions can be difficult to study experimentally due to the need for measurements across a wide range of spatial and temporal scales. On the other hand, integrative multiscale mathematical models have begun to show success in simulating the interactions between different mechanobiological mechanisms or cell/tissue-types across multiple scales. When appropriately informed by experimental data, these models have the potential to serve as extremely useful predictive tools, where physical mechanisms and emergent behaviours can be probed or hypothesised and, more importantly, exploited to propose new mechanopharmacological therapies for asthma and other respiratory diseases. In this review, we first demonstrate via an exemplar, how a multiscale mathematical model of acute bronchoconstriction in an airway could be exploited to propose new mechanopharmacological therapies. We then review current mathematical modelling approaches in respiratory disease and highlight hypotheses generated by such models that could have significant implications for therapies in asthma, but that have not yet been the subject of experimental attention or investigation. Finally we highlight modelling approaches that have shown promise in other biological systems that could be brought to bear in developing mathematical models for optimisation of mechanopharmacological therapies in asthma, with discussion of how they could complement and accelerate current experimental approaches.

Physiologic chemoattractant gradients are shaped by diffusion, advection, binding to an extracellular matrix, and removal by cells. Previous in vitro tools for studying these gradients and the cellular migratory response have required cells to be constrained to a 2D substrate or embedded in a gel devoid of fluid flow. Cell migration in fluid flow has been quantified in the absence of chemoattractant gradients and shown to be responsive to them, but there is a need for tools to investigate the synergistic, or antagonistic, effects of gradients and flow. We present a microfluidic chip in which we generated precisely controlled gradients of the chemokine CCL19 under advective-diffusive conditions. Using torque-actuated membranes situated between a gel region and the chip outlet, the resistance of fluid channels adjacent to the gel region could be modified, creating a controllable pressure difference across the gel at a resolution inferior to 10 Pa. Constant supply and removal of chemokine on either side of the chip facilitated the formation of stable gradients at Péclet numbers between −10 and +10 in a collagen type I hydrogel. The resulting interstitial flow was steady within 0.05 μm s−1 for at least 8 h and varied by less than 0.05 μm s−1 along the gel region. This method advances the physiologic relevance of the study of the formation and maintenance of molecular gradients and cell migration, which will improve the understanding of in vivo observations.

Computer simulation offers a fresh approach to traditional medical research that is particularly well suited to investigating issues related to mechanical ventilation. Patients receiving mechanical ventilation are routinely monitored in great detail, providing extensive high-quality data-streams for model design and configuration. Models based on such data can incorporate very complex system dynamics that can be validated against patient responses for use as investigational surrogates. Crucially, simulation offers the potential to "look inside" the patient, allowing unimpeded access to all variables of interest. In contrast to trials on both animal models and human patients, in silico models are completely configurable and reproducible; for example, different ventilator settings can be applied to an identical virtual patient, or the same settings applied to different patients, to understand their mode of action and quantitatively compare their effectiveness. Here, we review progress on the mathematical modeling and computer simulation of human anatomy, physiology, and pathophysiology in the context of mechanical ventilation, with an emphasis on the clinical applications of this approach in various disease states. We present new results highlighting the link between model complexity and predictive capability, using data on the responses of individual patients with acute respiratory distress syndrome to changes in multiple ventilator settings. The current limitations and potential of in silico modeling are discussed from a clinical perspective, and future challenges and research directions highlighted.

We present new results validating the capability of a high-fidelity computational simulator to accurately predict the responses of individual patients with acute respiratory distress syndrome to changes in mechanical ventilator settings. 26 pairs of data-points comprising arterial blood gasses collected before and after changes in inspiratory pressure, PEEP, FiO2, and I:E ratio from six mechanically ventilated patients were used for this study. Parallelized global optimization algorithms running on a high-performance computing cluster were used to match the simulator to each initial data point. Mean absolute percentage errors between the simulator predicted values of PaO2 and PaCO2 and the patient data after changing ventilator parameters were 10.3% and 12.6%, respectively. Decreasing the complexity of the simulator by reducing the number of independent alveolar compartments reduced the accuracy of its predictions. Clinical Relevance- These results provide further evidence that our computational simulator can accurately reproduce patient responses to mechanical ventilation, highlighting its usefulness as a clinical research tool.

Intravital microscopy and other direct-imaging techniques have allowed for a characterisation of leukocyte migration that has revolutionised the field of immunology, resulting in an unprecedented understanding of the mechanisms of immune response and adaptive immunity. However, there is an assumption within the field that modern imaging techniques permit imaging parameters where the resulting cell track accurately captures a cell’s motion. This notion is almost entirely untested, and the relationship between what could be observed at a given scale and the underlying cell behaviour is undefined. Insufficient spatial and temporal resolutions within migration assays can result in misrepresentation of important physiologic processes or cause subtle changes in critical cell behaviour to be missed. In this review, we contextualise how scale can affect the perceived migratory behaviour of cells, summarise the limited approaches to mitigate this effect, and establish the need for a widely implemented framework to account for scale and correct observations of cell motion. We then extend the concept of scale to new approaches that seek to bridge the current “black box” between single-cell behaviour and systemic response.

Precision-cut lung-slices (PCLS), in which viable airways embedded within lung parenchyma are stretched or induced to contract, are a widely used ex vivo assay to investigate bronchoconstriction and, more recently, mechanical activation of pro-remodelling cytokines in asthmatic airways. We develop a nonlinear fibre-reinforced biomechanical model accounting for smooth muscle contraction and extracellular matrix strain-stiffening. Through numerical simulation, we describe the stresses and contractile responses of an airway within a PCLS of finite thickness, exposing the importance of smooth muscle contraction on the local stress state within the airway. We then consider two simplifying limits of the model (a membrane representation and an asymptotic reduction in the thin-PCLS-limit), that permit analytical progress. Comparison against numerical solution of the full problem shows that the asymptotic reduction successfully captures the key elements of the full model behaviour. The more tractable reduced model that we develop is suitable to be employed in investigations to elucidate the time-dependent feedback mechanisms linking airway mechanics and cytokine activation in asthma.

Integrins regulate mechanotransduction between smooth muscle cells (SMCs) and the extracellular matrix (ECM). SMCs resident in the walls of airways or blood vessels are continuously exposed to dynamic mechanical forces due to breathing or pulsatile blood flow. However, the resulting effects of these forces on integrin dynamics and associated cell-matrix adhesion are not well understood. Here we present experimental results from atomic force microscopy (AFM) experiments, designed to study the integrin response to external oscillatory loading of varying amplitudes applied to live aortic SMCs, together with theoretical results from a mathematical model. In the AFM experiments, a fibronectin-coated probe was used cyclically to indent and retract from the surface of the cell. We observed a transition between states of firm adhesion and of complete detachment as the amplitude of oscillatory loading increased, revealed by qualitative changes in the force timecourses. Interestingly, for some of the SMCs in the experiments, switching behaviour between the two adhesion states is observed during single timecourses at intermediate amplitudes. We obtain two qualitatively similar adhesion states in the mathematical model, where we simulate the cell, integrins and ECM as an evolving system of springs, incorporating local integrin binding dynamics. In the mathematical model, we observe a region of bistability where both the firm adhesion and detachment states can occur depending on the initial adhesion state. The differences are seen to be a result of mechanical cooperativity of integrins and cell deformation. Switching behaviour is a phenomenon associated with bistability in a stochastic system, and bistability in our deterministic mathematical model provides a potential physical explanation for the experimental results. Physiologically, bistability provides a means for transient mechanical stimuli to induce long-term changes in adhesion dynamics-and thereby the cells' ability to transmit force-and we propose further experiments for testing this hypothesis. (C) 2020 Elsevier Ltd. All rights reserved.

In this paper, we revisit our previous work in which we derive an effective macroscale description suitable to describe the growth of biological tissue within a porous tissue-engineering scaffold. The underlying tissue dynamics is described as a multiphase mixture, thereby naturally accommodating features such as interstitial growth and active cell motion. Via a linearization of the underlying multiphase model (whose nonlinearity poses a significant challenge for such analyses), we obtain, by means of multiple-scale homogenization, a simplified macroscale model that nevertheless retains explicit dependence on both the microscale scaffold structure and the tissue dynamics, via so-called unit-cell problems that provide permeability tensors to parameterize the macroscale description. In our previous work, the cell problems retain macroscale dependence, posing significant challenges for computational implementation of the eventual macroscopic model; here, we obtain a decoupled system whereby the quasi-steady cell problems may be solved separately from the macroscale description. Moreover, we indicate how the formulation is influenced by a set of alternative microscale boundary conditions.

All protective and pathogenic immune and inflammatory responses rely heavily on leukocyte migration and localization. Chemokines are secreted chemoattractants that orchestrate the positioning and migration of leukocytes through concentration gradients. The mechanisms underlying chemokine gradient establishment and control include physical as well as biological phenomena. Mathematical models offer the potential to both understand this complexity and suggest interventions to modulate immune function. Constructing models that have powerful predictive capability relies on experimental data to estimate model parameters accurately, but even with a reductionist approach most experiments include multiple cell types, competing interdependent processes and considerable uncertainty. Therefore, we propose the use of reduced modeling and experimental frameworks in complement, to minimize the number of parameters to be estimated. We present a Bayesian optimization framework that accounts for advection and diffusion of a chemokine surrogate and the chemokine CCL19, transport processes that are known to contribute to the establishment of spatio-temporal chemokine gradients. Three examples are provided that demonstrate the estimation of the governing parameters as well as the underlying uncertainty. This study demonstrates how a synergistic approach between experimental and computational modeling benefits from the Bayesian approach to provide a robust analysis of chemokine transport. It provides a building block for a larger research effort to gain holistic insight and generate novel and testable hypotheses in chemokine biology and leukocyte trafficking.

Integrin-mediated adhesions between airway smooth muscle (ASM) cells and the extracellular matrix (ECM) regulate how contractile forces generated within the cell are transmitted to its external environment. Environmental cues are known to influence the formation, size, and survival of cell-matrix adhesions, but it is not yet known how they are affected by dynamic fluctuations associated with tidal breathing in the intact airway. Here, we develop two closely related theoretical models to study adhesion dynamics in response to oscillatory loading of the ECM, representing the dynamic environment of ASM cells in vivo. Using a discrete stochastic-elastic model, we simulate individual integrin binding and rupture events and observe two stable regimes in which either bond formation or bond rupture dominate, depending on the amplitude of the oscillatory loading. These regimes have either a high or low fraction of persistent adhesions, which could affect the level of strain transmission between contracted ASM cells and the airway tissue. For intermediate loading, we observe a region of bistability and hysteresis due to shared loading between existing bonds; the level of adhesion depends on the loading history. These findings are replicated in a related continuum model, which we use to investigate the effect of perturbations mimicking deep inspirations (DIs). Because of the bistability, a DI applied to the high adhesion state could either induce a permanent switch to a lower adhesion state or allow a return of the system to the high adhesion state. Transitions between states are further influenced by the frequency of oscillations, cytoskeletal or ECM stiffnesses, and binding affinities, which modify the magnitudes of the stable adhesion states as well as the region of bistability. These findings could explain (in part) the transient bronchodilatory effect of a DI observed in asthmatics compared to a more sustained effect in normal subjects.

It is suggested that the frequent strain the airways undergo in asthma because of repeated airway smooth muscle (ASM)-mediated constrictions contributes to airway wall remodeling. However, the effects of repeated constrictions on airway remodeling, as well as the ensuing impact of this presumptive remodeling on respiratory mechanics, have never been investigated in subjects without asthma. In this study, we set out to determine whether repeated constrictions lead to features that are reminiscent of asthma in mice without asthma. BALB/c mice were subjected to a 30-min constriction elicited by aerosolized methacholine every other day over 6 wk. Forty-eight hours after the last constriction, the mechanics of the respiratory system was evaluated at baseline and in response to incremental doses of nebulized methacholine with the flexiVent. The whole-lung lavages, the tracheas, and the lungs were also collected to evaluate inflammation, the contractile capacity of ASM, and the structural components of the airway wall, respectively. The resistance and the compliance of the respiratory system, as well as the Newtonian resistance and the resistive and elastic properties of the lung tissue, were not affected by repeated constrictions, both at baseline and in response to methacholine. All the other examined features also remained unaltered, except the number of goblet cells in the epithelium and the number of macrophages in the whole-lung lavages, which both increased with repeated constrictions. This study demonstrates that, despite causing goblet cell hyperplasia and a mild macrophagic inflammation, repeated constrictions with methacholine do not lead to structural changes that adversely impact the physiology. NEW & NOTEWORTHY Repeated airway constrictions led to signs of remodeling that are typically observed in asthma, which neither altered respiratory mechanics nor the contractile capacity of airway smooth muscle. These findings shed light on a debate between those claiming that constrictions induce remodeling and those convinced that methacholine challenges are harmless. Insofar as our results with mice relate to humans, the findings indicate that repeated challenges with methacholine can be performed safely.

Background The pathophysiological changes occurring during the onset and progression of airway remodelling in asthma are intensively researched. However, protocols examine only a small fraction of airways and resolution of remodelling is barely examined. A mathematical model developed by our group suggests that rate of inflammation resolution post-exacerbation is a critical determinant of long term airway remodelling.1 We therefore sought to assess remodelling in unprecedented detail and its resolution across a large number of airways in a well-characterised model of chronic ovalbumin (OVA)-induced airway remodelling.2 Methods 43 BALB/C mice underwent OVA sensitisation and 10 OVA or PBS control airway challenges over 34 days. Animals were sacrificed on days 34, 35, 37, 39 and 41, and their lungs analysed by immunohistochemistry and differential bronchoalveolar lavage cell counts. A custom MATLAB program was developed to quantify airway size, airway smooth muscle (ASM) and total collagen area fractions relative to basement membrane perimeter for approximately 30–80 airways/mouse lung. Results At maximal remodelling (day 34), ASM and collagen area fractions increased in OVA challenged mice compared to controls (ASM 0.15±0.07 vs 0.08±0.07, p<0.0001, n=158 and 164 airways respectively; Collagen 0.17±0.06 vs 0.10±0.05, p<0.0001, n=110 and 121 airways respectively). By day 41, ASM mass increase had reduced but remained above baseline (ASM 0.01±0.07 vs 0.08±0.06, p=0.007, n=90 and 138 airways respectively) whereas collagen increase persisted to a greater degree (0.19±0.06 vs 0.13±0.05, p<0.0001, n=120 and 150 airways respectively. Figure 1). To determine how remodelling varies with airway size, airways were categorised by epithelial basement membrane perimeter. ASM and collagen area fraction increased in all airways. Large airways (1000 mm–1500 mm) had the largest increase followed by medium (500 mm–1000 mm), then small (<500 mm) airways. Resolution of ASM occurred in all airway sizes whereas collagen persisted in large and medium sized airways. Conclusion The technique allows, for the first time, comprehensive assessment of airway remodelling and reveals heterogeneity in remodelling, and resolution across airway sizes. The different anatomical distributions and time-courses of components of the remodelling response has implications for use of mouse models and future prevention of airway remodelling. References Biomech Model Mechanobiol2018. https://doi.org/10.1007/s10237-018-1037-4 J Immunol2011. https://doi.org/10.4049/jimmunol.1003507