Personalized Plasma Medicine for Cancer: Transforming Treatment Strategies with Mathematical Modeling and AI Techniques

1. Introduction

Plasma technology, rapidly emerging field at the intersection of plasma physics and medicine holds immense potential for biomedical applications [1-9]. Plasma, known as the fourth state of matter is typically formed by heating gas such as inert gases like argon or helium, or air. When heated, the high-speed electrons collide with atoms or molecules causing the removal of electrons and generating highly reactive positive and negative ions. These ions are conductive and can oscillate in response to electric and magnetic fields. The oscillations can give rise to emission of various electromagnetic waves [10]. Additionally, there are also low energy electrons that can only excite particles without causing ionization. These excited particles release energy in the form of photons. Plasma or ionized gas, is a complex mixture comprising electrons, positively and negatively charged ions, radicals, neutral atoms and molecules, atoms at excited state, electromagnetic waves, and electromagnetic fields [11]. The degree of ionization and the specific composition of plasma is dependent on factors such as temperature, pressure, energy supply, nature of the gas, electron density ranges, the devise used and operational conditions utilized to generate the plasma [12,13]. The most common type of low temperature atmospheric pressure plasma is the cold atmospheric plasma jets (CAPJ) has been well established in the field of biology and medicine [14].

Atmospheric plasma, can self-organize into different patterns with modified plasma compositions in response to various operational parameters and interactions with the target environment [15,16]. This transition from spatially homogeneous state to self-organized patterns in response to various parameters like discharge voltage [17-19], electrical permittivity of target cells [20] can play an important role in the therapeutic outcome of plasma treatment for cancer [21,22]. Self-organization might allow an adaptive and self-adaptive plasma system that can dynamically adjust and optimize plasma treatment conditions based on real-time feedback [16]. It aims to maximize the therapeutics on cancer cells while ensuring safety and efficacy.

This review focuses specifically on the recent prominence of cold atmospheric plasma (CAP) in the field of oncology, with special emphasis on the application of various mathematical models and artificial intelligence (AI) techniques. CAP's potential to revolutionize cancer treatment is explored in this review, drawing attention to its unique adaptive and self-adaptive characteristics and the role of mathematical modelling and advanced algorithms in advancing its application in precision medicine.

2. Mathematical modeling

In cancer research, mathematical modeling plays a pivotal role in comprehending the intricate dynamics of cancer in response to various treatments [23,24]. It complements cancer research by providing valuable quantitative predictions to unravel the complexity of cancer and open new avenues for developing effective treatments [25]. Numerous mathematical models, often rooted in ordinary differential equations (ODEs), have explored various aspects of cancer research, including treatment strategies [26-34], immune responses [35-41], treatment sensitivity and resistance [42], the effects of treatment combinations [43-49], habitat dynamics [50], tumor heterogeneity [51,52], and treatment optimization [53]. Their collective contribution lies in furnishing predictions for optimal dosing, treatment regimens, and scheduling, all while minimizing adverse side effects and maximizing therapeutic gains. This avenue holds promise for personalized cancer care, customizing treatments based on individual patient traits and diverse tumor characteristics, including size, type, growth rate, heterogeneity, genetics, and immune composition [37,54]. For mathematical models to operate with precision, the accurate identification of critical parameters hinges on the acquisition of frequent and precise data [55]. ODE-based equations are commonly employed in mechanistic and deterministic models where underlying mechanisms and deterministic relationships are of primary interest. Beyond the realm of ODEs, fractional calculus emerges as a potential frontier for refining cancer modeling, particularly in capturing memory effects and intricate aspects of tumor growth [56-58]. Fractional calculus enables differentiation and integration of non-integer orders, extending beyond traditional calculus. In cancer research, it finds application by modeling anomalous diffusion processes, characterizing tumor behavior more accurately, and incorporating memory effects into models, deepening our understanding of tumor dynamics.

Several mathematical models have been validated through preclinical investigations and clinical trials, demonstrating their potential for shaping effective clinical trial designs [59-65]. Notably, Dean et al. [65] engineered a mathematical model tailored to refine radiation therapy schedules for glioblastoma, a formidable brain cancer. The model recommended an almost-optimal re-irradiation regimen for recurrent glioblastoma patients: 7 days of 3.96 Gy (administered once per day), followed by 9 days of 1.0 Gy (administered thrice per day). Strikingly, this regimen demonstrated both feasibility and safety in all 14 patients (100%) who received it, marking a notable achievement in glioblastoma treatment. Although preliminary results hint at enhanced tumor control, the imperative for larger-scale trials to substantiate its efficacy remains paramount. These findings prove the invaluable role of mathematical modeling in fine-tuning cancer treatment strategies, offering promising prospects for future clinical applications.

After the proposal of adaptive and self-adaptive plasma [66], an exponential growth model was developed [67] to predict the dynamic response of cancer cells (U-87 MG and MDA-MB-231) under CAP treatment [18]. This model successfully derived optimal treatment conditions for two distinct cancer cell lines: U-87 MG and MDA-MB-231. For U-87 MG, the study aimed for a desired ratio of cancer cell viability (rd) of 0.5, leading to optimal treatment parameters of ∆t (Treatment Duration) at 65.1 seconds and U (Plasma Discharge Voltage) at 3.367 kV. For MDA-MB-231, targeting a rd of 0.3 resulted in optimal settings of ∆t at 71.6 seconds and U at 3.315 kV. These specific values were attained through rigorous numerical optimization techniques applied to the mathematical model describing cancer cell responses to CAP exposure. Furthermore, the research extended the optimal control framework to employ an optimal feedback control strategy using Model Predictive Control (MPC). This approach facilitates real-time adaptation of treatment parameters based on actual cancer cell responses, effectively mitigating the impact of uncertainties, and ensuring consistent maintenance of the desired level of cancer cell growth inhibition. The model thus offers a powerful tool for quantitatively optimizing CAP treatment parameters, accounting for dynamic cancer cell responses over time to achieve precise and targeted levels of growth inhibition. However, it is important to note that the model's predictive accuracy is contingent upon the quality and representativeness of the experimental data, necessitating comprehensive validation through experiments. Additionally, the model may not encompass all biological complexities, potentially introducing uncertainties into its predictions.

In recent studies, indirect treatment using plasma treated liquids (PTLs) [68-70] or plasma treated hydrogels (PTHs) [71] has shown enhanced cytotoxicity and anticancer immune responses, attributed to the long-lived reactive oxygen and nitrogen species (RONS) such as H₂O₂, NO₂⁻, NO₃⁻ . These treatments have demonstrated greater effectiveness than direct plasma treatment [72-76]. However, despite their advantages, concerns regarding the lack of consistent molecular-level analysis and precise control over their chemical compositions have been raised, limiting their clinical suitability. Mathematical modeling has been instrumental in investigating the behavior of RONS in cancer treatment with PTLs, allowing for parameter exploration to optimize treatment strategies. Bengston and Bogaerts [77,78] developed a valuable quantitative framework using mathematical modeling to investigate the behavior of reactive oxygen and nitrogen species (RONS) in cancer treatment with PTLs, enabling parameter exploration for treatment optimization. This model suggests that specific cell features, such as the H₂O₂ membrane diffusion rate constant and intracellular catalase concentration, influence the response to PTLs. It also proposes that certain reactions involving CO₃^•– (carbonate radical anion) [79] and catalase may be responsible for the enhanced anti-cancer effect observed when combining H₂O₂ and NO₂⁻ in PTLs.

Limitations associated with mathematical models in the context of cold atmospheric plasma (CAP) treatment are multifaceted and have implications for their reliability and applicability. These limitations include a strong reliance on the accuracy of input data, potential oversimplification of complex biological processes, the critical need for experimental validation, a confined scope of parameterization, potential variations across different cell types, assumptions of homogeneity, reliance on literature-derived values, and inherent model uncertainty. Future advancements in this field should focus on developing patient-specific models, refining parameter estimation techniques, exploring the utility of biomarkers, enhancing data collection methods, and conducting rigorous validations. Notably, the integration of AI techniques holds promise in addressing these limitations by improving prediction accuracy, automating feature engineering, accommodating nonlinear relationships, handling noisy and incomplete data, enabling real-time adaptability, and incorporating diverse data types [80]. Mathematical modeling entails the creation of mathematical representations for real-world systems, while AI/ML approaches use data-driven techniques to learn patterns and make predictions, often incorporating mathematical principles, formulas, and statistical methods within their frameworks [81,82]. By combining the strengths of mathematical modeling and AI/ML, we can potentially offer improved patient care and treatment strategies [83], enhancing clinical trials and personalized medicine.

3. AI techniques for Adaptive Plasma system

Artificial intelligence (AI) is about creating “thinking machines” that can make decisions on their own. Machine learning (ML) is the subset of AI that aims at creating “learning machines” in which machines/tools learn from data and perform tasks without explicit programing [84]. A tutorial review on widely used ML methods that can help in discovering patterns and relationships in datasets that may be challenging for human intuition are well described by Bonzanini et al. [85].

The evolution of AI, particularly with the integration of ML, has opened new possibilities in oncology, revolutionizing every facet of cancer care. It has significantly enhanced cancer diagnosis [86-90], prognosis [91-95], and the prediction of metastasis [96-98]. Treatment selection [99], efficacy [100-102] and response assessment [103-107], and outcome prediction [108-112] have also seen remarkable enhancements. These advancements have paved the way for highly personalized cancer treatments, offering a ray of hope within the continually evolving healthcare landscape [113-115]. Although ML has been applied in various treatment approaches in cancer medicine, its use in plasma medicine is relatively limited (Figure 1). The potential of ML in accelerating plasma research towards personalized cancer treatment is well discussed [116-119].

3.1. Reinforcement learning

In machine learning (ML), algorithms are used to train and construct models using large datasets containing relevant information, such as input features (e.g., varying operational parameters of the adaptive plasma system) and target labels (e.g., treatment responses by the cancer cells). The objective is to analyze the datasets, identify patterns and relationships between input features and target labels, and adjust the internal parameters of the algorithm iteratively to improve its predictive accuracy (e.g., optimizing parameters in the adaptive plasma system for selective cytotoxicity towards cancer cells). The goal is to minimize the difference between the model's predictions and the actual outputs during training, making the model "trained" and capable of making accurate predictions.

Different ML approaches such as reinforcement learning (RL) and deep learning (DL) have different methods to update their parameters during training. For example, in RL process, the agent (adaptive plasma system) learns, gets trained and improves its behavior in an environment (cancer cells) through its interaction experience [120]. It takes actions, receives feedback in the form of rewards and penalties based on the effectiveness of its treatment strategies, and uses this feedback to update its internal parameters and improve its decision-making. The system aims to find an optimal strategy that maximizes the cumulative reward it receives.

Hou et al. [116], developed an adaptive plasma framework for CAP cancer treatments using integration of empirical dynamic modeling and reinforcement learning. The empirical dynamic model was constructed using data collected from in vitro experiments [18] that provided information on how cancer cell viability changes over time under various CAP treatment conditions (eg. treatment duration from 0 to 180 seconds, and the discharge voltage between 3.16 kV and 3.71 kV). The empirical data obtained from in vitro experiments may represent specific scenarios and treatment conditions. To estimate for a wide range of treatment scenarios, a Gaussian process, a type of statistical modeling tool, that helps the model to capture the variability and uncertainty inherent in real-world clinical settings was incorporated. The CAP cancer treatment was then modelled as a Markov decision process (MDP) and conjugated with safe Q-learning. The MDP represents the sequence of states and actions in the treatment process. Each state corresponds to a specific situation or condition of the cancer cells (eg. cancer cell viability) and each action represents a treatment strategy that the adaptive plasma system can take (eg. treatment duration, discharge voltage). MDP helps in defining the states, actions, and transition probabilities in the treatment process, but it does not inherently provide the optimal policy for selecting actions that lead to the best long-term rewards. Q-learning, a specific algorithm designed for reinforcement learning tasks [121], helps the adaptive plasma system to learn from its interactions with the environment and update its decision-making process by estimating the expected cumulative rewards for different actions in different states. This enables the system to make better decisions and optimize the treatment plan to achieve safer and more personalized cancer treatment (Figure 2). The study uses in vitro data to model cancer cell response, potentially limiting real-world applicability, but Gaussian processes aid in generalization. While the cancer treatment model as a Markov Decision Process lacks in-depth exploration of its limitations, it offers structured optimization with effective Q-learning adaptability. Safe Q-learning focuses on avoiding risky actions, leaving a gap in addressing other safety aspects but still enhances treatment safety. To enhance the model, future research should incorporate in vivo data, explore hybrid models, consider non-Markovian dynamics, investigate multi-agent systems, expand safety considerations, integrate real-time diagnostics, adopt personalized medicine, and validate through clinical trials for improved clinical relevance.

3.2. Gaussian process regression

Lin et al. [122] used Model Predictive Learning Control (MPLC), an extension of MPC that incorporates machine learning techniques for self-adaptive CAP jet optimization. While MPC typically uses a fixed mathematical model and optimization algorithm-based control strategy [67], MPLC integrates machine learning algorithms to capture system dynamics and adapt the control strategy based on real-time data. In the study, MPLC is implemented by using Gaussian Process (GP) regression, a statistical machine learning technique, to model the dynamic behavior of cancer cell viability in response to CAP treatment. The GP model is continuously updated with real-time feedback from the actual cancer cell responses, measured using real-time electrochemical impedance spectroscopy (EIS), after each treatment. This real-time feedback enables the MPLC algorithm to adapt and improve its predictions and treatment plans over time (Figure 3).

By dynamically adjusting the plasma treatment parameters based on actual system responses, the self-adaptive plasma jet can optimize its treatment strategy for a wide range of biomedical applications and variations in the system.

While the study demonstrates its use for cancer cell viability in response to CAP treatment, the transition to clinical applications may require additional research and validation. Pros include the adaptability of MPLC with GP regression, which enhances precision and effectiveness through real-time learning and feedback via electrochemical impedance spectroscopy (EIS). However, potential cons involve computational complexity and the reliability of GP models. Future directions should focus on clinical validation, scalability, and addressing computational challenges for practical healthcare adoption.

3.3. Deep learning

Deep learning uses artificial neural networks (ANNs) with multiple layers (deep neural networks) to make predictions from the labeled data (for instance real-time spectra from Optical Emission Spectroscopy). The self-adaptive plasma system empowered with AI holds great promise for advancing precision medicine and improving cancer treatment outcomes [119]. The self-adaptive plasma system is a plasma control system that can dynamically and autonomously diagnose plasma chemistry, adjust its operating parameters (eg. Gas and power inputs) to control and optimize plasma chemical composition in real-time according to the required species/dosage to kill cancer cells. This system typically employs artificial neural networks and Gradual-Mutation algorithms (GMA), to continuously monitor, analyze the datasets, control, and optimize plasma chemistry and thus make real-time decisions on how to modify the plasma conditions. The real-time spectra of plasma chemical composition and temperatures are obtained using spontaneous emission spectroscopy and processed by a diagnostic ANN. The diagnostic ANN provides valuable outputs on plasma chemistry, which are then used by a control ANN as inputs to adjust plasma parameters like gas injections and energy levels. The control ANN is trained by GMA to adjust the production of specific RONS associated with apoptosis of cancer cells. It receives feedback from the diagnostic ANN and dynamically adjusts the gas and power inputs to optimize the concentration of these species using in the plasma. GMA is used to train both the diagnostic and control ANNs effectively, allowing the self-adaptive plasma system to diagnose, control and optimize the plasma chemistry in real-time based on the OES data and specific objectives. Such an AI empowered self-adaptive plasma system allows for personalized treatments tailored to the specific characteristics of the patient's cancer

The integration of diagnostic ANN, chemical process network (CPN), and control ANN creates an adaptive and intelligent system for effective and personalized cancer treatment [123] (Figure 4).

AI-driven gas plasma can continuously learn from treatment outcomes, adapt to changing conditions, and optimize treatment plans. This personalized and dynamic approach has the potential to improve the efficacy of cancer therapies, reduce side effects, and advance precision medicine.

The absence of performance metrics and considerations is a critical limitation in the above discussed AI-based approaches. Performance evaluation is a fundamental aspect of any AI system. However, these research efforts primarily focus on the theoretical and conceptual aspects of AI-empowered plasma systems and their potential applications in cancer treatment. Given their early stage and limited access to real-world data, providing precise performance metrics is challenging. Addressing this gap necessitates future studies with interdisciplinary collaborations involving experts in computational science, machine learning, and medical engineering. These collaborations can facilitate the evaluation of computational efficiency, scalability, adaptability, and real-time processing capabilities of AI-empowered plasma systems. Additionally, benchmarking AI models against existing standards in the field enables a comparative analysis of efficiency and effectiveness. Adherence to established reporting standards and guidelines for AI research is essential for enhancing the rigor and impact of future studies.

As artificial intelligence gains broader acceptance in clinical applications, we foresee the imminent emergence of an artificial intelligence-driven adaptive plasma system for personalized cancer treatment, revolutionizing medical practice and paving the way for transformative advancements in oncology.

4. AI in Real-Time diagnostics

To exploit the adaptive and self-adaptive properties of CAP in developing personalized treatment protocols, it is important to estimate the operational parameters of the CAP sources and measure the cell response to CAP treatment in real-time.

4.1. Real-time diagnosis of operational parameters of CAP sources

Traditional diagnostics (eg. Laser induced fluorescence, mass spectrometry, spontaneous Raman scattering) of the different operational parameters of CAP sources are complex and expensive requiring sophisticated instrumentation setups and specialized analysis making them impractical for real-time use [124,125] and makes it challenging to control the plasma consistently and effectively. Using information-rich datasets collected from simpler diagnostic methods like optical emission spectroscopy (OES) [126], electro-acoustic emission and enabling fast, automated data processing and analysis using AI techniques in real-time monitoring and control, improves the feedback control, ensuring effective and optimal performance of CAP sources [124,125]. Simulated data [127,128], although not capturing all the complexities in real-world scenarios, complements real data by providing a controlled environment for analysis and experimentation.

Analysis of the datasets manually with traditional methods can be challenging due to complex relations and patterns in the data. ML and other computational approaches (Table 1) are designed to handle such complexity and can identify patterns and trends that may not be apparent to human analysis [125].

ML algorithms can be trained on the operational parameters and their corresponding data, allowing them to learn and generalize their knowledge for making predictions on new, unseen data. As new data is received the algorithms rapidly process and analyze data, enabling quick estimation of critical operational parameters from the spectral data or other input data in real-time. ML provides a promising pathway through the creation of input-output models that support real-time computations, thus enabling the implementation of more advanced feedback control strategies [117,135]. Constructing multivariable nonlinear prediction models to characterize the complex interactions between CAP and cancer cells is crucial for guiding effective cancer treatment approaches [133]. AI models can thus be used for real-time monitoring and diagnostics [124,129-131], detecting any deviations from the normal behavior [132,135], and predicting when maintenance or adjustment is required [119] for maintaining optimal real-time control of the operational parameters. Thus, AI- based approaches, specifically ML, can significantly improve the reliability and performance of CAP by adapting to dynamic and uncertain environments.

4.2. Real-time diagnosis of the cell responses to CAP treatment

Collecting real-time data on cancer cell responses to different CAP treatment modalities is challenging. Studies discussed in section 3.1 and 3.2 have utilized real-time EIS measurements [122,116] (Table 2) and has focused on incorporating automated feedback control systems into adaptive plasma system to optimize performance and safety (Figure 5).

Yet, advanced real-time diagnostic systems are still needed to provide sensitive, accurate, and reproducible data for these feedback control systems. To achieve optimal results, sophisticated diagnostic systems with high sensitivity, accuracy, and reproducibility are imperative. These systems should seamlessly integrate with the biological target and have minimal interference with the plasma treatment process. By fulfilling these criteria, the feedback control loop can make well-informed and precise adjustments, optimizing treatment outcomes for diverse cancer cells and individual patients. Developing electronic and optical sensors suitable for addressing this technological gap and to integrate these sensors into autonomous plasma systems must be focused [137]. Bridging this gap could lead to the development of next-generation medical plasma technologies, offering superior healthcare outcomes.

The applications of ML in modeling and simulating different aspects of CAP processing are well reviewed by Treischmann et al. [138]. Future advancements for CAP modelling and simulation promises precise control, pattern discovery, and transformative insights, advancing plasma science and technology. Open data access and collaboration are pivotal for breakthroughs [138].

5. Conclusions

Cancer is a challenging disease to treat due to its complexity, heterogeneity, invasion (metastasis), and resistance to treatments. The intricate nature of cancer manifests in the variability of responses to therapies among patients owing to the individualized genetic makeup and biological characteristics of their tumors. This necessitates tailored treatment approaches to optimize the chances of successful outcomes [139]. To achieve personalized treatment, with CAP is emerging as a promising approach as the parameters of the plasma device can be fine-tuned during the treatment to suit the patient’s specific dosage. CAP has shown to reprogram the tumor microenvironment [140-142] inhibiting tumor growth with high selectivity and even enhancing the effectiveness of other treatment modalities like chemotherapy [143-146], immunotherapy [147,148], radiotherapy [149-152], and nanomedicine [153-156] with improved treatment outcomes and minimized side-effects [157]. The self-adaptive nature of the adaptive plasma system complements the power of AI. As CAP devices can dynamically adjust treatment parameters during the therapy session, they can respond to real-time changes in tumor characteristics or patient physiology. AI-driven feedback loops can enhance this self-adaptation, ensuring that CAP treatment remains optimized and effective throughout the course of therapy, making it a promising avenue for achieving optimal treatment outcomes in personalized cancer care.

Better cross-disciplinary collaboration with plasma physicists, mathematicians, AI engineers, data scientist, oncologists, and clinicians can make these effective proposals achieve in the future that can be tailored towards personalized cancer treatment strategy. Advancing diagnostic tools, exploring new combination treatment strategies with CAP treatment, and modeling with AI will pave the way for more precise and personalized plasma-based therapies. AI is transforming plasma medicine, improving treatments with precise models, data analysis, real-time diagnostics, and protocols, despite ethical and transparency concerns [82]. The ongoing advancements at the frontiers of plasma technology in oncology are poised to revolutionize cancer treatment paradigms, providing new hope and improved outcomes for cancer patients worldwide. With continued efforts and interdisciplinary cooperation, plasma technology holds the potential to become an indispensable asset in the fight against cancer.