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Richard Magin

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Jocelyn SABATIER

Université de Bordeaux

Universidad de La Laguna

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Universidade Nova de Lisboa

Diego Caratelli

Eindhoven University of Technology

Universidad Nacional Autónoma de México

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Papers by Richard Magin

On the Equivalence between Integer- and Fractional Order-Models of Continuous-Time and Discrete-Time ARMA Systems

Fractal and Fractional

The equivalence of continuous-/discrete-time autoregressive-moving average (ARMA) systems is cons... more The equivalence of continuous-/discrete-time autoregressive-moving average (ARMA) systems is considered in this paper. For the integer-order cases, the interrelations between systems defined by continuous-time (CT) differential and discrete-time (DT) difference equations are found, leading to formulae relating partial fractions of the continuous and discrete transfer functions. Simple transformations are presented to allow interconversions between both systems, recovering formulae obtained with the impulse invariant method. These transformations are also used to formulate a covariance equivalence. The spectral correspondence implied by the bilinear (Tustin) transformation is used to study the equivalence between the two types of systems. The general fractional CT/DT ARMA systems are also studied by considering two DT differential fractional autoregressive-moving average (FARMA) systems based on the nabla/delta and bilinear derivatives. The interrelations CT/DT are also considered, p...

Article New Insights into the Fractional Order Diffusion Equation Using Entropy and Kurtosis

Fractional order derivative operators offer a concise description to model multi-scale, heterogen... more Fractional order derivative operators offer a concise description to model multi-scale, heterogeneous and non-local systems. Specifically, in magnetic resonance imaging, there has been recent work to apply fractional order derivatives to model the non-Gaussian diffusion signal, which is ubiquitous in the movement of water protons within biological tissue. To provide a new perspective for establishing the utility of fractional order models, we apply entropy for the case of anomalous diffusion governed by a fractional order diffusion equation generalized in space and in time. This fractional order representation, in the form of the Mittag-Leffler function, gives an entropy minimum for the integer case of Gaussian diffusion and greater values of spectral entropy for non-integer values of the space and time derivatives. Furthermore, we consider kurtosis, defined as the normalized fourth moment, as another probabilistic description of the fractional time derivative. Finally, we demonstrate the implementation of anomalous diffusion, entropy and kurtosis measurements in diffusion weighted magnetic resonance imaging in the brain of a chronic ischemic stroke patient.

High field magnetic resonance spectroscopy, imaging and elastography for cartilage tissue engineering

F1000Research, 2013

Cartilage tissue engineering is a promising technology for cartilage restoration and regeneration... more Cartilage tissue engineering is a promising technology for cartilage restoration and regeneration therapies. Cartilage is composed of chondrocytes cells (~1%), tissue fluid (~75% of wet weight) and extra cellular matrix (~25%, mainly proteoglycans and type II collagen). In order to mimic native cartilage, tissue engineers focus on production of the ECM components using a variety of approaches to assemble de novo tissue from appropriate cell types, biocompatible gels, biodegradable scaffolds and chondrogenic growth factors. The success of engineered tissue is normally assessed using histology and biochemical assays. Unfortunately, these techniques of visualizing growth can only be performed once. Magnetic Resonance Imaging (MRI) is emerging as an alternative, non-invasive tracking tool for tissue engineering because it provides a means for the periodic acquisition of quantitative information (T 1 , T 1ρ , T 2 , ADC and stiffness) about the development of the engineered tissue, both pre and post-implantation [1, 2]. We present here recent results for tracking cartilage tissue engineering at the early stages of growth in vitro and in vivo.

Active tissue stiffness modulation controls valve interstitial cell phenotype and osteogenic potential in 3D culture

Acta biomaterialia, May 3, 2016

Calcific aortic valve disease (CAVD) progression is a highly dynamic process whereby normally fib... more Calcific aortic valve disease (CAVD) progression is a highly dynamic process whereby normally fibroblastic valve interstitial cells (VIC) undergo osteogenic differentiation, maladaptive extracellular matrix (ECM) composition, structural remodeling, and tissue matrix stiffening. However, how VIC with different phenotypes dynamically affect matrix properties and how the altered matrix further affects VIC phenotypes in response to physiological and pathological conditions have not yet been determined. In this study, we develop 3D hydrogels with tunable matrix stiffness to investigate the dynamic interplay between VIC phenotypes and matrix biomechanics. We find that VIC populated within hydrogels with valve leaflet like stiffness differentiate towards myofibroblasts in osteogenic media, but surprisingly undergo osteogenic differentiation when cultured within lower initial stiffness hydrogels. VIC differentiation progressively stiffens the hydrogel microenvironment, which further upregul...

The intrinsic geometry of the human brain connectome

Brain Informatics, 2015

This paper describes novel methods for constructing the intrinsic geometry of the human brain con... more This paper describes novel methods for constructing the intrinsic geometry of the human brain connectome using dimensionality-reduction techniques. We posit that the high-dimensional, complex geometry that represents this intrinsic topology can be mathematically embedded into lower dimensions using coupling patterns encoded in the corresponding brain connectivity graphs. We tested both linear and nonlinear dimensionality-reduction techniques using the diffusion-weighted structural connectome data acquired from a sample of healthy subjects. Results supported the nonlinearity of brain connectivity data, as linear reduction techniques such as the multidimensional scaling yielded inferior lower-dimensional embeddings. To further validate our results, we demonstrated that for tractography-derived structural connectome more influential regions such as rich-club members of the brain are more centrally mapped or embedded. Further, abnormal brain connectivity can be visually understood by inspecting the altered geometry of these three-dimensional (3D) embeddings that represent the topology of the human brain, as illustrated using simulated lesion studies of both targeted and random removal. Last, in order to visualize brain's intrinsic topology we have developed software that is compatible with virtual reality technologies, thus allowing researchers to collaboratively and interactively explore and manipulate brain connectome data.

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

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

Journal of shoulder and elbow surgery / American Shoulder and Elbow Surgeons ... [et al.], Jan 31, 2015

Management of glenohumeral arthrosis in young patients is a considerable challenge, with a growin... more 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. 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 sy...

Analysis of YFP(J16)-R6/2 reporter mice and post-mortem brains reveals early pathology and increased vulnerability of callosal axons in Huntington's disease

Human molecular genetics, Jan 29, 2015

Cumulative evidence indicates that the onset and severity of Huntington's disease (HD) sympto... more Cumulative evidence indicates that the onset and severity of Huntington's disease (HD) symptoms correlate with connectivity deficits involving specific neuronal populations within cortical and basal ganglia circuits. Brain imaging studies and pathological reports further associated these deficits with alterations in cerebral white matter structure and axonal pathology. However, whether axonopathy represents an early pathogenic event or an epiphenomenon in HD remains unknown, nor is clear the identity of specific neuronal populations affected.To evaluate early axonal abnormalities in the context of HD in vivo, we bred transgenic YFP(J16) with R6/2 mice, a widely used HD model. Diffusion tensor imaging and fluorescence microscopy studies revealed a marked degeneration of callosal axons long before the onset of motor symptoms. Accordingly, a significant fraction of YFP-positive cortical neurons in YFP(J16) mice cortex were identified as callosal projection neurons. Callosal axon pa...

Magnetization Transfer Imaging Provides a Quantitative Measure of Chondrogenic Differentiation and Tissue Development

Tissue Engineering Part C: Methods, 2010

The goal of the present investigation was to test whether quantitative magnetization transfer ima... more 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 (T 1 and T 2), 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 ¼ 0.96 and 0.87, respectively, p < 0.05), whereas T 1 , T 2 , and apparent diffusion coefficient results did not show any significant changes over the 3-week measurement period.

Biomimetic Extracellular Matrix-Incorporated Scaffold Induces Osteogenic Gene Expression in Human Marrow Stromal Cells

Tissue Engineering Part A, 2012

Engineering biomaterials mimicking the biofunctionality of the extracellular matrix (ECM) is impo... more 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 threedimensional native ECM scaffold directly controls cell behavior and supports the osteogenic differentiation of mesenchymal stem cells. Departments of 1 Oral Biology, 2 Bioengineering, and

Fractional order models of viscoelasticity as an alternative in the analysis of red blood cell (RBC) membrane mechanics

Physical Biology, 2010

Application of sodium triple-quantum coherence NMR spectroscopy for the study of growth dynamics in cartilage tissue engineering

NMR in Biomedicine, 2013

We studied the tissue growth dynamics for tissue-engineered cartilage at the early growth stage a... more We studied the tissue growth dynamics for tissue-engineered cartilage at the early growth stage after cell seeding for four weeks using sodium triple-quantum coherence NMR spectroscopy. The following tissue-engineering constructs were studied: 1. Bovine chondrocytes cultured in alginate beads, 2. Bovine chondrocytes cultured as pellets (scaffold-free chondrocyte pellets), 3. Human Marrow Stromal Cells (HMSC) seeded in Collagen/Chitosan based scaffolds of chondrogenic extracellular matrix environment expecting chondrogenic differentiation, named as biomimetic scaffolds. We found that the sodium triple quantum coherence spectroscopy can differentiate between different tissue-engineering constructs and the native tissues based on the fast and the slow relaxation rates as well as based on the average quadrupolar coupling. Both the fast (T f) and the slow (T s) relaxation times were found to be longer in the chondrocyte pellets and the biomimetic scaffolds as compared to the chondrocytes suspended in alginate beads and the human articular cartilage tissues. In all cases, it was found that the relaxation rates and the motion of sodium ions, as measured from correlation time, were dependent on the amount of macromolecules, high cell density and the anisotropy of the cartilage tissue engineering constructs. Average quadrupolar couplings were found to be lower in the engineered tissue as compared to the native tissues, presumably due to the lack of order in collagen accumulated in the engineered tissue. These results indicate the use of sodium triple quantum coherence spectroscopy as a tool to investigate anisotropy and growth dynamics of cartilage tissue engineered constructs in a simple and reliable way.

Estimating material viscoelastic properties based on surface wave measurements: A comparison of techniques and modeling assumptions

The Journal of the Acoustical Society of America, 2011

Previous studies of the first author and others have focused on low audible frequency (<1 kHz)... more Previous studies of the first author and others have focused on low audible frequency (<1 kHz) shear and surface wave motion in and on a viscoelastic material comprised of or representative of soft biological tissue. A specific case considered has been surface (Rayleigh) wave motion caused by a circular disk located on the surface and oscillating normal to it. Different approaches to identifying the type and coefficients of a viscoelastic model of the material based on these measurements have been proposed. One approach has been to optimize coefficients in an assumed viscoelastic model type to match measurements of the frequency-dependent Rayleigh wave speed. Another approach has been to optimize coefficients in an assumed viscoelastic model type to match the complex-valued frequency response function (FRF) between the excitation location and points at known radial distances from it. In the present article, the relative merits of these approaches are explored theoretically, compu...

Modeling the modulated acoustic radiation force distribution in a viscoelastic medium driven by a spherically focused ultrasound transducer

The Journal of the Acoustical Society of America, 2008

Acoustic radiation force created by focused ultrasound transducers is gaining great interest in m... more Acoustic radiation force created by focused ultrasound transducers is gaining great interest in medical diagnosis. This study aims to clarify the acoustic power delivery by means of a modulated focused transducer and to predict the performance of such systems. A spherical-cap shaped transducer, made of piezoelectric material, is used to create ultrasonic waves at a focal point. Different modulation methods, given in the literature and reviewed here, are available for creating a concentrated alternating force due to the acoustic radiation pressure. The relationship between the voltage input to the piezoelectric transducer and its resulting mechanical deformation is examined using a finite element model (FEM) for high frequency harmonic excitation (3 - 10 MHz). The oscillating surface of the transducer drives the contacting media, which exerts an acoustic load on the transducer that is also considered in the FE analysis. Also, the motion of resulting acoustic waves in a lossy medium i...

Nondestructive evaluation of osteogenic differentiation in tissue-engineered constructs

Journal of Orthopaedic Research, 2006

Conventional measurements of osteogenesis in tissue-engineered constructs are destructive to livi... more 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 Â 4 Â 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 ¼ À0.57, À0.78, and À0.81, respectively) and calcium content (r to T1, T2, and ADC ¼ 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.

Ultrasonic absorption and permeability for liposomes near phase transition

Chemistry and Physics of Lipids, 1985

The specific ultrasonic absorption coefficient per wavelength as a function of temperature in the... more The specific ultrasonic absorption coefficient per wavelength as a function of temperature in the vicinity of the phase transition of liposomes, composed of a 4 : 1 mixturc of dipalmitoylphosphatidylcholine (DPPC) and dipalmitoylphosphatidylglyeerol (DPPG), of different sizes was determined using an acoustic interferometer. Small unilamellar vesicles {,SUV) and multilamellar vesiclcs (MLV) yielded results similar to those in the literature, viz., an absorption maximum at the transition temperature. Seven intermediate sizes including several size distributions of large unilamellar vesicles (LUV) were studied, yielding information on size dependencies of the temperatures at which the peaks occur, the widths at half peak amplitude, and the peak amplitudes. All liposome sizes except the SUV exhibited approximately the same transition temperature as did the largest MLV. The widths of the peaks were inversely related to liposome size, with a strong dependence for the smallest vesicles and an approach to independence for the largest vesicles. The amplitudes of the peaks exhibited a general increase with size with two exceptions, viz., the SUV and the vesicles with average diameters of 90-100 nm. It was also found that the membrane permeability increased near the transition temperature. The temperature dependencies of ultrasonic absorption and membrane permeability are compared.

Ultrasound interaction with large unilamellar vesicles at the phospholipid phase transition: perturbation by phospholipid side chain substitution with deuterium

Chemistry and Physics of Lipids, 1999

The ultrasonic absorption, hu, as a function of temperature and frequency was determined in large... more The ultrasonic absorption, hu, as a function of temperature and frequency was determined in large unilamellar vesicles (LUVs) in which specific phospholipid side chains were deuterated. Deuteration significantly altered the temperature and frequency dependence of hu. The frequency change was especially marked, with decreased frequency and broadening of the ultrasound relaxation, even with only minor changes in the phase transition temperature. Deuteration decreased the T m and enthalpy of the lipid phase transition, as shown by differential scanning calorimetry, whereas electron spin resonance showed that at and above the lipid phase transition, no differences in the mobility as a function of temperature were observed. These results show that the observed increase in ultrasonic absorption in LUVs at the phospholipid phase transition arises from the interaction of ultrasound with the hydrophobic side chains, probably coupling with structural reorganization of small domains of molecules, a process which is maximized at the phase transition temperature.

Effects of divalent cations on the ultrasonic absorption coefficient of negatively charged liposomes (LUV) near their phase transition temperature

Biochimica et Biophysica Acta (BBA) - Biomembranes, 1987

The ultrasonic absorption coefficient per wavelength (a~), as a function of temperature and frequ... more The ultrasonic absorption coefficient per wavelength (a~), as a function of temperature and frequency, was determined for large unilameilar vesicles (LUV) in the vicinity of their phospholipid phase transition temperature, using a double crystal acoustic intederometer. (The vesicles were composed of a 4:1 (w/w) mixture of dipalmitoylphosphatidylcholine (DPPC) and dipalmitoylphosphatidylglyceroi (DPPG)). It has been found that a3, reaches a maximum (a~)~ at the phase transition temperature (tin) of the phospholipids in the bilayer, at an ultrasonic relaxation frequency of 2.1 MHz. Divalent cations (Ca 2+ and Mg2+), added to LUV suspensions, shifted (ah)mx to higher temperatures, dependent upon the concentration of divalent cation. It was also found that the shape of the aX versus t curve was significantly changed, representing changes in the Van't Hoff enthalpy of the transition, and therefore, the cooperative unit of the transition. This suggests that divalent cations interact individually with the negatively charged phospholipid headgroups of DPPG and with DPPC headgroups, thus decreasing the cooperative unit of the transition. The observed upward shift in t m suggests an interaction that increases the activation energy and, therefore, the temperature of the phase transition. However, ah as a function of frequency did not change with the addition of divalent cations and, thus, the relaxation time of the event responsible for the absorption of ultrasound is not changed by the addition of divalent cations.

The effects of 2H2O on the phase transition of large unilamellar vesicle (LUV) suspensions as detected by ultrasound spectroscopy and electron spin resonance

Biochimica et Biophysica Acta (BBA) - Biomembranes, 1989

The importance of water in the molecular dynamics "f large unilamdlar vesicle (LUV) suspensions, ... more The importance of water in the molecular dynamics "f large unilamdlar vesicle (LUV) suspensions, in which increasing portions of the water were replaced by 2H20, was investigated. Determinations of the ultrasonic absorption coefficient per wavelength, a~, were pergonned as a function of temperature and frequency for LUVs (LUVs: 4:1 (w/w) mixture of dipalmitoy|phosphatidylcholine, DPPC, and dipalmitoylphosphatidyiglycerol, DPPG) in the vicinity of their phos° pholipid phase transition, using a double crystaJ acoustic intefferometer. Electron spin resonance (ESR) and differential scanning calorlmetry. (DSC) were also employed to probe this system. When increasing portions of the aqueous content of the LUV suspensions were replaced by 2H20 the phase transition temperature increased from 42.0°C to 42.9°C (indicating an increase in the activation energy of the transition), and the amplitude of a~ at the phase ~rans|tion increased. However, a~m. x as a function of frequency at the phase transition did not change with the addition of zH20 , indicating that the relaxation time of the event responsible for the absorption of ultrasound was unaffected. The increase in the activation energy of the transition with the addition of zHzO suggested that the mobility of phospholipids near the membrane/aqueous interface was changed. Electron spin resonance (ESR) experiments on LUVs with nitroxide spin probes positioned at the membrane/aqueous interface (5-doxyl stearate and CAT16) showed that LUVs in zHzO have a broader splitting, Amax, at the membrane/aqueous interface than do LUVs in HzO. These results suggest that ~HzO changes the mobility and/or structure of the phospholipids in the region of the membrane/ aqueous interface. This difference in Amx was not seen for the probe PC-12-doxy! stearate, which resides at the C-12 position of the bilayer.

Fractional Calculus Extension of the Kinetic Theory of Fluids: Molecular Models of Transport within and between Phases

Mathematics

The application of fractional calculus in the field of kinetic theory begins with questions raise... more The application of fractional calculus in the field of kinetic theory begins with questions raised by Bernoulli, Clausius, and Maxwell about the motion of molecules in gases and liquids. Causality, locality, and determinism underly the early work, which led to the development of statistical mechanics by Boltzmann, Gibbs, Enskog, and Chapman. However, memory and nonlocality influence the future course of molecular interactions (e.g., persistence of velocity and inelastic collisions); hence, modifications to the thermodynamic equations of state, the non-equilibrium transport equations, and the dynamics of phase transitions are needed to explain experimental measurements. In these situations, the inclusion of space- and time-fractional derivatives within the context of the continuous time random walk (CTRW) model of diffusion encodes particle jumps and trapping. Thus, we anticipate using fractional calculus to extend the classical equations of diffusion. The solutions obtained illumina...

On the Equivalence between Integer- and Fractional Order-Models of Continuous-Time and Discrete-Time ARMA Systems

Fractal and Fractional

The equivalence of continuous-/discrete-time autoregressive-moving average (ARMA) systems is cons... more The equivalence of continuous-/discrete-time autoregressive-moving average (ARMA) systems is considered in this paper. For the integer-order cases, the interrelations between systems defined by continuous-time (CT) differential and discrete-time (DT) difference equations are found, leading to formulae relating partial fractions of the continuous and discrete transfer functions. Simple transformations are presented to allow interconversions between both systems, recovering formulae obtained with the impulse invariant method. These transformations are also used to formulate a covariance equivalence. The spectral correspondence implied by the bilinear (Tustin) transformation is used to study the equivalence between the two types of systems. The general fractional CT/DT ARMA systems are also studied by considering two DT differential fractional autoregressive-moving average (FARMA) systems based on the nabla/delta and bilinear derivatives. The interrelations CT/DT are also considered, p...

Article New Insights into the Fractional Order Diffusion Equation Using Entropy and Kurtosis

Fractional order derivative operators offer a concise description to model multi-scale, heterogen... more Fractional order derivative operators offer a concise description to model multi-scale, heterogeneous and non-local systems. Specifically, in magnetic resonance imaging, there has been recent work to apply fractional order derivatives to model the non-Gaussian diffusion signal, which is ubiquitous in the movement of water protons within biological tissue. To provide a new perspective for establishing the utility of fractional order models, we apply entropy for the case of anomalous diffusion governed by a fractional order diffusion equation generalized in space and in time. This fractional order representation, in the form of the Mittag-Leffler function, gives an entropy minimum for the integer case of Gaussian diffusion and greater values of spectral entropy for non-integer values of the space and time derivatives. Furthermore, we consider kurtosis, defined as the normalized fourth moment, as another probabilistic description of the fractional time derivative. Finally, we demonstrate the implementation of anomalous diffusion, entropy and kurtosis measurements in diffusion weighted magnetic resonance imaging in the brain of a chronic ischemic stroke patient.

High field magnetic resonance spectroscopy, imaging and elastography for cartilage tissue engineering

F1000Research, 2013

Cartilage tissue engineering is a promising technology for cartilage restoration and regeneration... more Cartilage tissue engineering is a promising technology for cartilage restoration and regeneration therapies. Cartilage is composed of chondrocytes cells (~1%), tissue fluid (~75% of wet weight) and extra cellular matrix (~25%, mainly proteoglycans and type II collagen). In order to mimic native cartilage, tissue engineers focus on production of the ECM components using a variety of approaches to assemble de novo tissue from appropriate cell types, biocompatible gels, biodegradable scaffolds and chondrogenic growth factors. The success of engineered tissue is normally assessed using histology and biochemical assays. Unfortunately, these techniques of visualizing growth can only be performed once. Magnetic Resonance Imaging (MRI) is emerging as an alternative, non-invasive tracking tool for tissue engineering because it provides a means for the periodic acquisition of quantitative information (T 1 , T 1ρ , T 2 , ADC and stiffness) about the development of the engineered tissue, both pre and post-implantation [1, 2]. We present here recent results for tracking cartilage tissue engineering at the early stages of growth in vitro and in vivo.

Active tissue stiffness modulation controls valve interstitial cell phenotype and osteogenic potential in 3D culture

Acta biomaterialia, May 3, 2016

Calcific aortic valve disease (CAVD) progression is a highly dynamic process whereby normally fib... more Calcific aortic valve disease (CAVD) progression is a highly dynamic process whereby normally fibroblastic valve interstitial cells (VIC) undergo osteogenic differentiation, maladaptive extracellular matrix (ECM) composition, structural remodeling, and tissue matrix stiffening. However, how VIC with different phenotypes dynamically affect matrix properties and how the altered matrix further affects VIC phenotypes in response to physiological and pathological conditions have not yet been determined. In this study, we develop 3D hydrogels with tunable matrix stiffness to investigate the dynamic interplay between VIC phenotypes and matrix biomechanics. We find that VIC populated within hydrogels with valve leaflet like stiffness differentiate towards myofibroblasts in osteogenic media, but surprisingly undergo osteogenic differentiation when cultured within lower initial stiffness hydrogels. VIC differentiation progressively stiffens the hydrogel microenvironment, which further upregul...

The intrinsic geometry of the human brain connectome

Brain Informatics, 2015

This paper describes novel methods for constructing the intrinsic geometry of the human brain con... more This paper describes novel methods for constructing the intrinsic geometry of the human brain connectome using dimensionality-reduction techniques. We posit that the high-dimensional, complex geometry that represents this intrinsic topology can be mathematically embedded into lower dimensions using coupling patterns encoded in the corresponding brain connectivity graphs. We tested both linear and nonlinear dimensionality-reduction techniques using the diffusion-weighted structural connectome data acquired from a sample of healthy subjects. Results supported the nonlinearity of brain connectivity data, as linear reduction techniques such as the multidimensional scaling yielded inferior lower-dimensional embeddings. To further validate our results, we demonstrated that for tractography-derived structural connectome more influential regions such as rich-club members of the brain are more centrally mapped or embedded. Further, abnormal brain connectivity can be visually understood by inspecting the altered geometry of these three-dimensional (3D) embeddings that represent the topology of the human brain, as illustrated using simulated lesion studies of both targeted and random removal. Last, in order to visualize brain's intrinsic topology we have developed software that is compatible with virtual reality technologies, thus allowing researchers to collaboratively and interactively explore and manipulate brain connectome data.

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

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

Journal of shoulder and elbow surgery / American Shoulder and Elbow Surgeons ... [et al.], Jan 31, 2015

Management of glenohumeral arthrosis in young patients is a considerable challenge, with a growin... more 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. 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 sy...

Analysis of YFP(J16)-R6/2 reporter mice and post-mortem brains reveals early pathology and increased vulnerability of callosal axons in Huntington's disease

Human molecular genetics, Jan 29, 2015

Cumulative evidence indicates that the onset and severity of Huntington's disease (HD) sympto... more Cumulative evidence indicates that the onset and severity of Huntington's disease (HD) symptoms correlate with connectivity deficits involving specific neuronal populations within cortical and basal ganglia circuits. Brain imaging studies and pathological reports further associated these deficits with alterations in cerebral white matter structure and axonal pathology. However, whether axonopathy represents an early pathogenic event or an epiphenomenon in HD remains unknown, nor is clear the identity of specific neuronal populations affected.To evaluate early axonal abnormalities in the context of HD in vivo, we bred transgenic YFP(J16) with R6/2 mice, a widely used HD model. Diffusion tensor imaging and fluorescence microscopy studies revealed a marked degeneration of callosal axons long before the onset of motor symptoms. Accordingly, a significant fraction of YFP-positive cortical neurons in YFP(J16) mice cortex were identified as callosal projection neurons. Callosal axon pa...

Magnetization Transfer Imaging Provides a Quantitative Measure of Chondrogenic Differentiation and Tissue Development

Tissue Engineering Part C: Methods, 2010

The goal of the present investigation was to test whether quantitative magnetization transfer ima... more 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 (T 1 and T 2), 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 ¼ 0.96 and 0.87, respectively, p < 0.05), whereas T 1 , T 2 , and apparent diffusion coefficient results did not show any significant changes over the 3-week measurement period.

Biomimetic Extracellular Matrix-Incorporated Scaffold Induces Osteogenic Gene Expression in Human Marrow Stromal Cells

Tissue Engineering Part A, 2012

Engineering biomaterials mimicking the biofunctionality of the extracellular matrix (ECM) is impo... more 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 threedimensional native ECM scaffold directly controls cell behavior and supports the osteogenic differentiation of mesenchymal stem cells. Departments of 1 Oral Biology, 2 Bioengineering, and

Fractional order models of viscoelasticity as an alternative in the analysis of red blood cell (RBC) membrane mechanics

Physical Biology, 2010

Application of sodium triple-quantum coherence NMR spectroscopy for the study of growth dynamics in cartilage tissue engineering

NMR in Biomedicine, 2013

We studied the tissue growth dynamics for tissue-engineered cartilage at the early growth stage a... more We studied the tissue growth dynamics for tissue-engineered cartilage at the early growth stage after cell seeding for four weeks using sodium triple-quantum coherence NMR spectroscopy. The following tissue-engineering constructs were studied: 1. Bovine chondrocytes cultured in alginate beads, 2. Bovine chondrocytes cultured as pellets (scaffold-free chondrocyte pellets), 3. Human Marrow Stromal Cells (HMSC) seeded in Collagen/Chitosan based scaffolds of chondrogenic extracellular matrix environment expecting chondrogenic differentiation, named as biomimetic scaffolds. We found that the sodium triple quantum coherence spectroscopy can differentiate between different tissue-engineering constructs and the native tissues based on the fast and the slow relaxation rates as well as based on the average quadrupolar coupling. Both the fast (T f) and the slow (T s) relaxation times were found to be longer in the chondrocyte pellets and the biomimetic scaffolds as compared to the chondrocytes suspended in alginate beads and the human articular cartilage tissues. In all cases, it was found that the relaxation rates and the motion of sodium ions, as measured from correlation time, were dependent on the amount of macromolecules, high cell density and the anisotropy of the cartilage tissue engineering constructs. Average quadrupolar couplings were found to be lower in the engineered tissue as compared to the native tissues, presumably due to the lack of order in collagen accumulated in the engineered tissue. These results indicate the use of sodium triple quantum coherence spectroscopy as a tool to investigate anisotropy and growth dynamics of cartilage tissue engineered constructs in a simple and reliable way.

Estimating material viscoelastic properties based on surface wave measurements: A comparison of techniques and modeling assumptions

The Journal of the Acoustical Society of America, 2011

Previous studies of the first author and others have focused on low audible frequency (<1 kHz)... more Previous studies of the first author and others have focused on low audible frequency (<1 kHz) shear and surface wave motion in and on a viscoelastic material comprised of or representative of soft biological tissue. A specific case considered has been surface (Rayleigh) wave motion caused by a circular disk located on the surface and oscillating normal to it. Different approaches to identifying the type and coefficients of a viscoelastic model of the material based on these measurements have been proposed. One approach has been to optimize coefficients in an assumed viscoelastic model type to match measurements of the frequency-dependent Rayleigh wave speed. Another approach has been to optimize coefficients in an assumed viscoelastic model type to match the complex-valued frequency response function (FRF) between the excitation location and points at known radial distances from it. In the present article, the relative merits of these approaches are explored theoretically, compu...

Modeling the modulated acoustic radiation force distribution in a viscoelastic medium driven by a spherically focused ultrasound transducer

The Journal of the Acoustical Society of America, 2008

Acoustic radiation force created by focused ultrasound transducers is gaining great interest in m... more Acoustic radiation force created by focused ultrasound transducers is gaining great interest in medical diagnosis. This study aims to clarify the acoustic power delivery by means of a modulated focused transducer and to predict the performance of such systems. A spherical-cap shaped transducer, made of piezoelectric material, is used to create ultrasonic waves at a focal point. Different modulation methods, given in the literature and reviewed here, are available for creating a concentrated alternating force due to the acoustic radiation pressure. The relationship between the voltage input to the piezoelectric transducer and its resulting mechanical deformation is examined using a finite element model (FEM) for high frequency harmonic excitation (3 - 10 MHz). The oscillating surface of the transducer drives the contacting media, which exerts an acoustic load on the transducer that is also considered in the FE analysis. Also, the motion of resulting acoustic waves in a lossy medium i...

Nondestructive evaluation of osteogenic differentiation in tissue-engineered constructs

Journal of Orthopaedic Research, 2006

Conventional measurements of osteogenesis in tissue-engineered constructs are destructive to livi... more 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 Â 4 Â 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 ¼ À0.57, À0.78, and À0.81, respectively) and calcium content (r to T1, T2, and ADC ¼ 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.

Ultrasonic absorption and permeability for liposomes near phase transition

Chemistry and Physics of Lipids, 1985

The specific ultrasonic absorption coefficient per wavelength as a function of temperature in the... more The specific ultrasonic absorption coefficient per wavelength as a function of temperature in the vicinity of the phase transition of liposomes, composed of a 4 : 1 mixturc of dipalmitoylphosphatidylcholine (DPPC) and dipalmitoylphosphatidylglyeerol (DPPG), of different sizes was determined using an acoustic interferometer. Small unilamellar vesicles {,SUV) and multilamellar vesiclcs (MLV) yielded results similar to those in the literature, viz., an absorption maximum at the transition temperature. Seven intermediate sizes including several size distributions of large unilamellar vesicles (LUV) were studied, yielding information on size dependencies of the temperatures at which the peaks occur, the widths at half peak amplitude, and the peak amplitudes. All liposome sizes except the SUV exhibited approximately the same transition temperature as did the largest MLV. The widths of the peaks were inversely related to liposome size, with a strong dependence for the smallest vesicles and an approach to independence for the largest vesicles. The amplitudes of the peaks exhibited a general increase with size with two exceptions, viz., the SUV and the vesicles with average diameters of 90-100 nm. It was also found that the membrane permeability increased near the transition temperature. The temperature dependencies of ultrasonic absorption and membrane permeability are compared.

Ultrasound interaction with large unilamellar vesicles at the phospholipid phase transition: perturbation by phospholipid side chain substitution with deuterium

Chemistry and Physics of Lipids, 1999

The ultrasonic absorption, hu, as a function of temperature and frequency was determined in large... more The ultrasonic absorption, hu, as a function of temperature and frequency was determined in large unilamellar vesicles (LUVs) in which specific phospholipid side chains were deuterated. Deuteration significantly altered the temperature and frequency dependence of hu. The frequency change was especially marked, with decreased frequency and broadening of the ultrasound relaxation, even with only minor changes in the phase transition temperature. Deuteration decreased the T m and enthalpy of the lipid phase transition, as shown by differential scanning calorimetry, whereas electron spin resonance showed that at and above the lipid phase transition, no differences in the mobility as a function of temperature were observed. These results show that the observed increase in ultrasonic absorption in LUVs at the phospholipid phase transition arises from the interaction of ultrasound with the hydrophobic side chains, probably coupling with structural reorganization of small domains of molecules, a process which is maximized at the phase transition temperature.

Effects of divalent cations on the ultrasonic absorption coefficient of negatively charged liposomes (LUV) near their phase transition temperature

Biochimica et Biophysica Acta (BBA) - Biomembranes, 1987

The ultrasonic absorption coefficient per wavelength (a~), as a function of temperature and frequ... more The ultrasonic absorption coefficient per wavelength (a~), as a function of temperature and frequency, was determined for large unilameilar vesicles (LUV) in the vicinity of their phospholipid phase transition temperature, using a double crystal acoustic intederometer. (The vesicles were composed of a 4:1 (w/w) mixture of dipalmitoylphosphatidylcholine (DPPC) and dipalmitoylphosphatidylglyceroi (DPPG)). It has been found that a3, reaches a maximum (a~)~ at the phase transition temperature (tin) of the phospholipids in the bilayer, at an ultrasonic relaxation frequency of 2.1 MHz. Divalent cations (Ca 2+ and Mg2+), added to LUV suspensions, shifted (ah)mx to higher temperatures, dependent upon the concentration of divalent cation. It was also found that the shape of the aX versus t curve was significantly changed, representing changes in the Van't Hoff enthalpy of the transition, and therefore, the cooperative unit of the transition. This suggests that divalent cations interact individually with the negatively charged phospholipid headgroups of DPPG and with DPPC headgroups, thus decreasing the cooperative unit of the transition. The observed upward shift in t m suggests an interaction that increases the activation energy and, therefore, the temperature of the phase transition. However, ah as a function of frequency did not change with the addition of divalent cations and, thus, the relaxation time of the event responsible for the absorption of ultrasound is not changed by the addition of divalent cations.

The effects of 2H2O on the phase transition of large unilamellar vesicle (LUV) suspensions as detected by ultrasound spectroscopy and electron spin resonance

Biochimica et Biophysica Acta (BBA) - Biomembranes, 1989

The importance of water in the molecular dynamics "f large unilamdlar vesicle (LUV) suspensions, ... more The importance of water in the molecular dynamics "f large unilamdlar vesicle (LUV) suspensions, in which increasing portions of the water were replaced by 2H20, was investigated. Determinations of the ultrasonic absorption coefficient per wavelength, a~, were pergonned as a function of temperature and frequency for LUVs (LUVs: 4:1 (w/w) mixture of dipalmitoy|phosphatidylcholine, DPPC, and dipalmitoylphosphatidyiglycerol, DPPG) in the vicinity of their phos° pholipid phase transition, using a double crystaJ acoustic intefferometer. Electron spin resonance (ESR) and differential scanning calorlmetry. (DSC) were also employed to probe this system. When increasing portions of the aqueous content of the LUV suspensions were replaced by 2H20 the phase transition temperature increased from 42.0°C to 42.9°C (indicating an increase in the activation energy of the transition), and the amplitude of a~ at the phase ~rans|tion increased. However, a~m. x as a function of frequency at the phase transition did not change with the addition of zH20 , indicating that the relaxation time of the event responsible for the absorption of ultrasound was unaffected. The increase in the activation energy of the transition with the addition of zHzO suggested that the mobility of phospholipids near the membrane/aqueous interface was changed. Electron spin resonance (ESR) experiments on LUVs with nitroxide spin probes positioned at the membrane/aqueous interface (5-doxyl stearate and CAT16) showed that LUVs in zHzO have a broader splitting, Amax, at the membrane/aqueous interface than do LUVs in HzO. These results suggest that ~HzO changes the mobility and/or structure of the phospholipids in the region of the membrane/ aqueous interface. This difference in Amx was not seen for the probe PC-12-doxy! stearate, which resides at the C-12 position of the bilayer.

Fractional Calculus Extension of the Kinetic Theory of Fluids: Molecular Models of Transport within and between Phases

Mathematics

The application of fractional calculus in the field of kinetic theory begins with questions raise... more The application of fractional calculus in the field of kinetic theory begins with questions raised by Bernoulli, Clausius, and Maxwell about the motion of molecules in gases and liquids. Causality, locality, and determinism underly the early work, which led to the development of statistical mechanics by Boltzmann, Gibbs, Enskog, and Chapman. However, memory and nonlocality influence the future course of molecular interactions (e.g., persistence of velocity and inelastic collisions); hence, modifications to the thermodynamic equations of state, the non-equilibrium transport equations, and the dynamics of phase transitions are needed to explain experimental measurements. In these situations, the inclusion of space- and time-fractional derivatives within the context of the continuous time random walk (CTRW) model of diffusion encodes particle jumps and trapping. Thus, we anticipate using fractional calculus to extend the classical equations of diffusion. The solutions obtained illumina...