Point Angle Research Articles

Can Cadaver Testing Replicate In Vivo Kinematics of Total Knee Arthroplasty?

Whether the kinematics of cadaveric knees recreate those of the patient's knees after total knee arthroplasty (TKA) remains unknown. This study compared in vivo and in vitro fluoroscopic kinematics of knees after TKA during knee bending using the same implant design. Patients who had undergone cruciate-retaining and cruciate-substituting total knee arthroplasty (CR-TKA and CS-TKA) did squatting motions. Fresh-frozen human cadaveric knees were tested under dynamic closed-chain knee extension in an Oxford knee rig. Fluoroscopic kinematics were measured in vivo and in vitro using a 2-dimensional to 3-dimensional registration technique. The axial rotation angle and anterior-posterior translation of medial and lateral contact points of the femoral implant relative to the tibial implant was evaluated in each flexion angle. No notable differences in the axial rotation angles were found between in vivo and in vitro measurements in both CR-TKA and CS-TKA. In early flexion, the medial and lateral contact points in cadaver knees were located more posterior than those in in vivo after CR-TKA. From early flexion to high flexion, the medial and lateral contact points in cadaver knees were located more posterior than those in in vivo after CS-TKA. The axial rotation angle of cadaveric knees in the Oxford knee rig was similar to that measured in vivo after TKA. However, the anterior-posterior location of the femoral implant in cadaver knee was more posterior than that in in vivo knees after TKA.

Effect of Ankle Joint Flexion Angle on Lower Extremity Muscle Activity and Break Point Angle during Nordic Hamstring Exercises in Amateur Soccer Players

Effect of Ankle Joint Flexion Angle on Lower Extremity Muscle Activity and Break Point Angle during Nordic Hamstring Exercises in Amateur Soccer Players

Novels by A.A. Zinoviev as works of a new genre

The article analyzes the novels of A.A. Zinoviev from the perspective of genre specificity and artistic techniques that the author inherits from previous literature. Proximity to the artistic traditions of M.E. Saltykov-Shchedrin and J. Swift’s texts allow us to consider Zinoviev’s texts in the context of world artistic culture, but the peculiarities of the organization of the novel space and the angle of the writer's point of view on social reality indicate that his novels do not fit into the usual genre canons and should be considered as sociological novels. The results obtained expand the traditional understanding of the genre of the novel, describe interesting author’s intentions of the world order, reveal the relationship between the artistic word and sociological statistical data, and give impetus to further research of the creative work of an extraordinary writer.

Mapping the localization of the facial artery and vein at the inferior border of the mandible for clinical applications.

To spatially map the position of the facial artery and vein along the inferior border of the mandible based on specific facial reference points. This cross-sectional study included 40 sides of 21 formalin-fixed cadaver heads (11 female, 10 male) with a mean age of 72.92 ± 11.72years. Superficial dissection was performed to visualize the facial artery and vein at the inferior border of the mandible (FA and FV). Measurements were taken from the FA and FV to various facial landmarks using a digital caliper and medical protractor. Statistical analysis was conducted using Shapiro-Wilk, independent sample t-tests, and paired sample t-tests. The mean distance between FA and FV was 6.20 ± 2.97mm. Distances from FA and FV to gnathion, oral commissure, nasal wing, lateral canthus, angle of mandible, intertragic notch, and Manson's point were determined, with no significant differences found between sides and genders (p > 0.05). The closest distances from FA and FV to the line between the intertragic notch and oral commissure were 38.63 ± 4.86mm and 37.78 ± 5.28mm, respectively. The angular measurements of FA and FV with inferior border of mandible were 61.45 ± 13.71 and 76.56 ± 10.17 degrees, respectively. The angle between intertragic notch, FA and oral commisure was 102.40 ± 11.12 degrees. The detailed measurements and analysis provided in this study aim to enhance the precision of surgical interventions involving the facial artery and vein. The practical localization methods proposed can assist in minimizing the risk of vascular injuries, improving outcomes in reconstructive and aesthetic procedures.

Multi response optimization of process parameters in titanium alloy minimum quantity lubrication drilling operation

Abstract This work investigates the application of minimal quantity lubrication (MQL) in the drilling process, where a combination of liquid and air creates an aerosol in the form of a fine mist. This protective layer decreases friction and tool wear, hence improving overall efficiency. The study examines the conventional Gulfcut oil blend drilling technique to enhance drilling performance on the titanium alloy Ti-6Al-4V under MQL circumstances. The key drilling parameters, namely spindle speed (N), feed rate (F), and point angle (D), were analyzed using a Taguchi L16 orthogonal array. The experimental inquiry aimed to identify the most favorable conditions that lead to the least amount of torque (TQ), thrust force (TF), and surface roughness (SR). An Analysis of Variance (ANOVA) was used to examine the impact of control factors on drilling performance. The optimized drilling parameters led to a reduction in torque, thrust force, and surface roughness by 12.88%, 21.29%, and 25.76%, respectively. Furthermore, microstructure analysis demonstrated that the Gulfcut lubricant plays a pivotal role in reducing grain size during drilling. This research provides valuable insights into optimizing drilling conditions for titanium alloy using a conventional Gulfcut oil blend with MQL, aiming to reduce torque, thrust force, and surface roughness.

Optimization of Drill Bit Geometries for Minimum Thermal Damage in Bone Drilling

Thermal injury is a common post-operative effect in bone drilling surgeries. The extreme heat generated during the drilling process kills bone cells, which causes irreversible bone death. This bone death loosens medical fixations—screws, plates, and implants—and subsequently refractures the bone. Research on drill bit geometries in bone drilling has attracted interest from engineering and medical researchers. However, previous research has mainly focused on the simulation of bone drilling, which could generate an incorrect approximation of thermal bone damage if the simulation model is not validated. For this reason, this study focuses on the optimization and parametric analysis of the bone temperature elevations induced by customized drill bit features—point angle (60-180°), web thickness (25-50 %), and helix angle (10-55°)—in comprehensive ex-vivo bone (bovine) experimental drilling tests. The L9 Taguchi optimization method was then applied to determine the optimal design to minimize maximum bone temperature rise. Results from the parametric analysis revealed that the optimal setup for the drill point features can be obtained with the ranges of point angle of 160-180°, web thickness of 25-30 %, and helix angle of 30-40°. Based on the Taguchi optimization results, the minimum thermal damage is produced with the point angle of 180°, web thickness of 25 %, and helix angle of 35°. This work offers a promising solution for reducing thermal injury and preventing thermal osteonecrosis in bone drilling surgeries.

Impact of drilling parameters on the surface roughness of egg shell filled glass fibre/polyester composites

Abstract Glass fiber-reinforced polymers (GFRPs) are widely used in domestic applications such as doors, windows, and furniture, where drilling is a common machining process. The surface roughness of drilled hole walls is a critical factor, particularly in fastening applications, where smooth finishes are essential. This study explores the influence of drilling parameters on the surface roughness of GFRPs reinforced with different types of eggshell fillers viz.,un-carbonized, carbonized, and hybrid along with an unfilled variant. The research employs a Central Composite Design within the Response Surface Methodology (RSM) framework to investigate the effects of material type, spindle speed, feed rate, and point angle on surface roughness. Material type and point angle were treated as categorical variables, while spindle speed and feed rate were continuous, each with four levels, resulting in 16 experimental runs. The results showed that surface roughness values varied from 3.04 to 4.99μm, depending on the specific combination of drilling parameters. Statistical analysis using Analysis of Variance (ANOVA) confirmed that spindle speed and feed rate significantly impact surface roughness, with roughness increasing at higher speeds and feeds. Notably, the carbonized eggshell-filled GFRP variant achieved the lowest surface roughness. The study also developed a highly accurate regression model, validated through experimental data. The novel use of different variants of eggshell fillers in GFRPs provides a sustainable and effective way to enhance material properties. Further, conducting the drilling studies to observe the outcomes, offers potential industrial applications in the production of high-quality, durable composite materials.

EXPERIMENTAL INVESTIGATION ON FREE VIBRATIONAL DAMPING AND DRILLING BEHAVIOR OF FLAX REINFORCED EPOXY COMPOSITES USING ADAPTIVE NEURO FUZZY INFERENCE SYSTEM

Flax reinforced epoxy (F-Ep) composites were prepared by the compression moulding technique, varying the fiber content (0, 25, 35 and 45 wt%). The free vibration test was performed on the neat epoxy and F-Ep composites to understand their dynamic characteristics, and results showed that natural frequency and damping factor of the F-Ep composites increased with an increase in the fiber content. The F-Ep composite (45F-Ep) that exhibited better damping was selected for performing the drilling operation. Factors such as spindle speed (rpm), feed rate (mm/min) and drill point angle (degree) were chosen as input parameters and the tabulated set of experiments were in accordance with Taguchi’s design of experiment. The response measured was thrust force and the obtained values were found in the range of 19.66 to 50.75 N. The minimum value of thrust force was achieved when the F-Ep composite was drilled at high spindle speed (3000 rpm), with a feed rate of 75 mm/min using the drill point angle of 118°. ANOVA analysis showed that the developed regression model was significant and thrust force was mainly influenced by the spindle speed. Mathematical models were developed for drilling F-Ep composite using response surface methodology (RSM) and adaptive neuro fuzzy inference system (ANFIS) and compared for their efficacy.

Imaging Spectropolarimeter Using a Multifunctional Metasurface.

Spectral polarization imaging is critical for broad applications ranging from remote sensing to biomedicine. Here, we propose and experimentally demonstrate an imaging spectropolarimeter based on a single multifunctional metasurface. The designed metasurface accurately maps spectral and polarization information onto focal points and vortex beams, enabling simultaneous detection through intensity distributions. More specifically, spectral detection is achieved by determining the azimuthal angle of the strongest focal point, while polarization detection is accomplished by synthesizing the intensity of focal points and the interference pattern of output vortex beams. Experimental results indicate the successful reconstruction for six discrete wavelengths, with the average relative polarization error ranging from 7.85% to 13%. Additionally, the metasurface exhibits excellent imaging and edge detection capabilities owing to the focusing properties and the generation of vortex beams, achieving an imaging resolution of up to 1.4-fold wavelength and offering a new solution for a wide range of applications.

Continuously tunable ultrasonic focusing by Moiré metalenses

Tunable ultrasonic focusing holds great significance in both medicine and engineering. Recent advancements in metalenses have introduced approaches for tunable acoustic focusing, but their complex configurations and limited tuning range remain challenges. Here, acoustic Moiré metalenses (AMMs) are proposed to achieve continuously tunable ultrasonic focusing in water. Two cascading metasurfaces that can function as Moiré diffractive elements make up the AMM. By mutually rotating the metasurface, the focal point of the AMM can be continuously tuned in a large range. The focal length can be adjusted continuously from ∼14.3λ0to ∼50λ0for the axial focusing. We further show that the well-designed AMM can achieve the continuously tunable lateral focusing, with the deflection angle of the focal point being tunable between approximately -40°,40°. Both simulation and experimental results confirm the excellent tunable focusing performances of the AMMs. The proposed AMMs with continuously tunable focusing capability may have potential applications in ultrasonic imaging and ultrasound treatment.

Soft material drilling: A thermo-mechanical analysis of polyurethane foam for biomimetic bone scaffolds and optimization of process parameters using Taguchi method

Drilling is a widely employed technique in machining processes, crucial for efficient material removal. However, when applied to living tissues, its invasiveness must be carefully considered. This study investigates drilling processes on polyurethane foam blocks mimicking human bone mechanical properties. Various drill bit types (118° twist, 135° twist, spherical, and conical), drilling speeds (1000–1600 rpm), and feed rates (20–80 mm/min) were examined to assess temperature elevation during drilling. The Taguchi method facilitated systematic experiment design and optimization. Signal-to-noise (S/N) ratio and analysis of variance (ANOVA) identified significant drilling parameters affecting temperature rise. Validation was conducted through confirmation testing. Results indicate that standard twist drill bits with smaller point angles, lower drilling speeds, and higher feed rates effectively minimize temperature elevation during drilling.

The Assessment of Upper Airway Volume Changes Following Bimaxillary Advancement Surgery: A Radiological Evaluation in the Supine Position at Multiple Intervals.

Background: Bimaxillary surgeries (BiMax) are an essential part of the craniomaxillofacial specialty. The osteotomies and subsequent spatial rearrangement of the maxilla and the mandible enable the correction of facial deformities, asymmetry, and malocclusion. Moreover, the movements performed during the procedure affect the morphology of surrounding soft tissues, including the upper airway (UA). Objectives: The objective of this study was to radiologically assess the potential volumetric alterations of the UA in the supine position at various intervals following BiMax advancement surgeries. Methods: A group of 31 patients who underwent BiMax advancement surgery were included in the study. Medical computed tomography (CT) of the head and neck region was performed 2 weeks preoperatively, 1 day postoperatively, and 6 months postoperatively. The UA volumes were calculated and analyzed based on the acquired Digital Imaging and Communications in Medicine (DICOM) files using different software applications. The sella-nasion-A point (SNA) and sella-nasion-B point (SNB) angles were evaluated to measure the achieved maxillomandibular advancement. Results: When comparing the volume of the UA before surgery, post-surgery, and 6 months post-surgery, the p-value was <0.001, indicating statistically significant differences in UA volume between the successive examinations. A statistically significant difference was found between UA volume before surgery and 6 months post-surgery and between UA volume after surgery and 6 months post-surgery, with the obtained p-values being <0.001 and 0.001, respectively. A significantly larger UA volume was observed 6 months post-surgery (mean ± SD: 27.3 ± 7.3) compared to the volume before surgery (mean ± SD: 22.2 ± 6.4), as well as 6 months post-surgery compared to the volume assessed shortly after surgery (mean ± SD: 24.2 ± 7.3). Conclusions: BiMax advancement surgeries result in the significant enlargement of the UA. The volume of the UA does not diminish immediately following the procedure and is not constant; it increases significantly during the postoperative observation period.

Clinical study of immediate implant placement in posterior maxillary region assisted by dynamic real-time navigation: A randomized controlled trial

ObjectiveTo evaluate the accuracy of the implant accuracy and clinical effect of navigation-assisted immediate implant placement (IIP) in the posterior maxillary tooth region. MethodsThis study included 60 patients with 96 implants undergoing IIP in the posterior maxillary region from January 2021 to December 2022, stratified into dynamic navigation and freehand implant groups. All clinical indicators, including initial stability, implant deviation (entry point deviation, end point deviation, depth deviation and angle deviation), marginal bone resorption and implant success rate, were systematically recorded. ResultsAll implants were successfully placed with an average torque of (24.38 ± 1.84)N.cm. The mean entry point deviation, apex point deviation and angular deviation in the navigation group were significantly smaller than that of the freehand group (P < 0.05). Marginal bone resorption was significantly less in the navigated group than in the freehand group (P < 0.05). All dental implants were considered an operational success and the mean follow-up time was (27.8 ± 8.4) months. ConclusionThe application of dynamic navigation-assisted immediate implant placement in the maxillary posterior region can achieve good implant accuracy and satisfactory clinical results.

Analysis of the Application Value of Dynamic Navigation Guidance in Oral Implantation.

To investigate the application of dynamic navigation guidance technology in different implantation scenarios, and to provide a scientific basis for the innovation and advancement of implantation techniques. Fifteen cases of patients with malocclusions admitted between January 2021 and February 2023 were selected as the study subjects. All patients underwent dynamic navigation-guided oral implantation interventions. CBCT scans were taken after implantation surgery to record deviations of implantation points, including implantation point deviation, endpoint deviation, and angle deviation. Dynamic navigation guidance effectively improves the reliability and stability of implantation in oral implant patients. CBCT effectively evaluated the state of the patient's periodontal implant, analyzed the state of the patient's lesion area, and improved the quality of implant intervention through CBCT guidance. The implantation point deviation was (0.407±0.193) mm, the endpoint deviation was (0.492±0.201) mm, and the implant angle deviation was (2.162±0.283)°. There was no significant difference in implantation point deviation in the anterior and posterior parts of the upper and lower jaws after intervention (P>0.05). However, there were significant differences in endpoint deviation and implant angle deviation among the anterior and posterior parts of the upper and lower jaws (P<0.05). Dynamic navigation guidance effectively improves the reliability and stability of implantation in oral implant patients. However, there is relatively greater endpoint deviation and implant angle deviation in the posterior part of the upper jaw.

Mystery of the Muenke midface: spheno-occipital synchondrosis fusion and craniofacial skeletal patterns.

The spheno-occipital synchondrosis (SOS) is an important site of endochondral ossification in the cranial base that closes prematurely in Apert, Crouzon, and Pfeiffer syndromes, which contributes to varying degrees of midface hypoplasia. The facial dysmorphology of Muenke syndrome, in contrast, is less severe with low rates of midface hypoplasia. We thus evaluated the timing of SOS fusion and cephalometric landmarks in patients with Muenke syndrome compared to normal controls. Patients with Muenke syndrome who had at least one fine-cut head computed tomography scan performedfrom 2000 to 2020 were retrospectively reviewed. A case-control study was performed of patient scans and age- and sex-matched control scans. SOS fusion status was evaluated as open, partially closed, or closed. We included 28 patients and compared 77 patient scans with 77 control scans. Kaplan-Meier analysis demonstrated an insignificantly earlier timeline of SOS fusion in Muenke syndrome (p = 0.300). Mean sella-orbitale (SO) distance was shorter (44.0 ± 6.6 vs. 47.7 ± 6.7 mm, p < 0.001) and mean sella-nasion-Frankfort horizontal (SN-FH) angle was greater (12.1° ± 3.8° vs. 10.1° ± 3.2°, p < 0.001)in the Muenke group, whereas mean sella-nasion-A point (SNA) angle was similar and normal (81.1° ± 5.7° vs. 81.4° ± 4.7°, p = 0.762). Muenke syndrome is characterized by mild and often absent midfacial hypoplasia, with the exception of slight retropositioning of the infraorbital rim. Interestingly, SOS fusion patterns in these patientsare not significantly different from age- and sex-matched controls despite an increased odds of fusion. It is possible that differences in timing of SOS fusion may manifest phenotypically at the infraorbital rim rather than atthe maxilla.

Intraoperative Measurement-Based Approach to Supratip Deformity in Open Structural Rhinoplasty.

Supratip deformity is one of the most common complications after open rhinoplasty. This study aimed to define a new risk scoring system for supratip deformity and determine the distances that should be left between the tip defining point (TDP) and anterior septal angle (ASA) to prevent it. Four hundred sixty-nine patients who underwent open rhinoplasty between 2018-2022 were included in this retrospective study. The patients were evaluated according to the risk scoring system consisting of four parameters (skin thickness, lower lateral cartilage anatomy, amount of hump resection, and soft tissue procedures). Because of the presence of supratip deformity at the postoperative 12th month, the patients were divided into two groups: (i) without supratip deformity (n = 418) and (ii) with supratip deformity (n = 51). Statistical inferences were made regarding the development of supratip deformity by evaluating the relationship between the risk scores and the intraoperative TDP-ASA distances. There was a significant difference between the groups in risk scores (P < 0.05). In cases with high-risk scores, it was calculated that the probability of developing supratip deformity decreased significantly when the TDP-ASA distance was above 7.5 mm and increased significantly when the TDP-ASA distance was below 6.5 mm. In cases with low-risk scores, it was found that the probability of developing supratip deformity was reduced considerably when the TDP-ASA distance was over 6.0 mm. The authors recommend keeping the TDP-ASA distance above 6.0 mm in low-risk patients and 7.5 mm in high-risk patients to avoid supratip deformity.

Optimized collection optic design for divertor Thomson scattering diagnostics in KSTAR.

Last year, the KSTAR divertor material was changed from carbon to tungsten tiles. An optimized collection optic design for divertor Thomson scattering diagnostics in KSTAR was conducted for electron temperature (1-100eV) and electron density (1 × 1018-1 × 1019m-3) profile diagnostics. This diagnostic system will utilize a 1064nm Nd:YAG laser directly from the K-top port toward the beam dump located at K-bottom, while collecting scattered light from five spatial points in the divertor area via collection optics situated in the j-middle port. Given spatial limitations, the solid angle of measurement points is limited, and the collection optic design facing the tungsten divertor is susceptible to stray light. So, the design of the collection optic is important for divertor Thomson scattering diagnostics. For optimal performance, we performed two types of collection optic designs: Cooke-triplet and double-Gaussian. We present performance ray tracing analysis results for both designs and derive the optimal design.

Poster 291: Entry Point-Transition Point Angle as a Novel 3-Dimensional Metric of Patellar Instability

Objectives: Three-dimensional (3D) modeling has increasing utility in identifying differences in trochlear morphology in patients with patellar instability when compared to historical 2-dimensional (2D) attempts. Distortions in the proximal medial ridges of trochleas are a distinguishing feature of trochlear dysplasia. Recently, the entry-point to transition-point (EP-TP) angle was established as a novel 3D metric to quantify degree of dysplasia, as it captures the tracking of the patella within the trochlea. However, previous attempts relied on 3D prints, which are not widely accessible. The purpose of this study is to validate this new measurement and compare differences between patients with patellar instability and the general population. Methods: Forty-three patients with recurrent patellar dislocations who were treated by a single surgeon between January 2020 and July 2023 were included. The study received an institutional review board exemption. Individuals from the New Mexico Decedent Image Database with no history of patellar instability or patellofemoral pain were used to obtain computed tomography (CT) images from the general population. Stereolithography (STL) models of distal femurs in 3D were generated from CT images using ScanIP. Minimum and maximum principal curvature maps were taken as screenshots from maps generated in MeshLab. Two people independently conducted measurements using a custom measuring tool displaying anteroposterior views and curvature maps of the distal femur. The measurers were asked to locate the medial and lateral ridges, transition point, and apex of the trochlea groove for each femur. A Mann–Whitney U test was performed to evaluate whether the recurrent dislocators had higher EP-TP values. P values below 0.01 were regarded as significant. Interclass correlation for both raters (ICC (1, k), reliability of values within this study) and single rater (ICC (1,1), reliability of measurement within clinical practice) and the 95% CI thereof, was computed for the 2 independent measurements. Results: A total of 100 femurs were measured, including 43 recurrent dislocators and 57 population femurs. The recurrent dislocator cohort had a mean EP-TP of 40.9° with a standard deviation of 16.4°. The general population cohort had a mean EP-TP of 11.3° with a standard deviation of 12.3°. EP-TP for dislocators and general population was significantly different. (p &lt; 0.001). ICC (1, k) was 0.81 with a 95%-confidence interval of 0.72 to 0.87. ICC (1,1) was 0.69 with a 95% CI of 0.57 to 0.78. Conclusions: EP-TP angle is a novel metric that helps quantify trochlear dysplasia, which can help clinicians better understand patellar instability. In this study, we validate EP-TP angle by showing that EP-TP angle was significantly different between femurs of recurrent dislocators and the general population.

Fabrication and properties of hydrogel based on itaconic anhydride modified collagen

Based on the bioconjugation engineering, the structures and properties of collagen could be optimized, which is attractive for the development of novel collagen-based biomaterials. Here, itaconic anhydride was used to modify the amino groups in collagen to prepare the itaconic anhydride modified collagen (CITA) with different grafting density. The grafting density of CITAs was detected by TNBS assay. The integrity and thermostability of triple helical structure in CITAs were revealed by CD. Hydrophilicity of CITAs was studied by isoelectric point and water contact angles analysis. The concentration of CITA solution could be improved to 30 mg/mL under physiological environment. The hydrogelation of CITA was realized by photopolymerization, based on the introduction of double bonds. The storage modulus (G′) of CITA hydrogel could be improved to 680 Pa, compared with 67 Pa of Col hydrogel. The improved hemostasis property and antibacterial property of CITAs were confirmed, and CITAs also possessed good biocompatibility. This work provided a novel artificially modified collagen with optimized properties, which could be used for 3D bioprinting and fabrication of the in situ hemostatic hydrogel system.

Dynamic thermal analysis and drill bit temperature in AISI 430 stainless steel

This paper presents a novel numerical model applied specifically for the drilling of AISI 430 Ferritic Stainless Steel, a material of significant importance across various industries. The model thoroughly investigates the geometric parameters of drill bits, including Point Angle (PA), Helix Angle (HA), and rotational speed (RS), meticulously analyzing their impact on two crucial factors: heat generation and temperature distribution. The study covers a broad spectrum of PA (110°, 130°, 150°, and 170°) and HA (30°, 40°, and 50°), along with varying RS (1200 rpm, 1400 rpm, and 1600 rpm). Results indicate that the temperature of the drill bit rises with the increase in parameters such as PA, HA, and RS. Notably, a PA of 170° exhibits the highest temperature among different point angles, with the temperature at the contact surface during drilling escalating from 476 K to 520 K at a point edge angle of 130°. Furthermore, a helix angle of 50° records the highest temperature, while a 30° angle registers the lowest. Heat generation during the drilling process intensifies as PA, HA, and RS parameters advance. The developed numerical model accurately reflects drilling parameters, offering valuable insights for optimizing drilling operations.