Early-stage melanoma, squamous and basal cell carcinomas have local control rates of >90% with wide excision after pathologically clear margins and >95% with Mohs micrographic surgery. Local control rates for these approaches are not well defined in Merkel cell carcinoma (MCC). Herein, we analyzed data from 80 patients (pts) in a Seattle-based IRB-approved registry who had local MCC and underwent surgical excision with pathologically clear margins. Patients who had local radiation therapy after surgery were excluded as radiation affects recurrence rate independent of surgery. We also performed meta-analysis of 13 published studies (846 pts) based on a random-effects model. For the 80 pt cohort, local recurrence rate (LRR; ≤2 cm from the primary tumor) was 10%. In-transit recurrence rate (ITR; >2cm from primary) was 1%. Regional nodal recurrence rate (RRR) was 5%. This cohort had low-risk characteristics with small primary tumors (74% were ≤1 cm, 23% were 1-2, and 4% were >2 cm). No residual tumor was found in 60% of re-excisions while 29% had closest pathologic margins <1 cm. Meta-analysis of 9 published studies (745 pts) who underwent excision with clear pathological margins yielded 16.4% LRR [95% CI 8.3-26.5], 9.5% ITR [95% CI 5.4-14.6], and 32.1% RRR [95% CI 19.1-46.7]. Data from 4 studies (101 pts) who underwent Mohs yielded 3.6% LRR [95% CI 0-16.3], 12.8% ITR [95% CI 6.4-21.1], and 20.7% RRR [95% CI 13.8-38.3]. In each cohort, LRR/IRR following surgical excision with pathologically clear margins was >10%. This suggests MCC is more likely to recur near the excision site than other skin cancers and may reflect biological difference in the MCC local extension pattern (discontinuous spread beyond pathologically clear margins). Even for pathologically negative excisions, higher risk tumors may benefit from adjuvant radiotherapy.

Charged particles in the heliosphere can be continuously accelerated by interplanetary shocks and eventually escape from these shocks without returning to it. Acceleration and escape are highly intertwined and both contribute to the shaping of the particles’ momentum spectrum at the shock. The simplest model which describes this phenomenon is called Diffusive Shock Acceleration (DSA). DSA has been very successful in describing several observations. However, DSA does not include an energy-dependent escape from the foreshock region. We expand upon DSA by presenting a model for interplanetary shock acceleration which includes this energy-dependent particle escape. We analytically solve a one-dimensional transport equation with a diffusion coefficient and an escape time that describes both the turbulence self-generated by the shock and the far upstream pre-existing turbulence. We consider the case where a shock encounters a population of pre-existing charged particles with a power law energy distribution as measured by spacecraft. We find that at lower energies our solution is concave, whereas at higher energies it asymptotically approaches a power law whose slope depends on the original energy spectrum’s power law index and shock parameters. We fitted the solution obtained from this transport equation to shock data measured from multiple shock events collected by ACE/EPAM (the Electron, Proton, and Alpha Monitor aboard the Advanced Composition Explorer spacecraft). We find that for the shock events considered, our model’s best fit parameters match very well with the predicted values, obtained by using the measured shock parameters. From this model, we can better understand the mechanism of interplanetary shock acceleration and how this phenomenon energizes charged particles near the Sun and around other objects (for example, blazars and supernova remnants).