Speaker
Description
Traditional mathematical models for tumour growth are built upon simple assumptions regarding tumour-intrinsic population dynamics, including logistic growth, diffusion volumetric scaling. With progresses in experimental cancer research combined with advanced phenotyping, insights have been gained into how microenvironmental factors shape tumour growth. This motivated the development of more complex mathematical models that account for the microenvironment and tissue architecture. Although these models capture a wider range of biological phenomena in a cancer-type-agnostic fashion, few were calibrated against temporally resolved experimental data for colorectal-liver metastases. Here, we present a two-dimensional PDE model that accounts for spatial biases in proliferation and metastatic seeding position to investigate how liver architecture impacts tumour growth dynamics. By calibrating the PDE model against experimental data, we found that spatially nonuniform proliferation was required to recapitulate the tumour size distribution. By simulating the PDE model across a range of the spatial bias parameters, we predicted how altering liver zonation impacts tumour size distributions, which was validated in perturbation experiments. Our work reveals how liver architecture may shape tumour growth dynamics. In our ongoing work, were leveraging spatial transcriptomics to investigate molecular and cellular mechanisms underpinning tumour growth.
Bibliography
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title = {Mathematical {Biology} ({J}. {D}. {Murray})},
volume = {32},
issn = {0036-1445, 1095-7200},
url = {http://epubs.siam.org/doi/10.1137/1032093},
doi = {10.1137/1032093},
language = {en},
number = {3},
urldate = {2026-03-05},
journal = {SIAM Review},
author = {Bell, Jonathan G.},
month = sep,
year = {1990},
pages = {487--489},
}
@article{anderson_mathematical_2000,
title = {Mathematical {Modelling} of {Tumour} {Invasion} and {Metastasis}},
volume = {2},
issn = {1748-670X, 1748-6718},
url = {https://onlinelibrary.wiley.com/doi/10.1080/10273660008833042},
doi = {10.1080/10273660008833042},
abstract = {In this paper we present two types of mathematical model which describe the invasion of host tissue by tumour cells. In the models, we focus on three key variables implicated in the invasion process, namely, tumour cells, host tissue (extracellular matrix) and matrix‐degradative enzymes associated with the tumour cells. The first model focusses on the macro‐scale structure (cell population level) and considers the tumour as a single mass. The mathematical model consists of a system of partial differential equations describing the production and/or activation of degradative enzymes by the tumour cells, the degradation of the matrix and the migratory response of the tumour cells. Numerical simulations are presented in one and two space dimensions and compared qualitatively with experimental and clinical observations. The second type of model focusses on the micro‐scale (individual cell) level and uses a discrete technique developed in previous models of angiogenesis. This technique enables one to model migration and invasion at the level of individual cells and hence it is possible to examine the implications of metastatic spread. Finally, the results of the models are compared with actual clinical observations and the implications of the model for improved surgical treatment of patients are considered.},
language = {en},
number = {2},
urldate = {2026-03-05},
journal = {Computational and Mathematical Methods in Medicine},
author = {Anderson, A. R. A. and Chaplain, M. A. J. and Newman, E. L. and Steele, R. J. C. and Thompson, A. M.},
month = jan,
year = {2000},
pages = {129--154},
}
@article{gerlee_model_2013,
title = {The model muddle: in search of tumor growth laws},
volume = {73},
issn = {1538-7445},
shorttitle = {The model muddle},
doi = {10.1158/0008-5472.CAN-12-4355},
abstract = {In this article, we will trace the historical development of tumor growth laws, which in a quantitative fashion describe the increase in tumor mass/volume over time. These models are usually formulated in terms of differential equations that relate the growth rate of the tumor to its current state and range from the simple one-parameter exponential growth model to more advanced models that contain a large number of parameters. Understanding the assumptions and consequences of such models is important, as they often underpin more complex models of tumor growth. The conclusion of this brief survey is that although much improvement has occurred over the last century, more effort and new models are required if we are to understand the intricacies of tumor growth.},
language = {eng},
number = {8},
journal = {Cancer Research},
author = {Gerlee, Philip},
month = apr,
year = {2013},
pmid = {23393201},
keywords = {Algorithms, Animals, Humans, Models, Biological, Neoplasms, Tumor Burden},
pages = {2407--2411},
}
@article{jackson_mechanical_2002,
title = {A mechanical model of tumor encapsulation and transcapsular spread},
volume = {180},
issn = {0025-5564},
doi = {10.1016/s0025-5564(02)00118-9},
abstract = {In this paper, a mathematical modeling framework is presented which describes the growth, encapsulation, and transcapsular spread of solid tumors. The model is based on the physical forces and cellular interactions involved in tumorigenesis and is used to test and compare the active (foreign body hypothesis) and passive (expansive growth hypothesis) hypotheses of capsule formation, such investigations being ideally suited to our mechanical model. The model simulations lead us to predict that, although an active response can successfully control tumor growth via the deposition of large amounts of collagen, this alone is insufficient for capsule formation. In contrast, a solely passive responsive is capable of producing an encapsulated tumor with minimal accumulation of connective tissue within the tumor. When both responses are active, a denser capsule forms and there is a significant increase in connective tissue within the tumor. Using a modified version of the model, in which tumor cells are assumed to produce degradative proteases at a rate which depends on the pressure they experience, it is also possible to show that transcapsular spread or invasion of the tumor may be due to the production by the tumor cells of proteases and their subsequent action.},
language = {eng},
journal = {Mathematical Biosciences},
author = {Jackson, Trachette L. and Byrne, Helen M.},
year = {2002},
pmid = {12387930},
keywords = {Biomechanical Phenomena, Computer Simulation, Disease Progression, Endopeptidases, Extracellular Matrix, Humans, Models, Biological, Neoplasm Metastasis, Neoplasms},
pages = {307--328},
}
