Tumour growth is a force-sensitive process, regulated in part by mechanical feedback from surrounding tissue [1]. Such mechano-responsiveness can govern tissue-specific risk and progression of cancer. However, the underlying biomechanisms by which mechanical loading influences cellular growth and proliferation have not yet been uncovered. In this work, we propose a novel computational framework to determine how the feedback between growth, mechanical loading, and cell-cell exchange flow could restrict tumour cell proliferation.

Non-cycling cell volume is regulated by an interplay between energy-consuming pumps, mechanosensitive ion channels, and actomyosin tension that coordinate to manipulate cellular osmotic pressure. Growth may be induced by impermeable solute synthesis and associated increases in osmotic pressure, which drives water intake. Through a combination of novel finite element analyses (FEA) and agent-based modelling (ABM), we investigate how internal and external stresses arising from active cell tension and mechanical loading could oppose limit cell division by restricting growth below a critical mitotic volume.

Our model predictions for osmotic control of division indicate that cell cycle synthesis drives growth, and that compressive loading can limit the potential for a cell to surpass the size checkpoint for division. Simulations further suggest that exchange flow through gap junctions in connected cells can restrict osmotically-regulated cell growth and subsequently restrict proliferation. Using our integrated FEA-ABM modelling framework to characterize multicellular interactions and matrix loading, simulations reveal that increasing matrix stiffness reduces the rate of cell proliferation in tumour spheroids, due to the emergent stress-sensitivity of cell growth and division. Mean cell pressure is predicted to converge to a critical value, independent of matrix stiffness, at which proliferation is inhibited. Cells at the tumour core are revealed to experience higher stress than peripheral cells, as supported by data from excised tumours [2]. Overall, simulations suggest that tumour spheroid size reduces with increasing matrix stiffness in a stress-dependent manner, supported by our experiments of tumour spheroid growth in hydrogel.

Our analyses suggest that stress-dependent tumour growth emerges from a constraint on osmotically regulated cell growth, whereby cells cannot obtain a critical mitotic volume due to external loading. Simulation of multicellular proliferation with coupled finite element and agent-based models provides unique insight into the evolution of macro-scale tissue behavior and mechanosensitive growth, with broad applications to patient-specific cancer diagnosis.

References

1. M. Kalli and T. Stylianopoulos. Front. Oncol. 8 (2018)

2. H.T. Nia, et al. Nat. Biomed. Eng. 1 (2017).

One of the crucial steps of cancer metastasis is the extravasation of cancer cells from the vascular network into the neighbouring organs. The endothelial cells, which form the inner lining of blood vessels, develop homophilic bonds with neighbouring cells with the help of VE-cadherin proteins and form a preventive barrier against extravasation. But there is strong evidence of such cell-cell bonds abruptly broken in cancer patients that helps the trans-endothelial migration of cancer cells [1]. A diseased state leads to the abnormal dynamic behaviour of VE-cadherin junctions resulting in a larger gap size between cells and altering the frequency of their opening, a state termed hyperpermeability. Chemical cues such as Thrombin, along with mechanical properties of the cell and extracellular matrix (ECM) are known to affect permeability by regulating the actin-cytoskeleton machinery of endothelial cells. But details of how the coupled mechano-chemical stimuli affect endothelial permeability are not yet understood completely.

We have developed a continuum-level mathematical model to study the dynamics of such gap formation. The model considers the mechanical equilibrium of the cell by coupling the VE-cadherin to Actin-cytoskeleton. Taking inspiration from contact mechanics, we model VE-cadherin as a cohesive surface with damage following a traction-separation law. Actin cytoskeleton follows the tensegrity principle and is coupled with microtubules following non-linear material laws. Cells are modelled in 3D and hence we can study the behaviour of micro-vessels, which are hard to study experimentally. The ECM-cell interaction also follows a traction-separation law, allowing us to understand the role of ECM stiffness in cell-cell interactions. We use a non-linear finite element solver to solve the mechano-chemical coupled system of equations.

Numerical simulations showed that micro-vessels exhibit higher permeability than their planar monolayer counterparts. In-silico studies show that the permeability of micro-vessels increases with the stiffness of the extracellular matrix. Interestingly, it was observed that shear between cells is responsible for variation in permeability between bi-cellular and tri-cellular junctions, explaining the phenotypic differences observed in experiments. Simulations also show that permeability is higher in those regions of micro-vessels with high shear stress fluctuations, matching the observations that atherosclerotic plaques are usually formed in regions where blood flow is disturbed. The novel mathematical modelling framework is capable of simulating already known results along with developing several testable hypotheses. The versatile model can thus be used in a variety of studies, from the role of VE-cadherin in the extravasation of cancer cells to understanding the effect of nanoparticles in effective drug delivery.

1. T Tomita et al., “Regulation of vascular permeability in cancer metastasis”, Cancer Sci, 2021

Cell mechanics of living cells are vital for many cell functions, including mechanotransduction , migration, and differentiation. It is known that changes in cell mechanics are often correlated with disease progression. Cell-matrix adhesion is important for the patterning, integrity and homeostasis of tissues and may provide a target for therapy, for example in cancer metastasis. Cell mechanics and adhesion between cells and the matrix are also important for tissue engineering. Therefore, it is important to study cell mechanics and cell-to-material adhesion. However, simultaneous characterization of the cell-to-material adhesion and viscoelastic properties of the same cell is challenging. In this study, we present a new approach to simultaneously determine these properties for single cells, using Microfluidics-based Atomic Force Microscopy.

During the approach period, the cantilever touches the cell and rests for a few seconds, where the cell relaxation curve is recorded. Then, negative pressure is applied to the cell through the cantilever, and the hollow cantilever grabs the cell and pulls it away from the materials surfaces. During the relaxation period, the viscoelastic properties of the cell can be determined where the contact area between cell and the cantilever can be visualized and measured. The adhesive force and adhesive energy for cell-to-material can be determined based on the detachment curve when pulling the cell away from the substrate.

To explore the correlation between cell-materials adhesion and cell migration, the single cell tracking method was adopted. ImageJ with TrackMate plug-in was employed to identify the cells and then analyse their path. The mean migration speed is calculated by dividing the displacement of the cell between each frame by the time between frames to obtain the velocity of the cell moving between those two frames, and then averaging the movement velocity over the entire motion trajectory.

To reveal if the mechanical properties of biomaterials may affect the biomechanics of the breast cancer cells (MCF-7 cells), typical biomaterials Polydimethylsiloxane (PDMS) were used. The curing agent-to-base ratio was varied to yield PDMS with different stiffness. These PDMS samples were treated with Ozone to change the surface wetting properties to enable better cell attachment and proliferation.

The elastic modulus for MCF-7 cells on petri dish, determined here, is consistent with what was reported in literature. We have also demonstrated that both elastic cell moduli and viscosity of breast cancer cells (MCF-7 cells) can be affected by the mechanical properties of PDMS with different stiffness. The individual cell, which has stronger adhesion to the materials, appears to be stiffer. The cells seem to have stronger adhesion and slower migration when interfacing with stiffer materials.

According to the World Health Organization (WHO), prostate cancer (PCa) is the second most common cause of cancer worldwide¹.

Accurate risk stratification is crucial in treating prostate cancer. However, distinguishing high-risk from low-risk cases represents a significant challenge. Current diagnostic tools, such as blood-based prostate specific antigen (PSA) tests, digital rectal examination findings, and biopsies, often fail to differentiate the aggressiveness of cancer, leading to misclassification and under/over treatment². Consequently, new tools are urgently needed to predict outcomes and improve clinical decision-making to prevent unnecessary invasive treatments and associated morbidity³.

Therefore, the aim of this study is to develop an in-silico model of PCa tumour growth or degrowth that will predict prostate cancer outcome and provide an improved prognosis.

For the simulation of PCa tumour growth, a multispecies model of partial differential reaction-diffusion equations coupled with the mechanics of continuous media is here utilised. This multispecies model represents the phenomenological behaviour of PCa and its cellular processes, including proliferation, differentiation, and apoptosis. From these processes, the model simulates the evolution of the geometry, the distribution of tumour and healthy cells and stroma in the entire prostate. The model is implemented via the Finite Element Method. Magnetic Resonance Images (MRIs) are available to reconstruct the geometry of the prostate in a patient-specific manner. These images provide in-depth knowledge of the level of cellularity (DWI sequences) and vascularization (DCE sequences) of the tissue, which serve as input data to the model⁴. Real patient data are available for the validation of the model at a later time point.

The model has been tested on two clinical cases, showing promising preliminary results. The distribution of cellularity and PSA evolution are compared. Over time, the cellularity of the prostate obtained from the simulations reproduces closely the clinical values, with a similar spatial distribution. Furthermore, quantification of global cellularity does not give relative errors greater than 7%. On the other hand, the results obtained from the simulation of the PSA evolution suggest a close correlation with the observed clinical evolution, and the model can accurately predict the PSA's increase or decrease. However, further refinement of the model is necessary to improve its predictive capacity.

A patient specific model has been applied to simulate tumour growth in PCa. Moreover, this model can give predictions of the evolution of the PSA, which is the principal biomarker used by clinicians for the PCa follow-up. In future developments, different treatments will be incorporated which will allow for a better prognosis. Finally, the model will be further validated with additional patient-specific clinical data.

Acknowledgements

This publication is part of the project PLEC2021-007709 (ProCanAid), funded by MCIN/AEI/10.13039/501100011033/ and by the European Union NextGenerationEU/PRT and in collaboration with IISLAFE and QUIBIM. SHR was supported by the Government of Aragon (2019-23).

References

[1] Rebello, R.J., et al. Nat Rev Dis Primers. 7, 2021.

[2] Elwenspoek, M. et al. JAMA Netw open. 2:198427-198427, 2019.

[3] Moore, C.M. et al. Eur Urol, 64:544-52, 2013.

[4] Saiz-DeMena, D. et al. Eng Comput 3849–3865, 2022.

Tumour growth is usually hampered by poor blood supply when the tumour reaches a critical size. Under these circumstances, the process of growth tends to stall. When this supply is not verified, tumour cells may begin to secrete angiogenic growth factors that activate the process of angiogenesis, which is characterized by the formation of new blood vessels towards the tumour. Understanding this mechanism is one of the keys to comprehending tumour progression. To help in achieving this objective, computational models to describe angiogenesis in this context have emerged and have shown their potential to aid in this goal. Numerical methods are usually associated with these models, and numerous ones are documented in the literature. One of the most famous is Smoothed Particle Hydrodynamics (SPH).

The objective of this work was to enhance a 3D algorithm created by the authors, which simulates cell proliferation using the SPH algorithm along with the process of angiogenesis. In this algorithm, angiogenesis is triggered by VEGF concentration, and to test it, different concentrations and locations for the focus of concentration were considered.

The proposed algorithm uses SPH, and so the domain is discretized by particles with no connections between them. Through the particles, the approximation functions are derived, and the field function is approximated. Moreover, cell, extracellular matrix, boundary, and blood vessel particles are considered, and the initial velocity, internal pressure, and acceleration of all particles are calculated once the process of proliferation starts. Only one cell was initially considered and was allowed to grow and divide, following an exponential growth. Throughout the whole domain, a VEGF gradient was also defined, and firstly, the highest focus of VEGF was imposed near the cell. As the cells proliferate, a vessel is allowed to grow following the highest VEGF concentration.

Different simulations were run to see the viability of this new feature of the algorithm and to ensure that the generated vessel followed an appropriate path. In every simulation, the vessel grew towards the cluster of cells, which was considered a VEGF source. The growth was also regulated by the cell proliferation process to minimize excessive vessel growth. When this feature was validated, different values of concentration and different points of the focus of concentration were analysed to determine their impact on angiogenesis. Again, in all scenarios, the vessel growth followed the highest concentrations of VEGF, which corresponded to the different focus of concentration in each simulation.

The proposed algorithm was capable of combining the processes of cell proliferation and angiogenesis. As mentioned and reported in the literature, this new feature of the algorithm is dependent on the location of the source of VEGF, which is the factor that triggers the process, and on the cell proliferation process. The vessel growth followed the focus of concentration, as desired and anticipated. Despite the initial phase of the algorithm, the obtained results were reasonable and adequate.

Acknowledgements
The authors acknowledge the funding provided by Ministério da Ciência, Tecnologia e Ensino Superior – Fundação para a Ciência e a Tecnologia (Portugal), under the grant: SFRH/BD/146272/2019, and by LAETA, under the project UIDB/50022/2020.

Neuroblastoma (NB) is the most frequent solid cancer of early childhood. It is a type of cancer that is highly representative of the cancer disease itself, since NB is strongly heterogeneous with very diverse clinical courses that may vary from an indolent disease causing little or no harm and exhibiting spontaneous regression, to an aggressive disease with fatal progression. For these reasons, NB is considered a paradigm of cancer disease and an excellent context of application for the validation of novel developments which have the ambition to be of potential application in a large variety of solid cancers.

NB tumours consist of two main cell populations, neuroblasts and Schwann cells, and the current neuroblastoma classification is based on histological criteria, e. g. the quantity of Schwannian stroma. Neuroblasts and Schwann cells are primary interest herein for contribute directly to the mechanical properties of the tissue through the proliferation and death processes. Extracellular matrix also have a principal role in the cell-microenvironmental cross-talk therefore the tumour can promote to a better stage or keep growing.

We here present a phenomenological model which takes into account as detail as possible to better mimic the real tumour behaviour. Our hypothesis proposes that tumour evolution can be attributed to three distinct processes: growth, shrinkage, and remodelling. The biomechanical model is based on the mass and cellular balance equations coupled with elasticity. The multispecies model simulates the effect of the cellular processes that occur during tumour growth and shrinkage, namely proliferation and death.

The biomechanical finite element model of NB tumour growth starts from imaging data derived mainly from MRI sequences. This data comprises the geometry, the initial cellularity distribution and the tumour vasculature evaluation. At the end of the simulation, the results obtained are validated with a second set of imaging data obtained after treatment.

The study simulates three-month chemotherapy using real patient cases, and presents two distinct outcomes: in one of them, the tumour volume was reduced 20% and in the other one, the volume decreased 90%. One of the patients was classified as low-risk, following the International Neuroblastoma Risk Group (INRG) system, whereas the other was classified as intermediate-risk.
Differences appeared in the histology analysis, which reveal one tumour with a higher concentration of tumoural cells, and in the radiomic data obtained after image analysis. The model effectively reproduces these varying outcomes following the application of chemotherapy, facilitating the identification of cases in which the treatment may be effective.

Acknowledgments

The authors were supported by PRIMAGE (PRedictive In-silico Multiscale Analytics to support cancer personalized diaGnosis and prognosis, empowered by imaging biomarkers), a Horizon 2020 RIA project (Topic SC1-DTH-07-2018), grant agreement no: 826494.
SHR would like to thank the support of the Government of Aragon (Grant no 2019-23).
This work was supported by Grant PID2021-124271OB-I00 and PID2021-122409OB-C21 founded by MCIN/AEI/10.13039/501100011033 and ERDF A way of making Europe.