Multiscale modeling of the dynamic growth of cancerous tumors under the influence of chemotherapy drugs

A comprehensive model of chemotherapy treatment of cancer can help us to optimize the drug administration/dosage and improve the treatment outcome. In the present study, a multiscale mathematical model of tumor growth during chemotherapy treatment is developed to predict its response to the medication and cancer progression. The modeling is a continuous multiscale simulation consisting of three tissue phases including cancer cells, normal cells, and extracellular matrix. In addition to the drug administration, the impacts of immune cells, programmed cell death, nutrient competition, and glucose concentration are included. The outputs of our mathematical model conform to the published experimental and clinical data, and it can be used in optimizing chemotherapy, and personalized cancer treatment.

On minimising tumoural growth under treatment resistance

Drug resistance is a major challenge for curative cancer treatment, representing the main reason of death in patients. Evolutionary biology suggests pauses between treatment rounds as a way to delay or even avoid resistance emergence. Indeed, this approach has already shown promising preclinical and early clinical results, and stimulated the development of mathematical models for finding optimal treatment protocols. Due to their complexity, however, these models do not lend themself to a rigorous mathematical analysis, hence so far clinical recommendations generally relied on numerical simulations and ad-hoc heuristics. Here, we derive two mathematical models describing tumour growth under genetic and epigenetic treatment resistance, respectively, which are simple enough for a complete analytical investigation. First, we find key differences in response to treatment protocols between the two modes of resistance. Second, we identify the optimal treatment protocol which leads to the largest possible tumour shrinkage rate. Third, we fit the "epigenetic model" to previously published xenograft experiment data, finding excellent agreement, underscoring the biological validity of our approach. Finally, we use the fitted model to calculate the optimal treatment protocol for this specific experiment, which we demonstrate to cause curative treatment, making it superior to previous approaches which generally aimed at stabilising tumour burden. Overall, our approach underscores the usefulness of simple mathematical models and their analytical examination, and we anticipate our findings to guide future preclinical and, ultimately, clinical research in optimising treatment regimes.

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.

A calibration and uncertainty quantification analysis of classical, fractional and multiscale logistic models of tumour growth

BACKGROUND AND OBJECTIVE

The validation of mathematical models of tumour growth is frequently hampered by the lack of sufficient experimental data, resulting in qualitative rather than quantitative studies. Recent approaches to this problem have attempted to extract information about tumour growth by integrating multiscale experimental measurements, such as longitudinal cell counts and gene expression data. In the present study, we investigated the performance of several mathematical models of tumour growth, including classical logistic, fractional and novel multiscale models, in terms of quantifying in-vitro tumour growth in the presence and absence of therapy. We further examined the effect of genes associated with changes in chemosensitivity in cell death rates.

METHODS

The multiscale expansion of logistic growth models was performed by coupling gene expression profiles to the cell death rates. State-of-the-art Bayesian inference, likelihood maximisation and uncertainty quantification techniques allowed a thorough evaluation of model performance.

RESULTS

The results suggest that the classical single-cell population model (SCPM) was the best fit for the untreated and low-dose treatment conditions, while the multiscale model with a cell death rate symmetric with the expression profile of OCT4 (Sym-SCPM) yielded the best fit for the high-dose treatment data. Further identifiability analysis showed that the multiscale model was both structurally and practically identifiable under the condition of known OCT4 expression profiles.

CONCLUSIONS

Overall, the present study demonstrates that model performance can be improved by incorporating multiscale measurements of tumour growth when high-dose treatment is involved.

Reinforcement learning strategies in cancer chemotherapy treatments: A review

BACKGROUND AND OBJECTIVE

Cancer is one of the major causes of death worldwide and chemotherapies are the most significant anti-cancer therapy, in spite of the emerging precision cancer medicines in the last 2 decades. The growing interest in developing the effective chemotherapy regimen with optimal drug dosing schedule to benefit the clinical cancer patients has spawned innovative solutions involving mathematical modeling since the chemotherapy regimens are administered cyclically until the futility or the occurrence of intolerable adverse events. Thus, in this present work, we reviewed the emerging trends involved in forming a computational solution from the aspect of reinforcement learning.

METHODS

Initially, this survey in-depth focused on the details of the dynamic treatment regimens from a broad perspective and then narrowed down to inspirations from reinforcement learning that were advantageous to chemotherapy dosing, including both offline reinforcement learning and supervised reinforcement learning.

RESULTS

The insights established in the chemotherapy-planning problem associated with the Reinforcement Learning (RL) has been discussed in this study. It showed that the researchers were able to widen their perspectives in comprehending the theoretical basis, dynamic treatment regimens (DTR), use of the adaptive control on DTR, and the associated RL techniques.

CONCLUSIONS

This study reviewed the recent researches relevant to the topic, and highlighted the challenges, open questions, possible solutions, and future steps in inventing a realistic solution for the aforementioned problem.

A Model-Based Framework to Identify Optimal Administration Protocols for Immunotherapies in Castration-Resistance Prostate Cancer

Prostate cancer (PCa) is one of the most frequent cancer in male population. Androgen deprivation therapy is the first-line strategy for the metastatic stage of the disease, but, inevitably, PCa develops resistance to castration (CRPC), becoming incurable. In recent years, clinical trials are testing the efficacy of anti-CTLA4 on CRPC. However, this tumor seems to be resistant to immunotherapies that are very effective in other types of cancers, and, so far, only the dendritic cell vaccine sipuleucel-T has been approved. In this work, we employ a mathematical model of CRPC to determine the optimal administration protocol of ipilimumab, a particular anti-CTLA4, as single treatment or in combination with the sipuleucel-T, by considering both the effect on tumor population and the drug toxicity. To this end, we first introduce a dose-depending function of toxicity, estimated from experimental data, then we define two different optimization problems. We show the results obtained by imposing different constraints, and how these change by varying drug efficacy. Our results suggest administration of high-doses for a brief period, which is predicted to be more efficient than solutions with prolonged low-doses. The model also highlights a synergy between ipilimumab and sipuleucel-T, which leads to a better tumor control with lower doses of ipilimumab. Finally, tumor eradication is also conceivable, but it depends on patient-specific parameters.

Mathematical Approach to Differentiate Spontaneous and Induced Evolution to Drug Resistance During Cancer Treatment

Purpose

Drug resistance is a major impediment to the success of cancer treatment. Resistance is typically thought to arise from random genetic mutations, after which mutated cells expand via Darwinian selection. However, recent experimental evidence suggests that progression to drug resistance need not occur randomly, but instead may be induced by the treatment itself via either genetic changes or epigenetic alterations. This relatively novel notion of resistance complicates the already challenging task of designing effective treatment protocols.

Materials and Methods

To better understand resistance, we have developed a mathematical modeling framework that incorporates both spontaneous and drug-induced resistance.

Results

Our model demonstrates that the ability of a drug to induce resistance can result in qualitatively different responses to the same drug dose and delivery schedule. We have also proven that the induction parameter in our model is theoretically identifiable and propose an in vitro protocol that could be used to determine a treatment’s propensity to induce resistance.

TNF-α inhibitor reduces drug-resistance to anti-PD-1: A mathematical model

Drug resistance is a primary obstacle in cancer treatment. In many patients who at first respond well to treatment, relapse occurs later on. Various mechanisms have been explored to explain drug resistance in specific cancers and for specific drugs. In this paper, we consider resistance to anti-PD-1, a drug that enhances the activity of anti-cancer T cells. Based on results in experimental melanoma, it is shown, by a mathematical model, that resistances to anti-PD-1 can be significantly reduced by combining it with anti-TNF-α. The model is used to simulate the efficacy of the combined therapy with different range of doses, different initial tumor volume, and different schedules. In particular, it is shown that under a course of treatment with 3-week cycles where each drug is injected in the first day of either week 1 or week 2, injecting anti-TNF-α one week after anti-PD-1 is the most effective schedule in reducing tumor volume.

Individualized growth prediction of mice skin tumors with maximum likelihood estimators

BACKGROUND & OBJECTIVE

In this work, we focus on estimating the parameters of the Gompertz model in order to predict tumor growth. The estimation is based on measurements from mice skin tumors of de novo carcinogenesis. The main objective is to compare the Maximum Likelihood estimator with the best performance from our previous work with the Non-linear Least Squares estimator which is commonly used in the literature to estimate the growth parameters of the Gompertz model.

METHODS

To describe tumor growth, we propose a stochastic model which is based on the Gompertz growth function. The principle of Maximum Likelihood is used to estimate both the growth rate and the carrying capacity of the Gompertz function, along with the characteristics of the additive Gaussian process and measurement noise. Moreover, we examine whether a Maximum A Posteriori estimator is able to utilize any available prior knowledge in order to improve the predictions.

RESULTS

Experimental data from a total of 24 tumors in 8 mice (3 tumors each) were used to study the performance of the proposed methods with respect to prediction accuracy. Our results show that the Maximum Likelihood estimator is able to provide, in most cases, more accurate predictions. Moreover, the Maximum A Posteriori estimator has the potential to correct potentially non-realistic estimates for the carrying capacity at early growth stages.

CONCLUSION

In most cases, the Maximum Likelihood estimator is able to provide more reliable predictions for the tumor's growth on individual test subjects. The Maximum A Posteriori estimator, it has the potential to improve the prediction when the available experimental data do not provide adequate information by utilizing prior knowledge about the unknown parameters.

Investigation of solid tumor progression with account of proliferation/migration dichotomy via Darwinian mathematical model

A new continuous spatially-distributed model of solid tumor growth and progression is presented. The model explicitly accounts for mutations/epimutations of tumor cells which take place upon their division. The tumor grows in normal tissue and its progression is driven only by competition between populations of malignant cells for limited nutrient supply. Two reasons for the motion of tumor cells in space are taken into consideration, i.e., their intrinsic motility and convective fluxes, which arise due to proliferation of tumor cells. The model is applied to investigation of solid tumor progression under phenotypic alterations that inversely affect cell proliferation rate and cell motility by increasing the value of one of the parameters at the expense of another.It is demonstrated that the crucial feature that gives evolutionary advantage to a cell population is the speed of its intergrowth into surrounding normal tissue. Of note, increase in tumor intergrowth speed in not always associated with increase in motility of tumor cells. Depending on the parameters of functions, that describe phenotypic alterations, tumor cellular composition may evolve towards: (1) maximization of cell proliferation rate, (2) maximization of cell motility, (3) non-extremum values of cell proliferation rate and motility. Scenarios are found, where after initial tendency for maximization of cell proliferation rate, the direction of tumor progression sharply switches to maximization of cell motility, which is accompanied by decrease in total speed of tumor growth.

Modeling three-dimensional invasive solid tumor growth in heterogeneous microenvironment under chemotherapy

A systematic understanding of the evolution and growth dynamics of invasive solid tumors in response to different chemotherapy strategies is crucial for the development of individually optimized oncotherapy. Here, we develop a hybrid three-dimensional (3D) computational model that integrates pharmacokinetic model, continuum diffusion-reaction model and discrete cell automaton model to investigate 3D invasive solid tumor growth in heterogeneous microenvironment under chemotherapy. Specifically, we consider the effects of heterogeneous environment on drug diffusion, tumor growth, invasion and the drug-tumor interaction on individual cell level. We employ the hybrid model to investigate the evolution and growth dynamics of avascular invasive solid tumors under different chemotherapy strategies. Our simulations indicate that constant dosing is generally more effective in suppressing primary tumor growth than periodic dosing, due to the resulting continuous high drug concentration. In highly heterogeneous microenvironment, the malignancy of the tumor is significantly enhanced, leading to inefficiency of chemotherapies. The effects of geometrically-confined microenvironment and non-uniform drug dosing are also investigated. Our computational model, when supplemented with sufficient clinical data, could eventually lead to the development of efficient in silico tools for prognosis and treatment strategy optimization.

Tumor growth modeling: Parameter estimation with Maximum Likelihood methods

BACKGROUND & OBJECTIVE

In this work, we focus on estimating the parameters of the widely used Gompertz tumor growth model, based on measurements of the tumor's volume. Being able to accurately describe the dynamics of tumor growth on an individual basis is very important both for growth prediction and designing personalized, optimal therapy schemes (e.g. when using model predictive control).

METHODS

Our analysis aims to compute both the growth rate and the carrying capacity of the Gompertz function, along with the characteristics of the additive Gaussian process and measurement noise of the system. Three methods based on Maximum Likelihood estimation are proposed. The first utilizes an assumption regarding the measurement noise that simplifies the problem, the second combines the Extended Kalman Filter and Maximum Likelihood estimation, and the third is a nonstandard exact form of Maximum Likelihood estimation, where numerical integration is used to approximate the likelihood of the measurements, along with a novel way to reduce the required computations.

RESULTS

Synthetic data were used in order to perform extensive simulations aiming to compare the methods' effectiveness, with respect to the accuracy of the estimation. The proposed methods are able to estimate the growth dynamics, even when the noise characteristics are not estimated accurately. Another very important finding is that the methods perform best in the case that corresponds to the problem needed to be solved when dealing with experimental data.

CONCLUSION

Using nonstandard, problem specific techniques can improve the estimation accuracy and best exploit the available data.

Pharmacokinetic/pharmacodynamic modeling of combination-chemotherapy for lung cancer

Chemotherapy for non-small cell lung cancer (NSCLC) typically involves a doublet regimen for a number of cycles. For any particular patient, a course of treatment is usually chosen from a large number of combinational protocols with drugs in concomitant or sequential administration. In spite of newer drugs and protocols, half of patients with early disease will live less than five years and 95% of those with advanced disease survive for less than one year. Here, we apply mathematical modeling to simulate tumor response to multiple drug regimens, with the capability to assess maximum tolerated dose (MTD) as well as metronomic drug administration. We couple pharmacokinetic-pharmacodynamic intracellular multi-compartment models with a model of vascularized tumor growth, setting input parameters from in vitro data, and using the models to project potential response in vivo. This represents an initial step towards the development of a comprehensive virtual system to evaluate tumor response to combinatorial drug regimens, with the goal to more efficiently identify optimal course of treatment with patient tumor-specific data. We evaluate cisplatin and gemcitabine with clinically-relevant dosages, and simulate four treatment NSCLC scenarios combining MTD and metronomic therapy. This work thus establishes a framework for systematic evaluation of tumor response to combination chemotherapy. The results with the chosen parameter set indicate that although a metronomic regimen may provide advantage over MTD, the combination of these regimens may not necessarily offer improved response. Future model evaluation of chemotherapy possibilities may help to assess their potential value to obtain sustained NSCLC regression for particular patients, with the ultimate goal of optimizing multiple-drug chemotherapy regimens in clinical practice.

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.

PKPD modeling of acquired resistance to anti-cancer drug treatment

Non-small cell lung cancer (NSCLC) patients greatly benefit from the treatment with tyrosine kinase inhibitors (TKIs) targeting the epidermal growth factor receptor (EGFR). However, emergence of acquired resistance inevitable occurs after long-term treatment in most patients and limits clinical improvement. In the present study, resistance to drug treatment in patient-derived NSCLC xenograft mice was assessed and modeling and simulation was applied to understand the dynamics of drug resistance as a basis to explore more beneficial drug regimen. Two semi-mechanistic models were fitted to tumor growth inhibition profiles during and after treatment with erlotinib or gefitinib. The base model proposes that as a result of drug treatment, tumor cells stop proliferating and undergo several stages of damage before they eventually die. The acquired resistance model adds a resistance term to the base model which assumes that resistant cells are emerging from the pool of damaged tumor cells. As a result, tumor cells sensitive to drug treatment will either die or be converted to a drug resistant cell population which is proliferating at a slower growth rate as compared to the sensitive cells. The observed tumor growth profiles were better described by the resistance model and emergence of resistance was concluded. In simulation studies, the selection of resistant cells was explored as well as the time-variant fraction of resistant over sensitive cells. The proposed model provides insight into the dynamic processes of emerging resistance. It predicts tumor regrowth during treatment driven by the selection of resistant cells and explains why faster tumor regrowth may occur after discontinuation of TKI treatment. Finally, it is shown how the semi-mechanistic model can be used to explore different scenarios and to identify optimal treatment schedules in clinical trials.

Limiting the development of anti-cancer drug resistance in a spatial model of micrometastases

While chemoresistance in primary tumors is well-studied, much less is known about the influence of systemic chemotherapy on the development of drug resistance at metastatic sites. In this work, we use a hybrid spatial model of tumor response to a DNA damaging drug to study how the development of chemoresistance in micrometastases depends on the drug dosing schedule. We separately consider cell populations that harbor pre-existing resistance to the drug, and those that acquire resistance during the course of treatment. For each of these independent scenarios, we consider one hypothetical cell line that is responsive to metronomic chemotherapy, and another that with high probability cannot be eradicated by a metronomic protocol. Motivated by experimental work on ovarian cancer xenografts, we consider all possible combinations of a one week treatment protocol, repeated for three weeks, and constrained by the total weekly drug dose. Simulations reveal a small number of fractionated-dose protocols that are at least as effective as metronomic therapy in eradicating micrometastases with acquired resistance (weak or strong), while also being at least as effective on those that harbor weakly pre-existing resistant cells. Given the responsiveness of very different theoretical cell lines to these few fractionated-dose protocols, these may represent more effective ways to schedule chemotherapy with the goal of limiting metastatic tumor progression.

A tracking system for laboratory mice to support medical researchers in behavioral analysis

The behavioral analysis of laboratory mice plays a key role in several medical and scientific research areas, such as biology, toxicology, pharmacology, and so on. Important information on mice behavior and their reaction to a particular stimulus is deduced from a careful analysis of their movements. Moreover, behavioral analysis of genetically modified mice allows obtaining important information about particular genes, phenotypes or drug effects. The techniques commonly adopted to support such analysis have many limitations, which make the related systems particularly ineffective. Currently, the engineering community is working to explore innovative identification and sensing technologies to develop new tracking systems able to guarantee benefits to animals' behavior analysis. This work presents a tracking solution based on passive Radio Frequency Identification Technology (RFID) in Ultra High Frequency (UHF) band. Much emphasis is given to the software component of the system, based on a Web-oriented solution, able to process the raw tracking data coming from a hardware system, and offer 2D and 3D tracking information as well as reports and dashboards about mice behavior. The system has been widely tested using laboratory mice and compared with an automated video-tracking software (i.e., EthoVision). The obtained results have demonstrated the effectiveness and reliability of the proposed solution, which is able to correctly detect the events occurring in the animals' cage, and to offer a complete and user-friendly tool to support researchers in behavioral analysis of laboratory mice.

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.

Adaptive Mathematical Model of Tumor Response to Radiotherapy Based on CBCT Data

Mathematical modeling of tumor response to radiotherapy has the potential of enhancing the quality of the treatment plan, which can be even tailored on an individual basis. Lack of extensive in vivo validation has prevented, however, reliable clinical translation of modeling outcomes. Image-guided radiotherapy is a consolidated treatment modality based on computed tomographic (CT) imaging for tumor delineation and volumetric cone beam CT data for periodic checks during treatment. In this study, a macroscopic model of tumor growth and radiation response is proposed, being able to adapt along the treatment course as volumetric tumor data become available. Model parameter learning was based on cone beam CT images in 13 uterine cervical cancer patients, subdivided into three groups (G1, G2, G3) according to tumor type and treatment. Three group-specific parameter sets (PS1, PS2, and PS3) on one general parameter set (PSa) were applied. The corresponding average model fitting errors were 14%, 18%, 13%, and 21%, respectively. The model adaptation testing was performed using volume data of three patients, other than the ones involved in the parameter learning. The extrapolation performance of the general model was improved, while comparable prediction errors were found for the group-specific approach. This suggests that an online parameter tuning can overcome the limitations of a suboptimal patient stratification, which appeared otherwise a critical issue.

Modeling the Interplay Between Tumor Volume Regression and Oxygenation in Uterine Cervical Cancer During Radiotherapy Treatment

This paper describes a patient-specific mathematical model to predict the evolution of uterine cervical tumors at a macroscopic scale, during fractionated external radiotherapy. The model provides estimates of tumor regrowth and dead-cell reabsorption, incorporating the interplay between tumor regression rate and radiosensitivity, as a function of the tumor oxygenation level. Model parameters were estimated by minimizing the difference between predicted and measured tumor volumes, these latter being obtained from a set of 154 serial cone-beam computed tomography scans acquired on 16 patients along the course of the therapy. The model stratified patients according to two different estimated dynamics of dead-cell removal and to the predicted initial value of the tumor oxygenation. The comparison with a simpler model demonstrated an improvement in fitting properties of this approach (fitting error average value <5%, p < 0.01), especially in case of tumor late responses, which can hardly be handled by models entailing a constant radiosensitivity, failing to model changes from initial severe hypoxia to aerobic conditions during the treatment course. The model predictive capabilities suggest the need of clustering patients accounting for cancer cell line, tumor staging, as well as microenvironment conditions (e.g., oxygenation level).

Mathematical modeling of growth and death dynamics of mouse embryonic stem cells irradiated with γ-rays

Following ionizing radiation, mouse embryonic stem cells (mESCs) undergo both apoptosis and block at G2/M phase of the cell cycle. The dynamics of cell growth and the transition through the apoptotic phases cannot be directly inferred from experimental data, limiting the understanding of the biological response to the treatment. Here, we propose a semi-mechanistic mathematical model, defined by five compartments, able to describe the time curves of untreated and γ-rays irradiated mESCs and to extract the information therein embedded. To this end, mESCs were irradiated with 2 or 5 Gy γ-rays, collected over a period of 48 h and, at each time point, analyzed for apoptosis by using the Annexin V assay. When compared to unirradiated mESCs, the model estimates an additional 0.2 probability to undergo apoptosis for the 5 Gy-treated cells, and only a 0.07 (not statistically significantly different from zero) when a 2 Gy-irradiation dose is administered. Moreover, the model allows us to estimate the duration of the overall apoptotic process and also the time length of its early, intermediate, and late apoptotic phase.

Chemotherapy drug scheduling for the induction treatment of patients with acute myeloid leukemia

Leukemia is an immediately life-threatening cancer wherein immature blood cells are overproduced, accumulate in the bone marrow (BM) and blood and causes immune and blood system failure. Treatment with chemotherapy can be intensive or nonintensive and can also be life-threatening since only relatively few patient-specific and leukemia-specific factors are considered in current protocols. We have already presented a mathematical model for one intensive chemotherapy cycle with intravenous (i.v.) daunorubicin (DNR), and cytarabine (Ara-C). This model is now extended to nonintensive subcutaneous (SC) Ara-C and for a standard intensive chemotherapy course (four cycles), consistent with clinical practice. Model parameters mainly consist of physiological patient data, indicators of tumor burden and characteristics of cell cycle kinetics. A sensitivity analysis problem is solved and cell cycle parameters are identified to control treatment outcome. Simulation results using published cell cycle data from two acute myeloid leukemia patients are presented for a course of standard treatment using intensive and nonintensive protocols. The aim of remission-induction therapy is to debulk the tumor and achieve normal BM function; by treatment completion, the total leukemic population should be reduced to at most 10(9) cells, at which point BM hypoplasia is achieved. The normal cell number should be higher than that of the leukemic, and a 3-log reduction is the maximum permissible level of population reduction. This optimization problem is formulated and solved for the two patient case studies. The results clearly present the benefits from the use of optimization as an advisory tool for treatment design.