CT Reconstruction Research Articles

Full-Scale Pore Structure Characterization and Its Impact on Methane Adsorption Capacity and Seepage Capability: Differences between Shallow and Deep Coal from the Tiefa Basin in Northeastern China

Deep low-rank coalbed methane (CBM) resources are numerous and widely distributed in China, although their exploration remains in its infancy. In this work, gas adsorption (N2/CO2), mercury intrusion porosimetry, and 3D CT reconstruction were performed on five coal samples of deep and shallow low-rank coal from northeast China to analyze their pore structure. The impact of the features in the pore structure at full scale on the capacity for methane adsorption and seepage is discussed. The results indicate that there are significant differences between deep low-rank coal and shallow low-rank coal in terms of porosity, permeability, composition, and adsorption capacity. The full-scale pore distribution was dispersed over a broad range and exhibited a multi-peak distribution, with the majority of the peak concentrations occurring between 0.45–0.7 nm and 3–4 nm. Mesopores are prevalent in shallow coal rock, whereas micropores are the most numerous in deep coal rock. The primary contributors to the specific surface area of both deep and superficial coal rock are micropores. Three-dimensional CT reconstruction can characterize pores with pore size greater than 1 μm, while the dominating equivalent pore diameters (Deq) range from 1 to 10 μm. More mini-scale pores and fissures are observed in deep coal rock, while shallow coal rock processes greater total and connection porosity. Multifractal features are prevalent in the fractal qualities of all the numbered samples. An enhancement in pore structure heterogeneity occurs with increasing pore size. The pore structure of deep coal rock is more heterogeneous. Furthermore, methane adsorption capacity is favorably connected with D1 (0.4 nm < pore diameter ≤ 2 nm), D2 (2 nm < pore diameter ≤ 5 nm), micropore volume, and specific surface area and negatively correlated with D3 (5 nm < pore diameter ≤ 50 nm), showing that methane adsorption capability is primarily controlled by micropores and mesopores. Methane seepage capacity is favorably connected with the pore volume and connected porosity of macropores and negatively correlated with D4 (pore diameter > 50 nm), indicating that the macropores are the primary factor influencing methane seepage capacity.

Surrogate-driven respiratory motion model for projection-resolved motion estimation and motion compensated cone-beam CT reconstruction from unsorted projection data

Objective. As the most common solution to motion artefact for cone-beam CT (CBCT) in radiotherapy, 4DCBCT suffers from long acquisition time and phase sorting error. This issue could be addressed if the motion at each projection could be known, which is a severely ill-posed problem. This study aims to obtain the motion at each time point and motion-free image simultaneously from unsorted projection data of a standard 3DCBCT scan. Approach. Respiration surrogate signals were extracted by the Intensity Analysis method. A general framework was then deployed to fit a surrogate-driven motion model that characterized the relation between the motion and surrogate signals at each time point. Motion model fitting and motion compensated reconstruction were alternatively and iteratively performed. Stochastic subset gradient based method was used to significantly reduce the computation time. The performance of our method was comprehensively evaluated through digital phantom simulation and also validated on clinical scans from six patients. Results. For digital phantom experiments, motion models fitted with ground-truth or extracted surrogate signals both achieved a much lower motion estimation error and higher image quality, compared with non motion-compensated results.For the public SPARE Challenge datasets, more clear lung tissues and less blurry diaphragm could be seen in the motion compensated reconstruction, comparable to the benchmark 4DCBCT images but with a higher temporal resolution. Similar results were observed for two real clinical 3DCBCT scans. Significance. The motion compensated reconstructions and motion models produced by our method will have direct clinical benefit by providing more accurate estimates of the delivered dose and ultimately facilitating more accurate radiotherapy treatments for lung cancer patients.

Diagnostic CT of colorectal cancer with artificial intelligence iterative reconstruction: A clinical evaluation

ObjectivesTo investigate the clinical value of a novel deep-learning based CT reconstruction algorithm, artificial intelligence iterative reconstruction (AIIR), in diagnostic imaging of colorectal cancer (CRC). MethodsThis study retrospectively enrolled 217 patients with pathologically confirmed CRC. CT images were reconstructed with the AIIR algorithm and compared with those originally obtained with hybrid iterative reconstruction (HIR). Objective image quality was evaluated in terms of the signal-to-noise ratio (SNR) and contrast-to-noise ratio (CNR). Subjective image quality was graded on the conspicuity of tumor margin and enhancement pattern as well as the certainty in diagnosing organ invasion and regional lymphadenopathy. In patients with surgical pathology (n = 116), the performance of diagnosing visceral peritoneum invasion was characterized using receiver operating characteristic (ROC) analysis. Changes of diagnostic thinking in diagnosing hepatic metastases were assessed through lesion classification confidence. ResultsThe SNRs and CNRs on AIIR images were significantly higher than those on HIR images (all p < 0.001). The AIIR was scored higher for all subjective metrics (all p < 0.001) except for the certainty of diagnosing regional lymphadenopathy (p = 0.467). In diagnosing visceral peritoneum invasion, higher area under curve (AUC) of the ROC was found for AIIR than HIR (0.87 vs 0.77, p = 0.001). In assessing hepatic metastases, AIIR was found capable of correcting the misdiagnosis and improving the diagnostic confidence provided by HIR (p = 0.01). ConclusionsCompared to HIR, AIIR offers better image quality, improves the diagnostic performance regarding CRC, and thus has the potential for application in routine abdominal CT.

Supplementary value and diagnostic performance of computed tomography scout view in the detection of thoracolumbar spine injuries.

Assessing the diagnostic performance and supplementary value of whole-body computed tomography scout view (SV) images in the detection of thoracolumbar spine injuries in early resuscitation phase and identifying frequent image quality confounders. In this retrospective database analysis at a tertiary emergency center, three blinded senior experts independently assessed SV to detect thoracolumbar spine injuries. The findings were categorized according to the AO Spine classification system. Confounders impacting SV image quality were identified. The suspected injury level and severity, along with the confidence level, were indicated. Diagnostic performance was estimated using the caret package in R programming language. We assessed images of 199patients, encompassing 1592 vertebrae (T10-L5), and identified 56 spinal injuries (3.5%). Among the 199 cases, 39 (19.6%) exhibited at least one injury in the thoracolumbar spine, with 12 (6.0%) of them displaying multiple spinal injuries. The pooled sensitivity, specificity, and accuracy were 47%, 99%, and 97%, respectively. All experts correctly identified the most severe injury of AO type C. The most common image confounders were medical equipment (44.6%), hand position (37.6%), and bowel gas (37.5%). SV examination holds potential as a valuable supplementary tool for thoracolumbar spinal injury detection when CT reconstructions are not yet available. Our data show high specificity and accuracy but moderate sensitivity. While not sufficient for standalone screening, reviewing SV images expedites spinal screening in mass casualty incidents. Addressing modifiable factors like medical equipment or hand positioning can enhance SV image quality and assessment.

Direct tensile damage process of calcite vein shale based on 3D CT reconstruction

AbstractFrom core observations of shales of the Niutitang formation in the northern part of Guizhou Province, China, calcite was often found to act as a natural fracture filler and affect the extension of fractures in hydraulic fracturing. Therefore, it is crucial to understand the tensile mechanical behavior of shales by calcite veins. In this paper, by computed tomography scanning of shales containing calcite veins of different dip angles from the Niutitang formation, a three‐dimensional numerical model reflecting the internal fine structure of the shale was constructed. Direct tensile numerical simulations were carried out to investigate the effect of calcite veins at different angles on the fine‐scale damage process and mechanical properties of shale. The experimental results show that the tensile capacity of the shale increases with the increase in calcite veins. Depending on the dip angle of the calcite vein, the damage pattern of the shale is divided into three types of damage: pull‐off damage along the calcite vein, jagged damage, and horizontal damage perpendicular to the loading method. At high dip angles, the shale damage is more intense and the fracture network more complex. The temporal and spatial characteristics of the acoustic emissions provide a good indication of the microscopic behavior of the shale specimens during the damage process. The box dimension method was used to calculate the fractal dimension of the shale specimens at the final damage, and it was found that the damage was more intense and the fracture network was more complex at high dip angles, and there was an angular threshold.

Dual-energy CT revisited: a focused review of clinical use cases.

Dual-energy CT (DECT) has been available for more than 15 years and has undergone continuous technical development and refinement. Recently, the first photon-counting CT scanner became clinically available and has the potential to further expand the possibilities of spectral imaging. Numerous studies on DECT have been published since its creation, highlighting the clinical applications of the various reconstructions enabled by DECT. The aim of this focused review is to succinctly summarize basic principles and available technical concepts of DECT and to discuss established applications relevant to the daily clinical routine. DECT is instrumental for a broad variety of clinical use cases. While some DECT applications can enhance day-to-day clinical practice, others are still subject to broad-scale validation and should therefore be handled with restraint in the clinical routine. · Virtual monoenergetic images, virtual unenhanced images, and iodine maps are the most well-investigated and relevant dual-energy CT reconstructions for clinical application.. · Low-keV virtual monoenergetic images (VMIs) yield superior image and iodine contrast, which can be leveraged for improved vessel assessment and lesion conspicuity, or to reduce contrast media or radiation dose. VMIs at intermediate energies can serve as a replacement for conventional grey-scale images. VMIs at high keV enable efficient artifact reduction, which can be further optimized in combination with dedicated metal artifact reduction algorithms.. · Iodine maps and virtual unenhanced images can improve lesion detection in oncologic imaging and enable lesion assessment in monophasic CT examinations, which may allow a reduction of correlative and follow-up imaging..

Radiological classification of the Heidelberg triangle and its application in laparoscopic pancreaticoduodenectomy for malignancies

BackgroundThe TRIANGLE operation benefits patients with pancreatic cancer; however, the Heidelberg triangle, where the operation occurs, contains vessels that can impact safety, especially in laparoscopic pancreaticoduodenectomy (LPD) with the TRIANGLE operation. This study aimed to identify Heidelberg triangle vessel types and their implications in pancreaticoduodenectomy (PD).MethodsRetrospective collection of radiographic data was performed from January 2017 to April 2023. Three-dimensional (3D) CT reconstructions were performed on patients. Vascular types in the Heidelberg triangle were classified based on named vessels crossing its interior. The impact of these types on surgical outcomes and complications in PD with the TRIANGLE operation was assessed.ResultsPreoperative CT reconstruction was conducted on 184 pancreatic surgery patients. The findings revealed 99 patients (53.8%) with the type I Heidelberg triangle, lacking named vessels crossing the interior. Type II (n = 85, 46.2%), with named vessels crossing the interior, was identified. Among reconstructed patients who underwent PD with the TRIANGLE operation (n = 103), they were categorized as type I (n = 57) or type II (n = 46). The results showed that LPD patients with type II had significantly higher median intraoperative blood loss (300 mL vs. 200 mL, P = 0.030) and mean examined lymph nodes (17.2 ± 7.6 vs. 13.4 ± 5.2, P = 0.019) compared to those with type I. No significant differences were found in operative time or postoperative complications.ConclusionThe presence of named vessels crossing the interior of the Heidelberg triangle was associated with increased intraoperative bleeding during LPD combined with the TRIANGLE operation. Therefore, targeted preoperative planning is required before the operation, thus improving the safety of the TRIANGLE operation in minimally invasive surgery.

Convolutional sparse coding for compressed sensing photoacoustic CT reconstruction with partially known support.

In photoacoustic tomography (PAT), imaging speed is an essential metric that is restricted by the pulse laser repetition rate and the number of channels on the data acquisition card (DAQ). Reconstructing the initial sound pressure distribution with fewer elements can significantly reduce hardware costs and back-end acquisition pressure. However, undersampling will result in artefacts in the photoacoustic image, degrading its quality. Dictionary learning (DL) has been utilised for various image reconstruction techniques, but they disregard the uniformity of pixels in overlapping blocks. Therefore, we propose a compressive sensing (CS) reconstruction algorithm for circular array PAT based on gradient domain convolutional sparse coding (CSCGR). A small number of non-zero signal positions in the sparsely encoded feature map are used as partially known support (PKS) in the reconstruction procedure. The CS-CSCGR-PKS-based reconstruction algorithm can use fewer ultrasound transducers for signal acquisition while maintaining image fidelity. We demonstrated the effectiveness of this algorithm in sparse imaging through imaging experiments on the mouse torso, brain, and human fingers. Reducing the number of array elements while ensuring imaging quality effectively reduces equipment hardware costs and improves imaging speed.

Multi-Channel Optimization Generative Model for Stable Ultra-Sparse-View CT Reconstruction.

Score-based generative model (SGM) has risen to prominence in sparse-view CT reconstruction due to its impressive generation capability. The consistency of data is crucial in guiding the reconstruction process in SGM-based reconstruction methods. However, the existing data consistency policy exhibits certain limitations. Firstly, it employs partial data from the reconstructed image of the iteration process for image updates, which leads to secondary artifacts with compromising image quality. Moreover, the updates to the SGM and data consistency are considered as distinct stages, disregarding their interdependent relationship. Additionally, the reference image used to compute gradients in the reconstruction process is derived from the intermediate result rather than ground truth. Motivated by the fact that a typical SGM yields distinct outcomes with different random noise inputs, we propose a Multi-channel Optimization Generative Model (MOGM) for stable ultra-sparse-view CT reconstruction by integrating a novel data consistency term into the stochastic differential equation model. Notably, the unique aspect of this data consistency component is its exclusive reliance on original data for effectively confining generation outcomes. Furthermore, we pioneer an inference strategy that traces back from the current iteration result to ground truth, enhancing reconstruction stability through foundational theoretical support. We also establish a multi-channel optimization reconstruction framework, where conventional iterative techniques are employed to seek the reconstruction solution. Quantitative and qualitative assessments on 23 views datasets from numerical simulation, clinical cardiac and sheep's lung underscore the superiority of MOGM over alternative methods. Reconstructing from just 10 and 7 views, our method consistently demonstrates exceptional performance.

Bi-Constraints Diffusion: A Conditional Diffusion Model with Degradation Guidance for Metal Artifact Reduction.

In recent years, score-based diffusion models have emerged as effective tools for estimating score functions from empirical data distributions, particularly in integrating implicit priors with inverse problems like CT reconstruction. However, score-based diffusion models are rarely explored in challenging tasks such as metal artifact reduction (MAR). In this paper, we introduce the BiConstraints Diffusion Model for Metal Artifact Reduction (BCDMAR), an innovative approach that enhances iterative reconstruction with a conditional diffusion model for MAR. This method employs a metal artifact degradation operator in place of the traditional metal-excluded projection operator in the data-fidelity term, thereby preserving structure details around metal regions. However, scorebased diffusion models tend to be susceptible to grayscale shifts and unreliable structures, making it challenging to reach an optimal solution. To address this, we utilize a precorrected image as a prior constraint, guiding the generation of the score-based diffusion model. By iteratively applying the score-based diffusion model and the data-fidelity step in each sampling iteration, BCDMAR effectively maintains reliable tissue representation around metal regions and produces highly consistent structures in non-metal regions. Through extensive experiments focused on metal artifact reduction tasks, BCDMAR demonstrates superior performance over other state-of-the-art unsupervised and supervised methods, both quantitatively and in terms of visual results.

Wavelet-Inspired Multi-Channel Score-Based Model for Limited-Angle CT Reconstruction.

Score-based generative model (SGM) has demonstrated great potential in the challenging limited-angle CT (LA-CT) reconstruction. SGM essentially models the probability density of the ground truth data and generates reconstruction results by sampling from it. Nevertheless, direct application of the existing SGM methods to LA-CT suffers multiple limitations. Firstly, the directional distribution of the artifacts attributing to the missing angles is ignored. Secondly, the different distribution properties of the artifacts in different frequency components have not been fully explored. These drawbacks would inevitably degrade the estimation of the probability density and the reconstruction results. After an in-depth analysis of these factors, this paper proposes a Wavelet-Inspired Score-based Model (WISM) for LA-CT reconstruction. Specifically, besides training a typical SGM with the original images, the proposed method additionally performs the wavelet transform and models the probability density in each wavelet component with an extra SGM. The wavelet components preserve the spatial correspondence with the original image while performing frequency decomposition, thereby keeping the directional property of the artifacts for further analysis. On the other hand, different wavelet components possess more specific contents of the original image in different frequency ranges, simplifying the probability density modeling by decomposing the overall density into component-wise ones. The resulting two SGMs in the image-domain and wavelet-domain are integrated into a unified sampling process under the guidance of the observation data, jointly generating high-quality and consistent LA-CT reconstructions. The experimental evaluation on various datasets consistently verifies the superior performance of the proposed method over the competing method.

LOQUAT: Low-Rank Quaternion Reconstruction for Photon-Counting CT.

Photon-counting computed tomography (PCCT) may dramatically benefit clinical practice due to its versatility such as dose reduction and material characterization. However, the limited number of photons detected in each individual energy bin can induce severe noise contamination in the reconstructed image. Fortunately, the notable low-rank prior inherent in the PCCT image can guide the reconstruction to a denoised outcome. To fully excavate and leverage the intrinsic low-rankness, we propose a novel reconstruction algorithm based on quaternion representation (QR), called low-rank quaternion reconstruction (LOQUAT). First, we organize a group of nonlocal similar patches into a quaternion matrix. Then, an adjusted weighted Schatten-p norm (AWSN) is introduced and imposed on the matrix to enforce its low-rank nature. Subsequently, we formulate an AWSN-regularized model and devise an alternating direction method of multipliers (ADMM) framework to solve it. Experiments on simulated and real-world data substantiate the superiority of the LOQUAT technique over several state-of-the-art competitors in terms of both visual inspection and quantitative metrics. Moreover, our QR-based method exhibits lower computational complexity than some popular tensor representation (TR) based counterparts. Besides, the global convergence of LOQUAT is theoretically established under a mild condition. These properties bolster the robustness and practicality of LOQUAT, facilitating its application in PCCT clinical scenarios. The source code will be available at https://github.com/linzf23/LOQUAT.

Cas-PRED: A Limited-Angle Cone Beam CT Reconstruction Research Based on Prior Information

Cas-PRED: A Limited-Angle Cone Beam CT Reconstruction Research Based on Prior Information

Time-Reversion Fast-Sampling Score-Based Model for Limited-Angle CT Reconstruction.

The score-based generative model (SGM) has received significant attention in the field of medical imaging, particularly in the context of limited-angle computed tomography (LACT). Traditional SGM approaches achieved robust reconstruction performance by incorporating a substantial number of sampling steps during the inference phase. However, these established SGM-based methods require large computational cost to reconstruct one case. The main challenge lies in achieving high-quality images with rapid sampling while preserving sharp edges and small features. In this study, we propose an innovative rapid-sampling strategy for SGM, which we have aptly named the time-reversion fast-sampling (TIFA) score-based model for LACT reconstruction. The entire sampling procedure adheres steadfastly to the principles of robust optimization theory and is firmly grounded in a comprehensive mathematical model. TIFA's rapid-sampling mechanism comprises several essential components, including jump sampling, time-reversion with re-sampling, and compressed sampling. In the initial jump sampling stage, multiple sampling steps are bypassed to expedite the attainment of preliminary results. Subsequently, during the time-reversion process, the initial results undergo controlled corruption by introducing small-scale noise. The re-sampling process then diligently refines the initially corrupted results. Finally, compressed sampling fine-tunes the refinement outcomes by imposing regularization term. Quantitative and qualitative assessments conducted on numerical simulations, real physical phantom, and clinical cardiac datasets, unequivocally demonstrate that TIFA method (using 200 steps) outperforms other state-of-the-art methods (using 2000 steps) from available [0°, 90°] and [0°, 60°]. Furthermore, experimental results underscore that our TIFA method continues to reconstruct high-quality images even with 10 steps. Our code at https://github.com/tianzhijiaoziA/TIFADiffusion.

Low-dose CT reconstruction using dataset-free learning.

Low-Dose computer tomography (LDCT) is an ideal alternative to reduce radiation risk in clinical applications. Although supervised-deep-learning-based reconstruction methods have demonstrated superior performance compared to conventional model-driven reconstruction algorithms, they require collecting massive pairs of low-dose and norm-dose CT images for neural network training, which limits their practical application in LDCT imaging. In this paper, we propose an unsupervised and training data-free learning reconstruction method for LDCT imaging that avoids the requirement for training data. The proposed method is a post-processing technique that aims to enhance the initial low-quality reconstruction results, and it reconstructs the high-quality images by neural work training that minimizes the ℓ1-norm distance between the CT measurements and their corresponding simulated sinogram data, as well as the total variation (TV) value of the reconstructed image. Moreover, the proposed method does not require to set the weights for both the data fidelity term and the plenty term. Experimental results on the AAPM challenge data and LoDoPab-CT data demonstrate that the proposed method is able to effectively suppress the noise and preserve the tiny structures. Also, these results demonstrate the rapid convergence and low computational cost of the proposed method. The source code is available at https://github.com/linfengyu77/IRLDCT.

Tiny Defect-Oriented Single-View CT Reconstruction Based on a Hybrid Framework

Tiny Defect-Oriented Single-View CT Reconstruction Based on a Hybrid Framework

Blind CT Image Quality Assessment Using DDPM-Derived Content and Transformer-Based Evaluator.

Lowering radiation dose per view and utilizing sparse views per scan are two common CT scan modes, albeit often leading to distorted images characterized by noise and streak artifacts. Blind image quality assessment (BIQA) strives to evaluate perceptual quality in alignment with what radiologists perceive, which plays an important role in advancing low-dose CT reconstruction techniques. An intriguing direction involves developing BIQA methods that mimic the operational characteristic of the human visual system (HVS). The internal generative mechanism (IGM) theory reveals that the HVS actively deduces primary content to enhance comprehension. In this study, we introduce an innovative BIQA metric that emulates the active inference process of IGM. Initially, an active inference module, implemented as a denoising diffusion probabilistic model (DDPM), is constructed to anticipate the primary content. Then, the dissimilarity map is derived by assessing the interrelation between the distorted image and its primary content. Subsequently, the distorted image and dissimilarity map are combined into a multi-channel image, which is inputted into a transformer-based image quality evaluator. By leveraging the DDPM-derived primary content, our approach achieves competitive performance on a low-dose CT dataset.

Multi-Stage Dual-domain Networks with Informative Prior and Self-Augmentation for Dual-Energy Limited-Angle CT Reconstruction

Multi-Stage Dual-domain Networks with Informative Prior and Self-Augmentation for Dual-Energy Limited-Angle CT Reconstruction

Sparse-View Spectral CT Reconstruction and Material Decomposition Based on Multi-Channel SGM.

In medical applications, the diffusion of contrast agents in tissue can reflect the physiological function of organisms, so it is valuable to quantify the distribution and content of contrast agents in the body over a period. Spectral CT has the advantages of multi-energy projection acquisition and material decomposition, which can quantify K-edge contrast agents. However, multiple repetitive spectral CT scans can cause excessive radiation doses. Sparse-view scanning is commonly used to reduce dose and scan time, but its reconstructed images are usually accompanied by streaking artifacts, which leads to inaccurate quantification of the contrast agents. To solve this problem, an unsupervised sparse-view spectral CT reconstruction and material decomposition algorithm based on the multi-channel score-based generative model (SGM) is proposed in this paper. First, multi-energy images and tissue images are used as multi-channel input data for SGM training. Secondly, the organism is multiply scanned in sparse views, and the trained SGM is utilized to generate multi-energy images and tissue images driven by sparse-view projections. After that, a material decomposition algorithm using tissue images generated by SGM as prior images for solving contrast agent images is established. Finally, the distribution and content of the contrast agents are obtained. The comparison and evaluation of this method are given in this paper, and a series of mouse scanning experiments are carried out to verify the effectiveness of the method.

Stage-by-Stage Wavelet Optimization Refinement Diffusion Model for Sparse-View CT Reconstruction.

Diffusion model has emerged as a potential tool to tackle the challenge of sparse-view CT reconstruction, displaying superior performance compared to conventional methods. Nevertheless, these prevailing diffusion models predominantly focus on the sinogram or image domains, which can lead to instability during model training, potentially culminating in convergence towards local minimal solutions. The wavelet transform serves to disentangle image contents and features into distinct frequency-component bands at varying scales, adeptly capturing diverse directional structures. Employing the wavelet transform as a guiding sparsity prior significantly enhances the robustness of diffusion models. In this study, we present an innovative approach named the Stage-by-stage Wavelet Optimization Refinement Diffusion (SWORD) model for sparse-view CT reconstruction. Specifically, we establish a unified mathematical model integrating low-frequency and high-frequency generative models, achieving the solution with an optimization procedure. Furthermore, we perform the low-frequency and high-frequency generative models on wavelet's decomposed components rather than the original sinogram, ensuring the stability of model training. Our method is rooted in established optimization theory, comprising three distinct stages, including low-frequency generation, high-frequency refinement and domain transform. The experimental results demonstrated that the proposed method outperformed existing state-of-the-art methods both quantitatively and qualitatively.