Félix Sánchez-Morales’s research while affiliated with National Autonomous University of Mexico and other places

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Publications (5)


Fig. 1. Illustration of sprout angiogenesis. Tip cells lead the branch towards regions of high TAF concentration, providing the environment using Filopodia. On the other hand, stalk cells trail behind to form the lining separating the blood vessel lumen from the exterior. Regions of high accumulation of angiogenic factors are marked in the scheme with an opaque yellow color. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 3. Algorithm used to update the angiogenesis automaton at each simulation step.
Fig. 7. Network representation of the evolved angiogenesis automaton presented in Fig. 4. A central green node represents the tumor and is connected to blood vessel nodes near proliferating cancer cells. The number of iterations used to explore nodes in this test was í µí± BFS = 200. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 8. Maximum entropy values obtained when simulating tumor growth with 100 different initial vascular networks (each point corresponds to a network). The horizontal axis represents an initial metric extracted from the network, where we examined (a) average degree centrality, (b) average betweenness centrality, (c) average page rank, and (d) average clustering coefficient. The vertical axis is the maximum entropy reached by the tumor (bigger values correspond to higher cell proliferation).
Fig. 9. Minimum entropy values reached when applying radiotherapy on a simulated tumor that has grown under the support of 100 different vascular network configurations (each point corresponds to one of the networks). The horizontal axis indicates a metric for the networks: (a) degree centrality, (b) betweenness centrality, (c) page rank, and (d) clustering coefficient. The vertical axis represents the minimum entropy obtained (smaller entropies correspond to better treatment outcomes). Radiotherapy parameter values used were í µí»¾ 0,rad = 0.05, í µí»¼ rad = 0.1, í µí»½ rad = 0.05, í µí±‘ = 1, í µí±‡ í µí±›,rad = 0.35, í µí±ƒ 0,rad = 0.2, í µí±ƒ í µí±“ ,rad = 0.5.

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Understanding post-angiogenic tumor growth: Insights from vascular network properties in cellular automata modeling
  • Article
  • Full-text available

September 2024

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6 Reads

Chaos Solitons & Fractals

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Félix Sánchez-Morales

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Evaluation of entropy and fractal dimension as biomarkers for tumor growth and treatment response using cellular automata

March 2023

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21 Reads

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6 Citations

Journal of Theoretical Biology

Cell-based models provide a helpful approach for simulating complex systems that exhibit adaptive, resilient qualities, such as cancer. Their focus on individual cell interactions makes them a particularly appropriate strategy to study cancer therapies' effects, which are often designed to disrupt single-cell dynamics. In this work, we propose them as viable methods for studying the time evolution of cancer imaging biomarkers (IBM). We propose a cellular automata model for tumor growth and three different therapies: chemotherapy, radiotherapy, and immunotherapy, following well-established modeling procedures documented in the literature. The model generates a sequence of tumor images, from which a time series of two biomarkers: entropy and fractal dimension, is obtained. Our model shows that the fractal dimension increased faster at the onset of cancer cell dissemination. At the same time, entropy was more responsive to changes induced in the tumor by the different therapy modalities. These observations suggest that the prognostic value of the proposed biomarkers could vary considerably with time. Thus, it is essential to assess their use at different stages of cancer and for different imaging modalities. Another observation derived from the results was that both biomarkers varied slowly when the applied therapy attacked cancer cells scattered along the automatons' area, leaving multiple independent clusters of cells at the end of the treatment. Thus, patterns of change of simulated biomarkers time series could reflect on essential qualities of the spatial action of a given cancer intervention.



Fig. 1 Layer organization of cells in a tumor. The image was generated with the tumor model developed in this work.
Fig. 2 Elements considered in the proposed model for cancer growth and therapy.
Fig. 3 State transition diagram of the automaton's cells
Fig. 6 Images and cell count time series for the evolved tumor when radiotherapy was administered halfway through its growth. Parameters used for the radiotherapy treatment were: γ 0 = 0.05, α = 0.1, β = 0.05, d = 1, T n,rad = 0.35, τ rad,delay = 50, P rad,0 = 0.02 and P rad,f = 0.5
Fig. 7 Entropy and fractal dimension time series obtained in a case where a beam of radiation was administered midway through the tumor development (step 300).
Evaluation of Entropy and Fractal Dimension as Biomarkers for Tumor Growth and Treatment Response using Cellular Automata

November 2022

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106 Reads

Cell-based models provide a helpful approach for simulating complex systems that exhibit adaptive, resilient qualities, such as cancer. Their focus on individual cell interactions makes them a particularly appropriate strategy to study the effects of cancer therapies, which often are designed to disrupt single-cell dynamics. In this work, we also propose them as viable methods for studying the time evolution of cancer imaging biomarkers (IBM). We propose a cellular automata model for tumor growth and three different therapies: chemotherapy, radiotherapy, and immunotherapy, following well-established modeling procedures documented in the literature. The model generates a sequence of tumor images, from which time series of two biomarkers: entropy and fractal dimension, is obtained. Our model shows that the fractal dimension increased faster at the onset of cancer cell dissemination, while entropy was more responsive to changes induced in the tumor by the different therapy modalities. These observations suggest that the predictive value of the proposed biomarkers could vary considerably with time. Thus, it is important to assess their use at different stages of cancer and for different imaging modalities. Another observation derived from the results was that both biomarkers varied slowly when the applied therapy attacked cancer cells in a scattered fashion along the automatons' area, leaving multiple independent clusters of cells at the end of the treatment. Thus, patterns of change of simulated biomarkers time series could reflect on essential qualities of the spatial action of a given cancer intervention.


Citations (2)


... Clearly, by looking at figure 2, we can see that the scaling factor decreases with a very heavy tailed trend by the increase of N, whereas, in figure 3, the portrayed data shows that both ε ( the scaling factor) and FD(fractal dimension) are decreasing at the same time. The following section presents some influential open problems in fractal oncology [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28]. Exploring these open problems could lead to significant advancements in our understanding of cancer biology and therapy, potentially impacting diagnosis, treatment, and patient outcomes. ...

Reference:

Fractal Open Problems in Cancer Research, Medicine, Biomedicine, ClinicalSciences, and Dentistry
Evaluation of entropy and fractal dimension as biomarkers for tumor growth and treatment response using cellular automata
  • Citing Article
  • March 2023

Journal of Theoretical Biology

... In the last decade, the number of studies dedicated to the development of mathematical models of behavior in living multicellular tissues has increased [1][2][3][4][5][6]. This interest among scientists is associated with the rapid advancement of computer technologies, which enable in silico investigations without harm to real living organisms. ...

Evaluation of Entropy and Fractal Dimension as Biomarkers for Tumor Growth and Treatment Response Using Cellular Automata
  • Citing Article
  • January 2022

SSRN Electronic Journal