Early postoperative MRI findings following surgery for herniated lumbar disc. Part II: A gadolinium-enhanced study

The aim of our study was to evaluate the contrast-enhanced MR imaging (MRI) findings, in the early postoperative period, in unselected patients undergoing lumbar microdiscectomy (15/16 had total resolution of their symptoms). Contrast-enhanced imaging studies were performed, in all 16 patients of our series, before surgery, and at the third postoperative day and, two months after surgery. Postoperative paraspinal muscles enhancement was present in all patients. In the postoperative period, nerve root enhancement was present in 5/16 patients at the early survey and persisted in one after two months. A pseudohernia depicted as epidural intermediate signal intensity tissue, was seen in 13 patients at the third day MRI, and only in eight after two months. This pseudohernia enhanced peripherally in 8/13 patients and enhanced homogeneously in the remaining five at the first postsurgical examination; in the late MRI the peripheral enhancement was appreciable in only two patients while a homogeneous enhancement was observed in six. Clinical symptoms resolved completely in 14/16 patients on clinical evaluation at the third postoperative day, while the remaining two patients showed residual symptoms and signs of radicular compression. At the early MRI these two patients showed intradural nerve root enhancement. Two months later, one patient did not show the previously described nerve root enhancement and improved clinically, while the other had a positive Straight Leg Raising Sign with persistent intradural nerve root enhancement. In conclusion, no correlation between clinical course and contrast-enhancement of pseudohernia and extradural nerve root was appreciable, although intradural nerve root enhancement seems to represent a clinically relevant finding

A multi-time-scale analysis of chemical reaction networks: II. Stochastic systems

We consider stochastic descriptions of chemical reaction networks in which there are both fast and slow reactions, and for which the time scales are widely separated. We develop a computational algorithm that produces the generator of the full chemical master equation for arbitrary systems, and show how to obtain a reduced equation that governs the evolution on the slow time scale. This is done by applying a state space decomposition to the full equation that leads to the reduced dynamics in terms of certain projections and the invariant distributions of the fast system. The rates or propensities of the reduced system are shown to be the rates of the slow reactions conditioned on the expectations of fast steps. We also show that the generator of the reduced system is a Markov generator, and we present an efficient stochastic simulation algorithm for the slow time scale dynamics. We illustrate the numerical accuracy of the approximation by simulating several examples. Graph-theoretic techniques are used throughout to describe the structure of the reaction network and the state-space transitions accessible under the dynamics.clos