Clinically relevant cancer chemotherapy dose scheduling via mixed-integer optimization

Combination Chemotherapy Optimization with Discrete Dosing

Chemotherapy drug administration is a complex problem that often requires expensive clinical trials to evaluate potential regimens; one way to alleviate this burden and better inform future trials is to build reliable models for drug administration. This paper presents a mixed-integer program for combination chemotherapy (utilization of multiple drugs) optimization that incorporates various important operational constraints and, besides dose and concentration limits, controls treatment toxicity based on its effect on the count of white blood cells. To address the uncertainty of tumor heterogeneity, we also propose chance constraints that guarantee reaching an operable tumor size with a high probability in a neoadjuvant setting. We present analytical results pertinent to the accuracy of the model in representing biological processes of chemotherapy and establish its potential for clinical applications through a numerical study of breast cancer.

A computational tumor growth model experience based on molecular dynamics point of view using deep cellular automata

Cancer, as identified by the World Health Organization, stands as the second leading cause of death globally. Its intricate nature makes it challenging to study solely based on biological knowledge, often leading to expensive research endeavors. While tremendous strides have been made in understanding cancer, gaps remain, especially in predicting tumor behavior across various stages. The integration of artificial intelligence in oncology research has accelerated our insights into tumor behavior, right from its genesis to metastasis. Nevertheless, there's a pressing need for a holistic understanding of the interactions between cancer cells, their microenvironment, and their subsequent interplay with the broader body environment. In this landscape, deep learning emerges as a potent tool with its multifaceted applications in diverse scientific challenges. Motivated by this, our study presents a novel approach to modeling cancer tumor growth from a molecular dynamics' perspective, harnessing the capabilities of deep-learning cellular automata. This not only facilitates a microscopic examination of tumor behavior and growth but also delves deeper into its overarching behavioral patterns. Our work primarily focused on evaluating the developed tumor growth model through the proposed network, followed by a rigorous compatibility check with traditional mathematical tumor growth models using R and Matlab software. The outcomes notably aligned with the Gompertz growth model, accentuating the robustness of our approach. Our validated model stands out by offering adaptability to diverse tumor growth datasets, positioning itself as a valuable tool for predictions and further research.

Systems Engineering Approach to Modeling and Analysis of Chronic Obstructive Pulmonary Disease Part II: Extension for Variable Metabolic Rates

Recently, we developed a systems engineering model of the human cardiorespiratory system [Kurian et al. ACS Omega2023, 8 (23), 20524-20535. DOI: 10.1021/acsomega.3c00854] based on existing models of physiological processes and adapted it for chronic obstructive pulmonary disease (COPD)-an inflammatory lung disease with multiple manifestations and one of the leading causes of death in the world. This control engineering-based model is extended here to allow for variable metabolic rates established at different levels of physical activity. This required several changes to the original model: the model of the controller was enhanced to include the feedforward loop that is responsible for cardiorespiratory control under varying metabolic rates (activity level, characterized as metabolic equivalent of the task-Rm-and normalized to one at rest). In addition, a few refinements were made to the cardiorespiratory mechanics, primarily to introduce physiological processes that were not modeled earlier but became important at high metabolic rates. The extended model is verified by analyzing the impact of exercise (Rm > 1) on the cardiorespiratory system of healthy individuals. We further formally justify our previously proposed adaptation of the model for COPD patients through sensitivity analysis and refine the parameter tuning through the use of a parallel tempering stochastic global optimization method. The extended model successfully replicates experimentally observed abnormalities in COPD-the drop in arterial oxygen tension and dynamic hyperinflation under high metabolic rates-without being explicitly trained on any related data. It also supports the prospects of remote patient monitoring in COPD.

Treatment of evolving cancers will require dynamic decision support

Cancer research has traditionally focused on developing new agents, but an underexplored question is that of the dose and frequency of existing drugs. Based on the modus operandi established in the early days of chemotherapies, most drugs are administered according to predetermined schedules that seek to deliver the maximum tolerated dose and are only adjusted for toxicity. However, we believe that the complex, evolving nature of cancer requires a more dynamic and personalized approach. Chronicling the milestones of the field, we show that the impact of schedule choice crucially depends on processes driving treatment response and failure. As such, cancer heterogeneity and evolution dictate that a one-size-fits-all solution is unlikely-instead, each patient should be mapped to the strategy that best matches their current disease characteristics and treatment objectives (i.e. their 'tumorscape'). To achieve this level of personalization, we need mathematical modeling. In this perspective, we propose a five-step 'Adaptive Dosing Adjusted for Personalized Tumorscapes (ADAPT)' paradigm to integrate data and understanding across scales and derive dynamic and personalized schedules. We conclude with promising examples of model-guided schedule personalization and a call to action to address key outstanding challenges surrounding data collection, model development, and integration.

The combined effect of optimal control and swarm intelligence on optimization of cancer chemotherapy

BACKGROUND AND OBJECTIVES

In cancer therapy optimization, an optimal amount of drug is determined to not only reduce the tumor size but also to maintain the level of chemo toxicity in the patient's body. The increase in the number of objectives and constraints further burdens the optimization problem. The objective of the present work is to solve a Constrained Multi- Objective Optimization Problem (CMOOP) of the Cancer-Chemotherapy. This optimization results in optimal drug schedule through the minimization of the tumor size and the drug concentration by ensuring the patient's health level during dosing within an acceptable level.

METHODS

This paper presents two hybrid methodologies that combines optimal control theory with multi-objective swarm and evolutionary algorithms and compares the performance of these methodologies with multi-objective swarm intelligence algorithms such as MOEAD, MODE, MOPSO and M-MOPSO. The hybrid and conventional methodologies are compared by addressing CMOOP.

RESULTS

The minimized tumor and drug concentration results obtained by the hybrid methodologies demonstrate that they are not only superior to pure swarm intelligence or evolutionary algorithm methodologies but also consumes far less computational time. Further, Second Order Sufficient Condition (SSC) is also used to verify and validate the optimality condition of the constrained multi-objective problem.

CONCLUSION

The proposed methodologies reduce chemo-medicine administration while maintaining effective tumor killing. This will be helpful for oncologist to discover and find the optimum dose schedule of the chemotherapy that reduces the tumor cells while maintaining the patients' health at a safe level.

Design of diffusion-controlled drug delivery devices for controlled release of Paclitaxel

Controlled drug delivery devices were predicted in a reverse engineering framework for the controlled release of Paclitaxel, an anti-cancer drug, widely used in the treatment of solid tumors. Using quantitative structure-property relationship models for mutual diffusion coefficients of the drug in biocompatible and biodegradable polymers and partition coefficients of the drug between polymers and blood, a framework was developed to predict optimal drug delivery devices for desired dosage regimens. The validation of the predicted mutual diffusion and partition coefficients using experimental data was reported in previous studies. Optimal design parameters along with selection of most appropriate polymers suitable for different dosage regimens, selected based on current clinical practice, were predicted for maximum bioavailability of the drug while maintaining the released drug concentration in blood within the therapeutic range. Reservoir and monolithic type of diffusion-controlled drug delivery devices of different shapes and sizes were predicted with different initial drug loadings and bioavailability for different dosage regimens. The effects of the released Paclitaxel from these devices on the tumor growth were also modeled using a previously reported mathematical pharmacokinetic-pharmacodynamic model. The proposed approach can easily be used to design other diffusion-controlled drug delivery devices.

Optimizing multi-modal cancer treatment under 3D spatio-temporal tumor growth

In this paper we introduce a new mixed-integer linear programming (MIP) model that explicitly integrates the spread of cancer cells into a spatio-temporal reaction-diffusion (RD) model of cancer growth, while taking into account treatment effects. This linear but non-convex model appears to be the first of its kind by determining the optimal sequence of the typically prescribed cancer treatment methods-surgery (S), chemotherapy (C), and radiotherapy (R)-while minimizing the newly generated tumor cells for early-stage breast cancer in a unique three-dimensional (3D) spatio-temporal system. The quadratically-constrained cancer growth dynamics and treatment impact formulations are linearized by using linearization as well as approximation techniques. Under the supervision of medical oncologists and utilizing several literature resources for the parameter values, the effectiveness of treatment combinations for breast cancer specified with different sequences (i.e., SRC, SCR, CR, RC) are compared by tracking the number of cancer cells at the end of each treatment modality. Our results provide the optimal dosages for chemotherapy and radiation treatments, while minimizing the growth of new cancer cells.

Precision Medicine with Imprecise Therapy: Computational Modeling for Chemotherapy in Breast Cancer

Medical oncology is in need of a mathematical modeling toolkit that can leverage clinically-available measurements to optimize treatment selection and schedules for patients. Just as the therapeutic choice has been optimized to match tumor genetics, the delivery of those therapeutics should be optimized based on patient-specific pharmacokinetic/pharmacodynamic properties. Under the current approach to treatment response planning and assessment, there does not exist an efficient method to consolidate biomarker changes into a holistic understanding of treatment response. While the majority of research on chemotherapies focus on cellular and genetic mechanisms of resistance, there are numerous patient-specific and tumor-specific measures that contribute to treatment response. New approaches that consolidate multimodal information into actionable data are needed. Mathematical modeling offers a solution to this problem. In this perspective, we first focus on the particular case of breast cancer to highlight how mathematical models have shaped the current approaches to treatment. Then we compare chemotherapy to radiation therapy. Finally, we identify opportunities to improve chemotherapy treatments using the model of radiation therapy. We posit that mathematical models can improve the application of anticancer therapeutics in the era of precision medicine. By highlighting a number of historical examples of the contributions of mathematical models to cancer therapy, we hope that this contribution serves to engage investigators who may not have previously considered how mathematical modeling can provide real insights into breast cancer therapy.

A Robust Optimization Approach to Cancer Treatment under Toxicity Uncertainty

The design of optimal protocols plays an important role in cancer treatment. However, in clinical applications, the outcomes under the optimal protocols are sensitive to variations of parameter settings such as drug effects and the attributes of age, weight, and health conditions in human subjects. One approach to overcoming this challenge is to formulate the problem of finding an optimal treatment protocol as a robust optimization problem (ROP) that takes parameter uncertainty into account. In this chapter, we describe a method to model toxicity uncertainty. We then apply a mixed integer ROP to derive the optimal protocols that minimize the cumulative tumor size. While our method may be applied to other cancers, in this work we focus on the treatment of chronic myeloid leukemia (CML) with tyrosine kinase inhibitors (TKI). For simplicity, we focus on one particular mode of toxicity arising from TKI therapy, low blood cell counts, in particular low absolute neutrophil count (ANC). We develop optimization methods for locating optimal treatment protocols assuming that the rate of decrease of ANC varies within a given interval. We further investigated the relationship between parameter uncertainty and optimal protocols. Our results suggest that the dosing schedule can significantly reduce tumor size without recurrence in 360 weeks while insuring that toxicity constraints are satisfied for all realizations of uncertain parameters.

A Personalized Framework for Dynamic Modeling of Disease Trajectories in Chronic Lymphocytic Leukemia

Chronic lymphocytic leukemia (CLL) is the most common peripheral blood and bone marrow cancer in the developed world. This manuscript proposes mathematical model equations representing the disease dynamics of B-cell CLL. We interconnect delay differential cell cycle models in each of the tumor-involved disease centers using physiologically relevant cell migration. We further introduce five hypothetical case studies representing CLL heterogeneity commonly seen in clinical practice and demonstrate how the proposed CLL model framework may capture disease pathophysiology across patient types. We conclude by exploring the capacity of the proposed temporally- and spatially distributed model to capture the heterogeneity of CLL disease progression. By using global sensitivity analysis, the critical parameters influencing disease trajectory over space and time are: 1) the initial number of CLL cells in peripheral blood, the number of involved lymph nodes, the presence and degree of splenomegaly; 2) the migratory fraction of nonproliferating as well as proliferating CLL cells from bone marrow into blood and of proliferating CLL cells from blood into lymph nodes; and 3) the parameters inducing nonproliferative cells to proliferate. The proposed model offers a practical platform that may be explored in future personalized patient protocols once validated.

Model-Based Tumor Growth Dynamics and Therapy Response in a Mouse Model of De Novo Carcinogenesis

Tumorigenesis is a complex, multistep process that depends on numerous alterations within the cell and contribution from the surrounding stroma. The ability to model macroscopic tumor evolution with high fidelity may contribute to better predictive tools for designing tumor therapy in the clinic. However, attempts to model tumor growth have mainly been developed and validated using data from xenograft mouse models, which fail to capture important aspects of tumorigenesis including tumor-initiating events and interactions with the immune system. In the present study, we investigate tumor growth and therapy dynamics in a mouse model of de novo carcinogenesis that closely recapitulates tumor initiation, progression and maintenance in vivo. We show that the rate of tumor growth and the effects of therapy are highly variable and mouse specific using a Gompertz model to describe tumor growth and a two-compartment pharmacokinetic/ pharmacodynamic model to describe the effects of therapy in mice treated with 5-FU. We show that inter-mouse growth variability is considerably larger than intra-mouse variability and that there is a correlation between tumor growth and drug kill rates. Our results show that in vivo tumor growth and regression in a double transgenic mouse model are highly variable both within and between subjects and that mathematical models can be used to capture the overall characteristics of this variability. In order for these models to become useful tools in the design of optimal therapy strategies and ultimately in clinical practice, a subject-specific modelling strategy is necessary, rather than approaches that are based on the average behavior of a given subject population which could provide erroneous results.

ON THE CONTROL OF TUMOR GROWTH VIA TYPE-1 AND INTERVAL TYPE-2 FUZZY LOGIC

This paper deals with growth control of cancer cells population using type-1 and interval type-2 fuzzy logic. A type-1 fuzzy controller is designed in order to reduce the population of cancer cells, adjust the drug dosage in a manner that allows normal cells re-grow in treatment period and maintain the maximum drug delivery rate and plasma concentration of drug in an appropriate range. Two different approaches are studied. One deals with reducing the number of cancer cells without any concern about the rate of decreasing, and the other takes the rate of malignant cells damage into consideration. Due to the fact that uncertainty is an inherent part of real systems and affects controller efficacy, employing new methods of design such as interval type-2 fuzzy logic systems for handling uncertainties may be efficacious. Influence of noise on the system is investigated and the effect of altering free parameters of design is studied. Using an interval type-2 controller can diminish the effects of incomplete and uncertain information about the system, environmental noises, instrumentation errors, etc. Simulation results confirm the effectiveness of the proposed methods on tumor growth control.

Neutrophil dynamics during concurrent chemotherapy and G-CSF administration: Mathematical modelling guides dose optimisation to minimise neutropenia

The choice of chemotherapy regimens is often constrained by the patient's tolerance to the side effects of chemotherapeutic agents. This dose-limiting issue is a major concern in dose regimen design, which is typically focused on maximising drug benefits. Chemotherapy-induced neutropenia is one of the most prevalent toxic effects patients experience and frequently threatens the efficient use of chemotherapy. In response, granulocyte colony-stimulating factor (G-CSF) is co-administered during chemotherapy to stimulate neutrophil production, increase neutrophil counts, and hopefully avoid neutropenia. Its clinical use is, however, largely dictated by trial and error processes. Based on up-to-date knowledge and rational considerations, we develop a physiologically realistic model to mathematically characterise the neutrophil production in the bone marrow which we then integrate with pharmacokinetic and pharmacodynamic (PKPD) models of a chemotherapeutic agent and an exogenous form of G-CSF (recombinant human G-CSF, or rhG-CSF). In this work, model parameters represent the average values for a general patient and are extracted from the literature or estimated from available data. The dose effect predicted by the model is confirmed through previously published data. Using our model, we were able to determine clinically relevant dosing regimens that advantageously reduce the number of rhG-CSF administrations compared to original studies while significantly improving the neutropenia status. More particularly, we determine that it could be beneficial to delay the first administration of rhG-CSF to day seven post-chemotherapy and reduce the number of administrations from ten to three or four for a patient undergoing 14-day periodic chemotherapy.

Mathematical modelling of tumour volume dynamics in response to stereotactic ablative radiotherapy for non-small cell lung cancer

This paper reports a modelling study of tumour volume dynamics in response to stereotactic ablative radiotherapy (SABR). The main objective was to develop a model that is adequate to describe tumour volume change measured during SABR, and at the same time is not excessively complex as lacking support from clinical data. To this end, various modelling options were explored, and a rigorous statistical method, the Akaike information criterion, was used to help determine a trade-off between model accuracy and complexity. The models were calibrated to the data from 11 non-small cell lung cancer patients treated with SABR. The results showed that it is feasible to model the tumour volume dynamics during SABR, opening up the potential for using such models in a clinical environment in the future.

Data-driven modeling of pharmacological systems using endpoint information fusion

This study investigated the feasibility of deriving data-driven model of a class of pharmacological systems using the information fusion of endpoint responses. For a class of pharmacological systems subsuming conventional steady-state dose-response models, compartmental pharmacokinetic-pharmacodynamic models and indirect response models, a relation between multiple endpoint responses was formalized and analyzed to elucidate if this class of systems is identifiable, i.e., if the data-driven model of this class of systems can be derived from the endpoint responses alone. It was shown that this class of systems is fully identifiable in case all the responses involve effect compartments. However, it was also observed that persistently exciting dose profiles may be required in accurately deriving reliable data-driven model with low variance. The findings from the identifiability analysis were demonstrated using benchmark pharmacological system examples.

FINITE DURATION TREATMENT OF CANCER BY USING VACCINE THERAPY AND OPTIMAL CHEMOTHERAPY: STATE-DEPENDENT RICCATI EQUATION CONTROL AND EXTENDED KALMAN FILTER

The main purpose of this paper is to propose an optimal finite duration treatment method for preventing tumor growth. The obtained results show that changing the dynamics of the cancer model is essential for a finite duration treatment. Therefore, vaccine therapy is used for changing the parameters of the system and chemotherapy is applied for pushing the system to the domain of attraction of the healthy state. The state-dependent Riccati equation (SDRE)-based optimal control method is used for optimal chemotherapy. In this method, the special conditions of the patients could be considered by choosing suitable weighting matrices in the cost function and restricting the drug dosage. Also, there are infinite ways to choose these state-dependent matrices. In this paper, these interesting features of this method are used for each patient. Since measuring the states of the system is impossible at each time for states feedback; an extended Kalman filter (EKF) is designed as an observer in the nonlinear system. So, the SDRE method is employed just by measuring the population of normal cells. Numerical simulations show the flexibility and effectiveness of this treatment method.

Mathematical models for absorption and efficacy of ovarian cancer treatments

The creation of personal and individualized anti-cancer treatments has been a major goal in the progression of cancer discovery as evident by the continuous research efforts in genetics and population based PK/PD studies. In this paper we use our clinical decision support tool, called ChemoDSS, to evaluate the effectiveness of three treatments recommended by the NCCN guidelines for ovarian cancer using pre-clinical data from the literature. In particular, we analyze the treatments of PC (i.e., Paclitaxel and Cispaltin), DC (i.e., Docetaxel and Carboplatin), and PBC (i.e., Paclitaxel, Bevacizumab, and Carboplatin). Our in silico analysis of the ovarian cancer treatments shows that PC was the most effective regimen for treating ovarian cancer compared to DC and PBC, which is consistent with literature findings. We demonstrate that we can successfully evaluate the effectiveness of the selected ovarian cancer treatment regimens using ChemoDSS.

Ubiquity: a framework for physiological/mechanism-based pharmacokinetic/pharmacodynamic model development and deployment

Practitioners of pharmacokinetic/pharmacodynamic modeling routinely employ various software packages that enable them to fit differential equation based mechanistic or empirical models to biological/pharmacological data. The availability and choice of different analytical tools, while enabling, can also pose a significant challenge in terms of both, implementation and transferability. A package has been developed that addresses these issues by creating a simple text-based format, which provides methods to reduce coding complexity and enables the modeler to describe the components of the model based on the underlying physiochemical processes. A Perl script builds the system for multiple formats (ADAPT, MATLAB, Berkeley Madonna, etc.), enabling analysis across several software packages and reducing the chance for transcription error. Workflows can then be built around this package, which can increase efficiency and model availability. As a proof of concept, tools are included that allow models constructed in this format to be run with MATLAB both at the scripting level and through a generic graphical application that can be compiled and run as a stand-alone application.

Systems engineering medicine: engineering the inflammation response to infectious and traumatic challenges

The complexity of the systemic inflammatory response and the lack of a treatment breakthrough in the treatment of pathogenic infection demand that advanced tools be brought to bear in the treatment of severe sepsis and trauma. Systems medicine, the translational science counterpart to basic science's systems biology, is the interface at which these tools may be constructed. Rapid initial strides in improving sepsis treatment are possible through the use of phenomenological modelling and optimization tools for process understanding and device design. Higher impact, and more generalizable, treatment designs are based on mechanistic understanding developed through the use of physiologically based models, characterization of population variability, and the use of control-theoretic systems engineering concepts. In this review we introduce acute inflammation and sepsis as an example of just one area that is currently underserved by the systems medicine community, and, therefore, an area in which contributions of all types can be made.