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

DataXflow: Synergizing data-driven modeling with best parameter fit and optimal control - An efficient data analysis for cancer research

Building data-driven models is an effective strategy for information extraction from empirical data. Adapting model parameters specifically to data with a best fitting approach encodes the relevant information into a mathematical model. Subsequently, an optimal control framework extracts the most efficient targets to steer the model into desired changes via external stimuli. The DataXflow software framework integrates three software pipelines, D2D for model fitting, a framework solving optimal control problems including external stimuli and JimenaE providing graphical user interfaces to employ the other frameworks lowering the barriers for the need of programming skills, and simultaneously automating reoccurring modeling tasks. Such tasks include equation generation from a graph and script generation allowing also to approach systems with many agents, like complex gene regulatory networks. A desired state of the model is defined, and therapeutic interventions are modeled as external stimuli. The optimal control framework purposefully exploits the model-encoded information by providing those external stimuli that effect the desired changes most efficiently. The implementation of DataXflow is available under https://github.com/MarvelousHopefull/DataXflow. We showcase its application by detecting specific drug targets for a therapy of lung cancer from measurement data to lower proliferation and increase apoptosis. By an iterative modeling process refining the topology of the model, the regulatory network of the tumor is generated from the data. An application of the optimal control framework in our example reveals the inhibition of AURKA and the activation of CDH1 as the most efficient drug target combination. DataXflow paves the way to an agile interplay between data generation and its analysis potentially accelerating cancer research by an efficient drug target identification, even in complex networks.

Public health implications of computer-aided diagnosis and treatment technologies in breast cancer care

Breast cancer remains a significant public health issue, being a leading cause of cancer-related mortality among women globally. Timely diagnosis and efficient treatment are crucial for enhancing patient outcomes, reducing healthcare burdens and advancing community health. This systematic review, following the PRISMA guidelines, aims to comprehensively synthesize the recent advancements in computer-aided diagnosis and treatment for breast cancer. The study covers the latest developments in image analysis and processing, machine learning and deep learning algorithms, multimodal fusion techniques and radiation therapy planning and simulation. The results of the review suggest that machine learning, augmented and virtual reality and data mining are the three major research hotspots in breast cancer management. Moreover, this paper discusses the challenges and opportunities for future research in this field. The conclusion highlights the importance of computer-aided techniques in the management of breast cancer and summarizes the key findings of the review.

Application of uncertainty quantification to artificial intelligence in healthcare: A review of last decade (2013-2023)

Uncertainty estimation in healthcare involves quantifying and understanding the inherent uncertainty or variability associated with medical predictions, diagnoses, and treatment outcomes. In this era of Artificial Intelligence (AI) models, uncertainty estimation becomes vital to ensure safe decision-making in the medical field. Therefore, this review focuses on the application of uncertainty techniques to machine and deep learning models in healthcare. A systematic literature review was conducted using the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) guidelines. Our analysis revealed that Bayesian methods were the predominant technique for uncertainty quantification in machine learning models, with Fuzzy systems being the second most used approach. Regarding deep learning models, Bayesian methods emerged as the most prevalent approach, finding application in nearly all aspects of medical imaging. Most of the studies reported in this paper focused on medical images, highlighting the prevalent application of uncertainty quantification techniques using deep learning models compared to machine learning models. Interestingly, we observed a scarcity of studies applying uncertainty quantification to physiological signals. Thus, future research on uncertainty quantification should prioritize investigating the application of these techniques to physiological signals. Overall, our review highlights the significance of integrating uncertainty techniques in healthcare applications of machine learning and deep learning models. This can provide valuable insights and practical solutions to manage uncertainty in real-world medical data, ultimately improving the accuracy and reliability of medical diagnoses and treatment recommendations.

Ultrasensitive response explains the benefit of combination chemotherapy despite drug antagonism

Most aggressive lymphomas are treated with combination chemotherapy, commonly as multiple cycles of concurrent drug administration. Concurrent administration is in theory optimal when combination therapies have synergistic (more than additive) drug interactions. We investigated pharmacodynamic interactions in the standard 4-drug 'CHOP' regimen in Peripheral T-Cell Lymphoma (PTCL) cell lines, and found that CHOP consistently exhibits antagonism and not synergy. We tested whether staggered treatment schedules could improve tumor cell kill by avoiding antagonism, using month-long in vitro models of concurrent or staggered treatments. Surprisingly, we observed that tumor cell kill is maximized by concurrent drug administration despite antagonistic drug-drug interactions. We propose that an ultrasensitive dose response, as described in radiology by the linear-quadratic (LQ) model, can reconcile these seemingly contradictory experimental observations. The LQ model describes the relationship between cell survival and dose, and in radiology has identified scenarios favoring hypofractionated radiation - the administration of fewer large doses rather than multiple smaller doses. Specifically, hypofractionated treatment can be favored when cells require an accumulation of DNA damage, rather than a 'single hit', in order to die. By adapting the LQ model to combination chemotherapy and accounting for tumor heterogeneity, we find that tumor cell kill is maximized by concurrent administration of multiple drugs, even when chemotherapies have antagonistic interactions. Thus, our study identifies a new mechanism by which combination chemotherapy can be clinically beneficial that is not reliant on positive drug-drug interactions.

Quantification of long-term doxorubicin response dynamics in breast cancer cell lines to direct treatment schedules

While acquired chemoresistance is recognized as a key challenge to treating many types of cancer, the dynamics with which drug sensitivity changes after exposure are poorly characterized. Most chemotherapeutic regimens call for repeated dosing at regular intervals, and if drug sensitivity changes on a similar time scale then the treatment interval could be optimized to improve treatment performance. Theoretical work suggests that such optimal schedules exist, but experimental confirmation has been obstructed by the difficulty of deconvolving the simultaneous processes of death, adaptation, and regrowth taking place in cancer cell populations. Here we present a method of optimizing drug schedules in vitro through iterative application of experimentally calibrated models, and demonstrate its ability to characterize dynamic changes in sensitivity to the chemotherapeutic doxorubicin in three breast cancer cell lines subjected to treatment schedules varying in concentration, interval between pulse treatments, and number of sequential pulse treatments. Cell populations are monitored longitudinally through automated imaging for 600–800 hours, and this data is used to calibrate a family of cancer growth models, each consisting of a system of ordinary differential equations, derived from the bi-exponential model which characterizes resistant and sensitive subpopulations. We identify a model incorporating both a period of growth arrest in surviving cells and a delay in the death of chemosensitive cells which outperforms the original bi-exponential growth model in Akaike Information Criterion based model selection, and use the calibrated model to quantify the performance of each drug schedule. We find that the inter-treatment interval is a key variable in determining the performance of sequential dosing schedules and identify an optimal retreatment time for each cell line which extends regrowth time by 40%-239%, demonstrating that the time scale of changes in chemosensitivity following doxorubicin exposure allows optimization of drug scheduling by varying this inter-treatment interval.

Acquired chemoresistance is a common cause of treatment failure in cancer. The scheduling of a multi-dose course of chemotherapeutic treatment may influence the dynamics of acquired chemoresistance, and drug schedule optimization may increase the duration of effectiveness of a particular chemotherapeutic agent for a particular patient. Here we present a method for experimentally optimizing an in vitro drug schedule through iterative rounds of experimentation and computational analysis, and demonstrate the method’s ability to improve the performance of doxorubicin treatment in three breast carcinoma cell lines. Specifically, we find that the interval between drug exposures can be optimized while holding drug concentration and number of treatments constant, suggesting that this may be a key variable to explore in future drug schedule optimization efforts. We further use this method’s model calibration and selection process to extract information about the underlying biology of the doxorubicin response, and find that the incorporation of delays on both cell death and regrowth are necessary for accurate parameterization of cell growth data.

Polymer-Based Nanosystems-A Versatile Delivery Approach

Polymer-based nanoparticles of tailored size, morphology, and surface properties have attracted increasing attention as carriers for drugs, biomolecules, and genes. By protecting the payload from degradation and maintaining sustained and controlled release of the drug, polymeric nanoparticles can reduce drug clearance, increase their cargo's stability and solubility, prolong its half-life, and ensure optimal concentration at the target site. The inherent immunomodulatory properties of specific polymer nanoparticles, coupled with their drug encapsulation ability, have raised particular interest in vaccine delivery. This paper aims to review current and emerging drug delivery applications of both branched and linear, natural, and synthetic polymer nanostructures, focusing on their role in vaccine development.

Chemotherapeutic drugs: Cell death- and resistance-related signaling pathways. Are they really as smart as the tumor cells?

Chemotherapeutic drugs kill cancer cells or control their progression all over the patient's body, while radiation- and surgery-based treatments perform in a particular site. Based on their mechanisms of action, they are classified into different groups, including alkylating substrates, antimetabolite agents, anti-tumor antibiotics, inhibitors of topoisomerase I and II, mitotic inhibitors, and finally, corticosteroids. Although chemotherapeutic drugs have brought about more life expectancy, two major and severe complications during chemotherapy are chemoresistance and tumor relapse. Therefore, we aimed to review the underlying intracellular signaling pathways involved in cell death and resistance in different chemotherapeutic drug families to clarify the shortcomings in the conventional single chemotherapy applications. Moreover, we have summarized the current combination chemotherapy applications, including numerous combined-, and encapsulated-combined-chemotherapeutic drugs. We further discussed the possibilities and applications of precision medicine, machine learning, next-generation sequencing (NGS), and whole-exome sequencing (WES) in promoting cancer immunotherapies. Finally, some of the recent clinical trials concerning the application of immunotherapies and combination chemotherapies were included as well, in order to provide a practical perspective toward the future of therapies in cancer cases.

Handling of uncertainty in medical data using machine learning and probability theory techniques: a review of 30 years (1991-2020)

Understanding the data and reaching accurate conclusions are of paramount importance in the present era of big data. Machine learning and probability theory methods have been widely used for this purpose in various fields. One critically important yet less explored aspect is capturing and analyzing uncertainties in the data and model. Proper quantification of uncertainty helps to provide valuable information to obtain accurate diagnosis. This paper reviewed related studies conducted in the last 30 years (from 1991 to 2020) in handling uncertainties in medical data using probability theory and machine learning techniques. Medical data is more prone to uncertainty due to the presence of noise in the data. So, it is very important to have clean medical data without any noise to get accurate diagnosis. The sources of noise in the medical data need to be known to address this issue. Based on the medical data obtained by the physician, diagnosis of disease, and treatment plan are prescribed. Hence, the uncertainty is growing in healthcare and there is limited knowledge to address these problems. Our findings indicate that there are few challenges to be addressed in handling the uncertainty in medical raw data and new models. In this work, we have summarized various methods employed to overcome this problem. Nowadays, various novel deep learning techniques have been proposed to deal with such uncertainties and improve the performance in decision making.

Computational medicine, present and the future: obstetrics and gynecology perspective

Medicine is, in its essence, decision making under uncertainty; the decisions are made about tests to be performed and treatments to be administered. Traditionally, the uncertainty in decision making was handled using expertise collected by individual providers and, more recently, systematic appraisal of research in the form of evidence-based medicine. The traditional approach has been used successfully in medicine for a very long time. However, it has substantial limitations because of the complexity of the system of the human body and healthcare. The complex systems are a network of highly coupled components intensely interacting with each other. These interactions give those systems redundancy and thus robustness to failure and, at the same time, equifinality, that is, many different causative pathways leading to the same outcome. The equifinality of the complex systems of the human body and healthcare system demand the individualization of medical care, medicine, and medical decision making. Computational models excel in modeling complex systems and, consequently, enabling individualization of medical decision making and medicine. Computational models are theory- or knowledge-based models, data-driven models, or models that combine both approaches. Data are essential, although to a different degree, for computational models to successfully represent complex systems. The individualized decision making, made possible by the computational modeling of complex systems, has the potential to revolutionize the entire spectrum of medicine from individual patient care to policymaking. This approach allows applying tests and treatments to individuals who receive a net benefit from them, for whom benefits outweigh the risk, rather than treating all individuals in a population because, on average, the population benefits. Thus, the computational modeling-enabled individualization of medical decision making has the potential to both improve health outcomes and decrease the costs of healthcare.

Integrating transcriptomics and bulk time course data into a mathematical framework to describe and predict therapeutic resistance in cancer

A significant challenge in the field of biomedicine is the development of methods to integrate the multitude of dispersed data sets into comprehensive frameworks to be used to generate optimal clinical decisions. Recent technological advances in single cell analysis allow for high-dimensional molecular characterization of cells and populations, but to date, few mathematical models have attempted to integrate measurements from the single cell scale with other types of longitudinal data. Here, we present a framework that actionizes static outputs from a machine learning model and leverages these as measurements of state variables in a dynamic model of treatment response. We apply this framework to breast cancer cells to integrate single cell transcriptomic data with longitudinal bulk cell population (bulk time course) data. We demonstrate that the explicit inclusion of the phenotypic composition estimate, derived from single cell RNA-sequencing data (scRNA-seq), improves accuracy in the prediction of new treatments with a concordance correlation coefficient (CCC) of 0.92 compared to a prediction accuracy of CCC = 0.64 when fitting on longitudinal bulk cell population data alone. To our knowledge, this is the first work that explicitly integrates single cell clonally-resolved transcriptome datasets with bulk time-course data to jointly calibrate a mathematical model of drug resistance dynamics. We anticipate this approach to be a first step that demonstrates the feasibility of incorporating multiple data types into mathematical models to develop optimized treatment regimens from data.

The efficacy of chemotherapeutic drug combinations may be predicted by concordance of gene response to the single agents

Determining the expression of genes in response to different classes of chemotherapeutic drugs may allow for a better understanding as to which may be used effectively in combination. In the present study, the human colorectal cancer cell line HCT116 was cultured with equi-active concentrations of a series of anti-cancer agents. Gene expression profiles were then measured by whole-genome microarray. Although each drug induced a unique signature of gene expression in tumour cells, there were marked similarities between certain drugs, even in those from different classes. For example, the antimalarial agent artesunate and the platinum-containing alkylating agent, oxaliplatin, produced a very similar mRNA expression pattern in HCT116 cells with ~14,000 genes being affected by the two drugs in the same way. Furthermore, the overall correlation of gene responses between two agents could predict whether their use in combination would lead to a greater or lesser effect on cell number, determined experimentally, than predicted by single agent experiments. The results indicated that even when working through different mechanisms, combining drugs that initiate a similar transcriptional response may constitute the best option for determining drug-combination strategies for the treatment of cancer.

Predicting likelihood of in vivo chemotherapy response in canine lymphoma using ex vivo drug sensitivity and immunophenotyping data in a machine learning model

We report a precision medicine platform that evaluates the probability of chemotherapy drug efficacy for canine lymphoma by combining ex vivo chemosensitivity and immunophenotyping assays with computational modelling. We isolated live cancer cells from fresh fine needle aspirates of affected lymph nodes and collected post‐treatment clinical responses in 261 canine lymphoma patients scheduled to receive at least 1 of 5 common chemotherapy agents (doxorubicin, vincristine, cyclophosphamide, lomustine and rabacfosadine). We used flow cytometry analysis for immunophenotyping and ex vivo chemosensitivity testing. For each drug, 70% of treated patients were randomly selected to train a random forest model to predict the probability of positive Veterinary Cooperative Oncology Group (VCOG) clinical response based on input variables including antigen expression profiles and treatment sensitivity readouts for each patient's cancer cells. The remaining 30% of patients were used to test model performance. Most models showed a test set ROC‐AUC > 0.65, and all models had overall ROC‐AUC > 0.95. Predicted response scores significantly distinguished (P < .001) positive responses from negative responses in B‐cell and T‐cell disease and newly diagnosed and relapsed patients. Patient groups with predicted response scores >50% showed a statistically significant reduction (log‐rank P < .05) in time to complete response when compared to the groups with scores <50%. The computational models developed in this study enabled the conversion of ex vivo cell‐based chemosensitivity assay results into a predicted probability of in vivo therapeutic efficacy, which may help improve treatment outcomes of individual canine lymphoma patients by providing predictive estimates of positive treatment response.

Understanding the effect of measurement time on drug characterization

In order to determine correct dosage of chemotherapy drugs, the effect of the drug must be properly quantified. There are two important values that characterize the effect of the drug: εmax is the maximum possible effect of a drug, and IC50 is the drug concentration where the effect diminishes by half. There is currently a problem with the way these values are measured because they are time-dependent measurements. We use mathematical models to determine how the εmax and IC50 values depend on measurement time and model choice. Seven ordinary differential equation models (ODE) are used for the mathematical analysis; the exponential, Mendelsohn, logistic, linear, surface, Bertalanffy, and Gompertz models. We use the models to simulate tumor growth in the presence and absence of treatment with a known IC50 and εmax. Using traditional methods, we then calculate the IC50 and εmax values over fifty days to show the time-dependence of these values for all seven mathematical models. The general trend found is that the measured IC50 value decreases and the measured εmax increases with increasing measurement day for most mathematical models. Unfortunately, the measured values of IC50 and εmax rarely matched the values used to generate the data. Our results show that there is no optimal measurement time since models predict that IC50 estimates become more accurate at later measurement times while εmax is more accurate at early measurement times.

How and why to build a mathematical model: A case study using prion aggregation

Biological systems are inherently complex, and the increasing level of detail with which we are able to experimentally probe such systems continually reveals new complexity. Fortunately, mathematical models are uniquely positioned to provide a tool suitable for rigorous analysis, hypothesis generation, and connecting results from isolated in vitro experiments with results from in vivo and whole-organism studies. However, developing useful mathematical models is challenging because of the often different domains of knowledge required in both math and biology. In this work, we endeavor to provide a useful guide for researchers interested in incorporating mathematical modeling into their scientific process. We advocate for the use of conceptual diagrams as a starting place to anchor researchers from both domains. These diagrams are useful for simplifying the biological process in question and distinguishing the essential components. Not only do they serve as the basis for developing a variety of mathematical models, but they ensure that any mathematical formulation of the biological system is led primarily by scientific questions. We provide a specific example of this process from our own work in studying prion aggregation to show the power of mathematical models to synergistically interact with experiments and push forward biological understanding. Choosing the most suitable model also depends on many different factors, and we consider how to make these choices based on different scales of biological organization and available data. We close by discussing the many opportunities that abound for both experimentalists and modelers to take advantage of collaborative work in this field.

Experimentally-driven mathematical modeling to improve combination targeted and cytotoxic therapy for HER2+ breast cancer

The goal of this study is to experimentally and computationally investigate combination trastuzumab-paclitaxel therapies and identify potential synergistic effects due to sequencing of the therapies with in vitro imaging and mathematical modeling. Longitudinal alterations in cell confluence are reported for an in vitro model of BT474 HER2+ breast cancer cells following various dosages and timings of paclitaxel and trastuzumab combination regimens. Results of combination drug regimens are evaluated for drug interaction relationships based on order, timing, and quantity of dose of the drugs. Altering the order of treatments, with the same total therapeutic dose, provided significant changes in overall cell confluence (p < 0.001). Two mathematical models are introduced that are constrained by the in vitro data to simulate the tumor cell response to the individual therapies. A collective model merging the two individual drug response models was designed to investigate the potential mechanisms of synergy for paclitaxel-trastuzumab combinations. This collective model shows increased synergy for regimens where trastuzumab is administered prior to paclitaxel and suggests trastuzumab accelerates the cytotoxic effects of paclitaxel. The synergy derived from the model is found to be in agreement with the combination index, where both indicate a spectrum of additive and synergistic interactions between the two drugs dependent on their dose order. The combined in vitro results and development of a mathematical model of drug synergy has potential to evaluate and improve standard-of-care combination therapies in cancer.

Cancer cell population growth kinetics at low densities deviate from the exponential growth model and suggest an Allee effect

Most models of cancer cell population expansion assume exponential growth kinetics at low cell densities, with deviations to account for observed slowing of growth rate only at higher densities due to limited resources such as space and nutrients. However, recent preclinical and clinical observations of tumor initiation or recurrence indicate the presence of tumor growth kinetics in which growth rates scale positively with cell numbers. These observations are analogous to the cooperative behavior of species in an ecosystem described by the ecological principle of the Allee effect. In preclinical and clinical models, however, tumor growth data are limited by the lower limit of detection (i.e., a measurable lesion) and confounding variables, such as tumor microenvironment, and immune responses may cause and mask deviations from exponential growth models. In this work, we present alternative growth models to investigate the presence of an Allee effect in cancer cells seeded at low cell densities in a controlled in vitro setting. We propose a stochastic modeling framework to disentangle expected deviations due to small population size stochastic effects from cooperative growth and use the moment approach for stochastic parameter estimation to calibrate the observed growth trajectories. We validate the framework on simulated data and apply this approach to longitudinal cell proliferation data of BT-474 luminal B breast cancer cells. We find that cell population growth kinetics are best described by a model structure that considers the Allee effect, in that the birth rate of tumor cells increases with cell number in the regime of small population size. This indicates a potentially critical role of cooperative behavior among tumor cells at low cell densities with relevance to early stage growth patterns of emerging and relapsed tumors.

This study applied principles that describe the growth dynamics of species within an ecosystem in a novel attempt to understand the growth of tumors. At low cell densities, cooperative interactions among cancer cells may influence growth in a manner reminiscent of the ecological “Allee effect,” in contrast to conventional logistic growth models.

Upregulated Circular RNA circ-UBE2D2 Predicts Poor Prognosis and Promotes Breast Cancer Progression by Sponging miR-1236 and miR-1287

Emerging evidence suggests that circular RNAs (circRNAs) are linked to the development and progression of human cancers. Nevertheless, their contribution to breast cancer (BC) is still largely unknown. In the current study, we screened and identified a novel circRNA, circ-UBE2D2, which was highly expressed in BC cell lines and tissues and was closely related to aggressive clinical features and dismal prognosis. Small interfering RNA (siRNA)–mediated circ-UBE2D2 silencing notably inhibited the proliferation, migration and invasion of BC cells, whereas circ-UBE2D2 overexpression displayed opposite effects. Mechanistically, circ-UBE2D2 was able to simultaneously function as molecular sponges of miR-1236 and miR-1287 to regulate the expression of their respective target genes. Moreover, circ-UBE2D2–induced tumor-promoting effects could be effectively blocked by miR-1236 or miR-1287 in BC cells. More importantly, therapeutic delivery of cholesterol-conjugated si-circ-UBE2D2 oligonucleotides significantly delayed tumor growth in vivo. Overall, our findings indicate that circ-UBE2D2 plays an essential oncogenic role in BC, and targeting circ-UBE2D2 may be a feasible treatment for BC patients.

Leveraging Mathematical Modeling to Quantify Pharmacokinetic and Pharmacodynamic Pathways: Equivalent Dose Metric

Treatment response assays are often summarized by sigmoidal functions comparing cell survival at a single timepoint to applied drug concentration. This approach has a limited biophysical basis, thereby reducing the biological insight gained from such analysis. In particular, drug pharmacokinetic and pharmacodynamic (PK/PD) properties are overlooked in developing treatment response assays, and the accompanying summary statistics conflate these processes. Here, we utilize mathematical modeling to decouple and quantify PK/PD pathways. We experimentally modulate specific pathways with small molecule inhibitors and filter the results with mechanistic mathematical models to obtain quantitative measures of those pathways. Specifically, we investigate the response of cells to time-varying doxorubicin treatments, modulating doxorubicin pharmacology with small molecules that inhibit doxorubicin efflux from cells and DNA repair pathways. We highlight the practical utility of this approach through proposal of the “equivalent dose metric.” This metric, derived from a mechanistic PK/PD model, provides a biophysically-based measure of drug effect. We define equivalent dose as the functional concentration of drug that is bound to the nucleus following therapy. This metric can be used to quantify drivers of treatment response and potentially guide dosing of combination therapies. We leverage the equivalent dose metric to quantify the specific intracellular effects of these small molecule inhibitors using population-scale measurements, and to compare treatment response in cell lines differing in expression of drug efflux pumps. More generally, this approach can be leveraged to quantify the effects of various pharmaceutical and biologic perturbations on treatment response.

SS, Paggi M, Bordas SP. Advances in Carbon Based Nanomaterials for Bio-Medical Applications

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The unique mechanical, electrical, thermal, chemical and optical properties of carbon based nanomaterials (CBNs) like: Fullerenes, Graphene, Carbon nanotubes, and their derivatives made them widely used materials for various applications including biomedicine. Few recent applications of the CBNs in biomedicine include: cancer therapy, targeted drug delivery, bio-sensing, cell and tissue imaging and regenerative medicine. However, functionalization renders the toxicity of CBNs and makes them soluble in several solvents including water, which is required for biomedical applications. Hence, this review represents the complete study of development in nanomaterials of carbon for biomedical uses. Especially, CBNs as the vehicles for delivering the drug in carbon nanomaterials is described in particular. The computational modeling approaches of various CBNs are also addressed. Furthermore, prospectus, issues and possible challenges of this rapidly developing field are highlighted.

A multi-state model of chemoresistance to characterize phenotypic dynamics in breast cancer

The development of resistance to chemotherapy is a major cause of treatment failure in breast cancer. While mathematical models describing the dynamics of resistant cancer cell subpopulations have been proposed, experimental validation has been difficult due to the complex nature of resistance that limits the ability of a single phenotypic marker to sufficiently identify the drug resistant subpopulations. We address this problem with a coupled experimental/modeling approach to reveal the composition of drug resistant subpopulations changing in time following drug exposure. We calibrate time-resolved drug sensitivity assays to three mathematical models to interrogate the models' ability to capture drug response dynamics. The Akaike information criterion was employed to evaluate the three models, and it identified a multi-state model incorporating the role of population heterogeneity and cellular plasticity as the optimal model. To validate the model's ability to identify subpopulation composition, we mixed different proportions of wild-type MCF-7 and MCF-7/ADR resistant cells and evaluated the corresponding model output. Our blinded two-state model was able to estimate the proportions of cell types with an R-squared value of 0.857. To the best of our knowledge, this is the first work to combine experimental time-resolved drug sensitivity data with a mathematical model of resistance development.