Vascular Invasive Tumor Growth Optimization (VITGO): The Tumor Growth Machanism to Encounter Optimization Problems in Scientific and Technological Research and Development

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1. Introduction

Tumor is an abnormal growth of tissue [1]. The growth of tumor is a complex process, influenced by the interactions between tumor cells and their microenvironment, including their surrounding cells, as well as the extracellular matrix (ECM) [2], chemical signals, as well as metabolic substrates such as oxygen and glucose. Tumor tissue are still indispensable for diagnosis and treatment strategies of solid tumors and importantly, to extend the patients’ lifespan or contribute to their cure [3].

2. The Tumor Growth

It develops when cells in the body divide and grow at an excessive rate. Typically, the body is able to balance cell growth and division [4]. When old or damaged cells die, they are automatically replaced with new, healthy cells. In the case of tumors, dead cells remain and form a growth known as a tumor.

Fig 1: The Tumor growth

3. Inspiration

The VITGO algorithm enhances the search strategy inspired by tumor growth mechanism. The VITGO algorithm provides a new framework with three populations, four roles and five search rules [5]. Proliferative cells (Pcell), Quiescent cells (Qcell), and dying cells (Dcell) are three populations. Proliferative cell, quiescent cell, dying cell and invasive cell (Icell) are the four roles. Growth of Pcell, Growth of Icell, growth of Qcell, growth of Dcell, and random walk of cell are the five search strategies in tumor growth [6].

Fig 2: Growth Machanism of Tumor

4. Invasive tumor growth optimization model

Considering the invasion of tumor cells, tumor cells were divided into four layers: invasive cells, proliferative cells, quiescent cells, and dying cells [7].

4.1. The growth of proliferative cells (Pcell)

In order to reflect the intrusive behavior of proliferative cells, we use the levy flight to simulate it. The intrusive behavior of proliferative cells can also be viewed as a Levy flight.

Pcell presents the position of proliferative cell, Levy(c) presents the intrusive behavior of the proliferative cell and ß is the control size of step

Where Fit is the current number of fitness evaluation consumed, and Max Fit is the max number of fitness evaluations consumed. R denotes Random. Levy distribution usually appears in a simplified form, as follows

Ѱ is a constant

4.2. Quiescent cells of tumor (Qcell)

The Quiescent cells (Qcells) move toward the higher nutrient concentrations, which is guided by proliferative cells and they interact with each other

is the old position of quiescent cell and is the current position of quiescent cell. m, n is  an integer which indicates the two quiescent cells.

4.3. Dying cells of tumor (Dcell)

In dying cells region, nutrient concentration is very low, so these cells move toward the direction of quiescent cells and proliferative cells with a higher nutrient concentration.

Dcell m, n(t) indicates the position of the old dying cell, Dcellm,n(t + 1) indicates the position of the current dying cell, Qcellm,n (t) indicates the position of quiescent cell, BP cell (t)I, n indicates the position of proliferative cell the current best position, i is integer, which indicates a proliferative cell chosen randomly from the subpopulation of proliferative cells.

4.4. Invasive cells

A dying cell is replaced by the invasive cell

Here, γ ∈ rand [− 1, 1] presents the growth speed, R (I, c) produces a new solution randomly in the search space [8].

5. Advantages and Disadvantages of VITGO

Fig 3: Advantages & disadvantages of VITGO

6. Innovative approaches for Tumor treatment: current perspectives and new challenges

Fig 4: Innovative Approaches to Tumor Treatment

7. Can Tumor Cured?

Grade I brain tumors may be cured if they are completely removed by surgery. Grade II — the tumor cells grow and spread more slowly than grade III and IV tumor cells [10]. They may spread into nearby tissue and may recur (come back). Some tumors may become a higher-grade tumor [11]. Staying actively in our own risk to like exercise diet etc… can prevent us from tumor. An good tumor fighting ethics are represented in the below fig;

Fig 5: Ethics to Tumor Fighting

8. Flowchart of VITGO

Fig 6: Flowchart of VIT

9. Application of VITGO

      VITGO method can be used for the optimization of engineering design applications [12].-

Fig 7: Application of VITGO

Reference

[1] J. Zhou, S. Dong, D. Tang and X. Wu, “A Vascular Invasive Tumor Growth Optimization Algorithm for Multi-Objective Optimization”, IEEE Access, vol. 8, pp. 29467-29488, 2020. Available: 10.1109/access.2020.2972631.

[2]H. Seada and K. Deb, “A Unified Evolutionary Optimization Procedure for Single, Multiple, and Many Objectives”, IEEE Transactions on Evolutionary Computation, vol. 20, no. 3, pp. 358-369, 2016. Available: 10.1109/tevc.2015.2459718.

[3]H. Seada, M. Abouhawwash and K. Deb, “Multiphase Balance of Diversity and Convergence in Multiobjective Optimization”, IEEE Transactions on Evolutionary Computation, vol. 23, no. 3, pp. 503-513, 2019. Available: 10.1109/tevc.2018.2871362.

[4]D. Tang, S. Dong, Y. Jiang, H. Li and Y. Huang, “ITGO: Invasive tumor growth optimization algorithm”, Applied Soft Computing, vol. 36, pp. 670-698, 2015. Available: 10.1016/j.asoc.2015.07.045.

[5]J. Hirche, “Hwang, Ching-Lai/Masud, A. S. Md., Multiple Objective Decision Making — Methods and Applications. A State-of-the-Art Survey. In Collaboration with S. R. Paidy and Kwangsun Yoon. Lecture Notes in Economics and Mathematical Systems 164. Berlin-Heidelberg-New York, Springer-Verlag 1979. XII, 351 S., 39 Abb., 35 Tab., DM 35,50, US $19.60. ISBN 3-540-09111-4”, ZAMM – Zeitschrift für Angewandte Mathematik und Mechanik, vol. 60, no. 9, pp. 451-451, 1980. Available: 10.1002/zamm.19800600932.

[6]A. Esparcia, “PPSN 2016”, ACM SIGEVOlution, vol. 9, no. 3, pp. 12-13, 2017. Available: 10.1145/3066862.3066864.

[7]J. Cheng, J. Chen, Y. Guo, S. Cheng, L. Yang and P. Zhang, “Adaptive CCR-ELM with variable-length brain storm optimization algorithm for class-imbalance learning”, Natural Computing, 2019. Available: 10.1007/s11047-019-09735-9.

[8]M. Mollamotalebi and S. Hajireza, “Multi-objective dynamic management of virtual machines in cloud environments”, Journal of Cloud Computing, vol. 6, no. 1, 2017. Available: 10.1186/s13677-017-0086-z.

[9]Q. Kang, S. Feng, M. Zhou, A. Ammari and K. Sedraoui, “Optimal Load Scheduling of Plug-In Hybrid Electric Vehicles via Weight-Aggregation Multi-Objective Evolutionary Algorithms”, IEEE Transactions on Intelligent Transportation Systems, vol. 18, no. 9, pp. 2557-2568, 2017. Available: 10.1109/tits.2016.2638898.

[10]G. Diaz, J. Jones, T. Brandt, T. Gary and A. Yenamandra, “Translating Data into Discovery: Analysis of 10 Years of CDC Data of Mortality Indicates Level of Attainment of Education as a Suicide Risk Factor in USA”, Social Behavior Research and Practice – Open Journal, vol. 2, no. 1, pp. 1-17, 2017. Available: 10.17140/sbrpoj-2-107.

[11]N. Srinivas and K. Deb, “Muiltiobjective Optimization Using Nondominated Sorting in Genetic Algorithms”, Evolutionary Computation, vol. 2, no. 3, pp. 221-248, 1994. Available: 10.1162/evco.1994.2.3.221.

[12]T. Ray and K. Liew, “A Swarm Metaphor for Multiobjective Design Optimization”, Engineering Optimization, vol. 34, no. 2, pp. 141-153, 2002. Available: 10.1080/03052150210915.

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