# Chemotherapy Regimen Optimization Using a Two-Archive Multi-Objective Squirrel Search Algorithm
## 3 Proposed Model and Method  
### Mathematical Model of Tumor Dynamics  
The combined cell cycle-specific and non-cycle-specific chemotherapy proposed in this paper is based on the linear tumor growth model of drug resistance and cell cycle specificity proposed by [PERSON] et al. [21; 23] and further modified by [PERSON] et al. [22]. All cells in the body undergo a series of proliferation stages involving division and replication during growth, which are divided into the interphase and the mitotic phase, with a resting phase indicating temporary cell inactivity. The interphase includes the gap phases G1, synthesis phase S, and gap phase G2, while the mitotic phase is mainly the M phase. The resting phase is denoted as G0. Cells synthesize proteins and genetic material during the interphase, divide into two daughter cells during mitosis, and do not undergo any proliferation during the resting phase. Chemotherapeutic drugs that target specific phases of the cell cycle typically exert their effects by interfering with cells in the M phase. When establishing mathematical models, cells in the interphase and mitotic phase are often collectively classified as proliferating cell populations (\(P\)), while cells in the resting phase are modeled as quiescent cell populations (\(Q\)). In the absence of drug action, tumor cell growth can be modeled by a dual-compartment model, as shown in Figure 1.  
In Figure 1, a, b, c, and d, respectively, represent the natural growth rate of the proliferating cell population, the natural death rate of the proliferating cell population, the rate at which proliferating cells become quiescent, and the rate at which quiescent cells revert to proliferating cells. When using chemotherapy drugs, both the proliferating cell population and the quiescent cell population in the cell cycle-specific model may acquire resistance. The cell cycle-specific drug has no killing effect on the resistant cell population. According to this characteristic, the cell population can be further divided into drug-sensitive cell populations (\(S\)) and drug-resistant cell populations (\(R\)). The model proposed in this paper focuses on the combination chemotherapy of cisplatin and docetaxel, with the non-cycle-specific drug cisplatin represented as Drug A in the model and the cycle-specific drug docetaxel represented as Drug B. The main variables of the model include tumor proliferating cells (\(P\)) and tumor quiescent cells (\(Q\)) sensitive to both drugs; proliferating cells resistant only to cisplatin (\(P_{A}\)) and quiescent cells resistant only to cisplatin (\(Q_{A}\)), proliferating cells resistant only to docetaxel (\(P_{B}\)) and quiescent cells resistant only to docetaxel (\(Q_{B}\)), proliferating cells resistant to both drugs (\(P_{AB}\)) and quiescent cells resistant to both drugs (\(Q_{AB}\)), as well as bone marrow cells (\(M\)) significantly affected by the drugs. Quiescent cell populations \(Q\) and \(Q_{B}\) are affected by Drug A and have a certain probability of developing resistance, transferring to \(Q_{A}\) and \(Q_{AB}\). The total tumor cell population at the end of the treatment session and the cumulative damage to bone marrow cells are indicators of drug efficacy and toxicity levels in this model. As mentioned earlier, the modified linear tumor dynamics model consists of eight compartments, as shown in Figure 2, and can be represented by the following equations:  
Figure 1: Dual-compartment tumor model.