A Continuum Mechanics Model of Enzyme-Based Tissue Degradation in Cancer Therapies

Deville, Manon; Natalini, Roberto; Poignard, Clair

doi:10.1007/s11538-018-0515-2

Cited by 7 publications

(11 citation statements)

References 74 publications

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“…However, these models are not designed for describing the proliferation gradient that is observed in tumor spheroids. More complex models are needed to account for such a gradient [11,26,29,36] as well as the drug penetration in 3D tumors [16].…”

Section: Introductionmentioning

confidence: 99%

Mathematical modeling of the proliferation gradient in multicellular tumor spheroids

Michel

Fehrenbach

Lobjois

et al. 2018

Journal of Theoretical Biology

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MultiCellular Tumor Spheroids are 3D cell cultures that can accurately reproduce the behavior of solid tumors. It has been experimentally observed that large spheroids exhibit a decreasing gradient of proliferation from the periphery to the center of these multicellular 3D models: the proportion of proliferating cells is higher in the periphery while the non-proliferating quiescent cells increase in depth. In this paper, we propose to investigate the key mechanisms involved in the establishment of this gradient with a Partial Differential Equations model that mimics the experimental set-up of growing spheroids under different nutrients supply conditions. The model consists of mass balance equations on the two cell populations observed in the data: the proliferating cells and the quiescent cells. The spherical symmetry is used to rewrite the model in radial and relative coordinates. Thanks to a rigorous data postprocessing the model is then fit and compared quantitatively with the experimental quantification of the percentage of proliferating cells from EdU immunodetection on 2D spheroid cryosection images. The results of this calibration show that the proliferation gradient observed in spheroids can be quantitatively reproduced by our model.

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Section: Introductionmentioning

confidence: 99%

Mathematical modeling of the proliferation gradient in multicellular tumor spheroids

Michel

Fehrenbach

Lobjois

et al. 2018

Journal of Theoretical Biology

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“…In this section, we present the enzyme-based tissue degradation model proposed in [Deville et al, 2018]. The model combines the poroelastic theory of mixtures with the transport of enzymes and DNA plasmid densities in the extracellular space.…”

Section: Model Statementmentioning

confidence: 99%

“…The governing equations are set in the fixed reference domain -the tissue at the initial timedenoted by Ω 0 . For the sake of simplicity, we assume that our system undergoes very small perturbations (see [Deville et al, 2018] for more details).…”

Section: Model Statementmentioning

confidence: 99%

“…Paper is organized as follows: a section is devoted to the description of the mathematical model, previously introduced in [Deville et al, 2018]. Then, the numerical approach adopted for the determination of the most favorable conditions for the medical protocol are described, using metamodel interpolation, and the main results obtained by the optimization procedure are illustrated and discussed.…”

Section: Introductionmentioning

confidence: 99%

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Numerical optimization of plasmid DNA delivery combined with hyaluronidase injection for electroporation protocol

Peri

Deville

Poignard

et al. 2020

Computer Methods and Programs in Biomedicine

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The definition of an innovative therapeutic protocol requires the fine tuning of all the involved operations in order to maximize the efficiency. In some cases, the price of the experiments, or their duration, represents a great obstacle and the full potential of the protocol risks to be reduced or even hidden by a non-optimal application.The implementation of a numerical model of the protocol may represent the solution, allowing a systematic exploration of all the different alternatives, shedding the light on the most promising combination and also identifying the key elements/parameters.In this paper, the injection of a plasmid, preceded by a hyaluronidase injection, is simulated through a mathematical model. Some key elements of the administration protocol are identified by means of a mathematical optimization procedure, maximizing the efficacy of the therapy. As a side effect of the extensive investigation, robust solutions able to reduce the effects of human errors in the administration are also obtained.

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“…Different macroscale aspects of tumor growth have been investigated by continuum methods. 1,[11][12][13][14][15] Mechanical interactions, cell-cell adhesion, cell-matrix interactions, and ECM stiffness are studied by the so called method which occur in macroscales. On the other hand, most models use discrete framework to treat tumor growth numerically.…”

Section: Introductionmentioning

confidence: 99%

Mathematical simulation and prediction of tumor volume using RBF artificial neural network at different circumstances in the tumor microenvironment

Ghazani

Saghafian

Jalali

et al. 2021

Proc Inst Mech Eng H

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Uncontrolled proliferation of cells in a tissue caused by genetic mutations inside a cell is referred to as a tumor. A tumor which grows rapidly encounters a barrier when it grows to a certain size in presence of preexisting vasculature. This is the time when it has to find a way to go on the growth. The tumor starts to secrete tumor angiogenic factors (TAFs) and stimulate preexisting vessels to grow new sprouts. These new sprouts will find their way to the tumor in the extracellular matrix (ECM) by the gradient of TAF. As these new capillaries anastomose and reach tumor, fresh oxygen is available for the tumor and it will reinitiate the growth. Number of initial sprouts, distance of initial tumor cells from the vessel(s) and initial density of the tumor at the time of sprout formation are questions which are to be investigated. In the present study, the aim is to find the response of tumor cells and vessels to the reciprocal effects of each other in different circumstances in the tissue. Together with a mathematical formulation, a radial basis function (RBF) neural network is established to predict the number of tumor cells at different circumstances including size and distance of initial tumors from the parent vessel. A final formulation is given for the final number of tumor cells as a function of initial tumor size and distance between a parent vessel and a tumor. Results of this simulation demonstrate that, increasing the distance between a tumor and a parent vessel decreases the number of final tumor cells. Specially, this decrement becomes faster beyond a certain distance. Moreover, initial tumors in bigger domains must become much bigger before inducing angiogenesis which makes it harder for them to survive.

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A Continuum Mechanics Model of Enzyme-Based Tissue Degradation in Cancer Therapies

Cited by 7 publications

References 74 publications

Mathematical modeling of the proliferation gradient in multicellular tumor spheroids

Mathematical modeling of the proliferation gradient in multicellular tumor spheroids

Numerical optimization of plasmid DNA delivery combined with hyaluronidase injection for electroporation protocol

Mathematical simulation and prediction of tumor volume using RBF artificial neural network at different circumstances in the tumor microenvironment

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