Programme for Workshop on Mechanical Models in Health and Disease in Birmingham

The programme for our workshop 7-8th September is now ready. For late registration please email p.keshavanarayana@bham.ac.uk and f.spill@bham.ac.uk

Schedule

September 7, 2022

September 8, 2022

Abstracts

Modelling bacterial migration
Rachel Bearon, University of Liverpool

Many pathogenic bacteria are able to actively move in their environments, and I will discuss some modelling efforts to describe this movement. In particular I am interested in using mathematics to describe how bacterial shape and fluid shear can affect the transport of bacteria swimming in a channel, and what the impact of this may be on biofilm formation.

Airway remodelling in asthma - the chicken or the egg?
Bindi Brook, University of Nottingham

Inflammation, airway hyper-responsiveness (which causes constriction of the airways at lower trigger levels than in normal subject) and airway remodelling (long term structural changes of the airway wall) are key features of asthma. While this is well-established, it is not clear how they are linked or whether they are causes or symptoms of the disease. In this talk I will first describe the results of an experimental study using a mouse model of chronic asthma. Then I will describe a theoretical model, developed in parallel with the experimental study, that accounts for mechanochemical drivers of airway remodelling with some illustrative results. And finally I will discuss how the combination of both experimental data and mechanistic model might be used to understand how homoeostasis is maintained in healthy airways and therefore what perturbations might drive the airway into a diseased state. This is very much a work in progress and I hope will generate some interesting discussion.

Mother–Fetus Dialogue: Structural Determinants of Function in the Human Placenta  
Igor Chernyavsky, University of Manchester

Multiscale characterisation of biological tissues and organs is essential to gain insight into their structure–function relationship [1,2]. The human placenta is one of the most complex and unique, evolutionarily distinct organs. It is a crucial life-support system that not only nourishes a growing fetus but also determines their life-long health. The placental exchange units, terminal villi, host numerous dense networks of fetal capillaries and are interfaced with maternal blood, percolating a disordered porous medium. This talk summarises recent progress in massively multiscale 3D microscopy (covering the range of µm to cm) and its assimilation into mathematical models of placental transport [1]. The models explore a relationship between tissue architecture and function, quantify the associated uncertainty and demonstrate universality of upscaled approximations for a wide class of transported solutes [3]. The developed approaches could also be applied to characterising solute exchange in other complex microvascular systems.

References
1. Tun WM, et al. (2021) J R Soc Interface 18:20210140 (doi.org/10.1098/rsif.2021.0140).

2. Jensen OE & Chernyavsky IL (2019) Annu Rev Fluid Mech 51:25 (doi.org/10.1146/annurev-fluid-010518-040219).

3. Erlich A, et al. (2019) Sci Adv 5:eaav6326 (doi.org/10.1126/sciadv.aav6326).

What do cells and tissues feel? The integration of cellular contractility, extracellular adhesion and tissue stiffness in mechanosensing.
Carina Dunlop, University of Surrey

The role of the tissue stiffness in controlling cell behaviours is now well established. This has been shown across cell types and includes behaviours such as cell differentiation and even drug susceptibility, with obvious implications for health and disease. In experimental investigation of mechanosensation the use of bioengineered gels with defined mechanical properties have become essential to mimic varying tissue microenvironmenst. However, I show here that the stiffness experienced by the cell must not only be determined by the engineered stiffness but rather incorporates the interplay between contractility, cell adhesion. Using a theoretical model, I show how different cellular organisations can generate equivalent cell-mechanical responses on microenvironments of very different stiffnesses. The model also explains for the first time the experimentally observed growth and elongation of adhesions on stiff substrates from energetic principles. Finally, I will discuss how these observations may scale up in whole tissues.

Imaging-derived cardiac mechanics modelling toward personalized medicine

Hao Gao, University of Glasgow

The virtual twin of the heart, also known as a subject-specific digital model, built upon in-vivo clinical measurements, has the potential to provide effective and consistent risk-stratification of patients. Here, we would like to share our recent work on personalized biomechanical cardiac modelling with an aim of deepening our understanding of cardiac function, risk-stratification, and virtual testing [1].

To accurately describe the biomechanical behaviours of the heart, constitutive laws that describe the mechanical responses of cardiac tissue under loading hold the key. There have been ample choices of phenomenological constitutive models derived from experiments for describing myocardial responses, such as the Holzapfel-Ogden model. However, determining constitutive parameters from limited experimental data remains a great challenge in the cardiac modelling community. It is even challenging to infer those parameters of real patients using routinely available clinical data. We have proposed an initial attempt to address this issue from ex vivo to in vivo towards personalized modelling of the left ventricle (LV) using a two-stage approach [2]. Our results have shown that this personalized ventricular model can match measured LV wall motion very well, though not all parameters can be uniquely determined due to highly correlated parameters and limited measured data. To address this issue, we further adopted the framework of Bayesian optimisation (BO) [3], which is an efficient statistical technique of global optimisation, through seeking the optimum of an unknown black-box function by sequentially training a statistical surrogate model and using it to select the next query point by leveraging the associated exploration-exploitation trade-off.

Another challenge in cardiac modelling is to take into account the detailed fibre structure in the myocardium. Experimental studies have demonstrated that fibres in the myocardium, including both myocytes and collagen fibres, don't align along one unique direction, but are dispersed around the mean fibre direction. To that end, we have developed a fibre dispersion model for the myocardium based on a non-rotationally symmetric fibre distribution by including both in-plane and out-of-plane dispersions [4]. We then studied the effect of fibre dispersion on cardiac pump functions in a human left ventricular model. Our results demonstrated that both the diastolic filling and the systolic contraction will be affected by dispersed fibres, especially in systolic contraction. Our results also highlighted the necessity of using dispersed fibre models when modelling myocardial mechanics, especially when fibres are largely dispersed under pathological conditions.

References

1. Mangion K, Gao H, Husmeier D, Luo X, Berry C. Advances in computational modelling for personalised medicine after myocardial infarction. Heart. 104(7):550-557,2018
2. Gao H, Li WG, Cai L, Berry C, Luo XY. Parameter estimation in a Holzapfel–Ogden law for healthy myocardium. J Eng Math. 95(1):231-248, 2015
3. Borowska A, Gao H, Lazarus A, Husmeier D. Bayesian optimisation for efficient parameter inference in a cardiac mechanics model of the left ventricle. Numer Methods Biomed Eng. Published online April 7, 2022. doi:10.1002/cnm.3593

1. Guan D, Zhuan X, Holmes W, Luo X, Gao H. Modelling of fibre dispersion and its effects on cardiac mechanics from diastole to systole. J Eng Math. 128(1):1, 2021

Mechanobiology of cell-cell adhesions studied using in-silico biophysics-based computational models

Vijay Rajgopal, University of Melbourne

Adherens junctions (AJs) are protein complexes at the cell-cell interface that withstand mechanical forces and maintain tissue structure. They also regulate intracellular signalling for cell growth, division and death. Proper adherens junction structure and function is therefore critical for tissue development. Adherens junction dysfunction causes cancer metastasis. AJs involve extracellular bindings between cadherin molecules and intracellular interactions between cadherins and the actin cytoskeleton. Both cadherin and actomyosin cytoskeletal dynamics are reciprocally regulated by mechanical and chemical signals, which subsequently determine the strength of cell-cell adhesions and the emergent organization and stiffness of the tissues they form. We present a new mechanistic computational model of intercellular junction maturation in a cell doublet to investigate the mechano-chemical crosstalk that regulates AJ formation and homeostasis. The model couples a 2D lattice-based model of cadherin dynamics with a continuum, reaction diffusion model of the reorganizing actomyosin network through its regulation by Rho signaling at the intercellular junction. We demonstrate that local immobilization of cadherin induces cluster formation in a cis less dependent manner. We then recapitulate the process of cell-cell contact formation. Our model suggests that cortical tension applied on the contact rim can explain the ring distribution of cadherin and F-actin on the cell-cell contact of the cell-doublet. Furthermore, we propose and test the hypothesis that cadherin and F-actin interact like a positive feedback loop, which is necessary for formation of the ring structure. Different patterns of cadherin distribution were observed as an emergent property of disturbances of this positive feedback loop.

Modelling - the secret of understanding self-steering chemotactic gradients

Robert Insall, University of Glasgow

Chemotaxis is a universal feature of eukaryotic life.  It is used in embryonic development, growth, and immunity; it also underpins pathogenic processes like cancer metastasis.  Most approaches that aim to understand it address the mechanisms that allow cells to read gradients of attractants.  Equally important, however, is how attractant gradients are formed; we find cells create gradients by breaking down attractants as they respond to them, as well as by secreting attractants and agents that interfere with attractants. These processes are hard to follow, and yield strong positive feedback loops whose results are unpredictable. I describe how we use mathematical and computational modelling to understand self-steering and feed into experiments with real cells.

The role of endothelium and sub endothelial matrix mechanics on cancer cell transendothelial migration

Yousef Javanmardi, University College London

Tumour cell (TC) extravasation in one of the most critical steps in the metastasis cascade by which cancer spreads to metastatic sites from a primary tumour. Upon firm adhesion of tumour cells to vascular endothelium, TCs preferentially extravasate across endothelial junctions. Successful paracellular transmigration crucially relies on the ability of TCs to generate forces, maintain or enlarge the endothelial gap size during their transmigration, and squeeze through the endothelium to fully invade the subendothelial matrix. Despite its importance, the role of mechanical properties of the subendothelial matrix and endothelium mechanics on efficacy of the extravasation is poorly understood. To investigate the mechanics of cancer cell extravasation, we developed an extravasation assay to probe the force interactions between transmigrating TCs, endothelial monolayer and the subendothelial matrix. Combining experimental data with computer-simulations, we demonstrated that the mechanical properties of ECM, in particular its stiffness and porosity, regulates contractile traction and tugging forces generated by endothelial cells in a RhoA dependent manner. This, in turn, affects the efficiency of cancer cell extravasation and magnitude of forces generated by the TC during transmigration. Our results suggest that mechanical features of the subendothelial matrix play a fundamental role in setting the vasculature mechanics and consequently the transmigration rates.

Modeling of calcium transient in mouse detrusor smooth muscle cell with respect to spontaneous contraction for urinary incontinence

Chitaranjan Mahapatra, Paris-Saclay Institute of Neuroscience – CNRS

Urinary Incontinence (UI) is leakage of urine without voluntary control that makes up a social and embarrassing situation in every day’s social life. Although the UI is caused by several pathological maneuvers, detrusor smooth muscle (DSM) instability is considered as a predominant cause behind UI. According to various experimental documented results, DSM cells from several families of species invoke spontaneous contractile activity at different frequency. A good number of empirical and   clinical investigations point towards an association between calcium dynamics and spontaneous contraction in DSM cell. Computational models can compactly quantify the mechanisms of calcium dynamics and permit the user to explore the contribution of each mechanism in generating cellular mechanical activities. This study delivers an elementary realistic calcium dynamic model based on voltage gated calcium channel underlying the kinetic processes in DSM cell. Here the mathematical interpretation of DSM cell membrane is established on traditional Hodgkin-Huxley formalism. Voltage dependent calcium channels (ICa), voltage gated potassium channel (IKv), Calcium activated potassium channel (IKCa) and back ground leakage currents (Il) are incorporated to generate action potentials (APs) and calcium transient. An external stimulus current of 1-3nA is injected for 0.5-1ms to generate APs and calcium transients in our computational model. It is observed that 3nA current for a time period of 0.6 ms generates the first spike with voltage threshold at –30mV. Calcium transient is obtained at 2µm depth of cytoplasm from the surface membrane. The resting [Ca2+]i is set to 100 nM. The L-type channel is the major contributor for the rise in [Ca2+]i. The peak [Ca2+]i transient obtained is 1900 nM in this model. The similarity of the shape of [Ca2+]i transient and peak value with the experimental results reported in some experiments demonstrates that the kinetics of channels, pumps and calcium transient are represented to a good degree of accuracy in our model. At the present time, our computational model provides an elementary tool to analyze the physiological calcium dynamics and ionic channel kinetics underlying the contractions in DSM cells that successively will explore various hypotheses in genesis of bladder overactivity.

Modes of force generation in organoid development

Kieran Boniface, University of Surrey

The mechanical environment of a cell plays a crucial role in its development, influencing properties such as proliferation, growth, and cell type, with mechanical cues even overriding chemical signals over a longer period. Furthermore, cell-cell interactions generate stresses that can then feedback to influence themselves. This is made more complex in 3D cell structures such as tissues and organoids, where cell-cell interactions operate over different length scales. Thus, mechanical models of organoids and tissues can help shed light on the forces at play and can highlight parameters that may play a key role in any qualitative change in the force acting on the tissue. Here, we present an elasticity-based model for two key force generating mechanisms in tissue engineering problems, growth, and cellular contractility. We explore the interaction between growth and contractility, highlighting how potential signals for mechanotransduction may arise. We then investigate potential avenues in which we can incorporate mechanical feedback into the model and highlight a key difference between 2 and 3 dimensional models, reiterating the importance of 3D biophysical experiments in tissue engineering.

Mechanochemical Models of Calcium Signalling

Abhishek Chakraborty, Cardiff University

Cell division is vital for the growth and adaptation of tissues, the outcome of which is dependent of the spatial orientation of the division within the tissue. This is determined by the orientation of the mitotic spindle. From its assembly until chromosome segregation, the spindle dynamically rotates and explores the cell by the interaction of its astral microtubules with proteins at the cell periphery. The precise mechanisms which control these movements remain unclear, though it has been shown that spindle orientation is sensitive to tissue tension which suggests that a mechanosensitive mechanism may play a role. To determine how mechanosensitive spindle orientation is regulated, we study spindle movements in stretched and unstretched tissue, using a combination of biological and mathematical approaches. Nuclear mitotic apparatus protein (NuMA) is a key player in spindle positioning with a large coiled-coil domain. Coiled-coil domains have been implicated in mechanosensitive interactions. In preliminary data we find that NuMA demonstrates a tension- sensitive localization, suggesting that NuMA is a mechanosensitive link. Here we present a mathematical model of the interactions between astral microtubules and cortical elements such as NuMA using a Fokker-Planck system of partial differential equations. To make progress towards expanding the model to two spatial dimensions we simplify the system to a set of ordinary differential equations revealing factors that promote instability. An increase in cortical pulling elements pushes the model into an oscillatory regime which coincides with preliminary data.

Placental haemodynamics: Transport effects at the organ scale

Adam Blakey, University of Nottingham

The placenta provides nutrients such as oxygen to developing fetuses — and is therefore vital to a fetus’ survival. Diseases such as pre-eclampsia are characterised by maternal arteries failing to sufficiently widen; this forces blood to enter up to an order of magnitude quicker, which can disturb structures on the fetal side, as well as transit the exchange area quicker than nutrients can be diffused across the maternal-fetal barrier. It is therefore important to fully understand blood flow, and the resulting transport of nutrients, in the area of exchange between maternal and fetal blood.

I will present some computational simulations of maternal blood flow in human placentas, which use discontinuous Galerkin finite element method (DGFEM) discretisations of a porous medium equation. We will study the effect of modelling the whole-organ placenta in representative 2D slices and discuss the effect this may have on the transportation of nutrients.

Mathematical modelling of spindle dynamics in tissues under mechanical tension

Dionn Hargreaves, University of Manchester

Cell division is vital for the growth and adaptation of tissues, the outcome of which is dependent of the spatial orientation of the division within the tissue. This is determined by the orientation of the mitotic spindle. From its assembly until chromosome segregation, the spindle dynamically rotates and explores the cell by the interaction of its astral microtubules with proteins at the cell periphery. The precise mechanisms which control these movements remain unclear, though it has been shown that spindle orientation is sensitive to tissue tension which suggests that a mechanosensitive mechanism may play a role. To determine how mechanosensitive spindle orientation is regulated, we study spindle movements in stretched and unstretched tissue, using a combination of biological and mathematical approaches. Nuclear mitotic apparatus protein (NuMA) is a key player in spindle positioning with a large coiled-coil domain. Coiled-coil domains have been implicated in mechanosensitive interactions. In preliminary data we find that NuMA demonstrates a tension- sensitive localization, suggesting that NuMA is a mechanosensitive link. Here we present a mathematical model of the interactions between astral microtubules and cortical elements such as NuMA using a Fokker-Planck system of partial differential equations. To make progress towards expanding the model to two spatial dimensions we simplify the system to a set of ordinary differential equations revealing factors that promote instability. An increase in cortical pulling elements pushes the model into an oscillatory regime which coincides with preliminary data.

Digital Twin of the Fetal Heart

Choon Hwai Yap, Imperial College London

Congenital heart malformations (CHM) occur to 1% of births, and many more demised and aborted fetuses. A tremendous amount of funds is spent treating some CHM that nonetheless could not prevent death. Abnormal biomechanics can cause a progression to malformation at birth, and it is thus important to understand and model it. We propose that the digital twin of the fetal heart, which encompasses such patient-specific computational models based on clinical scans can help improve detection, evaluation, and outcome predictions. They can inform clinical management and interventions for precision medicine to improve outcomes.

Towards this goal, we have created and tested various tools. First, we developed cardiac motion estimation algorithms with cyclic motion regularizations, which can track cardiac motions accurately and compute 3D fetal myocardial strains for functional evaluations. With this tool, we demonstrated the reason that 2D strains have specific inaccuracies compared to 3D scans to explain discrepancies in the literature. Next, we developed methods for image-based fetal heart flow simulations, and fetal myocardial finite element models, so as to understand fluid and tissue mechanics. We analyzed fetal hearts with aortic stenosis and evolving hypoplastic left heart syndrome (eHLHS), which has a high risk of progressing to HLHS by birth. We also analyzed fetal aortic valvuloplasty intervention, which is a catheter intervention that can prevent this progression. Fluids modelling showed that diseased left ventricles (LV) have altered flow patterns and vorticity dynamics, excessive energy losses and low blood oxygen renewal. With the intervention, stroke volume improved, but due to aortic regurgitation, there is chaotic flow and even more excessive energy losses. This suggested that developing transcatheter valve replacement (TAVR) for fetal hearts may be helpful. With finite element modelling, we established a set of optimization algorithms to enable our models to match clinical measurements. We could then back-compute the magnitude of active tension generation in fetal myocardium, to gauge contractility. We find that diseased hearts have compromised contractility, and cases where contractility are low tended not to respond to interventions. Our computational model may thus be useful to inform physicians whether the interventions are suitable for specific patients. Further, we find that with the intervention, if the intervention causes significant aortic regurgitation, the left atrium will not resolve its excessive pressure, again suggesting that fetal TAVR may be helpful.

In conclusion, we have begun developing various models to form the digital twin technology for evaluating fetal hearts to help management and treatment of diseases. Much more, however, can be done, such as machine learning detection of diseases, and machine learning-enabled biomechanics simulations.

Combining image analysis with biophysical models of organoids for the prospect of individualised cancer treatment

Stan Marée, Cardiff University

Patient-Derived Organoids (PDOs) are multicellular, self-assembled 3D cell structures which mimic the tissue architecture of the organ that they are derived from. These mini organs e.g. mini guts can be used to duplicate normal behaviour or disease pathologies. Tumour-derived PDOs have the potential to make a marked impact on next-generation individualised cancer treatments, as they allow for patient-specific pre-clinical drug screenings. For this to be achieved, however, it is key to link pathological dynamics and drug impact to quantifiable morphometric features of the organoids. Using colorectal cancer organoid lines grown using Cellesce Limited’s bioprocessor technology, we are developing a morphomics pipeline to analyse 3D images of organoids and extract biologically relevant features. We then combine the image analysis with models of the organoids' growth and development, using the Cellular Potts Model framework for the biophysical embedding. The organoids' remarkable capacity of self-organisation arises through the biophysical interactions, combined with cellular regulation, together driving cell proliferation and organ shape formation. The combination of image analysis and modelling will be used to understand the impact of drug compounds on the underlying organoid biology and morphology.