Line Congruence Research Articles

Prediction of tumor board procedural recommendations using large language models.

Multidisciplinary tumor boards are meetings where a team of medical specialists, including medical oncologists, radiation oncologists, radiologists, surgeons, and pathologists, collaborate to determine the best treatment plan for cancer patients. While decision-making in this context is logistically and cost-intensive, it has a significant positive effect on overall cancer survival. METHODS: We evaluated the quality and accuracy of predictions by several large language models for recommending procedures by a Head and Neck Oncology tumor board, which we adapted for the task using parameter-efficient fine-tuning or in-context learning. Records were divided into two sets: n=229 used for training and n=100 records for validation of our approaches. Randomized, blinded, manual human expert classification was used to evaluate the different models. RESULTS: Treatment line congruence varied depending on the model, reaching up to 86%, with medically justifiable recommendations up to 98%. Parameter-efficient fine-tuning yielded better outcomes than in-context learning, and larger/commercial models tend to perform better. Providing precise, medically justifiable procedural recommendations for complex oncology patients is feasible. Extending the data corpus to a larger patient cohort and incorporating the latest guidelines, assuming the model can handle sufficient context length, could result in more factual and guideline-aligned responses and is anticipated to enhance model performance. We, therefore, encourage further research in this direction to improve the efficacy and reliability of large language models as support in medical decision-making processes.

Hemiepiphysiodesis Corrects Lower Extremity Coronal Plane Deformity in Children with Skeletal Dysplasia Irrespective of Intra-Articular Malalignment

BackgroundSkeletal dysplasias (SkD) are a rare group of disorders characterized by abnormal growth and development of bone and cartilage, often causing limb deformity. Many patients also have ligamentous instability that can accentuate the malalignment. This ligamentous instability can present either a generalized ligamentous laxity or focal coronal plane intra-articular malalignment. Temporary hemiepiphysiodesis (HE) is a commonly employed minimally invasive surgical technique for correcting coronal plane limb deformities. This study evaluated the effectiveness of HE in the correction of knee coronal plane deformity in children with SkD and the correlation of concurrent joint laxity. MethodsA retrospective cohort study was conducted to evaluate radiological outcomes of HE for coronal plane knee deformities in patients with SkD (aged <18 years) who had surgery between January 1, 2008 and December 31, 2020. Changes in distal femoral and proximal tibial mechanical angles, and knee joint line congruence angles (JLCA) prior to HE and at the final follow-up were analyzed. An increased JLCA of ≥±2° was considered a knee with ligamentous instability. Preoperative and postoperative patient-reported pain status was recorded. ResultsFifty-six tibial and 42 femoral HE procedures in 32 children (mean age at HE: 9.8 ± 2.8 years) were included. The deformity was fully corrected in 23/32 (72%) children, at an average annual rate of 6.3° at the distal femur and 3.3° at the proximal tibia, over 21.9 ± 12.6 months. The overall pre-HE JLCA improved by an average of 5.3° (P < .05). The improvement was more pronounced in varus knees (n = 45; P < .05) than valgus knees (n = 12; P = .11) but regardless of the severity of joint instability, pre-HE JLCA did not impede the rate of femoral (r = −0.22) or tibial (r = −0.21) corrections. Preoperative pain was reported by 78% of patients whereas only 25% of patients reported pain postoperatively at the final follow-up (mean follow-up: 26.4 ± 13.5 months). ConclusionsThe presence of coronal plane intra-articular malalignment did not affect the rate and the magnitude of correction with HE in this cohort. Coronal plane deformities and JLCA improve with deformity correction by HE in children with SkD. Key Concepts(1)Intra-articular malalignment at the knee does not impede the success of hemiepiphysiodesis in children with skeletal dysplasia.(2)While all coronal plane knee deformities improved, a more significant improvement was noted in children with varus than valgus.(3)Joint line congruency angles improved with guided growth for coronal plane deformities. Level of EvidenceIII

Dual relations between line congruences in $$\mathbb {R}^3$$ and surfaces in $$\mathbb {R}^4$$

Dual relations between line congruences in $$\mathbb {R}^3$$ and surfaces in $$\mathbb {R}^4$$

Pre-operative Planning of High Tibial Osteotomy With ChatGPT: Are We There Yet?

ChatGPT (Chat Generative Pre-trained Transformer), developed by OpenAI (San Francisco, CA, USA), has gained attention in the medical field. It has the potential to enhance and simplify tasks, such as preoperative planning in orthopedic surgery. We aimed to test ChatGPT's accuracy in measuring the angle of correction for high tibial osteotomy for cases planned and performed at a tertiary teaching hospital in Singapore. Peri-operative angular parameters from 114 consecutive patients who underwent medial opening wedge high tibial osteotomy (MOWHTO) were used to query ChatGPT 3.0. First ChatGPT 3.0 was queried on what information it required to plan a MOWHTO. Based on its response, pre-operative medial proximal tibial angle (MPTA) and joint line congruence angle (JLCA) were provided. ChatGPT 3.0 then responded with its recommended angle of correction. This was compared against the manually planned surgical correction by our fellowship-trained surgeon. A root mean square analysis was then performed to compare ChatGPT 3.0 and manual planning. The root mean square error (RMSE) of ChatGPT 3.0 in predicting correction angle in MWHTO was 2.96, suggesting a very poor model fit. Although ChatGPT 3.0 represents a significant breakthrough in large language models with extensive capabilities, it is not currently optimized to effectively perform complex pre-operative planning in orthopedic surgery, specifically in the context of MOWHTO. Further refinement and consideration of specific factors are necessary to enhance its accuracy and suitability for such applications.

A normal line congruence and minimal ruled Lagrangian submanifolds in [formula omitted

We characterize Lagrangian submanifolds in complex projective space for which each parallel submanifold along normal geodesics with respect to a unit normal vector field is Lagrangian, by using a normal line congruence of the Lagrangian submanifold to complex 2-plane Grassmannian and quaternionic Kähler structure. As a special case, we can construct minimal ruled Lagrangian submanifolds in complex projective space from an austere hypersurface in sphere with non-vanishing Gauss-Kronecker curvature.

Binary Differential Equations Associated to Congruences of Lines in Euclidean 3-Space

Binary Differential Equations Associated to Congruences of Lines in Euclidean 3-Space

Kinematic-geometry of a line trajectory and the invariants of the axodes

Abstract In this article, we investigate the relationships between the instantaneous invariants of a one-parameter spatial movement and the local invariants of the axodes. Specifically, we provide new proofs for the Euler-Savary and Disteli formulas using the E. Study map in spatial kinematics, showcasing its elegance and efficiency. In addition, we introduce two line congruences and thoroughly analyze their spatial equivalence. Our findings contribute to a deeper understanding of the interplay between spatial movements and axodes, with potential applications in fields such as robotics and mechanical engineering.

Mechanisms generating line trajectories

In this work the problem of designing mechanisms to guide a line along a ruled surface is considered. This is motivated by the idea of illustrating, by means of a physical model, the set of lines in a general linear line complex. Cylindrical symmetry implies that the problem reduces of designing a mechanism to move a line along the regulus of a rectangular hyperbolic paraboloid. This leads to the study of several simple ruled surfaces and congruences of lines. In particular the paper studies the regulus of the elliptical hyperboloid, the cylindroid and linear line congruences. In each case relatively simple mechanisms are designed to constrain a line in the mechanism to a given space of lines.

Kinematic Geometry of a Timelike Line Trajectory in Hyperbolic Locomotions

This study utilizes the axodes invariants to derive novel hyperbolic proofs of the Euler–Savary and Disteli formulae. The inflection circle, which is widely recognized, is situated on the hyperbolic dual unit sphere, in accordance with the principles of the kinematic theory of spherical locomotions. Subsequently, a timelike line congruence is defined and its spatial equivalence is thoroughly studied. The formulated assertions degenerate into a quadratic form, which facilitates a comprehensive understanding of the geometric features of the inflection line congruence.

A Study on a Spacelike Line Trajectory in Lorentzian Locomotions

In this study, we establish a novel Lorentzian interpretation of the Euler–Savary (E−S) and Disteli (Dis) formulae. Subsequently, we proceed to establish a theoretical structure for a Lorentzian torsion line congruence which is the spatial symmetry of the Lorentzian circling-point dual curve, in accordance with the principles of the kinematic theory of spherical locomotions. Further, a timelike (Tlike) torsion line congruence is defined and its spatial equivalence is examined. The findings contribute to an enhanced comprehension of the interplay between axodes and Lorentzian spatial movements, which has possible significance in various disciplines, such as the fields of robotics and mechanical engineering.

Projective geometry of homogeneous second-order Hamiltonian operators

We prove the invariance of homogeneous second-order Hamiltonian operators under the action of projective reciprocal transformations. We establish a correspondence between such operators in dimension n and 3-forms in dimension n + 1. In this way we classify second-order Hamiltonian operators using the known classification of 3-forms in dimensions . As a by-product, we identify such operators as linear line congruences, that are distinguished algebraic varieties in Plücker’s space of lines. Systems of first-order conservation laws that are Hamiltonian with respect to such operators are also explicitly found. The geometry and integrability of the systems is discussed in detail.

Supplementary Fibular-guided Growth in Treatment of Late-onset Blount Disease

Purpose: Blount disease is due to an idiopathic defect in the posteromedial proximal tibial physis resulting in increasing bowing of the leg in addition to lateral knee thrust with lateral collateral ligament laxity. Our rationale is that Blount disease has a bony and ligamentous laxity element of the lateral collateral ligament that can be corrected simultaneously through hemiepiphysiodesis of the tibia and epiphysiodesis of proximal fibula physis by cannulated screws. Patients and Methods: This is a retrospective study conducted on 23 limbs with tibia vara treated between 2010 and 2017 followed up for 2 to 6 years. Ages ranged from 9 to 13 years with a late-onset type of Blount disease. We used a percutaneous transphyseal fully threaded screws traversing the proximal tibial lateral hemiepiphysis, and another screw inserted traversing the proximal fibular epiphysis. Results: There was a statistically significant improvement of the radiographic parameters, especially in the form of joint line congruence angle in both supine and standing positions. All patients were clinically and radiographically completely corrected without complications, except 1 patient with a surgical site superficial infection, treated medically. Conclusion: Fibular-guided growth surgery with lateral proximal tibia epiphysiodesis is a minimally invasive technique that improves the corrective power of hemiepyphysiodesis of the posterolateral compartment of the knee. Level of Evidence: Level IV, retrospective case series.

Darboux integrability for diagonal systems of hydrodynamic type

We prove that (1) diagonal systems of hydrodynamic type are Darboux integrable if and only if the corresponding systems for commuting flows are Darboux integrable, (2) systems for commuting flows are Darboux integrable if and only if the Laplace transformation sequences terminate, (3) Darboux integrable systems are necessarily semihamiltonian. We give geometric interpretation for Darboux integrability of such systems in terms of congruences of lines and in terms of solution orbits with respect to symmetry subalgebras, discuss known and new examples.

The Artefactual Branch Effect and Phylogenetic Conflict: Species Delimitation with Gene Flow in Mangrove Pit Vipers (Trimeresurus purpureomaculatus-erythrurus Complex).

Mangrove pit vipers of the Trimeresurus purpureomaculatus-erythrurus complex are the only species of viper known to naturally inhabit mangroves. Despite serving integral ecological functions in mangrove ecosystems, the evolutionary history, distribution, and species boundaries of mangrove pit vipers remain poorly understood, partly due to overlapping distributions, confusing phenotypic variations, and the lack of focused studies. Here, we present the first genomic study on mangrove pit vipers and introduce a robust hypothesis-driven species delimitation framework that considers gene flow and phylogenetic uncertainty in conjunction with a novel application of a new class of speciation-based delimitation model implemented through the program Delineate. Our results showed that gene flow produced phylogenetic conflict in our focal species and substantiates the artefactual branch effect where highly admixed populations appear as divergent nonmonophyletic lineages arranged in a stepwise manner at the basal position of clades. Despite the confounding effects of gene flow, we were able to obtain unequivocal support for the recognition of a new species based on the intersection and congruence of multiple lines of evidence. This study demonstrates that an integrative hypothesis-driven approach predicated on the consideration of multiple plausible evolutionary histories, population structure/differentiation, gene flow, and the implementation of a speciation-based delimitation model can effectively delimit species in the presence of gene flow and phylogenetic conflict.

Spacelike Lines with Special Trajectories and Invariant Axodes

The association between the instantaneous invariants of a one-parameter Lorentzian spatial movement and the spacelike lines with certain trajectories is considered in this study. To be more precise, we present a theoretical formulation of a Lorentzian inflection line congruence, which is the spatial symmetrical of the inflection circle of planar kinematics. Finally, we establish novel Lorentzian explanations for the Disteli and Euler–Savary formulae. Our results add to a better understanding of the interaction between axodes and Lorentzian spatial movements, with potential implications in fields such as robotics and mechanical engineering.

Singularities of generic line congruences

Line congruences are 2-dimensional families of lines in 3-space. The singularities that appear in generic line congruences are folds, cuspidal edges and swallowtails. In this paper we give a geometric description of these singularities. The main tool used is the existence of an equiaffine pair defining a generic line congruence.

Effect of joint line orientation parameters on initial bone resection in mechanically aligned total knee arthroplasty: a retrospective clinicoradiological correlation study

BackgroundDiscrepancies in bone resection between the medial and lateral compartments are very common in total knee arthroplasty (TKA) when mechanical alignment (MA) is used. The purpose of this study was to explore whether and how joint line orientation affects the initial bone resection in mechanically aligned TKA.MethodsA total of 194 patients (225 knees) diagnosed with osteoarthritis (OA) were included. Virtual bone resection was conducted in the coronal view using full-length weight-bearing radiographs according to the technical requirements of MA, and the reliability of the virtual resection was verified via intraoperative caliper measurements. Correlation and regression analyses were conducted between the initial bone resection within the extension gap (EG) and various parameters, including the hip-knee-ankle (HKA) angle, mechanical lateral distal femoral angle (mLDFA), joint line congruence angle (JLCA), and medial proximal tibial angle (MPTA). Moreover, the correlation between intraoperative bone resection adjustments and joint line orientation parameters was also investigated.ResultsAll knees in the current case series were artificially divided into 4 subgroups: subgroup 1, containing 148 varus knees (65.8%) with valgus femurs; subgroup 2, containing 48 varus knees (21.3%) with varus femurs; subgroup 3, containing 17 valgus knees (7.6%) with varus tibias; and subgroup 4, containing 12 valgus knees (5.3%) with valgus tibias. In subgroup 1, the mLDFA and MPTA were positively correlated with the initial bone resection with regression coefficients of 0.670 and 0.089, respectively. Moreover, in all varus knees, intraoperative bone resection adjustments were negatively correlated with mLDFA and MPTA, with categorical regression coefficients of -0.426 and − 0.230, respectively.ConclusionWhen MA-TKAs are performed in varus knees with valgus femurs, the initial bone resection within the EG is mainly positively correlated with mLDFA, while the intraoperative bone resection adjustment is significantly correlated with mLDFA and MPTA in all varus knees.

Robotic-assisted medial unicompartmental knee arthroplasty restores estimated pre-arthritic coronal limb alignment: A retrospective cohort study

BackgroundRobotic-assisted medial unicompartmental knee arthroplasty (UKA) aims to restore pre-arthritic (constitutional) limb alignment, by re-tensioning of the medial collateral ligament (MCL). This study aimed to determine whether pre-arthritic coronal alignment was restored following robotic-assisted medial UKA in patients with medial compartment osteoarthritis. MethodA retrospective study was undertaken, including 102 patients with a unilateral robotic-assisted medial UKA and a contralateral unaffected knee. Both the validated arithmetic hip-knee-ankle angle (aHKA) and alignment of the contralateral unaffected knee were used to estimate pre-arthritic alignment. The aHKA is a radiographic method to estimate the pre-arthritic mechanical hip-knee-ankle angle (mHKA). To verify restoration of pre-arthritic alignment, postoperative mHKA was compared to the aHKA. Additionally, postoperative mHKA, joint line congruence (JLCA), and knee joint line obliquity (KJLO) angles were compared between the operative and contralateral unaffected knee. Equivalence between postoperative and pre-arthritic alignment was assessed through the two-one-sided t-test (TOST), using equivalence margins of ±2.0°. ResultsPostoperative mHKA was equivalent to the aHKA (mean difference −0.38°, 90% CI −0.69 to −0.07;p < .001), with 93 knees (91%) restored within 3.0° of their aHKA. Postoperative mHKA, JLCA and KJLO were equivalent between the operative and contralateral unaffected knees, with mean differences of −0.65°, −0.65°, and −0.40°, respectively; all p < .001. ConclusionsPostoperative and pre-arthritic coronal alignment were equivalent following robotic-assisted medial UKA, with 91% of knees restored within 3.0° of their pre-arthritic mechanical axis. These results demonstrate that both mechanical alignment and joint line congruence are restored by MCL re-tensioning in patients undergoing robotic-assisted medial UKA for medial compartment osteoarthritis.

Kinematic alignment in total knee arthroplasty: a five-year prospective, multicentre, survivorship study.

AimsThe mid-term results of kinematic alignment (KA) for total knee arthroplasty (TKA) using image derived instrumentation (IDI) have not been reported in detail, and questions remain regarding ligamentous stability and revisions. This paper aims to address the following: 1) what is the distribution of alignment of KA TKAs using IDI; 2) is a TKA alignment category associated with increased risk of failure or poor patient outcomes; 3) does extending limb alignment lead to changes in soft-tissue laxity; and 4) what is the five-year survivorship and outcomes of KA TKA using IDI?MethodsA prospective, multicentre, trial enrolled 100 patients undergoing KA TKA using IDI, with follow-up to five years. Alignment measures were conducted pre- and postoperatively to assess constitutional alignment and final implant position. Patient-reported outcome measures (PROMs) of pain and function were also included. The Australian Orthopaedic Association National Joint Arthroplasty Registry was used to assess survivorship.ResultsThe postoperative HKA distribution varied from 9° varus to 11° valgus. All PROMs showed statistical improvements at one year (p < 0.001), with further improvements at five years for Knee Osteoarthritis Outcome Score symptoms (p = 0.041) and Forgotten Joint Score (p = 0.011). Correlation analysis showed no difference (p = 0.610) between the hip-knee-ankle and joint line congruence angle at one and five years. Sub-group analysis showed no difference in PROMs for patients placed within 3° of neutral compared to those placed > 3°. There were no revisions for tibial loosening; however, there were reports of a higher incidence of poor patella tracking and patellofemoral stiffness.ConclusionPROMs were not impacted by postoperative alignment category. Ligamentous stability was maintained at five years with joint line obliquity. There were no revisions for tibial loosening despite a significant portion of tibiae placed in varus; however, KA executed with IDI resulted in a higher than anticipated rate of patella complications.Cite this article: Bone Jt Open 2022;3(8):656–665.

A Uniqueness Theorem for Incompressible Fluid Flows with Straight Streamlines

It is proven that the only incompressible Euler fluid flows with fixed straight streamlines are those generated by the normal lines to a round sphere, a circular cylinder or a flat plane, the fluid flow being that of a point source, a line source or a plane source at infinity, respectively. The proof uses the local differential geometry of oriented line congruences to integrate the Euler equations explicitly.