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

Abstract

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.

Keywords: agent-based models; cancer treatment; mathematical modelling; mathematical oncology; virtual clinical trials.

Figure 1.

Snapshots from simulations of normal organoids, multicellular spheroids and early tumour development. (a) A multi-lumen MDCK cyst analogue simulated using the Potts model, from [34]. (b) A 2D cross-sectional view of the MCF10A in silico acinus modelled using the hexagonal CA model, from [35]. (c) An MCF10A acinus simulated by the IBCell model, from [36]. (d) An analogue of the NSCLC spheroid with a necrotic core simulated with Voronoi tessellation-based CA, from [37]. (e) An invasive (fingered) spheroid modelled with the 3D Potts model, from [38]. (f) A stem cell-generated spheroid simulated with the CA model, from [39]. (g) An off-lattice agent-based model reproducing metabolite distribution inside the spheroid, from [40]. (h) Off-lattice agent-based model of spheroids exposed to the cell-cycle inhibitors, from [41]. (i) An agent-based hybrid model of a spheroid exposed to radiation, from [42]. (j) Micropapillary pattern of DCIS simulated with the IBCell model, from [43]. (k) DCIS with calcification simulated with an off-lattice agent-based model, from [44]. (l) Organization of stem cells in the intestinal crypt modelled using an off-lattice agent-based approach, from [45]. All images reprinted with permission.

Figure 2.

Snapshots from simulations of angiogenesis, vascularized tumour growth and tumour treatments. (a) Cellular Potts model of the vessel sprout formation, from [82]. (b) Off-lattice agent-based model of the vascular network formation and branching, from [83]. (c) Structural adaptation of tumour vasculature in response to external factors modelled as a network composed of straight vascular segments, from [84]. (d) Three-dimensional cellular Potts model studying vascular remodelling during the tumour growth, from [85]. (e) A hybrid CA model of tumour-induced angiogenesis and growth within a digitized vasculature, from [86]. (f) Heterogeneous CA vascular network, from [87]. (g) Distribution of a blood-borne drug simulated with the hybrid model of discrete vasculature, continuous tumour mass and drug kinetics, from [88]. (h) The Krogh cylinder model of the vasculature and the CA model of the tumour simulating treatment with an angiogenesis inhibitor, from [89]. (i) Tumour response to HAP treatment simulated with the regularized Stokeslets method, from [90]. (j) ECM degradation by chemotactic glioma simulated by a continuous model, from [64]. (k) Glioma spread within the 3D brain architecture modelled using the continuous model, from [91]. (l) Tumour oxygenation predicted by the 2D hybrid CA model, from [92]. All images reprinted with permission.

Figure 3.

Schematics of Virtual Clinical Trials. (a) Collection of standard-of-care data in the clinic. (b) Data evaluation for diagnostic purposes. (c) Quantitative data profiling, screening and analysis. (d) Design, calibration and simulations of mathematical models. (e) Experimental testing and treatment validation with an organ-on-chip platform. (f) Supportive tool for clinical decision-making based on mathematical and organ-on-chip predictions. (g) Collection of longitudinal data for treatment monitoring. (c–g) Treatment adaptation by repeating the analysis, mathematical and experimental predictions, and treatment monitoring processes.