Three-dimensional Imaging Research Articles

Nursing student’s perceptions, satisfaction, and knowledge toward utilizing immersive virtual reality application in human anatomy course: quasi-experimental

BackgroundA paradigm shift in nursing education is required to prepare Z generation of nursing students through integrated innovative technologies as teaching strategies such as immersive virtual reality in several bioscience and main courses to facilitate and enhance learning process.Aim/objectiveExamine the effect of utilizing an immersive virtual reality application on students’ perceptions, knowledge, and satisfaction in an anatomy course.MethodsA quasi-experimental (pre-post test, one group) design was conducted among 1st year nursing students (N = 138) enrolled in an anatomy course in the spring semester of 2023–2024 in the nursing program in the health professions faculty at Al-Quds University. The technology acceptance model (TAM) was used for data collection.ResultsThe results showed that 96% of participants were satisfied with using the VR application, and it retains their knowledge in the human anatomy course. 92% of the total, were under the age of twenty, and 84% were females. 80.1% (2.99 ± 0.58) of those students had more positive perspectives of VR applications in the nursing courses. Additionally, there were significant differences in students’ satisfaction and knowledge toward using VR applications after the anatomy lecture (p = 0.029, p = 0.05, respectively).ConclusionVirtual reality is a supplemental innovative tool for promoting learning. Nursing students perceive immersive virtual reality technologies positively and prefer using three-dimensional images in their anatomy courses, which helps them recall their knowledge, understand concepts of educational content, identify learning objectives, and improve learning outcomes. This study found that virtual reality can improve nursing students’ understanding, satisfaction, and knowledge of anatomy.

Equine Nuclear Medicine in 2024: Use and Value of Scintigraphy and PET in Equine Lameness Diagnosis.

Scintigraphy and Positron Emission Tomography (PET) are both nuclear medicine imaging techniques, providing functional information of the imaged areas. Scintigraphy is a two-dimensional projected imaging technique that was introduced in equine imaging in the late 1970s. Scintigraphy allows imaging of large body parts and can cover multiple areas, remaining the only technique commonly used in horses for whole body imaging. PET is a cross-sectional imaging technique, first used in horses in 2015, allowing higher resolution three-dimensional functional imaging of the equine distal limb. This manuscript will cover current use and values of these two modalities in equine lameness diagnosis.

A comparison of machine learning methods for recovering noisy and missing 4D flow MRI data.

Experimental blood flow measurement techniques are invaluable for a better understanding of cardiovascular disease formation, progression, and treatment. One of the emerging methods is time-resolved three-dimensional phase-contrast magnetic resonance imaging (4D flow MRI), which enables noninvasive time-dependent velocity measurements within large vessels. However, several limitations hinder the usability of 4D flow MRI and other experimental methods for quantitative hemodynamics analysis. These mainly include measurement noise, corrupt or missing data, low spatiotemporal resolution, and other artifacts. Traditional filtering is routinely applied for denoising experimental blood flow data without any detailed discussion on why it is preferred over other methods. In this study, filtering is compared to different singular value decomposition (SVD)-based machine learning and autoencoder-type deep learning methods for denoising and filling in missing data (imputation). An artificially corrupted and voxelized computational fluid dynamics (CFD) simulation as well as in vitro 4D flow MRI data are used to test the methods. SVD-based algorithms achieve excellent results for the idealized case but severely struggle when applied to in vitro data. The autoencoders are shown to be versatile and applicable to all investigated cases. For denoising, the in vitro 4D flow MRI data, the denoising autoencoder (DAE), and the Noise2Noise (N2N) autoencoder produced better reconstructions than filtering both qualitatively and quantitatively. Deep learning methods such as N2N can result in noise-free velocity fields even though they did not use clean data during training. This work presents one of the first comprehensive assessments and comparisons of various classical and modern machine-learning methods for enhancing corrupt cardiovascular flow data in diseased arteries for both synthetic and experimental test cases.

Three-dimensional visualization of gunshot cavities in ballistic gelatine with computed tomography – A forensic ballistics case study

Three-dimensional (3D) imaging, primarily computed tomography (CT), has proven valuable in the documentation and analysis of gunshot injuries. Explicit visualization of findings may play a pivotal role in judicial settings. This forensic ballistics case study aimed to examine the potential of CT-based 3D reconstruction to digitally visualize gunshot cavities in ballistic gelatine. Three .30 caliber bullets of different types (full metal jacket, soft point, and expanding monolithic) were fired into standardized blocks of 10% ballistic gelatine. The blocks underwent CT scanning with clinical equipment. Gelatine and air were segmented from the CT data using an open-source software. 3D reconstruction views of the segmented gelatine and air components were created. The gunshot cavities were clearly observed in both gelatine and air segmentation. The differences in cavitation between bullet types were evident in both reconstruction approaches, although gelatine segmentation produced higher resolution of small details. The obvious benefit of digital reconstruction was the ability to freely tilt and rotate the 3D images, with the possibility of taking measurements manually or automatically from any plane. Moreover, all the data can be stored for future analysis. This study introduces a preliminary method for digital visualization and documentation of gunshot cavitation in ballistic gelatine, to be fine-tuned and implemented for research purposes and routine practice in forensic institutions.

Coronary protective effect of the J-Valve during transcatheter aortic valve implantation for patients with aortic stenosis and low coronary artery openings

BackgroundIn recent years, transcatheter aortic valve implantation (TAVI) has become a widely used treatment for low-risk elderly patients. As an alternative to TAVI via the femoral artery, transapical TAVI (TA-TAVI) is a better surgical choice for patients with severe vascular diseases. The J-Valve assists doctors in completing valve implantation easily using its positioning locator device, which prevents the self-leaflet from approaching the sinus wall. This function acts as coronary artery protection to avoid coronary occlusion. However, the clinical prognosis of J-Valve implantation for patients with aortic valve stenosis and low coronary openings is unclear.MethodsA retrospective analysis was performed on 30 patients with aortic stenosis (AS) and coronary openings measuring ≤ 10 mm in height. All patients underwent TA-TAVI with J-Valve implantation. Patients were screened using preoperative computed tomography three-dimensional imaging of the aortic root, and the safety and efficacy of the procedure were evaluated. The collected indexes included patients’ general data, cardiac function, preoperative imaging parameters, intraoperative data and postoperative short-term prognosis.ResultsOf the 30 patients in the study successfully underwent TA-TAVI and J-Valve implantation. Two patients required temporary cardiopulmonary bypass assistance during the operation due to heart failure. The implant success rate was 100%, and there were no deaths within 30 days postoperatively. No patients experienced intraoperative or postoperative coronary artery occlusion. Postoperative echocardiography, physiological state and laboratory test results indicated that all patients recovered well. The electrocardiograms remained normal after TA-TAVI, and heart function improved within 30 days.ConclusionTransapical TAVI with J-Valve implantation is a safe and effective treatment option for patients with AS and a low coronary artery opening. Preoperative coronary artery evaluation and the locators of the J-Valve are crucial in preventing coronary artery occlusion. This treatment regimen provides beneficial outcomes and warrants further multi-centre clinical research in the future.

Harnessing forward multiple scattering for optical imaging deep inside an opaque medium

As light travels through a disordered medium such as biological tissues, it undergoes multiple scattering events. This phenomenon is detrimental to in-depth optical microscopy, as it causes a drastic degradation of contrast, resolution and brightness of the resulting image beyond a few scattering mean free paths. However, the information about the inner reflectivity of the sample is not lost; only scrambled. To recover this information, a matrix approach of optical imaging can be fruitful. Here, we report on a de-scanned measurement of a high-dimension reflection matrix R via low coherence interferometry. Then, we show how a set of independent focusing laws can be extracted for each medium voxel through an iterative multi-scale analysis of wave distortions contained in R. It enables an optimal and local compensation of forward multiple scattering paths and provides a three-dimensional confocal image of the sample as the latter one had become digitally transparent. The proof-of-concept experiment is performed on a human opaque cornea and an extension of the penetration depth by a factor five is demonstrated compared to the state-of-the-art.

Multiview Multistatic vs. Multimonostatic Three-Dimensional Ground-Penetrating Radar Imaging: A Comparison

The availability of multichannel ground-penetrating radar systems capable of gathering multiview, multistatic, multifrequency data provides novel chances to improve subsurface imaging results. However, customized data processing techniques and smart choices of the measurement setup are needed to find a trade-off between image quality and acquisition time. In this paper, we adopt a Born Approximation-based full 3D approach, which can manage multiview-multistatic, multifrequency data and faces the imaging as a linear inverse scattering problem. The inverse problem is solved by exploiting the truncated singular value decomposition as a regularization scheme. The paper presents a theoretical study aimed at assessing how the reconstruction capabilities of the imaging approach depend on the adopted measurement configuration. In detail, the performance achievable in the standard case of multimonostatic, multifrequency data is compared with that provided by a multiview-multistatic, multifrequency configuration, where the data are gathered by considering a progressively increasing number of transmitting antennas. The comparison of the achievable imaging performance is carried out by exploiting the spectral content and the point spread function, which are general tools to foresee the achievable reconstruction capabilities. Reconstruction results related to a numerical experiment based on full-wave data are also provided.

Three-dimensional computer holography based on two hybrid constraint iterative angular spectrum algorithms

A method for three-dimensional holographic image calculation based on angular spectrum layering is presented, which significantly reduces the noise resulting from image overlap during hologram reconstruction. In order to enhance the reconstruction quality, we proposed a two-hybrid constraint algorithm, which employs two parallel processing frameworks to allocate multiple plane images effectively. Additionally, by applying two different hybrid constraint factors, spatial resource allocation is utilized efficiently to mitigate the impact of axial inter-layer crosstalk noise. The numerical simulations and optical experiment results demonstrated that our method has successfully improved the reconstruction quality of holograms and proved its effectiveness and feasibility.

Radiomics based on diffusion tensor imaging and 3D T1-weighted MRI for essential tremor diagnosis.

Due to the absence of biomarkers, the misdiagnosis of essential tremor (ET) with other tremor diseases and enhanced physiologic tremor is very common in practice. Combined radiomics based on diffusion tensor imaging (DTI) and three-dimensional T1-weighted imaging (3D-T1) with machine learning (ML) give a most promising way to identify essential tremor (ET) at the individual level and further reveal the potential imaging biomarkers. Radiomics features were extracted from 3D-T1 and DTI in 103 ET patients and 103 age-and sex-matched healthy controls (HCs). After data dimensionality reduction and feature selection, five classifiers, including the support vector machine (SVM), random forest (RF), logistic regression (LR), extreme gradient boosting (XGBoost) and multi-layer perceptron (MLP), were adopted to discriminate ET from HCs. The mean values of the area under the curve (mAUC) and accuracy were used to assess the model's performance. Furthermore, a correlation analysis was conducted between the most discriminative features and clinical tremor characteristics. All classifiers achieved good classification performance (with mAUC at 0.987, 0.984, 0.984, 0.988 and 0.981 in the test set, respectively). The most powerful discriminative features mainly located in the cerebella-thalamo-cortical (CTC) and visual pathway. Furthermore, correlation analysis revealed that some radiomics features were significantly related to the clinical tremor characteristics in ET patients. These results demonstrated that combining radiomics with ML algorithms could not only achieve high classification accuracy for identifying ET but also help us to reveal the potential brain microstructure pathogenesis in ET patients.

A Corpus-Based Comparative Study of Chinese and Western Media Image Construction of TCM-Related Personnel

This study aims to explore the differences in image of personnel related to traditional Chinese medicine (TCM) between Chinese and Western mainstream media. Employing Fairclough’s three-dimensional critical discourse analysis (CDA) model and TCM Social Image Evaluation Index System, it analyzes the linguistic characteristics of high-frequency words and collocation with corpus methods. The findings reveal Chinese media’s emphasis on the management role and Western media’s focus on the alternative or marginalized status of TCM-related personnel. Chinese media portray TCM medical personnel as experienced and professionally excellent, while Western media tend to question their reliability, positioning them as supplementary to mainstream medicine. A certified, professional and reliable image of TCM health care personnel is painted by Chinese media, as opposed to the illegal practices among acupuncturists highlighted by Western media. Chinese media present TCM experts as integrated and top-notch professionals, whereas Western media may critique their viewpoints. TCM administrators are characterized by precision and authority in Chinese reports, contrasting with the negative depiction in Western media. Last but not least, Chinese patients are generally trustful to TCM more than their Western counterparts. The above differences are deeply rooted in the ideological stances of the media outlets.

Accelerating imaging research at large-scale scientific facilities through scientific computing.

To date, computed tomography experiments, carried-out at synchrotron radiation facilities worldwide, pose a tremendous challenge in terms of the breadth and complexity of the experimental datasets produced. Furthermore, near real-time three-dimensional reconstruction capabilities are becoming a crucial requirement in order to perform high-quality and result-informed synchrotron imaging experiments, where a large amount of data is collected and processed within a short time window. To address these challenges, we have developed and deployed a synchrotron computed tomography framework designed to automatically process online the experimental data from the synchrotron imaging beamlines, while leveraging the high-performance computing cluster capabilities to accelerate the real-time feedback to the users on their experimental results. We have, further, integrated it within a modern unified national authentication and data management framework, which we have developed and deployed, spanning the entire data lifecycle of a large-scale scientific facility. In this study, the overall architecture, functional modules and workflow design of our synchrotron computed tomography framework are presented in detail. Moreover, the successful integration of the imaging beamlines at the Shanghai Synchrotron Radiation Facility into our scientific computing framework is also detailed, which, ultimately, resulted in accelerating and fully automating their entire data processing pipelines. In fact, when compared with the original three-dimensional tomography reconstruction approaches, the implementation of our synchrotron computed tomography framework led to an acceleration in the experimental data processing capabilities, while maintaining a high level of integration with all the beamline processing software and systems.

Three-dimensional ghost imaging via the Scheimpflug detection

For previous three-dimensional ghost imaging, the acquisition of absolute distance information is mainly based on the principle of time-of-flight, which usually needs lots of measurements and a large detection/modulation bandwidth product. Here we present a technique called three-dimensional ghost imaging via the Scheimpflug detection (3D-GISD), which exploits the principle of a similar binocular stereoscopic vision for distance information acquisition and can dramatically reduce the measurements required for high-quality 3D image reconstruction. The experimental results demonstrate that high-quality 3D-GISD can be still obtained even if the target exceeds the depth of field of Scheimpflug imaging system and less than 500 measurements are adopted for an image with 128×128 pixels. What’s more, the ranging accuracy of 0.2 mm can be achieved by 3D-GISD at about 1.1 m detection distance for a real scenario. Factors influencing the accuracy of distance measurement for 3D-GISD are also discussed.

Run-time motion and first-order shim control by expanded servo navigation.

To provide a navigator-based run-time motion and first-order field correction for three-dimensional human brain imaging with high precision, minimal calibration and acquisition, and fast processing. A complex-valued linear perturbation model with feedback control is extended to estimate and correct for gradient shim fields using orbital navigators (2.3 ms). Two approaches for sensitizing the model to gradient fields are presented, one based on finite differences with three additional navigators, and another projection-based approximation requiring no additional navigators. A mechanism for noise decorrelation of the matrix and the data is proposed and evaluated to reduce unwanted parameter biases. The rigid motion and first-order field control achieves robust motion and gradient shim corrections improving image quality in a series of phantom and in vivo experiments with varying field conditions. In phantom scans, magnet drifts, forced gradient field perturbations and field distortions from shifts of a second bottle phantom are successfully corrected. Field estimates of the magnet drifts are in good agreement with concurrent field probe measurements. For in vivo scans, the proposed method mitigates field variations from torso motions while being robust to head motion. In vivo gradient field precisions were along with single-digit micrometer and millidegree rigid precisions. The navigator-based method achieves accurate, high-precision run-time motion and field corrections with low sequence impact and calibration requirements.

Navigating endodontic outcomes through cone-beam computed tomography: A narrative review

Abstract Periapical radiographs (PRs) have been the most reliable modality for assessing periapical health. Later, the evolution of cone-beam computed tomography (CBCT) revolutionized three-dimensional maxillofacial skeletal imaging. CBCT imaging has emerged as a superior diagnostic tool compared to PR. The aim of this narrative review was to provide a comprehensive overview of the outcomes related to the use of CBCT in evaluating various endodontic treatments, including primary root canal treatments, secondary treatments, endodontic microsurgeries, and vital pulp therapies and the associated prognostic factors. The research selection process involved systematically searching PubMed, Scopus, and Web of Science for literature on CBCT and endodontics. Criteria included English-language; peer-reviewed articles published from January 2010 to December 2023, reporting 1-year outcomes of various endodontic treatments using CBCT. Two independent reviewers screened titles, abstracts, and full texts. A total of 18 outcome study articles utilizing CBCT to evaluate primary root canal treatment were selected, as well as 7 for secondary root canal retreatment, 3 for vital pulp therapy, and 11 articles pertaining to endodontic microsurgery. The outcomes revealed varying success rates and prognostic factors. Consistent with outcome research employing PRs, studies that utilized CBCT also exhibited substantial variability in factors affecting initial and secondary treatment outcomes. The rate of favorable outcomes was significantly lower when assessed with CBCT compared to PR. The results from utilizing CBCT for primary and secondary root canal treatments, endodontic microsurgeries, and vital pulp therapies demonstrate diverse success rates and prognostic factors in comparison to outcomes based solely on PRs.

Translithospheric magma plumbing system fossilized in the Emeishan large igneous province

Lighting up the magma plumbing system beneath a large igneous province (LIP) is challenging because the complex magma migration paths are often covered by flood basalts and sediments. Here, we present a three-dimensional seismic image of the Permian Emeishan LIP in Southwest China, constructed by joint inversion of Rayleigh wave dispersions and receiver functions. The results outline a cylindrical, high-velocity anomaly extending to ~135 km depth below the inner zone of this continental LIP. The geometry and magnitude of the high-velocity anomaly suggest that it represents culminated crystallized materials of primary magmas, thereby mirroring a magma plumbing system fossilized in the lithosphere. Furthermore, our geodynamic models illustrate that the nearly vertical plumbing system was controlled by slow plate motion during the magma emplacement. The plume head beneath a nearly static plate has higher thermal buoyancy and thus promotes more intensive magma emplacement. This phenomenon may apply to other LIPs throughout Earth’s history

Correction of thermal airflow distortion in warpage measurements of microelectronic packaging structures via deep learning-based digital image correlation

The projected speckle-based three-dimensional digital image correlation method (3D-DIC) is being increasingly used in the reliability measurement of microelectronic packaging structures because of its noninvasive nature, high precision, and low cost. However, during the measurement of the thermal reliability of packaging structures, the thermal airflow generated by heating introduces distortions in the images captured by the DIC measurement system, impacting the accuracy and reliability of noncontact measurements. To address this challenge, a thermal airflow distortion correction model based on the transformer attention mechanism is proposed specifically for the measurement of thermal warpage in microelectronic packaging structures. This model avoids the oversmoothing issue associated with convolutional neural networks and the lack of physical constraints in generative adversarial networks, ensuring the precision of grayscale gradient changes in speckle patterns and minimizing adverse effects on DIC calculation accuracy. By inputting the distorted images captured by the DIC measurement system into the network, corrected images are obtained for 3D-DIC calculations, thus allowing the thermal warpage measurement results of the sample to be acquired. Through experiments measuring topography with customized step block specimens, the effectiveness of the proposed method in improving warpage measurement accuracy is confirmed; this is particularly true when captured images are affected by thermal airflow at 140 °C and 160 °C, temperatures commonly encountered in thermal reliability testing of packaging structures. The method successfully reduces the standard deviation from 9.829 to 5.943 µm and from 12.318 to 6.418 µm, respectively. The results demonstrate the substantial practical value of this method for measuring thermal warpage in microelectronic packaging structures.

Vasculature segmentation in 3D hierarchical phase-contrast tomography images of human kidneys.

Efficient algorithms are needed to segment vasculature in new three-dimensional (3D) medical imaging datasets at scale for a wide range of research and clinical applications. Manual segmentation of vessels in images is time-consuming and expensive. Computational approaches are more scalable but have limitations in accuracy. We organized a global machine learning competition, engaging 1,401 participants, to help develop new deep learning methods for 3D blood vessel segmentation. This paper presents a detailed analysis of the top-performing solutions using manually curated 3D Hierarchical Phase-Contrast Tomography datasets of the human kidney, focusing on the segmentation accuracy and morphological analysis, thereby establishing a benchmark for future studies in blood vessel segmentation within phase-contrast tomography imaging.

Cost-effectiveness of incorporating self-imaging optical coherence tomography into fundus photography-based diabetic retinopathy screening

Diabetic macular edema (DME) has emerged as the foremost cause of vision loss in the population with diabetes. Early detection of DME is paramount, yet the prevailing screening, relying on two-dimensional and labor-intensive fundus photography (FP), results in frequent unwarranted referrals and overlooked diagnoses. Self-imaging optical coherence tomography (SI-OCT), offering fully automated, three-dimensional macular imaging, holds the potential to enhance DR screening. We conducted an observational study within a cohort of 1822 participants with diabetes, who received comprehensive assessments, including visual acuity testing, FP, and SI-OCT examinations. We compared the performance of three screening strategies: the conventional FP-based strategy, a combination strategy of FP and SI-OCT, and a simulated combination strategy of FP and manual SD-OCT. Additionally, we undertook a cost-effectiveness analysis utilizing Markov models to evaluate the costs and benefits of the three strategies for referable DR. We found that the FP + SI-OCT strategy demonstrated superior sensitivity (87.69% vs 61.53%) and specificity (98.29% vs 92.47%) in detecting DME when compared to the FP-based strategy. Importantly, the FP + SI-OCT strategy outperformed the FP-based strategy, with an incremental cost-effectiveness ratio (ICER) of $8016 per quality-adjusted life year (QALY), while the FP + SD-OCT strategy was less cost-effective, with an ICER of $45,754/QALY. Our results were robust to extensive sensitivity analyses, with the FP + SI-OCT strategy standing as the dominant choice in 69.36% of simulations conducted at the current willingness-to-pay threshold. In summary, incorporating SI-OCT into FP-based screening offers substantial enhancements in sensitivity, specificity for detecting DME, and most notably, cost-effectiveness for DR screening.

Anatomical Position of the Mentonian Foramen in Relation to the Alveolar Ridge and Mandibular Base using Cone Beam Computed Tomography in Dentate Patients

Introduction: The mentonian foramen is an important structure of the anterior part of the mandible, referent in surgical procedures of the mandible, mainly of the interforaminal area. Therefore, for a more precise analysis of this anatomical structure we use Cone Beam CT scans, since it provides us with a three-dimensional image of higher quality of the maxillofacial massif as it does not present overlapping images, geometric distortion and false negatives that could increase the risk of iatrogenic lesions. Objective: To determine the distance of the mentonian foramen in relation to the alveolar ridge and the mandibular base by means of Cone Beam Computed Tomography of dentate patients. Methodology: The study was descriptive, cross-sectional and retrospective; 109 Cone Beam Computed Tomography scans of dentate patients were evaluated from March to October 2020, taken from the Maxillofacial Diagnostic Institute (IDM) Lima, Peru; between 18 and 50 years old, distributed in three age groups: 18 to 28 years old, 29 to 39 years old and 40 to 50 years old. The distances from the upper edge of the mentonian foramen to the alveolar ridge and from the lower edge of the mentonian foramen to the mandibular base were analyzed, taking into account sex and age group. For the statistical analysis, SPSS Statistics version 26.0 was used and the T student test for related tests was applied to evaluate the differences between the right and left sides, T student for independent tests to analyze the measures with the male and female sexes and ANOVA of one factor for the analysis with the age groups. All tests were performed at a significance level of 5%. Results: The mentonian foramen is closer to the mandibular base than to the alveolar ridge, whose means are 13.81mm and 14mm, respectively. The average distance was shorter in the 40 to 50 years age group and the female sex presented shorter distances. Conclusion: The mentonian foramen is 13.81mm above the mandibular base, the greatest distances were found in the male sex and the shortest distances in the 40 to 50 years age group.

Reduced warpage in semiconductor packages: Optimizing post-cure temperature profile considering cure shrinkage and viscoelasticity of epoxy molding compound

Warpage in semiconductor packages is a critical issue that affects their reliability and performance. This study aims to minimize the warpage of a bi-material dummy package by optimizing the post-mold curing (PMC) temperature profile. A warpage simulation model was developed considering the viscoelastic properties and cure shrinkage behavior of the epoxy molding compound (EMC). A compression molding monitoring system was also developed to analyze the cure behavior of the EMC. The gelation point of the EMC during compression molding was determined using a dielectric sensor, while cure shrinkage behaviors were analyzed using a fiber Bragg grating sensor. Viscoelastic properties were characterized through stress relaxation tests, and thermal properties were measured using three-dimensional digital image correlation. The developed simulation model was used to optimize the PMC temperature profile using a genetic algorithm. Experimental validation showed that the optimized temperature profile reduced the warpage from ∼1519 μm to 486 μm compared to a linear profile. The findings of this study have broader implications for the design and manufacturing of semiconductor packages, as the proposed approach can be applied to minimize warpage and improve package reliability.