Fast elastic registration of soft tissues under large deformations

Points of interest linear attention network for real-time non-rigid liver volume to surface registration

BACKGROUND

In laparoscopic liver surgery, accurately predicting the displacement of key intrahepatic anatomical structures is crucial for informing the doctor's intraoperative decision-making. However, due to the constrained surgical perspective, only a partial surface of the liver is typically visible. Consequently, the utilization of non-rigid volume to surface registration methods becomes essential. But traditional registration methods lack the necessary accuracy and cannot meet real-time requirements.

PURPOSE

To achieve high-precision liver registration with only partial surface information and estimate the displacement of internal liver tissues in real-time.

METHODS

We propose a novel neural network architecture tailored for real-time non-rigid liver volume to surface registration. The network utilizes a voxel-based method, integrating sparse convolution with the newly proposed points of interest (POI) linear attention module. POI linear attention module specifically calculates attention on the previously extracted POI. Additionally, we identified the most suitable normalization method RMSINorm.

RESULTS

We evaluated our proposed network and other networks on a dataset generated from real liver models and two real datasets. Our method achieves an average error of 4.23 mm and a mean frame rate of 65.4 fps in the generation dataset. It also achieves an average error of 8.29 mm in the human breathing motion dataset.

CONCLUSIONS

Our network outperforms CNN-based networks and other attention networks in terms of accuracy and inference speed.

Robotic Assistance in Percutaneous Liver Ablation Therapies: A Systematic Review and Meta-Analysis

Objective

The aim of this systematic review and meta-analysis is to identify current robotic assistance systems for percutaneous liver ablations, compare approaches, and determine how to achieve standardization of procedural concepts for optimized ablation outcomes.

Background

Image-guided surgical approaches are increasingly common. Assistance by navigation and robotic systems allows to optimize procedural accuracy, with the aim to consistently obtain adequate ablation volumes.

Methods

Several databases (PubMed/MEDLINE, ProQuest, Science Direct, Research Rabbit, and IEEE Xplore) were systematically searched for robotic preclinical and clinical percutaneous liver ablation studies, and relevant original manuscripts were included according to the Preferred Reporting items for Systematic Reviews and Meta-Analyses guidelines. The endpoints were the type of device, insertion technique (freehand or robotic), planning, execution, and confirmation of the procedure. A meta-analysis was performed, including comparative studies of freehand and robotic techniques in terms of radiation dose, accuracy, and Euclidean error.

Results

The inclusion criteria were met by 33/755 studies. There were 24 robotic devices reported for percutaneous liver surgery. The most used were the MAXIO robot (8/33; 24.2%), Zerobot, and AcuBot (each 2/33, 6.1%). The most common tracking system was optical (25/33, 75.8%). In the meta-analysis, the robotic approach was superior to the freehand technique in terms of individual radiation (0.5582, 95% confidence interval [CI] = 0.0167-1.0996, dose-length product range 79-2216 mGy.cm), accuracy (0.6260, 95% CI = 0.1423-1.1097), and Euclidean error (0.8189, 95% CI = -0.1020 to 1.7399).

Conclusions

Robotic assistance in percutaneous ablation for liver tumors achieves superior results and reduces errors compared with manual applicator insertion. Standardization of concepts and reporting is necessary and suggested to facilitate the comparison of the different parameters used to measure liver ablation results. The increasing use of image-guided surgery has encouraged robotic assistance for percutaneous liver ablations. This systematic review analyzed 33 studies and identified 24 robotic devices, with optical tracking prevailing. The meta-analysis favored robotic assessment, showing increased accuracy and reduced errors compared with freehand technique, emphasizing the need for conceptual standardization.

Density-adaptive registration of pointclouds based on Dirichlet Process Gaussian Mixture Models

We propose an algorithm for rigid registration of pre- and intra-operative patient anatomy, represented as pointclouds, during minimally invasive surgery. This capability is essential for development of augmented reality systems for guiding such interventions. Key challenges in this context are differences in the point density in the pre- and intra-operative pointclouds, and potentially low spatial overlap between the two. Solutions, correspondingly, must be robust to both of these phenomena. We formulated a pointclouds registration approach which considers the pointclouds after rigid transformation to be observations of a global non-parametric probabilistic model named Dirichlet Process Gaussian Mixture Model. The registration problem is solved by minimizing the Kullback-Leibler divergence in a variational Bayesian inference framework. By this means, all unknown parameters are recursively inferred, including, importantly, the optimal number of mixture model components, which ensures the model complexity efficiently matches that of the observed data. By presenting the pointclouds as KDTrees, both the data and model are expanded in a coarse-to-fine style. The scanning weight of each point is estimated by its neighborhood, imparting the algorithm with robustness to point density variations. Experiments on several datasets with different levels of noise, outliers and pointcloud overlap show that our method has a comparable accuracy, but higher efficiency than existing Gaussian Mixture Model methods, whose performance is sensitive to the number of model components.

Light-Weight Deformable Registration Using Adversarial Learning With Distilling Knowledge

Deformable registration is a crucial step in many medical procedures such as image-guided surgery and radiation therapy. Most recent learning-based methods focus on improving the accuracy by optimizing the non-linear spatial correspondence between the input images. Therefore, these methods are computationally expensive and require modern graphic cards for real-time deployment. In this paper, we introduce a new Light-weight Deformable Registration network that significantly reduces the computational cost while achieving competitive accuracy. In particular, we propose a new adversarial learning with distilling knowledge algorithm that successfully leverages meaningful information from the effective but expensive teacher network to the student network. We design the student network such as it is light-weight and well suitable for deployment on a typical CPU. The extensively experimental results on different public datasets show that our proposed method achieves state-of-the-art accuracy while significantly faster than recent methods. We further show that the use of our adversarial learning algorithm is essential for a time-efficiency deformable registration method. Finally, our source code and trained models are available at https://github.com/aioz-ai/LDR_ALDK.

Clinical use of augmented reality, mixed reality, three-dimensional-navigation and artificial intelligence in liver surgery

A precise knowledge of intra-parenchymal vascular and biliary architecture and the location of lesions in relation to the complex anatomy is indispensable to perform liver surgery. Therefore, virtual three-dimensional (3D)-reconstruction models from computed tomography/magnetic resonance imaging scans of the liver might be helpful for visualization. Augmented reality, mixed reality and 3D-navigation could transfer such 3D-image data directly into the operation theater to support the surgeon. This review examines the literature about the clinical and intraoperative use of these image guidance techniques in liver surgery and provides the reader with the opportunity to learn about these techniques. Augmented reality and mixed reality have been shown to be feasible for the use in open and minimally invasive liver surgery. 3D-navigation facilitated targeting of intraparenchymal lesions. The existing data is limited to small cohorts and description about technical details e.g., accordance between the virtual 3D-model and the real liver anatomy. Randomized controlled trials regarding clinical data or oncological outcome are not available. Up to now there is no intraoperative application of artificial intelligence in liver surgery. The usability of all these sophisticated image guidance tools has still not reached the grade of immersion which would be necessary for a widespread use in the daily surgical routine. Although there are many challenges, augmented reality, mixed reality, 3D-navigation and artificial intelligence are emerging fields in hepato-biliary surgery.

Morphologic Change of In Vivo Porcine Liver Under 13 mm Hg Pneumoperitoneum Pressure

BACKGROUND

Clinically, the total and residual liver volume must be accurately calculated before major hepatectomy. However, liver volume might be influenced by pneumoperitoneum during surgery. Changes in liver volume change also affect the accuracy of simulation and augmented reality navigation systems, which are commonly first validated in animal models. In this study, the morphologic changes in porcine livers in vivo under 13 mm Hg pneumoperitoneum pressure were investigated.

MATERIALS AND METHODS

Twenty male pigs were scanned with contrast-enhanced computed tomography without pneumoperitoneum and with 13 mm Hg pneumoperitoneum pressure.

RESULTS

The surface area and volume of the liver and the vascular diameter of the aortic lumen, inferior vena cava lumen, and portal vein lumen were measured. There were statistically significant differences in the surface area and volume of the liver (P=0.000), transverse diameter of the portal vein (P=0.038), longitudinal diameter of the inferior vena cava (P=0.033), longitudinal diameter of the portal vein (P=0.036), vascular cross-sectional area of the inferior vena cava (P=0.028), and portal vein (P=0.038) before and after 13 mm Hg pneumoperitoneum pressure.

CONCLUSIONS

This study indicated that the creation of pneumoperitoneum at 13 mm Hg pressure in a porcine causes liver morphologic alterations affecting the area and volume, as well as the diameter of a blood vessel.

An Abdominal Registration Technology for Integration of Nanomaterial Imaging-Aided Diagnosis and Treatment

Image registration technology is a key technology used in the process of nanomaterial imaging-aided diagnosis and targeted therapy effect monitoring for abdominal diseases. Recently, the deep-learning based methods have been increasingly used for large-scale medical image registration, because their iteration is much less than those of traditional ones. In this paper, a coarse-to-fine unsupervised learning-based three-dimensional (3D) abdominal CT image registration method is presented. Firstly, an affine transformation was used as an initial step to deal with large deformation between two images. Secondly, an unsupervised total loss function containing similarity, smoothness, and topology preservation measures was proposed to achieve better registration performances during convolutional neural network (CNN) training and testing. The experimental results demonstrated that the proposed method severally obtains the average MSE, PSNR, and SSIM values of 0.0055, 22.7950, and 0.8241, which outperformed some existing traditional and unsupervised learning-based methods. Moreover, our method can register 3D abdominal CT images with shortest time and is expected to become a real-time method for clinical application.

Registration of Magnetic Resonance Tomography (MRT) Data with a Low Frequency Adaption of Fourier-Mellin-SOFT (LF-FMS)

Fourier-Mellin-SOFT (FMS) is a rigid 3D registration method, which allows the robust registration of 3 degrees-of-freedom (dof) rotation, 1-dof scale, and 3-dof translation between scans on discrete grids. FMS is based on a spectral decomposition of these 7-dof. This complete spectral representation of the input data enables an adaption to certain frequency ranges. This special property is used here to focus on relevant mutual 3D information between bone structures with a Low Frequency adaptation of FMS (LF-FMS), that is, it is utilized for matching and concurrently determining corresponding transformation parameters. This process is applied on a set of Magnetic Resonance Tomography (MRT) data representing the hand region, in particular the carpal bone area, in a sequence of different hand positions. This data set is available for different probands, which allows a comparison of resulting parameter plots and furthermore matching in between bone structures.

Strain Energy Decay Predicts Elastic Registration Accuracy From Intraoperative Data Constraints

Image-guided intervention for soft tissue organs depends on the accuracy of deformable registration methods to achieve effective results. While registration techniques based on elastic theory are prevalent, no methods yet exist that can prospectively estimate registration uncertainty to regulate sources and mitigate consequences of localization error in deforming organs. This paper introduces registration uncertainty metrics based on dispersion of strain energy from boundary constraints to predict the proportion of target registration error (TRE) remaining after nonrigid elastic registration. These uncertainty metrics depend on the spatial distribution of intraoperative constraints provided to registration with relation to patient-specific organ geometry. Predictive linear and bivariate gamma models are fit and cross-validated using an existing dataset of 6291 simulated registration examples, plus 699 novel simulated registrations withheld for independent validation. Average uncertainty and average proportion of TRE remaining after elastic registration are strongly correlated ( r = 0.78 ), with mean absolute difference in predicted TRE equivalent to 0.9 ± 0.6 mm (cross-validation) and 0.9 ± 0.5 mm (independent validation). Spatial uncertainty maps also permit localized TRE estimates accurate to an equivalent of 3.0 ± 3.1 mm (cross-validation) and 1.6 ± 1.2 mm (independent validation). Additional clinical evaluation of vascular features yields localized TRE estimates accurate to 3.4 ± 3.2 mm. This work formalizes a lower bound for the inherent uncertainty of nonrigid elastic registrations given coverage of intraoperative data constraints, and demonstrates a relation to TRE that can be predictively leveraged to inform data collection and provide a measure of registration confidence for elastic methods.

Deformation modeling based on mechanical properties of liver tissue for virtuanormal vectors of trianglesl surgical simulation

PURPOSE

In this paper, a method for rapidly constructing a virtual surgical simulation system is proposed. A deformation model based on the mechanical properties of the liver and a rapid collision detection between the surgical micro-instruments and the liver tissue are included in this method. The purpose of this work is to improve the accuracy and real time of particle model deformation interaction in virtual surgery system.

METHODS

Firstly, a finite element model is established based on the constitutive model parameters of liver tissue. According to the simulation results, a mathematical model of node displacement is established. Secondly, the virtual liver is established based on the fast model reconstruction method, and the virtual manipulator is controlled by Geomagic Touch manipulator. Based on the hybrid bounding box, a rapid collision detection process between the instrument and liver is realized and the proposed deformation method is used to simulate the deformation of liver tissue.

RESULTS

The simulation and experiment results show that the proposed deformation model can achieve high deformation interaction accuracy. The collision detection algorithm based on the hybrid bounding boxes can realize the collision between the liver and the instrument, and the established virtual surgical simulation system can simulate the liver tissue deformation in the case of small loading displacement.

CONCLUSIONS

The effectiveness of the collision detection algorithm and deformation model was verified by an established virtual surgery simulation system. The proposed rapid construction method of virtual surgical simulation is feasible.

Image quality improvement of single-shot turbo spin-echo magnetic resonance imaging of female pelvis using a convolutional neural network

We have developed a deep learning-based approach to improve image quality of single-shot turbo spin-echo (SSTSE) images of female pelvis. We aimed to compare the deep learning-based single-shot turbo spin-echo (DL-SSTSE) images of female pelvis with turbo spin-echo (TSE) and conventional SSTSE images in terms of image quality.One hundred five and 21 subjects were used as training and test sets, respectively. We performed 6-fold cross validation. In the training process, low-quality images were generated from TSE images as input. TSE images were used as ground truth images. In the test process, the trained convolutional neural network was applied to SSTSE images. The output images were denoted as DL-SSTSE images. Apart from DL-SSTSE images, classical filtering methods were adopted to SSTSE images. Generated images were denoted as F-SSTSE images. Contrast ratio (CR) of gluteal fat and myometrium and signal-to-noise ratio (SNR) of gluteal fat were measured for all images. Two radiologists graded these images using a 5-point scale and evaluated the image quality with regard to overall image quality, contrast, noise, motion artifact, boundary sharpness of layers in the uterus, and the conspicuity of the ovaries. CRs, SNRs, and image quality scores were compared using the Steel-Dwass multiple comparison tests.CRs and SNRs were significantly higher in DL-SSTSE, F-SSTSE, and TSE images than in SSTSE images. Scores with regard to overall image quality, contrast, noise, and boundary sharpness of layers in the uterus were significantly higher on DL-SSTSE and TSE images than on SSTSE images. There were no significant differences in the CRs, SNRs, and respective scores between DL-SSTSE and TSE images. The score with regard to motion artifacts was significantly higher on DL-SSTSE, F-SSTSE, and SSTSE images than on TSE images. The score with regard to the conspicuity of ovaries was significantly higher on DL-SSTSE images than on F-SSTSE, SSTSE, and TSE images (P < .001).DL-SSTSE images showed higher image quality as compared with SSTSE images. In comparison with conventional TSE images, DL-SSTSE images had acceptable image quality while keeping the advantage of the motion artifact-robustness and acquisition time efficiency in SSTSE imaging.

Accelerating B-spline interpolation on GPUs: Application to medical image registration

BACKGROUND AND OBJECTIVE

B-spline interpolation (BSI) is a popular technique in the context of medical imaging due to its adaptability and robustness in 3D object modeling. A field that utilizes BSI is Image Guided Surgery (IGS). IGS provides navigation using medical images, which can be segmented and reconstructed into 3D models, often through BSI. Image registration tasks also use BSI to transform medical imaging data collected before the surgery and intra-operative data collected during the surgery into a common coordinate space. However, such IGS tasks are computationally demanding, especially when applied to 3D medical images, due to the complexity and amount of data involved. Therefore, optimization of IGS algorithms is greatly desirable, for example, to perform image registration tasks intra-operatively and to enable real-time applications. A traditional CPU does not have sufficient computing power to achieve these goals and, thus, it is preferable to rely on GPUs. In this paper, we introduce a novel GPU implementation of BSI to accelerate the calculation of the deformation field in non-rigid image registration algorithms.

METHODS

Our BSI implementation on GPUs minimizes the data that needs to be moved between memory and processing cores during loading of the input grid, and leverages the large on-chip GPU register file for reuse of input values. Moreover, we re-formulate our method as trilinear interpolations to reduce computational complexity and increase accuracy. To provide pre-clinical validation of our method and demonstrate its benefits in medical applications, we integrate our improved BSI into a registration workflow for compensation of liver deformation (caused by pneumoperitoneum, i.e., inflation of the abdomen) and evaluate its performance.

RESULTS

Our approach improves the performance of BSI by an average of 6.5×  and interpolation accuracy by 2×  compared to three state-of-the-art GPU implementations. Through pre-clinical validation, we demonstrate that our optimized interpolation accelerates a non-rigid image registration algorithm, which is based on the Free Form Deformation (FFD) method, by up to 34%.

CONCLUSION

Our study shows that we can achieve significant performance and accuracy gains with our novel parallelization scheme that makes effective use of the GPU resources. We show that our method improves the performance of real medical imaging registration applications used in practice today.

Intraoperative Correction of Liver Deformation Using Sparse Surface and Vascular Features via Linearized Iterative Boundary Reconstruction

During image guided liver surgery, soft tissue deformation can cause considerable error when attempting to achieve accurate localization of the surgical anatomy through image-to-physical registration. In this paper, a linearized iterative boundary reconstruction technique is proposed to account for these deformations. The approach leverages a superposed formulation of boundary conditions to rapidly and accurately estimate the deformation applied to a preoperative model of the organ given sparse intraoperative data of surface and subsurface features. With this method, tracked intraoperative ultrasound (iUS) is investigated as a potential data source for augmenting registration accuracy beyond the capacity of conventional organ surface registration. In an expansive simulated dataset, features including vessel contours, vessel centerlines, and the posterior liver surface are extracted from iUS planes. Registration accuracy is compared across increasing data density to establish how iUS can be best employed to improve target registration error (TRE). From a baseline average TRE of 11.4 ± 2.2 mm using sparse surface data only, incorporating additional sparse features from three iUS planes improved average TRE to 6.4 ± 1.0 mm. Furthermore, increasing the sparse coverage to 16 tracked iUS planes improved average TRE to 3.9 ± 0.7 mm, exceeding the accuracy of registration based on complete surface data available with more cumbersome intraoperative CT without contrast. Additionally, the approach was applied to three clinical cases where on average error improved 67% over rigid registration and 56% over deformable surface registration when incorporating additional features from one independent tracked iUS plane.

Estimation of boundary conditions for patient-specific liver simulation during augmented surgery

PURPOSE

Augmented reality can improve the outcome of hepatic surgeries, assuming an accurate liver model is available to estimate the position of internal structures. While researchers have proposed patient-specific liver simulations, very few have addressed the question of boundary conditions. Resulting mainly from ligaments attached to the liver, they are not visible in preoperative images, yet play a key role in the computation of the deformation.

METHOD

We propose to estimate both the location and stiffness of ligaments by using a combination of a statistical atlas, numerical simulation, and Bayesian inference. Ligaments are modeled as polynomial springs connected to a liver finite element model. They are initialized using an anatomical atlas and stiffness properties taken from the literature. These characteristics are then corrected using a reduced-order unscented Kalman filter based on observations taken from the laparoscopic image stream.

RESULTS

Our approach is evaluated using synthetic data and phantom data. By relying on a simplified representation of the ligaments to speed up computation times, it is not estimating the true characteristics of ligaments. However, results show that our estimation of the boundary conditions still improves the accuracy of the simulation by 75% when compared to typical methods involving Dirichlet boundary conditions.

CONCLUSION

By estimating patient-specific boundary conditions, using tracked liver motion from RGB-D data, our approach significantly improves the accuracy of the liver model. The method inherently handles noisy observations, a substantial feature in the context of augmented reality.

A case study: impact of target surface mesh size and mesh quality on volume-to-surface registration performance in hepatic soft tissue navigation

Purpose

Soft tissue deformation severely impacts the registration of pre- and intra-operative image data during computer-assisted navigation in laparoscopic liver surgery. However, quantifying the impact of target surface size, surface orientation, and mesh quality on non-rigid registration performance remains an open research question. This paper aims to uncover how these affect volume-to-surface registration performance.

Methods

To find such evidence, we design three experiments that are evaluated using a three-step pipeline: (1) volume-to-surface registration using the physics-based shape matching method or PBSM, (2) voxelization of the deformed surface to a \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1024^3$$\end{document}10243 voxel grid, and (3) computation of similarity (e.g., mutual information), distance (i.e., Hausdorff distance), and classical metrics (i.e., mean squared error or MSE).

Results

Using the Hausdorff distance, we report a statistical significance for the different partial surfaces. We found that removing non-manifold geometry and noise improved registration performance, and a target surface size of only 16.5% was necessary.

Conclusion

By investigating three different factors and improving registration results, we defined a generalizable evaluation pipeline and automatic post-processing strategies that were deemed helpful. All source code, reference data, models, and evaluation results are openly available for download: https://github.com/ghattab/EvalPBSM/.

The effect of intraoperative imaging on surgical navigation for laparoscopic liver resection surgery

Conventional surgical navigation systems rely on preoperative imaging to provide guidance. In laparoscopic liver surgery, insufflation of the abdomen (pneumoperitoneum) can cause deformations on the liver, introducing inaccuracies in the correspondence between the preoperative images and the intraoperative reality. This study evaluates the improvements provided by intraoperative imaging for laparoscopic liver surgical navigation, when displayed as augmented reality (AR). Significant differences were found in terms of accuracy of the AR, in favor of intraoperative imaging. In addition, results showed an effect of user-induced error: image-to-patient registration based on annotations performed by clinicians caused 33% more inaccuracy as compared to image-to-patient registration algorithms that do not depend on user annotations. Hence, to achieve accurate surgical navigation for laparoscopic liver surgery, intraoperative imaging is recommendable to compensate for deformation. Moreover, user annotation errors may lead to inaccuracies in registration processes.

[Navigated liver surgery : Current state and importance in the future]

The preoperative computer-assisted resection planning is the basis for every navigation. Thanks to modern algorithms, the prerequisites have been created to carry out a virtual resection planning and a risk analysis. Thus, individual segment resections can be precisely planned in any conceivable combination. The transfer of planning information and resection suggestions to the operating theater is still problematic. The so-called stereotactic liver navigation supports the exact intraoperative implementation of the planned resection strategy and provides the surgeon with real-time three-dimensional information on resection margins and critical structures during the resection. This is made possible by a surgical navigation system that measures the position of surgical instruments and then presents them together with the preoperative surgical planning data. Although surgical navigation systems have been indispensable in neurosurgery and spinal surgery for many years, these procedures have not yet become established as standard in liver surgery. This is mainly due to the technical challenge of navigating a moving organ. As the liver is constantly moving and deforming during surgery due to respiration and surgical manipulation, the surgical navigation system must be able to measure these alterations in order to adapt the preoperative navigation data to the current situation. Despite these advances, further developments are required until navigated liver resection enters clinical routine; however, it is already clear that laparoscopic liver surgery and robotic surgery will benefit most from navigation technology.

Learning soft tissue behavior of organs for surgical navigation with convolutional neural networks

PURPOSE

In surgical navigation, pre-operative organ models are presented to surgeons during the intervention to help them in efficiently finding their target. In the case of soft tissue, these models need to be deformed and adapted to the current situation by using intra-operative sensor data. A promising method to realize this are real-time capable biomechanical models.

METHODS

We train a fully convolutional neural network to estimate a displacement field of all points inside an organ when given only the displacement of a part of the organ's surface. The network trains on entirely synthetic data of random organ-like meshes, which allows us to use much more data than is otherwise available. The input and output data are discretized into a regular grid, allowing us to fully utilize the capabilities of convolutional operators and to train and infer in a highly parallelized manner.

RESULTS

The system is evaluated on in-silico liver models, phantom liver data and human in-vivo breathing data. We test the performance with varying material parameters, organ shapes and amount of visible surface. Even though the network is only trained on synthetic data, it adapts well to the various cases and gives a good estimation of the internal organ displacement. The inference runs at over 50 frames per second.

CONCLUSION

We present a novel method for training a data-driven, real-time capable deformation model. The accuracy is comparable to other registration methods, it adapts very well to previously unseen organs and does not need to be re-trained for every patient. The high inferring speed makes this method useful for many applications such as surgical navigation and real-time simulation.