## 4 Discussion
The observed periodicity means that the tumor size stably oscillates around the target state, which corresponds to the so-called Jeff's phenomenon [7; 20] observed in clinical practice. The personalized optimal treatment was compared with the suboptimal dosing protocol obtained by optimizing the response of the nominal (mean-population) model without tailoring the treatment to the characteristics of the subject. The suboptimal treatment responses in Figure 10 featured highly undesired fluctuations in the tumor cell population \(T(t)\) and the cytotoxic cell population \(L(t)\), resulting in a higher value of criterion \(J_{D}(\mathbf{D})\). Besides that, the total amount of administered chemotherapy was significantly higher, implying that the personalized optimal treatment ensures the desired therapeutic outcomes with lower chemotherapy doses. The paper presented a novel methodology for personalizing mathematical models of tumor growth dynamics, immune system interactions, and chemotherapy effects. By leveraging machine learning techniques and computer simulations, this study aimed to address the limitations of traditional approaches in chemotherapy dosing protocols, which often rely on mean-population models that fail to account for individual patient variability. This study offers practical benefits for clinicians by providing a framework for guiding decision-making. By integrating machine learning, dynamic models, and optimization, clinicians can simply make more informed decisions. By incorporating patient-specific responses into the treatment protocol, it is possible to reduce the trial-and-error approach, ensuring that patients receive the most effective dose for their unique needs. Clinicians could also use this approach to assess how an individual patient is likely to respond to treatment and whether successful remission is even feasible, leading to a more proactive approach to cancer therapy. The clinical workflow should be as follows:Conventionally determine and administer the leading dose \(D_{0}\). Determine the sampled patient responses \(N(t)\), \(L(t)\), \(T(t)\) via regular bloodwork and medical imagining tools during one dosing period (cycle). Feed the obtained data to the computer implementing the proposed methodology. The computer provides the following information to the clinician:  
Estimated parameters of the tumor model. Optimal sequence of chemotherapy doses. Feasibility of cancer remission and the estimated final tumor size. The clinician expertly assesses the results and finally determines the future steps and approves the treatment. The methodology involved generating training and validation datasets by simulating a diverse population of virtual patients. The parameter vector for each patient was assumed to follow a multivariate normal distribution, capturing inter-subject variability. Sensitivity analysis showed that some parameters had negligible effects on the state variables, narrowing down the number of practically identifiable parameters to 9 out of 14. The trained neural network was then capable of estimating personalized model parameters based on clinical data from a single chemotherapy dose, facilitating more accurate predictions of tumor behavior and treatment outcomes. Key innovations included the use of machine learning to personalize cancer model parameters and the application of parametric approximation of the state responses to simplify training data. The parametric approximation of sampled state responses by the sum of exponential functions reduced the complexity of the input data, ensuring feasible training of the MLP NN and better generalization capability. These advancements enable optimized chemotherapy dosing protocols tailored to individual patients, improving both treatment efficacy and safety. An important benefit of determining personalized steady states is the ability to predict cancer remission feasibility and estimate final tumor size. The proposed approach has several limitations that should be acknowledged.