Experimental designs for small randomised clinical trials: an algorithm for choice.

Background: Small clinical trials are necessary when there are difficulties in recruiting enough patients for conventional frequentist statistical analyses to provide an appropriate answer. These trials are often necessary for the study of rare diseases as well as specific study populations e.g.

A hierarchical modeling approach of hippocampus local circuit.

The modeling and simulation of a realistic nervous tissue are difficult because of the number of implied cell types (neuronal and glial), the topology of the networks, and the various heterogeneous molecular mechanisms. The MTIP (Mathematical Theory of Integrative Physiology) is used as a new modeling approach based on a representation in terms of functional interactions and a formalism (S-Propagator) related to n-level field theory. This work presents the passage from a theoretical description of the biological system to a computing implementation in the general case.

On the integration of physiological mechanisms in the nervous tissue using the MTIP: synaptic plasticity depending on neurons-astrocytes-capillaries interactions.

The objective in this work is twofold: (i) to illustrate the use of the Mathematical Theory of Integrative Physiology (MTIP) [13], that is a general theory and practical method for the systematic and progressive mathematical integration of physiological mechanisms; (ii) to study a complex neurobiological system taken as an example, i.e., the synaptic plasticity depending on brain activity, on astrocytic and neuronal metabolism, and on brain hemodynamics.