From cell death to embryo arrest: Mathematical models of human preimplantation embryo development

Human preimplantation embryos exhibit high levels of apoptotic cells and high rates of developmental arrest during the first week in vitro. The relation between the two is unclear and difficult to determine by conventional experimental approaches, partly because of limited numbers of embryos. We apply a mixture of experiment and mathematical modeling to show that observed levels of cell death can be reconciled with the high levels of embryo arrest seen in the human only if the developmental competence of embryos is already established at the zygote stage, and environmental factors merely modulate this. This suggests that research on improving in vitro fertilization success rates should move from its current concentration on optimizing culture media to focus more on the generation of a healthy zygote and on understanding the mechanisms that cause chromosomal and other abnormalities during early cleavage stages.

Failure of programmed cell death and differentiation as causes of tumors: some simple mathematical models.

Most models of tumorigenesis assume that the tumor grows by increased cell division. In these models, it is generally supposed that daughter cells behave as do their parents, and cell numbers have clear potential for exponential growth. We have constructed simple mathematical models of tumorigenesis through failure of programmed cell death (PCD) or differentiation. These models do not assume that descendant cells behave as their parents do. The models predict that exponential growth in cell numbers does sometimes occur, usually when stem cells fail to die or differentiate. At other times, exponential growth does not occur: instead, the number of cells in the population reaches a new, higher equilibrium. This behavior is predicted when fully differentiated cells fail to undergo PCD. When cells of intermediate differentiation fail to die or to differentiate further, the values of growth parameters determine whether growth is exponential or leads to a new equilibrium. The predictions of the model are sensitive to small differences in growth parameters. Failure of PCD and differentiation, leading to a new equilibrium number of cells, may explain many aspects of tumor behavior--for example, early premalignant lesions such as cervical intraepithelial neoplasia, the fact that some tumors very rarely become malignant, the observation of plateaux in the growth of some solid tumors, and, finally, long lag phases of growth until mutations arise that eventually result in exponential growth.

Proceedings of the Second American-Soviet Symposium on the Use of Mathematical Models to Optimize Water Quality Management, Bloomfield Hills, Michigan, USA, August 27-30, 1979 /

Mode of access: Internet.

Mathematical models in the social sciences

Mode of access: Internet.

The control of communicable diseases. : Report of a committee of the American public health association.

Reprint no. 1697 from the Public Health reports (revised 1945).

Improvement of mathematical models for simulation of vehicle handling. Volume 6: programmers' guide for the driver module. Final report.

National Highway Traffic Safety Administration, Washington, D.C.

Improvement of mathematical models for vehicle handling. Volume 7: technical manual for the general simulation. Final report.

National Highway Traffic Safety Administration, Washington, D.C.

Improvement of mathematical models for vehicle handling. Volume 8: summary report. Final report.

National Highway Traffic Safety Administration, Washington, D.C.

Improvement of mathematical models for simulation of vehicle handling. Volume 1: user's guide for the five degree of freedom models. Final report.

Mode of access: Internet.

Improvement of mathematical models for simulation of vehicle handling. Volume 2: programmers' guide for the five degree of freedom models. Final report.

National Highway Traffic Safety Administration, Washington, D.C.