Quasi-diffusion magnetic resonance imaging (QDI): A fast, high b-value diffusion imaging technique.

To enable application of non-Gaussian diffusion magnetic resonance imaging (dMRI) techniques in large-scale clinical trials and facilitate translation to clinical practice there is a requirement for fast, high contrast, techniques that are sensitive to changes in tissue structure which provide diagnostic signatures at the early stages of disease. Here we describe a new way to compress the acquisition of multi-shell b-value diffusion data, Quasi-Diffusion MRI (QDI), which provides a probe of subvoxel tissue complexity using short acquisition times (1-4 â€‹min). We also describe a coherent framework for multi-directional diffusion gradient acquisition and data processing that allows computation of rotationally invariant quasi-diffusion tensor imaging (QDTI) maps. QDI is a quantitative technique that is based on a special case of the Continuous Time Random Walk model of diffusion dynamics and assumes the presence of non-Gaussian diffusion properties within tissue microstructure. QDI parameterises the diffusion signal attenuation according to the rate of decay (i.e. diffusion coefficient, D in mm2 s-1) and the shape of the power law tail (i.e. the fractional exponent, α). QDI provides analogous tissue contrast to Diffusional Kurtosis Imaging (DKI) by calculation of normalised entropy of the parameterised diffusion signal decay curve, Hn, but does so without the limitations of a maximum b-value. We show that QDI generates images with superior tissue contrast to conventional diffusion imaging within clinically acceptable acquisition times of between 84 and 228 â€‹s. We show that QDI provides clinically meaningful images in cerebral small vessel disease and brain tumour case studies. Our initial findings suggest that QDI may be added to routine conventional dMRI acquisitions allowing simple application in clinical trials and translation to the clinical arena.

Capturing complexity of the diffusion-weighted MR signal decay.

Diffusion-weighted MRI (dMRI) is a key component of clinical radiology. When analyzing diffusion-weighted images, radiologists often seek to infer microscopic tissue structure through measurements of the diffusion coefficient, D0 (mm2/s). This multi-scale problem is framed by the creation of diffusion models of signal decay based on physical laws, histological structure, and biophysical constraints. The purpose of this paper is to simplify the model building process by focusing on the observed decay in the effective diffusion coefficient as a function of diffusion weighting (b-value), D(b), that is often observed in complex biological tissues. We call this approach the varying diffusion curvature (VDC) model. Since this is a heuristic model, the exact functional form of this decay is not important, so here we examine a simple exponential function, D(b) = D0exp(-bD1), where D0 and D1 capture aspects of hindered and restricted diffusion, respectively. As an example of the potential of the VDC model, we applied it to dMRI data collected from normal and diseased human brain tissue using Stejskal-Tanner diffusion gradient pulses. In order to illustrate the connection between D0 and D1 and the sub-voxel structure we also analyzed dMRI data from families of Sephadex beads selected with increasing tortuosity. Finally, we applied the VDC model to dMRI simulations of nested muscle fiber phantoms whose permeability, atrophy, and fiber size distribution could be changed. These results demonstrate that the VDC model is sensitive to sub-voxel tissue structure and composition (porosity, tortuosity, and permeability), hence can capture tissue complexity in a manner that could be easily applied in clinical dMRI.

Review of the Dielectric Properties of Animal and Human Tumors Determined from In Vivo Measurements.

In this article, we combine a review of the wide range of tissue dielectric studies and applications (e.g., safety, imaging, therapy) being pursued by the bioelectromagnetics community with a description of one specific application of dielectric measurements (in vivo tumor classification). The tumor measurements were acquired over a frequency range of 0.01-4.0 GHz using a technique based on the impedance change recorded by a short antenna when placed near or in a lossy dielectric. Substantial differences (up to 300%) were found between the dielectric properties of tumors (mammary adenocarcinoma, melanoma, lung carcinoma, glioblastoma and ependymoblastoma) and normal host tissues. Such differences reflect the known heterogeneity of abnormal cell growth in cancer. In addition, in vivo human measurements of breast carcinoma, normal skin and breast tissue indicate that a maximum differential power absorption (30% higher in tumor) occurs between 1.0 and 2.0 GHz. This information, when combined with tumor size, geometry, and anatomical location, enable the design and development of effective systems for the detection of tumors and for electromagnetically induced differential hyperthermia treatment. Finally, we also discuss these results in the context of other impedance and dielectric approaches used to characterize normal and neoplastic cells and tissues.

Anomalous T2 relaxation in normal and degraded cartilage.

PURPOSE: To compare the ordinary monoexponential model with three anomalous relaxation models-the stretched Mittag-Leffler, stretched exponential, and biexponential functions-using both simulated and experimental cartilage relaxation data. METHODS: Monte Carlo simulations were used to examine both the ability of identifying a given model under high signal-to-noise ratio (SNR) conditions and the accuracy and precision of parameter estimates under more modest SNR as would be encountered clinically. Experimental transverse relaxation data were analyzed from normal and enzymatically degraded cartilage samples under high SNR and rapid echo sampling to compare each model. RESULTS: Both simulation and experimental results showed improvement in signal representation with the anomalous relaxation models. The stretched exponential model consistently showed the lowest mean squared error in experimental data and closely represents the signal decay over multiple decades of the decay time (e.g., 1-10 ms, 10-100 ms, and >100 ms). The stretched exponential parameter αse showed an inverse correlation with biochemically derived cartilage proteoglycan content. CONCLUSION: Experimental results obtained at high field suggest potential application of αse as a measure of matrix integrity. Simulation reflecting more clinical imaging conditions, indicate the ability to robustly estimate αse and distinguish between normal and degraded tissue, highlighting its potential as a biomarker for human studies. Magn Reson Med 76:953-962, 2016. © 2015 Wiley Periodicals, Inc.

Differentiating low- and high-grade pediatric brain tumors using a continuous-time random-walk diffusion model at high b-values.

PURPOSE: To demonstrate that a continuous-time random-walk (CTRW) diffusion model can improve diagnostic accuracy of differentiating low- and high-grade pediatric brain tumors. METHODS: Fifty-four children with histopathologically confirmed brain tumors underwent diffusion MRI scans at 3Twith 12 b-values (0-4000 s/mm(2) ). The diffusion imageswere fit to a simplified CTRW model to extract anomalous diffusion coefficient, Dm , and temporal and spatial heterogeneity parameters, α and ß, respectively. Using histopathology results as reference, a k-means clustering algorithm and a receiver operating characteristic (ROC) analysis were employed to determine the sensitivity, specificity, and diagnostic accuracy of the CTRW parameters in differentiating tumor grades. RESULTS: Significant differences between the low- and high-grade tumors were observed in the CTRW parameters (p-values<0.001). The k-means analysis showed that the combination of three CTRW parameters produced higher diagnostic accuracy (85% vs. 75%) and specificity (83% vs. 54%) than the apparent diffusion coefficient (ADC) from a mono-exponential model. The ROC analysis revealed that any combination of the CTRW parameters gave a larger area under the curve (0.90-0.96) than using ADC (0.80). CONCLUSION: With its sensitivity to intravoxel heterogeneity, the simplified CTRW model is useful for non-invasive grading of pediatric brain tumors, particularly when surgical biopsy is not feasible. Magn Reson Med 76:1149-1157, 2016. © 2015 Wiley Periodicals, Inc.

Assessment of glenoid chondral healing: comparison of microfracture to autologous matrix-induced chondrogenesis in a novel rabbit shoulder model.

BACKGROUND: Management of glenohumeral arthrosis in young patients is a considerable challenge, with a growing need for non-arthroplasty alternatives. The objectives of this study were to develop an animal model to study glenoid cartilage repair and to compare surgical repair strategies to promote glenoid chondral healing. METHODS: Forty-five rabbits underwent unilateral removal of the entire glenoid articular surface and were divided into 3 groups--untreated defect (UD), microfracture (MFx), and MFx plus type I/III collagen scaffold (autologous matrix-induced chondrogenesis [AMIC])--for the evaluation of healing at 8 weeks (12 rabbits) and 32 weeks (33 rabbits) after injury. Contralateral shoulders served as unoperated controls. Tissue assessments included 11.7-T magnetic resonance imaging (long-term healing group only), equilibrium partitioning of an ionic contrast agent via micro-computed tomography (EPIC-µCT), and histologic investigation (grades on International Cartilage Repair Society II scoring system). RESULTS: At 8 weeks, x-ray attenuation, thickness, and volume did not differ by treatment group. At 32 weeks, the T2 index (ratio of T2 values of healing to intact glenoids) was significantly lower for the MFx group relative to the AMIC group (P = .01) whereas the T1ρ index was significantly lower for AMIC relative to MFx (P = .01). The micro-computed tomography-derived repair tissue volume was significantly higher for MFx than for UD. Histologic investigation generally suggested inferior healing in the AMIC and UD groups relative to the MFx group, which exhibited improvements in both integration of repair tissue with subchondral bone and tidemark formation over time. DISCUSSION: Improvements conferred by AMIC were limited to magnetic resonance imaging outcomes, whereas MFx appeared to promote increased fibrous tissue deposition via micro-computed tomography and more hyaline-like repair histologically. The findings from this novel model suggest that MFx promotes biologic resurfacing of full-thickness glenoid articular injury.

Magnetic resonance spectroscopy and imaging can differentiate between engineered bone and engineered cartilage.

In the situation when both cartilage and its underlying bone are damaged, osteochondral tissue engineering is being developed to provide a solution. In such cases, the ability to non-invasively monitor and differentiate the development of both cartilage and bone tissues is important. Nuclear magnetic resonance (NMR) spectroscopy and magnetic resonance imaging (MRI) have been widely used to non-invasively assess tissue-engineered cartilage and tissue-engineered bone. The purpose of this work is to assess differences in MR properties of tissue-engineered bone and tissue-engineered cartilage generated from the same cell-plus-scaffold combination at the early stage of tissue growth. We developed cartilage and bone tissue constructs by seeding human marrow stromal cells (HMSCs, 2 million/ml) in 1:1 collagen/chitosan gel for four weeks. The chondrogenic or osteogenic differentiation of cells was directed with the aid of a culture medium containing chondrogenic or osteogenic growth factors, respectively. The proton and sodium NMR and waterproton T1, T2 and diffusion MRI experiments were performed on these constructs and the control collagen/chitosan gel using a 9.4 T ((1)H freq. = 400 MHz) and a 11.7 T ((1)H freq. = 500 MHz) NMR spectrometers. In all cases, the development of bone and cartilage was found to be clearly distinguishable using NMR and MRI. We conclude that MRS and MRI are powerful tools to assess growing osteochondral tissue regeneration.

Biomimetic extracellular matrix-incorporated scaffold induces osteogenic gene expression in human marrow stromal cells.

Engineering biomaterials mimicking the biofunctionality of the extracellular matrix (ECM) is important in instructing and eliciting cell response. The native ECM is highly dynamic and has been shown to support cellular attachment, migration, and differentiation. The advantage of synthesizing an ECM-based biomaterial is that it mimics the native cellular environment. However, the ECM has tissue-specific composition and patterned arrangement. In this study, we have employed biomimetic strategies to develop a novel collagen/chitosan template that is embedded with the native ECM of differentiating human marrow stromal cells (HMSCs) to facilitate osteoblast differentiation. The scaffold was characterized for substrate stiffness by magnetic resonance imaging and nanoindentation and by immunohistochemical analysis for the presence of key ECM proteins. Gene expression analysis showed that the ECM scaffold supported osteogenic differentiation of undifferentiated HMSCs as significant changes were observed in the expression levels of growth factors, transcription factors, proteases, receptors, and ECM proteins. Finally, we demonstrate that the scaffold had the ability to nucleate calcium phosphate polymorphs to form a mineralized matrix. The results from this study suggest that the three-dimensional native ECM scaffold directly controls cell behavior and supports the osteogenic differentiation of mesenchymal stem cells.

Magnetization transfer imaging provides a quantitative measure of chondrogenic differentiation and tissue development.

The goal of the present investigation was to test whether quantitative magnetization transfer imaging can be used as a noninvasive evaluation method for engineered cartilage. In this work, we used magnetic resonance imaging (MRI) to monitor the chondrogenesis of stem-cell-based engineered tissue over a 3-week period by measuring on a pixel-by-pixel basis the relaxation times (T1 and T2), the apparent diffusion coefficient, and the magnetization transfer parameters: bound proton fraction and cross-relaxation rate (k). Tissue-engineered constructs for generating cartilage were created by seeding mesenchymal stem cells in a gelatin sponge. Every 7 days, tissue samples were analyzed using MRI, histological, and biochemical methods. The MRI measurements were verified by histological analysis, and the imaging data were correlated with biochemical analysis of the developing cartilage matrix for glycosaminoglycan content. The MRI analysis for bound proton fraction and k showed a statistically significant increase that was correlated with the increase of glycosaminoglycan (R = 0.96 and 0.87, respectively, p < 0.05), whereas T1, T2, and apparent diffusion coefficient results did not show any significant changes over the 3-week measurement period.

Anomalous diffusion expressed through fractional order differential operators in the Bloch-Torrey equation.

Diffusion weighted MRI is used clinically to detect and characterize neurodegenerative, malignant and ischemic diseases. The correlation between developing pathology and localized diffusion relies on diffusion-weighted pulse sequences to probe biophysical models of molecular diffusion-typically exp[-(bD)]-where D is the apparent diffusion coefficient (mm(2)/s) and b depends on the specific gradient pulse sequence parameters. Several recent studies have investigated the so-called anomalous diffusion stretched exponential model-exp[-(bD)(alpha)], where alpha is a measure of tissue complexity that can be derived from fractal models of tissue structure. In this paper we propose an alternative derivation for the stretched exponential model using fractional order space and time derivatives. First, we consider the case where the spatial Laplacian in the Bloch-Torrey equation is generalized to incorporate a fractional order Brownian model of diffusivity. Second, we consider the case where the time derivative in the Bloch-Torrey equation is replaced by a Riemann-Liouville fractional order time derivative expressed in the Caputo form. Both cases revert to the classical results for integer order operations. Fractional order dynamics derived for the first case were observed to fit the signal attenuation in diffusion-weighted images obtained from Sephadex gels, human articular cartilage and human brain. Future developments of this approach may be useful for classifying anomalous diffusion in tissues with developing pathology.

Functional MR microimaging of pancreatic beta-cell activation.

The increasing incidence of diabetes and the need to further understand its cellular basis has resulted in the development of new diagnostic and therapeutic techniques. Nonetheless, the quest to noninvasively ascertain beta-cell mass and function has not been achieved. Manganese (Mn)-enhanced MRI is presented here as a tool to image beta-cell functionality in cell culture and isolated islets. Similar to calcium, extracellular Mn was taken up by glucose-activated beta-cells resulting in 200% increase in MRI contrast enhancement, versus nonactivated cells. Similarly, glucose-activated islets showed an increase in MRI contrast up to 45%. Although glucose-stimulated Ca influx was depressed in the presence of 100 microM Mn, no significant effect was seen at lower Mn concentrations. Moreover, islets exposed to Mn showed normal glucose sensitivity and insulin secretion. These results demonstrate a link between image contrast enhancement and beta-cell activation in vitro, and provide the basis for future noninvasive in vivo imaging of islet functionality and beta-cell mass.

MR assessment of osteogenic differentiation in tissue-engineered constructs.

Bone marrow stromal cells (MSC) are a promising source of osteoprogenitor cells for bone tissue engineering. However, the population of the osteoprogenitor cells and their differentiation potentials change with the gender, age, and health of the donor. Development of a noninvasive method to assess osteogenic progression is critical for successful bone tissue regeneration. High-resolution magnetic resonance imaging (MRI) (at 11.7 T, with spatial resolution of 62.5 x 62.5 microm in 500 microm slices) is used in the present study to monitor osteogenic differentiation of tissue-engineered constructs prepared by seeding human bone MSCs on gelatin sponge scaffolds. Quantitative measurements of the MR relaxation times (T1, T2) and the apparent diffusion coefficient (ADC) were performed for four successive weeks on control tissue constructs and constructs exposed to osteogenic differentiation medium. The T1 and T2 relaxation times and ADC were found to decrease as osteogenic progression proceeded in samples exposed to osteogenic differentiation medium. At week 4, the T1, T2, and ADC of TE constructs were 1.81 +/- 0.11 s, 19.5 +/- 11.02 ms, and 1.01 +/- 0.47 x 10(3) mm(2)/s, respectively, for osteogenic differentiated constructs, significantly different from control constructs 2.22 +/- 0.08 s, 50.39 +/- 5.57 ms, and 1.86 +/- 0.18 x 107(3) mm(2)/s (p < 0.05). The MR parameters were also highly correlated with the cell seeding densities and alkaline phosphatase (ALP) activities of the osteogenic constructs. In conclusion, periodic measurements of MR parameters (T1, T2, and ADC) provide a promising method for noninvasive monitoring of the status of tissue-engineered bone growth and differentiation.

Nondestructive evaluation of osteogenic differentiation in tissue-engineered constructs.

Conventional measurements of osteogenesis in tissue-engineered constructs are destructive to living cells and incapable to provide three-dimensional information. In the present study, noninvasive magnetic resonance (MR) microscopy was used to evaluate osteogenic differentiation in vitro in human mesenchymal stem cell-based tissue-engineered constructs. The constructs were prepared by seeding the cells (10(6)cells/ml) on 4 x 4 x 4 mm gelatin sponge cubes and subsequently exposing them to osteogenic differentiation or basic medium. During the 4-week experiment, alkaline phosphatase (ALP) activity and calcium content of differentiated constructs were significantly increased compared to the basic medium controls. The T1, T2, and apparent diffusion coefficient (ADC) of differentiated constructs were significantly lower than those of the control group at each time point (p < 0.05). The MR parameters of constructs were significantly correlated to their ALP activities (r to T1, T2, and ADC = -0.57, -0.78, and -0.81, respectively) and calcium content (r to T1, T2, and ADC = 0.48, 0.90, and 0.92, respectively) measured by biochemical techniques. MR microscopy can be a promising tool for noninvasive assessment of osteogenic differentiation and to provide three-dimensional information about tissue-engineered constructs.

Magnetic resonance microscopy for monitoring osteogenesis in tissue-engineered construct in vitro.

Magnetic resonance microscopy (MRM) is used to monitor osteogenesis in tissue-engineered constructs. Measurements of the developing tissue's MR relaxation times (T(1) and T(2)), apparent diffusion coefficient (ADC) and elastic shear modulus were conducted over a 4-week growth period using an 11.74 T Bruker spectrometer with an imaging probe adapted for MR elastography (MRE). Both the relaxation times and the ADC show a statistically significant decrease after only one week of tissue development while the tissue stiffness increases progressively during the first two weeks of in vitro growth. The measured MR parameters are correlated with histologically monitored osteogenic tissue development. This study shows that MRM can provide quantitative data with which to characterize the growth and development of tissue-engineered bone.

Fractional calculus in bioengineering, part 2.

Fractional calculus (integral and differential operations of noninteger order) is not often used to model biological systems. Although the basic mathematical ideas were developed long ago by the mathematicians Leibniz (1695), Liouville (1834), Riemann (1892), and others and brought to the attention of the engineering world by Oliver Heaviside in the 1890s, it was not until 1974 that the first book on the topic was published by Oldham and Spanier. Recent monographs and symposia proceedings have highlighted the application of fractional calculus in physics, continuum mechanics, signal processing, and electromagnetics, but with few examples of applications in bioengineering. This is surprising because the methods of fractional calculus, when defined as a Laplace or Fourier convolution product, are suitable for solving many problems in biomedical research. For example, early studies by Cole (1933) and Hodgkin (1946) of the electrical properties of nerve cell membranes and the propagation of electrical signals are well characterized by differential equations of fractional order. The solution involves a generalization of the exponential function to the Mittag-Leffler function, which provides a better fit to the observed cell membrane data. A parallel application of fractional derivatives to viscoelastic materials establishes, in a natural way, hereditary integrals and the power law (Nutting/Scott Blair) stress-strain relationship for modeling biomaterials. In this review, I will introduce the idea of fractional operations by following the original approach of Heaviside, demonstrate the basic operations of fractional calculus on well-behaved functions (step, ramp, pulse, sinusoid) of engineering interest, and give specific examples from electrochemistry, physics, bioengineering, and biophysics. The fractional derivative accurately describes natural phenomena that occur in such common engineering problems as heat transfer, electrode/electrolyte behavior, and sub-threshold nerve propagation. By expanding the range of mathematical operations to include fractional calculus, we can develop new and potentially useful functional relationships for modeling complex biological systems in a direct and rigorous manner. In Part 1 of this review (Crit Rev Biomed Eng 2004; 32(1):1-104), the fundamental properties of fractional calculus were introduced. The reader should refer to that material, particularly the sections on special functions and fractional order differential equations, for background.

Fractional calculus in bioengineering.

Fractional calculus (integral and differential operations of noninteger order) is not often used to model biological systems. Although the basic mathematical ideas were developed long ago by the mathematicians Leibniz (1695), Liouville (1834), Riemann (1892), and others and brought to the attention of the engineering world by Oliver Heaviside in the 1890s, it was not until 1974 that the first book on the topic was published by Oldham and Spanier. Recent monographs and symposia proceedings have highlighted the application of fractional calculus in physics, continuum mechanics, signal processing, and electromagnetics, but with few examples of applications in bioengineering. This is surprising because the methods of fractional calculus, when defined as a Laplace or Fourier convolution product, are suitable for solving many problems in biomedical research. For example, early studies by Cole (1933) and Hodgkin (1946) of the electrical properties of nerve cell membranes and the propagation of electrical signals are well characterized by differential equations of fractional order. The solution involves a generalization of the exponential function to the Mittag-Leffler function, which provides a better fit to the observed cell membrane data. A parallel application of fractional derivatives to viscoelastic materials establishes, in a natural way, hereditary integrals and the power law (Nutting/Scott Blair) stress-strain relationship for modeling biomaterials. In this review, I will introduce the idea of fractional operations by following the original approach of Heaviside, demonstrate the basic operations of fractional calculus on well-behaved functions (step, ramp, pulse, sinusoid) of engineering interest, and give specific examples from electrochemistry, physics, bioengineering, and biophysics. The fractional derivative accurately describes natural phenomena that occur in such common engineering problems as heat transfer, electrode/electrolyte behavior, and sub-threshold nerve propagation. By expanding the range of mathematical operations to include fractional calculus, we can develop new and potentially useful functional relationships for modeling complex biological systems in a direct and rigorous manner.

Fractional calculus in bioengineering, part 3.

Fractional calculus (integral and differential operations of noninteger order) is not often used to model biological systems. Although the basic mathematical ideas were developed long ago by the mathematicians Leibniz (1695), Liouville (1834), Riemann (1892), and others and brought to the attention of the engineering world by Oliver Heaviside in the 1890s, it was not until 1974 that the first book on the topic was published by Oldham and Spanier. Recent monographs and symposia proceedings have highlighted the application of fractional calculus in physics, continuum mechanics, signal processing, and electromagnetics, but with few examples of applications in bioengineering. This is surprising because the methods of fractional calculus, when defined as a Laplace or Fourier convolution product, are suitable for solving many problems in biomedical research. For example, early studies by Cole (1933) and Hodgkin (1946) of the electrical properties of nerve cell membranes and the propagation of electrical signals are well characterized by differential equations of fractional order. The solution involves a generalization of the exponential function to the Mittag-Leffler function, which provides a better fit to the observed cell membrane data. A parallel application of fractional derivatives to viscoelastic materials establishes, in a natural way, hereditary integrals and the power law (Nutting/Scott Blair) stress-strain relationship for modeling biomaterials. In this review, I will introduce the idea of fractional operations by following the original approach of Heaviside, demonstrate the basic operations of fractional calculus on well-behaved functions (step, ramp, pulse, sinusoid) of engineering interest, and give specific examples from electrochemistry, physics, bioengineering, and biophysics. The fractional derivative accurately describes natural phenomena that occur in such common engineering problems as heat transfer, electrode/electrolyte behavior, and sub-threshold nerve propagation. By expanding the range of mathematical operations to include fractional calculus, we can develop new and potentially useful functional relationships for modeling complex biological systems in a direct and rigorous manner. In Part 2 of this review (Crit Rev Biomed Eng 2004; 32(1):105-193), fractional calculus was applied to problems in nerve stimulation, dielectric relaxation, and viscoelastic materials by extending the governing differential equations to include fractional order terms. In this third and final installment, we consider distributed systems that represent shear stress in fluids, heat transfer in uniform one-dimensional media, and subthreshold nerve depolarization. Classic electrochemical analysis and impedance spectroscopy are also reviewed from the perspective of fractional calculus, and selected examples from recent studies in neuroscience, bioelectricity, and tissue biomechanics are analyzed to illustrate the vitality of the field.