Subgroup Contributed Talks

eSMB2020 eSMB2020 Follow Monday at 1:30pm EDT
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Adam Malik

Chalmers University of Technology, University of Gothenburg
"Modelling glioblastoma growth and invasion using Diffusion Tensor Imaging-data"
Many human cancers are studied using xenograft mouse models, in which human cancer cells are transplanted into mice. This constitutes a versatile tool, where various imaging modalities can reveal the dynamics of tumour progression, and novel drug targets can be investigated. However, this research occurs at expense of animal su ering. With the advent of high-performance computing and increasing knowledge of cellular and physiological processes the opportunity arises to replace in vivo mouse models with computational models that describe the growth of the tumour and its interactions with the host animal. We have developed a computational model of glioblastoma, a malignant form of brain tumour, which utilises data from Di usion Tensor Imaging (DTI) to represent anatomical structures within the model. The model takes into account a DTI-map obtained from adult normal mouse brains. The corresponding di usion tensor encodes information about nerve bre direction and density, and is therefore assumed to in uence cancer cell migration. In contrast to previous DTI-models we consider a cell-based model, where each cancer cell resides within a voxel (of volume 40 x 40 x 40 m3), which, due to volumetric constraints can contain a maximum of K cells. If the local density is below K each cell divides with at a rate α placing the daughter cell in the same voxel. Cell migration occurs with a rate Davg, which is the average value of the diffusion tensor, into one of the 6 neighbouring voxels, where the probability of moving to each neighbouring cell depends on the di usion tensor. A parameter, which ranges from 0 to 1, controls the impact of the di usion tensor, such that q = 0 corresponds to random migration and cells ignoring the anatomical structure, whereas q = 1 results in cells always moving along the direction of largest di usion (i.e. along bres). Simulations are initiated with 10,000 cells at the site of injection and contain approximately 1 million cells upon termination. Our results show that the model can recapitulate both nodal and di use tumours seen in the mouse model depending on the model parameters. Currently we are estimating model parameters from xenograft tumours obtained from di erent patients with the aim of identifying patient-speci c di erences, which, in the future, could inform personalised treatments.

Emma Carrick Smith

Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford
"Modelling the Clonal Evolution of Drug-Resistant Cells in Non-Small Cell Lung Carcinoma"
High levels of clonal heterogeneity in non-small cell lung carcinoma (NSCLC) and the selection of drug-resistant cells during treatment drive the evolution to unresponsive tumours to tyrosine kinase inhibitors (TKIs). Cell-autonomous effects such as genetic instability and non-cell-autonomous effects such as cancer therapies and their ability to induce resistance and the local cellular composition of the surrounding microenvironment are key elements promoting high levels of clonal heterogeneity in these evolving ecosystems. To understand the effects such features have on the prevalence of resistance at diagnosis and to predict the impact two-drug treatment protocols have on the level of resistance within the tumour during treatment, we have developed a stochastic Lotka-Volterra model of tumour growth incorporating four cell populations with varying levels of resistance to two drugs. The model incorporates both spontaneous and drug-induced resistance via mutations and employs population-dependent birth rates derived from a recent game-theory study to account for the effects of cellular interactions. The effect of the fitness of drug-resistant cells relative to drug-sensitive cells is also considered by incorporating both advantageous and deleterious mutation cases. We calculated the proportion of resistance in a tumour at diagnosis. The proportion of resistance is an increasing function of the mutation probability and cell turnover ratio with significantly larger proportions when mutations are advantageous as opposed to deleterious. At diagnosis, we introduced four treatment protocols applying either two TKIs with inhibitory effects or two cytotoxic drugs and observed the proportion of resistance in the tumour once it had reached a clinically relevant size. Our model demonstrates the relative fitness of drug-resistant cells to drug-sensitive cells, the ability for the drugs to induce resistance and sequential application of two TKIs results in a notable difference in the level of resistance in the tumour during treatment as opposed to when the drugs are applied simultaneously. These estimates of the size of the drug-resistant tumour cell population prior to and during two-drug treatment protocols can inform treatment strategies when combining two TKIs.

Arturo Araujo

University of Roehampton
"Multi-Scale Model of Colorectal Cancer Initiation"
Colorectal cancer (CRC) is currently the fourth leading cause of cancer-related deaths in the world. Development of more effective treatments is hindered by gaps in our understanding of CRC initiation and evolution, as well as the limitations of in vitro and in vivo experimental techniques. Specifically, in CRC we don’t fully understand the role of initiation mutations on the subsequent evolution of the disease, making it unique to each patient and therefore limiting the efficacy of general treatments. To bridge this gap in our knowledge, we use computational techniques such as agent-based modelling, gene regulatory network and continuous mathematical techniques to integrate molecular and cellular scale information to explain tumour growth and evolution. One of the biggest challenges we face is that collecting biological data is not enough. We need to figure out which are the right methods to analyse and utilise the data. Specially in cancer research, there is an abundance of data in many scales, from molecular and cellular to epidemiological; but without the right tools, such as multi-scale models, most of it remains under-utilised. To tackle CRC initiation, where colon epithelium loses its homeostasis, it was important to first have a clear understanding of the normal case. We constructed a cell-based model of a healthy colon crypt, incorporating different biological data and choosing the appropriate modelling abstraction for each one. We decided that agent-based modelling would provide us with the emergent property of homeostasis, common throughout biology. Through the interaction of the elements, cells in this case, a global balance arises which was not programmed into the equation and which was then validated by biological data. We extended this model with gene-regulatory network techniques to create an in silico experimental environment in which the effects of oncogenic mutations can be investigated and analysed with unique granularity. We further incorporated molecular data within the agent-based model to suggest novel therapies that consider not only the tumour, but the complex cross-talk between cancer and the rest of the healthy colon. We are currently working on incorporating data from the impact of current treatments, with the goal of tailoring it to individual patients to help control their specific disease and prolong their life. We envision for multi-scale models in the computational sciences to enable a greater understanding of the dynamics and evolution of diseases such as CRC, helping us explore, understand and harness the complex biological landscape, as well as supporting the development of new clinical prevention and treatment interventions. Further, these techniques can be readily deployed in hospitals, and some of them have already, as an aid for the clinician to help make better decisions, minimise costs and maximise the patients’ quality of life.

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Virtual conference of the Society for Mathematical Biology, 2020.