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

Publisher Copyright: © 2022 by the authors. Licensee MDPI, Basel, Switzerland.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, paying special attention to the systems defined by the bilinear derivatives.publishersversionpublishe

Interplay between particle trapping and heterogeneity in anomalous diffusion

Heterogeneous media diffusion is often described using position-dependent diffusion coefficients and estimated indirectly through mean squared displacement in experiments. This approach may overlook other mechanisms and their interaction with position-dependent diffusion, potentially leading to erroneous conclusions. Here, we introduce a hybrid diffusion model that merges a position-dependent diffusion coefficient with the trapping mechanism of the comb model. We derive exact solutions for position distributions and mean squared displacements, validated through simulations of Langevin equations. Our model shows that the trapping mechanism attenuates the impact of media heterogeneity. Superdiffusion occurs when the position-dependent coefficient increases superlinearly, while subdiffusion occurs for sublinear and inverse power-law relations. This nontrivial interplay between heterogeneity and state-independent mechanisms also leads to anomalous yet Brownian and non-Brownian yet Gaussian regimes. These findings emphasize the need for cautious interpretations of experiments and highlight the limitations of relying solely on mean squared displacements or position distributions for diffusion characterization.Comment: 13 two-column pages, 6 figures; accepted for publication in Communications Physic

High-resolution/high-contrast MRI of human articular cartilage lesions.

BACKGROUND: Magnetic resonance microscopy (MRM) is an important experimental tool in the identification of early cartilage lesions. METHODS: Normal and degenerated cartilage samples were imaged at 11.74 T using a standard spin echo sequence. Quantitative MR measurements for T1, T2, and ADC were obtained and mapping for T2 and ADC was performed. The bi-exponential model for T2 relaxation was also explored. Histology was carried out for comparison with MR images. RESULTS: MR images of cartilage samples displaying early stages of degeneration were positively correlated to their histological appearance in 23-microm high-resolution images and also with much shorter imaging times at 47-microm resolution. T2 maps enable delineation of the actual cartilage zones, distinguishing the superficial zone in particular. The bi-exponential model can reflect cartilage components at different stages of degeneration. INTERPRETATION: At 11.74 T, with 23-microm resolution or with 47-microm resolution and shorter imaging times, MRM provides images that allow visualization of early stages of cartilage degeneration, including superficial fibrillation. This has not been shown previously. The images also allow quantitative measurements (T1, T2, and ADC) in each cartilage region, which can be indicative of different stages of cartilage degeneration

IMECE2008-68137 FRACTIONAL ORDER MODELS FOR VISCOELASTICITY OF SOFT BIOLOGICAL TISSUES

ABSTRACT Dynamic mechanical properties of soft tissues provide information that may be used in medical diagnosis. Developing a better fundamental understanding of the governing constitutive relations could improve diagnostic techniques. The mechanical behavior of soft tissues and tissue mimicking phantoms, such as gels, can be represented by viscoelastic material models. Static loading of viscoelastic materials yields information related to elasticity, creep and stress relaxation. However, a broader measure of ratedependent properties that affect mechanical wave propagation and wave attenuation in such materials can only be extracted from measured response to dynamic excitation. The well known linear viscoelastic material models of Voigt, Maxwell and Kelvin cannot represent the more complicated frequency dependency of these materials over a broad spectral range. Therefore, fractional calculus methods have been considered to model the viscoelastic behavior of soft tissue-like materials. Fractional order models capture the viscoelastic material behavior using fractional orders of differential equation

Assessing neuraxial microstructural changes in a transgenic mouse model of early stage Amyotrophic Lateral Sclerosis by ultra‐high field MRI and diffusion tensor metrics

bjective: Cell structural changes are one of the main features observed during the development of amyotrophic lateral sclerosis (ALS). In this work, we propose the useof diffusion tensor imaging (DTI) metrics to assess specific ultrastructural changes in the central nervous system during the early neurodegenerative stages of ALS.Methods: Ultra-high field MRI and DTI data at 17.6T were obtained from fixed, excised mouse brains, and spinal cords from ALS (G93A-SOD1) mice.Results: Changes in fractional anisotropy (FA) and linear, planar, and spherical anisotropy ratios (CL, CP, and CS, respectively) of the diffusion eigenvalues were measured in white matter (WM) and gray matter (GM) areas associated with early axonal degenerative processes (in both the brain and the spinal cord). Specifically, in WM structures (corpus callosum, corticospinal tract, and spinal cord funiculi) as the disease progressed, FA, CL, and CP values decreased, whereas CS values increased.In GM structures (prefrontal cortex, hippocampus, and central spinal cord) FA and CP decreased, whereas the CL a nd C values were unchanged or slightly smaller.Histological studies of a fluorescent mice model (YFP, G93A-SOD1 mouse) corroborated the early alterations in neuronal morphology and axonal connectivity measured by DTI.Conclusions: Changes in diffusion tensor shape were observed in this animal model at the early, nonsymptomatic stages of ALS. Further studies of CL, CP, and CSas imaging biomarkers should be undertaken to refine this neuroimaging tool for future clinical use in the detection of the early stages of ALSFil: Gatto, Rodolfo G.. University Of Illinois. Deparment Of Biological Science; Estados UnidosFil: Weissmann, Carina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Fisiología, Biología Molecular y Neurociencias. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Fisiología, Biología Molecular y Neurociencias; ArgentinaFil: Amin, Manish. University of Florida; Estados UnidosFil: Finkielsztein, Ariel. Northwestern University; Estados UnidosFil: Sumagin, Ronen. Northwestern University; Estados UnidosFil: Mareci, Thomas H.. University of Florida; Estados UnidosFil: Uchitel, Osvaldo Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Fisiología, Biología Molecular y Neurociencias. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Fisiología, Biología Molecular y Neurociencias; ArgentinaFil: Magin, Richard L.. University Of Illinois. Deparment Of Biological Science; Estados Unido

Evaluation of Early Microstructural Changes in the R6/1 Mouse Model of Huntington's Disease by Ultra-High Field Diffusion MR Imaging

Diffusion MRI (dMRI) has been able to detect early structural changes related to neurological symptoms present in Huntington's disease (HD). However, there is still a knowledge gap to interpret the biological significance at early neuropathological stages. The purpose of this study is two-fold: (i) establish if the combination of Ultra-High Field Diffusion MRI (UHFD-MRI) techniques can add a more comprehensive analysis of the early microstructural changes observed in HD, and (ii) evaluate if early changes in dMRI microstructural parameters can be linked to cellular biomarkers of neuroinflammation. Ultra-high field magnet (16.7T), diffusion tensor imaging (DTI), and neurite orientation dispersion and density imaging (NODDI) techniques were applied to fixed ex-vivo brains of a preclinical model of HD (R6/1 mice). Fractional anisotropy (FA) was decreased in deep and superficial grey matter (GM) as well as white matter (WM) brain regions with well-known early HD microstructure and connectivity pathology. NODDI parameters associated with the intracellular and extracellular compartment, such as intracellular ventricular fraction (ICVF), orientation dispersion index (ODI), and isotropic volume fractions (IsoVF) were altered in R6/1 mice GM. Further, histological studies in these areas showed that glia cell markers associated with neuroinflammation (GFAP & Iba1) were consistent with the dMRI findings. dMRI can be used to extract non-invasive information of neuropathological events present in the early stages of HD. The combination of multiple imaging techniques represents a better approach to understand the neuropathological process allowing the early diagnosis and neuromonitoring of patients affected by HD.Fil: Segatto, Rodolfo Guillermo. University Of Illinois. Deparment Of Biological Science; Estados UnidosFil: Weissmann, Carina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Fisiología, Biología Molecular y Neurociencias. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Fisiología, Biología Molecular y Neurociencias; ArgentinaFil: Amin, Manish. University of Florida. Department of Microbiology and Cell Science; Estados UnidosFil: Angeles López, Quetzalli D.. Consejo Nacional de Ciencia y Tecnologia de Mexico. Centro de Investigacion Cientifica y de Educacion Superior de Ensenada Baja California.; MéxicoFil: García Lara, Lucia. Consejo Nacional de Ciencia y Tecnologia de Mexico. Centro de Investigacion Cientifica y de Educacion Superior de Ensenada Baja California.; MéxicoFil: Salinas Castellanos, Libia Catalina. Consejo Nacional de Ciencia y Tecnologia de Mexico. Centro de Investigacion Cientifica y de Educacion Superior de Ensenada Baja California.; MéxicoFil: Deyoung, Daniel. University of Florida. Department of Microbiology and Cell Science; Estados UnidosFil: Segovia, Jose Manuel. Consejo Nacional de Ciencia y Tecnologia de Mexico. Centro de Investigacion Cientifica y de Educacion Superior de Ensenada Baja California.; MéxicoFil: Mareci, Thomas H.. University of Florida. Department of Microbiology and Cell Science; Estados UnidosFil: Uchitel, Osvaldo Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Fisiología, Biología Molecular y Neurociencias. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Fisiología, Biología Molecular y Neurociencias; ArgentinaFil: Magin, Richard L.. University Of Illinois. Deparment Of Biological Science; Estados Unido