Complete Knot Research Articles

The Reidemeister graph is a complete knot invariant

We describe two locally finite graphs naturally associated to each knot type K, called Reidemeister graphs. We determine several local and global properties of these graphs and prove that in one case the graph-isomorphism type is a complete knot invariant up to mirroring. Lastly, we introduce another object, relating the Reidemeister and Gordian graphs, and determine some of its properties.

Théorème de Whitehead stratifié et invariants de nœuds

By considering homotopies that preserve the stratification, one obtains a natural notion of homotopy for stratified spaces. In this short note, we introduce invariants of stratified homotopy, the stratified homotopy groups. We show that they satisfy a stratified version of Whitehead's theorem. As an example, we introduce a complete knot invariant defined via the stratified homotopy groups.

Evaluation of self-educational training methods to learn laparoscopic skills - a randomized controlled trial

BackgroundEvaluation of two different self-educational methods (video assisted learning versus video assisted learning plus a nodal point operation primer) on learning laparoscopic suturing and intracorporal knotting.MethodsRandomized controlled trial at the laparoscopic surgical training center, University of Tubingen with 45 surgical novices first year medical students being pretested for dexterity. After self-educational training for 90 min with either method (Group A: video assisted learning, Group B: video assisted learning plus a nodal point operation primer) participants had to perform five laparoscopic intracorporal knots. Assessed were number of knots completed (maximum of five knots counted, knot integrity, technical proficiency and knotting time per knot. Primary outcome measure is a composed knot score combining knot integrity, technical proficiency and knotting time.ResultsGroup B (n = 23) achieved a significantly higher composed knot score than Group A (n = 22) (53.3 ± 8.4 versus 46.5 ± 13.6 points respectively, p = 0.016). Median knotting time per completed knot was significantly different between Group B and Group A (308 s [100–1221] versus 394 s [138–1397] respectively, p = 0.001). Concerning number of completed knots there was a trend towards more knots achieved in Group B (4.2 ± 1.2 versus 3.55 ± 1.4 respectively, p = 0.075) .ConclusionsThe use of a nodal point operation primer highlighting essential key steps of a procedure augment the success of learning laparoscopic skills as suturing and intracorporal knotting. (UIN researchregistry3866, March 22, 2018).

Affine cubic surfaces and character varieties of knots

It is known that the fundamental group homomorphism π1(T2)→π1(S3∖K) induced by the inclusion of the boundary torus into the complement of a knot K in S3 is a complete knot invariant. Many classical invariants of knots arise from the natural (restriction) map induced by the above homomorphism on the SL2-character varieties of the corresponding fundamental groups. In our earlier work [3], we proposed a conjecture that the classical restriction map admits a canonical deformation into a two-parameter family of affine cubic surfaces in C3. In this paper, we show that (modulo some mild technical conditions) our conjecture follows from a known conjecture of Brumfiel and Hilden [1] on the algebraic structure of the peripheral system of a knot. We then confirm the Brumfiel–Hilden conjecture for an infinite class of knots, including all torus knots, 2-bridge knots, and certain pretzel knots. We also show the class of knots for which the Brumfiel–Hilden conjecture holds is closed under taking connect sums and knot coverings.

A complete knot invariant from contact homology

We construct an enhanced version of knot contact homology, and show that we can deduce from it the group ring of the knot group together with the peripheral subgroup. In particular, it completely determines a knot up to smooth isotopy. The enhancement consists of the (fully noncommutative) Legendrian contact homology associated to the union of the conormal torus of the knot and a disjoint cotangent fiber sphere, along with a product on a filtered part of this homology. As a corollary, we obtain a new, holomorphic-curve proof of a result of the third author that the Legendrian isotopy class of the conormal torus is a complete knot invariant.

Cabled Butterfly Closure: A Novel Technique for Sternal Closure

Impaired sternal wound healing remains problematic after median sternotomy and can lead to significant morbidity after cardiac surgical procedures. Although metal plating systems exist for closing the sternum, their use is limited by expense and practicality, and simple wire closure remains the most common technique to close the sternum. We describe a cabling technique for sternal closure that is secure, uses standard sternal wire, and may be used on every patient. We have used the technique routinely in 291 patients with no sternal dehiscence or wound healing problems.

Knotted ureteral stent: a rare complication of ureteral stent usage

The use of ureteral stents has become a routine urological practice. There are many different complications with ureteral stent use. One rare complication is knotting, which can be a very difficult condition to treat. We report a case in which a complete knot was found in the proximal part of an indwelling ureteral stent with a proximal ureteral stone.

Multiscale Entanglement in Ring Polymers under Spherical Confinement

The interplay of geometrical and topological entanglement in semiflexible knotted polymer rings confined inside a spherical cavity is investigated by using advanced numerical methods. By using stringent and robust algorithms for locating knots, we characterize how the knot length l(k) depends on the ring contour length L(c) and the radius of the confining sphere R(c). In the no- and strong-confinement cases, we observe weak knot localization and complete knot delocalization, respectively. We show that the complex interplay of l(k), L(c), and R(c) that seamlessly bridges these two limits can be encompassed by a simple scaling argument based on deflection theory. The same argument is used to rationalize the multiscale character of the entanglement that emerges with increasing confinement.

How do People Use Instructions in Procedural Tasks?

Instructions for procedural tasks are often designed to be read before starting the task, but evidence suggests that people often do not use instructions that way. Participants ( N = 20) completed knot and assembly tasks using stepwise instructions and the time viewing the instructions in the course of completing the tasks was measured. Half the participants reported that they read the instructions first and half say they usually attempt the task first, but no difference was found between those groups in how they used the instructions. Rather, it was found to depend on the type of task; instructions were used more in the course of completing the knot tasks than the assembly tasks. This indicates that the nature of the task determines how instructions are used and that people might not consistently adhere to a preferred strategy for using instructions.

Assessment of knot security in continuous intradermal wound closures

The traditionally used square knot used for commencement and termination of continuous wound closures is bulky, requiring a minimum of four to six throws to form a secure knot with most suture materials and sizes. This study evaluates the security of self-locking knots, which are significantly smaller in volume than the traditionally applied square knot, for the intradermal closure of standardized wounds in porcine skin. Porcine skin samples with standardized wounds were closed in one of five patterns with 3/0 PDS suture. Wounds were harvested and tested to failure on a materials testing machine. Load at failure, ultimate elongation, wound stiffness, and mode of failure was determined for each sample. Wound closures incorporating the chain stitch knot performed as well as closures incorporating the conventional square knot for load to failure, elongation, and stiffness. Partial slippage or complete knot failure of 4/40 (10%) of the square knots used in closures was observed. 0/20 (0%) of the chain stitch knots displayed slippage. The half-blood knot performed similarly to the square and chain stitch knot in load to failure, elongation, and stiffness, however, 16/20 (80%) of these knots displayed slippage or complete knot failure. The chain stitch knot is as secure as the traditionally used square knot when used for termination of a continuous intradermal wound closure. This knot displays characteristics such as smaller knot volume and ease of applications that may make it a superior knot to the square knot in many clinical situations.

Knot Formation at the Mid Portion of an Indwelling Ureteral Stent

Indwelling ureteral stents are commonly used in the management of upper urinary tract obstruction. A rare complication is the knotting of an indwelling ureteral stent at its proximal coiled end. 13 We report a case in which a complete knot was found in the middle of an indwelling ureteral stent, a finding that to our knowledge has not been described previously. CASE REPORT A 66-year-old female presented with an infected, partially obstructing 8 5 mm. stone at the right ureteropelvic junction. The patient was treated with antibiotics and underwent stent placement to decompress the infected kidney. Physical examination was notable for a large cystocele at the introitus. As a result the ureteral orifices could be identified cystoscopically only after manual transvaginal elevation of the prolapsed bladder. A 6Fr open-ended ureteral catheter was positioned at the right ureteral orifice and a 0.035-inch Bentson guide wire (Cook Urological, Spencer, Indiana) was advanced into the renal pelvis. The stone was dislodged by the advancing guide wire and ultimately settled in the lower pole of the collecting system. A 7Fr 24 cm. Double-J stent (Medical Engineering Corp., New York, New York) was placed over the guide wire. Fluoroscopically the proximal end coiled appropriately in the renal pelvis and the distal end was seen coiled in the bladder under direct cystoscopic examination. The patient quickly improved. Following a 2-week course of antibiotics she underwent extracorporeal shock wave lithotripsy (Lithostar, Siemens Medical Systems, Inc., Iselin, New Jersey), which resulted in excellent stone fragmentation. At the time of lithotripsy the stent was noted to have migrated into the proximal ureter. After lithotripsy the stent was cystoscopically visualized and removed intact without difficulty using endoscopic grasping forceps. Examination of the stent revealed a knot in its mid portion (see figure). DISCUSSION

A secure locking knot for microsuturing.

Perfect balance between maximal suture strength and minimal foreign-body reactivity guarantees success, using microsurgical techniques. The proposed initial locking knot allows optimal edge approximation. It has strength, it is simple to master, and is not too bulky. The knot is kept in its first position, without danger of slipping, before securing it with an additional knot of two loops. No additional knots are necessary, because the completed knot may fail by breaking, but never by slippage.

Initial throw locking internal knotting technique.

Internal knotting is a highly versatile technique that closely resembles classic suturing. However, most intracorporeal knots are cumbersome and require a long time to master. We describe a simple, easy, and safe method for internal knotting that can also be used in open procedures and practiced until mastery is achieved. With this technique, the initial throw will never fail to hold tissues in apposition until the whole knot is constructed. The completed knot combines the maximum in suture support with a minimum of foreign body reactivity.

A secure arthroscopic knot

The proposed arthroscopic knot tying technique procedure is simple, easy to master, time saving, and the knot formed is not bulky. The initial tie loop holding capacity securely overcomes tension force between structures repaired. The completed knot, secured with additional two throw square knot or with a three half-hitches incorporating the post switching and/or loop direction reversal, will fail by breakage rather than by slippage (for the most commercially available 0, 2 0 , 3 0 , absorbable and nonabsorbable, monofilament and braided sutures).

A simple modification to add strength to the Roeder knot

The Roeder knot is commonly used duing laparoscopic suturing because it may be tied extracorporeally and slid down to the target tissue with a single pass of a knot pusher. However, it is significantly weaker than extracorporeally tied knots with several throws. We compared the usual Roeder knot to one that was modified by adding a fourth loop around the standing end of the suture and a second half-hitch to the completed knot. The modified knot (26.6 newtons ±15.3) was significantly stronger (p<0.05) than the standard Roeder knot (18.0 newtons ± 12.1). If a single-pass extracorporeal knot is to be used, we recommend a modified Roeder knot when ligating pedicles at laparoscopy.

Knotting of Intracardiac Flow-Directed Balloon Catheter: Simple Surgical Method of Removal

A complete knot occurred in a 7F flow-directed balloon catheter inserted through the right internal jugular vein. The patient was intubated and placed under positive pressure ventilation. After gaining surgical exposure of the venipuncture site, a purse-string of Prolene 4--0 suture was placed around it. The patient was placed in the Trendelenburg position and the knotted catheter withdrawn, while the purse-string suture was immediately tightened avoiding uncontrollable hemorrhage or massive air embolism.