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The utility of diffusion chambers as models for the description of drug disposition.

Tissue cages were employed to explore the diffusion processes of several cephalosporins into extravascular fluids. Concentrations of cefotaxime in serum and in subcutaneous chambers increased proportionally to the amount of the drug injected. Administration of single equal doses of cephalothin, cephaloridine and cefotaxime resulted in different concentration-time courses in the serum and in diffusion chambers. These observations suggest that diffusion chambers are linked to the tissue at the implantation site. None of the classical compartmental approaches can be applied to evaluate the kinetics of drug diffusion into tissue cages. Correlations of total or non-protein bound drug concentrations in tissue cages to those in the peripheral compartment assumed concentration and time dependent diffusion processes. No specific diffusion constant based on the law of Fick could be derived for the diffusion chambers used in this study. Concentration-time courses in serum and interstitial fluid can be simultaneously evaluated according to pharmacokinetic-pharmacodynamic models. Based on the equation describing the effect site this model can be used to simulate drug concentrations in tissue cages by varying the dose size or the dose interval.

Analysis of Variance↗

Do indomethacin and propofol cause cerebral ischemic damage? Diffusion-weighted magnetic resonance imaging in patients undergoing craniotomy for brain tumors.

BACKGROUND: Diffusion-weighted magnetic resonance imaging was used to determine whether indomethacin and propofol induce cerebral ischemic damage in patients undergoing craniotomy for cerebral tumors. As a secondary aim, the authors investigated whether low jugular bulb oxygen saturation values were associated with brain parenchymal damage as evaluated by diffusion-weighted imaging. METHODS: Nine patients subjected to craniotomy for supratentorial brain tumors in propofol-fentanyl anesthesia were studied. Magnetic resonance imaging including diffusion- and perfusion-weighted and structural sequences were performed (1) on the day before surgery, (2) before and (3) 20 min after administration of indomethacin (bolus of 0.2 mg/kg followed by infusion of 0.2 mg.kg.h) in the propofol-fentanyl-anesthetized patient, and (4) 2 days after surgery. Apparent diffusion coefficient maps were calculated. Jugular bulb oxygen saturation, arteriovenous oxygen difference, mean arterial blood pressure, and arterial oxygen and carbon dioxide tensions were measured simultaneously with the magnetic resonance examinations performed during anesthesia. RESULTS: No ischemic lesions were detected in the diffusion-weighted or apparent diffusion coefficient images. A nonsignificant decrease in jugular bulb oxygen saturation from 51% (range, 40-61%) to 43% (range, 37-63%) and increase in arteriovenous oxygen difference from 4.4 mm (range, 2.7-4.6 mm) to 4.7 mm (range, 2.9-5.2 mm) was observed after indomethacin administration. CONCLUSION: Administration of indomethacin during propofol anesthesia is not associated with evidence of ischemic damage in patients with brain tumors, as evaluated by diffusion-weighted imaging.

Adult↗

Diffusion-weighted imaging as a problem-solving tool in the evaluation of patients with acute strokelike syndromes.

This article addresses syndromes that clinically and/or radiologically resemble acute stroke. These syndromes generally fall into four categories. (1) Patients with acute neurological deficits with nonischemic lesions and no acute abnormality on diffusion-weighted images. These patients may have peripheral vertigo, migraines, seizures, dementia, functional disorders, amyloid angiopathy, or metabolic disorders. When these patients present, we can confidently predict that they are not undergoing infarction. (2) Patients with ischemic lesions with reversible clinical deficits. Nearly 50% of patients with transient ischemic attacks have lesions with restricted diffusion. Patients with transient global amnesia may have punctate lesions with restricted diffusion in the medial hippocampus, parahippocampal gyms, and corpus callosum. (3) Vasogenic edema syndromes that may mimic acute infarction clinically and on conventional imaging. These include eclampsia/hypertensive encephalopathy, other posterior leukoencephalopathies, human immunodeficiency virus encephalopathy, hyperperfusion syndrome following carotid endarterectomy, venous sinus thrombosis, acute demyelination, and neoplasm. These syndromes demonstrate elevated diffusion rather than the restricted diffusion associated with acute ischemic stroke. (4) Entities in which restricted diffusion may resemble acute infarction. These include pyogenic infections, herpes virus encephalitis, Creutzfeldt-Jakob disease, diffuse axonal injury, tumors with dense cell packing, and rare acute demyelinative lesions.

Diffusion↗

Experimental measurements of the diffusion coefficient of 212Pb.

Knowledge of the diffusion coefficient of Rn progeny is necessary for assessing the radiation exposure resulting from exposure to Rn and its progeny. The diffusion coefficient for 220Rn progeny was determined in ambient air by two independent methods, measuring deposition using a cylindrical tube or screens. A sampling train consisting of a diffusion tube and a screen-type diffusion battery was used for the experimental study. A range of flow rates and relative humidities was investigated. For 35% less than or equal to RH less than or equal to 85%, results from the two systems agree with each other. The diffusion coefficient of 212Pb was 0.036 +/- 0.002 cm2 s-1 and 0.037 +/- 0.004 cm2 s-1 for the tube and screen penetration methods, respectively. In low humidity air (RH less than 30%), a linear relationship between the diffusion coefficient of 212Pb and relative humidity was observed. The observed diffusion coefficient is strongly affected by the amount of material agglomerated onto the 212Pb atom. Further studies on the effects of trace gases and organics are required to fully understand the results.

Bismuth↗

Ischemia-induced changes in the extracellular space diffusion parameters, K+, and pH in the developing rat cortex and corpus callosum.

Changes in the ability of substances to diffuse in the intersticial space of the brain are important factors in the pathophysiology of cerebrovascular diseases. Extracellular space (ECS) volume fraction alpha (alpha = ECS volume/ total tissue volume), tortuosity lambda (lambda 2 = free diffusion coefficient/apparent diffusion coefficient), and nonspecific uptake (k')-three diffusion parameters of brain tissue were studied in cortex and subcortical white matter (WM) of the developing rat during anoxia. Changes were compared with the rise in extracellular potassium concentration ([K+]e), extracellular pH (pHe) shifts, and anoxic depolarization (AD). Diffusion parameters were determined from extracellular concentration-time profiles of tetramethylammonium (TMA+) or tetraethylammonium (TEA+), TMA+, TEA+, K+, and pH changes were measured using ion-selective microelectrodes. In the cortex and WM of animals at 4-12 postnatal days (P4-P12), the volume fraction, alpha, is larger than that of animals at > or = P21. Anoxia evoked by cardiac arrest brought about a typical rise in [K+]e to approximately 60-70 mM, AD of 25-30 mV, decrease in alpha, increase in lambda, and increase in k'. At P4-P6, alpha decreased from approximately 0.43 to 0.05 in cortical layer V and from approximately 0.45 to 0.5 in WM. Tortuosity, lambda, increased in the cortex from 1.50 to 2.12 and in WM from approximately 1.48 to 2.08. At P10-P12 and at P21-P23, when alpha in normoxic rats is lower than at P4-P6 by approximately 25 and 50%, respectively, the final changes in values of alpha and lambda evoked by anoxia were not significantly different from those in P4-P6. However, the younger the animal, the longer the time course of the changes. On P4-P6 final changes in alpha, lambda and k' in cortex and WM were reached after 37 +/- 3 min and 54 +/- 2 min; on P10-P12, after 24 +/- 2 and 27 +/- 3 min; and on P21-P23 at 15 +/- 1 and 17 +/- 3 min, respectively (mean +/- SE, n = 6). The time course of the changes was longer in WM than in gray matter (GM), particularly during the first postnatal week, i.e., in the period during which WM is largely unmyelinated. Changes in diffusion parameters occurred in three phases. The first slow and second fast changes occurred simultaneously with the rise in [K+]e and AD. Peaks in [K+]e and AD were reached simultaneously; the younger the animal, the longer the time course of the changes. The third phase outlasted the rise in [K+]e and AD by 10-15 min and correlated with the acid shift in pHe. Linear regression analysis revealed a positive correlation between the normoxic size of the ECS volume and the time course of the changes. Slower changes in ECS volume fraction and tortuosity in nervous tissue during development can contribute to slower impairment of signal transmission, e.g., due to lower accumulation of ions and neuroactive substances released from cells and their better diffusion from the hypoxic area in uncompacted ECS.

Animals↗

MR imaging of anisotropically restricted diffusion of water in the nervous system: technical, anatomic, and pathologic considerations.

The use of MR imaging to image anisotropically restricted diffusion (ARD) of water in the nervous system is described. The theoretical basis for the use of the pulsed gradient spin echo sequences is outlined, including an estimate of the range of cell dimensions that can be studied with this technique. The importance of restricted diffusion across myelinated white matter fibre tracts is emphasised and the capacity of MR imaging to demonstrate fibre pathways as a function of their direction is illustrated. Technical developments that have been implemented include 256 x 256 spatial resolution, a wider range of diffusion times Td, and an increased range of diffusion sensitivity parameters b. Effects of these are illustrated together with the use of gradient moment nulling methods, oblique sensitisation, and a smaller set of gradient coils that enable shorter values of echo time to be used with the same value of b. The anatomical basis for ARD imaging is analysed, and association, commissural, and projection fibre tracts are demonstrated in different planes. The published literature on variations of the apparent diffusion coefficient from normal is reviewed and examples where diffusion weighted images revealed information that was not necessarily apparent with conventional sequences are illustrated. These include cases of multiple sclerosis, chronic head injury, progressive multifocal leucoencephalopathy, cerebrovascular disease, astrocytoma, and probable metastases to the brain. Imaging of ARD affords a fascinating conjunction between the microscopic movement of water, the properties of myelinated white matter fibres, gross anatomy of the brain, and changes of the diffusion of water in disease.

Adult↗

Identification of "premyelination" by diffusion-weighted MRI.

OBJECTIVE: The purpose of this study was to compare white matter maturation as demonstrated with diffusion-weighted MRI and with myelin-sensitive histological staining. MATERIALS AND METHODS: The diffusion-, T1-, and T2-weighted SE MRI at 4.7 T was performed weekly in a total of 16 rat pups, aged from 5 days to 8 weeks, 2 animals evaluated per week. Heavily diffusion-weighted sequences were obtained with the diffusion-sensitizing gradient switched alternately in two orthogonal directions. To enhance signal intensity of anisotropic structures, a synthesized image (referred to as the "anisotropy index map") was constructed from the ratio of pairs of images acquired with diffusion sensitization of identical magnitude but orthogonal direction sensitivity. The anisotropy index maps were used for comparison with T1-weighted and heavily T2-weighted SE sequences and histological sections, respectively. RESULTS: The first evidence of diffusion anisotropy on anisotropy index maps preceded initial myelin as well as neurofibril staining by 5-12 days and T2 shortening by 2 weeks. The T1-weighted sequences did not yield visible changes and were not helpful for the assessment of ongoing white matter maturation in this model. CONCLUSION: Magnetic resonance imaging signal intensity changes based on anisotropic water diffusion were demonstrated in regions of unmyelinated cerebral white matter tracts of albino rat pups before the onset of histologically detectable myelin. The ability of in vivo mapping of premyelinating white matter maturation indicates a new diagnostic use of MRI in evaluating cerebral white matter maturation.

Animals↗

The adoption and diffusion of CT and MRI in the United States. A comparative analysis.

This study examines and compares the rates and patterns of diffusion of computerized tomography (CT) and magnetic resonance imaging (MRI) over the first 4 years of their availability. Although early diffusion of CT was more rapid than that of MRI, adoption of MRI in nonhospital settings equaled that of CT. Analysis of attributes of the technologies and attributes of the regulatory, reimbursement, and market environments surrounding the early diffusion of these technologies provides insight into their different diffusion patterns. In particular, the technical and financial uncertainties surrounding MRI have inhibited its diffusion compared with that of CT. Medicare's DRG-based prospective reimbursement system and certificate-of-need (CON) regulation by states have reduced overall MRI diffusion and stimulated purchases of MRI by nonhospital organizations. The FDA's premarket approval (PMA) program has changed marketing strategies and influenced the diffusion of MRI to a lesser degree. This analysis identifies problems in how the present health care system evaluates and adopts new, expensive, diagnostic technologies and suggests changes to make the system more responsive to present needs.

Certificate of Need↗

Prefrontal cortex transcranial magnetic stimulation does not change local diffusion: a magnetic resonance imaging study in patients with depression.

OBJECTIVE: To determine whether transcranial magnetic stimulation over the left dorsolateral prefrontal cortex produces pathologic changes or leakage of the blood-brain barrier in patients with depression by using apparent diffusion coefficient magnetic resonance imaging. BACKGROUND: Transcranial magnetic stimulation is a new technology for noninvasively stimulating the brain. It appears to be a relatively safe technique, with some important exceptions. Its neurobiologic mechanisms of action are poorly understood. One theory to explain its apparent antidepressant effects involves a potential change in local blood-brain barrier settings, allowing passage of peripheral substances directly into brain parenchyma. Knowing whether transcranial magnetic stimulation changes local brain diffusion is important as well from a safety perspective. To test whether transcranial magnetic stimulation changes local brain diffusion, we used apparent diffusion coefficient magnetic resonance imaging in depressed patients undergoing interleaved transcranial magnetic stimulation/functional magnetic resonance imaging over the left prefrontal cortex. METHODS: Within a 1.5 Tesla magnetic resonance imaging scanner, 14 depressed patients were stimulated with a figure-eight transcranial magnetic stimulation coil over the left prefrontal cortex. Apparent diffusion coefficient magnetic resonance imaging was acquired before, and immediately after, 1 Hertz transcranial magnetic stimulation (147 stimuli) intermittently delivered at a motor threshold of more than 7.35 minutes. Phase maps of the transcranial magnetic stimulation magnetic fields were used to guide region-of-interest placement. RESULTS: No significant qualitative apparent diffusion coefficient differences were observed before and after 1 Hertz transcranial magnetic stimulation underneath the coil. CONCLUSIONS: One Hertz transcranial magnetic stimulation over the left dorsolateral prefrontal cortex as applied in this study did not result in pathologic changes or leakage of the blood-brain barrier in patients with depression. If prefrontal transcranial magnetic stimulation at these usage parameters changes local diffusion, it is not an obvious or large effect.

Adolescent↗

Anisotropic ion diffusivity in intervertebral disc: an electrical conductivity approach.

STUDY DESIGN: Investigation of the transport behavior of ions in intervertebral disc using an electrical conductivity method. OBJECTIVES: To determine the electrical conductivity and ion diffusivity of nucleus pulposus and anulus fibrosus in 3 major directions (axial, circumferential, and radial). SUMMARY OF BACKGROUND DATA: Knowledge of diffusivity of small molecules is important for understanding nutrition supply in intervertebral disc and disc degeneration. However, little is known on the anisotropic behaviors of ion diffusivity and of electrical conductivity in intervertebral disc. METHODS: Electrical conductivity measurement was performed on 24 axial, circumferential, and radial anulus fibrosus specimens and 24 axial nucleus pulposus specimens from bovine coccygeal discs. The diffusivity of Na and Cl were estimated by the analysis of conductivity data. RESULTS: The electrical conductivity (mean +/- standard deviation; n = 24) of the bovine anulus fibrosus was 4.70 +/- 1.08 mS/cm in the axial, 2.86 +/- 0.83 mS/cm in the radial, and 4.38 +/- 1.25 mS/cm in the circumferential direction. For nucleus pulposus, the electrical conductivity (mean +/- standard deviation; n = 24) was 8.95 +/- 0.89 mS/cm. The mean value for nucleus pulposus was significantly higher than that of anulus fibrosus (t test, P < 0.05). For anulus fibrosus, the conductivity in the radial direction was significantly lower than in axial or circumferential directions. Similar trends were found for both Na and Cl diffusivities. Both electrical conductivity and ion diffusivity were highly sensitive to water content. CONCLUSIONS: Electrical conductivity and ion diffusivity of anulus fibrosus are anisotropic.

Animals↗

Diffusion tensor magnetic resonance imaging.

Molecular diffusion plays an important role in many biologic phenomena. The ability to study diffusion, therefore, is extremely useful in physiology and medicine. MRI offers a non-invasive window to diffusion, particularly water self-diffusion. MRI techniques, which provide diffusion sensitivity or quantitation (diffusion tensor MRI [DTI]), have found widespread application in neuroscience and medicine, including the evaluation of stroke, brain development, tumor imaging, and demyelinating disorders. We discuss the tensor nature of diffusion and provide an overview of how DTI offers unique information on tissue organization, water mobility, and disease states, particularly those of neuro-ophthalmologic interest.

Brain↗

Lattice mean-field method for stationary polymer diffusion.

We present a method to study mean-field stationary diffusion (MFSD) in polymer systems. When gradients in chemical potentials vanish, our method reduces to the Scheutjens-Fleer self-consistent field (SF-SCF) method for inhomogeneous polymer systems in equilibrium. To illustrate the concept of our MFSD method, we studied stationary diffusion between two different bulk mixtures, containing, for simplicity, noninteracting homopolymers. Four alternatives for the diffusion equation are implemented. These alternatives are based on two different theories for polymer diffusion (the slow- and fast-mode theories) and on two different ways to evaluate the driving forces for diffusion, one of which is in the spirit of the SF-SCF method. The diffusion profiles are primarily determined by the diffusion theory and they are less sensitive to the evaluation of the driving forces. The numerical stationary state results are in excellent agreement with analytical results, in spite of a minor inconsistency at the system boundaries in the numerical method. Our extension of the equilibrium SF method might be useful for the study of fluxes, steady state profiles and chain conformations in membranes (e.g., during drug delivery), and for many other systems for which simulation techniques are too time consuming.

Biophysical Phenomena↗

Fractional diffusion modeling of ion channel gating.

An anomalous diffusion model for ion channel gating is put forward. This scheme is able to describe nonexponential, power-law-like distributions of residence time intervals in several types of ion channels. Our method presents a generalization of the discrete diffusion model by Millhauser, Salpeter, and Oswald [Proc. Natl. Acad. Sci. U.S.A. 85, 1503 (1988)] to the case of a continuous, anomalous slow conformational diffusion. The corresponding generalization is derived from a continuous-time random walk composed of nearest-neighbor jumps which in the scaling limit results in a fractional diffusion equation. The studied model contains three parameters only: the mean residence time, a characteristic time of conformational diffusion, and the index of subdiffusion. A tractable analytical expression for the characteristic function of the residence time distribution is obtained. In the limiting case of normal diffusion, our prior findings [Proc. Natl. Acad. Sci. U.S.A. 99, 3552 (2002)] are reproduced. Depending on the chosen parameters, the fractional diffusion model exhibits a very rich behavior of the residence time distribution with different characteristic time regimes. Moreover, the corresponding autocorrelation function of conductance fluctuations displays nontrivial power law features. Our theoretical model is in good agreement with experimental data for large conductance potassium ion channels.

Animals↗

Single molecule measurements of repressor protein 1D diffusion on DNA.

We used single-molecule imaging techniques and measured the one-dimensional diffusion of LacI repressor proteins along elongated DNA to address the long-standing puzzle of why some proteins find their targets faster than allowed by 3D diffusion. Our analysis of the LacI transcription factor's diffusion yielded four main results: (1) LacI diffuses along nonspecific sequences of DNA in the form of 1D Brownian motion; (2) the observed 1D diffusion coefficients D1vary over an unexpectedly large range, from 2.3x10(-12) cm2/s to 1.3x10(-9) cm2/s; (3) the lengths of DNA covered by these 1D diffusions vary from 120 nm to 2920 nm; and (4) the mean values of D1 and the diffusional lengths indeed predict a LacI target binding rate 90 times faster than the 3D diffusion limit.

Bacterial Proteins↗

Lateral diffusion of CO2 in leaves is not sufficient to support photosynthesis.

Lateral diffusion of CO(2) was investigated in photosynthesizing leaves with different anatomy by gas exchange and chlorophyll a fluorescence imaging using grease to block stomata. When one-half of the leaf surface of the heterobaric species Helianthus annuus was covered by 4-mm-diameter patches of grease, the response of net CO(2) assimilation rate (A) to intercellular CO(2) concentration (C(i)) indicated that higher ambient CO(2) concentrations (C(a)) caused only limited lateral diffusion into the greased areas. When single 4-mm patches were applied to leaves of heterobaric Phaseolus vulgaris and homobaric Commelina communis, chlorophyll a fluorescence images showed dramatic declines in the quantum efficiency of photosystem II electron transport (measured as F(q)'/F(m)') across the patch, demonstrating that lateral CO(2) diffusion could not support A. The F(q)'/F(m)' values were used to compute images of C(i) across patches, and their dependence on C(a) was assessed. At high C(a), the patch effect was less in C. communis than P. vulgaris. A finite-volume porous-medium model for assimilation rate and lateral CO(2) diffusion was developed to analyze the patch images. The model estimated that the effective lateral CO(2) diffusion coefficients inside C. communis and P. vulgaris leaves were 22% and 12% of that for free air, respectively. We conclude that, in the light, lateral CO(2) diffusion cannot support appreciable photosynthesis over distances of more than approximately 0.3 mm in normal leaves, irrespective of the presence or absence of bundle sheath extensions, because of the CO(2) assimilation by cells along the diffusion pathway.

Calibration↗

Image-based color ink diffusion rendering.

This paper proposes an image-based painterly rendering algorithm for automatically synthesizing an image with color ink diffusion. We suggest a mathematical model with a physical base to simulate the phenomenon of color colloidal ink diffusing into absorbent paper. Our algorithm contains three main parts: a feature extraction phase, a Kubelka-Munk (KM) color mixing phase, and a color ink diffusion synthesis phase. In the feature extraction phase, the information of the reference image is simplified by luminance division and color segmentation. In the color mixing phase, the KM theory is employed to approximate the result when one pigment is painted upon another pigment layer. Then, in the color ink diffusion synthesis phase, the physically-based model that we propose is employed to simulate the result of color ink diffusion in absorbent paper using a texture synthesis technique. Our image-based ink diffusing rendering (IBCIDR) algorithm eliminates the drawback of conventional Chinese ink simulations, which are limited to the black ink domain, and our approach demonstrates that, without using any strokes, a color image can be automatically converted to the diffused ink style with a visually pleasing appearance.

Algorithms↗

Restricted diffusion in the brain of transgenic mice with cerebral amyloidosis.

A prominent hallmark of Alzheimer's disease pathology is cerebral amyloidosis. However, it is not clear how extracellular amyloid-beta peptide (A beta) deposition and amyloid formation compromise brain function and lead to dementia. It has been argued that extracellular amyloid deposition is neurotoxic and/or that soluble A beta oligomers impair synaptic function. Amyloid deposits, by contrast, may affect diffusion properties of the brain interstitium with implications for the transport of endogenous signalling molecules during synaptic and/or extrasynaptic transmission. We have used diffusion-weighted magnetic resonance imaging to study diffusion properties in brains of young (6-month-old) and aged (25-month-old) APP23 transgenic mice and control littermates. Our results demonstrate that fibrillar amyloid deposits and associated gliosis in brains of aged APP23 transgenic mice are accompanied by a reduction in the apparent diffusion coefficient. This decrease was most pronounced in neocortical areas with a high percentage of congophilic amyloid and was not significant in the caudate putamen, an area with only modest and diffuse amyloid deposition. These findings suggest that extracellular deposition of fibrillar amyloid and/or associated glial proliferation and hypertrophy cause restrictions to interstitial fluid diffusion. Reduced diffusivity within the interstitial space may alter volume transmission and therefore contribute to the cognitive impairment in Alzheimer's disease.

Age Factors↗

How fast do cardioactive steroids act independently of diffusion in guinea-pig myocardium?

1 The rate of onset of the inotropic effect of different cardioactive steroids (in order of increasing potency: dihydroouabain, digoxigenin, digoxin, ouabain, digitoxin) was studied in guinea-pig papillary muscles stimulated at 0.5 Hz. For an estimate of diffusion rate the time to defined levels of effect was evaluated in relation to the diameter of cylindrical muscles. 2 The dependence of onset rates on muscle diameter was more pronounced with a highly potent steroid, e.g., digitoxin, than with a less potent compound, e.g., dihydroouabain; that is, the apparent rate of diffusion was inversely correlated with the inotropic potency. Reduction of the ratio of receptor to steroid concentration with increase of ouabain or K+ concentration enhanced the apparent rate of diffusion. 3 Extrapolation to negligibly short diffusion distance indicated that the effects of the various steroids develop faster in the absence of diffusion. The effect of 50 mumol l-1 of dihydroouabain appeared more quickly than with ouabain in the perfused heart. The time courses of the inotropic effect in perfused hearts and in papillary muscles of diameters less than 0.75 mm were superimposable, indicating that the onset of the dihydroouabain effect was not controlled by diffusion. 4 After the interference of diffusion had been excluded, the rates of onset of action correlated inversely with the inotropic potencies of the steroids. The dissociation rate of the drug-receptor complex appeared to be related to the different receptor affinities.

Animals↗