Time Dependence Of Diffusion Research Articles

NMR-Relaxation and PFG NMR Studies of Water Dynamics in Oriented Collagen Fibres with Different Degree of Cross-linking

For collagen based tissue engineering it is important to know how the changes in water-biomolecules interactions are handled by the degree of cross-links in collagen nano-scaffolds. When hydration properties of collagens with different cross-linking are detailed by NMR a role of water interactions in improving collagen scaffold characteristics for tissue engineering could be clarified. A description of water diffusion in collagen fibres with cross-links should lead to better understanding of internal interactions and knowledge of porous media structure of collagen tissues. This paper presents the results of one- and two-dimensional NMR methods in studying molecular anisotropy and microstructure of collagen fibres from 2 connective tissues with different cross-linking levels (fibres from adult steer and young calf) at water content of 0.6 g water/g of dry matter. The NMR relaxation times (T1 and T2) have been studied in oriented collagen fibres (at 0° to the static magnetic field B0). The apparent translation diffusion coefficients (Dapp) at two directions of applied gradient – along the direction of static magnetic field B0 and perpendicular to B0 – have been studied in oriented collagen fibres (at 0° to the static magnetic field B0). The diffusion time dependence of Dapp showed for both directions of applied gradient a restriction for motion of water molecules. A model of equally spaced plane parallel permeable barriers developed by Tanner for NMR diffusion studies has been used for the estimation of restricted distance and permeability coefficient. Anisotropy of Dapp in oriented fibres was observed in both collagen tissues. Application of 2D DDCOSY NMR spectroscopy with two pairs of collinear gradients on collagen fibres oriented along the static magnetic field and simulations of diffusion anisotropy showed similar features on 2D diffusion maps.

Imaging cell size and permeability in biological tissue using the diffusion-time dependence of the apparent diffusion coefficient

The purpose of this study was to analyze and evaluate a model of restricted water diffusion between equidistant permeable membranes for cell-size and permeability measurements in biological tissue. Based on the known probability distribution of diffusion distances after the diffusion time τ in a system of permeable membranes characterized by three parameters (membrane permeability P, membrane distance L, and free diffusivity D0), an equivalent dimensionless model was derived with a probability distribution characterized by only a single (dimensionless) tissue parameter . Evaluating this proposed model function, the dimensionless diffusion coefficient was numerically calculated for 60 values of the dimensionless diffusion time and 35 values of . Diffusion coefficients were measured in a carrot by diffusion-weighted magnetic resonance imaging (MRI) at 18 diffusion times between 9.9 and 1022.7 ms and fitted to the simulation results to determine L, P, and D0. The measured diffusivities followed the simulated dependence of . Determined cell sizes varied from 21 to 76 μm, permeabilities from 0.007 to 0.039 μm−1, and the free diffusivities from 1354 to 1713 μm2 s−1. In conclusion, the proposed dimensionless tissue model can be used to determine tissue parameters (D0, L, P) based on diffusion MRI with multiple diffusion times. Measurements in a carrot showed a good agreement of the cell diameter, L, determined by diffusion MRI and by light microscopy.

Lithium ion diffusion in Li β-alumina single crystals measured by pulsed field gradient NMR spectroscopy

The lithium ion diffusion coefficient of a 93% Li β-alumina single crystal was measured for the first time using pulsed field gradient (PFG) NMR spectroscopy with two different crystal orientations. The diffusion coefficient was found to be 1.2 × 10(-11) m(2)/s in the direction perpendicular to the c axis at room temperature. The Li ion diffusion coefficient along the c axis direction was found to be very small (6.4 × 10(-13) m(2)/s at 333 K), which suggests that the macroscopic diffusion of the Li ion in the β-alumina crystal is mainly two-dimensional. The diffusion coefficient for the same sample was also estimated using NMR line narrowing data and impedance measurements. The impedance data show reasonable agreement with PFG-NMR data, while the line narrowing measurements provided a lower value for the diffusion coefficient. Line narrowing measurements also provided a relatively low value for the activation energy and pre-exponential factor. The temperature dependent diffusion coefficient was obtained in the temperature range 297-333 K by PFG-NMR, from which the activation energy for diffusion of the Li ion was estimated. The activation energy obtained by PFG-NMR was smaller than that obtained by impedance measurements, which suggests that thermally activated defect formation energy exists for 93% Li β-alumina single crystals. The diffusion time dependence of the diffusion coefficient was observed for the Li ion in the 93% Li β-alumina single crystal by means of PFG-NMR experiments. Motion of Li ion in fractal dimension might be a possible explanation for the observed diffusion time dependence of the diffusion coefficient in the 93% Li β-alumina system.

Length Scales and Structural Dynamics in Nematogen Pseudonematic Domains Measured with 2D IR Vibrational Echoes and Optical Kerr Effect Experiments

Nematogen liquids in the isotropic phase are macroscopically homogeneous but on multinanometer length scales have pseudonematic domains with correlation lengths that grow as the isotropic to nematic phase transition temperature (TNI) is approached from above. Orientational relaxation of nematogens in the isotropic phase manifests as two fast power laws and a slow exponential decay when measured by optical heterodyne detected optical Kerr effect (OHD-OKE) experiments. The long time exponential relaxation is associated with complete randomization of pseudonematic domains. We examine the effect of local orientational correlation on spectral diffusion (structural evolution) experienced by a vibrational probe molecule within the pseudonematic domains of 4-cyano-4'-pentylbiphenyl (5CB) using two-dimensional infrared (2D IR) vibrational echo spectroscopy. The addition of low concentration 4-pentyl-4'-thiocyanobiphenyl (5SCB) as a long-lived vibrational probe to 5CB is shown to lower TNI of the sample slightly, but the fast power law dynamics and exponential decays observed by OHD-OKE spectroscopy are unchanged. We compare the complete orientational relaxation and spectral diffusion for samples of 5SCB in 5CB to 5SCB in 4-pentylbiphenyl (5B) at four temperatures above TNI. 5B has a molecular structure similar to 5CB but is not a nematogen. At all but the lowest temperature, the spectral diffusion in 5CB and 5B is described well as a triexponential decay with very similar time constants. The results demonstrate that the presence of local orientational order at temperatures well above TNI does not affect the spectral diffusion (structural evolution) within pseudonematic domains when the correlation lengths are short. However, when the temperature of the sample is held very close to TNI, the spectral diffusion in 5CB slows dramatically while that in 5B does not. It is only as the correlation length becomes very long that its presence impacts the spectral diffusion (structural fluctuations) sensed by the vibrational probes located in pseudonematic domains. The orientational relaxation is modeled with schematic mode coupling theory (MCT). Fitting with MCT provides density and orientational correlation functions. The density correlation decays are similar for 5B and 5CB, but the orientational correlation decays are much slower for 5CB. Additionally, the time dependence of the spectral diffusion in 5CB is strikingly similar to that of the density correlation function decay, while the orientational correlation function decay is far too slow to contribute to the spectral diffusion. Therefore, density fluctuations are likely the source of spectral diffusion at temperatures at least 5 K above TNI.

Response to Commentary on “The influence of lung airways branching structure and diffusion time on measurements and models of short-range 3He gas MR diffusion”

Our extensive investigation of the cylinder model theory through numerical modelling and purpose-designed experiments has demonstrated that it does produce inaccurate estimates of airway dimensions at all diffusion times currently used. This is due to a variety of effects: incomplete treatment of non-Gaussian effects, finite airway size, branching geometry, background susceptibility gradients and diffusion time dependence of the 3He MR diffusion behaviour in acinar airways. The cylinder model is a good starting point for the development of a lung morphometry technique from 3He diffusion MR but its limitations need to be understood and documented in the interest of reliable clinical interpretation.

Relationship between the diffusion time and the diffusion MRI signal observed at 17.2 tesla in the healthy rat brain cortex

To investigate the diffusion time dependency of water diffusion in cortical brain tissue. We have combined an oscillating gradient spin-echo (OGSE) and a pulse gradient spin echo (PGSE) spin-echo sequence to acquire diffusion-weighted MRI images in vivo in healthy rat brains over a wide range of diffusion times (1.9-29.2 ms) and estimated the parameters of the biexponential and cumulant expansion diffusion MRI signal models. Diffusion images were obtained at 17.2 Tesla with maximum gradient strength of 1000 mT/m allowing 40 b values up to approximately 4000 s/mm(2). At all diffusion times the log plot of diffusion signal attenuation versus b value was curved, confirming that diffusion is not free, even at very short diffusion times. This suggests that the length scale of obstacles to diffusion must be smaller than the corresponding shortest observed diffusion distance (approximately 1.7 μm). The diffusion MRI signal was also not found in a steady-state, even at our longest diffusion time (29.2 ms), suggesting some degree of segregation of water in pools. Overall, the results showed that the parameters derived from the two diffusion models could not well be related to specific tissue features. More specific models must be developed taking into account diffusion signal behavior at high b values and short diffusion times.

On the Time Dependency of the Chloride Diffusion in High Performance Concrete

The chloride diffusion coefficient of concrete is time dependent. The high performance concrete (HPC) was prepared and the specimens were tested by ASTM C1202 and the durability of HPC in long period is analyzed with the time dependency of diffusion in this paper. The results show that the chloride diffusion coefficients of the HPC with only fly ash are large than those of the HPC with multi-admixtures, but the attenuation of the chloride diffusion coefficients of the formers are faster than the latters. The analysis results show that the chloride concentrations in concrete is over estimated when time-dependence of chloride diffusion is not considered, and the durability of concrete in long period is determined by both chloride diffusion coefficient and age factor.

Coarsening kinetics in demixed lead borate melts

Lead borate melts have been demixed at temperatures in range from 723 to 773 K for times up to 20 h. It is found that increasing time and temperature lead to characteristic changes in the size distribution of boron trioxide drops in the lead-rich glassy matrix (<80.7 mol. % B2O3). The increase of the mean drop size with annealing time followed the cube root time dependence of diffusion controlled coarsening. The diffusivity of the coarsening process was determined using liquid-liquid interfacial energy associated with drop deformation in glass specimens subjected to uniaxial compression. Diffusion coefficients of coarsening were found to match with those of (207)Pb and (18)O tracer ions in the lead borate system but differ up to four orders of magnitude from the Eyring diffusivity and by a factor of ≈7 from the activation energy of viscous flow. The results indicate that coarsening in demixed lead borate melts is most likely controlled by the short range dynamics of the interaction between lead cations and BO4 units, which are decoupled from the time scales of cooperative rearrangements of the glassy network at T < 1.1 Tg.

Investigation of field and diffusion time dependence of the diffusion‐weighted signal at ultrahigh magnetic fields

Over the last decade, there has been a significant increase in the number of high-magnetic-field MRI magnets. However, the exact effect of a high magnetic field strength (B0 ) on diffusion-weighted MR signals is not yet fully understood. The goal of this study was to investigate the influence of different high magnetic field strengths (9.4 T and 14.1 T) and diffusion times (9, 11, 13, 15, 17 and 24 ms) on the diffusion-weighted signal in rat brain white matter. At a short diffusion time (9 ms), fractional anisotropy values were found to be lower at 14.1 T than at 9.4 T, but this difference disappeared at longer diffusion times. A simple two-pool model was used to explain these findings. The model describes the white matter as a first hindered compartment (often associated with the extra-axonal space), characterized by a faster orthogonal diffusion and a lower fractional anisotropy, and a second restricted compartment (often associated with the intra-axonal space), characterized by a slower orthogonal diffusion (i.e. orthogonal to the axon direction) and a higher fractional anisotropy. Apparent T2 relaxation time measurements of the hindered and restricted pools were performed. The shortening of the pseudo-T2 value from the restricted compartment with B0 is likely to be more pronounced than the apparent T2 changes in the hindered compartment. This study suggests that the observed differences in diffusion tensor imaging parameters between the two magnetic field strengths at short diffusion time may be related to differences in the apparent T2 values between the pools.

The influence of lung airways branching structure and diffusion time on measurements and models of short-range 3He gas MR diffusion

Hyperpolarized 3He diffusion experiments have been shown to be sensitive to changes in acinar structure due to emphysematous lung disease. Extracting quantitative information about lung microstructure from the diffusion signal is complicated due its dependence on a number of factors including diffusion time and the complex branching acinar geometry. A theoretical model (cylinder model) has been proposed as a means of estimating acinar airway dimensions from measured diffusivities. This model assumes that the effects of acinar branching geometry and finite airway length upon 3He diffusion behaviour are negligible. In this work, we use finite element simulations of diffusion in a model of branching alveolar ducts to investigate in detail the effects of acinar branching structure and finite airway length on short-range 3He diffusion measurements. The results show that branching effects have a significant influence upon 3He diffusivity, even at short diffusion times. The expressions of the cylinder model theory do not account for significant dependences upon diffusion time, branching geometry and airway length, as a consequence of the oversimplified geometrical model used. The effect of diffusion time on 3He ADC was also investigated through experiments with healthy human volunteers. The results demonstrate that the cylinder model can produce inaccurate estimates of the airway dimensions as a consequence of incompletely accounting for the diffusion-time dependence in the model equations and confirmed the predicted limitations of the cylinder model for reliable lung morphometry measurements. The results and models presented in this work may help in the development of a more realistic theoretical framework for ‘in vivo lung morphometry’ using 3He diffusion MR.

Control of Li configuration and electrical properties of Li-doped ZnO

Li-doped ZnO after different thermal treatments was characterized by depth-resolved cathodoluminescence spectroscopy (DRCLS), secondary ion mass spectrometry, surface photovoltage spectroscopy (SPS), coupled with other surface science techniques. It is found that the Li configuration and electrical properties of Li-doped ZnO could be controlled by different thermal processes. Within a 500–600 °C annealing temperature range, subsequent quenching of ZnO leaves Li as interstitial donors, resulting in n-type low room temperature resistivity. In contrast, slower cooling in air enables these interstitials to fill Zn vacancies, forming Li acceptors 3.0 eV below the conduction band edge. Emergence of this acceptor and the resultant resistivity increase agree with the calculated diffusion lengths based on published diffusion coefficients. In general, these acceptors are compensated by residual intrinsic and extrinsic donors, resulting in a semi-insulating material. DRCL spectra exhibit a 3.0 eV optical signature of the LiZn acceptor and its depth distribution in slow-cooled ZnO. A 3.0 eV SPS absorption feature corresponding to a conduction band-to-acceptor level transition confirms this acceptor assignment. Nanoscale SPS spectra reveal p-type band bending localized near ZnO surface nano-mounds, where VZn and LiZn acceptor densities increase. The slow-cooled and quenched Li-doped ZnO spectra display an inverse relationship between the optical emission densities of lithium on zinc versus zinc vacancy sites, demonstrating the time dependence of Li interstitial diffusion to reach zinc vacancies and form substitutional Li acceptors.

Correlation of Surface Alloyed Microstructure of Pure Magnesium With its Corrosion Behavior

This paper represents a summary of experimental results dealing with the time dependence of surface diffusion alloyed microstructure and its corrosion behavior at given temperature. The experiments were performed at 485°C for different solid diffusion time (6h, 12h, 18h ) and thus the surface alloyed microstructure of pure magnesium has been obtained. Optical and electrical microscopy and EDS compositions analysis were used to examine the cross sectional microstructure characteristics of alloyed layers of treated samples. It is shown that the new phases formed and its continuity, depending on the diffusion treated time at given temperature, have a noticeable influence on corrosion resistance and corrosion mechanism. The new formed phase Al5Mg11Zn4 was inert to the chloride solution compared with pure magnesium and acted as a corrosion barrier. It was concluded that the continuous Al5Mg11Zn4 phase was beneficial from the point of view of corrosion resistance.

Temporal scaling characteristics of diffusion as a new MRI contrast: Findings in rat hippocampus

Features of the diffusion-time dependence of the diffusion-weighted magnetic resonance imaging (MRI) signal provide a new contrast that could be altered by numerous biological processes and pathologies in tissue at microscopic length scales. An anomalous diffusion model, based on the theory of Brownian motion in fractal and disordered media, is used to characterize the temporal scaling (TS) characteristics of diffusion-related quantities, such as moments of the displacement and zero-displacement probabilities, in excised rat hippocampus specimens. To reduce the effect of noise in magnitude-valued MRI data, a novel numerical procedure was employed to yield accurate estimation of these quantities even when the signal falls below the noise floor. The power-law dependencies characterize the TS behavior in all regions of the rat hippocampus, providing unique information about its microscopic architecture. The relationship between the TS characteristics and diffusion anisotropy is investigated by examining the anisotropy of TS, and conversely, the TS of anisotropy. The findings suggest the robustness of the technique as well as the reproducibility of estimates. TS characteristics of the diffusion-weighted signals could be used as a new and useful marker of tissue microstructure.

The effect of a non-zero Lagrangian time scale on bounded shear dispersion

AbstractPrevious studies of shear dispersion in bounded velocity fields have assumed random velocities with zero Lagrangian time scale (i.e. velocities are$\delta $-function correlated in time). However, many turbulent (geophysical and engineering) flows with mean velocity shear exist where the Lagrangian time scale is non-zero. Here, the longitudinal (along-flow) shear-induced diffusivity in a two-dimensional bounded velocity field is derived for random velocities with non-zero Lagrangian time scale${\tau }_{L} $. A non-zero${\tau }_{L} $results in two-time transverse (across-flow) displacements that are correlated even for large (relative to the diffusive time scale${\tau }_{D} $) times. The longitudinal (along-flow) shear-induced diffusivity${D}_{S} $is derived, accurate for all${\tau }_{L} $, using a Lagrangian method where the velocity field is periodically extended to infinity so that unbounded transverse particle spreading statistics can be used to determine${D}_{S} $. The non-dimensionalized${D}_{S} $depends on time and two parameters: the ratio of Lagrangian to diffusive time scales${\tau }_{L} / {\tau }_{D} $and the release location. Using a parabolic velocity profile, these dependencies are explored numerically and through asymptotic analysis. The large-time${D}_{S} $is enhanced relative to the classic Taylor diffusivity, and this enhancement increases with$ \sqrt{{\tau }_{L} } $. At moderate${\tau }_{L} / {\tau }_{D} = 0. 1$this enhancement is approximately a factor of 3. For classic shear dispersion with${\tau }_{L} = 0$, the diffusive time scale${\tau }_{D} $determines the time dependence and large-time limit of the shear-induced diffusivity. In contrast, for sufficiently large${\tau }_{L} $, a shear time scale${\tau }_{S} = \mathop{ ({\tau }_{L} {\tau }_{D} )}\nolimits ^{1/ 2} $, anticipated by a simple analysis of the particle’s domain-crossing time, determines both the${D}_{S} $time dependence and the large-time limit. In addition, the scalings for turbulent shear dispersion are recovered from the large-time${D}_{S} $using properties of wall-bounded turbulence.

Diffusion time dependence of magnetic resonance diffusion signal decays: an investigation of water exchange in human brain in vivo

To understand the behavior of diffusion signal decays of water in white matter of human brain in vivo and to estimate tissue microstructure parameters such as exchange time of diffusing water molecules in human brain. Diffusion decays were measured over an extended range of diffusion weightings (b-values) up to a maximum of 12,500 s/mm(2) and diffusion times between 19.9 and 53.8 ms in eight healthy human subjects using MRI scans. The diffusion signal decays were all Rician noise corrected and then analyzed using multi-component non-negative least squares (NNLS) data analysis. Three diffusion coefficients including one at (0.930 ± 0.003) × 10(-3) (80 ± 1%) mm(2)/s, another at (0.067 ± 0.002) × 10(-3) (19 ± 1%) mm(2)/s and a small contribution at (1.20 ± 0.02) × 10(-2) (1.00 ± 0.01%) mm(2)/s were observed in the diffusion decay using the highest b-value. The diffusion decays show diffusion time dependence for the slow diffusion coefficient which has not previously been reported. This study presents the accurate diffusion parameters by the use of very large b-values along with Rician noise correction and multi-component data analysis. The experimental results are consistent with the theoretical predictions used to estimate the exchange time of diffusing water molecules for a model of human brain tissue.

Effects of grain growth on interface diffusion in nanostructured Cu

Considerable grain growth occurred in a nanostructured Cu sample produced by surface mechanical attrition treatment during isothermal annealing at 423 K. The time-dependence of diffusion of (63)Ni in the nanostructured Cu was investigated by the radio-tracer technique. It was shown that the apparent interfacial diffusivity determined by taking into account the grain growth effects was higher by a factor of 10 than the value determined according to the model of stationary interfaces. (C) 2011 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Acinar determinants of the apparent diffusion coefficient for helium-3

The apparent diffusion coefficient (ADC) obtained by helium-3 magnetic resonance imaging over several seconds is thought to reflect diffusion impairment due to both intra- and interacinar structure. In this study, numerical simulations of intra-acinar gas mixing and effective diffusion were performed in a multiple-branch-point model of the human acinus. Using a previously described method, we computed the instantaneous effective diffusion resulting from the diffusive impairment imposed by intra-acinar branching for varying times up to 5 s. We also tested the influence on effective diffusion of intra-acinar collateral channels in the fully alveolated intra-acinar airways to mimic the effect of emphysema. Randomly connecting two or four pairs of airways per generation (in generations 19-25) led to a 40 and 142% increase, respectively, in effective diffusion coefficient cumulated over the time interval of 0.2-5 s. Finally, we also used a system of two coupled multiple branch-point models to simulate diffusive attenuation over a 50-s interval in cases of purely acinar tagging (i.e., the initial gas concentration = 1 in one acinus and 0 in the other) and of partial tagging astride on two acini. It is shown that, in the latter case, the decay rate cannot be approximated by a mono-exponential with a several-fold faster decay for times below 10 s due to intra-acinar diffusion. We conclude that both the characteristic biphasic time dependence of simulated effective diffusion and its sensitivity to intra-acinar structural change mimic experimental ADC behavior. Additional simulations of combined inter- and intra-acinar diffusion strongly suggest that neglecting intra-acinar branching would in fact lead to considerable error of simulated ADC.

Bicellar Mixtures Containing Pluronic F68: Morphology and Lateral Diffusion from Combined SANS and PFG NMR Studies

Small angle neutron scattering (SANS) and pulsed field gradient (PFG) nuclear magnetic resonance (NMR) diffusion measurements were applied to examine morphology and diffusion in dimyristoyl- plus dihexanoyl-phosphatidylcholine bicellar mixtures, either neutral or negatively charged, incorporating a Pluronic triblock copolymer (F68). Negatively charged bicellar mixtures, doped with dimyristoylphosphatidylglycerol (DMPG), exhibited SANS profiles consistent with a perforated lamellar morphology for the magnetically alignable phase. Correspondingly, F68 diffusion in this magnetically aligned phase was normal Gaussian, in that the mean square displacements increased linearly with the experimental diffusion time, with a lateral diffusion coefficient of 1.9 x 10(-11) m(2) s(-1) consistent with a lipid bilayer inserted configuration. Neutral bicellar mixtures, that is, lacking DMPG, in contrast, displayed SANS profiles characteristic of ribbons arranged in such a fashion as to produce extended lamellae. Within the lamellae, the ribbons exhibited an in-plane periodicity (interribbon) of between 120 and 140 A. Correspondingly, F68 diffusion was non-Gaussian, exhibiting a square root diffusion time dependence of the mean square displacement indicative of one-dimensional curvilinear diffusion. The presence or absence of DMPG, rather than of F68, dictated the ribbon versus lamellar morphology, with F68 reflecting this difference via its lateral diffusion behavior. Although ribbons have been reported previously, this is the first study to show that they aggregate, most likely into extended lamellar sheets, and eventually fold into multilamellar vesicles.

Diffusion‐weighted MRI measurements on stroke patients reveal water‐exchange mechanisms in sub‐acute ischaemic lesions

The aim of this study was to investigate the diffusion time dependence of signal-versus-b curves obtained from diffusion-weighted magnetic resonance imaging (DW-MRI) of sub-acute ischaemic lesions in stroke patients. In this case series study, 16 patients with sub-acute ischaemic stroke were examined with DW-MRI using two different diffusion times (60 and 260 ms). Nine of these patients showed sufficiently large lesions without artefacts to merit further analysis. The signal-versus-b curves from the lesions were plotted and analysed using a two-compartment model including compartmental exchange. To validate the model and to aid the interpretation of the estimated model parameters, Monte Carlo simulations were performed. In eight cases, the plotted signal-versus-b curves, obtained from the lesions, showed a signal-curve split-up when data for the two diffusion times were compared, revealing effects of compartmental water exchange. For one of the patients, parametric maps were generated based on the extracted model parameters. These novel observations suggest that water exchange between different water pools is measurable and thus potentially useful for clinical assessment. The information can improve the understanding of the relationship between the DW-MRI signal intensity and the microstructural properties of the lesions.

Anomalous Diffusion Induced by Cristae Geometry in the Inner Mitochondrial Membrane

Diffusion of inner membrane proteins is a prerequisite for correct functionality of mitochondria. The complicated structure of tubular, vesicular or flat cristae and their small connections to the inner boundary membrane impose constraints on the mobility of proteins making their diffusion a very complicated process. Therefore we investigate the molecular transport along the main mitochondrial axis using highly accurate computational methods. Diffusion is modeled on a curvilinear surface reproducing the shape of mitochondrial inner membrane (IM). Monte Carlo simulations are carried out for topologies resembling both tubular and lamellar cristae, for a range of physiologically viable crista sizes and densities. Geometrical confinement induces up to several-fold reduction in apparent mobility. IM surface curvature per se generates transient anomalous diffusion (TAD), while finite and stable values of projected diffusion coefficients are recovered in a quasi-normal regime for short- and long-time limits. In both these cases, a simple area-scaling law is found sufficient to explain limiting diffusion coefficients for permeable cristae junctions, while asymmetric reduction of the junction permeability leads to strong but predictable variations in molecular motion rate. A geometry-based model is given as an illustration for the time-dependence of diffusivity when IM has tubular topology. Implications for experimental observations of diffusion along mitochondria using methods of optical microscopy are drawn out: a non-homogenous power law is proposed as a suitable approach to TAD. The data demonstrate that if not taken into account appropriately, geometrical effects lead to significant misinterpretation of molecular mobility measurements in cellular curvilinear membranes.