Step Of Procedure Research Articles

Anterior Cruciate Ligament Reconstruction: Common Intraoperative Mistakes and Techniques for Error Recovery.

Anterior cruciate ligament (ACL) reconstruction is a commonly performed procedure among general orthopedists, and is a logged procedure required for graduation from accredited orthopaedic residency programs. ACL reconstruction surgery has a number of critical steps, and intraoperative errors can significantly impact the success rate and morbidity of this operation. Technical errors are frequently cited as some of the most common reasons for ACL reconstruction failure. This narrative review provides low-volume surgeons and trainees with an overview of the common errors that can be made during the critical steps of an ACL reconstruction procedure. We suggest technical points for avoiding commonly-encountered errors and provide a description of evidence-supported error recovery techniques to address these errors if they occur intraoperatively. These key steps include femoral tunnel creation, tibial tunnel creation, graft harvest and preparation, and graft fixation within the tunnels. We discuss a number of primary and backup fixation strategies as well as all commonly used autografts (bone-patellar tendon-bone, hamstring, and quadriceps tendon). Additionally, we provide a brief overview on address intra-operative graft contamination citing currently available evidence.

Microlearning in Complex Surgical Oncology: Proof of Concept and Impact on Surgical Skills Acquisition During Residency.

Recent structural changes to residency programs, such as workforce shortages and work-hour restrictions, have reduced operating room exposition for residents in surgical specialties. Complementary strategies need to be developed to support surgical educators and provide residents with the optimal learning environment. This study aimed to assess the feasibility of integrating microlearning in a general surgery residency program and to evaluate its impact on surgical skills acquisition in surgical oncology. An online module structured in six different microlearning units was created. Each unit was designed to present key concepts of a specific surgical procedure, including anatomic landmarks, series of standardized steps, and a narrated video. The procedures included were right and left hepatectomy, cytoreductive surgery with hyperthermic intraperitoneal chemotherapy, total/subtotal gastrectomy, pancreatoduodenectomy, and distal pancreatectomy. The study included 20 general surgery residents completing a 3-month rotation in complex surgical oncology, 10 of whom had access to the online module. The participants in both groups completed a self- assessment survey at the conclusion of the study. The residents who had access to the online module exhibited greater comfort regarding theoretical aspects of the procedures (p = 0.0322) and increased confidence performing procedural steps of the procedures (p = 0.0433) at the end of their rotation. Most of the residents considered the module to be highly beneficial to their learning. All the residents considered the online module helpful in preparing for real-life scenarios. The study demonstrated the feasibility and potential benefits of introducing a microlearning environment to enhance residents' knowledge and behavior in complex surgical oncology.

Evaluating the Performance of Peak Calling Algorithms Available for Intracellular G-Quadruplex Sequencing

DNA G-quadruplexes (G4) are non-canonical DNA structures that play key roles in various biological processes. Antibody-dependent sequencing is an important tool for identifying intracellularly formed DNA G4s, and peak calling is a crucial step in processing the sequencing data. As the applicability of existing peak calling algorithms to intracellular G4 data has not been previously assessed, we systematically compared and evaluated these algorithms to determine those best suited for G4 detection. We selected seven representative candidates from 43 published peak calling algorithms for detailed evaluation. The performance of each candidate on six published intracellular G4 sequencing datasets (GSE107690, GSE145090, GSE133379, GSE178668ChIP-seq, GSE178668CUT&Tag, GSE221437) were assessed by precision and recall against customized benchmarks integrating results from multiple algorithms, as well as consistency with known G4 information (pG4 predicted by pqsfinder, oG4 from GSE63874, and multi-cell-line conserved G4s) and epigenetic signals. We identified MACS2, PeakRanger, and GoPeaks as the most effective algorithms for analyzing intracellular G4 sequencing data, and attributed their superior performance partially to the distribution model of sequencing reads/fragments used in the hypothesis testing step of the peak calling procedures. These findings provide guidance and rationale for selecting peak callers appropriate for intracellular G4 data.

Selection of Low-Carbon Contractors in a Fuzzy Multi-Objective Environment

The selection of contractors entails multiple uncertainties, including the lack of clear delineation of contractor qualifications, ambiguity surrounding project manager capabilities, and the uncertain nature of carbon emissions. These uncertainties compound the complexity involved in genuinely evaluating and choosing contractors. This paper establishes a fuzzy multi-objective contractor selection model that accounts for cost reduction, optimization of contractor qualifications, organizational management enhancement, carbon emissions reduction, and reputation optimization. Leveraging the Fuzzy Analytic Hierarchy Process (F-AHP) and Fuzzy Compromise Programming (F-CP) methods, we have devised a fuzzy multi-objective contractor selection model and outlined the procedural steps for its implementation. A case study was conducted to validate the effectiveness of the model we proposed.By applying this model to the case, we successfully transformed the complex multi-objective programming into a straightforward single-objective linear programming. Furthermore, based on the model, the weights assigned to cost, qualification indicators, management level, carbon emissions, and contractor reputation are 0.54, 0.09, 0.05, 0.19, and 0.13, respectively. By solving the model, we were able to identify the most suitable contractor.This paper aids the decision-making process in selecting an appropriate low-carbon contractor.

Technical note: A fast and reproducible autosampler for direct vapor equilibration isotope measurements

Abstract. To investigate water movement in environmental systems, stable isotope (2H and 18O) ratios of water are commonly used tracers. Analyzing the isotopic ratios of water in or adsorbed to substances like soil or plant tissue necessitates the extraction or equilibration of water prior to analysis. One such method, direct vapor equilibration, is popular due to its cost-effectiveness and straightforward sample processing. However, sample analysis requires significant manual labor, thereby limiting the number of samples that can be analyzed. This limitation is compounded by the fact that stored samples undergo evaporative isotopic changes over time. Moreover, manual measurements require many laborious procedural steps that can easily compromise reproducibility. The operator has to subjectively decide if the measurements are stable and then record the analyzer readings. To address these challenges, we have developed a system that automates the analysis process. Our autosampler for vapor samples, named VapAuSa, features a modular design that allows for up to 350 ports for direct vapor equilibration samples. These ports sequentially connect the prepared samples to a laser isotope analyzer, enabling continuous automated measurements. Within the accompanying software, measurement criteria can be specified, facilitating reproducible analysis. The developed system was tested by co-measuring 90 soil samples and 21 liquid water samples with known δ values. VapAuSa measurements have a negligible measurement bias (<1×10-13 ‰ for both δ2H and δ18O) and similar measurement repeatability compared to manual analysis of identical samples (δ2H=±4.5 ‰ and δ18O=±0.58 ‰ for VapAuSa measurements vs. δ2H=±5.7 ‰ and δ18O=±0.37 ‰ for manual analysis). However, the increased sample throughput minimizes storage-induced isotopic changes. Moreover, VapAuSa triples sample throughput per week while also reducing the direct labor time to just 10 % of that required for manual processing.

"At the Table or Behind the Curtain":A Randomized Study to Evaluate the Influence of Students' Position in Theatre-Based Learning.

The influence of students' positioning within the theatre on their learning progress is unknown. The present study aimed to investigate whether position of undergraduate medical students in the operating theatre-at the operating table or behind surgical drapes-influences their learning. We conducted a single-blind prospective randomized study with 2 parallel arms. Undergraduate medical students allocated to the operating theatre in the course of the regular surgical curriculum were invited to participate. Participants were randomly assigned to either a position at the operating table, or behind surgical drapes during a visit to the operating theatre. After surgery, the students prepared sketches of essential procedural steps, which were evaluated by 3 independent surgeons using a predefined scoring system in a blinded fashion. Additionally, students were asked to answer a questionnaire for comparative self-assessment of pre- and postvisit knowledge concerning 4 aspects: routines within the theatre, sterile behaviour, essential procedural steps of the surgery and insight into the work of a surgical resident. In total, 84 sketches and questionnaires (= 42 surgeries) were evaluated. Sketches prepared by the group positioned at the operating table reached significantly higher scores with regard to the essential procedural steps of the surgery (p = 0.012). Comparative self-assessment revealed a significant learning progress, with no significant difference between the groups. Visiting the operating theatre significantly improved undergraduate medical students' understanding of procedural steps and theatre-specific routines regardless of the position within the theatre. However, specific knowledge of surgical procedures is significantly was enhanced when students are positioned at the operating table rather than behind the surgical drapes. Appropriate structures, enabling involvement of students directly at the operating table, should be enforced in hospitals partaking in undergraduate surgical education.

Protocol for oral fecal gavage to reshape thegutmicrobiota in mice.

Fecal microbiota transplantation (FMT) is clinically applied, while oral FMT (oral fecal gavage [OFG]) is preferred for experimental mice. Here, we present a protocol for OFG in antibiotic-pretreated mice, demonstrating the progressive, time-dependent evolution of the gut microbiota in the recipients. We describe steps for fecal sample collection and preparation procedures, oral gavage, and monitoring gut microbiota changes. This protocol serves as a general guide forreshaping the gut microbiota in recipient mice for various experimental applications. For complete details on the use and execution of this protocol, please refer to Yang etal.1.

Functional Near-Infrared Spectroscopy Hyperscanning Study in Psychological Counseling.

Functional Near-Infrared Spectroscopy (fNIRS) hyperscanning is an innovative technique that enables real-time monitoring of brain activity among multiple individuals engaged in social interactions. Researchers in this field quantify concurrent brain activities through the index of inter-brain synchrony (IBS). In psychological counseling research, the use of fNIRS to measure IBS has garnered attention for its potential to illuminate the dynamics of counselor-client interactions. Nevertheless, the field currently lacks a standardized protocol for precisely measuring IBS between counselors and clients, which would facilitate the revelation of real-time interaction patterns during counseling sessions. To address this need, this paper proposes a detailed standardized protocol, outlining the procedural steps for conducting fNIRS hyperscanning in psychological counseling settings, focusing on the acquisition of brain signals, calculation of IBS between counselors and clients, and analysis of lead-lag patterns of IBS throughout counseling sessions. Implementing this standardized fNIRS hyperscanning pipeline not only enhances the reproducibility and reliability of IBS measurements in psychological counseling research but also facilitates deeper insights into the neural mechanisms underlying working alliance. By integrating fNIRS hyperscanning into naturalistic counseling environments, researchers can advance understanding of how IBS correlates with counseling outcomes, potentially informing personalized approaches to mental health treatment.

Revealing the nature of mathematical procedural knowledge by analysing students’ deficiencies and errors

In this paper, error analyses are used to reveal the nature of mathematical procedural knowledge. In particular, the aim is to empirically confirm the structure of procedural knowledge described in theory and to further differentiate the corresponding terms. In this context, the coding of the processing of procedural tasks by students at the end of their high school years (n = 455) shows that knowledge of the procedure and arithmetic/algebraic skills can be objectively reconstructed as components of procedural knowledge. The analyses show that procedural knowledge and corresponding difficulties become visible in many ways when working on relevant tasks and that anecdotal experiences about a lack of mathematical procedural knowledge among students must fall short. The didactic implication is that the support of procedural knowledge acquisition needs to be both individualised and task specific. The results also reveal interesting correlations between deficiencies and errors in the processing of procedural tasks and specific item characteristics. For example, deficiencies in knowledge of the procedure tend to occur more frequently in tasks at higher grade levels and in analysis, while specific errors in arithmetic/algebraic skills are more likely to be found in algebra and tasks that require more procedural steps.

Enhancing Clinical Insights: New Radiographic Grading for Lumbar Facet Joint Degeneration, A Reliability Study.

Lumbar facet joint diseases can often lead to reduced work efficiency and increased medical costs. As a primary imaging tool in orthopedics, X-rays offer numerous advantages. However, there is no consensus on the classification of lumbar facet joints based on X-ray imaging. This study was conducted for 356 patients between November 2017 and September 2023. A senior radiologist and a senior orthopedic surgeon discussed and established a grading system for lumbar facet joints based on both X-ray and MRI findings. Two double-blind attending spinal surgeons were asked to evaluate and grade the included cases. The intra-rater reliability and inter-rater reliability were evaluated by assessing the weighted kappa (κw) coefficient. The level of inter-rater reliability of MRI for complete agreement was good for Doctor A (κw = 0.792) and Doctor B (κw = 0.869). The inter-rater reliability coefficient for grading lumbar facet joint degeneration based on the radiograph was as follows: for Doctor A (κw = 0.702, session 1; κw = 0.847, session 2) and Doctor B (κw = 0.714, session 1; κw = 0.828, session 2). Moreover, the level of intra-rater reliability based on X-ray for complete agreement was excellent for Doctor A (κw = 0.843) and Doctor B (κw = 0.836). We propose a new grading system for lumbar facet joint degeneration based on X-rays, which serves as a supplement to the Weishaupt and Pathria classifications. This grading system aims to provide clinicians with a more comprehensive understanding of lumbar facet joint degeneration, allowing for the use of a broader range of diagnostic tools to evaluate facet joint degeneration from multiple perspectives. We believe that this grading system can be valuable in assessing potential anatomical changes related to the facet joint, thereby informing modifications to surgical techniques and procedural steps.

Glenoid-Anchor Cerclage for the Unstable Reverse Shoulder Arthroplasty: A Surgical Technique

Instability following reverse shoulder arthroplasty (RSA) is a notable complication, with challenges arising from various surgical and patient-specific factors that negatively impact the glenohumeral compressive forces necessary for RSA stability. This paper introduces a novel glenoid-anchor cerclage technique to address the instability in high-risk RSA cases. By placing an all-suture anchor superiorly above the glenosphere and integrating it through a transosseous tunnel through the greater tuberosity, this method serves as an adjunct for improving stability by counteracting superior and anterior translation. Here, we detail our preferred procedural steps, preoperative considerations, and postoperative management for this approach, emphasizing its potential to reduce recurrent instability.

Advancements in Temporomandibular Joint Arthroscopy: Refinements in Surgical Techniques for Treating the Superior Joint Spaces.

This study introduces a novel technique for arthroscopic surgery of the temporomandibular joint (TMJ), developed by the first author. Traditional TMJ arthroscopy techniques typically utilize a reference plane extending from the lateral canthus to the tragus, which may misalign with the zygomatic arch and create technical challenges during percutaneous joint access. The proposed method addresses these limitations by leveraging coronal and sagittal tomographic measurements alongside 3-dimensional reconstructions to determine precise and anatomically appropriate entry points. The inclusion of a 3-port video arthroscopy system enhances intraoperative visualization and access to the superior joint spaces. Compared with conventional techniques, this refined method demonstrates increased procedural efficiency, improved safety, simplified technical execution, and enhanced reproducibility. Detailed procedural steps are presented, supplemented with illustrative diagrams to ensure clarity and replicability. This innovative approach significantly advances surgical maneuverability, allowing for a comprehensive assessment and treatment of the glenoid fossa, condyle, and articular disc while minimizing the risk of iatrogenic complications often associated with traditional techniques.

Dry Bondable Porous Silk Fibroin Films for Embedding Micropatterned Electronics in Hierarchical Silk Nacre.

Future structural materials is not only be lightweight, strong, and tough, but also capable of integrating functions like sensing, adaptation, self-healing, deformation, and recovery as needed. Although bio-inspired materials are well developed, directly integrating microelectronic patterns into nacre-mimetic structures remains challenging, limiting the widespread application of electronic biomimetic materials. Here, an in situ freeze-drying method is reported for the successful preparation of porous silk fibroin materials that can achieve dry bonding. The in situ freeze-drying method preserves the structural integrity of the lyophilized membrane while reducing procedural steps, achieving control over pore gradient not feasible with traditional freeze-drying techniques. By leveraging their smooth surfaces and capacity to support heat transfer patterns, layer-by-layer assembly at a macroscopic scale is achieved. The material's excellent mechanical properties, controllable graded structure, and adjustable degradation behavior enable the construction of electronically functionalized hierarchical structures. Additionally, the dry-state, layer-by-layer bonding method for porous polymer films provides advantages in precision control, mechanical stability, functional versatility, hierarchical structuring, and scalability. It represents an innovative approach, offering multi-functional and customizable bulk materials, especially suited for biomedical applications. This work offers an effective pathway for developing high-performance and multifunctional biomimetic devices with controllable hierarchical structures.

MHealth Apps in German Outpatient Mental Health Care: Protocol for a Mixed Methods Approach.

Mental disorders are complex diseases that affect 28% (about 17.8 million people) of the adult population in Germany annually. Since 2020, certain mobile health (mHealth) apps, so-called digital health applications (DiGA), are reimbursable in the German statutory health insurance system. A total of 27 of the 56 currently available DiGA are approved for the treatment of mental and behavioral diseases. An indicator of existing problems hindering the use of DiGA is the rather hesitant prescribing behavior. This project aims to develop health policy recommendations for the optimal integration of DiGA into outpatient psychotherapeutic care. The project is funded by the Innovation Fund of the Joint Federal Committee (grant 01VSF22029). The current status quo of the use of DiGA will be analyzed. Furthermore, concepts for the integration of mHealth apps, as well as their transfer into the care process will be investigated. In addition, barriers will be identified, and existing expectations of different perspectives captured. The project will be based on a mixed methods approach. A scoping review and a qualitative analysis of focus groups and expert interviews will be carried out. Additionally, an analysis of claims data of the statutory health insurance will be conducted. This will be followed by a written survey of insured persons and health care providers. Finally, health policy recommendations will be derived in cooperation with stakeholders. The scoping reviews and qualitative analyses have been completed, and the quantitative surveys are currently being carried out. The target number of responses in the survey of insured persons has already been achieved. Furthermore, the analysis claims data of the statutory health insurance is currently being conducted. There is a need for research on how DiGA can be optimally integrated into the care process of patients with mental disorders as evidence regarding the topic is limited and prescribing behavior low. Although the potential of DiGA in mental health care has not yet fully unfolded, Germany serves as a model for other countries regarding reimbursable mHealth apps. This project aims to explore the potentials of DiGA and to describe the organizational, institutional, and procedural steps necessary for them to best support mental health care. DERR1-10.2196/56205.

Innovative Modifications in Diamond Umbilicoplasty: Simplified Techniques for Improved Cosmetic Results.

Umbilicoplasty is one of the main steps in abdominoplasty procedures. Various techniques of umbilicoplasty are performed by surgeons from diverse backgrounds, all aiming for a naturally appearing umbilicus with minimal scarring. In this report, we present two umbilicoplasty methods practiced at our center. The key steps involved in both techniques include securing the umbilicus in its new position, creating a natural umbilical depth, and preventing visible scarring. These two methods are easily reproducible, time-effective, and consistently yield aesthetically pleasing results. We also discuss alternative umbilicoplasty methods performed in other facilities.

Efficient Solution of Sequences of Parametrized Lyapunov Equations With Applications

ABSTRACTSequences of parametrized Lyapunov equations can be encountered in many application settings. Moreover, solutions of such equations are often intermediate steps of an overall procedure whose main goal is the computation of , where denotes the solution of a Lyapunov equation and is a given matrix. We are interested in addressing problems where the parameter dependency of the coefficient matrix is encoded as a low‐rank modification to a seed, fixed matrix. We propose two novel numerical procedures that fully exploit such a common structure. The first one builds upon the Sherman‐Morrison‐Woodbury (SMW) formula and recycling Krylov techniques, and it is well‐suited for small dimensional problems as it makes use of dense numerical linear algebra tools. The second algorithm can instead address large‐scale problems by relying on state‐of‐the‐art projection techniques based on the extended Krylov subspace. We test the new algorithms on several problems arising in the study of damped vibrational systems and the analyses of output synchronization problems for multi‐agent systems. Our results show that the algorithms we propose are superior to state‐of‐the‐art techniques as they are able to remarkably speed up the computation of accurate solutions.

Intrafascial Colpotomy, Edge-to-Edge Closure, and Peritoneal Graft Technique for Minimizing Mesh Erosion in Concurrent Robotic Hysterectomy and Sacrocolpopexy.

Sacrocolpopexy (SCP) is a recognized treatment for apical pelvic organ prolapse (POP). However, mesh erosion remains a concern, particularly when performed with concomitant hysterectomy. This video presents data on one case of a modified technique aimed at potentially minimizing mesh erosion in robotic SCP. This technique focuses on reinforcing the vaginal cuff and using a pedicled peritoneal graft to create a tissue barrier between the mesh and the vaginal vault. Procedural steps include intrafascial colpotomy, edge-to-edge cuff closure using barbed sutures, and joining anterior and posterior meshes away from the vaginal cuff. The surgical technique was successfully implemented in this single patient presented in the video and was performed in ten more patients with no intraoperative or postoperative complications. During the follow-up period, there were no signs of mesh erosion or exposure. This approach emphasizing vaginal cuff strengthening and mesh separation using a pedicled peritoneal graft can be an option for reducing mesh erosion risk. This report does not provide definitive evidence that this approach reduces mesh erosion risk and further research and long-term follow-up are required to validate these findings and integrate this technique into standard management practices.

An efficient droplet-vitrification cryopreservation procedure for high imperatorin-yielding hairy root clones of Urena lobata

The valuable anti-cancer and anti-inflammatory secondary metabolite, imperatorin, has been found in the hairy roots (HRs) of Urena lobata. However, an increasing number of problems related to cryo-injury and cryoprotectant toxicity could potentially reduce the quality of root clones, highlighting the need to develop a reliable technique for long-term preservation. Based on the impact of the successive steps of the initial droplet-vitrification procedure employed for cryopreservation of HRs using the histological evaluation of plasmolysis, various selected factors were independently investigated. The maximum plasmolysis was observed after the preculture with 0.5 M sucrose (46.59 %) and the dehydration treatment (48.32 %). In the improved cryopreservation procedure, when prolonged preculture for 72 h in liquid WPM with 0.3 M sucrose and dehydration in the appropriate vitrification solution, which included 30 % (w/v) glycerol and 50 % (w/v) sucrose, for 10 min at 0 °C, the plasmolysis in the two steps was significantly reduced in comparison with the untreated control. The cryopreserved HRs could increase their regeneration to 93.3 % and regenerated root length to 4.65 cm. Their growth and imperatorin production were almost the same as those of untreated controls after three to five subsequent subcultures. Our results have demonstrated that our new approach, which only focuses on the key factors that significantly increase the plasmolysis, modifies their level to fit with the HR cells of U. lobata. The early application of the plasmolysis evaluation method may immediately screen the impact of factors on individual root cells instead of spending time and cost evaluating the recovery of root tips at each step to develop an efficient cryopreservation procedure.

Topology Optimization of Periodic Cellular Materials through the Progressive Directional Selection Method and Finite-Volume Theory

This investigation presents the Progressive Directional Selection (PDS) method to optimize the topology of periodic cellular materials, achieving high performance and minimal weight. The homogenized elastic properties of cellular materials are determined using the homogenization method applied to periodic materials based on the unit cell concept as an intermediate step of the topology optimization procedure. The literature often constructs the design domain to conduct a finite element analysis. However, some problems are related to numerical issues, such as the checkerboard pattern and mesh dependence. The checkerboard effect is related to the assumptions of the finite element method, as the satisfaction of equilibrium and continuity conditions at the element nodes, particularly for linear triangular and quadrilateral discretizations in the absence of regularization schemes. This problem can be overcome by the Finite-Volume Theory (FVT), which satisfies the equilibrium equations at the subvolume level, and the compatibility conditions are established through the adjacent subvolume interfaces. The PDS method is inspired by natural selection processes found in biology and employs a strategy to meet the objective function of a discretized analyzed domain subject to a volume constraint. Population selection is based on performance criteria specific to the problem through an iterative process that concludes when the optimized topology ceases to evolve. Numerical examples of topology optimization for materials with periodic cellular microstructures are analyzed using PDS and FVT.

A formulation of the fast multipole boundary element method applied to the analysis of anisotropic materials under body forces

This work presents a formulation of the boundary element method with fast multipole expansion (MECMP) applied to the analysis of anisotropic elastic materials subject to body forces. Integral equations are obtained using the Somigliana identity. Integrals are divided into near field and far field. Near field, when the source points and integration elements are close, are treated as in the standard boundary element method, that is, integrating along the element and considering the interaction between source points (nodes) and the elements. On the other hand, in the far field, when the source points and integration elements are far away, the fast multipole method is applied. In this case, the fundamental solution is expanded in a Laurent series and the node-to-node interaction is replaced by a cell-to-cell interaction. Cells are generated by a hierarchical decomposition of the domain using the quad-tree algorithm. Different fast multipole operations are used to take advantage of the hierarchical domain decomposition and expansions of the fundamental solutions. Influence matrices are never explicitly obtained and the matrix-vector product are carried out with linear complexity. The linear system is solved by an iterative method. A preconditioning matrix is used to reduce the number of iterations to obtain a result with an specified accuracy. Effectiveness and efficiency in solving large-scale problems are discussed. The treatment of problems involving body forces are taken into account by the utilization of the modified boundary condition method. This approach entails augmenting the boundary condition with a specific solution tailored to the problem. Following the solution of the linear system, the particular solution is subsequently subtracted from both displacements and tractions. Importantly, this procedural step obviates the need for generating additional vectors or matrices within the matrix equation. The formulation presented in this article is based on a representation of complex variables of the integrands, similar to the formulation previously developed for potential (scalar) problems. Validation is carried out by comparing the results obtained by the two formulations: the standard boundary element method and the boundary element method with fast multipole expansion. The influence of the number of terms of the series expansion in the calculation of fundamental solutions and influence matrices is analyzed. Numerical examples are presented to demonstrate the efficiency, accuracy, and potential of the boundary element method with fast multipole expansion to solve large-scale problems, i.e., with tens of thousands of degrees of freedom.