Front instabilities and invasiveness of simulated 3D avascular tumors

An agent-based modelling framework to study growth mechanisms in EGFR-L858R mutant cell alveolar type II cells

Mutations in the epidermal growth factor receptor (EGFR) are common in non-small cell lung cancer (NSCLC), particularly in never-smoker patients. However, these mutations are not always carcinogenic, and have recently been reported in histologically normal lung tissue from patients with and without lung cancer. To investigate the outcome of EGFR mutation in healthy lung stem cells, we grow murine alveolar type II organoids monoclonally in a three-dimensional Matrigel. Our experiments show that the EGFR-L858R mutation induces a change in organoid structure: mutated organoids display more 'budding', in comparison with non-mutant controls, which are nearly spherical. We perform on-lattice computational simulations, which suggest that this can be explained by the concentration of division among a small number of cells on the surface of the mutated organoids. We are currently unable to distinguish the cell-based mechanisms that lead to this spatial heterogeneity in growth, but suggest a number of future experiments which could be used to do so. We suggest that the likelihood of L858R-fuelled tumorigenesis is affected by whether the mutation arises in a spatial environment that allows the development of these surface protrusions. These data may have implications for cancer prevention strategies and for understanding NSCLC progression.

The relationship between hematoma morphology and intraventricular hemorrhage in supratentorial deep intracerebral hemorrhage

Background

Intraventricular hemorrhage (IVH) after intracerebral hemorrhage (ICH) is a strong independent predictor of poor outcomes. Although the location and volume of ICH are associated with IVH, our knowledge concerning the mechanism of IVH after ICH is still limited. This study aimed to investigate the relationship between hematoma morphology and IVH in patients with supratentorial deep ICH.

Methods

We retrospectively analyzed adult patients (aged ≥18 years) with spontaneous supratentorial deep ICH who underwent computed tomography (CT) within 48 h after ICH symptom onset in Peking University First Hospital between January 2017 and August 2022. We collected the clinical and imaging data of the patients and assessed hematoma morphology using several quantitative radiological parameters including hematoma volume, sphericity index, A/B ratio (A: the largest area of hematoma; B: the largest diameter 90° to A on the same slice), and our newly proposed largest diameter-midline angle (LMA). Multivariable logistic regression analysis was used to analyze the relationship between these parameters and the presence of IVH on the initial CT scan.

Results

Among 114 patients with spontaneous supratentorial deep ICH, 41 (36.0%) had IVH. In patients with IVH, the sphericity index was lower than that in individuals without IVH, while the LMA was larger. Multivariate logistic regression analysis showed that sphericity index [0.1-unit odds ratio (OR) =0.252; 95% CI: 0.089-0.709; P=0.009] and the LMA (10-unit OR =1.281; 95% CI: 1.007-1.630; P=0.04) were independently associated with the presence of IVH in patients with supratentorial deep ICH. Univariate analyses showed that hematoma volume, A/B ratio, sphericity index, and the LMA were significantly associated with poor outcomes at discharge.

Conclusions

Two quantitative parameters of hematoma morphology, sphericity index and the LMA, were significantly associated with the presence of IVH in patients with supratentorial deep ICH. Further prospective studies with larger sample sizes are needed to validate our results.

Exploration of Multiparameter Hematoma 3D Image Analysis for Predicting Outcome After Intracerebral Hemorrhage

BACKGROUND

Rapid diagnosis and proper management of intracerebral hemorrhage (ICH) play a crucial role in the outcome. Prediction of the outcome with a high degree of accuracy based on admission data including imaging information can potentially influence clinical decision-making practice.

METHODS

We conducted a retrospective multicenter study of consecutive ICH patients admitted between 2012-2017. Medical history, admission data, and initial head computed tomography (CT) scan were collected. CT scans were semiautomatically segmented for hematoma volume, hematoma density histograms, and sphericity index (SI). Discharge unfavorable outcomes were defined as death or severe disability (modified Rankin Scores 4-6). We compared (1) hematoma volume alone; (2) multiparameter imaging data including hematoma volume, location, density heterogeneity, SI, and midline shift; and (3) multiparameter imaging data with clinical information available on admission for ICH outcome prediction. Multivariate analysis and predictive modeling were used to determine the significance of hematoma characteristics on the outcome.

RESULTS

We included 430 subjects in this analysis. Models using automated hematoma segmentation showed incremental predictive accuracies for in-hospital mortality using hematoma volume only: area under the curve (AUC): 0.85 [0.76-0.93], multiparameter imaging data (hematoma volume, location, CT density, SI, and midline shift): AUC: 0.91 [0.86-0.97], and multiparameter imaging data plus clinical information on admission (Glasgow Coma Scale (GCS) score and age): AUC: 0.94 [0.89-0.99]. Similarly, severe disability predictive accuracy varied from AUC: 0.84 [0.76-0.93] for volume-only model to AUC: 0.88 [0.80-0.95] for imaging data models and AUC: 0.92 [0.86-0.98] for imaging plus clinical predictors.

CONCLUSIONS

Multiparameter models combining imaging and admission clinical data show high accuracy for predicting discharge unfavorable outcome after ICH.

Mathematical modelling reveals cellular dynamics within tumour spheroids

Tumour spheroids are widely used as an in vitro assay for characterising the dynamics and response to treatment of different cancer cell lines. Their popularity is largely due to the reproducible manner in which spheroids grow: the diffusion of nutrients and oxygen from the surrounding culture medium, and their consumption by tumour cells, causes proliferation to be localised at the spheroid boundary. As the spheroid grows, cells at the spheroid centre may become hypoxic and die, forming a necrotic core. The pressure created by the localisation of tumour cell proliferation and death generates an cellular flow of tumour cells from the spheroid rim towards its core. Experiments by Dorie et al. showed that this flow causes inert microspheres to infiltrate into tumour spheroids via advection from the spheroid surface, by adding microbeads to the surface of tumour spheroids and observing the distribution over time. We use an off-lattice hybrid agent-based model to re-assess these experiments and establish the extent to which the spatio-temporal data generated by microspheres can be used to infer kinetic parameters associated with the tumour spheroids that they infiltrate. Variation in these parameters, such as the rate of tumour cell proliferation or sensitivity to hypoxia, can produce spheroids with similar bulk growth dynamics but differing internal compositions (the proportion of the tumour which is proliferating, hypoxic/quiescent and necrotic/nutrient-deficient). We use this model to show that the types of experiment conducted by Dorie et al. could be used to infer spheroid composition and parameters associated with tumour cell lines such as their sensitivity to hypoxia or average rate of proliferation, and note that these observations cannot be conducted within previous continuum models of microbead infiltration into tumour spheroids as they rely on resolving the trajectories of individual microbeads.

Tumour spheroids are an experimental assay used to characterise the dynamics and response to treatment of different cancer cell lines. Previous experiments have demonstrated that the localisation of tumour cell proliferation to the spheroid edge (due to the gradient formed by nutrient diffusing from the surrounding medium) causes cells to be pushed from the proliferative rim towards the nutrient-deficient necrotic core. This movement allows inert particles to infiltrate tumour spheroids. We use a hybrid agent-based model to reproduce this data. We show further how data from individual microbead trajectories can be used to infer the composition of simulated tumour spheroids, and to estimate model parameters pertaining to tumour cell proliferation rates and their responses to hypoxia. Since these measurements are possible using modern imaging techniques, this could motivate new experiments in which spheroid composition could be inferred by observing passive infiltration of inert particles.

Morphophenotypic classification of tumor organoids as an indicator of drug exposure and penetration potential

The dynamics of tumor progression is driven by multiple factors, which can be exogenous to the tumor (microenvironment) or intrinsic (genetic, epigenetic or due to intercellular interactions). While tumor heterogeneity has been extensively studied on the level of cell genetic profiles or cellular composition, tumor morphological diversity has not been given as much attention. The limited analysis of tumor morphophenotypes may be attributed to the lack of accurate models, both experimental and computational, capable of capturing changes in tumor morphology with fine levels of spatial detail. Using a three-dimensional, agent-based, lattice-free computational model, we generated a library of multicellular tumor organoids, the experimental analogues of in vivo tumors. By varying three biologically relevant parameters-cell radius, cell division age and cell sensitivity to contact inhibition, we showed that tumor organoids with similar growth dynamics can express distinct morphologies and possess diverse cellular compositions. Taking advantage of the high-resolution of computational modeling, we applied the quantitative measures of compactness and accessible surface area, concepts that originated from the structural biology of proteins. Based on these analyses, we demonstrated that tumor organoids with similar sizes may differ in features associated with drug effectiveness, such as potential exposure to the drug or the extent of drug penetration. Both these characteristics might lead to major differences in tumor organoid's response to therapy. This indicates that therapeutic protocols should not be based solely on tumor size, but take into account additional tumor features, such as their morphology or cellular packing density.

Towards personalized computational oncology: from spatial models of tumour spheroids, to organoids, to tissues

A main goal of mathematical and computational oncology is to develop quantitative tools to determine the most effective therapies for each individual patient. This involves predicting the right drug to be administered at the right time and at the right dose. Such an approach is known as precision medicine. Mathematical modelling can play an invaluable role in the development of such therapeutic strategies, since it allows for relatively fast, efficient and inexpensive simulations of a large number of treatment schedules in order to find the most effective. This review is a survey of mathematical models that explicitly take into account the spatial architecture of three-dimensional tumours and address tumour development, progression and response to treatments. In particular, we discuss models of epithelial acini, multicellular spheroids, normal and tumour spheroids and organoids, and multi-component tissues. Our intent is to showcase how these in silico models can be applied to patient-specific data to assess which therapeutic strategies will be the most efficient. We also present the concept of virtual clinical trials that integrate standard-of-care patient data, medical imaging, organ-on-chip experiments and computational models to determine personalized medical treatment strategies.

Stability and Roughness of Interfaces in Mechanically Regulated Tissues

Cell division and death can be regulated by the mechanical forces within a tissue. We study the consequences for the stability and roughness of a propagating interface by analyzing a model of mechanically regulated tissue growth in the regime of small driving forces. For an interface driven by homeostatic pressure imbalance or leader-cell motility, long and intermediate-wavelength instabilities arise, depending, respectively, on an effective viscosity of cell number change, and on substrate friction. A further mechanism depends on the strength of directed motility forces acting in the bulk. We analyze the fluctuations of a stable interface subjected to cell-level stochasticity, and find that mechanical feedback can help preserve reproducibility at the tissue scale. Our results elucidate mechanisms that could be important for orderly interface motion in developing tissues.

Modeling of xenobiotic transport and metabolism in virtual hepatic lobule models

Computational models of normal liver function and xenobiotic induced liver damage are increasingly being used to interpret in vitro and in vivo data and as an approach to the de novo prediction of the liver’s response to xenobiotics. The microdosimetry (dose at the level of individual cells) of xenobiotics vary spatially within the liver because of both compound-independent and compound-dependent factors. In this paper, we build model liver lobules to investigate the interplay between vascular structure, blood flow and cellular transport that lead to regional variations in microdosimetry. We then compared simulation results obtained using this complex spatial model with a simpler linear pipe model of a sinusoid and a very simple single box model. We found that variations in diffusive transport, transporter-mediated transport and metabolism, coupled with complex liver sinusoid architecture and blood flow distribution, led to three essential patterns of xenobiotic exposure within the virtual liver lobule: (1) lobular-wise uniform, (2) radially varying and (3) both radially and azimuthally varying. We propose to use these essential patterns of exposure as a reference for selection of model representations when a computational study involves modeling detailed hepatic responses to xenobiotics.

Translational models of tumor angiogenesis: A nexus of in silico and in vitro models

Emerging evidence shows that endothelial cells are not only the building blocks of vascular networks that enable oxygen and nutrient delivery throughout a tissue but also serve as a rich resource of angiocrine factors. Endothelial cells play key roles in determining cancer progression and response to anti-cancer drugs. Furthermore, the endothelium-specific deposition of extracellular matrix is a key modulator of the availability of angiocrine factors to both stromal and cancer cells. Considering tumor vascular network as a decisive factor in cancer pathogenesis and treatment response, these networks need to be an inseparable component of cancer models. Both computational and in vitro experimental models have been extensively developed to model tumor-endothelium interactions. While informative, they have been developed in different communities and do not yet represent a comprehensive platform. In this review, we overview the necessity of incorporating vascular networks for both in vitro and in silico cancer models and discuss recent progresses and challenges of in vitro experimental microfluidic cancer vasculature-on-chip systems and their in silico counterparts. We further highlight how these two approaches can merge together with the aim of presenting a predictive combinatorial platform for studying cancer pathogenesis and testing the efficacy of single or multi-drug therapeutics for cancer treatment.

The influence of soluble fragments of extracellular matrix (ECM) on tumor growth and morphology

A major challenge in matrix-metalloproteinase (MMP) target validation and MMP-inhibitor-drug development for anti-cancer clinical trials is to better understand their complex roles (often competing with each other) in tumor progression. While there is extensive research on the growth-promoting effects of MMPs, the growth-inhibiting effects of MMPs has not been investigated thoroughly. So we develop a continuum model of tumor growth and invasion including chemotaxis and haptotaxis in order to examine the complex interaction between the tumor and its host microenvironment and to explore the inhibiting influence of the gradients of soluble fragments of extracellular matrix (ECM) density on tumor growth and morphology. Previously, it was shown both computationally (in one spatial dimension) and experimentally that the chemotactic pull due to soluble ECM gradients is anti-invasive, contrary to the traditional view of the role of chemotaxis in malignant invasion [1]. With two-dimensional numerical simulation and using a level set based tumor-host interface capturing method, we examine the effects of chemotaxis on the progression and morphology of a tumor growing in nutrient-rich and nutrient-poor microenvironments which was not investigated before. In particular we examine how the geometry of the growing tumor is affected when placed in different environments. We also investigate the effects of varying ECM degradation rate, the production rate of matrix degrading enzymes (MDE), and the conversion of ECM into soluble ECM. We find that chemotaxis due to ECM-fragment gradients strongly influences tumor growth and morphology, and that the instabilities caused by tumor cell proliferation and haptotactic movements can be prevented if chemotaxis is sufficiently strong. The influence of chemotaxis and the above factors on tumor growth and morphology are found to be more prominent in nutrient-poor environments than in nutrient-rich environments. So we extend our investigations of these antinvasive chemotactic influences by examining the effects of cell-cell and cell-ECM adhesion and low proliferation rate for tumors growing in low-nutrient environments. We find that as the extent of chemotaxis increases, the effects of adhesion on tumor growth and shape become negligible. Under conditions of low cell mitosis, chemotaxis may cause the tumor to shrink, as the extent of chemotaxis increases. Both stable and unstable tumor shrinkage are predicted by our model. Unexpectedly, in some cases chemotaxis may contribute toward developing instability where haptotaxis alone induces stable growth.

Phenomenological modelling and simulation of cell clusters in 3D cultures

Cell clustering and aggregation are fundamental processes in the development of several tissues and the progression of many diseases. The formation of these aggregates also has a direct impact on the oxygen concentration in their surroundings due to cellular respiration and poor oxygen diffusion through clusters. In this work, we propose a mathematical model that is capable of simulating cell cluster formation in 3D cultures through combining a particle-based and a finite element approach to recreate complex experimental conditions. Cells are modelled considering cell proliferation, cell death and cell-cell mechanical interactions. Additionally, the oxygen concentration profile is calculated through finite element analysis using a reaction-diffusion model that considers cell oxygen consumption and diffusion through the extracellular matrix and the cell clusters. In our model, the local oxygen concentration in the medium determines both cell proliferation and cell death. Numerical predictions are also compared with experimental data from the literature. The simulation results indicate that our model can predict cell clustering, cluster growth and oxygen distribution in 3D cultures. We conclude that the initial cell distribution, cell death and cell proliferation dynamics determine the size and density of clusters. Moreover, these phenomena are directly affected by the oxygen transport in the 3D culture.

Integrative models of vascular remodeling during tumor growth

Malignant solid tumors recruit the blood vessel network of the host tissue for nutrient supply, continuous growth, and gain of metastatic potential. Angiogenesis (the formation of new blood vessels), vessel cooption (the integration of existing blood vessels into the tumor vasculature), and vessel regression remodel the healthy vascular network into a tumor-specific vasculature that is in many respects different from the hierarchically organized arterio-venous blood vessel network of the host tissues. Integrative models based on detailed experimental data and physical laws implement in silico the complex interplay of molecular pathways, cell proliferation, migration, and death, tissue microenvironment, mechanical and hydrodynamic forces, and the fine structure of the host tissue vasculature. With the help of computer simulations high-precision information about blood flow patterns, interstitial fluid flow, drug distribution, oxygen and nutrient distribution can be obtained and a plethora of therapeutic protocols can be tested before clinical trials. In this review, we give an overview over the current status of integrative models describing tumor growth, vascular remodeling, blood and interstitial fluid flow, drug delivery, and concomitant transformations of the microenvironment. WIREs Syst Biol Med 2015, 7:113-129. doi: 10.1002/wsbm.1295 For further resources related to this article, please visit the WIREs website.

CONFLICT OF INTEREST

The authors have declared no conflicts of interest for this article.

On the evolution of morphogenetic models: mechano-chemical interactions and an integrated view of cell differentiation, growth, pattern formation and morphogenesis

In the 1950s, embryology was conceptualized as four relatively independent problems: cell differentiation, growth, pattern formation and morphogenesis. The mechanisms underlying the first three traditionally have been viewed as being chemical in nature, whereas those underlying morphogenesis have usually been discussed in terms of mechanics. Often, morphogenesis and its mechanical processes have been regarded as subordinate to chemical ones. However, a growing body of evidence indicates that the biomechanics of cells and tissues affect in striking ways those phenomena often thought of as mainly under the control of cell-cell signalling. This accumulation of data has led to a revival of the mechano-transduction concept in particular, and of complexity in general, causing us now to consider whether we should retain the traditional conceptualization of development. The researchers' semantic preferences for the terms 'patterning', 'pattern formation' or 'morphogenesis' can be used to describe three main 'schools of thought' which emerged in the late 1970s. In the 'molecular school', the term patterning is deeply tied to the positional information concept. In the 'chemical school', the term 'pattern formation' regularly implies reaction-diffusion models. In the 'mechanical school', the term 'morphogenesis' is more frequently used in relation to mechanical instabilities. Major differences among these three schools pertain to the concept of self-organization, and models can be classified as morphostatic or morphodynamic. Various examples illustrate the distorted picture that arises from the distinction among differentiation, growth, pattern formation and morphogenesis, based on the idea that the underlying mechanisms are respectively chemical or mechanical. Emerging quantitative approaches integrate the concepts and methods of complex sciences and emphasize the interplay between hierarchical levels of organization via mechano-chemical interactions. They draw upon recent improvements in mathematical and numerical morphogenetic models and upon considerable progress in collecting new quantitative data. This review highlights a variety of such models, which exhibit important advances, such as hybrid, stochastic and multiscale simulations.

Invasion from a cell aggregate--the roles of active cell motion and mechanical equilibrium

Cell invasion from an aggregate into a surrounding extracellular matrix (ECM) is an important process during development disease, e.g., vascular network assembly or tumor progression. To describe the behavior emerging from autonomous cell motility, cell-cell adhesion and contact guidance by ECM filaments, we propose a suitably modified cellular Potts model. We consider an active cell motility process in which internal polarity is governed by a positive feedback from cell displacements, a mechanism that can result in highly persistent motion when constrained by an oriented ECM structure. The model allows us to explore the interplay between haptotaxis, matrix degradation and active cell movement. We show that for certain conditions the cells are able to both invade the ECM and follow the ECM tracks. Furthermore, we argue that enforcing mechanical equilibrium within a bulk cell mass is of key importance in multicellular simulations.