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Analytical expressions for the NMR apparent diffusion coefficients in an anisotropic system and a simplified method for determining fiber orientation.

NMR measurements of anisotropic diffusion were studied using a three-dimensional random-walk model. It was found that the apparent diffusion coefficient can be expressed in a canonical form as the product of a diagonal matrix, an orthonormal rotation matrix, and a vector representing the encoding magnetic field gradient. The diffusion coefficient can be interpreted as the sum of the corresponding coefficients measured along the principal diffusion axes, weighted by the squares of the directional cosines of the encoding direction with respect to the principal axes. The analysis revealed that determining the orientation of anisotropy, in a cylindrically symmetric system, requires a minimum of four diffusion measurements. A special pulse sequence which minimized gradient cross-terms and possible restricted diffusion effects was used to characterize diffusion anisotropy in cut chicken gizzards. Diffusion coefficients parallel to the muscle fibers were found to be approximately two to three times larger than those in the transverse direction. Furthermore, the method was successful in detecting the angular change when the sample was rotated by 30 degrees. Results indicate that the proposed approach to measure fiber orientation is valid and may be used to improve the time efficiency of diffusion anisotropy measurements.

Algorithms↗

Toward a quantitative assessment of diffusion anisotropy.

Indices of diffusion anisotropy calculated from diffusion coefficients acquired in two or three perpendicular directions are rotationally variant. In living monkey brain, these indices severely underestimate the degree of diffusion anisotropy. New indices calculated from the entire diffusion tensor are rotationally invariant (RI). They show that anisotropy is highly variable in different white matter regions depending on the degree of coherence of fiber tract directions. In structures with a regular, parallel fiber arrangement, water diffusivity in the direction parallel to the fibers (Dparallel approximately 1400-1800 x 10(-6) mm2/s) is almost 10 times higher than the average diffusivity in directions perpendicular to them (D + D)/2 [corrected] approximately 150-300 x 10(-6) mm2/s), and is almost three times higher than previously reported. In structures where the fiber pattern is less coherent (e.g., where fiber bundles merge), diffusion anisotropy is significantly reduced. However, RI anisotropy indices are still susceptible to noise contamination. Monte Carlo simulations show that these indices are statistically biased, particularly those requiring sorting of the eigenvalues of the diffusion tensor based on their magnitude. A new intervoxel anisotropy index is proposed that locally averages inner products between diffusion tensors in neighboring voxels. This "lattice" RI index has an acceptably low error variance and is less susceptible to bias than any other RI anisotropy index proposed to date.

Animals↗

Hyperpolarized 3He diffusion MRI and histology in pulmonary emphysema.

Diffusion MRI of hyperpolarized (3)He shows that the apparent diffusion coefficient (ADC) of (3)He gas is highly restricted in the normal lung and becomes nearly unrestricted in severe emphysema. The nature of this restricted diffusion provides information about lung structure; however, no direct comparison with histology in human lungs has been reported. The purpose of this study is to provide information about (3)He gas diffusivity in explanted human lungs, and describe the relationship between (3)He diffusivity and the surface area to lung volume ratio (SA/V) and mean linear intercept (L(m)) measurements--the gold standard for diagnosis of emphysema. Explanted lungs from patients who were undergoing lung transplantation for advanced COPD, and donor lungs that were not used for transplantation were imaged via (3)He diffusion MRI. Histological measurements were made on the same specimens after they were frozen in the position of study. There is an inverse correlation between diffusivity and SA/V (and a positive correlation between diffusivity and L(m)). An important result is that restricted (3)He diffusivity separated normal from emphysematous lung tissue more clearly than the morphometric analyses. This effect may be due to the smaller histologic sampling size compared to the MRI voxel sizes.

Administration, Inhalation↗

The effects of microscopic tissue parameters on the diffusion weighted magnetic resonance imaging experiment.

This review examines the way in which microscopic tissue parameters can affect MR experiments which are sensitive to diffusion. The interaction between the intra- and extravascular as well as that between the intra- and extracellular spaces is examined. Susceptibility gradients due to the presence of deoxyhemoglobin can cause diffusion-induced signal losses which are significant in functional magnetic resonance experiments, particularly at higher main magnetic field strengths. This is also true of the fast response that manifests itself as an early negative signal change in functional magnetic resonance experiments. The fields surrounding paramagnetic vessels are described and the way in which diffusion in these fields contributes to functional signal changes is examined. Flow in the capillary bed can be a confounding factor in experiments which aim to examine the diffusion characteristics of extravascular water. It is potentially also a method for assessing capillary perfusion. The intravoxel incoherent motion experiment is described in terms of how significantly this effect can influence diffusion attenuation curves from water. The major models for describing water diffusion in tissue are presented, as are the main experimental results that have contributed to an understanding of the mechanisms of diffusion contrast. The widely accepted view that changes in the diffusion characteristics are caused by a shift of water to the intracellular space and a concomitant change in extracellular tortuosity is examined critically. More recent experiments that indicate that a reduction in the intracellular diffusion may occur simultaneously with the cell swelling are described and their compatibility with existing models discussed.

Blood Vessels↗

Diffusion and emissions of 1,3-dichloro propene in Florida sandy soil in microplots affected by soil moisture, organic matter, and plastic film.

The main objective of this study was to determine the influence of soil moisture, organic matter amendment and plastic cover (a virtually impermeable film, VIF) on diffusion and emissions of (Z)- and (E)-1,3-dichloropropene (1,3-D) in microplots of Florida sandy soil (Arredondo fine sand). Upward diffusion of the two isomers in the Arredondo soil without a plastic cover was greatly influenced by soil-water content and (Z)-1,3-D diffused faster than (E)-1,3-D. In less than 5 h after 1,3-D injection to 30 cm depth, (Z)- and (E)-1,3-D in air dry soil had diffused to a 10 cm depth, whereas diffusion for the two isomers was negligible in near-water-saturated soil, even 101 h after injection. The diffusion rate of (Z)- and (E)-1,3-D in near-field-capacity soil was between the rates in the two water regimes. Yard waste compost (YWC) amendment greatly reduced diffusion of (Z)- and (E)-1,3-D, even in air-dry soil. Although upward diffusion of (Z)- and (E)-1,3-D in soil with VIF cover was slightly less than in the corresponding bare soil; the cover promoted retention of vapors of the two isomers in soil pore air in the shallow subsurface. More (Z)-1,3-D vapor was found initially in soil pore air than (E)-1,3-D although the difference declined thereafter. As a result of rapid upward movement in air-dry bare soil, (Z)- and (E)-1,3-D were rapidly volatilized into the atmosphere, but emissions from the near-water-saturated soil were minimal. Virtually impermeable film and YWC amendment retarded emissions. This study indicated that adequate soil water in this sandy soil is needed to prevent rapid emissions, but excess soil water slows diffusion of (Z)- and (E)-1,3-D. Thus, management for optimum water in soil is critical for pesticidal efficacy and the environment.

Allyl Compounds↗

Condition number as a measure of noise performance of diffusion tensor data acquisition schemes with MRI.

Diffusion tensor mapping with MRI can noninvasively track neural connectivity and has great potential for neural scientific research and clinical applications. For each diffusion tensor imaging (DTI) data acquisition scheme, the diffusion tensor is related to the measured apparent diffusion coefficients (ADC) by a transformation matrix. With theoretical analysis we demonstrate that the noise performance of a DTI scheme is dependent on the condition number of the transformation matrix. To test the theoretical framework, we compared the noise performances of different DTI schemes using Monte-Carlo computer simulations and experimental DTI measurements. Both the simulation and the experimental results confirmed that the noise performances of different DTI schemes are significantly correlated with the condition number of the associated transformation matrices. We therefore applied numerical algorithms to optimize a DTI scheme by minimizing the condition number, hence improving the robustness to experimental noise. In the determination of anisotropic diffusion tensors with different orientations, MRI data acquisitions using a single optimum b value based on the mean diffusivity can produce ADC maps with regional differences in noise level. This will give rise to rotational variances of eigenvalues and anisotropy when diffusion tensor mapping is performed using a DTI scheme with a limited number of diffusion-weighting gradient directions. To reduce this type of artifact, a DTI scheme with not only a small condition number but also a large number of evenly distributed diffusion-weighting gradients in 3D is preferable.

Algorithms↗

Influence of dietary fiber and intraluminal pressure on absorption and pre-epithelial diffusion resistance (unstirred layer) in rat jejunum in situ.

The appearance rates of antipyrine, benzoic acid, benzylamine, urea, and alpha-methyl-D-glucoside (MG) in jejunal venous blood of anesthetized rats were measured with and without dietary fibers methylcellulose, carboxymethylcellulose sodium, guaran, and sodium alginate in the luminal solution. Raising the concentration of methylcellulose from 0 to 17.5 g/l resulted in an exponential increase in the viscosity of the solution to 98 cSt, a linear decrease of the diffusion coefficient for antipyrine by 28%, and an increase in antipyrine absorption in the perfused jejunal segment by 23%. The simultaneous increase in intraluminal pressure and radius resulted in a linear relation between absorption rate and apparent mucosal surface area. Similar results were obtained by raising intraluminal pressure directly using a carbohydrate-free perfusion solution. In the perfused rat jejunum, the effect of increased pre-epithelial diffusion resistance (i.e. reduced diffusion coefficient and lengthened diffusion distance) induced by methylcellulose on absorption was overcome by the effect of the enlarged apparent mucosal surface area. Preperfusion of a substrate-free, guaran containing solution followed by perfusion with a guaran-free solution containing antipyrine and MG retarded the increase in the appearance rate of these substrates due to the additional viscous guaran layer left after preperfusion. Constant distension of the intestinal wall was achieved by injecting 0.5 ml of the solution into a closed jejunal segment. Addition of the carbohydrates to the injection solution (approx. 100 cSt viscosity) resulted in a 3% to 20% reduction in the diffusion coefficients and in the absorption of antipyrine, benzoic acid, and MG. Diffusion coefficients for urea and benzylamine were reduced by 5% to 12%; absorption varied in the range of the control (-22% to +43%). Model analysis revealed that, in the closed jejunal segment of the rat, the limiting step in the absorption process of antipyrine, benzoic acid, and MG was pre-epithelial diffusion resistance; the reduction of absorption, therefore, corresponded roughly to that of the diffusion coefficient. In the case of urea and benzylamine, pre-epithelial diffusion resistance was only 20% of the total permeation resistance: the influence of the polymers on absorption, therefore, was not always significant.

Animals↗

Axial tissue diffusion can account for the disparity between current models of hepatic elimination for lipophilic drugs.

An assumption of previous models of hepatic elimination is that there is negligible axial diffusion in the liver. We show, by construction of a stochastic model and analysis of published data, that compounds which are readily diffusible and partitioned into hepatocytes may undergo axial tissue diffusion. The compounds most likely to be affected by axial tissue diffusion are the lipophilic drugs for which the cell membranes provide little resistance and which are highly extracted, thereby creating steep concentration gradients along the sinusoid at steady state. This phenomenon greatly modifies the availability of the compound under conditions of altered hepatic blood flow and protein binding. For moderately diffusible compounds, these relationships are similar to those predicted by the simplistic venous-equilibrium model. Hence, the paradoxical ability of the venous-equilibrium model to describe the steady-state kinetics of lipophilic drugs such as lidocaine, meperidine, and propranolol may be finally resolved. The effects of axial tissue diffusion and vascular dispersion on hepatic availability of drugs are compared. Vascular dispersion is of major importance to the availability of poorly diffusible compounds, whereas axial tissue diffusion becomes increasingly dominant for highly diffusive and partitioned substances.

Computer Simulation↗

Water diffusion in rat brain in vivo as detected at very large b values is multicompartmental.

The diffusion-weighted signal attenuation of water in rat brain was measured with pulsed-field gradient nuclear magnetic resonance methods in a single voxel under in vivo and global ischemic conditions. The diffusion-attenuated water signal was observed in vivo at b values of 300 ms/microm2 (strength of diffusion weighting) and diffusion times up to 400 ms. A series of constant diffusion time (CT) experiments with varied gradient directions and diffusion times revealed a multiexponential decay with apparent diffusion coefficients (ADC) covering two orders of magnitude from 1 to 0.01 microm2/ms. In a four-exponential fit, the observed changes during global ischemia could be fully explained by changes in the relative volume fractions only with unchanged ADCs. An anisotropy of the ADC, detected at small b values, was not observed for the ADC at large b values, but for the concomitant volume fractions. An inverse Laplace Transform of the CT curves, performed with CONTIN, resulted in continuously distributed diffusion coefficients, for which the term 'diffusogram' is proposed. This approach was more appropriate than a discrete exponential model with four to six components, being related to the morphology of brain tissue and its cell size distribution. On the basis of an analytical, quantitative model, it is suggested that the measured ADC at small b values reflects mainly properties of the restricting boundaries, i.e. the relative volume fractions and the extracellular tortuosity, while the intrinsic intracellular diffusion constant and the exchange time are predicted to have minor influence.

Animals↗

Signal losses in diffusion preparation: comparison between spin-echo, stimulated echo and SEASON.

Diffusion-weighted magnetic resonance imaging and spectroscopy commonly apply a spin-echo or stimulated echo preparation including sensitizing field gradients. The article reports on a systematic numerical approach to an optimum diffusion preparation considering undesired signal losses caused by relaxation. A large range of possible applications on whole-body units and animal scanners is covered. Instructions for an optimized type and timing of the diffusion preparation are provided for the readership, based on the desired diffusion weighting (b-value), the available maximum field gradient amplitudes, the RF pulse durations and gradient ramp times, and the relaxation characteristics of the specimen (or tissue) of interest. In addition, a new type of diffusion preparation named SEASON (simultaneous Spin-Echo And Stimulated echO preparatioN) is introduced and compared with spin-echo and stimulated echo diffusion preparation. It is demonstrated that spin-echo preparation is superior to stimulated echo preparation in all cases with T2 approximately T1 and in all cases with relatively low diffusion weighting resulting in short duration of diffusion sensitizing gradients delta << T2. For tissues with T2 << T1 (as musculature or red bone marrow) stimulated echo preparation becomes superior to spin-echo preparation for high ratios b/A2 (h-value indicates diffusion weighting, A is the maximum gradient amplitude). The new SEASON technique allows a higher yield in signal intensity compared to spin-echo or stimulated echo preparations in clinically relevant cases.

Diffusion↗

Diffusion through narrow pores: movement of ions, water and nonelectrolytes through track-etched PETP membranes.

The rates at which ions (86Rb+, [3H]-choline, 36Cl), 3H2O and nonelectrolytes ([14C]-urea, [14C]-glycerol, and [14C]-sugars) equilibrate across track-etched polyethyleneterephthalate (PETP) membranes (isotopic diffusion) have been measured by a 'static' and a 'dynamic' technique under conditions where no net flow takes place; the two techniques give essentially the same results. All tracers diffuse faster the longer the membranes are etched, consistent with an increase in pore size. Water and neutral solutes diffuse at rates that are relatively independent of ionic strength, pH or the presence of divalent cations. Diffusion of cations is decreased by high ionic strength, by reducing pH or by addition of divalent cations; diffusion of chloride is increased by these procedures. Treatment of the membrane with diazomethane to reduce the negative fixed charge decreases diffusion of cations and increases that of anions; diffusion of water and neutral solutes is unaffected by methylation except in the membranes with the narrowest pores (i.e., those etched for the shortest time), in which case diffusion is reduced. We conclude (1) that the special features of flow near a charged surface apply to ions but not to water or nonelectrolytes and (2) that calculation of absolute rates of diffusion leads to values for the radii of pores through track-etched PETP membranes that are in remarkably good agreement with measured values.

Anions↗

Kinetics of proton diffusion in the regimes of fast and slow exchange between the membrane surface and the bulk solution.

The phenomenological model developed in our recent publications [9,10] is used to investigate the kinetics of proton diffusion from a source to a detector on the membrane surface. In most cases the observed kinetics shows a single diffusional maximum with the exponential ascending front and the power-law descending tail. The kinetics depends on the distance between the source and the detector. If the detector is located inside the proton collecting antenna, the kinetics corresponds to the surface diffusion at the times near the maximum and shortly thereafter, and it turns into the bulk diffusion kinetics at longer times, after the equilibrium is established between the membrane surface and the bulk solution. If the detector is located outside the antenna, the kinetics corresponds to the bulk diffusion at all times where the signal is nonvanishing. What is seen at locations near the antenna radius depends on the exchange regime. In the regime of fast exchange between the surface and the bulk as compared to the bulk diffusion, the kinetics shows a single peak whose location is intermediate between the peaks for the surface and bulk diffusion. In the regime of slow exchange there are two maxima corresponding to the surface and bulk diffusion. In buffered solutions the antenna radius decreases with increasing buffer concentration, which changes the kinetics from the surface to bulk diffusion. The theory is applied to interprete recent experiments on a phospholipid membrane [25]. It is found that (i) the fast exchange regime is operating since only a single maximum is observed; (ii) the shift of the maximum toward longer times with increasing buffer concentration is a manifestation of the transition from the surface to bulk diffusion kinetics.

Algorithms↗

Finite element modeling of coupled diffusion with partitioning in transdermal drug delivery.

The finite element method is employed to simulate two-dimensional (axisymmetric) drug diffusion from a finite drug reservoir into the skin. The numerical formulation is based on a general mathematical model for multicomponent nonlinear diffusion that takes into account the coupling effects between the different components. The presence of several diffusing components is crucial, as many transdermal drug delivery formulations contain one or more permeation enhancers in addition to the drug. The coupling between the drug and permeation enhancer(s) results in nonlinear diffusion with concentration-dependent diffusivities of the various components. The framework is suitable for modeling both linear and nonlinear, single- and multicomponent diffusions, however, as it reduces to the correct formulation simply by setting the relevant parameters to zero. In addition, we show that partitioning of the penetrants from the reservoir into the skin can be treated in a straightforward manner in this framework using the mixed method. Partitioning at interface boundaries poses some difficulty with the standard finite element method as it creates a discontinuity in the concentration variable at the interface. To our knowledge, nonlinear (concentration-dependent) partitioning in diffusion problems has not been treated numerically before, and we demonstrate that nonlinear partitioning may have an important role in the effect of permeation enhancers. The mixed method that we adopt includes the flux at the interface explicitly in the formulation, allowing the modeling of concentration-dependent partitioning of the permeants between the reservoir and the skin as well as constant (linear) partitioning. The result is a versatile finite element framework suitable for modeling both linear and nonlinear diffusions in heterogeneous media where the diffusivities and partition coefficients may vary in each subregion.

Administration, Cutaneous↗

Diffusion of small ionic species in human saliva, plaque fluid and plaque residue in vitro.

The tracer diffusion of small ionic species was investigated in water, saliva, dental plaque fluid and in plaque residue packed by a range of g forces. Diffusion rate of NaCl was similar in water, saliva and plaque fluid. The rate of CaCl2, NaH2PO4, Na2HPO4 and Na2SO4 was less in both saliva and plaque fluid. Diffusion rate of all ionic species tested was significantly less in plaque residue, most of all for CaCl2. In plaque fluid, plaque residue and water, an inverse linear relationship was found between log diffusion coefficients and log molecular weights. Increasing the tortuosity of the diffusion path, by packing plaque residue, further reduced the diffusion rate of NaH2PO4 and NaHCO3. In terms of three-dimensional diffusion, in plaque fluid, NaH2PO4, Na2HPO4 and CaCl2 diffused a distance of 300 microns within 25 s, whereas in plaque residue the equivalent diffusion times were 1.5-5.7 min. The unique retardation of CaCl2 in plaque residue implicated both non-specific and specific binding interactions.

Adolescent↗

Measurement of optic nerve blood flow with iodoantipyrine: limitations caused by diffusion from the choroid.

Radioactively labelled iodoantipyrine has been used to measure optic nerve blood flow in experimental animals. The reliability of blood flow measurements with this technique may be limited by diffusion of tracer from the nearby choroid. The activity of tracer in the peripapillary choroid and anterior optic nerve was measured in a series of in vivo optic nerve blood flow experiments in cats. The diffusion of iodoantipyrine into cat optic nerve segments was also measured in vitro, and a model for diffusion of tracer from the peripapillary choroid into the anterior optic nerve was developed. The activity profiles established by simple diffusion experiments were similar to the activity profiles in the anterior optic nerve established by blood flow experiments. Apparent blood flow measurements in the anterior optic nerve made with iodoantipyrine may be largely influenced by tracer diffusion from the nearby choroid. For measurements of tracer activity which are statistically similar between control and experimental optic nerve samples, and with a total diffusion time of 60 sec (a well-done experiment), real blood flow in the experimental sample may differ by as much as 60% from the control at a point 50 micron from the choroid. At 300 micron from the choroid, the maximum undetectable difference because of diffusion declines to approx. 12%. These estimates assume an autoradiographic technique which can reliably detect tissue tracer activity differences of +/- 10%. Measurements of optic nerve blood flow made with diffusible tracers are affected by diffusion from the choroid and should be reported with estimated limits of reliability.

Animals↗

Kinetics of diffusion in a spherical cell. II. Solute buffering included.

This paper on diffusion kinetics in neurons presents an analysis of diffusion in the presence of solute buffering. Computational rather than theoretical methods are usually necessary since buffering generally precludes an analytical solution to the diffusion equations. As in the companion paper, our methods are illustrated in the context of calcium diffusion in a spherical cell. However, the same methods can be applied to the spread of any second messenger and other geometries. Analytical or computational predictions of the time course of diffusion and buffering may help guide further experiments and simulations. For example, simulations of calcium diffusion in a model of the bullfrog sympathetic ganglion cell show that buffering at depths greater than 5-6 microns is almost instantaneous compared to diffusion from sources at the cell membrane. Since buffering complicates the design of multicompartmental models, we demonstrate that a few compartments designed on the basis of diffusion alone (Carnevale and Rosenthal, 1992) may be a satisfactory framework for a model that includes bimolecular buffering. An analytical solution may be possible if the buffering reaction can be linearized. We describe a method for linearizing bimolecular saturating buffering, i.e., approximating it by a unimolecular non-saturating process that immobilizes solute. The analytical solution for the linearized reactive diffusion problem fits a non-linear model of calcium movement in the bullfrog sympathetic ganglion cell quite well after a few milliseconds.

Animals↗

The association reaction of yeast alcohol dehydrogenase with coenzyme is partly diffusion-controlled in solvents of increased viscosity.

The steady-state kinetics of the yeast and liver alcohol dehydrogenase catalyzed reduction of aldehydes were examined in solvent mixtures of increased viscosity. This was done to investigate the effects of diffusion control on the fast association of NADH with the enzymes. Both glycerol and sucrose were unsatisfactory as viscosogens, as they inhibited the enzyme, but poly(ethylene glycol)/water mixtures were satisfactory. The 5-fold faster reaction of yeast alcohol dehydrogenase with NADH is partly diffusion controlled, whereas the slower liver alcohol dehydrogenase reaction showed no diffusion effects. These results are consistent with a yeast alcohol dehydrogenase active site that has relatively little steric hindrance to NADH binding. It is estimated that contributions to this association reaction from diffusion control and chemical activation control are equal at a solvent viscosity of 10 cP. Thus, under physiological conditions of increased viscosity the NADH association may be significantly affected by diffusion effects. In order to estimate accurately the maximum diffusion-controlled rate constant from diffusion theory, the diffusion coefficients of NADH were measured in poly(ethylene glycol)/water mixtures and were found to vary inversely as the solvent viscosity raised to the power of 0.5. The non-Stokesian behaviour of molecules as large as NADH in polymer/water mixtures may be a serious limitation to the routine use of poly(ethylene glycol) as a viscosogen for diffusion studies.

Alcohol Dehydrogenase↗

Nitric oxide diffusion coefficients in solutions, proteins and membranes determined by phosphorescence.

The reactivity of nitric oxide under a given condition is a complex function of its diffusivity and the concentration of reacting partners. Quenching by NO of luminescence from Ru and Pd chelates of mesoporphyrin IX, two molecules which exhibit phosphorescence at room temperature, was utilized to evaluate the gas concentration and apparent diffusion coefficients. The properties of Ru-mesoporphyrin, a dye not previously employed as a probe for O2 or NO, were determined and the assay was verified and used to quantify NO produced by decomposition of nitrosocysteine. The pseudo-second order quenching constants were obtained from Stern-Volmer plots measured under various conditions and used to calculate diffusion coefficients for nitric oxide in solutions, proteins and membranes. The diffusion coefficients were greater at 37 than at 25 degrees C and, at a given temperature, smaller in proteins and membranes than in water. The conclusion is that NO and O2 closely resemble each other in diffusivity but that NO is slightly less lipophilic, resulting in somewhat faster apparent diffusion in protein and slower diffusivity in lipid, relative to O2. Taking a mean diffusion coefficient for NO of 10(-7) cm2s-1, then within 10 s the mean path is 10(-3) cm, or less than the diameter of a single cell. However, at low NO and O2 concentrations, the halflife of NO will be considerably longer than 10 s, and consequently the path of NO diffusion much greater.

Animals↗