Neurostimulation in Theory and Practice

**3**

**Chapter 1**

*Denis Larrivee*

impairments.

that they be reconstructed.

their utility to therapeutic design uncertain.

Introductory Chapter:

Neurostimulation and the

**1. Introduction: neurostimulation and global organization**

Structural Basis of Brain Activity

Despite its remarkable clinical efficacy and several decades of use, neurostimulation remains a therapy whose neurophysiological basis is yet undetermined [1]. This lack of basic scientific understanding has imposed a conceptual barrier that has broader implications for therapeutic efficacy. Nonetheless, an improved understanding of the mechanisms of brain activity, observations on the etiological basis of neurological diseases, and insights from diverse therapeutic applications offer hope for understanding how the therapy physiologically impacts neural

Because the form of neurostimulation is rhythmic, it has been suggested that neural mechanisms responding to stimulation are similarly rhythmic [2]. Rhythmic activity is notably ubiquitous in brain operation, and has been observed in single neurons that display patterned spiking, as well as at network levels, where variable inhibitory and excitatory feedback configure repetitive activity [3]. Increasingly, these are proposed to be oscillatory [4]. Significantly, oscillators are prone to pairing and can combine in an indefinite number of permutations to recreate encoded feature representations. The therapeutic role played by neurostimulation thus plausibly entails oscillatory interactions, where neurostimulation could modify dysfunctional oscillations, presumably by altering their intrinsic features, like patterning, synchronization, and desynchronization. Recent studies show in fact that brain activity is globally structured through oscillatory interactions, with key elements distributed throughout the brain. Such elements would be expected to be similarly perturbed in various impairments; hence, restoring normal function would require

Consistent with this proposal, it is known that global brain activity is coordinated by slow frequency oscillations that resonate between subcortical and cortical regions [4]. These activity structures mediate organismal functions, which are cohesively ordered to the good of the individual; hence, their investigation can be expected to provide a basis for understanding the higher order organization that underlies brain dynamics at global scales. Indeed, without such understanding, the effects induced by neuromodulation and neurostimulation remain anecdotal and

How then is global brain activity affected by neurostimulation? Some insight into this question can be expected from the study of diseases known to disrupt global brain events. One candidate is epilepsy, which has been treated by neurostimulation for several decades. Significantly, a characteristic feature of epilepsy is the occurrence of epileptogenesis outside initial seizure foci. The processes associated with this distribution are not known, but current evidence implicates


**4. Open-Loop Instability of the Boost Converter Dynamics with a CPL**

Consider the dynamic system represented by Equations (14) and (15). The following shows that an operating point of such a system can be unstable either in DCM or CCM operation.

**Proposition 1.** *At least, one operating point of the dynamic system represented by the Equations* (14) *and* (15)*, is Lyapunov-unstable for P*, *L* > 0*.*

**Proof.** See Appendix A.1.

It is worth mentioning that different operating points may be open-loop stable; however, in general, open-loop stability cannot be ensured by a constant control input. The interested reader will surely obtain parameters and constant values of *u*1 for which the operating point is stable. However, the question remains whether there is a control signal *u*1 capable of avoiding unstable system dynamics.


**Abstract**

The enhanced oil recovery phase of oil reservoirs production usually comes after the water/gas injection (secondary recovery) phase. The main objective of EOR application is to mobilize the remaining oil through enhancing the oil displacement and volumetric sweep efficiency. The oil displacement efficiency enhances by reducing the oil viscosity and/or by reducing the interfacial tension, while the volumetric sweep efficiency improves by developing a favorable mobility ratio between the displacing fluid and the remaining oil. It is important to identify remaining oil and the production mechanisms that are necessary to improve oil recovery prior to implementing an EOR phase. Chemical enhanced oil recovery is one of the major EOR methods that reduces the residual oil saturation by lowering water-oil interfacial tension (surfactant/alkaline) and increases the volumetric sweep efficiency by reducing the water-oil mobility ratio (polymer). In this chapter, the basic mechanisms of different chemical methods have been discussed including the interactions of different chemicals with the reservoir rocks and fluids. In addition, an up-to-date status of chemical flooding at the laboratory scale, pilot projects and field applications have been reported.

**Keywords:** enhanced oil recovery, EOR, chemical flooding, alkaline, surfactant, polymer, interfacial tension, IFT