CT and Functional Outcomes of Primarily Ligamentous and Combined Ligamentous-Bony Lisfranc Injuries: A Retrospective Review.

Lisfranc injuries have been rising in incidence and can cause significant and lasting morbidity. There is no consensus on the optimal surgical treatment for these injuries, be they primarily ligamentous or combined (bony and ligamentous). No study has ever followed Lisfranc injury patients postoperatively using advanced imaging. The purpose of this study was to compare the functional and radiographic outcomes of primarily ligamentous and combined osseous and ligamentous Lisfranc injuries treated operatively with reduction and fixation. We performed a retrospective review of all Lisfranc injuries treated operatively in a single institution over a 6-year period. Injuries were classified as primarily ligamentous or combined by independent evaluation of available computed tomography (CT) or magnetic resonance imaging. Outcomes were measured using the Short Musculoskeletal Function Assessment (SMFA). CT of 29 patients was performed at last follow-up to evaluate reduction and degenerative changes. Of the 56 patients identified, 38 were available for follow-up. The average follow-up was 3.8 years. There were 26 combined injuries and 12 primarily ligamentous injuries. Outcomes were excellent in all patients and there was no statistical difference in SMFA scores in any category between the groups. On follow-up CT, all injuries were anatomically reduced, and 26 of 29 patients had degenerative changes. Our results support that reduction and stable fixation of Lisfranc injuries may be suitable treatment regardless of classification as combined or primarily ligamentous. Future larger-scale prospective studies should be pursued to supplement existing data.

Theoretical description of quantum mechanical permeation of graphene membranes by charged hydrogen isotopes.

It has been recently shown that in the presence of an applied voltage, hydrogen and deuterium nuclei can be separated from one another using graphene membranes as a nuclear sieve, resulting in a 10-fold enhancement in the concentration of the lighter isotope. While previous studies, both experimental and theoretical, have attributed this effect mostly to differences in vibrational zero point energy (ZPE) of the various isotopes near the membrane surface, we propose that multi-dimensional quantum mechanical tunneling of nuclei through the graphene membrane influences this proton permeation process in a fundamental way. We perform ring polymer molecular dynamics calculations in which we include both ZPE and tunneling effects of various hydrogen isotopes as they permeate the graphene membrane and compute rate constants across a range of temperatures near 300 K. While capturing the experimentally observed separation factor, our calculations indicate that the transverse motion of the various isotopes across the surface of the graphene membrane is an essential part of this sieving mechanism. An understanding of the multi-dimensional quantum mechanical nature of this process could serve to guide the design of other such isotopic enrichment processes for a variety of atomic and molecular species of interest.

Quantum Mechanical Enhancement of Rate Constants and Kinetic Isotope Effects for Water-Mediated Proton Transfer in a Model Biological System.

Biological systems have been shown to shuttle excess protons long distances by taking advantage of tightly organized hydrogen-bonded water bridges in hydrophobic protein cavities, and similar effects have been observed in carbon nanotubes. In this theoretical study we investigate how quantum effects of proton motion impact the rate constants for charge transfer in a model system consisting of a donor and acceptor molecule separated by a single-molecule water bridge. We calculate quantum and classical rate constants for the transfer of an excess proton over two possible paths, one with an H3O+ intermediate, and one with an OH- intermediate. Quantum effects are included through ring polymer molecular dynamics (RPMD) calculations. We observe a 4-fold enhancement of reaction rate constants due to proton tunneling at temperatures between 280 and 320 K, as shown by transmission coefficient calculations. Deuteration of the donor and acceptor proton are shown to decrease the reaction rate constant by a factor of 50, and this is another indicator that tunneling plays an important role in this proton transfer mechanism.

The Schrödinger equation with friction from the quantum trajectory perspective.

Similarity of equations of motion for the classical and quantum trajectories is used to introduce a friction term dependent on the wavefunction phase into the time-dependent Schrödinger equation. The term describes irreversible energy loss by the quantum system. The force of friction is proportional to the velocity of a quantum trajectory. The resulting Schrödinger equation is nonlinear, conserves wavefunction normalization, and evolves an arbitrary wavefunction into the ground state of the system (of appropriate symmetry if applicable). Decrease in energy is proportional to the average kinetic energy of the quantum trajectory ensemble. Dynamics in the high friction regime is suitable for simple models of reactions proceeding with energy transfer from the system to the environment. Examples of dynamics are given for single and symmetric and asymmetric double well potentials.

Flouroscopic arthrography versus MR arthrography of the lesser metatarsophalangeal joints for the detection of tears of the plantar plate and joint capsule: a prospective comparative study.

BACKGROUND: Derangements of the plantar plate and joint capsule are an underrecognized cause of lesser metatarsalgia. Fluoroscopic arthrography and magnetic resonance (MR) arthrography are both used for diagnosis. Currently there are no studies comparing the effectiveness of these two modalities. METHODS: Patients suspected of having plantar plate or capsular tears underwent both fluoroscopic arthrography and MR arthrography; the imaging findings were then compared and correlated with intraoperative findings, when available, to evaluate the effectiveness of the different imaging modalities. Forty consecutive patients underwent both fluoroscopic and MR arthrography. RESULTS: Thirty-two of 40 patients (80%) were found to have tears of the plantar plate, joint capsule, or both. MR arthrography identified all 32 tears. Four cases in the first 29 patients, 13.8%, demonstrated discrepancy where a tear was identified only on the MR arthrogram. A midpoint review of the data was performed. Of the 4 missed tears they were all noted to be plantar lateral in location. Four other patients in this group had plantar lateral tears that were not missed. These patients had an additional steep lateral oblique image on fluoroscopic arthrography, which showed the plantar lateral tear. Therefore an additional steep lateral oblique image was performed routinely capturing these small tears in the last 11 patients. CONCLUSION: MR arthrography was more accurate in identifying tears of the plantar plate and capsule than fluoroscopic arthrography. Fluoroscopic arthrography with additional views, like a steep lateral oblique view, was found to be as reliable, and more cost-effective, than MR arthrography. LEVEL OF EVIDENCE: Level II, prospective comparative study.

Efficient quantum trajectory representation of wavefunctions evolving in imaginary time.

The Boltzmann evolution of a wavefunction can be recast as imaginary-time dynamics of the quantum trajectory ensemble. The quantum effects arise from the momentum-dependent quantum potential--computed approximately to be practical in high-dimensional systems--influencing the trajectories in addition to the external classical potential [S. Garashchuk, J. Chem. Phys. 132, 014112 (2010)]. For a nodeless wavefunction represented as ψ(x, t) = exp(-S(x, t)/h) with the trajectory momenta defined by ∇S(x, t), analysis of the Lagrangian and Eulerian evolution shows that for bound potentials the former is more accurate while the latter is more practical because the Lagrangian quantum trajectories diverge with time. Introduction of stationary and time-dependent components into the wavefunction representation generates new Lagrangian-type dynamics where the trajectory spreading is controlled improving efficiency of the trajectory description. As an illustration, different types of dynamics are used to compute zero-point energy of a strongly anharmonic well and low-lying eigenstates of a high-dimensional coupled harmonic system.