Mathematical analysis of a model for the growth of the bovine corpus luteum.

The corpus luteum (CL) is an ovarian tissue that grows in the wound space created by follicular rupture. It produces the progesterone needed in the uterus to maintain pregnancy. Rapid growth of the CL and progesterone transport to the uterus require angiogenesis, the creation of new blood vessels from pre-existing ones, a process which is regulated by proteins that include fibroblast growth factor 2 (FGF2). In this paper we develop a system of time-dependent ordinary differential equations to model CL growth. The dependent variables represent FGF2, endothelial cells (ECs), luteal cells, and stromal cells (like pericytes), by assuming that the CL volume is a continuum of the three cell types. We assume that if the CL volume exceeds that of the ovulated follicle, then growth is inhibited. This threshold volume partitions the system dynamics into two regimes, so that the model may be classified as a Filippov (piecewise smooth) system. We show that normal CL growth requires an appropriate balance between the growth rates of luteal and stromal cells. We investigate how angiogenesis influences CL growth by considering how the system dynamics depend on the dimensionless EC proliferation rate, ρ5. We find that weak (low ρ5) or strong (high ρ5) angiogenesis leads to 'pathological' CL growth, since the loss of CL constituents compromises progesterone production or delivery. However, for intermediate values of ρ5, normal CL growth is predicted. The implications of these results for cow fertility are also discussed. For example, inadequate angiogenesis has been linked to infertility in dairy cows.

IL-2 sensitivity and exogenous IL-2 concentration gradient tune the productive contact duration of CD8(+) T cell-APC: a multiscale modeling study.

BACKGROUND: The CD8(+) T cell immune response fights acute infections by intracellular pathogens and, by generating an immune memory, enables immune responses against secondary infections. Activation of the CD8(+) T cell immune response involves a succession of molecular events leading to modifications of CD8(+) T cell population. To understand the endogenous and exogenous mechanisms controlling the activation of CD8(+) T cells and to investigate the influence of early molecular events on the long-term cell population behavior, we developed a multiscale computational model. It integrates three levels of description: a Cellular Potts model describing the individual behavior of CD8(+) T cells, a system of ordinary differential equations describing a decision-making molecular regulatory network at the intracellular level, and a partial differential equation describing the diffusion of IL-2 in the extracellular environment. RESULTS: We first calibrated the model parameters based on in vivo data and showed the model's ability to reproduce early dynamics of CD8(+) T cells in murine lymph nodes after influenza infection, both at the cell population and intracellular levels. We then showed the model's ability to reproduce the proliferative responses of CD5(hi) and CD5(lo) CD8(+) T cells to exogenous IL-2 under a weak TCR stimulation. This stressed the role of short-lasting molecular events and the relevance of explicitly describing both intracellular and cellular scale dynamics. Our results suggest that the productive contact duration of CD8(+) T cell-APC is influenced by the sensitivity of individual CD8(+) T cells to the activation signal and by the IL-2 concentration in the extracellular environment. CONCLUSIONS: The multiscale nature of our model allows the reproduction and explanation of some acquired characteristics and functions of CD8(+) T cells, and of their responses to multiple stimulation conditions, that would not be accessible in a classical description of cell population dynamics that would not consider intracellular dynamics.

Abscopal Benefits of Localized Radiotherapy Depend on Activated T-cell Trafficking and Distribution between Metastatic Lesions.

It remains unclear how localized radiotherapy for cancer metastases can occasionally elicit a systemic antitumor effect, known as the abscopal effect, but historically, it has been speculated to reflect the generation of a host immunotherapeutic response. The ability to purposefully and reliably induce abscopal effects in metastatic tumors could meet many unmet clinical needs. Here, we describe a mathematical model that incorporates physiologic information about T-cell trafficking to estimate the distribution of focal therapy-activated T cells between metastatic lesions. We integrated a dynamic model of tumor-immune interactions with systemic T-cell trafficking patterns to simulate the development of metastases. In virtual case studies, we found that the dissemination of activated T cells among multiple metastatic sites is complex and not intuitively predictable. Furthermore, we show that not all metastatic sites participate in systemic immune surveillance equally, and therefore the success in triggering the abscopal effect depends, at least in part, on which metastatic site is selected for localized therapy. Moreover, simulations revealed that seeding new metastatic sites may accelerate the growth of the primary tumor, because T-cell responses are partially diverted to the developing metastases, but the removal of the primary tumor can also favor the rapid growth of preexisting metastatic lesions. Collectively, our work provides the framework to prospectively identify anatomically defined focal therapy targets that are most likely to trigger an immune-mediated abscopal response and therefore may inform personalized treatment strategies in patients with metastatic disease.

A proliferation saturation index to predict radiation response and personalize radiotherapy fractionation.

BACKGROUND: Although altered protocols that challenge conventional radiation fractionation have been tested in prospective clinical trials, we still have limited understanding of how to select the most appropriate fractionation schedule for individual patients. Currently, the prescription of definitive radiotherapy is based on the primary site and stage, without regard to patient-specific tumor or host factors that may influence outcome. We hypothesize that the proportion of radiosensitive proliferating cells is dependent on the saturation of the tumor carrying capacity. This may serve as a prognostic factor for personalized radiotherapy (RT) fractionation. METHODS: We introduce a proliferation saturation index (PSI), which is defined as the ratio of tumor volume to the host-influenced tumor carrying capacity. Carrying capacity is as a conceptual measure of the maximum volume that can be supported by the current tumor environment including oxygen and nutrient availability, immune surveillance and acidity. PSI is estimated from two temporally separated routine pre-radiotherapy computed tomography scans and a deterministic logistic tumor growth model. We introduce the patient-specific pre-treatment PSI into a model of tumor growth and radiotherapy response, and fit the model to retrospective data of four non-small cell lung cancer patients treated exclusively with standard fractionation. We then simulate both a clinical trial hyperfractionation protocol and daily fractionations, with equal biologically effective dose, to compare tumor volume reduction as a function of pretreatment PSI. RESULTS: With tumor doubling time and radiosensitivity assumed constant across patients, a patient-specific pretreatment PSI is sufficient to fit individual patient response data (R(2) = 0.98). PSI varies greatly between patients (coefficient of variation >128 %) and correlates inversely with radiotherapy response. For this study, our simulations suggest that only patients with intermediate PSI (0.45-0.9) are likely to truly benefit from hyperfractionation. For up to 20 % uncertainties in tumor growth rate, radiosensitivity, and noise in radiological data, the absolute estimation error of pretreatment PSI is <10 % for more than 75 % of patients. CONCLUSIONS: Routine radiological images can be used to calculate individual PSI, which may serve as a prognostic factor for radiation response. This provides a new paradigm and rationale to select personalized RT dose-fractionation.