Supplementary Material for: Gamma Knife Radiosurgery in the Treatment of Tumor-Related Facial Pain

<i>Background:</i> Intracranial neoplasms can cause pain similar to trigeminal neuralgia. Literature regarding radiosurgery for this is limited. We present a retrospective review of patients with tumor-related facial pain from benign lesions treated with gamma knife radiosurgery (GKRS) at Wake Forest University. <i>Objectives: </i>The primary objectives were to determine long-term pain relief and predictive factors for pain alleviation. <i>Methods:</i> We reviewed 515 patients treated with GKRS for benign meningioma, vestibular schwannoma or trigeminal schwannoma between August 1999 and August 2010. Twenty-one eligible patients had tumor-related facial pain prior to GKRS. The median marginal tumor dose was 12 Gy. Long-term pain relief data were obtained by chart review and telephone interview. <i>Results:</i> The median follow-up for symptom evaluation was 3.8 years. Seventeen of 21 patients (81%) experienced a Barrow Neurological Institute (BNI) score of I–III at 6 months following GKRS. Kaplan-Meier estimates of freedom from BNI IV–V relapse were 66% at 1 year and 53% at 2 years. No pain relapses occurred after 2 years. <i>Conclusion:</i> GKRS of benign lesions is a noninvasive option for patients with tumor-related facial pain. Pain relief is modest, with the majority of pain relapses occurring within 2 years and approximately one half of patients maintaining relief beyond 2 years

Granular electrostatics: Progress and outstanding questions

Every physicist studies electrostatics in the first year of graduate study, and learns that the electric field is a linear superposition of contributions from charges, each of which obeys a 1/r2 law. Every physicist also studies classical mechanics, and learns that the problem of three or more bodies in a 1/r2 field is intrinsically nonlinear. The contradiction between these two teachings is seldom commented upon. In this paper, I overview what is known, what is believed, and what remains entirely unknown about the behaviors of multiple electrically polarized or charged particles. I show that the nonlinearity recognized in classical mechanics leads to highly complex dynamics when particles are permitted to act in the presence of electric fields. I describe several simple problems that lead to effects that are not understood in any way, and I conclude with the proposition that what we know and believe are insignificant compared with the effects that we know to exist but cannot explain