A system and mathematical framework to model shear flow effects in biomedical DW-imaging and spectroscopy

Metabolic activity diffusion imaging (MADI): I. Metabolic, cytometric modeling and simulations

Evidence mounts that the steady-state cellular water efflux (unidirectional) first-order rate constant (k_io [s^-1 ]) magnitude reflects the ongoing, cellular metabolic rate of the cytolemmal Na⁺ , K⁺ -ATPase (NKA), ^c MR_NKA (pmol [ATP consumed by NKA]/s/cell), perhaps biology's most vital enzyme. Optimal ¹ H₂ O MR k_io determinations require paramagnetic contrast agents (CAs) in model systems. However, results suggest that the homeostatic metabolic k_io biomarker magnitude in vivo is often too large to be reached with allowable or possible CA living tissue distributions. Thus, we seek a noninvasive (CA-free) method to determine k_io in vivo. Because membrane water permeability has long been considered important in tissue water diffusion, we turn to the well-known diffusion-weighted MRI (DWI) modality. To analyze the diffusion tensor magnitude, we use a parsimoniously primitive model featuring Monte Carlo simulations of water diffusion in virtual ensembles comprising water-filled and -immersed randomly sized/shaped contracted Voronoi cells. We find this requires two additional, cytometric properties: the mean cell volume (V [pL]) and the cell number density (ρ [cells/μL]), important biomarkers in their own right. We call this approach metabolic activity diffusion imaging (MADI). We simulate water molecule displacements and transverse MR signal decays covering the entirety of b-space from pure water (ρ = V = 0; k_io undefined; diffusion coefficient, D₀ ) to zero diffusion. The MADI model confirms that, in compartmented spaces with semipermeable boundaries, diffusion cannot be described as Gaussian: the nanoscopic D (D_n ) is diffusion time-dependent, a manifestation of the "diffusion dispersion". When the "well-mixed" (steady-state) condition is reached, diffusion becomes limited, mainly by the probabilities of (1) encountering (ρ, V), and (2) permeating (k_io ) cytoplasmic membranes, and less so by D_n magnitudes. Importantly, for spaces with large area/volume (A/V; claustrophobia) ratios, this can happen in less than a millisecond. The model matches literature experimental data well, with implications for DWI interpretations.

Comparison of microvascular perfusion evaluation among IVIM-DWI, CT perfusion imaging and histological microvessel density in rabbit liver VX2 tumors

OBJECT

To explore microcirculation features with intravoxel incoherent motion (IVIM) and to compare IVIM with CT perfusion imaging (CTPI) and microvessel density (MVD).

MATERIALS AND METHODS

Hepatic CTPI and IVIM were performed in 16 rabbit liver VX2 tumor models. Hepatic arterial perfusion (HAP), hepatic arterial perfusion index (HPI), Blood flow (BF), and blood volume (BV) from CTPI were measured. Apparent diffusion coefficient (ADC), true diffusion coefficient (D), perfusion fraction (f), and pseudo-diffusion coefficient (D*) from IVIM were measured. MVD was counted with CD34 stain. The microcirculation features with IVIM were compared with CTPI parameters and MVD.

RESULTS

Strong linear correlations were found between D value (0.89±0.21×10^-3mm²/s) and HAP (15.83±6.97ml/min/100mg) (r=0.755, P=0.001) and between f value (12.64±6.66%) and BV (9.74±5.04ml/100mg) (r=0.693, P=0.004). Moderate linear correlations were observed between ADC (1.07±0.32×10^-3mm²/s) and HAP (r=0.538, P=0.039), respectively; and between D value and MVD (9.31±2.57 vessels at 400×magnification) (r=0.509, P=0.044). No correlations were found between D* (119.90±37.67×10^-3mm²/s) and HAP, HPI (68.34±12.91%), BF (4.95±2.16ml/min/100mg), BV.

CONCLUSION

IVIM parameters can characterize microcirculation to certain extent and separate it from pure water molecular diffusion. There is fair correlation between D or ADC value and CTPI parameters or MVD, but no correlation between D* or f value and CTPI parameters or MVD except f value and BV, which is still unclear and need further clinical studies to validate.

A two-pool model to describe the IVIM cerebral perfusion

IntraVoxel Incoherent Motion (IVIM) is a magnetic resonance imaging (MRI) technique capable of measuring perfusion-related parameters. In this manuscript, we show that the mono-exponential model commonly used to process IVIM data might be challenged, especially at short diffusion times. Eleven rat datasets were acquired at 7T using a diffusion-weighted pulsed gradient spin echo sequence with b-values ranging from 7 to 2500 s/mm² at three diffusion times. The IVIM signals, obtained by removing the diffusion component from the raw MR signal, were fitted to the standard mono-exponential model, a bi-exponential model and the Kennan model. The Akaike information criterion used to find the best model to fit the data demonstrates that, at short diffusion times, the bi-exponential IVIM model is most appropriate. The results obtained by comparing the experimental data to a dictionary of numerical simulations of the IVIM signal in microvascular networks support the hypothesis that such a bi-exponential behavior can be explained by considering the contribution of two vascular pools: capillaries and somewhat larger vessels.

Assessing the sensitivity of diffusion MRI to detect neuronal activity directly

Functional MRI (fMRI) is widely used to study brain function in the neurosciences. Unfortunately, conventional fMRI only indirectly assesses neuronal activity via hemodynamic coupling. Diffusion fMRI was proposed as a more direct and accurate fMRI method to detect neuronal activity, yet confirmative findings have proven difficult to obtain. Given that the underlying relation between tissue water diffusion changes and neuronal activity remains unclear, the rationale for using diffusion MRI to monitor neuronal activity has yet to be clearly established. Here, we studied the correlation between water diffusion and neuronal activity in vitro by simultaneous calcium fluorescence imaging and diffusion MR acquisition. We used organotypic cortical cultures from rat brains as a biological model system, in which spontaneous neuronal activity robustly emerges free of hemodynamic and other artifacts. Simultaneous fluorescent calcium images of neuronal activity are then directly correlated with diffusion MR signals now free of confounds typically encountered in vivo. Although a simultaneous increase of diffusion-weighted MR signals was observed together with the prolonged depolarization of neurons induced by pharmacological manipulations (in which cell swelling was demonstrated to play an important role), no evidence was found that diffusion MR signals directly correlate with normal spontaneous neuronal activity. These results suggest that, whereas current diffusion MR methods could monitor pathological conditions such as hyperexcitability, e.g., those seen in epilepsy, they do not appear to be sensitive or specific enough to detect or follow normal neuronal activity.

Drag of the cytosol as a transport mechanism in neurons

Axonal transport is typically divided into two components, which can be distinguished by their mean velocity. The fast component includes steady trafficking of different organelles and vesicles actively transported by motor proteins. The slow component comprises nonmembranous materials that undergo infrequent bidirectional motion. The underlying mechanism of slow axonal transport has been under debate during the past three decades. We propose a simple displacement mechanism that may be central for the distribution of molecules not carried by vesicles. It relies on the cytoplasmic drag induced by organelle movement and readily accounts for key experimental observations pertaining to slow-component transport. The induced cytoplasmic drag is predicted to depend mainly on the distribution of microtubules in the axon and the organelle transport rate.

Neuronal activity significantly reduces water displacement: DWI of a vital rat spinal cord with no hemodynamic effect

Changes in the diffusion weighted MRI (DWI) signal were observed to be correlated with neuronal activity during chemically induced brain activity, epileptic seizures, or visual stimulation. These changes suggest a possible reduction in water displacement that accompanies neuronal activity, but were possibly affected by other physiological mechanisms such as blood oxygenation level and blood flow. We developed an imaging experiment of an excised and vital newborn rat spinal cord to examine the effect of neuronal function on the displacement of water molecules as measured by DWI signal. This approach provides a DWI experiment of a vital mammalian CNS tissue in the absence of some of the systemic sources of noise. We detected a significant and reproducible drop with an average value of 19.5 ± 1.6% (mean ± SE) upon activation. The drop repeated itself in three orthogonal directions. ADC values corresponded to an oblate anisotropy. This result was validated by high resolution DWI of a fixed tissue, imaged with an ultra-high field MRI. The results support our working hypothesis that water displacement is affected by neuronal activation. These results further imply that water displacement might serve as a potential marker for brain function, and that, although commonly viewed as wholly electrochemical, neuronal activity includes a significant mechanical dimension that affects water displacement.

A spin echo sequence with a single-sided bipolar diffusion gradient pulse to obtain snapshot diffusion weighted images in moving media

In vivo MRI data can be corrupted by motion. Motion artifacts are particularly troublesome in Diffusion Weighted MRI (DWI), since the MR signal attenuation due to Brownian motion can be much less than the signal loss due to dephasing from other types of complex tissue motion, which can significantly degrade the estimation of self-diffusion coefficients, diffusion tensors, etc. This paper describes a snapshot DWI sequence, which utilizes a novel single-sided bipolar diffusion sensitizing gradient pulse within a spin echo sequence. The proposed method shortens the diffusion time by applying a single refocused bipolar diffusion gradient on one side of a refocusing RF pulse, instead of a set of diffusion sensitizing gradients, separated by a refocusing RF pulse, while reducing the impact of magnetic field inhomogeneity by using a spin echo sequence. A novel MRI phantom that can exhibit a range of complex motions was designed to demonstrate the robustness of the proposed DWI sequence.

Interstitial fluid pressure correlates with intravoxel incoherent motion imaging metrics in a mouse mammary carcinoma model

The effective delivery of a therapeutic drug to the core of a tumor is often impeded by physiological barriers, such as the interstitial fluid pressure (IFP). There are a number of therapies that can decrease IFP and induce tumor vascular normalization. However, a lack of a noninvasive means to measure IFP hinders the utilization of such a window of opportunity for the maximization of the treatment response. Thus, the purpose of this study was to investigate the feasibility of using intravoxel incoherent motion (IVIM) diffusion parameters as noninvasive imaging biomarkers for IFP. Mice bearing the 4T1 mammary carcinoma model were studied using diffusion-weighted imaging (DWI), immediately followed by wick-in-needle IFP measurement. Voxelwise analysis was conducted with a conventional monoexponential diffusion model, as well as a biexponential model taking IVIM into account. There was no significant correlation of IFP with either the median apparent diffusion coefficient from the monoexponential model (r = 0.11, p = 0.78) or the median tissue diffusivity from the biexponential model (r = 0.30, p = 0.44). However, IFP was correlated with the median pseudo-diffusivity (D(p)) of apparent vascular voxels (r = 0.76, p = 0.02) and with the median product of the perfusion fraction and pseudo-diffusivity (f(p)D(p)) of apparent vascular voxels (r = 0.77, p = 0.02). Although the effect of IVIM in tumors has been reported previously, to our knowledge, this study represents the first direct comparison of IVIM metrics with IFP, with the results supporting the feasibility of the use of IVIM DWI metrics as noninvasive biomarkers for tumor IFP.

Tracking accuracy of T2- and diffusion-weighted magnetic resonance imaging for infusate distribution by convection-enhanced delivery

OBJECT

Because convection-enhanced delivery relies on bulk flow of fluid in the interstitial spaces, MR imaging techniques that detect extracellular fluid and fluid movement may be useful for tracking convective drug distribution. To determine the tracking accuracy of T2-weighted and diffusion-weighted MR imaging sequences, the authors followed convective distribution of radiolabeled compounds using these imaging sequences in nonhuman primates.

METHODS

Three nonhuman primates underwent thalamic convective infusions (5 infusions) with (14)C-sucrose (MW 342 D) or (14)C-dextran (MW 70,000 D) during serial MR imaging (T2- and diffusion-weighted imaging). Imaging, histological, and autoradiographic findings were analyzed.

RESULTS

Real-time T2- and diffusion-weighted imaging clearly demonstrated the region of infusion, and serial images revealed progressive filling of the bilateral thalami during infusion. Imaging analysis for T2- and diffusion-weighted sequences revealed that the tissue volume of distribution (Vd) increased linearly with volume of infusion (Vi; R(2) = 0.94, R(2) = 0.91). Magnetic resonance imaging analysis demonstrated that the mean ± SD Vd/Vi ratios for T2-weighted (3.6 ± 0.5) and diffusion-weighted (3.3 ± 0.4) imaging were similar (p = 0.5). While (14)C-sucrose and (14)C-dextran were homogeneously distributed over the infused region, autoradiographic analysis revealed that T2-weighted and diffusion-weighted imaging significantly underestimated the Vd of both (14)C-sucrose (mean differences 51.3% and 52.3%, respectively; p = 0.02) and (14)C-dextran (mean differences 49.3% and 59.6%; respectively, p = 0.001).

CONCLUSIONS

Real-time T2- and diffusion-weighted MR imaging significantly underestimate tissue Vd during convection-enhanced delivery over a wide range of molecular sizes. Application of these imaging modalities may lead to inaccurate estimation of convective drug distribution.