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Importantly, we find that collocation techniques are able to replicate solutions obtained using more standard Fourier based methods on a flat, periodic domain, independent of the underlying mesh. This result is particularly significant given the highly irregular nature of the type of meshes derived from modern neuroimaging data.One of the key contributions of this thesis is our ability to solve neural models on curved geometries for which no analytic formula for the geodesic distance exists. Indeed, by deploying efficient numerical schemes to compute geodesics, our approach is not only capable of modelling macroscopic pattern formation on realistic cortical geometries, such as the rat brain considered herein, but can also be extended to include cortical architectures of more physiological relevance.

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But that doesn mean it isn effective in reducing opioid use. When researchers administered Exparel to knee surgery patients instead of the standard bupivacaine total opioid consumption decreased by 78 percent in the first 72 hours after surgery, with 10 percent remaining opioid free, according to a study published Journal of Arthroplasty. That makes sense considering that Exparel lasts approximately 60 hours longer.The key issue has been widespread opioid over prescribing for many types of medical procedures.

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