Mathematical modeling of tumor cell proliferation kinetics and label retention in a mouse model of lung cancer

Kinetic modeling and numerical simulations to predict patient-specific responses to radiotherapy

Recent research indicates that quiescent tumor cells are significantly less radiosensitive with a greater repair capacity than proliferative cells. In order to better predict patient-specific responses to radiotherapy, we develop a mathematical model with treatment terms to describe dynamical behaviors of tumor growth. The global stabilities of the tumor-free equilibrium, the tumor-present equilibrium and the corresponding sufficient criteria are obtained. In addition, we simulate volumetric imaging data from 12 head-and-neck cancer patients and estimate the patient-specific responses to radiotherapy. Results indicate that radiosensitivity of proliferative cells is a critical factor that determines a successful radiotherapy. By comparison with previous simulation results, we find that the model presented in this paper is more suitable to describe the radiotherapy procedure of head-and-neck cancer. Finally, we discuss the influences of different radiotherapy strategies on therapeutic effect. The results show that treatment strategies with large dose or short treatment cycle can obtain better treatment effect.

Modeling cell proliferation in human acute myeloid leukemia xenografts

Motivation

Acute myeloid leukemia (AML) is one of the most common hematological malignancies, characterized by high relapse and mortality rates. The inherent intra-tumor heterogeneity in AML is thought to play an important role in disease recurrence and resistance to chemotherapy. Although experimental protocols for cell proliferation studies are well established and widespread, they are not easily applicable to in vivo contexts, and the analysis of related time-series data is often complex to achieve. To overcome these limitations, model-driven approaches can be exploited to investigate different aspects of cell population dynamics.

Results

In this work, we present ProCell, a novel modeling and simulation framework to investigate cell proliferation dynamics that, differently from other approaches, takes into account the inherent stochasticity of cell division events. We apply ProCell to compare different models of cell proliferation in AML, notably leveraging experimental data derived from human xenografts in mice. ProCell is coupled with Fuzzy Self-Tuning Particle Swarm Optimization, a swarm-intelligence settings-free algorithm used to automatically infer the models parameterizations. Our results provide new insights on the intricate organization of AML cells with highly heterogeneous proliferative potential, highlighting the important role played by quiescent cells and proliferating cells characterized by different rates of division in the progression and evolution of the disease, thus hinting at the necessity to further characterize tumor cell subpopulations.

Availability and implementation

The source code of ProCell and the experimental data used in this work are available under the GPL 2.0 license on GITHUB at the following URL: https://github.com/aresio/ProCell.

Supplementary information

Supplementary data are available at Bioinformatics online.

Evolution of model specific relative growth rate: Its genesis and performance over Fisher's growth rates

Growth curve models play an instrumental role to quantify the growth of biological processes and have immense practical applications across disciplines. In the modelling approach, the absolute growth rate and relative growth rate (RGR) are two most commonly used measures of growth rates. RGR is empirically estimated by Fisher (1921) assuming exponential growth between two consecutive time points and remains invariant under any choice of the underlying growth model. In this article, we propose a new measure of RGR, called modified RGR, which is sensitive to the choice of underlying growth law. The mathematical form of the growth equations are utilized to develop the formula for model dependent growth rates and can be easily computed for commonly used growth models. We compare the efficiency of Fisher's measure of RGR and modified RGR to infer the true growth profile. To achieve this, we develop a goodness of fit testing procedure using Gompertz model as a test bed. The relative efficiency of the two rate measures is compared by generating power curves of the goodness of fit testing procedure. The asymptotic distributions of the associated test statistics are elaborately studied under Gompertz set up. The simulation experiment shows that the proposed formula has better discriminatory power than the existing one in identifying the true profile. The claim is also verified using existing real data set on fish growth. An algorithm for the model selection mechanism is also proposed based on the modified RGR and is generalized for some commonly used other growth models. The proposed methodology may serve as a valuable tool in growth studies in different research areas.

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.

A conceptual review on systems biology in health and diseases: from biological networks to modern therapeutics

Human physiology is an ensemble of various biological processes spanning from intracellular molecular interactions to the whole body phenotypic response. Systems biology endures to decipher these multi-scale biological networks and bridge the link between genotype to phenotype. The structure and dynamic properties of these networks are responsible for controlling and deciding the phenotypic state of a cell. Several cells and various tissues coordinate together to generate an organ level response which further regulates the ultimate physiological state. The overall network embeds a hierarchical regulatory structure, which when unusually perturbed can lead to undesirable physiological state termed as disease. Here, we treat a disease diagnosis problem analogous to a fault diagnosis problem in engineering systems. Accordingly we review the application of engineering methodologies to address human diseases from systems biological perspective. The review highlights potential networks and modeling approaches used for analyzing human diseases. The application of such analysis is illustrated in the case of cancer and diabetes. We put forth a concept of cell-to-human framework comprising of five modules (data mining, networking, modeling, experimental and validation) for addressing human physiology and diseases based on a paradigm of system level analysis. The review overtly emphasizes on the importance of multi-scale biological networks and subsequent modeling and analysis for drug target identification and designing efficient therapies.