A theoretical analysis of the scale separation in a model to predict solid tumour growth

Quintela, Bárbara de Melo; Hervas-Raluy, Silvia; Aznar, José Manuel García; Walker, Dawn; Wertheim, Kenneth Y.; Viceconti, Marco

doi:10.1016/j.jtbi.2022.111173

Cited by 10 publications

(9 citation statements)

References 31 publications

(31 reference statements)

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“…4a. Cancer cells are conceived as a continuum cell aggregate to assess the spatial distribution of both proliferation and collective cell invasion [33]. Here, we define the cell aggregate as a continuum where local mechanical stimuli at the cellular level can be globally transmitted in the form of mechanical waves and thus can transport interaction forces within the cell continuum [34, 35, 36, 37].…”

Section: Resultsmentioning

confidence: 99%

Tumor proliferation and invasion are coupled through cell-extracellular matrix friction

Crawford

Gomez-Cruz

Russo

et al. 2022

Preprint

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Cell proliferation and invasion are two key drivers of tumor progression and are traditionally considered two independent cellular processes regulated by distinct pathways. Throughin vitroandin silicomethods, we provide evidence that these two processes are intrinsically coupled through matrix-adhesion friction. Using novel tumor spheroids, we show that both tumor cell proliferation and invasion are limited by a volumetric carrying capacity of the system, i.e. maximum spatial cell concentration supported by the system’s total cell count, nutrient consumption rate, and collagen gel mechanical properties. To manipulate these phenotypes in breast cancer cells, we modulate the expression of E-cadherin and its associated role in adhesion, invasion, and proliferation. We integrate these results into a mixed-constitutive formulation to computationally delineate the contributions of cellular and extracellular adhesion, stiffness, and mechanical properties of the extracellular matrix (ECM) to the proliferative and invasive fates of breast cancer tumor spheroids. Both approaches conclude that the dominant drivers of tumor fate are system properties modulating cell-ECM friction, such as E-cadherin dependent cell-ECM adhesion and matrix pore size.

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Section: Resultsmentioning

confidence: 99%

Tumor proliferation and invasion are coupled through cell-extracellular matrix friction

Crawford

Gomez-Cruz

Russo

et al. 2022

Preprint

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“…A recent publication reports the use of dynamical systems theory to reveal the relationship between neuroblastoma cells, the immune system, and the oncolytic adenovirus ICOVIR-5 within the context of Celyvir, a kind of oncolytic virotherapy [ 48 ]. Another trend centres around the development of a digital twin, empowered by multi-scale modelling and imaging biomarkers [ 49 , 50 , 51 , 52 , 53 ].…”

Section: Discussionmentioning

confidence: 99%

Mathematical Model of Clonal Evolution Proposes a Personalised Multi-Modal Therapy for High-Risk Neuroblastoma

Italia

Wertheim

Taschner‐Mandl

et al. 2023

Cancers

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Neuroblastoma is the most common extra-cranial solid tumour in children. Despite multi-modal therapy, over half of the high-risk patients will succumb. One contributing factor is the one-size-fits-all nature of multi-modal therapy. For example, during the first step (induction chemotherapy), the standard regimen (rapid COJEC) administers fixed doses of chemotherapeutic agents in eight two-week cycles. Perhaps because of differences in resistance, this standard regimen results in highly heterogeneous outcomes in different tumours. In this study, we formulated a mathematical model comprising ordinary differential equations. The equations describe the clonal evolution within a neuroblastoma tumour being treated with vincristine and cyclophosphamide, which are used in the rapid COJEC regimen, including genetically conferred and phenotypic drug resistance. The equations also describe the agents’ pharmacokinetics. We devised an optimisation algorithm to find the best chemotherapy schedules for tumours with different pre-treatment clonal compositions. The optimised chemotherapy schedules exploit the cytotoxic difference between the two drugs and intra-tumoural clonal competition to shrink the tumours as much as possible during induction chemotherapy and before surgical removal. They indicate that induction chemotherapy can be improved by finding and using personalised schedules. More broadly, we propose that the overall multi-modal therapy can be enhanced by employing targeted therapies against the mutations and oncogenic pathways enriched and activated by the chemotherapeutic agents. To translate the proposed personalised multi-modal therapy into clinical use, patient-specific model calibration and treatment optimisation are necessary. This entails a decision support system informed by emerging medical technologies such as multi-region sequencing and liquid biopsies. The results and tools presented in this paper could be the foundation of this decision support system.

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“…Scale separation analysis 1 suggested to decompose the problem into three single‐scale models, properly orchestrated. The cell model, which computes Equation (1), needs to be run only once at the outset.…”

Section: Methodsmentioning

confidence: 99%

“…If we assume the cellularity does not change as much as the tumour grows, the change of volume of the tumour over space and time can then be formulated as a partial differential equation function of the changes in the local concentration of cells. The complete mathematical treatment can be found in reference 1.…”

Section: Methodsmentioning

confidence: 99%

“…Same applies for the temporal scale: chemical reactions taking place in a few milliseconds may produce effects observable over years. For example, with reference to the modelling of solid tumours growth, the space-time scales to span are 10 À8 to 10 À1 m, and 10 À2 to 10 7 s. 1 Hereinafter, we define range of a model, the largest portion of space or time the model accounts for, and grain, the smallest portion of it. 2 The grain is frequently referred to also as the representative volume element (RVE).…”

Section: Introductionmentioning

confidence: 99%

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Effect of particularisation size on the accuracy and efficiency of a multiscale tumours' growth model

Vinicius

Quintela

Kasztelnik

et al. 2022

Numer Methods Biomed Eng

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In silico, medicine models are frequently used to represent a phenomenon across multiples space-time scales. Most of these multiscale models require impracticable execution times to be solved, even using high performance computing systems, because typically each representative volume element in the upper scale model is coupled to an instance of the lower scale model; this causes a combinatory explosion of the computational cost, which increases exponentially as the number of scales to be modelled increases. To attenuate this problem, it is a common practice to interpose between the two models a particularisation operator, which maps the upper-scale model results into a smaller number of lower-scale models, and an operator, which maps the fewer results of the lower-scale models on the whole space-time homogenisation domain of upper-scale model. The aim of this study is to explore what is the simplest particularisation / homogenisation scheme that can couple a model aimed to predict the growth of a whole solid tumour (neuroblastoma) to a tissue-scale model of the cell-tissue biology with an acceptable approximation error and a viable computational cost. Using an idealised initial dataset with spatial gradients representative of those of real neuroblastomas, but small enough to be solved without any particularisation, we determined the approximation error and the computational cost of a very simple particularisation strategy based on binning. We found that even such simple algorithm can significantly reduce the computational cost with negligible approximation errors.

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A theoretical analysis of the scale separation in a model to predict solid tumour growth

Cited by 10 publications

References 31 publications

Tumor proliferation and invasion are coupled through cell-extracellular matrix friction

Tumor proliferation and invasion are coupled through cell-extracellular matrix friction

Mathematical Model of Clonal Evolution Proposes a Personalised Multi-Modal Therapy for High-Risk Neuroblastoma

Effect of particularisation size on the accuracy and efficiency of a multiscale tumours' growth model

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