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Wieslaw L Nowinski

Publications and source records attributed to Wieslaw L Nowinski.

At least 19 recordsLinked to original sources

Correlation between the anatomical and functional human subthalamic nucleus.

This work addresses the spatial correlation between the anatomical and functional human subthalamic nucleus (STN). The anatomical STN (A-STN), derived from the Schaltenbrand-Wahren brain atlas, is histology based. The functional STN (F-STN) is probabilistic, constructed from neuroelectrophysiological and neuroimaging data of 184 Parkinson's disease patients. The A-STN and F-STN are placed in the same space and compared in terms of mutual relative overlapping of anatomy with function. The F-STN and A-STN correlate well for medium and high probabilities of the F-STN. For probability p >or= 0.3, >95% of F-STN is inside the A-STN, and for p >or= 0.5, the complete F-STN is inside the A-STN for each left and right STN. Therefore, the F-STN for p = 0.5 can potentially be used for identification of the STN in neuroimages.

Anatomy, Artistic↗

Quantification and visualization of three-dimensional inconsistency of the globus pallidus internus in the Schaltenbrand-Wahren brain atlas.

The major shortcomings of the Schaltenbrand-Wahren (SW) brain atlas include 3-dimensional (3D) inconsistency and spatial sparseness. This work quantifies and visualizes 3D inconsistency of the globus pallidus internus (GPi), a stereotactic target for the treatment of Parkinson's disease, dystonia and Huntington disease. The GPi 3D models 3D-A, 3D-C and 3D-S are reconstructed from the SW axial, coronal and sagittal microseries, respectively, by applying a shape-based (Nonuniform Rational B Splines) method. All three 3D models, placed in the SW coordinate system, are compared quantitatively in terms of location (centroids), size (volumes), shape (normalized eigen values), orientation (eigen vectors) and mutual spatial relationships (overlaps and inclusions). The analysis is done in 3D within each orientation and across them. The reconstructed 3D GPi models substantially differ in location, size and inclusion rate. The centroid of 3D-C is located more medially (15.6 mm) than those of 3D-A (17.5 mm) and 3D-S (18.2 mm), and that of 3D-A more ventrally (-2.3 mm) than those of 3D-C (-0.1 mm) and 3D-S (-0.4 mm). 3D-S has the smallest volume (347.3 mm3); 3D-A is 1.18 and 3D-C 1.85 times larger. The highest inclusion rate is for 3D-S (54.3 and 56.3%) and the lowest for 3D-C (28.8 and 30.6%). A smaller variability is observed in shape, orientation and overlap size (196.8, 196.1 and 185.5 mm3). To get a better correspondence between 3D-C and 3D-S, the coronal microseries were scaled laterally by 1.1667. This results in a substantial improvement of the inclusion rate of 3D-S (87.9%), though raising the volume mismatch to 2.16. The GPi in the SW atlas has a substantial 3D inaccuracy within each orientation and across them. Therefore, absolute and direct reliance on the original atlas is unsafe, and this atlas has to be used with great care and understanding of its limitations. As matching various SW microseries by global scaling is not feasible, we propose the target-dependent scaling based on structure centroid matching.

Brain↗

Extraction of the midsagittal plane from morphological neuroimages using the Kullback-Leibler's measure.

A theoretically simple and computationally efficient method to extract the midsagittal plane (MSP) from volumetric neuroimages is presented. The method works in two stages (coarse and fine) and is based on calculation of the Kullback and Leibler's (KL) measure, which characterizes the difference between two distributions. Slices along the sagittal direction are analyzed with respect to a reference slice to determine the coarse MSP. To calculate the final MSP, a local search algorithm is applied. The proposed method does not need any preprocessing, like reformatting, skull stripping, etc. The algorithm was validated quantitatively on 75 MRI datasets of different pulse sequences (T1WI, T2WI, FLAIR and SPGR) and MRA. The angular and distance errors between the calculated MSP and the ground truth lines marked by the expert were calculated. The average distance and angular deviation were 1.25 pixels and 0.63 degrees , respectively. In addition, the algorithm was tested qualitatively on PD, FLAIR, MRA, and CT datasets. To analyze the robustness of the method against rotation, inhomogeneity and noise, the phantom data were used.

Arachnoid Cysts↗

Quantification and visualization of the three-dimensional inconsistency of the subthalamic nucleus in the Schaltenbrand-Wahren brain atlas.

The Schaltenbrand-Wahren (SW) brain atlas has many limitations: the major two are three-dimensional (3D) inconsistency and spatial sparseness. In this work, we quantify and visualize the 3D inconsistency of the subthalamic nucleus (STN). The STN 3D models, 3D-A, 3D-C and 3D-S, are reconstructed from the SW axial, coronal, and sagittal microseries, respectively, by using a shape-based (NURBS) approach. All three models are placed in the SW coordinate system and compared quantitatively in terms of location (centroids), size (volumes), shape (normalized eigenvalues), orientation (eigenvectors), and mutual spatial relationships (overlaps and inclusions). Analysis is done in 3D within each orientation and across them. A dedicated tool is developed for quantitative validation of 3D modeling. The average error achieved is 0.088 mm, which is at the resolution limit of the digital SW atlas. The reconstructed 3D STN models differ in location, size, shape, orientation, overlap size, and inclusion rate. The 3D-S volume is 1.27 times larger than that of 3D-A and 1.38 times larger than that of 3D-C. The highest overlap size is found between 3D-A and 3D-S. The highest inclusion rates of 52.5 and 66.6% are for 3D-A and 3D-S. 3D-C has the lowest overlap size and results in the lowest inclusion rates (around 20-30%), meaning that 3D-C is substantially displaced in comparison to 3D-A and 3D-S. The lateral centroid coordinate of 3D-C is 9.18 mm while that of 3D-S is 12.17 mm. Each of the 3D models has some limitation: 3D-A in orientation, 3D-C in location, and 3D-S in shape realism. The STN in comparison to the actual almond is smaller, and relatively (i.e. normalized to the same height) 2.2-2.4 times wider and 3.7-5.5 times longer. 3D-C becomes more similar to 3D-S by scaling the SW coronal microseries laterally by 1.3257. Then the lateral coordinates of their centroids coincide, the difference between them in orientation is 0.11 mm, and 3D-S is only 1.06 times larger than the scaled 3D-C. This operation substantially improves registration of the SW atlas with the probabilistic functional atlas. However, 3D visualization shows that both 3D-S and scaled 3D-C models are heavily interwoven resulting in low inclusion rates of about 60%. The STN in the SW atlas shows severe 3D inaccuracy within each orientation and across them, and it has to be employed with great care and understanding of its limitations.

Anatomy, Artistic↗

IVME: a tool for editing, manipulation, quantification, and labeling of cerebrovascular models.

Three-dimensional (3D) vascular models are important in medical education, interventional radiology and vascular surgery. Because of a limited quality of angiographic images and inaccuracies introduced during their processing, interactive enhancement of the resulting models is required. We introduce here a novel tool, the interactive vascular modeling environment (IVME) for editing, manipulation, quantification, and labeling of cerebrovascular models. We describe the IVME architecture and design along with the functionality supporting anatomy terminology linking, 2D and 3D labeling, editing, 2D-3D cross-referencing, measurements, and quantification. The IVME is a useful platform in education, research, and clinics to explore and manipulate the angiography data in 2D and 3D.

Cerebral Angiography↗

A probabilistic functional atlas of the VIM nucleus constructed from pre-, intra- and postoperative electrophysiological and neuroimaging data acquired during the surgical treatment of Parkinson's disease patients.

We have previously introduced a concept of a probabilistic functional atlas (PFA) to overcome limitations of the current electronic stereotactic brain atlases: anatomical nature, spatial sparseness, inconsistency and lack of population information. The PFA for the STN has already been developed. This work addresses construction of the PFA for the ventrointermediate nucleus (PFA-VIM). The PFA-VIM is constructed from pre-, intra- and postoperative electrophysiological and neuroimaging data acquired during the surgical treatment of Parkinson's disease patients. The data contain the positions of the chronically implanted electrodes and their best contacts. For each patient, the intercommissural distance, height of the thalamus and width of the third ventricle were measured. An algorithm was developed to convert these data into the PFA-VIM, and to present them on axial, coronal and sagittal planes and in 3-D. The PFA-VIM gives a spatial distribution of the best contacts, and its probability is proportional to best contact concentration in a given location. The region with the highest probability corresponds to the best target. The PFA-VIM is calculated with 0.25-mm3 resolution from 107 best contacts in two situations: with and without lateral compensation against the width of the third ventricle. For the PFA-VIM compensated laterally, the anterior, lateral and dorsal coordinates of the mean value are (in mm) 6.24, 13.83, 1.68 for the left VIM and 6.54, -13.84, 2.10 for the right VIM. The coordinates of the mean value of the highest probability region along with the highest number of the best contacts (P) are: 6.25, 14.25, 1.75, P = 16, for the left VIM, and 6.0, -14.0, 1.00, P = 18, for the right VIM. The coordinate system origin is at the posterior commissure. For the PFA-VIM not compensated laterally, the coordinates of the mean value are 6.24, 13.99, 1.68 for the left VIM and 6.53, -14.13, 2.10 for the right VIM. The coordinates of the mean value of the highest probability region along with the highest number of the best contacts are 5.58, 13.67, 1.33, P = 14, for the left VIM, and 6.36, -14.03, 1.11, P = 17, for the right VIM. The PFA-VIM atlas overcomes several limitations of the current anatomical atlases and can improve targeting of thalamotomies and thalamic stimulations. It is dynamic and can easily be extended with new cases.

Algorithms↗

A medical imaging and visualization toolkit in Java.

Medical imaging research and clinical applications usually require combination and integration of various techniques ranging from image processing and analysis to realistic visualization to user-friendly interaction. Researchers with different backgrounds coming from diverse areas have been using numerous types of hardware, software, and environments to obtain their results. We also observe that students often build their tools from scratch resulting in redundant work. A generic and flexible medical imaging and visualization toolkit would be helpful in medical research and educational institutes to reduce redundant development work and hence increase research efficiency. This paper presents our experience in developing a Medical Imaging and Visualization Toolkit (BIL-kit) that is a set of comprehensive libraries as well as a number of interactive tools. The BIL-kit covers a wide range of fundamental functions from image conversion and transformation, image segmentation, and analysis to geometric model generation and manipulation, all the way up to 3D visualization and interactive simulation. The toolkit design and implementation emphasize the reusability and flexibility. BIL-kit is implemented in the Java language so that it works in hybrid and dynamic research and educational environments. This also allows the toolkit to extend its usage for the development of Web-based applications. Several BIL-kit-based tools and applications are presented including image converter, image processor, general anatomy model simulator, vascular modeling environment, and volume viewer. BIL-kit is a suitable platform for researchers and students to develop visualization and simulation prototypes, and it can also be used for the development of clinical applications.

Algorithms↗

Morphologic relationship among the corpus callosum, fornix, anterior commissure, and posterior commissure MRI-based variability study.

RATIONALE AND OBJECTIVES: This study explores morphological relationships and structural variability of the corpus callosum (CC), fornix (Fo), anterior (AC), and posterior commissures (PC). MATERIALS AND METHODS: These structures are extracted automatically on the midsagittal plane. The CC and Fo are modeled using best-fit ellipses. The parameters characterizing these structures and relationships among them are points, distances, angles, and eccentricities. The minimum, maximum and mean values, standard deviations, and coefficients of variation for all parameters are calculated for 62 diversified MRI datasets. Subsequently, the regression analysis and parameter distribution study are performed. RESULTS: The parameters have at least 10% variations. The major axis of CC and eccentricities of CC and Fo vary much less than the other parameters The major axis of CC is approximately parallel to the AC-PC line. The mean eccentricity of each of CC and Fo is greater than 0.95. The most significant correlation (P < .05) is observed between various angles and the angle between the major axes of CC and Fo. The correlation is also significant between other angles and distances. The Weibull distribution characterizes the major axis of CC, and distance between the AC and the most superior point of CC. Distribution of angle between the major axes of CC and Fo is log (logistic), and normal for the AC-PC distance. CONCLUSIONS: The AC-PC distance, used prevalently for brain normalization, is not correlated with any parameters except with the distance between the AC and the most superior point on the body of the CC with P < .05.

Brain Mapping↗

Rapid and automatic localization of the anterior and posterior commissure point landmarks in MR volumetric neuroimages.

RATIONALE AND OBJECTIVE: Accurate identification of the anterior commissure (AC) and posterior commissure (PC) is critical in neuroradiology, functional neurosurgery, human brain mapping, and neuroscience research. Moreover, major stereotactic brain atlases are based on the AC and PC. Our goal is to provide an algorithm for a rapid, robust, accurate and automatic identification of AC and PC. MATERIALS AND METHOD: The method exploits anatomical and radiological properties of AC, PC and surrounding structures, including morphological variability. The localization is done in two stages: coarse and fine. The coarse stage locates the AC and PC on the midsagittal plane by analyzing their relationships with the corpus callosum, fornix, and brainstem. The fine stage refines the AC and PC in a well-defined volume of interest, analyzing locations of lateral and third ventricles, interhemispheric fissure, and massa intermedia. RESULTS: The algorithm was developed using simple operations, like histogramming, thresholding, region growing, 1D projections. It was tested on 94 diversified T1W and SPGR datasets. After the fine stage, 71 (76%) volumes had an error between 0-1 mm for the AC and 55 (59%) for the PC. The mean errors were 1.0 mm (AC) and 1.0 mm (PC). The accuracy has improved twice due to fine stage processing. The algorithm took about 1 second for coarse and 4 seconds for fine processing on P4, 2.5 GHz. CONCLUSION: The use of anatomical and radiological knowledge including variability in algorithm formulation aids in localization of structures more accurately and robustly. This fully automatic algorithm is potentially useful in clinical setting and for research.

Algorithms↗

Quantitative analysis of brain asymmetry by using the divergence measure: normal-pathological brain discrimination.

RATIONALE AND OBJECTIVES: The human brain demonstrates approximate bilateral symmetry of anatomy, function, neurochemical activity, and electrophysiology. This symmetry reflected in radiological images may be affected by pathology. Hence quantitative analysis of brain symmetry may enable the normal and pathological brain discrimination. We propose a method based on the Jeffreys divergence measure (J-divergence), which attempts to quantify "approximate symmetry" and also aids to classify the brain as bilaterally symmetrical/asymmetrical (normal/abnormal). MATERIALS AND METHODS: The dataset included studies of 101 patients (59 without detectable pathologies and 42 with different abnormalities). First, the midsagittal plane is computed for the volume data that divides the head into two hemispheres. The J-divergence is calculated from the density functions of intensities of both the hemispheres. Statistical analysis was conducted to find the best distribution for normal/abnormal datasets. RESULTS: Statistical tests showed that the lognormal distribution best characterizes the values of the J-divergence for both normal and abnormal cases, and the threshold value for the Jeffreys divergence measure to classify the brains with and without detectable pathologies is T = 0.007. The threshold value had a sensitivity of 88.1% and specificity of 90.9%. CONCLUSION: The proposed method is fast and simple to compute. The high sensitivity and specificity indicate the results are encouraging. This method can be used for the initial analysis of data, detection of pathology, classification of dataset as presumably normal/abnormal, and localization of abnormality.

Algorithms↗

Rapid and automatic calculation of the midsagittal plane in magnetic resonance diffusion and perfusion images.

RATIONALE AND OBJECTIVES: A near real-time and fully automatic method for calculation of the midsagittal plane (MSP) for magnetic resonance (MR) diffusion and perfusion images is introduced. MATERIALS AND METHODS: The method is based on the Kullback-Leibler's (KL) measure quantifying the difference between two intensity distributions. The MSP is a sagittal plane with the highest KL measure. The method was validated quantitatively for 61 diffusion-weighted imaging (DWI), cerebral blood flow (CBF), cerebral blood volume (CBV), mean transit time (MTT), peak height (PKHT), and time to peak (TPP) data sets of 11 stroke patients based on the ground truth provided by two raters. RESULTS: Average angular errors are less than 1 degrees for DWI and less than 2 degrees for CBF and CBV. Average distance errors measured in the worst case (on the brain's bounding box) are less than 2.5 mm for DWI and less than 5 mm for CBF and CBV. This algorithmic accuracy is at the level of interrater variability. Results obtained for the other perfusions maps (MTT, PKHT, TTP) were inferior; therefore, processing of CBF or CBV is preferred for accurate and robust calculation of the MSP from perfusion maps. Calculation of the MSP takes about half a second on a standard computer. CONCLUSIONS: The proposed method is near real-time and fully automatic, and neither user interaction nor parameter setting is needed. It does not require preprocessing of data. The method potentially is useful in rapid and automated processing of MR stroke diffusion and perfusion images.

Algorithms↗

Analysis of ischemic stroke MR images by means of brain atlases of anatomy and blood supply territories.

RATIONALE AND OBJECTIVES: A method for atlas-assisted analysis of stroke magnetic resonance images that is a part of a stroke computer-assisted diagnosis system supporting rapid and quantitative checking of thrombolysis conditions is presented. MATERIALS AND METHODS: Two brain atlases are used for analysis: atlas of anatomy (AA) and atlas of blood supply territories (BSTs). To map these atlases onto scans, two methods are used at present: (1) fast Talairach transformation and (2) midsagittal plane and brain's bounding box matching. After atlas-to-scan mapping, both atlases are superimposed onto the studied images and can be used to get their underlying anatomy and BSTs. To speed up the process of analysis, the system automatically analyzes entire regions occupied by the infarct and penumbra. RESULTS: By using both atlases, the system calculates the following values for each infarct and penumbra region: (1) names of all anatomic structures and BSTs within the region, (2) volumes of occupancy for each structure and territory, and (3) percentages of occupancy for each structure and territory. In addition, the system calculates the infarct-middle cerebral artery (MCA) territory ratio for diffusion-weighted images and the penumbra-MCA territory ratio for perfusion images. Atlas-assisted analysis is fast, and calculations take less than 10 seconds. CONCLUSION: This method potentially facilitates and speeds up stroke data analysis, as well as supports decision making.

Atlases as Topic↗

Identification, segmentation, and image property study of acute infarcts in diffusion-weighted images by using a probabilistic neural network and adaptive Gaussian mixture model.

RATIONALE AND OBJECTIVES: Accurate identification of infarcted regions of the brain is critical in management of stroke patients. An efficient and fast method for identification and segmentation of infarcts in the diffusion-weighted images (DWI) is proposed. MATERIALS AND METHODS: Thirteen stroke patients were studied. DWI scans were acquired with a slice thickness of 5 mm. We have used a probabilistic neural network for selecting infarct slices and an adaptive (two-level) Gaussian mixture model for segmentation of the infarcts. Statistical analysis, such as identification of distribution, first-order statistics calculation, and receiver operating characteristic curve analysis, was performed. RESULTS: The average dice index is about 0.6, and average sensitivity and specificity are about 81% and 99%, respectively. The value of sensitivity and dice index are influenced by the number of false positives and false negatives. Because artifacts and infarcts have similar imaging characteristics, it is difficult to completely eliminate the artifacts. The accuracy of localization is nearly 100% as there were only two false-positive and three false-negative slices of all 381 slices. The algorithm takes about 1 minute in the Matlab computing environment to process a volume. CONCLUSION: A method to localize and segment the acute brain infarcts is proposed. The method aids the clinician in reducing the time needed to localize and segment the infarcts. The speed of localization and segmentation can be enhanced further by implementing the algorithm in VC++ and using fast algorithms for selection of Gaussian mixture model parameters.

Algorithms↗

A virtual reality simulator for remote interventional radiology: concept and prototype design.

We present a virtual reality simulator to realize interventional radiology (IR) procedures remotely. The simulator contains two subsystems: one at the local site and the other at the remote site. At the local site, the interventional radiologist interacts with a three-dimensional (3-D) vascular model extracted from the patient's data and inserts IR devices through the Motion Tracking Box (MTB), which converts physical motion (translation and rotation) of IR devices into digital signal. This signal is transferred to the Actuator Box (AB) at the remote site that drives the IR devices in the patient. The status of the IR devices is subsequently fed back to the local site and displayed on the vascular model. To prove the concept, the prototype developed employs a physical angiography phantom (mimicking the patient) and its corresponding 3-D digital model. A magnetic tracking system provides information about positioning of the IR devices in the phantom. The initial results are encouraging. The AB controlled remotely drives IR devices with resolution of 0.00288 mm/step in translation and 0.079 deg/step in rotation.

Angiography↗

Supervised range-constrained thresholding.

A novel thresholding approach to confine the intensity frequency range of the object based on supervision is introduced. It consists of three steps. First, the region of interest (ROI) is determined in the image. Then, from the histogram of the ROI, the frequency range in which the proportion of the background to the ROI varies is estimated through supervision. Finally, the threshold is determined by minimizing the classification error within the constrained variable background range. The performance of the approach has been validated against 54 brain MR images, including images with severe intensity inhomogeneity and/or noise, CT chest images, and the Cameraman image. Compared with nonsupervised thresholding methods, the proposed approach is substantially more robust and more reliable. It is also computationally efficient and can be applied to a wide class of computer vision problems, such as character recognition, fingerprint identification, and segmentation of a wide variety of medical images.

Algorithms↗

A hybrid approach to shape-based interpolation of stereotactic atlases of the human brain.

Stereotactic human brain atlases, either in print or electronic form, are useful not only in functional neurosurgery, but also in neuroradiology, human brain mapping, and neuroscience education. The existing atlases represent structures on 2D plates taken at variable, often large intervals, which limit their applications. To overcome this problem, we propose a hybrid interpolation approach to build high-resolution brain atlases from the existing ones. In this approach, all section regions of each object are grouped into two types of components: simple and complex. A NURBS-based method is designed for interpolation of the simple components, and a distance map-based method for the complex components. Once all individual objects in the atlas are interpolated, the results are combined hierarchically in a bottom-up manner to produce the interpolation of the entire atlas. In the procedure, different knowledge-based and heuristic strategies are used to preserve various topological relationships. The proposed approach has been validated quantitatively and used for interpolation of two stereotactic brain atlases: the Talairach-Tournoux atlas and Schaltenbrand-Wahren atlas. The interpolations produced are of high resolution and feature high accuracy, 3D consistency, smooth surface, and preserved topology. They potentially open new applications for electronic stereotactic brain atlases, such as atlas reformatting, accurate 3D display, and 3D nonlinear warping against normal and pathological scans. The proposed approach is also potentially useful in other applications, which require interpolation and 3D modeling from sparse and/or variable intersection interval data. An example of 3D modeling of an infarct from MR diffusion images is presented.

Algorithms↗

Fast, accurate, and automatic extraction of the modified Talairach cortical landmarks from magnetic resonance images.

The Talairach transformation is the most prevalent way to normalize brains and is hindered by, among others things, a lack of automatic determination of cortical landmarks. An algorithm to locate the modified Talairach cortical landmarks in three steps is proposed: determination of the three planes containing the landmarks; segmentation of the planes based on range-constrained thresholding and morphologic operations; and local refinement of the segmentation to locate the landmarks. The algorithm has been validated against 62 T(1)-weighted and SPGR MR diversified data sets. For each data set, it takes less than 2 s on a Pentium 4 to extract all six landmarks. The average landmark location errors are below 0.9 mm. The algorithm is robust due to incorporation of anatomic knowledge. A low computational cost results from processing of three 2D images and employing only simple operations like thresholding, basic morphologic operations, and distance transform.

Algorithms↗

Toward atlas-assisted automatic interpretation of MRI morphological brain scans in the presence of tumor.

RATIONALE AND OBJECTIVES: Determination of distorted brain anatomy surrounding a tumor causing a mass effect is much more difficult than interpretation of normal brain scans, particularly because this distortion is not easily predictable a tumor may be located in any place and vary substantially in size, shape, and radiological appearance. The objective of our work is to provide a qualitative means for rapid estimation of brain anatomy distorted by tumor. MATERIALS AND METHODS: Toward achieving this objective, we use an electronic and deformable brain atlas of gross anatomy along with a fast atlas-to-data warping technique. The deformed atlas determines the distorted anatomy surrounding a tumor and can be used for structure labeling (naming). The warping algorithm uses the Talairach transformation followed by three-dimensional nonlinear tumor deformation based on a geometric assumption that the tumor, delineated on radiological images, compresses its surrounding tissues radially. RESULTS: The approach is implemented and a dedicated application is developed. It processes the data automatically in five steps: (1) load data, (2) set the Talairach landmarks and perform the Talairach transformation, (3) segment the tumor, (4) warp the scan nonlinearly in three dimensions, and (5) explore the scan. The approach is very fast, and a magnetic resonance imaging scan is processed in 10-15 seconds on a standard personal computer. It is fully automatic and gives the user control over the entire process. CONCLUSION: Despite its limitations in modeling and validation, this practical solution provides a rapid and potentially useful qualitative assessment of anatomy deformed by a mass effect tumor.

Anatomy, Artistic↗