On the cohomology rings of tree braid groups

Let $\Gamma$ be a finite connected graph. The (unlabelled) configuration space $UC^n \Gamma$ of $n$ points on $\Gamma$ is the space of $n$-element subsets of $\Gamma$. The $n$-strand braid group of $\Gamma$, denoted $B_n\Gamma$, is the fundamental group of $UC^n \Gamma$. We use the methods and results of our paper "Discrete Morse theory and graph braid groups" to get a partial description of the cohomology rings $H^*(B_n T)$, where $T$ is a tree. Our results are then used to prove that $B_n T$ is a right-angled Artin group if and only if $T$ is linear or $n<4$. This gives a large number of counterexamples to Ghrist's conjecture that braid groups of planar graphs are right-angled Artin groups.Comment: 25 pages, 7 figures. Revised version, accepted by the Journal of Pure and Applied Algebr

A simulation-enhanced intraoperative planning tool for robotic-assisted total knee arthroplasty

The purpose of the present study was to investigate current methods of surgical planning used in conjunction with robotics-assisted total knee arthroplasty (raTKA) to determine if improvements could be made using advanced computational techniques. Thus, through the use of musculoskeletal multi-body dynamic simulations, an enhanced surgical planning tool was developed, which provides insight on active postoperative joint mechanics. Development of the tool relied on patient-specific simulations using single-leg and full-body models. These simulations were constructed using two publicly-available datasets (Orthoload and SimTK); in particular, joint loading data obtained from subjects during various activities. Simulation parameters were optimized using a design-of experiments (DOE) methodology and validation of each of the models was conducted by calculating the root mean square error (RMSE) between joint loading calculated using the model and the corresponding results given in the appropriate dataset. Optimized and validated variants of each of the models were used in conjunction with the results of DOE studies that characterized the influence of a number of surgical planning variables on various biomechanical responses and linear regression analysis to derive knee performance equations (KPEs). In literature studies, some of the aforementioned responses have been strongly correlated with two outcomes commonly reported by dissatisfied TKA patients, namely, anterior knee pain and poor proprioception. In a proof-of-concept study, KPEs were used to calculate optimal positions and orientations of the femoral and tibial components in the case of one subject featured in the SimTK dataset. These results differed from corresponding ones reportedly achieved for the implant components in the subject. This trend suggests there is potential to improve robotic surgical planning for current-generation raTKA systems through the use of musculoskeletal simulation. Use of the proposed surgical planning tool does not require computational resources beyond what are used with a specified current-generation raTKA system (Navio Surgical System). Furthermore, there are only minimal differences between the workflow involving the proposed planning tool and that when Navio Surgical System is used. A number of recommendations for future studies are made, such as larger scale simulation validation work and use of more complex regression techniques when deriving the KPEs