Sodium ion apparent diffusion coefficient in living rat brain

Are standing osmotic gradients the main driver of cerebrospinal fluid production? A computational analysis

BACKGROUND

The mechanisms of cerebrospinal fluid (CSF) production by the ventricular choroid plexus (ChP) have not been fully deciphered. One prominent hypothesized mechanism is trans-epithelial water transport mediated by accumulation of solutes at the luminal ChP membrane that produces local osmotic gradients. However, this standing osmotic gradient hypothesis has not been systematically tested.

METHODS

To assess the plausibility of the standing gradient mechanism serving as the main driver of CSF production by the ChP, we developed a three-dimensional (3D) and a one-dimensional (1D) computational model to quantitatively describe the associated processes in the rat ChP inter-microvillar spaces and in CSF pools between macroscopic ChP folds (1D only). The computationally expensive 3D model was used to examine the applicability of the 1D model for hypothesis testing. The 1D model was employed to predict the rate of CSF produced by the standing gradient mechanism for 200,000 parameter permutations. Model parameter values for each permutation were chosen by random sampling from distributions derived from published experimental data.

RESULTS

Both models predict that the CSF production rate by the standing osmotic gradient mechanism is below 10% of experimentally measured values that reflect the contribution of all actual production mechanisms. The 1D model indicates that increasing the size of CSF pools between ChP folds, where diffusion dominates solute transport, would increase the contribution of the standing gradient mechanism to CSF production.

CONCLUSIONS

The models suggest that the effect of standing osmotic gradients is too small to contribute substantially to CSF production. ChP motion and movement of CSF in the ventricles, which are not accounted for in the models, would further reduce this effect, making it unlikely that standing osmotic gradients are the main drivers of CSF production.

Comprehensive Account of Sodium Imaging and Spectroscopy for Brain Research

Sodium (²³Na) is a vital component of neuronal cells and plays a key role in various signal transmission processes. Hence, information on sodium distribution in the brain using magnetic resonance imaging (MRI) provides useful information on neuronal health. ²³Na MRI and MR spectroscopy (MRS) improve the diagnosis, prognosis, and clinical monitoring of neurological diseases but confront some inherent limitations that lead to low signal-to-noise ratio, longer scan time, and diminished partial volume effects. Recent advancements in multinuclear MR technology have helped in further exploration in this domain. We aim to provide a comprehensive description of ²³Na MRI and MRS for brain research including the following aspects: (a) theoretical background for understanding ²³Na MRI and MRS fundamentals; (b) technological advancements of ²³Na MRI with respect to pulse sequences, RF coils, and sodium compartmentalization; (c) applications of ²³Na MRI in the early diagnosis and prognosis of various neurological disorders; (d) structural-chronological evolution of sodium spectroscopy in terms of its numerous applications in human studies; (e) the data-processing tools utilized in the quantitation of sodium in the respective anatomical regions.

Distinctive ionic transport of freshly excised human epileptogenic brain tissue

Epileptogenic lesions have higher concentrations of sodium than does normal brain tissue. Such lesions are palpably recognized by a surgeon and then excised in order to eliminate epileptic seizures with their associated abnormal electrical behavior. Here, we study the frequency-dependent electrical conductivities of lesion-laden tissues excised from the brains of epilepsy patients. The low-frequency (<1000 Hz) conductivity of biological tissue primarily probes extracellular solvated sodium-cations traveling parallel to membranes within regions bounded by blockages. This conductivity rises monotonically toward saturation as the frequency surpasses the rate with which diffusing solvated sodium cations encounter blockages. We find that saturation occurs at dramatically higher frequencies in excised brain tissue containing epileptogenic lesions than it does in normal brain tissue. By contrast, such an effect is not reported for tumors embedded in other excised biological tissue. All told, epileptogenic lesions generate frequency-dependent conductivities that differ qualitatively from those of both normal brain tissues and tumors.

Understanding the sodium cation conductivity of human epileptic brain tissue

Transient and frequency-dependent conductivity measurements on excised brain-tissue lesions from epilepsy patients indicate that sodium cations are the predominant charge carriers. The transient conductivity ultimately vanishes as ions encounter blockages. The initial and final values of the transient conductivity correspond to the high-frequency and low-frequency limits of the frequency-dependent conductivity, respectively. Carrier dynamics determines the conductivity between these limits. Typically, the conductivity rises monotonically with increasing frequency. By contrast, when pathology examinations found exceptionally disorganized excised tissue, the conductivity falls with increasing frequency as it approaches its high-frequency limit. To analyze these measurements, excised tissues are modeled as mixtures of "normal" tissue within which sodium cations can diffuse and "abnormal" tissue within which sodium cations are trapped. The decrease in the conductivity with increasing frequency indicates the predominance of trapping. The high-frequency conductivity decreases as the rate with which carriers are liberated from traps decreases. A relatively low conductivity results when most sodium cations remain trapped in "abnormal" brain tissue, while few move within "normal" brain tissue. Thus, the high densities of sodium nuclei observed by ²³Na-MRI in epilepsy patients' lesions are consistent with the low densities of diffusing sodium cations inferred from conductivity measurements of excised lesions.

Characterizing extracellular diffusion properties using diffusion-weighted MRS of sucrose injected in mouse brain

Brain water and some critically important energy metabolites, such as lactate or glucose, are present in both intracellular and extracellular spaces (ICS/ECS) at significant levels. This ubiquitous nature makes diffusion MRI/MRS data sometimes difficult to interpret and model. While it is possible to glean information on the diffusion properties in ICS by measuring the diffusion of purely intracellular endogenous metabolites (such as NAA), the absence of endogenous markers specific to ECS hampers similar analyses in this compartment. In past experiments, exogenous probes have therefore been injected into the brain to assess their apparent diffusion coefficient (ADC) and thus estimate tortuosity in ECS. Here, we use a similar approach in mice by injecting sucrose, a well-known ECS marker, in either the lateral ventricles or directly in the prefrontal cortex. For the first time, we propose a thorough characterization of ECS diffusion properties encompassing (1) short-range restriction by looking at signal attenuation at high b values, (2) tortuosity and long-range restriction by measuring ADC time-dependence at long diffusion times and (3) microscopic anisotropy by performing double diffusion encoding (DDE) measurements. Overall, sucrose diffusion behavior is strikingly different from that of intracellular metabolites. Acquisitions at high b values not only reveal faster sucrose diffusion but also some sensitivity to restriction, suggesting that the diffusion in ECS is not fully Gaussian at high b. The time evolution of the ADC at long diffusion times shows that the tortuosity regime is not reached yet in the case of sucrose, while DDE experiments suggest that it is not trapped in elongated structures. No major difference in sucrose diffusion properties is reported between the two investigated routes of injection and brain regions. These original experimental insights should be useful to better interpret and model the diffusion signal of molecules that are distributed between ICS and ECS compartments.

Challenges for biophysical modeling of microstructure

The biophysical modeling efforts in diffusion MRI have grown considerably over the past 25 years. In this review, we dwell on the various challenges along the journey of bringing a biophysical model from initial design to clinical implementation, identifying both hurdles that have been already overcome and outstanding issues. First, we describe the critical initial task of selecting which features of tissue microstructure can be estimated using a model and which acquisition protocol needs to be implemented to make the estimation possible. The model performance should necessarily be tested in realistic numerical simulations and in experimental data - adapting the fitting strategy accordingly, and parameter estimates should be validated against complementary techniques, when/if available. Secondly, the model performance and validity should be explored in pathological conditions, and, if appropriate, dedicated models for pathology should be developed. We build on examples from tumors, ischemia and demyelinating diseases. We then discuss the challenges associated with clinical translation and added value. Finally, we single out four major unresolved challenges that are related to: the availability of a microstructural ground truth, the validation of model parameters which cannot be accessed with complementary techniques, the development of a generalized standard model for any brain region and pathology, and the seamless communication between different parties involved in the development and application of biophysical models of diffusion.

Regulation of CSF and Brain Tissue Sodium Levels by the Blood-CSF and Blood-Brain Barriers During Migraine

Cerebrospinal fluid (CSF) and brain tissue sodium levels increase during migraine. However, little is known regarding the underlying mechanisms of sodium homeostasis disturbance in the brain during the onset and propagation of migraine. Exploring the cause of sodium dysregulation in the brain is important, since correction of the altered sodium homeostasis could potentially treat migraine. Under the hypothesis that disturbances in sodium transport mechanisms at the blood-CSF barrier (BCSFB) and/or the blood-brain barrier (BBB) are the underlying cause of the elevated CSF and brain tissue sodium levels during migraines, we developed a mechanistic, differential equation model of a rat's brain to compare the significance of the BCSFB and the BBB in controlling CSF and brain tissue sodium levels. The model includes the ventricular system, subarachnoid space, brain tissue and blood. Sodium transport from blood to CSF across the BCSFB, and from blood to brain tissue across the BBB were modeled by influx permeability coefficients P_BCSFB and P_BBB, respectively, while sodium movement from CSF into blood across the BCSFB, and from brain tissue to blood across the BBB were modeled by efflux permeability coefficients PBCSFB′ and PBBB′, respectively. We then performed a global sensitivity analysis to investigate the sensitivity of the ventricular CSF, subarachnoid CSF and brain tissue sodium concentrations to pathophysiological variations in P_BCSFB, P_BBB, PBCSFB′ and PBBB′. Our results show that the ventricular CSF sodium concentration is highly influenced by perturbations of P_BCSFB, and to a much lesser extent by perturbations of PBCSFB′. Brain tissue and subarachnoid CSF sodium concentrations are more sensitive to pathophysiological variations of P_BBB and PBBB′ than variations of P_BCSFB and PBCSFB′ within 30 min of the onset of the perturbations. However, P_BCSFB is the most sensitive model parameter, followed by P_BBB and PBBB′, in controlling brain tissue and subarachnoid CSF sodium levels within 3 h of the perturbation onset.

Estimation of microvascular capillary physical parameters using MRI assuming a pseudo liquid drop as model of fluid exchange on the cellular level

Aim

One of the most important microvasculatures' geometrical variables is number of pores per capillary length that can be evaluated using MRI. The transportation of blood from inner to outer parts of the capillary is studied by the pores and the relationship among capillary wall thickness, size and the number of pores is examined.

Background

Characterization of capillary space may obtain much valuable information on the performance of tissues as well as the angiogenesis.

Methods

To estimate the number of pores, a new pseudo-liquid drop model along with appropriate quantitative physiological purposes has been investigated toward indicating a package of data on the capillary space. This model has utilized the MRI perfusion, diffusion and relaxivity parameters such as cerebral blood volume (CBV), apparent diffusion coefficient (ADC), ΔR ₂ and Δ R 2 * values. To verify the model, a special protocol was designed and tested on various regions of eight male Wistar rats.

Results

The maximum number of pores per capillary length in the various conditions such as recovery, core, normal-recovery, and normal-core were found to be 183 ± 146, 176 ± 160, 275 ± 166, and 283 ± 143, respectively. This ratio in the normal regions was more than that of the damaged ones. The number of pores increased with increasing mean radius of the capillary and decreasing the thickness of the wall in the capillary space.

Conclusion

Determination of the number of capillary pore may most likely help to evaluate angiogenesis in the tissues and treatment planning of abnormal ones.

Simultaneous multi-parametric mapping of total sodium concentration, T1, T2 and ADC at 7 T using a multi-contrast unbalanced SSFP

PURPOSE

Quantifying multiple NMR properties of sodium could be of benefit to assess changes in cellular viability in biological tissues. A proof of concept of Quantitative Imaging using Configuration States (QuICS) based on a SSFP sequence with multiple contrasts was implemented to extract simultaneously 3D maps of applied flip angle (FA), total sodium concentration, T₁, T₂, and Apparent Diffusion Coefficient (ADC).

METHODS

A 3D Cartesian Gradient Recalled Echo (GRE) sequence was used to acquire 11 non-balanced SSFP contrasts at a 6 × 6 × 6 mm³ isotropic resolution with carefully-chosen gradient spoiling area, RF amplitude and phase cycling, with TR/TE = 20/3.2 ms and 25 averages, leading to a total acquisition time of 1 h 18 min. A least-squares fit between the measured and the analytical complex signals was performed to extract quantitative maps from a mono-exponential model. Multiple sodium phantoms with different compositions were studied to validate the ability of the method to measure sodium NMR properties in various conditions.

RESULTS

Flip angle maps were retrieved. Relaxation times, ADC and sodium concentrations were estimated with controlled precision below 15%, and were in accordance with measurements from established methods and literature.

CONCLUSION

The results illustrate the ability to retrieve sodium NMR properties maps, which is a first step toward the estimation of FA, T₁, T₂, concentration and ADC of ²³Na for clinical research. With further optimization of the acquired QuICS contrasts, scan time could be reduced to be suitable with in vivo applications.

The Soliton and the Action Potential - Primary Elements Underlying Sentience

At present the neurological basis of sentience is poorly understood and this problem is exacerbated by only a partial knowledge of how one of the primary elements of sentience, the action potential, actually works. This has consequences for our understanding of how communication within the brain and in artificial brain neural networks (BNNs). Reverse engineering models of brain activity assume processing works like a conventional binary computer and neglects speed of cognition, latencies, error in nerve conduction and the true dynamic structure of neural networks in the brain. Any model of nerve conduction that claims inspiration from nature must include these prerequisite parameters, but current western computer modeling of artificial BNNs assumes that the action potential is binary and binary mathematics has been assumed by force of popular acceptance to mediate computation in the brain. Here we present evidence that the action potential is a temporal compound ternary structure, described as the computational action potential (CAP). The CAP contains the refractory period, an analog third phase capable of phase-ternary computation via colliding action potentials. This would best fit a realistic BNN and provides a plausible mechanism to explain transmission, in preference to Cable Theory. The action potential pulse (APPulse), is made up of the action potential combined with a coupled synchronized soliton pressure pulse in the cell membrane. We describe a model of an ion channel in a membrane where a soliton deforms the channel sufficiently to destroy the electrostatic insulation thereby instigating a mechanical contraction across the membrane by electrostatic forces. Such a contraction has the effect of redistributing the force lengthways thereby increasing the volume of the ion channel in the membrane. Na ions, once attracted to the interior, balance the forces and the channel reforms to its original shape. A refractory period then occurs until the Na ions diffuse from the adjacent interior space. Finally, a computational model of the action potential (the CAP) is proposed with single action potentials significantly including the refractory period as a computational element capable of computation between colliding action potentials.

High cell density suppresses BMP4-induced differentiation of human pluripotent stem cells to produce macroscopic spatial patterning in a unidirectional perfusion culture chamber

Spatial pattern formation is a critical step in embryogenesis. Bone morphogenetic protein 4 (BMP4) and its inhibitors are major factors for the formation of spatial patterns during embryogenesis. However, spatial patterning of the human embryo is unclear because of ethical issues and isotropic culture environments resulting from conventional culture dishes. Here, we utilized human pluripotent stem cells (hiPSCs) and a simple anisotropic (unidirectional perfusion) culture chamber, which creates unidirectional conditions, to measure the cell community effect. The influence of cell density on BMP4-induced differentiation was explored during static culture using a conventional culture dish. Immunostaining of the early differentiation marker SSEA-1 and the mesendoderm marker BRACHYURY revealed that high cell density suppressed differentiation, with small clusters of differentiated and undifferentiated cells formed. Addition of five-fold higher concentration of BMP4 showed similar results, suggesting that suppression was not caused by depletion of BMP4 but rather by high cell density. Quantitative RT-PCR array analysis showed that BMP4 induced multi-lineage differentiation, which was also suppressed under high-density conditions. We fabricated an elongated perfusion culture chamber, in which proteins were transported unidirectionally, and hiPSCs were cultured with BMP4. At low density, the expression was the same throughout the chamber. However, at high density, SSEA-1 and BRACHYURY were expressed only in upstream cells, suggesting that some autocrine/paracrine factors inhibited the action of BMP4 in downstream cells to form the spatial pattern. Human iPSCs cultured in a perfusion culture chamber might be useful for studying in vitro macroscopic pattern formation in human embryogenesis.

Local tissue manipulation via a force- and pressure-controlled AFM micropipette for analysis of cellular processes

Local manipulation of complex tissues at the single-cell level is challenging and requires excellent sealing between the specimen and the micromanipulation device. Here, biological applications for a recently developed loading technique for a force- and pressure-controlled fluidic force microscope micropipette are described. This technique allows for the exact positioning and precise spatiotemporal control of liquid delivery. The feasibility of a local loading technique for tissue applications was investigated using two fluorescent dyes, with which local loading behaviour could be optically visualised. Thus, homogeneous intracellular distribution of CellTracker Red and accumulation of SYTO 9 Green within nuclei was realised in single cells of a tissue preparation. Subsequently, physiological micromanipulation experiments were performed. Salivary gland tissue was pre-incubated with the Ca2+-sensitive dye OGB-1. An intracellular Ca2+ rise was then initiated at the single-cell level by applying dopamine via micropipette. When pre-incubating tissue with the nitric oxide (NO)-sensitive dye DAF-FM, NO release and intercellular NO diffusion was observed after local application of the NO donor SNP. Finally, local micromanipulation of a well-defined area along irregularly shaped cell surfaces of complex biosystems was shown for the first time for the fluidic force microscope micropipette. Thus, this technique is a promising tool for the investigation of the spatiotemporal effects of locally applied substances in complex tissues.

Distribution of brain sodium long and short relaxation times and concentrations: a multi-echo ultra-high field 23Na MRI study

Sodium (²³Na) MRI proffers the possibility of novel information for neurological research but also particular challenges. Uncertainty can arise in in vivo ²³Na estimates from signal losses given the rapidity of T2* decay due to biexponential relaxation with both short (T₂*_short) and long (T₂*_long) components. We build on previous work by characterising the decay curve directly via multi-echo imaging at 7 T in 13 controls with the requisite number, distribution and range to assess the distribution of both in vivo T₂*_short and T₂*_long and in variation between grey and white matter, and subregions. By modelling the relationship between signal and reference concentration and applying it to in vivo ²³Na-MRI signal, ²³Na concentrations and apparent transverse relaxation times of different brain regions were measured for the first time. Relaxation components and concentrations differed substantially between regions of differing tissue composition, suggesting sensitivity of multi-echo ²³Na-MRI toward features of tissue composition. As such, these results raise the prospect of multi-echo ²³Na-MRI as an adjunct source of information on biochemical mechanisms in both physiological and pathophysiological states.

Design and validation of diffusion MRI models of white matter

Diffusion MRI is arguably the method of choice for characterizing white matter microstructure in vivo. Over the typical duration of diffusion encoding, the displacement of water molecules is conveniently on a length scale similar to that of the underlying cellular structures. Moreover, water molecules in white matter are largely compartmentalized which enables biologically-inspired compartmental diffusion models to characterize and quantify the true biological microstructure. A plethora of white matter models have been proposed. However, overparameterization and mathematical fitting complications encourage the introduction of simplifying assumptions that vary between different approaches. These choices impact the quantitative estimation of model parameters with potential detriments to their biological accuracy and promised specificity. First, we review biophysical white matter models in use and recapitulate their underlying assumptions and realms of applicability. Second, we present up-to-date efforts to validate parameters estimated from biophysical models. Simulations and dedicated phantoms are useful in assessing the performance of models when the ground truth is known. However, the biggest challenge remains the validation of the "biological accuracy" of estimated parameters. Complementary techniques such as microscopy of fixed tissue specimens have facilitated direct comparisons of estimates of white matter fiber orientation and densities. However, validation of compartmental diffusivities remains challenging, and complementary MRI-based techniques such as alternative diffusion encodings, compartment-specific contrast agents and metabolites have been used to validate diffusion models. Finally, white matter injury and disease pose additional challenges to modeling, which are also discussed. This review aims to provide an overview of the current state of models and their validation and to stimulate further research in the field to solve the remaining open questions and converge towards consensus.

Spatial model of convective solute transport in brain extracellular space does not support a "glymphatic" mechanism

A “glymphatic mechanism” has been proposed to mediate convective fluid transport from para-arterial to paravenous extracellular space in the brain. Jin et al. model such a system and find that diffusion, rather than convection, can account for the transport of solutes.

A “glymphatic system,” which involves convective fluid transport from para-arterial to paravenous cerebrospinal fluid through brain extracellular space (ECS), has been proposed to account for solute clearance in brain, and aquaporin-4 water channels in astrocyte endfeet may have a role in this process. Here, we investigate the major predictions of the glymphatic mechanism by modeling diffusive and convective transport in brain ECS and by solving the Navier–Stokes and convection–diffusion equations, using realistic ECS geometry for short-range transport between para-arterial and paravenous spaces. Major model parameters include para-arterial and paravenous pressures, ECS volume fraction, solute diffusion coefficient, and astrocyte foot-process water permeability. The model predicts solute accumulation and clearance from the ECS after a step change in solute concentration in para-arterial fluid. The principal and robust conclusions of the model are as follows: (a) significant convective transport requires a sustained pressure difference of several mmHg between the para-arterial and paravenous fluid and is not affected by pulsatile pressure fluctuations; (b) astrocyte endfoot water permeability does not substantially alter the rate of convective transport in ECS as the resistance to flow across endfeet is far greater than in the gaps surrounding them; and (c) diffusion (without convection) in the ECS is adequate to account for experimental transport studies in brain parenchyma. Therefore, our modeling results do not support a physiologically important role for local parenchymal convective flow in solute transport through brain ECS.

Ionic charge transport between blockages: Sodium cation conduction in freshly excised bulk brain tissue

We analyze the transient-dc and frequency-dependent electrical conductivities between blocking electrodes. We extend this analysis to measurements of ions' transport in freshly excised bulk samples of human brain tissue whose complex cellular structure produces blockages. The associated ionic charge-carrier density and diffusivity are consistent with local values for sodium cations determined non-invasively in brain tissue by MRI (NMR) and diffusion-MRI (spin-echo NMR). The characteristic separation between blockages, about 450 microns, is very much shorter than that found for sodium-doped gel proxies for brain tissue, >1 cm.

Lithium compartmentation in brain by 7Li MRS: effect of total lithium concentration

In previous work at 4.7 T, the individual components of biexponential (7) Li transverse (T2 ) spin relaxation in rat brain in vivo were tentatively identified with intra- and extracellular Li. The goal in this work was to estimate Li's compartmental distribution as a function of total Li concentration in brain from the biexponential decays. Here a localized, biexponential (7) Li T2 MR spin-relaxation study with isotopically enriched (7) LiCl is reported in rat brain in vivo at 7 T. Additionally, a simple linear interpolation using the biexponential T2 values to estimate intracellular Li from individual monoexponential T2 decays was assessed. Intracellular T2 was 14.8 ± 4.3 ms and extracellular T2 was 295 ± 61 ms. The fraction of intracellular brain Li ranged from 37.3 to 64.8% (mean 54.5 ± 6.7%) and did not correlate with total Li concentration. The estimated intracellular Li concentration ranged from 47 to 80% (mean 68.3 ± 8.5%) of the total brain Li concentration and was highly correlated with it. The monoexponential estimates of the intracellular-Li fractions and derived concentrations averaged about 15% higher than the corresponding biexponential estimates. This work supports the previous conclusion that a large fraction of Li in the brain is within the intracellular compartment.

Sodium MRI and the assessment of irreversible tissue damage during hyper-acute stroke

Sodium MRI (sMRI) has undergone a tremendous amount of technical development during the last two decades that makes it a suitable tool for the study of human pathology in the acute setting within the constraints of a clinical environment. The salient role of the sodium ion during impaired ATP production during the course of brain ischemia makes sMRI an ideal tool for the study of ischemic tissue viability during stroke. In this paper, the current limitations of conventional MRI for the determination of tissue viability during evolving brain ischemia are discussed. This discussion is followed by a summary of the known findings about the dynamics of tissue sodium changes during brain ischemia. A mechanistic model for the explanation of these findings is presented together with the technical requirements for its investigation using clinical MRI scanners. An illustration of the salient features of the technique is also presented using a nonhuman primate model of reversible middle cerebral artery occlusion.

MRI & MRS assessment of the role of the tumour microenvironment in response to therapy

MRI and MRS techniques are being applied to the characterisation of various aspects of the tumour microenvironment and to the assessment of tumour response to therapy. For example, kinetic parameters describing tumour blood vessel flow and permeability can be derived from dynamic contrast-enhanced MRI data and have been correlated with a positive tumour response to antivascular therapies. The ongoing development and validation of noninvasive, high-resolution anatomical/molecular MR techniques will equip us with the means to detect specific tumour biomarkers early on, and then to monitor the efficacy of cancer treatments efficiently and reliably, all within a clinically relevant time frame. Reliable tumour microenvironment imaging biomarkers will provide obvious advantages by enabling tumour-specific treatment tailoring and potentially improving patient outcome. However, for routine clinical application across many disease types, such imaging biomarkers must be quantitative, robust, reproducible, sufficiently sensitive and cost-effective. These characteristics are all difficult to achieve in practice, but image biomarker development and validation have been greatly facilitated by an increasing number of pertinent preclinical in vivo cancer models. Emphasis must now be placed on discovering whether the preclinical results translate into an improvement in patient care and, therefore, overall survival.

General requirement for harvesting antennae at ca and h channels and transporters

The production and dissipation of energy in cells is intimately linked to the movement of small molecules in and out of enzymes, channels, and transporters. An analytical model of diffusion was described previously, which was used to estimate local effects of these proteins acting as molecular sources. The present article describes a simple but more general model, which can be used to estimate the local impact of proteins acting as molecular sinks. The results show that the enzymes, transporters, and channels, whose substrates are present at relatively high concentrations like ATP, Na⁺, glucose, lactate, and pyruvate, do not operate fast enough to deplete their vicinity to a meaningful extent, supporting the notion that for these molecules the cytosol is a well-mixed compartment. One specific consequence of this analysis is that the well-documented cross-talk existing between the Na⁺/K⁺ ATPase and the glycolytic machinery should not be explained by putative changes in local ATP concentration. In contrast, Ca2⁺ and H⁺ transporters like the Na⁺/Ca2⁺ exchanger NCX and the Na⁺/H⁺ exchanger NHE, show experimental rates of transport that are two to three orders of magnitude faster than the rates at which the aqueous phase may possibly feed their binding sites. This paradoxical result implies that Ca2⁺ and H⁺ transporters do not extract their substrates directly from the bulk cytosol, but from an intermediate “harvesting” compartment located between the aqueous phase and the transport site.

The use of MR-detectable reporter molecules and ions to evaluate diffusion in normal and ischemic brain

As a result of the technical challenges associated with distinguishing the MR signals arising from intracellular and extracellular water, a variety of endogenous and exogenous MR-detectable molecules and ions have been employed as compartment-specific reporters of water motion. Although these reporter molecules and ions do not have the same apparent diffusion coefficients (ADCs) as water, their ADCs are assumed to be directly related to the ADC of the water in which they are solvated. This approach has been used to probe motion in the intra- and extracellular space of cultured cells and intact tissue. Despite potential interpretative challenges with the use of reporter molecules or ions and the wide variety used, the following conclusions are consistent considering all studies: (i) the apparent free diffusive motion in the intracellular space is approximately one-half of that in dilute aqueous solution; (ii) ADCs for intracellular and extracellular water are similar; (iii) the intracellular ADC decreases in association with brain injury. These findings provide support for the hypothesis that the overall brain water ADC decrease that accompanies brain injury is driven primarily by a decrease in the ADC of intracellular water. We review the studies supporting these conclusions, and interpret them in the context of explaining the decrease in overall brain water ADC that accompanies brain injury.

In vivo chlorine-35, sodium-23 and proton magnetic resonance imaging of the rat brain

In this study we demonstrate the feasibility of combined chlorine-35, sodium-23 and proton magnetic resonance imaging (MRI) at 9.4 Tesla, and present the first in vivo chlorine-35 images obtained by means of MRI. With the experimental setup used in this study all measurements could be done in one session without changing the setup or moving the subject. The multinuclear measurement requires a total measurement time of 2 h and provides morphological (protons) and physiological (sodium-23, chlorine-35) information in one scanning session. Chlorine-35, sodium-23 and high resolution proton images were acquired from a phantom, a healthy rat and from a rat displaying a focal cerebral infarction. Compared to the healthy tissue a signal enhancement of a factor of 2.2 +/- 0.2 in the chlorine-35 and a factor of 2.9 +/- 0.6 in the sodium-23 images is observed in the areas of infarction. Exemplary unlocalized measurement of the in vivo longitudinal and transversal relaxation time of chlorine-35 in a healthy rat showed multi-exponential behaviour. A biexponential fit revealed a fast and a slow relaxing component with T(1,a) = (1.7 +/- 0.4) ms, T(1,b) = (25.1 +/- 1.4) ms, amplitudes of A = 0.26 +/- 0.02, (1-A) = 0.74 +/- 0.02 and T(2,a) = (1.3 +/- 0.1) ms, T(2,b) = (11.8 +/- 1.1) ms, A = 0.64 +/- 0.02, (1-A) = 0.36 +/- 0.02. Combined proton, sodium-23 and chlorine-35 MRI may provide a new approach for non-invasive studies of ionic regulatory processes under physiological and pathological conditions in vivo.

Fixed negative charge and the Donnan effect: a description of the driving forces associated with brain tissue swelling and oedema

Cerebral oedema or brain tissue swelling is a significant complication following traumatic brain injury or stroke that can increase the intracranial pressure (ICP) and impair blood flow. Here, we have identified a potential driver of oedema: the negatively charged molecules fixed within cells. This fixed charge density (FCD), once exposed, could increase ICP through the Donnan effect. We have shown that metabolic processes and membrane integrity are required for concealing this FCD as slices of rat cortex swelled immediately (within 30 min) following dissection if treated with 2 deoxyglucose + cyanide (2DG+CN) or Triton X-100. Slices given ample oxygen and glucose, however, did not swell significantly. We also found that dead brain tissue swells and shrinks in response to changes in ionic strength of the bathing medium, which suggests that the Donnan effect is capable of pressurizing and swelling brain tissue. As predicted, a non-ionic osmolyte, 1,2 propanediol, elicited no volume change at 2000 x 10(-3) osmoles l(-1) (Osm). Swelling data were well described by triphasic mixture theory with the calculated reference state FCD similar to that measured with a 1,9 dimethylmethylene blue assay. Taken together, these data suggest that intracellular fixed charges may contribute to the driving forces responsible for brain swelling.

Proton, diffusion-weighted imaging, and sodium (23Na) MRI of uterine leiomyomata after MR-guided high-intensity focused ultrasound: a preliminary study

PURPOSE

To determine the feasibility of using combined proton (1H), diffusion-weighted imaging (DWI), and sodium (23Na) magnetic resonance imaging (MRI) to monitor the treatment of uterine leiomyomata (fibroids).

MATERIALS AND METHODS

Eight patients with uterine leiomyomata were enrolled and treated using MRI-guided high-intensity frequency ultrasound surgery (MRg-HIFUS). MRI scans collected at baseline and posttreatment consisted of T2-, T1-, and 1H DWI, as well as posttreatment 23Na MRI. The 23Na and 1H MRi were coregistered using a replacement phantom method. Regions of interest in treated and untreated uterine leiomyoma tissue were drawn on 1H MRI and DWI, wherein the tissue apparent diffusion coefficient of water (ADC) and absolute sodium concentrations were measured.

RESULTS

Regions of treated uterine tissue were clearly identified on both DWI and 23Na images. The sodium concentrations in normal myometrium tissue were 35.8+/-2.1 mmol (mM), in the fundus; 43.4+/-3.8 mM, and in the bladder; 65.3+/-0.8 mM with ADC in normal myometrium of 2.2+/-0.3x10(-3) mm2/sec. Sodium concentration in untreated leiomyomata were 28+/-5 mM, and were significantly elevated (41.6+/-7.6 mM, P<0.05) after treatment. Apparent diffusion coefficient values in the treated leiomyomata (1.30+/-0.38x10(-3) mm2/sec) were decreased compared to areas of untreated leiomyomata (1.75+/--4048micro-4050micro36x10(-3) mm2/sec; P=0.04).

CONCLUSION

Multiparametric imaging permits identification of uterine leiomyomata, revealing altered 23Na MRI and DWI levels following noninvasive treatment that provides a mechanism to explore the molecular and metabolic pathways after treatment.

A novel role for MNTB neuron dendrites in regulating action potential amplitude and cell excitability during repetitive firing

Principal cells of the medial nucleus of the trapezoid body (MNTB) are simple round neurons that receive a large excitatory synapse (the calyx of Held) and many small inhibitory synapses on the soma. Strangely, these neurons also possess one or two short tufted dendrites, whose function is unknown. Here we assess the role of these MNTB cell dendrites using patch-clamp recordings, imaging and immunohistochemistry techniques. Using outside-out patches and immunohistochemistry, we demonstrate the presence of dendritic Na+ channels. Current-clamp recordings show that tetrodotoxin applied onto dendrites impairs action potential (AP) firing. Using Na+ imaging, we show that the dendrite may serve to maintain AP amplitudes during high-frequency firing, as Na+ clearance indendritic compartments is faster than axonal compartments. Prolonged high-frequency firing can diminish Na+ gradients in the axon while the dendritic gradient remains closer to resting conditions; therefore, the dendrite can provide additional inward current during prolonged firing. Using electron microscopy, we demonstrate that there are small excitatory synaptic boutons on dendrites. Multi-compartment MNTB cell simulations show that, with an active dendrite, dendritic excitatory postsynaptic currents (EPSCs) elicit delayed APs compared with calyceal EPSCs. Together with high- and low-threshold voltage-gated K+ currents, we suggest that the function of the MNTB dendrite is to improve high-fidelity firing, and our modelling results indicate that an active dendrite could contribute to a 'dual' firing mode for MNTB cells (an instantaneous response to calyceal inputs and a delayed response to non-calyceal dendritic excitatory postsynaptic potentials).

Diffusion in brain extracellular space

Diffusion in the extracellular space (ECS) of the brain is constrained by the volume fraction and the tortuosity and a modified diffusion equation represents the transport behavior of many molecules in the brain. Deviations from the equation reveal loss of molecules across the blood-brain barrier, through cellular uptake, binding, or other mechanisms. Early diffusion measurements used radiolabeled sucrose and other tracers. Presently, the real-time iontophoresis (RTI) method is employed for small ions and the integrative optical imaging (IOI) method for fluorescent macromolecules, including dextrans or proteins. Theoretical models and simulations of the ECS have explored the influence of ECS geometry, effects of dead-space microdomains, extracellular matrix, and interaction of macromolecules with ECS channels. Extensive experimental studies with the RTI method employing the cation tetramethylammonium (TMA) in normal brain tissue show that the volume fraction of the ECS typically is approximately 20% and the tortuosity is approximately 1.6 (i.e., free diffusion coefficient of TMA is reduced by 2.6), although there are regional variations. These parameters change during development and aging. Diffusion properties have been characterized in several interventions, including brain stimulation, osmotic challenge, and knockout of extracellular matrix components. Measurements have also been made during ischemia, in models of Alzheimer's and Parkinson's diseases, and in human gliomas. Overall, these studies improve our conception of ECS structure and the roles of glia and extracellular matrix in modulating the ECS microenvironment. Knowledge of ECS diffusion properties is valuable in contexts ranging from understanding extrasynaptic volume transmission to the development of paradigms for drug delivery to the brain.

Evaluation of extra- and intracellular apparent diffusion coefficient of sodium in rat skeletal muscle: effects of prolonged ischemia

The mechanism of water and sodium apparent diffusion coefficient (ADC) changes in rat skeletal muscle during global ischemia was examined by in vivo 1H and 23Na magnetic resonance spectroscopy (MRS). The ADCs of Na+ and water are expected to have similar characteristics because sodium is present as an aqua-cation in tissue. The shift reagent, TmDOTP5(-), was used to separate intra- and extracellular sodium (Na+i and Na+e, respectively) signals. Water, total tissue sodium (Na+t), Na+i, and Na+e ADCs were measured before and 1, 2, 3, and 4 hr after ischemia. Contrary to the general perception, Na+i and Na+e ADCs were identical before ischemia. Thus, ischemia-induced changes in Na+e ADC cannot be explained by a simple change in the size of relative intracellular or extracellular space. Na+t and Na+e ADCs decreased after 2-4 hr of ischemia, while water and Na+i ADC remained unchanged. The correlation between Na+t and Na+e ADCs was observed because of high Na+e concentration. Similarly, the correlation between water and Na+i ADCs was observed because cells occupy 80% of the tissue space in the skeletal muscle. Ischemia also caused an increase in the Na+i and an equal decrease in Na+e signal intensity due to cessation of Na+/K+-ATPase function.

Cs + ADC in rat brain decreases markedly at death

Spectroscopic resolution of intracellular and extracellular compartments can be used to probe the kinetic environment of those spaces and the compartment-specific changes that occur following injury. This is important for understanding the biophysical mechanisms that underlie the remarkable diffusion-weighted MRI contrast of injured central nervous system (CNS) tissue. Cesium-133 is a physiologic analog of potassium that is actively taken up by cells and resides primarily in the intracellular space. The (133)Cs(+) signal can, thus, be exploited to probe the kinetic environment of the intracellular space. Two principal (133)Cs(+) resonances were observed at 11.74 T. These resonances arise separately from (133)Cs(+) in brain and temporalis muscle. The apparent diffusion coefficient (ADC) of Cs(+) in brain decreased from 1.0 +/- 0.2 microm(2)/ms in healthy tissue to 0.24 +/- 0.04 microm(2)/ms following global ischemia (average ADC +/- average uncertainty), while there was no significant change in the ADC of Cs(+) in temporalis muscle after injury. This finding underscores the tissue-specific nature of the decrease in ADC that accompanies brain injury. Further, as the Cs(+) ADC should reflect water ADC in the intracellular space, these results strongly support the hypothesis that the decrease in water ADC associated with CNS injury arises largely from kinetic changes taking place in the intracellular space.

An enquiry into metabolite domains

It is currently assumed that two or more pools of the same metabolite can coexist in the cytosolic compartment of mammalian cells. These pools are thought to be generated by the differential subcellular location of enzymes and transporters, much in the way calcium microdomains arise by the combined workings of channels, buffers, and pumps. With the aim of estimating the amplitude and spatial dimensions of these metabolite pools, we developed an analytical tool based on Brownian diffusion and the turnover numbers of the proteins involved. The outcome of the analysis is that ATP, glucose, pyruvate, lactate, and glutamate cannot be concentrated at their sources to an extent that would affect their downstream targets. For these metabolites, and others produced by slow enzymes or transporters and present at micromolar concentrations or higher, the cytosol behaves as a well-mixed, homogenous compartment. In contrast, the analysis showed microdomains known to be generated by calcium channels and revealed that calcium and pH nanodomains are to be found in the vicinity of slow enzymes and transporters in the steady state. The analysis can be readily applied to any other molecule, provided knowledge is available about rate of production, average concentration, and diffusion coefficient. Our main conclusion is that the notion of cytosolic compartmentation of metabolites needs reevaluation, as it seems to be in conflict with the underlying physical chemistry.

Integration of quantitative DCE-MRI and ADC mapping to monitor treatment response in human breast cancer: initial results

PURPOSE

The objective of this study was to assess changes in the water apparent diffusion coefficient (ADC) and in pharmacokinetic parameters obtained from the fast-exchange regime (FXR) modeling of dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) during neoadjuvant chemotherapy in breast cancer.

MATERIALS AND METHODS

Eleven patients with locally advanced breast cancer underwent MRI examination prior to and after chemotherapy but prior to surgery. A 1.5-T scanner was used to obtain T1, ADC and DCE-MRI data. DCE-MRI data were analyzed by the FXR model returning estimates of K(trans) (volume transfer constant), v(e) (extravascular extracellular volume fraction) and tau(i) (average intracellular water lifetime). Histogram and correlation analyses assessed parameter changes post-treatment.

RESULTS

Significant (P < .05) changes or trends towards significance (P < .10) were seen in all parameters except tau(i), although there was qualitative reduction in tau(i) values post-treatment. In particular, there was reduction (P < .035) in voxels with K(trans) values in the range 0.2-0.5 min(-1) and a decrease (P < .05) in voxels with ADC values in the range 0.99 x 10(-3) to 1.35 x 10(-3) mm2/s. ADC and v(e) were negatively correlated (r = -.60, P < .02). Parameters sensitive to water distribution and geometry (T(1), v(e), tau(i) and ADC) correlated with a multivariable linear regression model.

CONCLUSION

The analysis presented here is sensitive to longitudinal changes in breast tumor status; K(trans) and ADC are most sensitive to these changes. Relationships between parameters provide information on water distribution and geometry in the tumor environment.

Sodium and proton diffusion MRI as biomarkers for early therapeutic response in subcutaneous tumors

The ability to quantitate early effects of tumor therapeutic response using noninvasive imaging would have a major impact in clinical oncology. One area of active research interest is the ability to use MR techniques to detect subtle changes in tumor cellular density. In this study, sodium and proton diffusion MRI were compared for their ability to detect early cellular changes in tumors treated with a cytotoxic chemotherapy. Subcutaneous 9L gliosarcomas were treated with a single dose of 1,3-bis(2-chloroethyl)-1-nitrosourea. Both sodium and diffusion imaging modalities were able to detect changes in tumor cellularity as early as 2 days after treatment, which continued to evolve as increased signal intensities reached a maximum approximately 8 days posttreatment. Early changes in tumor sodium and apparent diffusion coefficient values were predictive of subsequent tumor shrinkage, which occurred approximately 10 days later. Overall, therapeutical induced changes in sodium and diffusion values were found to have similar dynamic and spatial changes. These findings suggest that these imaging modalities detected similar early cellular changes after treatment. The results of this study support the continued clinical testing of diffusion MRI for evaluation of early tumor treatment response and demonstrate the complementary insights of sodium MRI for oncology applications.