Universal scaling laws rule explosive growth in human cancers

Pérez-Garcı́a, Vı́ctor M.; Calvo, Gabriel F.; Bosque, Jesús J.; León-Triana, Odelaisy; Jiménez, Juan Antonio Mondéjar; Pérez-Beteta, Julián; Belmonte-Beitia, Juan; Valiente, Manuel; Zhu, Lucía; García-Gómez, Pedro; Sánchez-Gómez, Pilar; Miguel, Esther Hernández-San; Hortigüela, Rafael; Azimzade, Youness; Molina-García, David; Martínez, Álvaro; Rojas, Ángel Acosta; Méndivil, Ana Ortiz de; Vallette, François M.; Schucht, Philippe; Murek, Michael; Perez-Cano, M.; Albers, David; Martínez, Antonio Francisco Honguero; Londoño, G.A. Jiménez; Arana, Estanislao; Vicente, Ana María García

doi:10.1038/s41567-020-0978-6

Cited by 59 publications

(94 citation statements)

References 43 publications

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“…Median differences were found to be small, due to lack of treatment, but highly significant. These results indicate that surface regularity and rim width had prognostic value in silico, as happens in real tumors [ 22 – 24 , 50 ]. Poor prognosis was associated with larger rim widths and lower surface regularity.…”

Section: Resultsmentioning

confidence: 80%

“…Despite the logistic nature of each voxel’s dynamics, the whole tumor showed sustained growth, first linear and then accelerating as a result of the diversification and interplay of the populations, in a process that selects for more aggressive clones. Curve fitting resulted in power law being the most accurate description, over other unbounded laws like exponential or linear radial, pointing towards a relationship between metabolic activity, evolutionary dynamics and aggressiveness [ 50 ]. The dynamics of simulated tumors changed from run to run as a result of the stochastic nature of the model, which allowed the influence of one-off events and parameter variability to be studied.…”

Section: Discussionmentioning

confidence: 99%

“…Motivated by the morphological analysis described above we also tried to fit to a power law, a variation of the von Bertalanffy equation and another usual candidate for tumor growth law. The equations to be fitted are therefore: where V 0 is initial volume and r 0 the corresponding mean initial radius, α denotes respective growth rates, K is the carrying capacity in the Gompertz model and β is the scaling exponent in the power law (it is positive and can be greater than 1, see [ 50 ]). We used Matlab function to obtain fitted parameters and root-mean-square error in order to compare goodness of fit.…”

Section: Methodsmentioning

confidence: 99%

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A mesoscopic simulator to uncover heterogeneity and evolutionary dynamics in tumors

et al. 2021

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Increasingly complex in silico modeling approaches offer a way to simultaneously access cancerous processes at different spatio-temporal scales. High-level models, such as those based on partial differential equations, are computationally affordable and allow large tumor sizes and long temporal windows to be studied, but miss the discrete nature of many key underlying cellular processes. Individual-based approaches provide a much more detailed description of tumors, but have difficulties when trying to handle full-sized real cancers. Thus, there exists a trade-off between the integration of macroscopic and microscopic information, now widely available, and the ability to attain clinical tumor sizes. In this paper we put forward a stochastic mesoscopic simulation framework that incorporates key cellular processes during tumor progression while keeping computational costs to a minimum. Our framework captures a physical scale that allows both the incorporation of microscopic information, tracking the spatio-temporal emergence of tumor heterogeneity and the underlying evolutionary dynamics, and the reconstruction of clinically sized tumors from high-resolution medical imaging data, with the additional benefit of low computational cost. We illustrate the functionality of our modeling approach for the case of glioblastoma, a paradigm of tumor heterogeneity that remains extremely challenging in the clinical setting.

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Section: Resultsmentioning

confidence: 80%

Section: Discussionmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

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A mesoscopic simulator to uncover heterogeneity and evolutionary dynamics in tumors

et al. 2021

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“…In addition, it can properly describe tumour relapse from an infiltrative disseminated tumour. More complex growth models can also describe the limited experimental data available [ 46 ], and others have recently been proposed to be in better agreement with new metabolic and longitudinal growth data [ 47 ]. However, for the analysis described in this paper, we will keep the simplest form given by Equation ( 2 ).…”

Section: Mathematical Modelsmentioning

confidence: 99%

Dual-Target CAR-Ts with On- and Off-Tumour Activity May Override Immune Suppression in Solid Cancers: A Mathematical Proof of Concept

León-Triana

Pérez‐Martínez

Ramírez-Orellana

et al. 2021

Cancers

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Chimeric antigen receptor (CAR)-T cell-based therapies have achieved substantial success against B-cell malignancies, which has led to a growing scientific and clinical interest in extending their use to solid cancers. However, results for solid tumours have been limited up to now, in part due to the immunosuppressive tumour microenvironment, which is able to inactivate CAR-T cell clones. In this paper we put forward a mathematical model describing the competition of CAR-T and tumour cells, taking into account their immunosuppressive capacity. Using the mathematical model, we show that the use of large numbers of CAR-T cells targetting the solid tumour antigens could overcome the immunosuppressive potential of cancer. To achieve such high levels of CAR-T cells we propose, and study computationally, the manufacture and injection of CAR-T cells targetting two antigens: CD19 and a tumour-associated antigen. We study in silico the resulting dynamics of the disease after the injection of this product and find that the expansion of the CAR-T cell population in the blood and lymphopoietic organs could lead to the massive production of an army of CAR-T cells targetting the solid tumour, and potentially overcoming its immune suppression capabilities. This strategy could benefit from the combination with PD-1 inhibitors and low tumour loads. Our computational results provide theoretical support for the treatment of different types of solid tumours using T cells engineered with combination treatments of dual CARs with on- and off-tumour activity and anti-PD-1 drugs after completion of classical cytoreductive treatments.

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“…The spread of populations is a phenomenon that exhibits resemblance with processes that are governed by the reaction-diffusion equations 10 . Invasion of various populations 11 and tumor growth 6 , 7 , 12 , 13 is described by different versions of Fisher-Kolomogorov-Petrovsky-Piskunov (FKPP) equation which in its classical form is described as: in which C ( x , t ) is the density of the population, R is the growth rate, and D is the diffusion constant for the population. Equation ( 1 ) represents a diffusion equation with a nonlinear reaction, that leads to the propagation of the Fisher waves.…”

Section: Introductionmentioning

confidence: 99%

Invasion front dynamics in disordered environments

Azimzade

Sasar

Maleki

2020

Sci Rep

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Invasion occurs in environments that are normally spatially disordered, however, the effect of such a randomness on the dynamics of the invasion front has remained less understood. Here, we study Fisher’s equation in disordered environments both analytically and numerically. Using the Effective Medium Approximation, we show that disorder slows down invasion velocity and for ensemble average of invasion velocity in disordered environment we have $$\bar{v}=v_0 (1-|\xi |^2/6)$$ v ¯ = v 0 ( 1 - | ξ | 2 / 6 ) where $$|\xi |$$ | ξ | is the amplitude of disorder and $$v_0$$ v 0 is the invasion velocity in the corresponding homogeneous environment given by $$v_0=2\sqrt{RD_0}$$ v 0 = 2 R D 0 . Additionally, disorder imposes fluctuations on the invasion front. Using a perturbative approach, we show that these fluctuations are Brownian with a diffusion constant of: $$D_{C}= \dfrac{1}{8} \xi ^2\sqrt{RD_0 (1-|\xi |^2/3)}$$ D C = 1 8 ξ 2 R D 0 ( 1 - | ξ | 2 / 3 ) . These findings were approved by numerical analysis. Alongside this continuum model, we use the Stepping Stone Model to check how our findings change when we move from the continuum approach to a discrete approach. Our analysis suggests that individual-based models exhibit inherent fluctuations and the effect of environmental disorder becomes apparent for large disorder intensity and/or high carrying capacities.

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Universal scaling laws rule explosive growth in human cancers

Cited by 59 publications

References 43 publications

A mesoscopic simulator to uncover heterogeneity and evolutionary dynamics in tumors

A mesoscopic simulator to uncover heterogeneity and evolutionary dynamics in tumors

Dual-Target CAR-Ts with On- and Off-Tumour Activity May Override Immune Suppression in Solid Cancers: A Mathematical Proof of Concept

Invasion front dynamics in disordered environments

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