ABSTRACT
In this paper, we study the competition of healthcare institutions for medical supplies in emergencies caused by natural disasters. In particular, we develop a two-stage procurement planning model in a random environment. We consider a pre-event policy, in which each healthcare institution seeks to minimize the purchasing cost of medical items and the transportation time from the first stage, and a recourse decision process to optimize the expected overall costs and the penalty for the prior plan, in response to each disaster scenario. Thus, each institution deals with a two-stage stochastic programming model that takes into account the unmet demand at the first stage, and the consequent penalty. Then, the institutions simultaneously solve their own stochastic optimization problems and reach a stable state governed by the stochastic Nash equilibrium concept. Moreover, we formulate the problem as a variational inequality; both the discrete and the general probability distribution cases are described. We also present an alternative formulation using infinite-dimensional duality tools. Finally, we discuss some numerical illustrations applying the progressive hedging algorithm.
ABSTRACT
The objective was to study whether repetitive transcranial magnetic stimulation (rTMS) of the motor cortex could induce modification of peripheral blood lactate values. Nineteen young healthy volunteers were included; during the study, all subjects were at rest, sitting on a comfortable armchair. The muscular activation was evaluated by continuous electromyographic record. TMS was performed by using a circular coil at the vertex. Resting motor threshold (rMT) was defined as the lowest TMS intensity able to induce motor responses of an amplitude >50 microV in the relaxed contralateral target muscle in approximately 50% of 20 consecutive stimuli. Venous blood lactate values were measured before, immediately after and 10 min after a single session of low frequencies (1Hz for 15 min) rTMS (LF rTMS) or high frequency (20 Hz for 15 min) rTMS (HF rTMS). As expected, LF rTMS induced a decrease of motor cortex excitability, whereas HF rTMS evoked an increase of motor cortex excitability. However, in the present investigation we observed that both conditions are associated to a significant increase of blood lactate. Since in our experimental conditions we can exclude a muscular production of lactate, the significant increment of peripheral blood lactate values, observed 10 min after the end of the rTMS session, is probably due to the crossing by brain-produced lactate of the blood-brain barrier.
