Behavior of tumors under nonstationary therapy

Sotolongo‐Costa, Oscar; Molina, Luisana; Pérez, Daniel Rodríguez; Antoranz, J. C.; Reyes, M.

doi:10.1016/s0167-2789(03)00005-8

Cited by 77 publications

(76 citation statements)

References 18 publications

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“…For particular functions f (x), d x (x, y), p y (x, y), d y (x, y), a y (y), and φ(t), the generic model (6) reduces to specific models derived in the literature (Forys et al 2006;Galach 2003;Kuznetsov et al 1994;Stepanova 1980;Sotolongo-Costa et al 2003;de Vladar and González 2004). For instance, the model derived in Kuznetsov et al (1994) is obtained by setting…”

Section: Two-equation Models: Interactions Between Tumor Cells and Gementioning

confidence: 99%

Interactions Between the Immune System and Cancer: A Brief Review of Non-spatial Mathematical Models

2010

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We briefly review spatially homogeneous mechanistic mathematical models describing the interactions between a malignant tumor and the immune system. We begin with the simplest (single equation) models for tumor growth and proceed to consider greater immunological detail (and correspondingly more equations) in steps. This approach allows us to clarify the necessity for expanding the complexity of models in order to capture the biological mechanisms we wish to understand. We conclude by discussing some unsolved problems in the mathematical modeling of cancer-immune system interactions.

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Section: Two-equation Models: Interactions Between Tumor Cells and Gementioning

confidence: 99%

Interactions Between the Immune System and Cancer: A Brief Review of Non-spatial Mathematical Models

2010

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“…In this model a constant flow, u, of lymphocytes arrives from the immune system. So, we model tumor-immune system interaction using the already known equations [9]: The inclusion of both populations affection brings a new equation for the tumor non clonogenic cells [12], Z, originated from radiation damage. We assume that those cells will also stimulate the lymphocytes population, as pZY , will decay exponentially as -rZ due to the death of damaged cells, and as -qZY due to the interaction with immune system.…”

Section: Modelmentioning

confidence: 99%

“…Such models have been used to explain and to describe immune depression effects [9], the role of time delays in immune response [10,11], radiovirotherapy treatments [12], chemotherapy treatments [13] and even surgery [14].…”

Section: Introductionmentioning

confidence: 99%

Radioterapia y el papel del sistema inmunitario

Grau

Pérez

Antoranz

et al. 2014

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ResumenSe simuló computacionalmente un gran número de pacientes bajo tratamiento de radioterapia, mediante un sistema dinámico. De los resultados, se halló un método para cambiar el número de sesiones de radiación manteniendo óptimo el tratamiento. Además, se obtuvo que la relación entre la fracción sistema inmune-eficiencia tumoral para un paciente dado y la máxima probabilidad de éxito del tratamiento sigue una ley de potencias. Palabras clave: Sistemas Dinámicos, RadiobiologíaRecepción: 23-01-201223-01- Aceptación: 26-03-2012 Abstract Using a population dynamics formulation to model radiotherapy treatments a large amount of patients under treatment was mimicked. From the obtained results a method to change the number of radiation sessions while keeping the optimized treatment is found. Also a power law relating immune system -tumor effciency ratio (ISTER) for a given patient and maximum success probability of radiotherapy treatment is obtained.

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“…A Volterra-like model was proposed in [7] for the interaction between a population of tumor cells (whose number is denoted by x) and a population of lymphocyte cells, y and it is given by…”

Section: A General Family Of Tumor-immune Systemsmentioning

confidence: 99%

Review of Stochastic Stability and Analysis Tumor-Immune Systems

Chiş¹,

Opris²,

Concu

2013

CBIO

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Abstract:In this paper we review and at the same time investigate some stochastic models for tumor-immune systems. To describe these models, we used a Wiener process, as the noise has a stabilization effect. Their dynamics are studied in terms of stochastic stability around the equilibrium points, by constructing the Lyapunov exponent, depending on the parameters that describe the model. Stochastic stability was also proved by constructing a Lyapunov function and the second order moments. We have studied and analyzed a Kuznetsov-Taylor like stochastic model and a Bell stochastic model for tumor-immune systems. These stochastic models are studied from stability point of view and they were graphically represented using the second order Euler scheme and Maple 12 software.

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Behavior of tumors under nonstationary therapy

Cited by 77 publications

References 18 publications

Interactions Between the Immune System and Cancer: A Brief Review of Non-spatial Mathematical Models

Interactions Between the Immune System and Cancer: A Brief Review of Non-spatial Mathematical Models

Radioterapia y el papel del sistema inmunitario

Review of Stochastic Stability and Analysis Tumor-Immune Systems

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